From 83dea87c62a44e8d180811e4d1b5c9da211dddeb Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sat, 28 Jan 2017 19:29:21 +0100
Subject: [PATCH 001/643] Splay Tree Initial Commit

---
 Splay Tree/readme.md | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Splay Tree/readme.md

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
new file mode 100644
index 000000000..2282502fa
--- /dev/null
+++ b/Splay Tree/readme.md	
@@ -0,0 +1 @@
+In progress

From eb54bc8544f0d482336878e211269ea43da9a7a7 Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Mon, 30 Jan 2017 11:38:32 +0100
Subject: [PATCH 002/643] Add Simulated annealing

---
 Simulated annealing/README.md | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Simulated annealing/README.md

diff --git a/Simulated annealing/README.md b/Simulated annealing/README.md
new file mode 100644
index 000000000..bee8ffe94
--- /dev/null
+++ b/Simulated annealing/README.md	
@@ -0,0 +1 @@
+# Simulated annealing

From a6afbc107e25b96bdb86b9186f4a5794046b004b Mon Sep 17 00:00:00 2001
From: Mike Taghavi <mitghi@me.com>
Date: Mon, 30 Jan 2017 18:18:50 +0100
Subject: [PATCH 003/643] Initial

---
 Simulated annealing/README.md            |  32 ++++
 Simulated annealing/simann.swift         | 105 +++++++++++
 Simulated annealing/simann_example.swift | 222 +++++++++++++++++++++++
 3 files changed, 359 insertions(+)
 create mode 100644 Simulated annealing/simann.swift
 create mode 100644 Simulated annealing/simann_example.swift

diff --git a/Simulated annealing/README.md b/Simulated annealing/README.md
index bee8ffe94..e7fe75778 100644
--- a/Simulated annealing/README.md	
+++ b/Simulated annealing/README.md	
@@ -1 +1,33 @@
 # Simulated annealing
+
+Simulated Annealing is a nature inspired global optimization technique and a metaheuristic to approximate global maxima in a (often discrete)large search space. The name comes from the process of annealing in metallurgy where a material is heated and cooled down under controlled conditions in order to improve its strength and durabilility. The objective is to find a minimum cost solution in the search space by exploiting properties of a thermodynamic system. 
+Unlike hill climbing techniques which usually gets stuck in a local maxima ( downward moves are not allowed ), simulated annealing can escape local maxima. The interesting property of simulated annealing is that probability of allowing downward moves is high at the high temperatures and gradually reduced as it cools down. In other words, high temperature relaxes the acceptance criteria for the search space and triggers chaotic behavior of acceptance function in the algorithm (e.x initial/high temperature stages) which should make it possible to escape from local maxima and cooler temperatures narrows it and focuses on improvements.
+
+Pseucocode
+
+	Input: initial, temperature, coolingRate, acceptance
+	Output: Sbest
+	Scurrent <- CreateInitialSolution(initial)
+	Sbest <- Scurrent
+	while temperature is not minimum:
+		Snew <- FindNewSolution(Scurrent)
+		if acceptance(Energy(Scurrent), Energy(Snew), temperature) > Rand():
+			Scurrent = Snew
+		if Energy(Scurrent) < Energy(Sbest):
+			Sbest = Scurrent
+		temperature = temperature * (1-coolingRate)
+	
+Common acceptance criteria : P(accept) <- exp((e-ne)/T) where 
+	e is the current energy ( current solution ), 
+	ne is new energy ( new solution ),
+	T is current temperature.
+
+
+We use this algorithm to solve a Travelling salesman problem instance with 20 cities. The code is in `simann_example.swift`
+
+#See also
+
+[Simulated annealing on Wikipedia](https://en.wikipedia.org/wiki/Simulated_annealing) 
+[Travelling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem)
+
+Written for Swift Algorithm Club by [Mike Taghavi](https://github.com/mitghi)
diff --git a/Simulated annealing/simann.swift b/Simulated annealing/simann.swift
new file mode 100644
index 000000000..8adfbf817
--- /dev/null
+++ b/Simulated annealing/simann.swift	
@@ -0,0 +1,105 @@
+// The MIT License (MIT)
+// Copyright (c) 2017 Mike Taghavi (mitghi[at]me.com)
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#if os(OSX)
+  import Foundation
+#elseif os(Linux)
+  import Glibc
+#endif
+
+public extension Double {  
+  public static func random(_ lower: Double, _ upper: Double) -> Double {
+    #if os(OSX)
+      return (Double(arc4random()) / 0xFFFFFFFF) * (upper - lower) + lower
+    #elseif os(Linux)
+      return (Double(random()) / 0xFFFFFFFF) * (upper - lower) + lower
+    #endif
+  }
+}
+
+protocol Clonable {
+  init(current: Self)
+}
+
+// MARK: - create a clone from instance
+
+extension Clonable {
+  func clone() -> Self {
+    return Self.init(current: self)
+  }
+}
+
+protocol SAObject: Clonable {
+  var count: Int { get }
+  func randSwap(a: Int, b: Int)
+  func currentEnergy() -> Double
+  func shuffle()
+}
+
+// MARK: - create a new copy of elements
+
+extension Array where Element: Clonable {
+  func clone() -> Array {
+    var newArray = Array<Element>()
+    for elem in self {
+      newArray.append(elem.clone())
+    }
+    
+    return newArray
+  }
+}
+
+typealias AcceptanceFunc = (Double, Double, Double) -> Double
+
+func SimulatedAnnealing<T: SAObject>(initial: T, temperature: Double, coolingRate: Double, acceptance: AcceptanceFunc) -> T {
+  // Step 1:
+  //  Calculate the initial feasible solution based on a random permutation.
+  //  Set best and current solutions to initial solution
+  
+  var temp: Double = temperature
+  var currentSolution = initial.clone()
+  currentSolution.shuffle()
+  var bestSolution = currentSolution.clone()
+
+  // Step 2:
+  //  Repeat while the system is still hot
+  //   Randomly modify the current solution by swapping its elements
+  //   Randomly decide if the new solution ( neighbor ) is acceptable and set current solution accordingly
+  //   Update the best solution *iff* it had improved ( lower energy = improvement )
+  //   Reduce temperature
+  
+  while temp > 1 {    
+    let newSolution: T = currentSolution.clone()
+    let pos1: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    let pos2: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    newSolution.randSwap(a: pos1, b: pos2)
+    let currentEnergy: Double  = currentSolution.currentEnergy()
+    let newEnergy: Double = newSolution.currentEnergy()
+    
+    if acceptance(currentEnergy, newEnergy, temp) > Double.random(0, 1) {
+      currentSolution = newSolution.clone()
+    }
+    if currentSolution.currentEnergy() < bestSolution.currentEnergy() {
+      bestSolution = currentSolution.clone()
+    }
+    
+    temp *= 1-coolingRate
+  }
+  
+  return bestSolution
+}
diff --git a/Simulated annealing/simann_example.swift b/Simulated annealing/simann_example.swift
new file mode 100644
index 000000000..a0dfaa19a
--- /dev/null
+++ b/Simulated annealing/simann_example.swift	
@@ -0,0 +1,222 @@
+// The MIT License (MIT)
+// Copyright (c) 2017 Mike Taghavi (mitghi[at]me.com)
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#if os(OSX)
+  import Foundation
+#elseif os(Linux)
+  import Glibc
+#endif
+
+public extension Double {
+  
+  public static func random(_ lower: Double, _ upper: Double) -> Double {
+    #if os(OSX)
+      return (Double(arc4random()) / 0xFFFFFFFF) * (upper - lower) + lower
+    #elseif os(Linux)
+      return (Double(random()) / 0xFFFFFFFF) * (upper - lower) + lower
+    #endif
+  }
+}
+
+protocol Clonable {
+  init(current: Self)
+}
+
+extension Clonable {
+  func clone() -> Self {
+    return Self.init(current: self)
+  }
+}
+
+protocol SAObject: Clonable {
+  var count: Int { get }
+  func randSwap(a: Int, b: Int)
+  func currentEnergy() -> Double
+  func shuffle()
+}
+
+// MARK: - create a new copy of elements
+
+extension Array where Element: Clonable {
+  func clone() -> Array {
+    var newArray = Array<Element>()
+    for elem in self {
+      newArray.append(elem.clone())
+    }
+    
+    return newArray
+  }
+}
+
+typealias Points = [Point]
+typealias AcceptanceFunc = (Double, Double, Double) -> Double
+
+class Point: Clonable {
+  var x: Int
+  var y: Int
+  
+  init(x: Int, y: Int) {
+    self.x = x
+    self.y = y
+  }
+  
+  required init(current: Point){
+    self.x = current.x
+    self.y = current.y
+  }
+}
+
+// MARK: - string representation
+
+extension Point: CustomStringConvertible {
+  public var description: String {
+    return "Point(\(x), \(y))"
+  }
+}
+
+// MARK: - return distance between two points using operator '<->'
+
+infix operator <->: AdditionPrecedence
+extension Point {
+  static func <-> (left: Point, right: Point) -> Double {
+    let xDistance = (left.x - right.x)
+    let yDistance = (left.y - right.y)
+    
+    return Double(sqrt(Double((xDistance * xDistance) + (yDistance * yDistance))))
+  }
+}
+
+
+class Tour: SAObject {
+  var tour: Points
+  var energy: Double = 0.0
+  var count: Int {
+    get {
+      return self.tour.count
+    }
+  }
+  
+  init(points: Points){
+    self.tour = points.clone()
+  }
+  
+  required init(current: Tour) {
+    self.tour = current.tour.clone()
+  }
+}
+
+// MARK: - calculate current tour distance ( energy ).
+
+extension Tour {
+  func randSwap(a: Int, b: Int) -> Void {
+    let (cpos1, cpos2) = (self[a], self[b])
+    self[a] = cpos2
+    self[b] = cpos1
+  }
+  
+  func shuffle() {
+    for i in stride(from:  self.count - 1, through: 1, by: -1) {
+      let j = Int(arc4random()) % (i + 1)
+      if i != j {
+        swap(&self.tour[i], &self.tour[j])
+      }
+    }
+  }
+
+  func currentEnergy() -> Double {
+    if self.energy == 0 {
+      var tourEnergy: Double = 0.0
+      for i in 0..<self.count {
+        let fromCity = self[i]
+        var destCity = self[0]
+        if i+1 < self.count {
+          destCity = self[i+1]
+        }
+        let e = fromCity<->destCity
+        tourEnergy = tourEnergy + e
+        
+      }
+      self.energy = tourEnergy
+    }
+    return self.energy
+  }
+  
+}
+
+// MARK: - subscript to manipulate elements of Tour.
+
+extension Tour {
+  subscript(index: Int) -> Point {
+    get {
+      return self.tour[index]
+    }
+    set(newValue) {
+      self.tour[index] = newValue
+    }
+  }
+}
+
+func SimulatedAnnealing<T: SAObject>(initial: T, temperature: Double, coolingRate: Double, acceptance: AcceptanceFunc) -> T {
+  var temp: Double = temperature
+  var currentSolution = initial.clone()
+  currentSolution.shuffle()
+  var bestSolution = currentSolution.clone()
+  print("Initial solution: ", bestSolution.currentEnergy())
+  
+  while temp > 1 {
+    let newSolution: T = currentSolution.clone()
+    let pos1: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    let pos2: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    newSolution.randSwap(a: pos1, b: pos2)
+    let currentEnergy: Double  = currentSolution.currentEnergy()
+    let newEnergy: Double = newSolution.currentEnergy()
+    
+    if acceptance(currentEnergy, newEnergy, temp) > Double.random(0, 1) {
+      currentSolution = newSolution.clone()
+    }
+    if currentSolution.currentEnergy() < bestSolution.currentEnergy() {
+      bestSolution = currentSolution.clone()
+    }
+    
+    temp *= 1-coolingRate
+  }
+  
+  print("Best solution: ", bestSolution.currentEnergy())
+  return bestSolution
+}
+
+let points: [Point] = [
+  (60 , 200), (180, 200), (80 , 180), (140, 180),
+  (20 , 160), (100, 160), (200, 160), (140, 140),
+  (40 , 120), (100, 120), (180, 100), (60 , 80) ,
+  (120, 80) , (180, 60) , (20 , 40) , (100, 40) ,
+  (200, 40) , (20 , 20) , (60 , 20) , (160, 20) ,
+  ].map{ Point(x: $0.0, y: $0.1) }
+
+let acceptance : AcceptanceFunc = {
+  (e: Double, ne: Double, te: Double) -> Double in
+  if ne < e {
+    return 1.0
+  }
+  return exp((e - ne) / te)
+}
+
+let result: Tour = SimulatedAnnealing(initial     : Tour(points: points),
+                                      temperature : 100000.0,
+                                      coolingRate : 0.003,
+                                      acceptance  : acceptance)

From a794dec1522cd0df09b96a2d8744b261b8185f2a Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Mon, 30 Jan 2017 18:23:23 +0100
Subject: [PATCH 004/643] Update README.md

---
 Simulated annealing/README.md | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/Simulated annealing/README.md b/Simulated annealing/README.md
index e7fe75778..3a36464d7 100644
--- a/Simulated annealing/README.md	
+++ b/Simulated annealing/README.md	
@@ -17,10 +17,12 @@ Pseucocode
 			Sbest = Scurrent
 		temperature = temperature * (1-coolingRate)
 	
-Common acceptance criteria : P(accept) <- exp((e-ne)/T) where 
-	e is the current energy ( current solution ), 
-	ne is new energy ( new solution ),
-	T is current temperature.
+Common acceptance criteria : 
+
+	P(accept) <- exp((e-ne)/T) where 
+		e is the current energy ( current solution ), 
+		ne is new energy ( new solution ),
+		T is current temperature.
 
 
 We use this algorithm to solve a Travelling salesman problem instance with 20 cities. The code is in `simann_example.swift`
@@ -28,6 +30,7 @@ We use this algorithm to solve a Travelling salesman problem instance with 20 ci
 #See also
 
 [Simulated annealing on Wikipedia](https://en.wikipedia.org/wiki/Simulated_annealing) 
+
 [Travelling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem)
 
 Written for Swift Algorithm Club by [Mike Taghavi](https://github.com/mitghi)

From 94c9b5f2b0306e9924c01486889b69934f34575a Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 19 Feb 2017 16:46:31 +0100
Subject: [PATCH 005/643] initial implementation fro Splay Trees

Test in progress
Debug in progress
Playground in progress
Documentation not started
---
 .../SplayTree.playground/Contents.swift       |   7 +
 .../Sources/SplayTree.swift                   | 509 ++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Splay Tree/SplayTree.swift                    | 552 ++++++++++++++++++
 Splay Tree/Tests/Info.plist                   |  22 +
 Splay Tree/Tests/SplayTreeTests.swift         |  19 +
 Splay Tree/Tests/Tests-Bridging-Header.h      |   4 +
 .../Tests/Tests.xcodeproj/project.pbxproj     | 279 +++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/xcschemes/Tests.xcscheme     | 101 ++++
 11 files changed, 1511 insertions(+)
 create mode 100644 Splay Tree/SplayTree.playground/Contents.swift
 create mode 100644 Splay Tree/SplayTree.playground/Sources/SplayTree.swift
 create mode 100644 Splay Tree/SplayTree.playground/contents.xcplayground
 create mode 100644 Splay Tree/SplayTree.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Splay Tree/SplayTree.swift
 create mode 100644 Splay Tree/Tests/Info.plist
 create mode 100644 Splay Tree/Tests/SplayTreeTests.swift
 create mode 100644 Splay Tree/Tests/Tests-Bridging-Header.h
 create mode 100644 Splay Tree/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Splay Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Splay Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Splay Tree/SplayTree.playground/Contents.swift b/Splay Tree/SplayTree.playground/Contents.swift
new file mode 100644
index 000000000..951ad4c5c
--- /dev/null
+++ b/Splay Tree/SplayTree.playground/Contents.swift	
@@ -0,0 +1,7 @@
+//: Playground - Splay Tree Implementation
+
+
+let splayTree = SplayTree(array: [1])
+splayTree.insert(value: 2)
+splayTree.insert(value: 10)
+splayTree.insert(value: 6)
diff --git a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift
new file mode 100644
index 000000000..f0c45e831
--- /dev/null
+++ b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
@@ -0,0 +1,509 @@
+/*
+ *  Splay Tree 
+ *
+ * Based on Binary Search Tree Implementation written by Nicolas Ameghino and Matthijs Hollemans for Swift Algorithms Club
+ * https://github.com/raywenderlich/swift-algorithm-club/blob/master/Binary%20Search%20Tree
+ * And extended for the specifics of a Splay Tree by Barbara Martina Rodeker
+ *
+ */
+
+/**
+    Represent the 3 possible operations (combinations of rotations) that
+    could be performed during the Splay phase in Splay Trees
+ 
+    - zigZag       Left child of a right child OR right child of a left child
+    - zigZig       Left child of a left child OR right child of a right child
+    - zig          Only 1 parent and that parent is the root
+ 
+ */
+public enum SplayOperation {
+    case zigZag
+    case zigZig
+    case zig
+    
+    
+    /**
+        Splay the given node up to the root of the tree
+     
+        - Parameters:
+            - node      SplayTree node to move up to the root
+     */
+    public static func splay<T: Comparable>(node: SplayTree<T>) {
+        
+        while (node.parent != nil) {
+            operation(forNode: node).apply(onNode: node)
+        }
+    }
+    
+    /**
+        Compares the node and its parent and determine
+        if the rotations should be performed in a zigZag, zigZig or zig case.
+     
+        - Parmeters:
+            - forNode       SplayTree node to be checked
+        - Returns
+            - Operation     Case zigZag - zigZig - zig
+     */
+    private static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
+        
+        if let parent = node.parent, let grandParent = parent.parent {
+            if (node.isLeftChild && grandParent.isRightChild) || (node.isRightChild && grandParent.isLeftChild) {
+                return .zigZag
+            }
+            return .zigZig
+        }
+        return .zig
+    }
+    
+    /**
+        Applies the rotation associated to the case 
+        Modifying the splay tree and briging the received node further to the top of the tree
+     
+        - Parameters:
+            - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
+     */
+    private func apply<T: Comparable>(onNode node: SplayTree<T>) {
+        switch self {
+        case .zigZag:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node, parent: node.parent!)
+            rotate(child: node, parent: node.parent!)
+
+        case .zigZig:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node.parent!, parent: node.parent!.parent!)
+            rotate(child: node, parent: node.parent!)
+        
+        case .zig:
+            assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
+            rotate(child: node, parent: node.parent!)
+        }
+    }
+    
+    /**
+        Performs a single rotation from a node to its parent
+        re-arranging the children properly
+     */
+    private func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
+        
+        assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
+        
+        var grandchildToMode: SplayTree<T>?
+        if child.isLeftChild {
+            
+            grandchildToMode = child.right
+            child.right = parent
+            parent.left = grandchildToMode
+            
+        } else {
+            
+            grandchildToMode = child.left
+            child.left = parent
+            parent.right = grandchildToMode
+        }
+
+        let grandParent = parent.parent
+        parent.parent = child
+        child.parent = grandParent
+    }
+}
+
+public class SplayTree<T: Comparable> {
+    
+    fileprivate(set) public var value: T
+    fileprivate(set) public var parent: SplayTree?
+    fileprivate(set) public var left: SplayTree?
+    fileprivate(set) public var right: SplayTree?
+    
+    public init(value: T) {
+        self.value = value
+    }
+    
+    public convenience init(array: [T]) {
+        precondition(array.count > 0)
+        self.init(value: array.first!)
+        for v in array.dropFirst() {
+            insert(value: v)
+        }
+    }
+    
+    public var isRoot: Bool {
+        return parent == nil
+    }
+    
+    public var isLeaf: Bool {
+        return left == nil && right == nil
+    }
+    
+    public var isLeftChild: Bool {
+        return parent?.left === self
+    }
+    
+    public var isRightChild: Bool {
+        return parent?.right === self
+    }
+    
+    public var hasLeftChild: Bool {
+        return left != nil
+    }
+    
+    public var hasRightChild: Bool {
+        return right != nil
+    }
+    
+    public var hasAnyChild: Bool {
+        return hasLeftChild || hasRightChild
+    }
+    
+    public var hasBothChildren: Bool {
+        return hasLeftChild && hasRightChild
+    }
+    
+    /* How many nodes are in this subtree. Performance: O(n). */
+    public var count: Int {
+        return (left?.count ?? 0) + 1 + (right?.count ?? 0)
+    }
+}
+
+// MARK: - Adding items
+
+extension SplayTree {
+    
+    /*
+     Inserts a new element into the tree. You should only insert elements
+     at the root, to make to sure this remains a valid binary tree!
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func insert(value: T) {
+        if value < self.value {
+            if let left = left {
+                left.insert(value: value)
+            } else {
+                
+                left = SplayTree(value: value)
+                left?.parent = self
+                
+                if let left = left {
+                    SplayOperation.splay(node: left)
+                    self.parent = nil
+                    self.value = left.value
+                    self.left = left.left
+                    self.right = left.right
+                }
+            }
+        } else {
+            
+            if let right = right {
+                right.insert(value: value)
+            } else {
+                
+                right = SplayTree(value: value)
+                right?.parent = self
+                
+                if let right = right {
+                    SplayOperation.splay(node: right)
+                    self.parent = nil
+                    self.value = right.value
+                    self.left = right.left
+                    self.right = right.right
+                }
+            }
+        }
+    }
+}
+
+// MARK: - Deleting items
+
+extension SplayTree {
+    /*
+     Deletes a node from the tree.
+     Returns the node that has replaced this removed one (or nil if this was a
+     leaf node). That is primarily useful for when you delete the root node, in
+     which case the tree gets a new root.
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    @discardableResult public func remove() -> SplayTree? {
+        let replacement: SplayTree?
+        
+        if let left = left {
+            if let right = right {
+                replacement = removeNodeWithTwoChildren(left, right)
+            } else {
+                // This node only has a left child. The left child replaces the node.
+                replacement = left
+            }
+        } else if let right = right {
+            // This node only has a right child. The right child replaces the node.
+            replacement = right
+        } else {
+            // This node has no children. We just disconnect it from its parent.
+            replacement = nil
+        }
+
+        // Save the parent to splay before reconnecting
+        var parentToSplay: SplayTree?
+        if let replacement = replacement {
+            parentToSplay = replacement.parent
+        } else {
+            parentToSplay = self.parent
+        }
+        
+        reconnectParentTo(node: replacement)
+        
+        // performs the splay operation
+        if let parentToSplay = parentToSplay {
+            SplayOperation.splay(node: parentToSplay)
+        }
+        
+        // The current node is no longer part of the tree, so clean it up.
+        parent = nil
+        left = nil
+        right = nil
+        
+        return replacement
+    }
+    
+    private func removeNodeWithTwoChildren(_ left: SplayTree, _ right: SplayTree) -> SplayTree {
+        // This node has two children. It must be replaced by the smallest
+        // child that is larger than this node's value, which is the leftmost
+        // descendent of the right child.
+        let successor = right.minimum()
+        
+        // If this in-order successor has a right child of its own (it cannot
+        // have a left child by definition), then that must take its place.
+        successor.remove()
+        
+        // Connect our left child with the new node.
+        successor.left = left
+        left.parent = successor
+        
+        // Connect our right child with the new node. If the right child does
+        // not have any left children of its own, then the in-order successor
+        // *is* the right child.
+        if right !== successor {
+            successor.right = right
+            right.parent = successor
+        } else {
+            successor.right = nil
+        }
+        
+        // And finally, connect the successor node to our parent.
+        return successor
+    }
+    
+    private func reconnectParentTo(node: SplayTree?) {
+        if let parent = parent {
+            if isLeftChild {
+                parent.left = node
+            } else {
+                parent.right = node
+            }
+        }
+        node?.parent = parent
+    }
+}
+
+// MARK: - Searching
+
+extension SplayTree {
+    
+    /*
+     Finds the "highest" node with the specified value.
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func search(value: T) -> SplayTree? {
+        var node: SplayTree? = self
+        while case let n? = node {
+            if value < n.value {
+                node = n.left
+            } else if value > n.value {
+                node = n.right
+            } else {
+                
+                if let node = node {
+                    SplayOperation.splay(node: node)
+                }
+                
+                return node
+            }
+        }
+        
+        if let node = node {
+            SplayOperation.splay(node: node)
+        }
+        
+        return nil
+    }
+    
+    public func contains(value: T) -> Bool {
+        return search(value: value) != nil
+    }
+    
+    /*
+     Returns the leftmost descendent. O(h) time.
+     */
+    public func minimum() -> SplayTree {
+        var node = self
+        while case let next? = node.left {
+            node = next
+        }
+        
+        SplayOperation.splay(node: node)
+
+        return node
+    }
+    
+    /*
+     Returns the rightmost descendent. O(h) time.
+     */
+    public func maximum() -> SplayTree {
+        var node = self
+        while case let next? = node.right {
+            node = next
+        }
+        
+        SplayOperation.splay(node: node)
+        
+        return node
+    }
+    
+    /*
+     Calculates the depth of this node, i.e. the distance to the root.
+     Takes O(h) time.
+     */
+    public func depth() -> Int {
+        var node = self
+        var edges = 0
+        while case let parent? = node.parent {
+            node = parent
+            edges += 1
+        }
+        return edges
+    }
+    
+    /*
+     Calculates the height of this node, i.e. the distance to the lowest leaf.
+     Since this looks at all children of this node, performance is O(n).
+     */
+    public func height() -> Int {
+        if isLeaf {
+            return 0
+        } else {
+            return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
+        }
+    }
+    
+    /*
+     Finds the node whose value precedes our value in sorted order.
+     */
+    public func predecessor() -> SplayTree<T>? {
+        if let left = left {
+            return left.maximum()
+        } else {
+            var node = self
+            while case let parent? = node.parent {
+                if parent.value < value { return parent }
+                node = parent
+            }
+            return nil
+        }
+    }
+    
+    /*
+     Finds the node whose value succeeds our value in sorted order.
+     */
+    public func successor() -> SplayTree<T>? {
+        if let right = right {
+            return right.minimum()
+        } else {
+            var node = self
+            while case let parent? = node.parent {
+                if parent.value > value { return parent }
+                node = parent
+            }
+            return nil
+        }
+    }
+}
+
+// MARK: - Traversal
+extension SplayTree {
+    
+    public func traverseInOrder(process: (T) -> Void) {
+        left?.traverseInOrder(process: process)
+        process(value)
+        right?.traverseInOrder(process: process)
+    }
+    
+    public func traversePreOrder(process: (T) -> Void) {
+        process(value)
+        left?.traversePreOrder(process: process)
+        right?.traversePreOrder(process: process)
+    }
+    
+    public func traversePostOrder(process: (T) -> Void) {
+        left?.traversePostOrder(process: process)
+        right?.traversePostOrder(process: process)
+        process(value)
+    }
+    
+    /*
+     Performs an in-order traversal and collects the results in an array.
+     */
+    public func map(formula: (T) -> T) -> [T] {
+        var a = [T]()
+        if let left = left { a += left.map(formula: formula) }
+        a.append(formula(value))
+        if let right = right { a += right.map(formula: formula) }
+        return a
+    }
+}
+
+/*
+ Is this binary tree a valid binary search tree?
+ */
+extension SplayTree {
+    
+    public func isBST(minValue: T, maxValue: T) -> Bool {
+        if value < minValue || value > maxValue { return false }
+        let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
+        let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
+        return leftBST && rightBST
+    }
+}
+
+// MARK: - Debugging
+
+extension SplayTree: CustomStringConvertible {
+    public var description: String {
+        var s = ""
+        if let left = left {
+            s += "(\(left.description)) <- "
+        }
+        s += "\(value)"
+        if let right = right {
+            s += " -> (\(right.description))"
+        }
+        return s
+    }
+}
+
+extension SplayTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        var s = "value: \(value)"
+        if let parent = parent {
+            s += ", parent: \(parent.value)"
+        }
+        if let left = left {
+            s += ", left = [" + left.debugDescription + "]"
+        }
+        if let right = right {
+            s += ", right = [" + right.debugDescription + "]"
+        }
+        return s
+    }
+    
+    public func toArray() -> [T] {
+        return map { $0 }
+    }
+}
diff --git a/Splay Tree/SplayTree.playground/contents.xcplayground b/Splay Tree/SplayTree.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Splay Tree/SplayTree.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Splay Tree/SplayTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Splay Tree/SplayTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Splay Tree/SplayTree.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
new file mode 100644
index 000000000..727ff8f50
--- /dev/null
+++ b/Splay Tree/SplayTree.swift	
@@ -0,0 +1,552 @@
+/*
+ *  Splay Tree 
+ *
+ * Based on Binary Search Tree Implementation written by Nicolas Ameghino and Matthijs Hollemans for Swift Algorithms Club
+ * https://github.com/raywenderlich/swift-algorithm-club/blob/master/Binary%20Search%20Tree
+ * And extended for the specifics of a Splay Tree by Barbara Martina Rodeker
+ *
+ */
+
+/**
+    Represent the 3 possible operations (combinations of rotations) that
+    could be performed during the Splay phase in Splay Trees
+ 
+    - zigZag       Left child of a right child OR right child of a left child
+    - zigZig       Left child of a left child OR right child of a right child
+    - zig          Only 1 parent and that parent is the root
+ 
+ */
+public enum SplayOperation {
+    case zigZag
+    case zigZig
+    case zig
+    
+    
+    /**
+        Splay the given node up to the root of the tree
+     
+        - Parameters:
+            - node      SplayTree node to move up to the root
+     */
+    public static func splay<T: Comparable>(node: SplayTree<T>) {
+        
+        while (node.parent != nil) {
+            operation(forNode: node).apply(onNode: node)
+        }
+    }
+    
+    /**
+        Compares the node and its parent and determine
+        if the rotations should be performed in a zigZag, zigZig or zig case.
+     
+        - Parmeters:
+            - forNode       SplayTree node to be checked
+        - Returns
+            - Operation     Case zigZag - zigZig - zig
+     */
+    private static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
+        
+        if let parent = node.parent, let _ = parent.parent {
+            if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
+                return .zigZag
+            }
+            return .zigZig
+        }
+        return .zig
+    }
+    
+    /**
+        Applies the rotation associated to the case 
+        Modifying the splay tree and briging the received node further to the top of the tree
+     
+        - Parameters:
+            - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
+     */
+    private func apply<T: Comparable>(onNode node: SplayTree<T>) {
+        switch self {
+        case .zigZag:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node, parent: node.parent!)
+            rotate(child: node, parent: node.parent!)
+
+        case .zigZig:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node.parent!, parent: node.parent!.parent!)
+            rotate(child: node, parent: node.parent!)
+        
+        case .zig:
+            assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
+            rotate(child: node, parent: node.parent!)
+        }
+    }
+    
+    /**
+        Performs a single rotation from a node to its parent
+        re-arranging the children properly
+     */
+    private func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
+        
+        assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
+        
+        var grandchildToMode: SplayTree<T>?
+        if child.isLeftChild {
+            
+            grandchildToMode = child.right
+            child.right = parent
+            parent.left = grandchildToMode
+            
+        } else {
+            
+            grandchildToMode = child.left
+            child.left = parent
+            parent.right = grandchildToMode
+        }
+
+        let grandParent = parent.parent
+        parent.parent = child
+        child.parent = grandParent
+    }
+}
+
+public class Node<T: Comparable> {
+    
+    fileprivate(set) public var value: T
+    fileprivate(set) public var parent: SplayTree<T>?
+    fileprivate(set) public var left: SplayTree<T>?
+    fileprivate(set) public var right: SplayTree<T>?
+    
+    init(value: T){
+        self.value = value
+    }
+}
+
+public class SplayTree<T: Comparable> {
+
+
+    fileprivate(set) public var root: Node<T>?
+    public var value: T? {
+        get {
+            return root?.value
+        }
+        set {
+            if let value = newValue {
+                root?.value = value
+            }
+        }
+    }
+
+    fileprivate(set) public var parent: SplayTree? {
+        get {
+            return root?.parent
+        }
+        set {
+            root?.parent = newValue
+        }
+    }
+    
+    fileprivate(set) public var left: SplayTree? {
+        get {
+            return root?.left
+        }
+        set {
+            root?.left = newValue
+        }
+    }
+    fileprivate(set) public var right: SplayTree? {
+        get {
+            return root?.right
+        }
+        set {
+            root?.right = newValue
+        }
+    }
+
+    //MARK: - Initializer
+    
+    public init(value: T) {
+        self.root = Node(value:value)
+    }
+    
+    public var isRoot: Bool {
+        return parent == nil
+    }
+    
+    public var isLeaf: Bool {
+        return left == nil && right == nil
+    }
+    
+    public var isLeftChild: Bool {
+        return parent?.left === self
+    }
+    
+    public var isRightChild: Bool {
+        return parent?.right === self
+    }
+    
+    public var hasLeftChild: Bool {
+        return left != nil
+    }
+    
+    public var hasRightChild: Bool {
+        return right != nil
+    }
+    
+    public var hasAnyChild: Bool {
+        return hasLeftChild || hasRightChild
+    }
+    
+    public var hasBothChildren: Bool {
+        return hasLeftChild && hasRightChild
+    }
+    
+    /* How many nodes are in this subtree. Performance: O(n). */
+    public var count: Int {
+        return (left?.count ?? 0) + 1 + (right?.count ?? 0)
+    }
+}
+
+// MARK: - Adding items
+
+extension SplayTree {
+    
+    /*
+     Inserts a new element into the tree. You should only insert elements
+     at the root, to make to sure this remains a valid binary tree!
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func insert(value: T) -> SplayTree? {
+        if let selfValue = self.value {
+            if value < selfValue {
+                if let left = left {
+                    return left.insert(value: value)
+                } else {
+                    
+                    left = SplayTree(value: value)
+                    left?.parent = self
+                    
+                    if let left = left {
+                        SplayOperation.splay(node: left)
+                        return left
+                    }
+                }
+            } else {
+                
+                if let right = right {
+                    return right.insert(value: value)
+                } else {
+                    
+                    right = SplayTree(value: value)
+                    right?.parent = self
+                    
+                    if let right = right {
+                        SplayOperation.splay(node: right)
+                        return right
+                    }
+                }
+            }
+        } else {
+            self.root = Node(value: value)
+            return self
+        }
+        return nil
+    }
+}
+
+// MARK: - Deleting items
+
+extension SplayTree {
+    /*
+     Deletes a node from the tree.
+     Returns the node that has replaced this removed one (or nil if this was a
+     leaf node). That is primarily useful for when you delete the root node, in
+     which case the tree gets a new root.
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    @discardableResult public func remove() -> SplayTree? {
+        let replacement: SplayTree?
+        
+        if let left = left {
+            if let right = right {
+                replacement = removeNodeWithTwoChildren(left, right)
+            } else {
+                // This node only has a left child. The left child replaces the node.
+                replacement = left
+            }
+        } else if let right = right {
+            // This node only has a right child. The right child replaces the node.
+            replacement = right
+        } else {
+            // This node has no children. We just disconnect it from its parent.
+            replacement = nil
+        }
+
+        // Save the parent to splay before reconnecting
+        var parentToSplay: SplayTree?
+        if let replacement = replacement {
+            parentToSplay = replacement.parent
+        } else {
+            parentToSplay = self.parent
+        }
+        
+        reconnectParentTo(node: replacement)
+        
+        // performs the splay operation
+        if let parentToSplay = parentToSplay {
+            SplayOperation.splay(node: parentToSplay)
+        }
+        
+        // The current node is no longer part of the tree, so clean it up.
+        parent = nil
+        left = nil
+        right = nil
+        
+        return replacement
+    }
+    
+    private func removeNodeWithTwoChildren(_ left: SplayTree, _ right: SplayTree) -> SplayTree {
+        // This node has two children. It must be replaced by the smallest
+        // child that is larger than this node's value, which is the leftmost
+        // descendent of the right child.
+        let successor = right.minimum()
+        
+        // If this in-order successor has a right child of its own (it cannot
+        // have a left child by definition), then that must take its place.
+        successor.remove()
+        
+        // Connect our left child with the new node.
+        successor.left = left
+        left.parent = successor
+        
+        // Connect our right child with the new node. If the right child does
+        // not have any left children of its own, then the in-order successor
+        // *is* the right child.
+        if right !== successor {
+            successor.right = right
+            right.parent = successor
+        } else {
+            successor.right = nil
+        }
+        
+        // And finally, connect the successor node to our parent.
+        return successor
+    }
+    
+    private func reconnectParentTo(node: SplayTree?) {
+        if let parent = parent {
+            if isLeftChild {
+                parent.left = node
+            } else {
+                parent.right = node
+            }
+        }
+        node?.parent = parent
+    }
+}
+
+// MARK: - Searching
+
+extension SplayTree {
+    
+    /*
+     Finds the "highest" node with the specified value.
+     Performance: runs in O(h) time, where h is the height of the tree.
+     */
+    public func search(value: T) -> SplayTree? {
+        var node: SplayTree? = self
+        while case let n? = node, n.value != nil {
+            if value < n.value! {
+                node = n.left
+            } else if value > n.value! {
+                node = n.right
+            } else {
+                
+                if let node = node {
+                    SplayOperation.splay(node: node)
+                }
+                
+                return node
+            }
+        }
+        
+        if let node = node {
+            SplayOperation.splay(node: node)
+        }
+        
+        return nil
+    }
+    
+    public func contains(value: T) -> Bool {
+        return search(value: value) != nil
+    }
+    
+    /*
+     Returns the leftmost descendent. O(h) time.
+     */
+    public func minimum() -> SplayTree {
+        var node = self
+        while case let next? = node.left {
+            node = next
+        }
+        
+        SplayOperation.splay(node: node)
+
+        return node
+    }
+    
+    /*
+     Returns the rightmost descendent. O(h) time.
+     */
+    public func maximum() -> SplayTree {
+        var node = self
+        while case let next? = node.right {
+            node = next
+        }
+        
+        SplayOperation.splay(node: node)
+        
+        return node
+    }
+    
+    /*
+     Calculates the depth of this node, i.e. the distance to the root.
+     Takes O(h) time.
+     */
+    public func depth() -> Int {
+        var node = self
+        var edges = 0
+        while case let parent? = node.parent {
+            node = parent
+            edges += 1
+        }
+        return edges
+    }
+    
+    /*
+     Calculates the height of this node, i.e. the distance to the lowest leaf.
+     Since this looks at all children of this node, performance is O(n).
+     */
+    public func height() -> Int {
+        if isLeaf {
+            return 0
+        } else {
+            return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
+        }
+    }
+    
+    /*
+     Finds the node whose value precedes our value in sorted order.
+     */
+    public func predecessor() -> SplayTree<T>? {
+        if let left = left {
+            return left.maximum()
+        } else {
+            var node = self
+            while case let parent? = node.parent, parent.value != nil, value != nil {
+                if parent.value! < value! { return parent }
+                node = parent
+            }
+            return nil
+        }
+    }
+    
+    /*
+     Finds the node whose value succeeds our value in sorted order.
+     */
+    public func successor() -> SplayTree<T>? {
+        if let right = right {
+            return right.minimum()
+        } else {
+            var node = self
+            while case let parent? = node.parent, parent.value != nil , value != nil {
+                if parent.value! > value! { return parent }
+                node = parent
+            }
+            return nil
+        }
+    }
+}
+
+// MARK: - Traversal
+extension SplayTree {
+    
+    public func traverseInOrder(process: (T) -> Void) {
+        left?.traverseInOrder(process: process)
+        process(value!)
+        right?.traverseInOrder(process: process)
+    }
+    
+    public func traversePreOrder(process: (T) -> Void) {
+        process(value!)
+        left?.traversePreOrder(process: process)
+        right?.traversePreOrder(process: process)
+    }
+    
+    public func traversePostOrder(process: (T) -> Void) {
+        left?.traversePostOrder(process: process)
+        right?.traversePostOrder(process: process)
+        process(value!)
+    }
+    
+    /*
+     Performs an in-order traversal and collects the results in an array.
+     */
+    public func map(formula: (T) -> T) -> [T] {
+        var a = [T]()
+        if let left = left { a += left.map(formula: formula) }
+        a.append(formula(value!))
+        if let right = right { a += right.map(formula: formula) }
+        return a
+    }
+}
+
+/*
+ Is this binary tree a valid binary search tree?
+ */
+extension SplayTree {
+    
+    public func isBST(minValue: T, maxValue: T) -> Bool {
+        if let value = value {
+            if value < minValue || value > maxValue { return false }
+            let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
+            let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
+            return leftBST && rightBST
+        }
+        return false
+    }
+}
+
+// MARK: - Debugging
+
+extension SplayTree: CustomStringConvertible {
+    public var description: String {
+        var s = ""
+        if let left = left {
+            s += "(\(left.description)) <- "
+        }
+        s += "\(value)"
+        if let right = right {
+            s += " -> (\(right.description))"
+        }
+        return s
+    }
+}
+
+extension SplayTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        var s = "value: \(value)"
+        if let parent = parent {
+            s += ", parent: \(parent.value)"
+        }
+        if let left = left {
+            s += ", left = [" + left.debugDescription + "]"
+        }
+        if let right = right {
+            s += ", right = [" + right.debugDescription + "]"
+        }
+        return s
+    }
+    
+    public func toArray() -> [T] {
+        return map { $0 }
+    }
+}
diff --git a/Splay Tree/Tests/Info.plist b/Splay Tree/Tests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/Splay Tree/Tests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Splay Tree/Tests/SplayTreeTests.swift b/Splay Tree/Tests/SplayTreeTests.swift
new file mode 100644
index 000000000..35bdedb71
--- /dev/null
+++ b/Splay Tree/Tests/SplayTreeTests.swift	
@@ -0,0 +1,19 @@
+import XCTest
+
+class SplayTreeTests: XCTestCase {
+  var tree: SplayTree<Int>!
+  
+  override func setUp() {
+    super.setUp()
+    tree = SplayTree<Int>(value: 1)
+  }
+  
+  func testElements() {
+    print(tree)
+    let tree1 = tree.insert(value: 10)
+    print(tree1!)
+    let tree2 = tree1!.insert(value: 2)
+    print(tree2!)
+  }
+
+}
diff --git a/Splay Tree/Tests/Tests-Bridging-Header.h b/Splay Tree/Tests/Tests-Bridging-Header.h
new file mode 100644
index 000000000..1b2cb5d6d
--- /dev/null
+++ b/Splay Tree/Tests/Tests-Bridging-Header.h	
@@ -0,0 +1,4 @@
+//
+//  Use this file to import your target's public headers that you would like to expose to Swift.
+//
+
diff --git a/Splay Tree/Tests/Tests.xcodeproj/project.pbxproj b/Splay Tree/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..8a900fcd3
--- /dev/null
+++ b/Splay Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,279 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		763F9E771E59DAEF00AC5031 /* SplayTree.swift in Sources */ = {isa = PBXBuildFile; fileRef = 763F9E761E59DAEF00AC5031 /* SplayTree.swift */; };
+		763F9E791E59DAFE00AC5031 /* SplayTreeTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 763F9E781E59DAFE00AC5031 /* SplayTreeTests.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		056E92A21E25D04D00B30F52 /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		056E92A61E25D04D00B30F52 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		763F9E761E59DAEF00AC5031 /* SplayTree.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = SplayTree.swift; path = ../SplayTree.swift; sourceTree = "<group>"; };
+		763F9E781E59DAFE00AC5031 /* SplayTreeTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = SplayTreeTests.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		056E929F1E25D04D00B30F52 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		056E92851E25D03300B30F52 = {
+			isa = PBXGroup;
+			children = (
+				056E92A31E25D04D00B30F52 /* Tests */,
+				056E928F1E25D03300B30F52 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		056E928F1E25D03300B30F52 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				056E92A21E25D04D00B30F52 /* Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		056E92A31E25D04D00B30F52 /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				056E92A61E25D04D00B30F52 /* Info.plist */,
+				763F9E781E59DAFE00AC5031 /* SplayTreeTests.swift */,
+				763F9E761E59DAEF00AC5031 /* SplayTree.swift */,
+			);
+			name = Tests;
+			sourceTree = SOURCE_ROOT;
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		056E92A11E25D04D00B30F52 /* Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 056E92A71E25D04D00B30F52 /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildPhases = (
+				056E929E1E25D04D00B30F52 /* Sources */,
+				056E929F1E25D04D00B30F52 /* Frameworks */,
+				056E92A01E25D04D00B30F52 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = Tests;
+			productName = Tests;
+			productReference = 056E92A21E25D04D00B30F52 /* Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		056E92861E25D03300B30F52 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0820;
+				LastUpgradeCheck = 0820;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					056E92A11E25D04D00B30F52 = {
+						CreatedOnToolsVersion = 8.2;
+						LastSwiftMigration = 0820;
+						ProvisioningStyle = Automatic;
+					};
+				};
+			};
+			buildConfigurationList = 056E92891E25D03300B30F52 /* Build configuration list for PBXProject "Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 056E92851E25D03300B30F52;
+			productRefGroup = 056E928F1E25D03300B30F52 /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				056E92A11E25D04D00B30F52 /* Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		056E92A01E25D04D00B30F52 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		056E929E1E25D04D00B30F52 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				763F9E771E59DAEF00AC5031 /* SplayTree.swift in Sources */,
+				763F9E791E59DAFE00AC5031 /* SplayTreeTests.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		056E92991E25D03300B30F52 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.12;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		056E929A1E25D03300B30F52 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.12;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+			};
+			name = Release;
+		};
+		056E92A81E25D04D00B30F52 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = Swift.Algorithm.Club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OBJC_BRIDGING_HEADER = "Tests-Bridging-Header.h";
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		056E92A91E25D04D00B30F52 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = Swift.Algorithm.Club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OBJC_BRIDGING_HEADER = "Tests-Bridging-Header.h";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		056E92891E25D03300B30F52 /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				056E92991E25D03300B30F52 /* Debug */,
+				056E929A1E25D03300B30F52 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		056E92A71E25D04D00B30F52 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				056E92A81E25D04D00B30F52 /* Debug */,
+				056E92A91E25D04D00B30F52 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 056E92861E25D03300B30F52 /* Project object */;
+}
diff --git a/Splay Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Splay Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Splay Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Splay Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Splay Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..b3f6d696a
--- /dev/null
+++ b/Splay Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,101 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0820"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "056E92A11E25D04D00B30F52"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From cc973dcb62d310f1af0d08d408c782a57e3523cb Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Fri, 3 Mar 2017 21:01:11 +0100
Subject: [PATCH 006/643] Fixes for connecting nodes during rotations

---
 Splay Tree/SplayTree.swift            | 53 ++++++++++++++++++---------
 Splay Tree/Tests/SplayTreeTests.swift | 41 +++++++++++++--------
 2 files changed, 61 insertions(+), 33 deletions(-)

diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
index 727ff8f50..2e008ba50 100644
--- a/Splay Tree/SplayTree.swift	
+++ b/Splay Tree/SplayTree.swift	
@@ -44,7 +44,7 @@ public enum SplayOperation {
         - Returns
             - Operation     Case zigZag - zigZig - zig
      */
-    private static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
+    public static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
         
         if let parent = node.parent, let _ = parent.parent {
             if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
@@ -62,7 +62,7 @@ public enum SplayOperation {
         - Parameters:
             - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
      */
-    private func apply<T: Comparable>(onNode node: SplayTree<T>) {
+    public func apply<T: Comparable>(onNode node: SplayTree<T>) {
         switch self {
         case .zigZag:
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
@@ -84,7 +84,7 @@ public enum SplayOperation {
         Performs a single rotation from a node to its parent
         re-arranging the children properly
      */
-    private func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
+    public func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
         
         assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
         
@@ -95,16 +95,22 @@ public enum SplayOperation {
             child.right = parent
             parent.left = grandchildToMode
             
+    
+
         } else {
             
             grandchildToMode = child.left
             child.left = parent
             parent.right = grandchildToMode
-        }
 
+        }
+        
         let grandParent = parent.parent
         parent.parent = child
         child.parent = grandParent
+        
+        grandParent?.left = child
+
     }
 }
 
@@ -210,9 +216,15 @@ public class SplayTree<T: Comparable> {
 extension SplayTree {
     
     /*
-     Inserts a new element into the tree. You should only insert elements
-     at the root, to make to sure this remains a valid binary tree!
-     Performance: runs in O(h) time, where h is the height of the tree.
+     Inserts a new element into the tree. 
+     Returns the new Tree generated by the insertion.
+     
+     - Parameters:
+            - value T value to be inserted. Will be splayed to the root position
+     
+     - Returns
+            - SplayTree Containing the inserted value in the root node
+     
      */
     public func insert(value: T) -> SplayTree? {
         if let selfValue = self.value {
@@ -255,14 +267,17 @@ extension SplayTree {
 // MARK: - Deleting items
 
 extension SplayTree {
+    
     /*
-     Deletes a node from the tree.
-     Returns the node that has replaced this removed one (or nil if this was a
-     leaf node). That is primarily useful for when you delete the root node, in
-     which case the tree gets a new root.
-     Performance: runs in O(h) time, where h is the height of the tree.
+     Deletes the given node from the tree.
+     Return the new tree generated by the removal. 
+     The removed node (not necessarily the one containing the value), will be splayed to the root.
+     
+     - Returns:
+            - SplayTree     Resulting from the deletion and the splaying of the removed node
+     
      */
-    @discardableResult public func remove() -> SplayTree? {
+    public func remove() -> SplayTree? {
         let replacement: SplayTree?
         
         if let left = left {
@@ -521,11 +536,13 @@ extension SplayTree: CustomStringConvertible {
     public var description: String {
         var s = ""
         if let left = left {
-            s += "(\(left.description)) <- "
+            s += "left: (\(left.description)) <- "
+        }
+        if let v = value {
+            s += "\(v)"
         }
-        s += "\(value)"
         if let right = right {
-            s += " -> (\(right.description))"
+            s += " -> (right: \(right.description))"
         }
         return s
     }
@@ -534,8 +551,8 @@ extension SplayTree: CustomStringConvertible {
 extension SplayTree: CustomDebugStringConvertible {
     public var debugDescription: String {
         var s = "value: \(value)"
-        if let parent = parent {
-            s += ", parent: \(parent.value)"
+        if let parent = parent, let v = parent.value {
+            s += ", parent: \(v)"
         }
         if let left = left {
             s += ", left = [" + left.debugDescription + "]"
diff --git a/Splay Tree/Tests/SplayTreeTests.swift b/Splay Tree/Tests/SplayTreeTests.swift
index 35bdedb71..998c6d3c4 100644
--- a/Splay Tree/Tests/SplayTreeTests.swift	
+++ b/Splay Tree/Tests/SplayTreeTests.swift	
@@ -1,19 +1,30 @@
 import XCTest
 
 class SplayTreeTests: XCTestCase {
-  var tree: SplayTree<Int>!
-  
-  override func setUp() {
-    super.setUp()
-    tree = SplayTree<Int>(value: 1)
-  }
-  
-  func testElements() {
-    print(tree)
-    let tree1 = tree.insert(value: 10)
-    print(tree1!)
-    let tree2 = tree1!.insert(value: 2)
-    print(tree2!)
-  }
-
+   
+    var tree: SplayTree<Int>!
+    var tree1: SplayTree<Int>!
+    
+    override func setUp() {
+        super.setUp()
+        tree = SplayTree<Int>(value: 1)
+        tree1 = tree.insert(value: 10)?.insert(value: 20)?.insert(value: 3)//?.insert(value: 6)?.insert(value: 100)?.insert(value: 44)
+    }
+    
+    func testInsertion() {
+        let tree1 = tree.insert(value: 10)
+        assert(tree1?.root?.value == 10)
+        
+        let tree2 = tree1!.insert(value: 2)
+        assert(tree2?.root?.value == 2)
+    }
+    
+    
+    func testDeleteExisting() {
+        print(tree1)
+        let tree2 = tree1.search(value: 6)?.remove()
+        
+    }
+    
+    
 }

From 72740a17e7bd9b74716e32f1ef9ef4a92534b302 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sat, 4 Mar 2017 09:20:25 +0100
Subject: [PATCH 007/643] Test for search function + fixes for rotations

---
 Splay Tree/SplayTree.swift            | 17 +++++++++--------
 Splay Tree/Tests/SplayTreeTests.swift |  7 ++++---
 2 files changed, 13 insertions(+), 11 deletions(-)

diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
index 2e008ba50..bbe8491e2 100644
--- a/Splay Tree/SplayTree.swift	
+++ b/Splay Tree/SplayTree.swift	
@@ -94,7 +94,7 @@ public enum SplayOperation {
             grandchildToMode = child.right
             child.right = parent
             parent.left = grandchildToMode
-            
+            grandchildToMode?.parent = parent
     
 
         } else {
@@ -102,6 +102,7 @@ public enum SplayOperation {
             grandchildToMode = child.left
             child.left = parent
             parent.right = grandchildToMode
+            grandchildToMode?.parent = parent
 
         }
         
@@ -368,23 +369,23 @@ extension SplayTree {
      */
     public func search(value: T) -> SplayTree? {
         var node: SplayTree? = self
+        var nodeParent: SplayTree? = self
         while case let n? = node, n.value != nil {
             if value < n.value! {
+                if n.left != nil { nodeParent = n.left }
                 node = n.left
             } else if value > n.value! {
                 node = n.right
-            } else {
-                
-                if let node = node {
-                    SplayOperation.splay(node: node)
-                }
-                
-                return node
+                if n.right != nil { nodeParent = n.right }
             }
         }
         
         if let node = node {
             SplayOperation.splay(node: node)
+            return node
+        } else if let nodeParent = nodeParent {
+            SplayOperation.splay(node: nodeParent)
+            return nodeParent
         }
         
         return nil
diff --git a/Splay Tree/Tests/SplayTreeTests.swift b/Splay Tree/Tests/SplayTreeTests.swift
index 998c6d3c4..042344193 100644
--- a/Splay Tree/Tests/SplayTreeTests.swift	
+++ b/Splay Tree/Tests/SplayTreeTests.swift	
@@ -8,7 +8,7 @@ class SplayTreeTests: XCTestCase {
     override func setUp() {
         super.setUp()
         tree = SplayTree<Int>(value: 1)
-        tree1 = tree.insert(value: 10)?.insert(value: 20)?.insert(value: 3)//?.insert(value: 6)?.insert(value: 100)?.insert(value: 44)
+        tree1 = tree.insert(value: 10)?.insert(value: 20)?.insert(value: 3)?.insert(value: 6)?.insert(value: 100)?.insert(value: 44)
     }
     
     func testInsertion() {
@@ -20,9 +20,10 @@ class SplayTreeTests: XCTestCase {
     }
     
     
-    func testDeleteExisting() {
+    func testSearchNonExisting() {
         print(tree1)
-        let tree2 = tree1.search(value: 6)?.remove()
+        let tree2 = tree1.search(value: 5)
+        assert(tree2?.root?.value == 10)
         
     }
     

From 84e75b73e246e76fe8a22c97ef49c9d5277ea35b Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:23:31 +0100
Subject: [PATCH 008/643] Completing implementation + debug fixes of Splay Tree

---
 Splay Tree/SplayTree.swift | 321 +++++++++++++++++++++----------------
 1 file changed, 186 insertions(+), 135 deletions(-)

diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
index bbe8491e2..f50af7349 100644
--- a/Splay Tree/SplayTree.swift	
+++ b/Splay Tree/SplayTree.swift	
@@ -28,7 +28,7 @@ public enum SplayOperation {
         - Parameters:
             - node      SplayTree node to move up to the root
      */
-    public static func splay<T: Comparable>(node: SplayTree<T>) {
+    public static func splay<T: Comparable>(node: Node<T>) {
         
         while (node.parent != nil) {
             operation(forNode: node).apply(onNode: node)
@@ -44,7 +44,7 @@ public enum SplayOperation {
         - Returns
             - Operation     Case zigZag - zigZig - zig
      */
-    public static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
+    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
         
         if let parent = node.parent, let _ = parent.parent {
             if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
@@ -62,7 +62,7 @@ public enum SplayOperation {
         - Parameters:
             - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
      */
-    public func apply<T: Comparable>(onNode node: SplayTree<T>) {
+    public func apply<T: Comparable>(onNode node: Node<T>) {
         switch self {
         case .zigZag:
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
@@ -84,95 +84,65 @@ public enum SplayOperation {
         Performs a single rotation from a node to its parent
         re-arranging the children properly
      */
-    public func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
+    public func rotate<T: Comparable>(child: Node<T>, parent: Node<T>) {
         
         assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
         
-        var grandchildToMode: SplayTree<T>?
+        var grandchildToMode: Node<T>?
+        
         if child.isLeftChild {
             
             grandchildToMode = child.right
-            child.right = parent
             parent.left = grandchildToMode
             grandchildToMode?.parent = parent
+
+            let grandParent = parent.parent
+            child.parent = grandParent
+
+            if parent.isLeftChild {
+                grandParent?.left = child
+            } else {
+                grandParent?.right = child
+            }
+
+            child.right = parent
+            parent.parent = child
     
 
         } else {
             
             grandchildToMode = child.left
-            child.left = parent
             parent.right = grandchildToMode
             grandchildToMode?.parent = parent
 
+            let grandParent = parent.parent
+            child.parent = grandParent
+
+            if parent.isLeftChild {
+                grandParent?.left = child
+            } else {
+                grandParent?.right = child
+            }
+
+            child.left = parent
+            parent.parent = child
+
         }
         
-        let grandParent = parent.parent
-        parent.parent = child
-        child.parent = grandParent
-        
-        grandParent?.left = child
 
     }
 }
 
 public class Node<T: Comparable> {
     
-    fileprivate(set) public var value: T
-    fileprivate(set) public var parent: SplayTree<T>?
-    fileprivate(set) public var left: SplayTree<T>?
-    fileprivate(set) public var right: SplayTree<T>?
+    fileprivate(set) public var value: T?
+    fileprivate(set) public var parent: Node<T>?
+    fileprivate(set) public var left: Node<T>?
+    fileprivate(set) public var right: Node<T>?
     
-    init(value: T){
+    init(value: T) {
         self.value = value
     }
-}
-
-public class SplayTree<T: Comparable> {
-
-
-    fileprivate(set) public var root: Node<T>?
-    public var value: T? {
-        get {
-            return root?.value
-        }
-        set {
-            if let value = newValue {
-                root?.value = value
-            }
-        }
-    }
-
-    fileprivate(set) public var parent: SplayTree? {
-        get {
-            return root?.parent
-        }
-        set {
-            root?.parent = newValue
-        }
-    }
-    
-    fileprivate(set) public var left: SplayTree? {
-        get {
-            return root?.left
-        }
-        set {
-            root?.left = newValue
-        }
-    }
-    fileprivate(set) public var right: SplayTree? {
-        get {
-            return root?.right
-        }
-        set {
-            root?.right = newValue
-        }
-    }
-
-    //MARK: - Initializer
-    
-    public init(value: T) {
-        self.root = Node(value:value)
-    }
     
     public var isRoot: Bool {
         return parent == nil
@@ -212,29 +182,66 @@ public class SplayTree<T: Comparable> {
     }
 }
 
+public class SplayTree<T: Comparable> {
+
+    internal var root: Node<T>?
+    
+    var value: T? {
+        return root?.value
+    }
+
+    //MARK: - Initializer
+    
+    public init(value: T) {
+        self.root = Node(value:value)
+    }
+    
+    public func insert(value: T) {
+        root = root?.insert(value: value)
+    }
+    
+    public func remove(value: T) {
+        root = root?.remove(value: value)
+    }
+
+    public func search(value: T) -> Node<T>? {
+        root = root?.search(value: value)
+        return root
+    }
+    
+    public func minimum() -> Node<T>? {
+        root = root?.minimum(splayed: true)
+        return root
+    }
+    
+    public func maximum() -> Node<T>? {
+        root = root?.maximum(splayed: true)
+        return root
+    }
+    
+}
+
 // MARK: - Adding items
 
-extension SplayTree {
+extension Node {
     
     /*
-     Inserts a new element into the tree. 
-     Returns the new Tree generated by the insertion.
+     Inserts a new element into the node tree.
      
      - Parameters:
             - value T value to be inserted. Will be splayed to the root position
      
-     - Returns
-            - SplayTree Containing the inserted value in the root node
-     
+     - Returns:
+            - Node inserted
      */
-    public func insert(value: T) -> SplayTree? {
+    public func insert(value: T) -> Node {
         if let selfValue = self.value {
             if value < selfValue {
                 if let left = left {
                     return left.insert(value: value)
                 } else {
                     
-                    left = SplayTree(value: value)
+                    left = Node(value: value)
                     left?.parent = self
                     
                     if let left = left {
@@ -248,7 +255,7 @@ extension SplayTree {
                     return right.insert(value: value)
                 } else {
                     
-                    right = SplayTree(value: value)
+                    right = Node(value: value)
                     right?.parent = self
                     
                     if let right = right {
@@ -257,78 +264,104 @@ extension SplayTree {
                     }
                 }
             }
-        } else {
-            self.root = Node(value: value)
-            return self
         }
-        return nil
+        return self
     }
 }
 
 // MARK: - Deleting items
 
-extension SplayTree {
+extension Node {
     
     /*
-     Deletes the given node from the tree.
+     Deletes the given node from the nodes tree.
      Return the new tree generated by the removal. 
      The removed node (not necessarily the one containing the value), will be splayed to the root.
      
+     - Parameters:
+            - value         To be removed
+     
      - Returns:
-            - SplayTree     Resulting from the deletion and the splaying of the removed node
+            - Node     Resulting from the deletion and the splaying of the removed node
      
      */
-    public func remove() -> SplayTree? {
-        let replacement: SplayTree?
+    public func remove(value: T) -> Node<T>? {
+        let replacement: Node<T>?
         
-        if let left = left {
-            if let right = right {
-                replacement = removeNodeWithTwoChildren(left, right)
+        if let v = self.value, v == value {
+            
+            var parentToSplay: Node<T>?
+            if let left = left {
+                if let right = right {
+                    
+                    replacement = removeNodeWithTwoChildren(left, right)
+                    
+                    if let replacement = replacement,
+                        let replacementParent = replacement.parent,
+                        replacementParent.value != self.value {
+                        
+                        parentToSplay = replacement.parent
+                        
+                    } else {
+                        parentToSplay = self.parent
+                    }
+                    
+                } else {
+                    // This node only has a left child. The left child replaces the node.
+                    replacement = left
+                    parentToSplay = parent
+                }
+            } else if let right = right {
+                // This node only has a right child. The right child replaces the node.
+                replacement = right
+                parentToSplay = parent
             } else {
-                // This node only has a left child. The left child replaces the node.
-                replacement = left
+                // This node has no children. We just disconnect it from its parent.
+                replacement = nil
+                parentToSplay = parent
             }
-        } else if let right = right {
-            // This node only has a right child. The right child replaces the node.
-            replacement = right
-        } else {
-            // This node has no children. We just disconnect it from its parent.
-            replacement = nil
-        }
+            
+            reconnectParentTo(node: replacement)
+            
+            // performs the splay operation
+            if let parentToSplay = parentToSplay {
+                SplayOperation.splay(node: parentToSplay)
+            }
+            
+            // The current node is no longer part of the tree, so clean it up.
+            parent = nil
+            left = nil
+            right = nil
 
-        // Save the parent to splay before reconnecting
-        var parentToSplay: SplayTree?
-        if let replacement = replacement {
-            parentToSplay = replacement.parent
+            return parentToSplay
+            
+        } else if let v = self.value, value < v {
+            if left != nil {
+                return left!.remove(value: value)
+            } else {
+                let node = self
+                SplayOperation.splay(node: node)
+                return node
+                
+            }
         } else {
-            parentToSplay = self.parent
-        }
-        
-        reconnectParentTo(node: replacement)
-        
-        // performs the splay operation
-        if let parentToSplay = parentToSplay {
-            SplayOperation.splay(node: parentToSplay)
+            if right != nil {
+                return right?.remove(value: value)
+            } else {
+                let node = self
+                SplayOperation.splay(node: node)
+                return node
+                
+            }
         }
-        
-        // The current node is no longer part of the tree, so clean it up.
-        parent = nil
-        left = nil
-        right = nil
-        
-        return replacement
     }
     
-    private func removeNodeWithTwoChildren(_ left: SplayTree, _ right: SplayTree) -> SplayTree {
+    private func removeNodeWithTwoChildren(_ left: Node, _ right: Node) -> Node {
         // This node has two children. It must be replaced by the smallest
         // child that is larger than this node's value, which is the leftmost
         // descendent of the right child.
         let successor = right.minimum()
         
-        // If this in-order successor has a right child of its own (it cannot
-        // have a left child by definition), then that must take its place.
-        successor.remove()
-        
         // Connect our left child with the new node.
         successor.left = left
         left.parent = successor
@@ -347,7 +380,7 @@ extension SplayTree {
         return successor
     }
     
-    private func reconnectParentTo(node: SplayTree?) {
+    private func reconnectParentTo(node: Node?) {
         if let parent = parent {
             if isLeftChild {
                 parent.left = node
@@ -361,15 +394,15 @@ extension SplayTree {
 
 // MARK: - Searching
 
-extension SplayTree {
+extension Node {
     
     /*
      Finds the "highest" node with the specified value.
      Performance: runs in O(h) time, where h is the height of the tree.
      */
-    public func search(value: T) -> SplayTree? {
-        var node: SplayTree? = self
-        var nodeParent: SplayTree? = self
+    public func search(value: T) -> Node<T>? {
+        var node: Node? = self
+        var nodeParent: Node? = self
         while case let n? = node, n.value != nil {
             if value < n.value! {
                 if n.left != nil { nodeParent = n.left }
@@ -377,6 +410,8 @@ extension SplayTree {
             } else if value > n.value! {
                 node = n.right
                 if n.right != nil { nodeParent = n.right }
+            } else {
+                break
             }
         }
         
@@ -398,27 +433,31 @@ extension SplayTree {
     /*
      Returns the leftmost descendent. O(h) time.
      */
-    public func minimum() -> SplayTree {
+    public func minimum(splayed: Bool = false) -> Node<T> {
         var node = self
         while case let next? = node.left {
             node = next
         }
         
-        SplayOperation.splay(node: node)
-
+        if splayed == true {
+            SplayOperation.splay(node: node)
+        }
+        
         return node
     }
     
     /*
      Returns the rightmost descendent. O(h) time.
      */
-    public func maximum() -> SplayTree {
+    public func maximum(splayed: Bool = false) -> Node<T> {
         var node = self
         while case let next? = node.right {
             node = next
         }
         
-        SplayOperation.splay(node: node)
+        if splayed == true {
+            SplayOperation.splay(node: node)
+        }
         
         return node
     }
@@ -452,7 +491,7 @@ extension SplayTree {
     /*
      Finds the node whose value precedes our value in sorted order.
      */
-    public func predecessor() -> SplayTree<T>? {
+    public func predecessor() -> Node<T>? {
         if let left = left {
             return left.maximum()
         } else {
@@ -468,7 +507,7 @@ extension SplayTree {
     /*
      Finds the node whose value succeeds our value in sorted order.
      */
-    public func successor() -> SplayTree<T>? {
+    public func successor() -> Node<T>? {
         if let right = right {
             return right.minimum()
         } else {
@@ -483,7 +522,7 @@ extension SplayTree {
 }
 
 // MARK: - Traversal
-extension SplayTree {
+extension Node {
     
     public func traverseInOrder(process: (T) -> Void) {
         left?.traverseInOrder(process: process)
@@ -518,7 +557,7 @@ extension SplayTree {
 /*
  Is this binary tree a valid binary search tree?
  */
-extension SplayTree {
+extension Node {
     
     public func isBST(minValue: T, maxValue: T) -> Bool {
         if let value = value {
@@ -533,7 +572,7 @@ extension SplayTree {
 
 // MARK: - Debugging
 
-extension SplayTree: CustomStringConvertible {
+extension Node: CustomStringConvertible {
     public var description: String {
         var s = ""
         if let left = left {
@@ -549,7 +588,13 @@ extension SplayTree: CustomStringConvertible {
     }
 }
 
-extension SplayTree: CustomDebugStringConvertible {
+extension SplayTree: CustomStringConvertible {
+    public var description: String {
+        return root?.description ?? "Empty tree"
+    }
+}
+
+extension Node: CustomDebugStringConvertible {
     public var debugDescription: String {
         var s = "value: \(value)"
         if let parent = parent, let v = parent.value {
@@ -568,3 +613,9 @@ extension SplayTree: CustomDebugStringConvertible {
         return map { $0 }
     }
 }
+
+extension SplayTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        return root?.debugDescription ?? "Empty tree"
+    }
+}

From efa2f4856c6e80ccd36e8de11f3fb279974d9e3e Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:23:43 +0100
Subject: [PATCH 009/643] Tests for max, min, search, insert and remove

---
 Splay Tree/Tests/SplayTreeTests.swift | 52 ++++++++++++++++++++-------
 1 file changed, 40 insertions(+), 12 deletions(-)

diff --git a/Splay Tree/Tests/SplayTreeTests.swift b/Splay Tree/Tests/SplayTreeTests.swift
index 042344193..0209f8afe 100644
--- a/Splay Tree/Tests/SplayTreeTests.swift	
+++ b/Splay Tree/Tests/SplayTreeTests.swift	
@@ -2,30 +2,58 @@ import XCTest
 
 class SplayTreeTests: XCTestCase {
    
-    var tree: SplayTree<Int>!
     var tree1: SplayTree<Int>!
+    var tree2: SplayTree<Int>!
     
     override func setUp() {
         super.setUp()
-        tree = SplayTree<Int>(value: 1)
-        tree1 = tree.insert(value: 10)?.insert(value: 20)?.insert(value: 3)?.insert(value: 6)?.insert(value: 100)?.insert(value: 44)
+        tree1 = SplayTree<Int>(value: 1)
+        
+        tree2 = SplayTree<Int>(value: 1)
+        tree2.insert(value: 10)
+        tree2.insert(value: 20)
+        tree2.insert(value: 3)
+        tree2.insert(value: 6)
+        tree2.insert(value: 100)
+        tree2.insert(value: 44)
     }
     
     func testInsertion() {
-        let tree1 = tree.insert(value: 10)
-        assert(tree1?.root?.value == 10)
+        tree1.insert(value: 10)
+        assert(tree1.value == 10)
         
-        let tree2 = tree1!.insert(value: 2)
-        assert(tree2?.root?.value == 2)
+        tree2.insert(value: 2)
+        assert(tree2.root?.value == 2)
     }
     
-    
     func testSearchNonExisting() {
-        print(tree1)
-        let tree2 = tree1.search(value: 5)
-        assert(tree2?.root?.value == 10)
-        
+        let t = tree2.search(value: 5)
+        assert(t?.value == 10)
+    }
+
+    func testSearchExisting() {
+        let t = tree2.search(value: 6)
+        assert(t?.value == 6)
+    }
+    
+    func testDeleteExistingOnlyLeftChild() {
+        tree2.remove(value: 3)
+        assert(tree2.value == 6)
+    }
+
+    func testDeleteExistingOnly2Children() {
+        tree2.remove(value: 6)
+        assert(tree2.value == 20)
     }
     
+    func testMinimum() {
+        let v = tree2.minimum()
+        assert(v?.value == 1)
+    }
+
+    func testMaximum() {
+        let v = tree2.maximum()
+        assert(v?.value == 100)
+    }
     
 }

From c27fdde75dc064f55ea7dfdcd5c7d0d4a44aaea6 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:24:22 +0100
Subject: [PATCH 010/643] Replacing SplayTree implementation inside Playground

---
 .../Sources/SplayTree.swift                   | 398 +++++++++++-------
 1 file changed, 255 insertions(+), 143 deletions(-)

diff --git a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift
index f0c45e831..f50af7349 100644
--- a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
+++ b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
@@ -28,7 +28,7 @@ public enum SplayOperation {
         - Parameters:
             - node      SplayTree node to move up to the root
      */
-    public static func splay<T: Comparable>(node: SplayTree<T>) {
+    public static func splay<T: Comparable>(node: Node<T>) {
         
         while (node.parent != nil) {
             operation(forNode: node).apply(onNode: node)
@@ -44,10 +44,10 @@ public enum SplayOperation {
         - Returns
             - Operation     Case zigZag - zigZig - zig
      */
-    private static func operation<T: Comparable>(forNode node: SplayTree<T>) -> SplayOperation {
+    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
         
-        if let parent = node.parent, let grandParent = parent.parent {
-            if (node.isLeftChild && grandParent.isRightChild) || (node.isRightChild && grandParent.isLeftChild) {
+        if let parent = node.parent, let _ = parent.parent {
+            if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
                 return .zigZag
             }
             return .zigZig
@@ -62,7 +62,7 @@ public enum SplayOperation {
         - Parameters:
             - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
      */
-    private func apply<T: Comparable>(onNode node: SplayTree<T>) {
+    public func apply<T: Comparable>(onNode node: Node<T>) {
         switch self {
         case .zigZag:
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
@@ -84,49 +84,66 @@ public enum SplayOperation {
         Performs a single rotation from a node to its parent
         re-arranging the children properly
      */
-    private func rotate<T: Comparable>(child: SplayTree<T>, parent: SplayTree<T>) {
+    public func rotate<T: Comparable>(child: Node<T>, parent: Node<T>) {
         
         assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
         
-        var grandchildToMode: SplayTree<T>?
+        var grandchildToMode: Node<T>?
+        
         if child.isLeftChild {
             
             grandchildToMode = child.right
-            child.right = parent
             parent.left = grandchildToMode
-            
+            grandchildToMode?.parent = parent
+
+            let grandParent = parent.parent
+            child.parent = grandParent
+
+            if parent.isLeftChild {
+                grandParent?.left = child
+            } else {
+                grandParent?.right = child
+            }
+
+            child.right = parent
+            parent.parent = child
+    
+
         } else {
             
             grandchildToMode = child.left
-            child.left = parent
             parent.right = grandchildToMode
+            grandchildToMode?.parent = parent
+
+            let grandParent = parent.parent
+            child.parent = grandParent
+
+            if parent.isLeftChild {
+                grandParent?.left = child
+            } else {
+                grandParent?.right = child
+            }
+
+            child.left = parent
+            parent.parent = child
+
         }
+        
 
-        let grandParent = parent.parent
-        parent.parent = child
-        child.parent = grandParent
     }
 }
 
-public class SplayTree<T: Comparable> {
+public class Node<T: Comparable> {
     
-    fileprivate(set) public var value: T
-    fileprivate(set) public var parent: SplayTree?
-    fileprivate(set) public var left: SplayTree?
-    fileprivate(set) public var right: SplayTree?
+    fileprivate(set) public var value: T?
+    fileprivate(set) public var parent: Node<T>?
+    fileprivate(set) public var left: Node<T>?
+    fileprivate(set) public var right: Node<T>?
     
-    public init(value: T) {
+    init(value: T) {
         self.value = value
     }
     
-    public convenience init(array: [T]) {
-        precondition(array.count > 0)
-        self.init(value: array.first!)
-        for v in array.dropFirst() {
-            insert(value: v)
-        }
-    }
-    
     public var isRoot: Bool {
         return parent == nil
     }
@@ -165,114 +182,186 @@ public class SplayTree<T: Comparable> {
     }
 }
 
+public class SplayTree<T: Comparable> {
+
+    internal var root: Node<T>?
+    
+    var value: T? {
+        return root?.value
+    }
+
+    //MARK: - Initializer
+    
+    public init(value: T) {
+        self.root = Node(value:value)
+    }
+    
+    public func insert(value: T) {
+        root = root?.insert(value: value)
+    }
+    
+    public func remove(value: T) {
+        root = root?.remove(value: value)
+    }
+
+    public func search(value: T) -> Node<T>? {
+        root = root?.search(value: value)
+        return root
+    }
+    
+    public func minimum() -> Node<T>? {
+        root = root?.minimum(splayed: true)
+        return root
+    }
+    
+    public func maximum() -> Node<T>? {
+        root = root?.maximum(splayed: true)
+        return root
+    }
+    
+}
+
 // MARK: - Adding items
 
-extension SplayTree {
+extension Node {
     
     /*
-     Inserts a new element into the tree. You should only insert elements
-     at the root, to make to sure this remains a valid binary tree!
-     Performance: runs in O(h) time, where h is the height of the tree.
+     Inserts a new element into the node tree.
+     
+     - Parameters:
+            - value T value to be inserted. Will be splayed to the root position
+     
+     - Returns:
+            - Node inserted
      */
-    public func insert(value: T) {
-        if value < self.value {
-            if let left = left {
-                left.insert(value: value)
-            } else {
-                
-                left = SplayTree(value: value)
-                left?.parent = self
-                
+    public func insert(value: T) -> Node {
+        if let selfValue = self.value {
+            if value < selfValue {
                 if let left = left {
-                    SplayOperation.splay(node: left)
-                    self.parent = nil
-                    self.value = left.value
-                    self.left = left.left
-                    self.right = left.right
+                    return left.insert(value: value)
+                } else {
+                    
+                    left = Node(value: value)
+                    left?.parent = self
+                    
+                    if let left = left {
+                        SplayOperation.splay(node: left)
+                        return left
+                    }
                 }
-            }
-        } else {
-            
-            if let right = right {
-                right.insert(value: value)
             } else {
                 
-                right = SplayTree(value: value)
-                right?.parent = self
-                
                 if let right = right {
-                    SplayOperation.splay(node: right)
-                    self.parent = nil
-                    self.value = right.value
-                    self.left = right.left
-                    self.right = right.right
+                    return right.insert(value: value)
+                } else {
+                    
+                    right = Node(value: value)
+                    right?.parent = self
+                    
+                    if let right = right {
+                        SplayOperation.splay(node: right)
+                        return right
+                    }
                 }
             }
         }
+        return self
     }
 }
 
 // MARK: - Deleting items
 
-extension SplayTree {
+extension Node {
+    
     /*
-     Deletes a node from the tree.
-     Returns the node that has replaced this removed one (or nil if this was a
-     leaf node). That is primarily useful for when you delete the root node, in
-     which case the tree gets a new root.
-     Performance: runs in O(h) time, where h is the height of the tree.
+     Deletes the given node from the nodes tree.
+     Return the new tree generated by the removal. 
+     The removed node (not necessarily the one containing the value), will be splayed to the root.
+     
+     - Parameters:
+            - value         To be removed
+     
+     - Returns:
+            - Node     Resulting from the deletion and the splaying of the removed node
+     
      */
-    @discardableResult public func remove() -> SplayTree? {
-        let replacement: SplayTree?
+    public func remove(value: T) -> Node<T>? {
+        let replacement: Node<T>?
         
-        if let left = left {
-            if let right = right {
-                replacement = removeNodeWithTwoChildren(left, right)
+        if let v = self.value, v == value {
+            
+            var parentToSplay: Node<T>?
+            if let left = left {
+                if let right = right {
+                    
+                    replacement = removeNodeWithTwoChildren(left, right)
+                    
+                    if let replacement = replacement,
+                        let replacementParent = replacement.parent,
+                        replacementParent.value != self.value {
+                        
+                        parentToSplay = replacement.parent
+                        
+                    } else {
+                        parentToSplay = self.parent
+                    }
+                    
+                } else {
+                    // This node only has a left child. The left child replaces the node.
+                    replacement = left
+                    parentToSplay = parent
+                }
+            } else if let right = right {
+                // This node only has a right child. The right child replaces the node.
+                replacement = right
+                parentToSplay = parent
             } else {
-                // This node only has a left child. The left child replaces the node.
-                replacement = left
+                // This node has no children. We just disconnect it from its parent.
+                replacement = nil
+                parentToSplay = parent
             }
-        } else if let right = right {
-            // This node only has a right child. The right child replaces the node.
-            replacement = right
-        } else {
-            // This node has no children. We just disconnect it from its parent.
-            replacement = nil
-        }
+            
+            reconnectParentTo(node: replacement)
+            
+            // performs the splay operation
+            if let parentToSplay = parentToSplay {
+                SplayOperation.splay(node: parentToSplay)
+            }
+            
+            // The current node is no longer part of the tree, so clean it up.
+            parent = nil
+            left = nil
+            right = nil
 
-        // Save the parent to splay before reconnecting
-        var parentToSplay: SplayTree?
-        if let replacement = replacement {
-            parentToSplay = replacement.parent
+            return parentToSplay
+            
+        } else if let v = self.value, value < v {
+            if left != nil {
+                return left!.remove(value: value)
+            } else {
+                let node = self
+                SplayOperation.splay(node: node)
+                return node
+                
+            }
         } else {
-            parentToSplay = self.parent
-        }
-        
-        reconnectParentTo(node: replacement)
-        
-        // performs the splay operation
-        if let parentToSplay = parentToSplay {
-            SplayOperation.splay(node: parentToSplay)
+            if right != nil {
+                return right?.remove(value: value)
+            } else {
+                let node = self
+                SplayOperation.splay(node: node)
+                return node
+                
+            }
         }
-        
-        // The current node is no longer part of the tree, so clean it up.
-        parent = nil
-        left = nil
-        right = nil
-        
-        return replacement
     }
     
-    private func removeNodeWithTwoChildren(_ left: SplayTree, _ right: SplayTree) -> SplayTree {
+    private func removeNodeWithTwoChildren(_ left: Node, _ right: Node) -> Node {
         // This node has two children. It must be replaced by the smallest
         // child that is larger than this node's value, which is the leftmost
         // descendent of the right child.
         let successor = right.minimum()
         
-        // If this in-order successor has a right child of its own (it cannot
-        // have a left child by definition), then that must take its place.
-        successor.remove()
-        
         // Connect our left child with the new node.
         successor.left = left
         left.parent = successor
@@ -291,7 +380,7 @@ extension SplayTree {
         return successor
     }
     
-    private func reconnectParentTo(node: SplayTree?) {
+    private func reconnectParentTo(node: Node?) {
         if let parent = parent {
             if isLeftChild {
                 parent.left = node
@@ -305,31 +394,33 @@ extension SplayTree {
 
 // MARK: - Searching
 
-extension SplayTree {
+extension Node {
     
     /*
      Finds the "highest" node with the specified value.
      Performance: runs in O(h) time, where h is the height of the tree.
      */
-    public func search(value: T) -> SplayTree? {
-        var node: SplayTree? = self
-        while case let n? = node {
-            if value < n.value {
+    public func search(value: T) -> Node<T>? {
+        var node: Node? = self
+        var nodeParent: Node? = self
+        while case let n? = node, n.value != nil {
+            if value < n.value! {
+                if n.left != nil { nodeParent = n.left }
                 node = n.left
-            } else if value > n.value {
+            } else if value > n.value! {
                 node = n.right
+                if n.right != nil { nodeParent = n.right }
             } else {
-                
-                if let node = node {
-                    SplayOperation.splay(node: node)
-                }
-                
-                return node
+                break
             }
         }
         
         if let node = node {
             SplayOperation.splay(node: node)
+            return node
+        } else if let nodeParent = nodeParent {
+            SplayOperation.splay(node: nodeParent)
+            return nodeParent
         }
         
         return nil
@@ -342,27 +433,31 @@ extension SplayTree {
     /*
      Returns the leftmost descendent. O(h) time.
      */
-    public func minimum() -> SplayTree {
+    public func minimum(splayed: Bool = false) -> Node<T> {
         var node = self
         while case let next? = node.left {
             node = next
         }
         
-        SplayOperation.splay(node: node)
-
+        if splayed == true {
+            SplayOperation.splay(node: node)
+        }
+        
         return node
     }
     
     /*
      Returns the rightmost descendent. O(h) time.
      */
-    public func maximum() -> SplayTree {
+    public func maximum(splayed: Bool = false) -> Node<T> {
         var node = self
         while case let next? = node.right {
             node = next
         }
         
-        SplayOperation.splay(node: node)
+        if splayed == true {
+            SplayOperation.splay(node: node)
+        }
         
         return node
     }
@@ -396,13 +491,13 @@ extension SplayTree {
     /*
      Finds the node whose value precedes our value in sorted order.
      */
-    public func predecessor() -> SplayTree<T>? {
+    public func predecessor() -> Node<T>? {
         if let left = left {
             return left.maximum()
         } else {
             var node = self
-            while case let parent? = node.parent {
-                if parent.value < value { return parent }
+            while case let parent? = node.parent, parent.value != nil, value != nil {
+                if parent.value! < value! { return parent }
                 node = parent
             }
             return nil
@@ -412,13 +507,13 @@ extension SplayTree {
     /*
      Finds the node whose value succeeds our value in sorted order.
      */
-    public func successor() -> SplayTree<T>? {
+    public func successor() -> Node<T>? {
         if let right = right {
             return right.minimum()
         } else {
             var node = self
-            while case let parent? = node.parent {
-                if parent.value > value { return parent }
+            while case let parent? = node.parent, parent.value != nil , value != nil {
+                if parent.value! > value! { return parent }
                 node = parent
             }
             return nil
@@ -427,16 +522,16 @@ extension SplayTree {
 }
 
 // MARK: - Traversal
-extension SplayTree {
+extension Node {
     
     public func traverseInOrder(process: (T) -> Void) {
         left?.traverseInOrder(process: process)
-        process(value)
+        process(value!)
         right?.traverseInOrder(process: process)
     }
     
     public func traversePreOrder(process: (T) -> Void) {
-        process(value)
+        process(value!)
         left?.traversePreOrder(process: process)
         right?.traversePreOrder(process: process)
     }
@@ -444,7 +539,7 @@ extension SplayTree {
     public func traversePostOrder(process: (T) -> Void) {
         left?.traversePostOrder(process: process)
         right?.traversePostOrder(process: process)
-        process(value)
+        process(value!)
     }
     
     /*
@@ -453,7 +548,7 @@ extension SplayTree {
     public func map(formula: (T) -> T) -> [T] {
         var a = [T]()
         if let left = left { a += left.map(formula: formula) }
-        a.append(formula(value))
+        a.append(formula(value!))
         if let right = right { a += right.map(formula: formula) }
         return a
     }
@@ -462,37 +557,48 @@ extension SplayTree {
 /*
  Is this binary tree a valid binary search tree?
  */
-extension SplayTree {
+extension Node {
     
     public func isBST(minValue: T, maxValue: T) -> Bool {
-        if value < minValue || value > maxValue { return false }
-        let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
-        let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
-        return leftBST && rightBST
+        if let value = value {
+            if value < minValue || value > maxValue { return false }
+            let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
+            let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
+            return leftBST && rightBST
+        }
+        return false
     }
 }
 
 // MARK: - Debugging
 
-extension SplayTree: CustomStringConvertible {
+extension Node: CustomStringConvertible {
     public var description: String {
         var s = ""
         if let left = left {
-            s += "(\(left.description)) <- "
+            s += "left: (\(left.description)) <- "
+        }
+        if let v = value {
+            s += "\(v)"
         }
-        s += "\(value)"
         if let right = right {
-            s += " -> (\(right.description))"
+            s += " -> (right: \(right.description))"
         }
         return s
     }
 }
 
-extension SplayTree: CustomDebugStringConvertible {
+extension SplayTree: CustomStringConvertible {
+    public var description: String {
+        return root?.description ?? "Empty tree"
+    }
+}
+
+extension Node: CustomDebugStringConvertible {
     public var debugDescription: String {
         var s = "value: \(value)"
-        if let parent = parent {
-            s += ", parent: \(parent.value)"
+        if let parent = parent, let v = parent.value {
+            s += ", parent: \(v)"
         }
         if let left = left {
             s += ", left = [" + left.debugDescription + "]"
@@ -507,3 +613,9 @@ extension SplayTree: CustomDebugStringConvertible {
         return map { $0 }
     }
 }
+
+extension SplayTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        return root?.debugDescription ?? "Empty tree"
+    }
+}

From 4aaec9d94b5b6a5c75b07c35fd0e4def6830ac44 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:38:15 +0100
Subject: [PATCH 011/643] Test for root removal and multiple operations
 executed

---
 Splay Tree/Tests/SplayTreeTests.swift | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/Splay Tree/Tests/SplayTreeTests.swift b/Splay Tree/Tests/SplayTreeTests.swift
index 0209f8afe..01201a108 100644
--- a/Splay Tree/Tests/SplayTreeTests.swift	
+++ b/Splay Tree/Tests/SplayTreeTests.swift	
@@ -46,6 +46,11 @@ class SplayTreeTests: XCTestCase {
         assert(tree2.value == 20)
     }
     
+    func testDeleteRoot() {
+        tree2.remove(value: 44)
+        assert(tree2.value == 100)
+    }
+    
     func testMinimum() {
         let v = tree2.minimum()
         assert(v?.value == 1)
@@ -56,4 +61,16 @@ class SplayTreeTests: XCTestCase {
         assert(v?.value == 100)
     }
     
+    func testInsertionRemovals() {
+        let splayTree = SplayTree(value: 1)
+        splayTree.insert(value: 2)
+        splayTree.insert(value: 10)
+        splayTree.insert(value: 6)
+        
+        splayTree.remove(value: 10)
+        splayTree.remove(value: 6)
+        
+        assert(splayTree.value == 2)
+    }
+    
 }

From 9da711ddf62bdc9b77d73ad64da8285a94f2b4cc Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:38:47 +0100
Subject: [PATCH 012/643] Fixes for root removal & insertions with nil root

---
 .../Sources/SplayTree.swift                   | 106 ++++++++++--------
 Splay Tree/SplayTree.swift                    |  22 +++-
 2 files changed, 78 insertions(+), 50 deletions(-)

diff --git a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift
index f50af7349..a4feda7ef 100644
--- a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
+++ b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
@@ -1,5 +1,5 @@
 /*
- *  Splay Tree 
+ *  Splay Tree
  *
  * Based on Binary Search Tree Implementation written by Nicolas Ameghino and Matthijs Hollemans for Swift Algorithms Club
  * https://github.com/raywenderlich/swift-algorithm-club/blob/master/Binary%20Search%20Tree
@@ -8,12 +8,12 @@
  */
 
 /**
-    Represent the 3 possible operations (combinations of rotations) that
-    could be performed during the Splay phase in Splay Trees
+ Represent the 3 possible operations (combinations of rotations) that
+ could be performed during the Splay phase in Splay Trees
  
-    - zigZag       Left child of a right child OR right child of a left child
-    - zigZig       Left child of a left child OR right child of a right child
-    - zig          Only 1 parent and that parent is the root
+ - zigZag       Left child of a right child OR right child of a left child
+ - zigZig       Left child of a left child OR right child of a right child
+ - zig          Only 1 parent and that parent is the root
  
  */
 public enum SplayOperation {
@@ -23,10 +23,10 @@ public enum SplayOperation {
     
     
     /**
-        Splay the given node up to the root of the tree
+     Splay the given node up to the root of the tree
      
-        - Parameters:
-            - node      SplayTree node to move up to the root
+     - Parameters:
+     - node      SplayTree node to move up to the root
      */
     public static func splay<T: Comparable>(node: Node<T>) {
         
@@ -36,13 +36,13 @@ public enum SplayOperation {
     }
     
     /**
-        Compares the node and its parent and determine
-        if the rotations should be performed in a zigZag, zigZig or zig case.
+     Compares the node and its parent and determine
+     if the rotations should be performed in a zigZag, zigZig or zig case.
      
-        - Parmeters:
-            - forNode       SplayTree node to be checked
-        - Returns
-            - Operation     Case zigZag - zigZig - zig
+     - Parmeters:
+     - forNode       SplayTree node to be checked
+     - Returns
+     - Operation     Case zigZag - zigZig - zig
      */
     public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
         
@@ -56,11 +56,11 @@ public enum SplayOperation {
     }
     
     /**
-        Applies the rotation associated to the case 
-        Modifying the splay tree and briging the received node further to the top of the tree
+     Applies the rotation associated to the case
+     Modifying the splay tree and briging the received node further to the top of the tree
      
-        - Parameters:
-            - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
+     - Parameters:
+     - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
      */
     public func apply<T: Comparable>(onNode node: Node<T>) {
         switch self {
@@ -68,12 +68,12 @@ public enum SplayOperation {
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
             rotate(child: node, parent: node.parent!)
             rotate(child: node, parent: node.parent!)
-
+            
         case .zigZig:
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
             rotate(child: node.parent!, parent: node.parent!.parent!)
             rotate(child: node, parent: node.parent!)
-        
+            
         case .zig:
             assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
             rotate(child: node, parent: node.parent!)
@@ -81,8 +81,8 @@ public enum SplayOperation {
     }
     
     /**
-        Performs a single rotation from a node to its parent
-        re-arranging the children properly
+     Performs a single rotation from a node to its parent
+     re-arranging the children properly
      */
     public func rotate<T: Comparable>(child: Node<T>, parent: Node<T>) {
         
@@ -95,41 +95,41 @@ public enum SplayOperation {
             grandchildToMode = child.right
             parent.left = grandchildToMode
             grandchildToMode?.parent = parent
-
+            
             let grandParent = parent.parent
             child.parent = grandParent
-
+            
             if parent.isLeftChild {
                 grandParent?.left = child
             } else {
                 grandParent?.right = child
             }
-
+            
             child.right = parent
             parent.parent = child
-    
-
+            
+            
         } else {
             
             grandchildToMode = child.left
             parent.right = grandchildToMode
             grandchildToMode?.parent = parent
-
+            
             let grandParent = parent.parent
             child.parent = grandParent
-
+            
             if parent.isLeftChild {
                 grandParent?.left = child
             } else {
                 grandParent?.right = child
             }
-
+            
             child.left = parent
             parent.parent = child
-
+            
         }
         
-
+        
     }
 }
 
@@ -183,13 +183,13 @@ public class Node<T: Comparable> {
 }
 
 public class SplayTree<T: Comparable> {
-
+    
     internal var root: Node<T>?
     
     var value: T? {
         return root?.value
     }
-
+    
     //MARK: - Initializer
     
     public init(value: T) {
@@ -197,13 +197,17 @@ public class SplayTree<T: Comparable> {
     }
     
     public func insert(value: T) {
-        root = root?.insert(value: value)
+        if let root = root {
+            self.root = root.insert(value: value)
+        } else {
+            root = Node(value: value)
+        }
     }
     
     public func remove(value: T) {
         root = root?.remove(value: value)
     }
-
+    
     public func search(value: T) -> Node<T>? {
         root = root?.search(value: value)
         return root
@@ -229,10 +233,10 @@ extension Node {
      Inserts a new element into the node tree.
      
      - Parameters:
-            - value T value to be inserted. Will be splayed to the root position
+     - value T value to be inserted. Will be splayed to the root position
      
      - Returns:
-            - Node inserted
+     - Node inserted
      */
     public func insert(value: T) -> Node {
         if let selfValue = self.value {
@@ -275,14 +279,14 @@ extension Node {
     
     /*
      Deletes the given node from the nodes tree.
-     Return the new tree generated by the removal. 
+     Return the new tree generated by the removal.
      The removed node (not necessarily the one containing the value), will be splayed to the root.
      
      - Parameters:
-            - value         To be removed
+     - value         To be removed
      
      - Returns:
-            - Node     Resulting from the deletion and the splaying of the removed node
+     - Node     Resulting from the deletion and the splaying of the removed node
      
      */
     public func remove(value: T) -> Node<T>? {
@@ -302,19 +306,29 @@ extension Node {
                         
                         parentToSplay = replacement.parent
                         
-                    } else {
+                    } else if self.parent != nil {
                         parentToSplay = self.parent
+                    } else {
+                        parentToSplay = replacement
                     }
                     
                 } else {
                     // This node only has a left child. The left child replaces the node.
                     replacement = left
-                    parentToSplay = parent
+                    if self.parent != nil {
+                        parentToSplay = self.parent
+                    } else {
+                        parentToSplay = replacement
+                    }
                 }
             } else if let right = right {
                 // This node only has a right child. The right child replaces the node.
                 replacement = right
-                parentToSplay = parent
+                if self.parent != nil {
+                    parentToSplay = self.parent
+                } else {
+                    parentToSplay = replacement
+                }
             } else {
                 // This node has no children. We just disconnect it from its parent.
                 replacement = nil
@@ -332,7 +346,7 @@ extension Node {
             parent = nil
             left = nil
             right = nil
-
+            
             return parentToSplay
             
         } else if let v = self.value, value < v {
diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
index f50af7349..a7b20743d 100644
--- a/Splay Tree/SplayTree.swift	
+++ b/Splay Tree/SplayTree.swift	
@@ -197,7 +197,11 @@ public class SplayTree<T: Comparable> {
     }
     
     public func insert(value: T) {
-        root = root?.insert(value: value)
+        if let root = root {
+            self.root = root.insert(value: value)
+        } else {
+            root = Node(value: value)
+        }
     }
     
     public func remove(value: T) {
@@ -302,19 +306,29 @@ extension Node {
                         
                         parentToSplay = replacement.parent
                         
-                    } else {
+                    } else if self.parent != nil {
                         parentToSplay = self.parent
+                    } else {
+                        parentToSplay = replacement
                     }
                     
                 } else {
                     // This node only has a left child. The left child replaces the node.
                     replacement = left
-                    parentToSplay = parent
+                    if self.parent != nil {
+                        parentToSplay = self.parent
+                    } else {
+                        parentToSplay = replacement
+                    }
                 }
             } else if let right = right {
                 // This node only has a right child. The right child replaces the node.
                 replacement = right
-                parentToSplay = parent
+                if self.parent != nil {
+                    parentToSplay = self.parent
+                } else {
+                    parentToSplay = replacement
+                }
             } else {
                 // This node has no children. We just disconnect it from its parent.
                 replacement = nil

From ecba738935641768526277d908153adc3f9d8ca6 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 5 Mar 2017 19:38:55 +0100
Subject: [PATCH 013/643] Playground Splay Tree

---
 .../SplayTree.playground/Contents.swift       | 24 ++++++++++++++++++-
 1 file changed, 23 insertions(+), 1 deletion(-)

diff --git a/Splay Tree/SplayTree.playground/Contents.swift b/Splay Tree/SplayTree.playground/Contents.swift
index 951ad4c5c..4406a759d 100644
--- a/Splay Tree/SplayTree.playground/Contents.swift	
+++ b/Splay Tree/SplayTree.playground/Contents.swift	
@@ -1,7 +1,29 @@
 //: Playground - Splay Tree Implementation
 
 
-let splayTree = SplayTree(array: [1])
+let splayTree = SplayTree(value: 1)
 splayTree.insert(value: 2)
 splayTree.insert(value: 10)
 splayTree.insert(value: 6)
+
+splayTree.remove(value: 10)
+splayTree.remove(value: 6)
+
+splayTree.insert(value: 55)
+splayTree.insert(value: 559)
+splayTree.remove(value: 2)
+splayTree.remove(value: 1)
+splayTree.remove(value: 55)
+splayTree.remove(value: 559)
+
+splayTree.insert(value: 1843000)
+splayTree.insert(value: 1238)
+splayTree.insert(value: -1)
+splayTree.insert(value: 87)
+
+splayTree.minimum()
+splayTree.maximum()
+
+
+
+

From 1c43c804633f9fd36e67f9988d17e8402ac258d8 Mon Sep 17 00:00:00 2001
From: Arkalyk Akash <arkalyk@arkalyks-macbook-pro.local>
Date: Mon, 13 Mar 2017 17:00:42 +0600
Subject: [PATCH 014/643] Egg Drop Dynamic Problem Added

---
 Egg Drop Problem/EggDrop.swift                | 31 +++++++++++++++++++
 .../contents.xcworkspacedata                  |  7 +++++
 2 files changed, 38 insertions(+)
 create mode 100644 Egg Drop Problem/EggDrop.swift

diff --git a/Egg Drop Problem/EggDrop.swift b/Egg Drop Problem/EggDrop.swift
new file mode 100644
index 000000000..6d0aab2a1
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.swift	
@@ -0,0 +1,31 @@
+func eggDrop(_ numberOfEggs: Int, numberOfFloors: Int) -> Int {
+    var eggFloor: [[Int]] = [] //egg(rows) floor(cols) array to store the solutions
+    var attempts: Int = 0
+    
+    for var i in (0..<numberOfFloors){
+        eggFloor[1][i] = i
+    }
+    eggFloor[2][1] = 1
+    
+    for var i in (2..<=numberOfEggs){
+        for var j in (2..numberOfFloors){
+            eggFloor[i][j] = 1000000
+            for var k in (1..<=j){
+                //there are two cases
+                //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> k-1
+                //case 2: egg doesn't break. meaning we'll still have 'i' number of eggs, and we'll go upstairs -> j-k
+                attempts = 1 + max(eggFloor[i-1][k-1], eggFloor[i][j-k])//we add one taking into account the attempt we're taking at the moment
+                
+                if attempts < eggFloor[i][j]{ //finding the min
+                    eggFloor[i][j] = attempts;
+                }
+            }
+        }
+    }
+    
+    return eggFloor[numberOfEggs][numberOfFloors]
+}
+
+func max(_ x1: Int, _ x2: Int){
+    return x1 > x2 ? x1 : x2
+}
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index b2ffce836..5ac8577f5 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1,6 +1,13 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Workspace
    version = "1.0">
+   <Group
+      location = "group:Egg Drop Problem"
+      name = "Egg Drop Problem">
+      <FileRef
+         location = "group:/Users/arkalyk/Desktop/SwiftAlgorithmClub/swift-algorithm-club/Egg Drop Problem/EggDrop.swift">
+      </FileRef>
+   </Group>
    <FileRef
       location = "group:README.markdown">
    </FileRef>

From 55c11cadd38ee59e89a3128860b53f63e8b0457d Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Fri, 14 Apr 2017 21:37:24 +0200
Subject: [PATCH 015/643] Claim Naive Bayes Classifier

---
 Naive Bayes Classifier/README.md | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Naive Bayes Classifier/README.md

diff --git a/Naive Bayes Classifier/README.md b/Naive Bayes Classifier/README.md
new file mode 100644
index 000000000..e69de29bb

From 85f8085de5131657a9f8f5e7ab8f8d3e42f39edf Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Fri, 14 Apr 2017 21:38:44 +0200
Subject: [PATCH 016/643] Add initial version of NB

---
 Naive Bayes Classifier/NaiveBayes.swift | 141 ++++++++++++++++++++++++
 1 file changed, 141 insertions(+)
 create mode 100644 Naive Bayes Classifier/NaiveBayes.swift

diff --git a/Naive Bayes Classifier/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.swift
new file mode 100644
index 000000000..c988cacbe
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.swift	
@@ -0,0 +1,141 @@
+//
+//  main.swift
+//  NaiveBayes
+//
+//  Created by Philipp Gabriel on 14.04.17.
+//  Copyright © 2017 ph1ps. All rights reserved.
+//
+
+//TODO naming
+import Foundation
+
+extension Array where Element == Double {
+
+    func mean() -> Double {
+        return self.reduce(0, +) / Double(count)
+    }
+    
+    func standardDeviation() -> Double {
+        let calculatedMean = mean()
+        
+        let sum = self.reduce(0.0) { (previous, next) in
+            return previous + pow(next - calculatedMean, 2)
+        }
+        
+        return sqrt(sum / Double(count - 1))
+    }
+}
+
+extension Array where Element == Int {
+    
+    //Is this the best way?!
+    func uniques() -> [Int] {
+        return Array(Set(self))
+    }
+    
+}
+
+class NaiveBayes {
+
+    var data: [[Double]]
+    var classes: [Int]
+    var variables: [Int: [(feature: Int, mean: Double, stDev: Double)]]
+    
+    init(data: [[Double]], classes: [Int]) {
+        self.data = data
+        self.classes = classes
+        self.variables = [Int: [(feature: Int, mean: Double, stDev: Double)]]()
+    }
+    
+    //TODO
+    //init(dataAndClasses: [[Double]], index ofClassRow: Int) {}
+
+    //TODO: Does it really need to be n^2 runtime?
+    func train() {
+
+        for `class` in 0..<classes.uniques().count {
+            variables[`class`] = [(feature: Int, mean: Double, stDev: Double)]()
+            
+            for feature in 0..<data[0].count {
+                
+                let values = data.map{ $0[feature] }.enumerated().filter { (offset, _) in
+                    return classes[offset] == `class`
+                }.map { $0.element }
+
+                variables[`class`]?.append((feature, values.mean(), values.standardDeviation()))
+            }
+        }
+
+        data.removeAll(keepingCapacity: false)
+    }
+    
+    func predictClass(input: [Double]) -> Int {
+        let likelihoods = predictLikelihood(input: input).max { (first, second) -> Bool in
+            return first.1 < second.1
+        }
+        
+        guard let `class` = likelihoods?.0 else {
+            return -1
+        }
+        
+        return `class`
+    }
+    
+    func predictLikelihood(input: [Double]) -> [(Int, Double)] {
+    
+        var probabilityOfClasses = [Int: Double]()
+        let amount = classes.uniques().count
+        
+        classes.forEach { `class` in
+            let individual = classes.filter { $0 == `class` }.count
+            probabilityOfClasses[`class`] = Double(amount) / Double(individual)
+        }
+        
+        let probaClass = variables.map { (key, value) -> (Int, [Double]) in
+            let probaFeature = value.map { (feature, mean, stDev) -> Double in
+                let featureValue = input[feature]
+                let eulerPart = pow(M_E, -1 * pow(featureValue - mean, 2) / (2 * pow(stDev, 2)))
+                let distribution = eulerPart / sqrt(2 * .pi) / stDev
+                return distribution
+            }
+            return (key, probaFeature)
+        }
+        
+        let likelihoods = probaClass.map { (key, probaFeature) in
+            return (key, probaFeature.reduce(1, *) * (probabilityOfClasses[key] ?? 1.0))
+        }
+
+        let sum = likelihoods.map { $0.1 }.reduce(0, +)
+        let normalized = likelihoods.map { (`class`, likelihood) in
+            return (`class`, likelihood / sum)
+        }
+        
+        return normalized
+    }
+}
+
+let data: [[Double]] = [
+    [6,180,12],
+    [5.92,190,11],
+    [5.58,170,12],
+    [5.92,165,10],
+    [5,100,6],
+    [5.5,150,8],
+    [5.42,130,7],
+    [5.75,150,9]
+]
+
+let classes = [0,0,0,0,1,1,1,1]
+
+let naive = NaiveBayes(data: data, classes: classes)
+naive.train()
+let result = naive.predictLikelihood(input: [6,130,8])
+print(result)
+
+
+
+
+
+
+
+

From be4ac46a126d4f1b744bb84216ab0ef68686e2e7 Mon Sep 17 00:00:00 2001
From: Philipp Gabriel <ph1ps@users.noreply.github.com>
Date: Fri, 14 Apr 2017 21:40:52 +0200
Subject: [PATCH 017/643] Add NB to README

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

diff --git a/README.markdown b/README.markdown
index 29fc9d748..7df847960 100644
--- a/README.markdown
+++ b/README.markdown
@@ -116,6 +116,7 @@ Bad sorting algorithms (don't use these!):
 - Logistic Regression
 - Neural Networks
 - PageRank
+- [Naive Bayes Classifier](Naive%20Bayes%20Classifier/)
 
 ## Data structures
 

From f536ff10804f32066a5fdea1becfc6b80ebbf25f Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk@ARKALYKs-MacBook-Pro.local>
Date: Sat, 15 Apr 2017 02:06:55 +0600
Subject: [PATCH 018/643] Bugs fied. Readme added.

---
 .../EggDrop.playground/Contents.swift         |  5 +++
 .../EggDrop.playground/Sources/EggDrop.swift  | 41 +++++++++++++++++
 .../EggDrop.playground/contents.xcplayground  |  4 ++
 Egg Drop Problem/EggDrop.swift                | 36 +++++++++------
 Egg Drop Problem/README.markdown              | 44 +++++++++++++++++++
 .../contents.xcworkspacedata                  |  6 +++
 6 files changed, 123 insertions(+), 13 deletions(-)
 create mode 100644 Egg Drop Problem/EggDrop.playground/Contents.swift
 create mode 100644 Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift
 create mode 100644 Egg Drop Problem/EggDrop.playground/contents.xcplayground
 create mode 100644 Egg Drop Problem/README.markdown

diff --git a/Egg Drop Problem/EggDrop.playground/Contents.swift b/Egg Drop Problem/EggDrop.playground/Contents.swift
new file mode 100644
index 000000000..4ddb936b3
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/Contents.swift	
@@ -0,0 +1,5 @@
+ //: Playground - noun: a place where people can play
+
+import Cocoa
+
+eggDrop(numberOfEggs: 2, numberOfFloors: 4)
diff --git a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift
new file mode 100644
index 000000000..f69284491
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
@@ -0,0 +1,41 @@
+public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
+    if numberOfEggs == 0 || numberOfFloors == 0{
+        return 0
+    }
+    if numberOfEggs == 1 || numberOfFloors == 1{
+        return 1
+    }
+    
+    var eggFloor = [[Int]](repeating: [Int](repeating: 0, count: numberOfFloors+1), count: numberOfEggs+1) //egg(rows) floor(cols) array to store the solutions
+    var attempts: Int = 0
+    
+    for var floorNumber in (0..<(numberOfFloors+1)){
+        eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
+        for var eggNumber in (2..<(numberOfEggs+1)){
+            eggFloor[eggNumber][floorNumber] = 0
+        }
+    }
+    eggFloor[2][1] = 1 //base case: if there's are two eggs and one floor, it takes one attempt
+    
+    for var eggNumber in (2..<(numberOfEggs+1)){
+        for var floorNumber in (2..<(numberOfFloors+1)){
+            eggFloor[eggNumber][floorNumber] = 1000000
+            for var visitingFloor in (1..<(floorNumber+1)){
+                //there are two cases
+                //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> visitingFloor-1
+                //case 2: egg doesn't break. meaning we'll still have 'eggs' number of eggs, and we'll go upstairs -> floorNumber-visitingFloor
+                attempts = 1 + max(eggFloor[eggNumber-1][visitingFloor-1], eggFloor[eggNumber][floorNumber-visitingFloor])//we add one taking into account the attempt we're taking at the moment
+                
+                if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
+                    eggFloor[eggNumber][floorNumber] = attempts;
+                }
+            }
+        }
+    }
+    
+    return eggFloor[numberOfEggs][numberOfFloors]
+}
+
+public func max(_ x1: Int, _ x2: Int) -> Int{
+    return x1 > x2 ? x1 : x2
+}
diff --git a/Egg Drop Problem/EggDrop.playground/contents.xcplayground b/Egg Drop Problem/EggDrop.playground/contents.xcplayground
new file mode 100644
index 000000000..63b6dd8df
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Egg Drop Problem/EggDrop.swift b/Egg Drop Problem/EggDrop.swift
index 6d0aab2a1..a525793db 100644
--- a/Egg Drop Problem/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.swift	
@@ -1,23 +1,33 @@
-func eggDrop(_ numberOfEggs: Int, numberOfFloors: Int) -> Int {
-    var eggFloor: [[Int]] = [] //egg(rows) floor(cols) array to store the solutions
+public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
+    if numberOfEggs == 0 || numberOfFloors == 0{
+        return 0
+    }
+    if numberOfEggs == 1 || numberOfFloors == 1{
+        return 1
+    }
+    
+    var eggFloor = [[Int]](repeating: [Int](repeating: 0, count: numberOfFloors+1), count: numberOfEggs+1) //egg(rows) floor(cols) array to store the solutions
     var attempts: Int = 0
     
-    for var i in (0..<numberOfFloors){
-        eggFloor[1][i] = i
+    for var floorNumber in (0..<(numberOfFloors+1)){
+        eggFloor[1][floorNumber] = floorNumber
+        for var eggNumber in (2..<(numberOfEggs+1)){
+            eggFloor[eggNumber][floorNumber] = 0
+        }
     }
     eggFloor[2][1] = 1
     
-    for var i in (2..<=numberOfEggs){
-        for var j in (2..numberOfFloors){
-            eggFloor[i][j] = 1000000
-            for var k in (1..<=j){
+    for var eggNumber in (2..<(numberOfEggs+1)){
+        for var floorNumber in (2..<(numberOfFloors+1)){
+            eggFloor[eggNumber][floorNumber] = 1000000
+            for var floors in (1..<(floorNumber+1)){
                 //there are two cases
                 //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> k-1
-                //case 2: egg doesn't break. meaning we'll still have 'i' number of eggs, and we'll go upstairs -> j-k
-                attempts = 1 + max(eggFloor[i-1][k-1], eggFloor[i][j-k])//we add one taking into account the attempt we're taking at the moment
+                //case 2: egg doesn't break. meaning we'll still have 'eggs' number of eggs, and we'll go upstairs -> floors-k
+                attempts = 1 + max(eggFloor[eggNumber-1][floors-1], eggFloor[eggNumber][floorNumber-floors])//we add one taking into account the attempt we're taking at the moment
                 
-                if attempts < eggFloor[i][j]{ //finding the min
-                    eggFloor[i][j] = attempts;
+                if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
+                    eggFloor[eggNumber][floorNumber] = attempts;
                 }
             }
         }
@@ -26,6 +36,6 @@ func eggDrop(_ numberOfEggs: Int, numberOfFloors: Int) -> Int {
     return eggFloor[numberOfEggs][numberOfFloors]
 }
 
-func max(_ x1: Int, _ x2: Int){
+public func max(_ x1: Int, _ x2: Int) -> Int{
     return x1 > x2 ? x1 : x2
 }
diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
new file mode 100644
index 000000000..a58827ba3
--- /dev/null
+++ b/Egg Drop Problem/README.markdown	
@@ -0,0 +1,44 @@
+#Egg Drop Dynamic Problem
+
+#Problem Description 
+
+Given some number of floors and some number of eggs, what is the minimum number of attempts it will take to find out from which floor egg will break.
+
+Suppose that we wish to know which stories in a 36-story building are safe to drop eggs from, and which will cause the eggs to break on landing. We make a few assumptions:
+
+- An egg that survives a fall can be used again.
+- A broken egg must be discarded.
+- The effect of a fall is the same for all eggs.
+- If an egg breaks when dropped, then it would break if dropped from a higher floor.
+- If an egg survives a fall then it would survive a shorter fall.
+
+If only one egg is available and we wish to be sure of obtaining the right result, the experiment can be carried out in only one way. Drop the egg from the first-floor window; if it survives, drop it from the second floor window. Continue upward until it breaks. In the worst case, this method may require 36 droppings. Suppose 2 eggs are available. What is the least number of egg-droppings that is guaranteed to work in all cases?
+The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
+
+#Solution
+We store all the solutions in a 2D array. Where rows represents number of eggs and columns represent number of floors. 
+
+First, we set base cases:
+1) If there's only one egg, it takes as many attempts as number of floors
+2) If there's are two eggs and one floor, it takes one attempt
+
+eggNumber ==> Number of eggs at the moment
+floorNumber ==> Floor number at the moment
+visitingFloor ==> Floor being visited at the moment
+attempts ==> Minimum number of attempts it will take to find out from which floor egg will break
+
+When we drop an egg from a floor 'floorNumber', there can be two cases (1) The egg breaks (2) The egg doesn’t break.
+
+1) If the egg breaks after dropping from 'floorNumberth' floor, then we only need to check for floors lower than 'floorNumber' with remaining eggs; so the problem reduces to 'floorNumber'-1 floors and 'eggNumber'-1 eggs
+2) If the egg doesn’t break after dropping from the xth floor, then we only need to check for floors higher than 'floorNumber'; so the problem reduces to floors-'floorNumber' floors and 'eggNumber' eggs.
+
+Since we need to minimize the number of trials in worst case, we take the maximum of two cases. We consider the max of above two cases for every floor and choose the floor which yields minimum number of trials.
+
+```swift
+
+attempts = 1 + max(eggFloor[eggNumber-1][floors-1], eggFloor[eggNumber][floorNumber-floors])//we add one taking into account the attempt we're taking at the moment
+
+if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
+    eggFloor[eggNumber][floorNumber] = attempts;
+}
+```
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 5ac8577f5..1c6b407c3 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -7,6 +7,12 @@
       <FileRef
          location = "group:/Users/arkalyk/Desktop/SwiftAlgorithmClub/swift-algorithm-club/Egg Drop Problem/EggDrop.swift">
       </FileRef>
+      <FileRef
+         location = "group:EggDrop.playground">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
    </Group>
    <FileRef
       location = "group:README.markdown">

From 75d3b5b59977a1cc54bcac2ce42e2c884eab5e69 Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 02:12:30 +0600
Subject: [PATCH 019/643] Bugs fixed

---
 Egg Drop Problem/README.markdown | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index a58827ba3..44af8174a 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -23,19 +23,21 @@ First, we set base cases:
 2) If there's are two eggs and one floor, it takes one attempt
 
 eggNumber ==> Number of eggs at the moment
+
 floorNumber ==> Floor number at the moment
+
 visitingFloor ==> Floor being visited at the moment
+
 attempts ==> Minimum number of attempts it will take to find out from which floor egg will break
 
 When we drop an egg from a floor 'floorNumber', there can be two cases (1) The egg breaks (2) The egg doesn’t break.
 
-1) If the egg breaks after dropping from 'floorNumberth' floor, then we only need to check for floors lower than 'floorNumber' with remaining eggs; so the problem reduces to 'floorNumber'-1 floors and 'eggNumber'-1 eggs
-2) If the egg doesn’t break after dropping from the xth floor, then we only need to check for floors higher than 'floorNumber'; so the problem reduces to floors-'floorNumber' floors and 'eggNumber' eggs.
+1) If the egg breaks after dropping from 'visitingFloorth' floor, then we only need to check for floors lower than 'visitingFloor' with remaining eggs; so the problem reduces to 'visitingFloor'-1 floors and 'eggNumber'-1 eggs.
+2) If the egg doesn’t break after dropping from the 'visitingFloorth' floor, then we only need to check for floors higher than 'visitingFloor'; so the problem reduces to floors-'visitingFloor' floors and 'eggNumber' eggs.
 
 Since we need to minimize the number of trials in worst case, we take the maximum of two cases. We consider the max of above two cases for every floor and choose the floor which yields minimum number of trials.
 
 ```swift
-
 attempts = 1 + max(eggFloor[eggNumber-1][floors-1], eggFloor[eggNumber][floorNumber-floors])//we add one taking into account the attempt we're taking at the moment
 
 if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min

From 61949ab24314ee060f888642c59d6d20bcfa4841 Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:09:53 +0600
Subject: [PATCH 020/643] Minor changes in README

---
 .../EggDrop.playground/Sources/EggDrop.swift  |  9 +++------
 Egg Drop Problem/EggDrop.swift                | 16 ++++++++--------
 Egg Drop Problem/README.markdown              | 19 ++++++++++++-------
 3 files changed, 23 insertions(+), 21 deletions(-)

diff --git a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift
index f69284491..897ba2dee 100644
--- a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
@@ -1,5 +1,5 @@
 public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
-    if numberOfEggs == 0 || numberOfFloors == 0{
+    if numberOfEggs == 0 || numberOfFloors == 0{ //edge case: When either number of eggs or number of floors is 0, answer is 0
         return 0
     }
     if numberOfEggs == 1 || numberOfFloors == 1{
@@ -11,15 +11,12 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     
     for var floorNumber in (0..<(numberOfFloors+1)){
         eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
-        for var eggNumber in (2..<(numberOfEggs+1)){
-            eggFloor[eggNumber][floorNumber] = 0
-        }
     }
-    eggFloor[2][1] = 1 //base case: if there's are two eggs and one floor, it takes one attempt
+    eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
     
     for var eggNumber in (2..<(numberOfEggs+1)){
         for var floorNumber in (2..<(numberOfFloors+1)){
-            eggFloor[eggNumber][floorNumber] = 1000000
+            eggFloor[eggNumber][floorNumber] = Int.max   //setting the final result a high number to find out minimum
             for var visitingFloor in (1..<(floorNumber+1)){
                 //there are two cases
                 //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> visitingFloor-1
diff --git a/Egg Drop Problem/EggDrop.swift b/Egg Drop Problem/EggDrop.swift
index a525793db..7be691f57 100644
--- a/Egg Drop Problem/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.swift	
@@ -1,5 +1,5 @@
 public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
-    if numberOfEggs == 0 || numberOfFloors == 0{
+    if numberOfEggs == 0 || numberOfFloors == 0{ //edge case: When either number of eggs or number of floors is 0, answer is 0
         return 0
     }
     if numberOfEggs == 1 || numberOfFloors == 1{
@@ -10,21 +10,21 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     var attempts: Int = 0
     
     for var floorNumber in (0..<(numberOfFloors+1)){
-        eggFloor[1][floorNumber] = floorNumber
+        eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
         for var eggNumber in (2..<(numberOfEggs+1)){
             eggFloor[eggNumber][floorNumber] = 0
         }
     }
-    eggFloor[2][1] = 1
+    eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
     
     for var eggNumber in (2..<(numberOfEggs+1)){
         for var floorNumber in (2..<(numberOfFloors+1)){
-            eggFloor[eggNumber][floorNumber] = 1000000
-            for var floors in (1..<(floorNumber+1)){
+            eggFloor[eggNumber][floorNumber] = Int.max   //setting the final result a high number to find out minimum
+            for var visitingFloor in (1..<(floorNumber+1)){
                 //there are two cases
-                //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> k-1
-                //case 2: egg doesn't break. meaning we'll still have 'eggs' number of eggs, and we'll go upstairs -> floors-k
-                attempts = 1 + max(eggFloor[eggNumber-1][floors-1], eggFloor[eggNumber][floorNumber-floors])//we add one taking into account the attempt we're taking at the moment
+                //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> visitingFloor-1
+                //case 2: egg doesn't break. meaning we'll still have 'eggs' number of eggs, and we'll go upstairs -> floorNumber-visitingFloor
+                attempts = 1 + max(eggFloor[eggNumber-1][visitingFloor-1], eggFloor[eggNumber][floorNumber-visitingFloor])//we add one taking into account the attempt we're taking at the moment
                 
                 if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
                     eggFloor[eggNumber][floorNumber] = attempts;
diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 44af8174a..2df3088b5 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -22,19 +22,24 @@ First, we set base cases:
 1) If there's only one egg, it takes as many attempts as number of floors
 2) If there's are two eggs and one floor, it takes one attempt
 
-eggNumber ==> Number of eggs at the moment
-
-floorNumber ==> Floor number at the moment
-
-visitingFloor ==> Floor being visited at the moment
-
-attempts ==> Minimum number of attempts it will take to find out from which floor egg will break
+- eggNumber ==> Number of eggs at the moment
+- floorNumber ==> Floor number at the moment
+- visitingFloor ==> Floor being visited at the moment
+- attempts ==> Minimum number of attempts it will take to find out from which floor egg will break
 
 When we drop an egg from a floor 'floorNumber', there can be two cases (1) The egg breaks (2) The egg doesn’t break.
 
 1) If the egg breaks after dropping from 'visitingFloorth' floor, then we only need to check for floors lower than 'visitingFloor' with remaining eggs; so the problem reduces to 'visitingFloor'-1 floors and 'eggNumber'-1 eggs.
 2) If the egg doesn’t break after dropping from the 'visitingFloorth' floor, then we only need to check for floors higher than 'visitingFloor'; so the problem reduces to floors-'visitingFloor' floors and 'eggNumber' eggs.
 
+```swift
+for var floorNumber in (0..<(numberOfFloors+1)){
+    eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
+}
+
+eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
+```
+
 Since we need to minimize the number of trials in worst case, we take the maximum of two cases. We consider the max of above two cases for every floor and choose the floor which yields minimum number of trials.
 
 ```swift

From 4ab987c592763cd13719411b829d8d513a64707b Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:14:18 +0600
Subject: [PATCH 021/643] Minor changes in README

---
 Egg Drop Problem/README.markdown | 25 +++++++++++++------------
 1 file changed, 13 insertions(+), 12 deletions(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 2df3088b5..eda28fa6f 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -16,32 +16,33 @@ If only one egg is available and we wish to be sure of obtaining the right resul
 The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
 
 #Solution
+- eggNumber -> Number of eggs at the moment
+- floorNumber -> Floor number at the moment
+- visitingFloor -> Floor being visited at the moment
+- attempts -> Minimum number of attempts it will take to find out from which floor egg will break
+
 We store all the solutions in a 2D array. Where rows represents number of eggs and columns represent number of floors. 
 
 First, we set base cases:
 1) If there's only one egg, it takes as many attempts as number of floors
 2) If there's are two eggs and one floor, it takes one attempt
 
-- eggNumber ==> Number of eggs at the moment
-- floorNumber ==> Floor number at the moment
-- visitingFloor ==> Floor being visited at the moment
-- attempts ==> Minimum number of attempts it will take to find out from which floor egg will break
-
-When we drop an egg from a floor 'floorNumber', there can be two cases (1) The egg breaks (2) The egg doesn’t break.
-
-1) If the egg breaks after dropping from 'visitingFloorth' floor, then we only need to check for floors lower than 'visitingFloor' with remaining eggs; so the problem reduces to 'visitingFloor'-1 floors and 'eggNumber'-1 eggs.
-2) If the egg doesn’t break after dropping from the 'visitingFloorth' floor, then we only need to check for floors higher than 'visitingFloor'; so the problem reduces to floors-'visitingFloor' floors and 'eggNumber' eggs.
-
 ```swift
 for var floorNumber in (0..<(numberOfFloors+1)){
-    eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
+eggFloor[1][floorNumber] = floorNumber      //base case 1: if there's only one egg, it takes 'numberOfFloors' attempts
 }
 
-eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
+eggFloor[2][1] = 1 //base case 2: if there are two eggs and one floor, it takes one attempt
 ```
 
+When we drop an egg from a floor 'floorNumber', there can be two cases (1) The egg breaks (2) The egg doesn’t break.
+
+1) If the egg breaks after dropping from 'visitingFloorth' floor, then we only need to check for floors lower than 'visitingFloor' with remaining eggs; so the problem reduces to 'visitingFloor'-1 floors and 'eggNumber'-1 eggs.
+2) If the egg doesn’t break after dropping from the 'visitingFloorth' floor, then we only need to check for floors higher than 'visitingFloor'; so the problem reduces to floors-'visitingFloor' floors and 'eggNumber' eggs.
+
 Since we need to minimize the number of trials in worst case, we take the maximum of two cases. We consider the max of above two cases for every floor and choose the floor which yields minimum number of trials.
 
+We find the answer based on the base cases and previously found answers as follows. 
 ```swift
 attempts = 1 + max(eggFloor[eggNumber-1][floors-1], eggFloor[eggNumber][floorNumber-floors])//we add one taking into account the attempt we're taking at the moment
 

From 1fbb40efe14b80d6187a9ebd698960ba3520fe3b Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:35:40 +0600
Subject: [PATCH 022/643] Example added

---
 Egg Drop Problem/EggDrop.playground/Contents.swift |  6 +++++-
 Egg Drop Problem/EggDrop.swift                     |  3 ---
 Egg Drop Problem/README.markdown                   | 14 +++++++++++++-
 3 files changed, 18 insertions(+), 5 deletions(-)

diff --git a/Egg Drop Problem/EggDrop.playground/Contents.swift b/Egg Drop Problem/EggDrop.playground/Contents.swift
index 4ddb936b3..d452e7f9f 100644
--- a/Egg Drop Problem/EggDrop.playground/Contents.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Contents.swift	
@@ -2,4 +2,8 @@
 
 import Cocoa
 
-eggDrop(numberOfEggs: 2, numberOfFloors: 4)
+eggDrop(numberOfEggs: 2, numberOfFloors: 2) //expected answer: 2
+eggDrop(numberOfEggs: 2, numberOfFloors: 4) //expected answer: 3
+eggDrop(numberOfEggs: 2, numberOfFloors: 6) //expected answer: 3
+eggDrop(numberOfEggs: 5, numberOfFloors: 5) //expected answer: 2
+eggDrop(numberOfEggs: 5, numberOfFloors: 20) //expected answer: 4
\ No newline at end of file
diff --git a/Egg Drop Problem/EggDrop.swift b/Egg Drop Problem/EggDrop.swift
index 7be691f57..897ba2dee 100644
--- a/Egg Drop Problem/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.swift	
@@ -11,9 +11,6 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     
     for var floorNumber in (0..<(numberOfFloors+1)){
         eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
-        for var eggNumber in (2..<(numberOfEggs+1)){
-            eggFloor[eggNumber][floorNumber] = 0
-        }
     }
     eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
     
diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index eda28fa6f..1a436c374 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -25,7 +25,7 @@ We store all the solutions in a 2D array. Where rows represents number of eggs a
 
 First, we set base cases:
 1) If there's only one egg, it takes as many attempts as number of floors
-2) If there's are two eggs and one floor, it takes one attempt
+2) If there are two eggs and one floor, it takes one attempt
 
 ```swift
 for var floorNumber in (0..<(numberOfFloors+1)){
@@ -50,3 +50,15 @@ if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
     eggFloor[eggNumber][floorNumber] = attempts;
 }
 ```
+Example:
+Let's assume we have 2 eggs and 2 floors.
+1) We drop one egg from the first floor. If it breaks, then we get the answer. If it doesn't we'll have 2 eggs and 1 floors to work with.
+    attempts = 1 + maximum of 0(got the answer) and eggFloor[2][1] (base case 2 which gives us 1)
+    attempts = 1 + 1 = 2
+2) We drop one egg from the second floor. If it breaks, we'll have 1 egg and 1 floors to work with. If it doesn't, we'll get the answer.
+    attempts = 1 + maximum of eggFloor[1][1](base case 1 which gives us 1) and 0(got the answer)
+    attempts = 1 + 1 = 2
+3) Finding the minimum of 2 and 2 gives us 2, so the answer is 2. 
+   2 is the minimum number of attempts it will take to find out from which floor egg will break.
+
+

From 082385a5ac58967b8eaf565654f1620444383ebf Mon Sep 17 00:00:00 2001
From: Arkalyk Akash <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:37:09 +0600
Subject: [PATCH 023/643] Update README.markdown

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

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 1a436c374..5ff6ebb1d 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -1,6 +1,6 @@
-#Egg Drop Dynamic Problem
+# Egg Drop Dynamic Problem
 
-#Problem Description 
+# Problem Description 
 
 Given some number of floors and some number of eggs, what is the minimum number of attempts it will take to find out from which floor egg will break.
 
@@ -15,7 +15,7 @@ Suppose that we wish to know which stories in a 36-story building are safe to dr
 If only one egg is available and we wish to be sure of obtaining the right result, the experiment can be carried out in only one way. Drop the egg from the first-floor window; if it survives, drop it from the second floor window. Continue upward until it breaks. In the worst case, this method may require 36 droppings. Suppose 2 eggs are available. What is the least number of egg-droppings that is guaranteed to work in all cases?
 The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
 
-#Solution
+# Solution
 - eggNumber -> Number of eggs at the moment
 - floorNumber -> Floor number at the moment
 - visitingFloor -> Floor being visited at the moment

From ffea424eec7b80d010d731f6f1b44c442c26cab8 Mon Sep 17 00:00:00 2001
From: Arkalyk Akash <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:37:55 +0600
Subject: [PATCH 024/643] Update README.markdown

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

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 5ff6ebb1d..82543502d 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -1,6 +1,6 @@
 # Egg Drop Dynamic Problem
 
-# Problem Description 
+## Problem Description 
 
 Given some number of floors and some number of eggs, what is the minimum number of attempts it will take to find out from which floor egg will break.
 
@@ -15,7 +15,7 @@ Suppose that we wish to know which stories in a 36-story building are safe to dr
 If only one egg is available and we wish to be sure of obtaining the right result, the experiment can be carried out in only one way. Drop the egg from the first-floor window; if it survives, drop it from the second floor window. Continue upward until it breaks. In the worst case, this method may require 36 droppings. Suppose 2 eggs are available. What is the least number of egg-droppings that is guaranteed to work in all cases?
 The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
 
-# Solution
+## Solution
 - eggNumber -> Number of eggs at the moment
 - floorNumber -> Floor number at the moment
 - visitingFloor -> Floor being visited at the moment
@@ -50,7 +50,7 @@ if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
     eggFloor[eggNumber][floorNumber] = attempts;
 }
 ```
-Example:
+## Example
 Let's assume we have 2 eggs and 2 floors.
 1) We drop one egg from the first floor. If it breaks, then we get the answer. If it doesn't we'll have 2 eggs and 1 floors to work with.
     attempts = 1 + maximum of 0(got the answer) and eggFloor[2][1] (base case 2 which gives us 1)

From 260948a2b7af625ea0fe6590e3cf966975c420dd Mon Sep 17 00:00:00 2001
From: ARKALYK AKASH <arkalyk.akash@nu.edu.kz>
Date: Sat, 15 Apr 2017 11:41:32 +0600
Subject: [PATCH 025/643] Comments added

---
 Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift | 3 ++-
 Egg Drop Problem/EggDrop.swift                            | 3 ++-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift
index 897ba2dee..db1e48b95 100644
--- a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
@@ -2,7 +2,7 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     if numberOfEggs == 0 || numberOfFloors == 0{ //edge case: When either number of eggs or number of floors is 0, answer is 0
         return 0
     }
-    if numberOfEggs == 1 || numberOfFloors == 1{
+    if numberOfEggs == 1 || numberOfFloors == 1{ //edge case: When either number of eggs or number of floors is 1, answer is 1
         return 1
     }
     
@@ -33,6 +33,7 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     return eggFloor[numberOfEggs][numberOfFloors]
 }
 
+//Helper function to find max of two integers
 public func max(_ x1: Int, _ x2: Int) -> Int{
     return x1 > x2 ? x1 : x2
 }
diff --git a/Egg Drop Problem/EggDrop.swift b/Egg Drop Problem/EggDrop.swift
index 897ba2dee..db1e48b95 100644
--- a/Egg Drop Problem/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.swift	
@@ -2,7 +2,7 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     if numberOfEggs == 0 || numberOfFloors == 0{ //edge case: When either number of eggs or number of floors is 0, answer is 0
         return 0
     }
-    if numberOfEggs == 1 || numberOfFloors == 1{
+    if numberOfEggs == 1 || numberOfFloors == 1{ //edge case: When either number of eggs or number of floors is 1, answer is 1
         return 1
     }
     
@@ -33,6 +33,7 @@ public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
     return eggFloor[numberOfEggs][numberOfFloors]
 }
 
+//Helper function to find max of two integers
 public func max(_ x1: Int, _ x2: Int) -> Int{
     return x1 > x2 ? x1 : x2
 }

From 903ce26995d275e858dc535726df8a649260a4cd Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Sun, 16 Apr 2017 14:37:34 +0200
Subject: [PATCH 026/643] Add fully functional gaussian NB & examples

---
 Naive Bayes Classifier/NaiveBayes.swift | 122 ++++++++++++++----------
 1 file changed, 74 insertions(+), 48 deletions(-)

diff --git a/Naive Bayes Classifier/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.swift
index c988cacbe..63edd9981 100644
--- a/Naive Bayes Classifier/NaiveBayes.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.swift	
@@ -1,16 +1,15 @@
 //
-//  main.swift
+//  NaiveBayes.swift
 //  NaiveBayes
 //
 //  Created by Philipp Gabriel on 14.04.17.
 //  Copyright © 2017 ph1ps. All rights reserved.
 //
 
-//TODO naming
 import Foundation
 
 extension Array where Element == Double {
-
+    
     func mean() -> Double {
         return self.reduce(0, +) / Double(count)
     }
@@ -28,18 +27,17 @@ extension Array where Element == Double {
 
 extension Array where Element == Int {
     
-    //Is this the best way?!
-    func uniques() -> [Int] {
-        return Array(Set(self))
+    func uniques() -> Set<Element> {
+        return Set(self)
     }
     
 }
 
 class NaiveBayes {
-
-    var data: [[Double]]
-    var classes: [Int]
-    var variables: [Int: [(feature: Int, mean: Double, stDev: Double)]]
+    
+    private var data: [[Double]]
+    private var classes: [Int]
+    private var variables: [Int: [(feature: Int, mean: Double, stDev: Double)]]
     
     init(data: [[Double]], classes: [Int]) {
         self.data = data
@@ -47,30 +45,37 @@ class NaiveBayes {
         self.variables = [Int: [(feature: Int, mean: Double, stDev: Double)]]()
     }
     
-    //TODO
-    //init(dataAndClasses: [[Double]], index ofClassRow: Int) {}
-
-    //TODO: Does it really need to be n^2 runtime?
+    convenience init(dataAndClasses: [[Double]], rowOfClass: Int) {
+        let classes = dataAndClasses.map { Int($0[rowOfClass]) }
+        let data = dataAndClasses.map { row in
+            return row.enumerated().filter { $0.offset != rowOfClass }.map { $0.element }
+        }
+        
+        self.init(data: data, classes: classes)
+    }
+    
     func train() {
-
-        for `class` in 0..<classes.uniques().count {
+        
+        for `class` in classes.uniques() {
+            
             variables[`class`] = [(feature: Int, mean: Double, stDev: Double)]()
             
             for feature in 0..<data[0].count {
                 
-                let values = data.map{ $0[feature] }.enumerated().filter { (offset, _) in
+                let values = data.map { $0[feature] }.enumerated().filter { (offset, _) in
                     return classes[offset] == `class`
-                }.map { $0.element }
-
+                    }.map { $0.element }
+                
                 variables[`class`]?.append((feature, values.mean(), values.standardDeviation()))
             }
         }
-
+        
+        //This is just for the sake of clearing RAM
         data.removeAll(keepingCapacity: false)
     }
     
-    func predictClass(input: [Double]) -> Int {
-        let likelihoods = predictLikelihood(input: input).max { (first, second) -> Bool in
+    func classify(with input: [Double]) -> Int {
+        let likelihoods = calcLikelihoods(with: input).max { (first, second) -> Bool in
             return first.1 < second.1
         }
         
@@ -81,30 +86,30 @@ class NaiveBayes {
         return `class`
     }
     
-    func predictLikelihood(input: [Double]) -> [(Int, Double)] {
-    
-        var probabilityOfClasses = [Int: Double]()
-        let amount = classes.uniques().count
+    func calcLikelihoods(with input: [Double]) -> [(Int, Double)] {
+        
+        var probaClass = [Int: Double]()
+        let amount = classes.count
         
         classes.forEach { `class` in
             let individual = classes.filter { $0 == `class` }.count
-            probabilityOfClasses[`class`] = Double(amount) / Double(individual)
+            probaClass[`class`] = Double(individual) / Double(amount)
         }
         
-        let probaClass = variables.map { (key, value) -> (Int, [Double]) in
-            let probaFeature = value.map { (feature, mean, stDev) -> Double in
+        let classesAndFeatures = variables.map { (key, value) -> (Int, [Double]) in
+            let distributions = value.map { (feature, mean, stDev) -> Double in
                 let featureValue = input[feature]
                 let eulerPart = pow(M_E, -1 * pow(featureValue - mean, 2) / (2 * pow(stDev, 2)))
                 let distribution = eulerPart / sqrt(2 * .pi) / stDev
                 return distribution
             }
-            return (key, probaFeature)
+            return (key, distributions)
         }
         
-        let likelihoods = probaClass.map { (key, probaFeature) in
-            return (key, probaFeature.reduce(1, *) * (probabilityOfClasses[key] ?? 1.0))
+        let likelihoods = classesAndFeatures.map { (key, probaFeature) in
+            return (key, probaFeature.reduce(1, *) * (probaClass[key] ?? 1.0))
         }
-
+        
         let sum = likelihoods.map { $0.1 }.reduce(0, +)
         let normalized = likelihoods.map { (`class`, likelihood) in
             return (`class`, likelihood / sum)
@@ -115,27 +120,48 @@ class NaiveBayes {
 }
 
 let data: [[Double]] = [
-    [6,180,12],
-    [5.92,190,11],
-    [5.58,170,12],
-    [5.92,165,10],
-    [5,100,6],
-    [5.5,150,8],
-    [5.42,130,7],
-    [5.75,150,9]
+    [6, 180, 12],
+    [5.92, 190, 11],
+    [5.58, 170, 12],
+    [5.92, 165, 10],
+    [5, 100, 6],
+    [5.5, 150, 8],
+    [5.42, 130, 7],
+    [5.75, 150, 9]
 ]
 
-let classes = [0,0,0,0,1,1,1,1]
+let classes = [0, 0, 0, 0, 1, 1, 1, 1]
 
 let naive = NaiveBayes(data: data, classes: classes)
 naive.train()
-let result = naive.predictLikelihood(input: [6,130,8])
-print(result)
-
-
-
-
+print(naive.classify(with: [6, 130, 8]))
+
+let otherData: [[Double]] = [
+    [6, 180, 12, 0],
+    [5.92, 190, 11, 0],
+    [5.58, 170, 12, 0],
+    [5.92, 165, 10, 0],
+    [5, 100, 6, 1],
+    [5.5, 150, 8, 1],
+    [5.42, 130, 7, 1],
+    [5.75, 150, 9, 1]
+]
 
+let otherNaive = NaiveBayes(dataAndClasses: otherData, rowOfClass: 3)
+otherNaive.train()
+print(otherNaive.calcLikelihoods(with: [6, 130, 8]))
 
+guard let csv = try? String(contentsOfFile: "/Users/ph1ps/Desktop/wine.csv") else {
+    print("file not found")
+    exit(0)
+}
 
+let rows = csv.characters.split(separator: "\r\n").map { String($0) }
+let wineData = rows.map { row -> [Double] in
+    let split = row.characters.split(separator: ";")
+    return split.map { Double(String($0))! }
+}
 
+let wineNaive = NaiveBayes(dataAndClasses: wineData, rowOfClass: 0)
+wineNaive.train()
+print(wineNaive.calcLikelihoods(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015]))

From b6d40144c5ac91bd3155036fbcefca231a6dba0d Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Sun, 16 Apr 2017 23:52:57 +0200
Subject: [PATCH 027/643] Split into seperate types of NB classifier, implement
 strategy pattern

---
 Naive Bayes Classifier/NaiveBayes.swift | 209 +++++++++++++++++-------
 1 file changed, 146 insertions(+), 63 deletions(-)

diff --git a/Naive Bayes Classifier/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.swift
index 63edd9981..dbbf3cd9f 100644
--- a/Naive Bayes Classifier/NaiveBayes.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.swift	
@@ -33,49 +33,143 @@ extension Array where Element == Int {
     
 }
 
+enum NBType {
+    
+    case gaussian(data: [[Double]], classes: [Int])
+    case multinomial(data: [[Int]], classes: [Int])
+    //case bernoulli(data: [[Bool]], classes: [Int]) --> TODO
+    
+    var classes: [Int] {
+        if case .gaussian(_, let classes) = self {
+            return classes
+        } else if case .multinomial(_, let classes) = self {
+            return classes
+        }
+        
+        return []
+    }
+    
+    var data: [[Any]] {
+        if case .gaussian(let data, _) = self {
+            return data
+        } else if case .multinomial(let data, _) = self {
+            return data
+        }
+        
+        return []
+    }
+    
+    func calcLikelihood(variables: [Any], input: Any) -> Double? {
+        
+        if case .gaussian = self {
+            
+            guard let input = input as? Double else {
+                return nil
+            }
+            
+            guard let mean = variables[0] as? Double else {
+                return nil
+            }
+            
+            guard let stDev = variables[1] as? Double else {
+                return nil
+            }
+            
+            let eulerPart = pow(M_E, -1 * pow(input - mean, 2) / (2 * pow(stDev, 2)))
+            let distribution = eulerPart / sqrt(2 * .pi) / stDev
+            
+            return distribution
+            
+        } else if case .multinomial = self {
+            
+            guard let variables = variables as? [(category: Int, probability: Double)] else {
+                return nil
+            }
+            
+            guard let input = input as? Double else {
+                return nil
+            }
+            
+            return variables.first { variable in
+                return variable.category == Int(input)
+                }?.probability
+            
+        }
+        
+        return nil
+    }
+    
+    func train(values: [Any]) -> [Any]? {
+        
+        if case .gaussian = self {
+            
+            guard let values = values as? [Double] else {
+                return nil
+            }
+            
+            return [values.mean(), values.standardDeviation()]
+            
+        } else if case .multinomial = self {
+            
+            guard let values = values as? [Int] else {
+                return nil
+            }
+            
+            let count = values.count
+            let categoryProba = values.uniques().map { value -> (Int, Double) in
+                return (value, Double(values.filter { $0 == value }.count) / Double(count))
+            }
+            return categoryProba
+        }
+        
+        return nil
+    }
+}
+
 class NaiveBayes {
     
-    private var data: [[Double]]
-    private var classes: [Int]
-    private var variables: [Int: [(feature: Int, mean: Double, stDev: Double)]]
+    private var variables: [Int: [(feature: Int, variables: [Any])]]
+    private var type: NBType
     
-    init(data: [[Double]], classes: [Int]) {
-        self.data = data
-        self.classes = classes
-        self.variables = [Int: [(feature: Int, mean: Double, stDev: Double)]]()
+    init(type: NBType) {
+        self.type = type
+        self.variables = [Int: [(Int, [Any])]]()
     }
     
-    convenience init(dataAndClasses: [[Double]], rowOfClass: Int) {
-        let classes = dataAndClasses.map { Int($0[rowOfClass]) }
+    static func convert<T: Any>(dataAndClasses: [[T]], rowOfClasses: Int) -> (data: [[T]], classes: [Int]) {
+        let classes = dataAndClasses.map { Int($0[rowOfClasses] as! Double) } //TODO
+        
         let data = dataAndClasses.map { row in
-            return row.enumerated().filter { $0.offset != rowOfClass }.map { $0.element }
+            return row.enumerated().filter { $0.offset != rowOfClasses }.map { $0.element }
         }
         
-        self.init(data: data, classes: classes)
+        return (data, classes)
     }
     
+    //TODO remake pliss, i dont like this at all
     func train() {
         
+        var classes = type.classes
+        
         for `class` in classes.uniques() {
             
-            variables[`class`] = [(feature: Int, mean: Double, stDev: Double)]()
+            variables[`class`] = [(Int, [Any])]()
             
-            for feature in 0..<data[0].count {
+            for feature in 0..<type.data[0].count {
                 
-                let values = data.map { $0[feature] }.enumerated().filter { (offset, _) in
+                let values = type.data.map { $0[feature] }.enumerated().filter { (offset, _) in
                     return classes[offset] == `class`
                     }.map { $0.element }
                 
-                variables[`class`]?.append((feature, values.mean(), values.standardDeviation()))
+                let trained = type.train(values: values) ?? [Any]()
+                
+                variables[`class`]?.append((feature, trained))
             }
         }
-        
-        //This is just for the sake of clearing RAM
-        data.removeAll(keepingCapacity: false)
     }
     
     func classify(with input: [Double]) -> Int {
-        let likelihoods = calcLikelihoods(with: input).max { (first, second) -> Bool in
+        let likelihoods = classifyProba(with: input).max { (first, second) -> Bool in
             return first.1 < second.1
         }
         
@@ -86,8 +180,10 @@ class NaiveBayes {
         return `class`
     }
     
-    func calcLikelihoods(with input: [Double]) -> [(Int, Double)] {
+    //TODO fix this doesnt have to be a double
+    func classifyProba(with input: [Double]) -> [(Int, Double)] {
         
+        let classes = type.classes
         var probaClass = [Int: Double]()
         let amount = classes.count
         
@@ -96,18 +192,15 @@ class NaiveBayes {
             probaClass[`class`] = Double(individual) / Double(amount)
         }
         
-        let classesAndFeatures = variables.map { (key, value) -> (Int, [Double]) in
-            let distributions = value.map { (feature, mean, stDev) -> Double in
-                let featureValue = input[feature]
-                let eulerPart = pow(M_E, -1 * pow(featureValue - mean, 2) / (2 * pow(stDev, 2)))
-                let distribution = eulerPart / sqrt(2 * .pi) / stDev
-                return distribution
+        let classesAndFeatures = variables.map { (`class`, value) -> (Int, [Double]) in
+            let distribution = value.map { (feature, variables) -> Double in
+                return type.calcLikelihood(variables: variables, input: input[feature]) ?? 0.0
             }
-            return (key, distributions)
+            return (`class`, distribution)
         }
         
-        let likelihoods = classesAndFeatures.map { (key, probaFeature) in
-            return (key, probaFeature.reduce(1, *) * (probaClass[key] ?? 1.0))
+        let likelihoods = classesAndFeatures.map { (`class`, distribution) in
+            return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 1.0))
         }
         
         let sum = likelihoods.map { $0.1 }.reduce(0, +)
@@ -119,38 +212,6 @@ class NaiveBayes {
     }
 }
 
-let data: [[Double]] = [
-    [6, 180, 12],
-    [5.92, 190, 11],
-    [5.58, 170, 12],
-    [5.92, 165, 10],
-    [5, 100, 6],
-    [5.5, 150, 8],
-    [5.42, 130, 7],
-    [5.75, 150, 9]
-]
-
-let classes = [0, 0, 0, 0, 1, 1, 1, 1]
-
-let naive = NaiveBayes(data: data, classes: classes)
-naive.train()
-print(naive.classify(with: [6, 130, 8]))
-
-let otherData: [[Double]] = [
-    [6, 180, 12, 0],
-    [5.92, 190, 11, 0],
-    [5.58, 170, 12, 0],
-    [5.92, 165, 10, 0],
-    [5, 100, 6, 1],
-    [5.5, 150, 8, 1],
-    [5.42, 130, 7, 1],
-    [5.75, 150, 9, 1]
-]
-
-let otherNaive = NaiveBayes(dataAndClasses: otherData, rowOfClass: 3)
-otherNaive.train()
-print(otherNaive.calcLikelihoods(with: [6, 130, 8]))
-
 guard let csv = try? String(contentsOfFile: "/Users/ph1ps/Desktop/wine.csv") else {
     print("file not found")
     exit(0)
@@ -162,6 +223,28 @@ let wineData = rows.map { row -> [Double] in
     return split.map { Double(String($0))! }
 }
 
-let wineNaive = NaiveBayes(dataAndClasses: wineData, rowOfClass: 0)
+let convertedWine = NaiveBayes.convert(dataAndClasses: wineData, rowOfClasses: 0)
+let wineNaive = NaiveBayes(type: .gaussian(data: convertedWine.data, classes: convertedWine.classes))
 wineNaive.train()
-print(wineNaive.calcLikelihoods(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015]))
+print(wineNaive.classifyProba(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015]))
+
+let golfData = [
+    [0, 0, 0, 0],
+    [0, 0, 0, 1],
+    [1, 0, 0, 0],
+    [2, 1, 0, 0],
+    [2, 2, 1, 0],
+    [2, 2, 1, 1],
+    [1, 2, 1, 1],
+    [0, 1, 0, 0],
+    [0, 2, 1, 0],
+    [2, 1, 1, 0],
+    [0, 1, 1, 1],
+    [1, 1, 0, 1],
+    [1, 0, 1, 0],
+    [2, 1, 0, 1]
+]
+let golfClasses =  [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]
+let golfNaive = NaiveBayes(type: .multinomial(data: golfData, classes: golfClasses))
+golfNaive.train()
+print(golfNaive.classifyProba(with: [0, 2, 0, 1]))

From edafd431fab46087ff805f6ad419b076a076bf82 Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Mon, 17 Apr 2017 21:15:01 +0200
Subject: [PATCH 028/643] Add playground

---
 .../NaiveBayes.playground/Contents.swift      |  60 ++++++
 .../NaiveBayes.playground/Resources/wine.csv  | 177 ++++++++++++++++
 .../Sources/NaiveBayes.swift                  | 196 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Naive Bayes Classifier/NaiveBayes.swift       | 124 ++++-------
 6 files changed, 479 insertions(+), 89 deletions(-)
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/Contents.swift
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/Resources/wine.csv
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift
new file mode 100644
index 000000000..cb820272e
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
@@ -0,0 +1,60 @@
+import Foundation
+
+/*:
+ ## Naive Bayes Classifier
+ 
+ This playground uses the given algorithm and utilizes its features with some example datasets
+ 
+ ### Gaussian Naive Bayes
+ - Note:
+ When using Gaussian NB you have to have continuous features (Double). 
+ 
+ For this example we are going to use a famous dataset with different types of wine. The labels of the features can be viewed [here](https://gist.github.com/tijptjik/9408623)
+ */
+guard let wineCSV = Bundle.main.path(forResource: "wine", ofType: "csv") else {
+    print("Resource could not be found!")
+    exit(0)
+}
+
+guard let csv = try? String(contentsOfFile: wineCSV) else {
+    print("File could not be read!")
+    exit(0)
+}
+
+/*:
+ Reading the .csv file line per line
+ */
+let rows = csv.characters.split(separator: "\r\n").map { String($0) }
+/*:
+ Splitting on the ; sign and converting the value to a Double
+ 
+ - Important:
+ Do not force unwrap the mapped values in your real application. Carefully convert them! This is just for the sake of showing how the algorithm works.
+ */
+let wineData = rows.map { row -> [Double] in
+    let split = row.characters.split(separator: ";")
+    return split.map { Double(String($0))! }
+}
+
+/*:
+ The algorithm wants the classes and the data seperated since this gives a huge performance boost. Also I haven't implemented this in the NB class itself since it is not in the scope of it.
+ */
+let rowOfClasses = 0
+let classes = wineData.map { Int($0[rowOfClasses]) }
+let data = wineData.map { row in
+    return row.enumerated().filter { $0.offset != rowOfClasses }.map { $0.element }
+}
+
+/*:
+ Again use `guard` on the result of a `try?` or simply `do-try-catch` because this would crash your application if an error occured.
+ 
+ The array in the `classifyProba` method I passed is a former entry in the .csv file which I removed in order to classify it.
+ */
+let wineBayes = try! NaiveBayes(type: .gaussian, data: data, classes: classes).train()
+let result = wineBayes.classifyProba(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015])
+print(result)
+/*:
+ I can assure you that this is the correct result and as you can see the classifier thinks that its ***99.99%*** correct too.
+ 
+ ### Multinomial Naive Bayes
+ */
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Resources/wine.csv b/Naive Bayes Classifier/NaiveBayes.playground/Resources/wine.csv
new file mode 100644
index 000000000..89e14fd02
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Resources/wine.csv	
@@ -0,0 +1,177 @@
+1;14.23;1.71;2.43;15.6;127;2.8;3.06;.28;2.29;5.64;1.04;3.92;1065
+1;13.2;1.78;2.14;11.2;100;2.65;2.76;.26;1.28;4.38;1.05;3.4;1050
+1;13.16;2.36;2.67;18.6;101;2.8;3.24;.3;2.81;5.68;1.03;3.17;1185
+1;14.37;1.95;2.5;16.8;113;3.85;3.49;.24;2.18;7.8;.86;3.45;1480
+1;13.24;2.59;2.87;21;118;2.8;2.69;.39;1.82;4.32;1.04;2.93;735
+1;14.2;1.76;2.45;15.2;112;3.27;3.39;.34;1.97;6.75;1.05;2.85;1450
+1;14.39;1.87;2.45;14.6;96;2.5;2.52;.3;1.98;5.25;1.02;3.58;1290
+1;14.06;2.15;2.61;17.6;121;2.6;2.51;.31;1.25;5.05;1.06;3.58;1295
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+3;13.4;3.91;2.48;23;102;1.8;.75;.43;1.41;7.3;.7;1.56;750
+3;13.27;4.28;2.26;20;120;1.59;.69;.43;1.35;10.2;.59;1.56;835
+3;13.17;2.59;2.37;20;120;1.65;.68;.53;1.46;9.3;.6;1.62;840
+3;14.13;4.1;2.74;24.5;96;2.05;.76;.56;1.35;9.2;.61;1.6;560
\ No newline at end of file
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift
new file mode 100644
index 000000000..3af8102c7
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift	
@@ -0,0 +1,196 @@
+//
+//  NaiveBayes.swift
+//  NaiveBayes
+//
+//  Created by Philipp Gabriel on 14.04.17.
+//  Copyright © 2017 ph1ps. All rights reserved.
+//
+
+import Foundation
+
+extension String: Error {}
+
+extension Array where Element == Double {
+    
+    func mean() -> Double {
+        return self.reduce(0, +) / Double(count)
+    }
+    
+    func standardDeviation() -> Double {
+        let calculatedMean = mean()
+        
+        let sum = self.reduce(0.0) { (previous, next) in
+            return previous + pow(next - calculatedMean, 2)
+        }
+        
+        return sqrt(sum / Double(count - 1))
+    }
+}
+
+extension Array where Element == Int {
+    
+    func uniques() -> Set<Element> {
+        return Set(self)
+    }
+    
+}
+
+public enum NBType {
+    
+    case gaussian
+    case multinomial
+    //case bernoulli --> TODO
+    
+    func calcLikelihood(variables: [Any], input: Any) -> Double? {
+        
+        if case .gaussian = self {
+            
+            guard let input = input as? Double else {
+                return nil
+            }
+            
+            guard let mean = variables[0] as? Double else {
+                return nil
+            }
+            
+            guard let stDev = variables[1] as? Double else {
+                return nil
+            }
+            
+            let eulerPart = pow(M_E, -1 * pow(input - mean, 2) / (2 * pow(stDev, 2)))
+            let distribution = eulerPart / sqrt(2 * .pi) / stDev
+            
+            return distribution
+            
+        } else if case .multinomial = self {
+            
+            guard let variables = variables as? [(category: Int, probability: Double)] else {
+                return nil
+            }
+            
+            guard let input = input as? Int else {
+                return nil
+            }
+            
+            return variables.first { variable in
+                return variable.category == input
+                }?.probability
+            
+        }
+        
+        return nil
+    }
+    
+    func train(values: [Any]) -> [Any]? {
+        
+        if case .gaussian = self {
+            
+            guard let values = values as? [Double] else {
+                return nil
+            }
+            
+            return [values.mean(), values.standardDeviation()]
+            
+        } else if case .multinomial = self {
+            
+            guard let values = values as? [Int] else {
+                return nil
+            }
+            
+            let count = values.count
+            let categoryProba = values.uniques().map { value -> (Int, Double) in
+                return (value, Double(values.filter { $0 == value }.count) / Double(count))
+            }
+            return categoryProba
+        }
+        
+        return nil
+    }
+}
+
+public class NaiveBayes<T> {
+    
+    var variables: [Int: [(feature: Int, variables: [Any])]]
+    var type: NBType
+    
+    var data: [[T]]
+    var classes: [Int]
+    
+    public init(type: NBType, data: [[T]], classes: [Int]) throws {
+        self.type = type
+        self.data = data
+        self.classes = classes
+        self.variables = [Int: [(Int, [Any])]]()
+        
+        if case .gaussian = type, T.self != Double.self {
+            throw "When using Gaussian NB you have to have continuous features (Double)"
+        } else if case .multinomial = type, T.self != Int.self {
+            throw "When using Multinomial NB you have to have categorical features (Int)"
+        }
+    }
+    
+    public func train() throws -> Self {
+        
+        for `class` in classes.uniques() {
+            variables[`class`] = [(Int, [Any])]()
+            
+            let classDependent = data.enumerated().filter { (offset, _) in
+                return classes[offset] == `class`
+            }
+            
+            for feature in 0..<data[0].count {
+                
+                let featureDependent = classDependent.map { $0.element[feature] }
+                
+                guard let trained = type.train(values: featureDependent) else {
+                    throw "Critical! Data could not be casted even though it was checked at init"
+                }
+                
+                variables[`class`]?.append((feature, trained))
+            }
+        }
+        
+        return self
+    }
+    
+    public func classify(with input: [T]) -> Int {
+        let likelihoods = classifyProba(with: input).max { (first, second) -> Bool in
+            return first.1 < second.1
+        }
+        
+        guard let `class` = likelihoods?.0 else {
+            return -1
+        }
+        
+        return `class`
+    }
+    
+    public func classifyProba(with input: [T]) -> [(Int, Double)] {
+        
+        var probaClass = [Int: Double]()
+        let amount = classes.count
+        
+        classes.forEach { `class` in
+            let individual = classes.filter { $0 == `class` }.count
+            probaClass[`class`] = Double(individual) / Double(amount)
+        }
+        
+        let classesAndFeatures = variables.map { (`class`, value) -> (Int, [Double]) in
+            let distribution = value.map { (feature, variables) -> Double in
+                return type.calcLikelihood(variables: variables, input: input[feature]) ?? 0.0
+            }
+            return (`class`, distribution)
+        }
+        
+        let likelihoods = classesAndFeatures.map { (`class`, distribution) in
+            return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 0.0))
+        }
+        
+        let sum = likelihoods.map { $0.1 }.reduce(0, +)
+        let normalized = likelihoods.map { (`class`, likelihood) in
+            return (`class`, likelihood / sum)
+        }
+        
+        return normalized
+    }
+}
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground
new file mode 100644
index 000000000..b1148fc50
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos' display-mode='raw'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/playground.xcworkspace/contents.xcworkspacedata b/Naive Bayes Classifier/NaiveBayes.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Naive Bayes Classifier/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.swift
index dbbf3cd9f..9b9ace86d 100644
--- a/Naive Bayes Classifier/NaiveBayes.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.swift	
@@ -8,6 +8,8 @@
 
 import Foundation
 
+extension String: Error {}
+
 extension Array where Element == Double {
     
     func mean() -> Double {
@@ -35,29 +37,9 @@ extension Array where Element == Int {
 
 enum NBType {
     
-    case gaussian(data: [[Double]], classes: [Int])
-    case multinomial(data: [[Int]], classes: [Int])
-    //case bernoulli(data: [[Bool]], classes: [Int]) --> TODO
-    
-    var classes: [Int] {
-        if case .gaussian(_, let classes) = self {
-            return classes
-        } else if case .multinomial(_, let classes) = self {
-            return classes
-        }
-        
-        return []
-    }
-    
-    var data: [[Any]] {
-        if case .gaussian(let data, _) = self {
-            return data
-        } else if case .multinomial(let data, _) = self {
-            return data
-        }
-        
-        return []
-    }
+    case gaussian
+    case multinomial
+    //case bernoulli --> TODO
     
     func calcLikelihood(variables: [Any], input: Any) -> Double? {
         
@@ -86,12 +68,12 @@ enum NBType {
                 return nil
             }
             
-            guard let input = input as? Double else {
+            guard let input = input as? Int else {
                 return nil
             }
             
             return variables.first { variable in
-                return variable.category == Int(input)
+                return variable.category == input
                 }?.probability
             
         }
@@ -126,49 +108,52 @@ enum NBType {
     }
 }
 
-class NaiveBayes {
+class NaiveBayes<T> {
     
-    private var variables: [Int: [(feature: Int, variables: [Any])]]
-    private var type: NBType
+    var variables: [Int: [(feature: Int, variables: [Any])]]
+    var type: NBType
     
-    init(type: NBType) {
+    var data: [[T]]
+    var classes: [Int]
+    
+    init(type: NBType, data: [[T]], classes: [Int]) throws {
         self.type = type
+        self.data = data
+        self.classes = classes
         self.variables = [Int: [(Int, [Any])]]()
-    }
-    
-    static func convert<T: Any>(dataAndClasses: [[T]], rowOfClasses: Int) -> (data: [[T]], classes: [Int]) {
-        let classes = dataAndClasses.map { Int($0[rowOfClasses] as! Double) } //TODO
         
-        let data = dataAndClasses.map { row in
-            return row.enumerated().filter { $0.offset != rowOfClasses }.map { $0.element }
+        if case .gaussian = type, T.self != Double.self {
+            throw "When using Gaussian NB you have to have continuous features (Double)"
+        } else if case .multinomial = type, T.self != Int.self {
+            throw "When using Multinomial NB you have to have categorical features (Int)"
         }
-        
-        return (data, classes)
     }
     
-    //TODO remake pliss, i dont like this at all
-    func train() {
-        
-        var classes = type.classes
+    func train() throws -> Self {
         
         for `class` in classes.uniques() {
-            
             variables[`class`] = [(Int, [Any])]()
             
-            for feature in 0..<type.data[0].count {
+            let classDependent = data.enumerated().filter { (offset, _) in
+                return classes[offset] == `class`
+            }
+            
+            for feature in 0..<data[0].count {
                 
-                let values = type.data.map { $0[feature] }.enumerated().filter { (offset, _) in
-                    return classes[offset] == `class`
-                    }.map { $0.element }
+                let featureDependent = classDependent.map { $0.element[feature] }
                 
-                let trained = type.train(values: values) ?? [Any]()
+                guard let trained = type.train(values: featureDependent) else {
+                    throw "Critical! Data could not be casted even though it was checked at init"
+                }
                 
                 variables[`class`]?.append((feature, trained))
             }
         }
+        
+        return self
     }
     
-    func classify(with input: [Double]) -> Int {
+    func classify(with input: [T]) -> Int {
         let likelihoods = classifyProba(with: input).max { (first, second) -> Bool in
             return first.1 < second.1
         }
@@ -180,10 +165,8 @@ class NaiveBayes {
         return `class`
     }
     
-    //TODO fix this doesnt have to be a double
-    func classifyProba(with input: [Double]) -> [(Int, Double)] {
+    func classifyProba(with input: [T]) -> [(Int, Double)] {
         
-        let classes = type.classes
         var probaClass = [Int: Double]()
         let amount = classes.count
         
@@ -200,7 +183,7 @@ class NaiveBayes {
         }
         
         let likelihoods = classesAndFeatures.map { (`class`, distribution) in
-            return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 1.0))
+            return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 0.0))
         }
         
         let sum = likelihoods.map { $0.1 }.reduce(0, +)
@@ -211,40 +194,3 @@ class NaiveBayes {
         return normalized
     }
 }
-
-guard let csv = try? String(contentsOfFile: "/Users/ph1ps/Desktop/wine.csv") else {
-    print("file not found")
-    exit(0)
-}
-
-let rows = csv.characters.split(separator: "\r\n").map { String($0) }
-let wineData = rows.map { row -> [Double] in
-    let split = row.characters.split(separator: ";")
-    return split.map { Double(String($0))! }
-}
-
-let convertedWine = NaiveBayes.convert(dataAndClasses: wineData, rowOfClasses: 0)
-let wineNaive = NaiveBayes(type: .gaussian(data: convertedWine.data, classes: convertedWine.classes))
-wineNaive.train()
-print(wineNaive.classifyProba(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015]))
-
-let golfData = [
-    [0, 0, 0, 0],
-    [0, 0, 0, 1],
-    [1, 0, 0, 0],
-    [2, 1, 0, 0],
-    [2, 2, 1, 0],
-    [2, 2, 1, 1],
-    [1, 2, 1, 1],
-    [0, 1, 0, 0],
-    [0, 2, 1, 0],
-    [2, 1, 1, 0],
-    [0, 1, 1, 1],
-    [1, 1, 0, 1],
-    [1, 0, 1, 0],
-    [2, 1, 0, 1]
-]
-let golfClasses =  [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]
-let golfNaive = NaiveBayes(type: .multinomial(data: golfData, classes: golfClasses))
-golfNaive.train()
-print(golfNaive.classifyProba(with: [0, 2, 0, 1]))

From 8ac88ae7fe6134885956502bd9551e7b6cd0a083 Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Mon, 17 Apr 2017 21:29:43 +0200
Subject: [PATCH 029/643] Change macOS playground to iOS

---
 .../NaiveBayes.playground/Contents.swift      | 51 +++++++++++++++++--
 .../contents.xcplayground                     |  2 +-
 .../NaiveBayes.playground/timeline.xctimeline | 21 ++++++++
 3 files changed, 70 insertions(+), 4 deletions(-)
 create mode 100644 Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline

diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift
index cb820272e..321e7a04a 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
@@ -7,7 +7,7 @@ import Foundation
  
  ### Gaussian Naive Bayes
  - Note:
- When using Gaussian NB you have to have continuous features (Double). 
+ When using Gaussian NB you have to have continuous features (Double).
  
  For this example we are going to use a famous dataset with different types of wine. The labels of the features can be viewed [here](https://gist.github.com/tijptjik/9408623)
  */
@@ -52,9 +52,54 @@ let data = wineData.map { row in
  */
 let wineBayes = try! NaiveBayes(type: .gaussian, data: data, classes: classes).train()
 let result = wineBayes.classifyProba(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015])
-print(result)
 /*:
- I can assure you that this is the correct result and as you can see the classifier thinks that its ***99.99%*** correct too.
+ I can assure you that ***class 1*** is the correct result and as you can see the classifier thinks that its ***99.99%*** likely too.
  
  ### Multinomial Naive Bayes
+ 
+ - Note:
+ When using Multinomial NB you have to have categorical features (Int).
+ 
+ Now this dataset is commonly used to describe the classification problem and it is categorical which means you don't have real values you just have categorical data as stated before. The structure of this dataset is as follows.
+ 
+ Outlook,Temperature,Humidity,Windy
+ 
+ ***Outlook***: 0 = rainy, 1 = overcast, 2 = sunny
+ 
+ ***Temperature***: 0 = hot, 1 = mild, 2 = cool
+ 
+ ***Humidity***: 0 = high, 1 = normal
+ 
+ ***Windy***: 0 = false, 1 = true
+ 
+ The classes are either he will play golf or not depending on the weather conditions. (0 = won't play, 1 = will play)
+ */
+
+let golfData = [
+    [0, 0, 0, 0],
+    [0, 0, 0, 1],
+    [1, 0, 0, 0],
+    [2, 1, 0, 0],
+    [2, 2, 1, 0],
+    [2, 2, 1, 1],
+    [1, 2, 1, 1],
+    [0, 1, 0, 0],
+    [0, 2, 1, 0],
+    [2, 1, 1, 0],
+    [0, 1, 1, 1],
+    [1, 1, 0, 1],
+    [1, 0, 1, 0],
+    [2, 1, 0, 1]
+]
+let golfClasses =  [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]
+
+let golfNaive = try! NaiveBayes(type: .multinomial, data: golfData, classes: golfClasses).train()
+
+/*:
+ The weather conditions is as follows now: Outlook=rainy, Temperature=cool, Humidity=high, Windy=true
+ */
+let golfResult = golfNaive.classifyProba(with: [0, 2, 0, 1])
+
+/*:
+ Naive Bayes tells us that the golf player will ***not*** play with a likelihood of almost ***80%***. Which is true of course.
  */
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground
index b1148fc50..35968656f 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='macos' display-mode='raw'>
+<playground version='5.0' target-platform='ios' display-mode='raw'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline b/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline
new file mode 100644
index 000000000..b15fdda55
--- /dev/null
+++ b/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline	
@@ -0,0 +1,21 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=1&amp;CharacterRangeLoc=2051&amp;EndingColumnNumber=14&amp;EndingLineNumber=53&amp;StartingColumnNumber=1&amp;StartingLineNumber=53&amp;Timestamp=514147811.827527"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=6&amp;CharacterRangeLoc=1936&amp;EndingColumnNumber=11&amp;EndingLineNumber=53&amp;StartingColumnNumber=5&amp;StartingLineNumber=53&amp;Timestamp=514147811.848778"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=10&amp;CharacterRangeLoc=3424&amp;EndingColumnNumber=15&amp;EndingLineNumber=100&amp;StartingColumnNumber=5&amp;StartingLineNumber=100&amp;Timestamp=514149150.852782"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+   </TimelineItems>
+</Timeline>

From 9fafc9278d72240fda1117d010b1544ff106dccb Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Tue, 18 Apr 2017 13:47:17 +0200
Subject: [PATCH 030/643] Add README with explanation

---
 .../NaiveBayes.playground/Contents.swift      |  28 ++---
 .../Sources/NaiveBayes.swift                  | 100 +++++++++---------
 .../contents.xcplayground                     |   2 +-
 .../NaiveBayes.playground/timeline.xctimeline |  10 ++
 Naive Bayes Classifier/NaiveBayes.swift       | 100 +++++++++---------
 Naive Bayes Classifier/README.md              |  99 +++++++++++++++++
 Naive Bayes Classifier/images/bayes.gif       | Bin 0 -> 1095 bytes
 .../images/code_example.png                   | Bin 0 -> 122044 bytes
 Naive Bayes Classifier/images/mean.gif        | Bin 0 -> 590 bytes
 Naive Bayes Classifier/images/multinomial.gif | Bin 0 -> 703 bytes
 .../images/normal_distribution.gif            | Bin 0 -> 925 bytes
 .../images/standard_deviation.gif             | Bin 0 -> 1125 bytes
 .../images/tennis_dataset.png                 | Bin 0 -> 61477 bytes
 13 files changed, 224 insertions(+), 115 deletions(-)
 create mode 100644 Naive Bayes Classifier/images/bayes.gif
 create mode 100644 Naive Bayes Classifier/images/code_example.png
 create mode 100644 Naive Bayes Classifier/images/mean.gif
 create mode 100644 Naive Bayes Classifier/images/multinomial.gif
 create mode 100644 Naive Bayes Classifier/images/normal_distribution.gif
 create mode 100644 Naive Bayes Classifier/images/standard_deviation.gif
 create mode 100644 Naive Bayes Classifier/images/tennis_dataset.png

diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift
index 321e7a04a..66aefaa32 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
@@ -2,13 +2,13 @@ import Foundation
 
 /*:
  ## Naive Bayes Classifier
- 
+
  This playground uses the given algorithm and utilizes its features with some example datasets
- 
+
  ### Gaussian Naive Bayes
  - Note:
  When using Gaussian NB you have to have continuous features (Double).
- 
+
  For this example we are going to use a famous dataset with different types of wine. The labels of the features can be viewed [here](https://gist.github.com/tijptjik/9408623)
  */
 guard let wineCSV = Bundle.main.path(forResource: "wine", ofType: "csv") else {
@@ -27,7 +27,7 @@ guard let csv = try? String(contentsOfFile: wineCSV) else {
 let rows = csv.characters.split(separator: "\r\n").map { String($0) }
 /*:
  Splitting on the ; sign and converting the value to a Double
- 
+
  - Important:
  Do not force unwrap the mapped values in your real application. Carefully convert them! This is just for the sake of showing how the algorithm works.
  */
@@ -47,31 +47,31 @@ let data = wineData.map { row in
 
 /*:
  Again use `guard` on the result of a `try?` or simply `do-try-catch` because this would crash your application if an error occured.
- 
+
  The array in the `classifyProba` method I passed is a former entry in the .csv file which I removed in order to classify it.
  */
 let wineBayes = try! NaiveBayes(type: .gaussian, data: data, classes: classes).train()
 let result = wineBayes.classifyProba(with: [12.85, 1.6, 2.52, 17.8, 95, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015])
 /*:
  I can assure you that ***class 1*** is the correct result and as you can see the classifier thinks that its ***99.99%*** likely too.
- 
+
  ### Multinomial Naive Bayes
- 
+
  - Note:
  When using Multinomial NB you have to have categorical features (Int).
- 
+
  Now this dataset is commonly used to describe the classification problem and it is categorical which means you don't have real values you just have categorical data as stated before. The structure of this dataset is as follows.
- 
+
  Outlook,Temperature,Humidity,Windy
- 
+
  ***Outlook***: 0 = rainy, 1 = overcast, 2 = sunny
- 
+
  ***Temperature***: 0 = hot, 1 = mild, 2 = cool
- 
+
  ***Humidity***: 0 = high, 1 = normal
- 
+
  ***Windy***: 0 = false, 1 = true
- 
+
  The classes are either he will play golf or not depending on the weather conditions. (0 = won't play, 1 = will play)
  */
 
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift
index 3af8102c7..6e6d7b4c0 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Sources/NaiveBayes.swift	
@@ -11,186 +11,186 @@ import Foundation
 extension String: Error {}
 
 extension Array where Element == Double {
-    
+
     func mean() -> Double {
         return self.reduce(0, +) / Double(count)
     }
-    
+
     func standardDeviation() -> Double {
         let calculatedMean = mean()
-        
+
         let sum = self.reduce(0.0) { (previous, next) in
             return previous + pow(next - calculatedMean, 2)
         }
-        
+
         return sqrt(sum / Double(count - 1))
     }
 }
 
 extension Array where Element == Int {
-    
+
     func uniques() -> Set<Element> {
         return Set(self)
     }
-    
+
 }
 
 public enum NBType {
-    
+
     case gaussian
     case multinomial
     //case bernoulli --> TODO
-    
+
     func calcLikelihood(variables: [Any], input: Any) -> Double? {
-        
+
         if case .gaussian = self {
-            
+
             guard let input = input as? Double else {
                 return nil
             }
-            
+
             guard let mean = variables[0] as? Double else {
                 return nil
             }
-            
+
             guard let stDev = variables[1] as? Double else {
                 return nil
             }
-            
+
             let eulerPart = pow(M_E, -1 * pow(input - mean, 2) / (2 * pow(stDev, 2)))
             let distribution = eulerPart / sqrt(2 * .pi) / stDev
-            
+
             return distribution
-            
+
         } else if case .multinomial = self {
-            
+
             guard let variables = variables as? [(category: Int, probability: Double)] else {
                 return nil
             }
-            
+
             guard let input = input as? Int else {
                 return nil
             }
-            
+
             return variables.first { variable in
                 return variable.category == input
                 }?.probability
-            
+
         }
-        
+
         return nil
     }
-    
+
     func train(values: [Any]) -> [Any]? {
-        
+
         if case .gaussian = self {
-            
+
             guard let values = values as? [Double] else {
                 return nil
             }
-            
+
             return [values.mean(), values.standardDeviation()]
-            
+
         } else if case .multinomial = self {
-            
+
             guard let values = values as? [Int] else {
                 return nil
             }
-            
+
             let count = values.count
             let categoryProba = values.uniques().map { value -> (Int, Double) in
                 return (value, Double(values.filter { $0 == value }.count) / Double(count))
             }
             return categoryProba
         }
-        
+
         return nil
     }
 }
 
 public class NaiveBayes<T> {
-    
+
     var variables: [Int: [(feature: Int, variables: [Any])]]
     var type: NBType
-    
+
     var data: [[T]]
     var classes: [Int]
-    
+
     public init(type: NBType, data: [[T]], classes: [Int]) throws {
         self.type = type
         self.data = data
         self.classes = classes
         self.variables = [Int: [(Int, [Any])]]()
-        
+
         if case .gaussian = type, T.self != Double.self {
             throw "When using Gaussian NB you have to have continuous features (Double)"
         } else if case .multinomial = type, T.self != Int.self {
             throw "When using Multinomial NB you have to have categorical features (Int)"
         }
     }
-    
+
     public func train() throws -> Self {
-        
+
         for `class` in classes.uniques() {
             variables[`class`] = [(Int, [Any])]()
-            
+
             let classDependent = data.enumerated().filter { (offset, _) in
                 return classes[offset] == `class`
             }
-            
+
             for feature in 0..<data[0].count {
-                
+
                 let featureDependent = classDependent.map { $0.element[feature] }
-                
+
                 guard let trained = type.train(values: featureDependent) else {
                     throw "Critical! Data could not be casted even though it was checked at init"
                 }
-                
+
                 variables[`class`]?.append((feature, trained))
             }
         }
-        
+
         return self
     }
-    
+
     public func classify(with input: [T]) -> Int {
         let likelihoods = classifyProba(with: input).max { (first, second) -> Bool in
             return first.1 < second.1
         }
-        
+
         guard let `class` = likelihoods?.0 else {
             return -1
         }
-        
+
         return `class`
     }
-    
+
     public func classifyProba(with input: [T]) -> [(Int, Double)] {
-        
+
         var probaClass = [Int: Double]()
         let amount = classes.count
-        
+
         classes.forEach { `class` in
             let individual = classes.filter { $0 == `class` }.count
             probaClass[`class`] = Double(individual) / Double(amount)
         }
-        
+
         let classesAndFeatures = variables.map { (`class`, value) -> (Int, [Double]) in
             let distribution = value.map { (feature, variables) -> Double in
                 return type.calcLikelihood(variables: variables, input: input[feature]) ?? 0.0
             }
             return (`class`, distribution)
         }
-        
+
         let likelihoods = classesAndFeatures.map { (`class`, distribution) in
             return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 0.0))
         }
-        
+
         let sum = likelihoods.map { $0.1 }.reduce(0, +)
         let normalized = likelihoods.map { (`class`, likelihood) in
             return (`class`, likelihood / sum)
         }
-        
+
         return normalized
     }
 }
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground
index 35968656f..89da2d470 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios' display-mode='raw'>
+<playground version='5.0' target-platform='ios' display-mode='rendered'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline b/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline
index b15fdda55..7bc414f58 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/timeline.xctimeline	
@@ -17,5 +17,15 @@
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=10&amp;CharacterRangeLoc=3410&amp;EndingColumnNumber=15&amp;EndingLineNumber=100&amp;StartingColumnNumber=5&amp;StartingLineNumber=100&amp;Timestamp=514208705.303681"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "#CharacterRangeLen=6&amp;CharacterRangeLoc=1931&amp;EndingColumnNumber=11&amp;EndingLineNumber=53&amp;StartingColumnNumber=5&amp;StartingLineNumber=53&amp;Timestamp=514208705.303681"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
    </TimelineItems>
 </Timeline>
diff --git a/Naive Bayes Classifier/NaiveBayes.swift b/Naive Bayes Classifier/NaiveBayes.swift
index 9b9ace86d..46a0bb4f5 100644
--- a/Naive Bayes Classifier/NaiveBayes.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.swift	
@@ -11,186 +11,186 @@ import Foundation
 extension String: Error {}
 
 extension Array where Element == Double {
-    
+
     func mean() -> Double {
         return self.reduce(0, +) / Double(count)
     }
-    
+
     func standardDeviation() -> Double {
         let calculatedMean = mean()
-        
+
         let sum = self.reduce(0.0) { (previous, next) in
             return previous + pow(next - calculatedMean, 2)
         }
-        
+
         return sqrt(sum / Double(count - 1))
     }
 }
 
 extension Array where Element == Int {
-    
+
     func uniques() -> Set<Element> {
         return Set(self)
     }
-    
+
 }
 
 enum NBType {
-    
+
     case gaussian
     case multinomial
     //case bernoulli --> TODO
-    
+
     func calcLikelihood(variables: [Any], input: Any) -> Double? {
-        
+
         if case .gaussian = self {
-            
+
             guard let input = input as? Double else {
                 return nil
             }
-            
+
             guard let mean = variables[0] as? Double else {
                 return nil
             }
-            
+
             guard let stDev = variables[1] as? Double else {
                 return nil
             }
-            
+
             let eulerPart = pow(M_E, -1 * pow(input - mean, 2) / (2 * pow(stDev, 2)))
             let distribution = eulerPart / sqrt(2 * .pi) / stDev
-            
+
             return distribution
-            
+
         } else if case .multinomial = self {
-            
+
             guard let variables = variables as? [(category: Int, probability: Double)] else {
                 return nil
             }
-            
+
             guard let input = input as? Int else {
                 return nil
             }
-            
+
             return variables.first { variable in
                 return variable.category == input
                 }?.probability
-            
+
         }
-        
+
         return nil
     }
-    
+
     func train(values: [Any]) -> [Any]? {
-        
+
         if case .gaussian = self {
-            
+
             guard let values = values as? [Double] else {
                 return nil
             }
-            
+
             return [values.mean(), values.standardDeviation()]
-            
+
         } else if case .multinomial = self {
-            
+
             guard let values = values as? [Int] else {
                 return nil
             }
-            
+
             let count = values.count
             let categoryProba = values.uniques().map { value -> (Int, Double) in
                 return (value, Double(values.filter { $0 == value }.count) / Double(count))
             }
             return categoryProba
         }
-        
+
         return nil
     }
 }
 
 class NaiveBayes<T> {
-    
+
     var variables: [Int: [(feature: Int, variables: [Any])]]
     var type: NBType
-    
+
     var data: [[T]]
     var classes: [Int]
-    
+
     init(type: NBType, data: [[T]], classes: [Int]) throws {
         self.type = type
         self.data = data
         self.classes = classes
         self.variables = [Int: [(Int, [Any])]]()
-        
+
         if case .gaussian = type, T.self != Double.self {
             throw "When using Gaussian NB you have to have continuous features (Double)"
         } else if case .multinomial = type, T.self != Int.self {
             throw "When using Multinomial NB you have to have categorical features (Int)"
         }
     }
-    
+
     func train() throws -> Self {
-        
+
         for `class` in classes.uniques() {
             variables[`class`] = [(Int, [Any])]()
-            
+
             let classDependent = data.enumerated().filter { (offset, _) in
                 return classes[offset] == `class`
             }
-            
+
             for feature in 0..<data[0].count {
-                
+
                 let featureDependent = classDependent.map { $0.element[feature] }
-                
+
                 guard let trained = type.train(values: featureDependent) else {
                     throw "Critical! Data could not be casted even though it was checked at init"
                 }
-                
+
                 variables[`class`]?.append((feature, trained))
             }
         }
-        
+
         return self
     }
-    
+
     func classify(with input: [T]) -> Int {
         let likelihoods = classifyProba(with: input).max { (first, second) -> Bool in
             return first.1 < second.1
         }
-        
+
         guard let `class` = likelihoods?.0 else {
             return -1
         }
-        
+
         return `class`
     }
-    
+
     func classifyProba(with input: [T]) -> [(Int, Double)] {
-        
+
         var probaClass = [Int: Double]()
         let amount = classes.count
-        
+
         classes.forEach { `class` in
             let individual = classes.filter { $0 == `class` }.count
             probaClass[`class`] = Double(individual) / Double(amount)
         }
-        
+
         let classesAndFeatures = variables.map { (`class`, value) -> (Int, [Double]) in
             let distribution = value.map { (feature, variables) -> Double in
                 return type.calcLikelihood(variables: variables, input: input[feature]) ?? 0.0
             }
             return (`class`, distribution)
         }
-        
+
         let likelihoods = classesAndFeatures.map { (`class`, distribution) in
             return (`class`, distribution.reduce(1, *) * (probaClass[`class`] ?? 0.0))
         }
-        
+
         let sum = likelihoods.map { $0.1 }.reduce(0, +)
         let normalized = likelihoods.map { (`class`, likelihood) in
             return (`class`, likelihood / sum)
         }
-        
+
         return normalized
     }
 }
diff --git a/Naive Bayes Classifier/README.md b/Naive Bayes Classifier/README.md
index e69de29bb..9c0f0082a 100644
--- a/Naive Bayes Classifier/README.md	
+++ b/Naive Bayes Classifier/README.md	
@@ -0,0 +1,99 @@
+# Naive Bayes Classifier
+
+> ***Disclaimer:*** Do not get scared of complicated formulas or terms, I will describe them right after I use them. Also the math skills you need to understand this are very basic.
+
+The goal of a classifier is to predict the class of a given data entry based on previously fed data and its features. 
+
+Now what is a class or a feature? The best I can do is to describe it with a table. 
+This is a dataset that uses height, weight and foot size of a person to illustrate the relationship between those values and the sex.
+
+| Sex       | height (feet)          | weight(lbs)  | foot size (inches) |
+| ------------- |:-------------:|:-----:|:---:|
+| male      | 6     | 180 | 12  |
+| male      | 5.92  | 190 | 11  |
+| male      | 5.58  | 170 | 12  |
+| male      | 5.92  | 165 | 10  |
+| female    | 5     | 100 | 6   |
+| female    | 5.5   | 150 | 8   |
+| female    | 5.42  | 130 | 7   |
+| female    | 5.75  | 150 | 9   |
+
+The ***classes*** of this table is the data in the sex column (male/female). You "classify" the rest of the data and bind them to a sex.
+
+The ***features*** of this table are the labels of the other columns (height, weight, foot size) and the numbers right under the labels.
+
+Now that I've told you what a classifier is I will tell you what exactly a ***Naive Bayes classifier*** is. There are a lot of other classifiers out there but what's so special about this specific is that it only needs a very small dataset to get good results. The others like Random Forests normally need a very large dataset.
+
+Why isn't this algorithm used more you might ask (or not). Because it is normally ***outperformed*** in accuracy by ***Random Forests*** or ***Boosted Trees***.
+
+## Theory
+
+The Naive Bayes classifier utilizes the ***Bayes Theorem*** (as its name suggests) which looks like this.
+
+![](images/bayes.gif)
+
+***P*** always means the probability of something.
+
+***A*** is the class, ***B*** is the data depending on a feature and the ***pipe*** symbol means given. 
+
+P(A | B) therefore is: probability of the class given the data (which is dependent on the feature).
+
+This is all you have to know about the Bayes Theorem. The important thing for us is now how to calculate all those variables, plug them into this formula and you are ready to classify data.
+
+### **P(A)**
+This is the probability of the class. To get back to the example I gave before: Let's say we want to classify this data entry:
+
+| height (feet)          | weight(lbs)  | foot size (inches) |
+|:-------------:|:-----:|:---:|
+| 6     | 130 | 8  |
+
+What Naive Bayes classifier now does: it checks the probability for every class possible which is in our case either male or female. Look back at the original table and count the male and the female entries. Then divide them by the overall count of data entries.
+
+P(male) = 4 / 8 = 0.5
+
+P(female) = 4 / 8 = 0.5
+
+This should be a very easy task to do. Basically just the probability of all classes.
+
+### **P(B)**
+This variable is not needed in a Naive Bayes classifier. It is the probability of the data. It does not change, therefore it is a constant. And what can you do with a constant? Exactly! Discard it. This saves time and code.
+
+### **P(B | A)**
+This is the probability of the data given the class. To calculate this I have to introduce you to the subtypes of NB. You have to decide which you use depending on your data which you want to classify.
+
+### **Gaussian Naive Bayes**
+If you have a dataset like the one I showed you before (continuous features -> `Double`s) you have to use this subtype. There are 3 formulas you need for Gaussian NB to calculate P(B | A).
+
+![mean](images/mean.gif)
+
+![standard deviation](images/standard_deviation.gif)
+
+![normal distribution](images/normal_distribution.gif)
+
+and **P(x | y) = P(B | A)**
+
+Again, very complicated looking formulas but they are very easy. The first formula with µ is just the mean of the data (adding all data points and dividing them by the count). The second with σ is the standard deviation. You might have heard of it somewhen in school. It is just the sum of all values minus the mean, squared and that divided by the count of the data minus 1 and a sqaure root around it. The third equation is the Gaussian or normal distribution if you want to read more about it I suggest reading [this](https://en.wikipedia.org/wiki/Normal_distribution).
+
+Why the Gaussian distribution? Because we assume that the continuous values associated with each class are distributed according to the Gaussian distribution. Simple as that.
+
+### **Multinomial Naive Bayes**
+
+What do we do if we have this for examples:
+
+![tennis or golf](images/tennis_dataset.png)
+
+We can't just calculate the mean of sunny, overcast and rainy. This is why we need the categorical model which is the multinomial NB. This is the last formula, I promise!
+
+![multinomial](images/multinomial.gif)
+
+Now this is the number of times feature **i** appears in a sample **N** of class **y** in the data set divided by the count of the sample just depending on the class **y**. That θ is also just a fancy way of writing P(B | A).
+
+You might have noticed that there is still the α in this formula. This solves a problem called "zero-frequency-problem". Because what happens if there is no sample with feature **i** and class **y**? The whole equation would result in 0 (because 0 / something is always 0). This is a huge problem but there is a simple solution to this. Just add 1 to any count of the sample (α = 1).
+
+## Those formulas in action
+
+Enough talking! This is the code. If you want a deeper explanation of how the code works just look at the Playground I provided.
+
+![code example](images/code_example.png)
+
+*Written for Swift Algorithm Club by Philipp Gabriel*
\ No newline at end of file
diff --git a/Naive Bayes Classifier/images/bayes.gif b/Naive Bayes Classifier/images/bayes.gif
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From d2f02efd49d2367382c7a6fffc5fa1e3b74c8eff Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Sun, 21 May 2017 21:46:01 +0200
Subject: [PATCH 031/643] Initial Docs template and text

---
 Splay Tree/readme.md | 61 +++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 60 insertions(+), 1 deletion(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index 2282502fa..aa6bdd4db 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -1 +1,60 @@
-In progress
+# Splay Tree
+Splay tree is a data structure, structurally identitical to a Balanced Binary Search Tree. Every operation performed on a Splay Tree causes a readjustment in order to provide fast access to recently operated values. On every access, the tree is rearranged and the node accessed is moved to the root of the tree using a set of specific rotations, which together are referred to as **Splaying**.
+
+
+## Rotations
+
+### Zig-Zig
+
+Given a node *a* if *a* is not the root, and *a* has a child *b*, and both *a* and *b* are left children or right children, a **Zig-Zig** is performed.
+
+### Zig-Zag
+
+Given a node *a* if *a* is not the root, and *a* has a child *b*, and *b* is the left child of *a* being the right child (or the opporsite), a **Zig-Zag** is performed.
+
+### Zig
+
+A **Zig** is performed when the node *a* to be rotated has the root as parent.
+
+## Splaying
+
+## Operations
+
+### Insertion 
+
+### Deletion 
+
+### Search 
+
+## Examples 
+
+### Example 1
+
+### Example 2
+
+### Example 3
+
+## Advantages 
+
+Splay trees provide an efficient way to quickly access elements that are frequently requested. This characteristic makes then a good choice to implement, for exmaple, caches or garbage collection algorithms, or in any other problem involving frequent access to a certain numbers of elements from a data set.
+
+## Disadvantages
+
+Splay tree are not perfectly balanced always, so in case of accessing all the elements in the tree in an increasing order, the height of the tree becomes *n*.
+
+## Time complexity
+
+| Case        |    Performance        |
+| ------------- |:-------------:|
+| Average      | O(log n) |
+| Worst      | n |
+
+With *n* being the number of items in the tree.
+
+
+## See also
+
+[Splay Tree on Wikipedia](https://en.wikipedia.org/wiki/Splay_tree)
+[Splay Tree by University of California in Berkeley - CS 61B Lecture 34](https://www.youtube.com/watch?v=G5QIXywcJlY)
+
+*Written for Swift Algorithm Club by Mike Taghavi and Matthijs Hollemans*

From 7f751918b92881d93aabce634a891b95f46a90f0 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 21 May 2017 22:03:23 +0200
Subject: [PATCH 032/643] images for documentation

---
 Splay Tree/Images /zig.png     | Bin 0 -> 7793 bytes
 Splay Tree/Images /zigzag1.png | Bin 0 -> 13964 bytes
 Splay Tree/Images /zigzag2.png | Bin 0 -> 13877 bytes
 Splay Tree/Images /zigzig1.png | Bin 0 -> 13855 bytes
 Splay Tree/Images /zigzig2.png | Bin 0 -> 15179 bytes
 5 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Splay Tree/Images /zig.png
 create mode 100644 Splay Tree/Images /zigzag1.png
 create mode 100644 Splay Tree/Images /zigzag2.png
 create mode 100644 Splay Tree/Images /zigzig1.png
 create mode 100644 Splay Tree/Images /zigzig2.png

diff --git a/Splay Tree/Images /zig.png b/Splay Tree/Images /zig.png
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From 6c1c12651247ed73e3e727c0e7dc28e2a0b1e518 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 21 May 2017 22:17:44 +0200
Subject: [PATCH 033/643] Images for examples documentation

---
 Splay Tree/Images /example1-1.png     | Bin 0 -> 13964 bytes
 Splay Tree/Images /example1-2.png     | Bin 0 -> 15451 bytes
 Splay Tree/Images /example1-3.png     | Bin 0 -> 14778 bytes
 Splay Tree/Images /examplezig.svg     |   2 ++
 Splay Tree/Images /examplezig1.png    | Bin 0 -> 6583 bytes
 Splay Tree/Images /examplezig2.png    | Bin 0 -> 9317 bytes
 Splay Tree/Images /examplezigzig.svg  |   2 ++
 Splay Tree/Images /examplezigzig1.png | Bin 0 -> 13855 bytes
 Splay Tree/Images /examplezigzig2.png | Bin 0 -> 15247 bytes
 Splay Tree/Images /examplezigzig3.png | Bin 0 -> 18128 bytes
 10 files changed, 4 insertions(+)
 create mode 100644 Splay Tree/Images /example1-1.png
 create mode 100644 Splay Tree/Images /example1-2.png
 create mode 100644 Splay Tree/Images /example1-3.png
 create mode 100644 Splay Tree/Images /examplezig.svg
 create mode 100644 Splay Tree/Images /examplezig1.png
 create mode 100644 Splay Tree/Images /examplezig2.png
 create mode 100644 Splay Tree/Images /examplezigzig.svg
 create mode 100644 Splay Tree/Images /examplezigzig1.png
 create mode 100644 Splay Tree/Images /examplezigzig2.png
 create mode 100644 Splay Tree/Images /examplezigzig3.png

diff --git a/Splay Tree/Images /example1-1.png b/Splay Tree/Images /example1-1.png
new file mode 100644
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diff --git a/Splay Tree/Images /example1-2.png b/Splay Tree/Images /example1-2.png
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diff --git a/Splay Tree/Images /example1-3.png b/Splay Tree/Images /example1-3.png
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diff --git a/Splay Tree/Images /examplezigzig.svg b/Splay Tree/Images /examplezigzig.svg
new file mode 100644
index 000000000..7bd4dcf6f
--- /dev/null
+++ b/Splay Tree/Images /examplezigzig.svg	
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From 47a412279d3e05ae4edfacc8220f5d6050540783 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Sun, 21 May 2017 22:20:42 +0200
Subject: [PATCH 034/643] delete blank images space

---
 Splay Tree/{Images  => Images}/example1-1.png     | Bin
 Splay Tree/{Images  => Images}/example1-2.png     | Bin
 Splay Tree/{Images  => Images}/example1-3.png     | Bin
 Splay Tree/{Images  => Images}/examplezig.svg     |   0
 Splay Tree/{Images  => Images}/examplezig1.png    | Bin
 Splay Tree/{Images  => Images}/examplezig2.png    | Bin
 Splay Tree/{Images  => Images}/examplezigzig.svg  |   0
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 rename Splay Tree/{Images  => Images}/example1-1.png (100%)
 rename Splay Tree/{Images  => Images}/example1-2.png (100%)
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 rename Splay Tree/{Images  => Images}/examplezig.svg (100%)
 rename Splay Tree/{Images  => Images}/examplezig1.png (100%)
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 rename Splay Tree/{Images  => Images}/zigzag2.png (100%)
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diff --git a/Splay Tree/Images /example1-1.png b/Splay Tree/Images/example1-1.png
similarity index 100%
rename from Splay Tree/Images /example1-1.png
rename to Splay Tree/Images/example1-1.png
diff --git a/Splay Tree/Images /example1-2.png b/Splay Tree/Images/example1-2.png
similarity index 100%
rename from Splay Tree/Images /example1-2.png
rename to Splay Tree/Images/example1-2.png
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similarity index 100%
rename from Splay Tree/Images /example1-3.png
rename to Splay Tree/Images/example1-3.png
diff --git a/Splay Tree/Images /examplezig.svg b/Splay Tree/Images/examplezig.svg
similarity index 100%
rename from Splay Tree/Images /examplezig.svg
rename to Splay Tree/Images/examplezig.svg
diff --git a/Splay Tree/Images /examplezig1.png b/Splay Tree/Images/examplezig1.png
similarity index 100%
rename from Splay Tree/Images /examplezig1.png
rename to Splay Tree/Images/examplezig1.png
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similarity index 100%
rename from Splay Tree/Images /examplezig2.png
rename to Splay Tree/Images/examplezig2.png
diff --git a/Splay Tree/Images /examplezigzig.svg b/Splay Tree/Images/examplezigzig.svg
similarity index 100%
rename from Splay Tree/Images /examplezigzig.svg
rename to Splay Tree/Images/examplezigzig.svg
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similarity index 100%
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rename to Splay Tree/Images/examplezigzig1.png
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rename to Splay Tree/Images/examplezigzig2.png
diff --git a/Splay Tree/Images /examplezigzig3.png b/Splay Tree/Images/examplezigzig3.png
similarity index 100%
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diff --git a/Splay Tree/Images /zig.png b/Splay Tree/Images/zig.png
similarity index 100%
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similarity index 100%
rename from Splay Tree/Images /zigzag1.png
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similarity index 100%
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rename to Splay Tree/Images/zigzag2.png
diff --git a/Splay Tree/Images /zigzig1.png b/Splay Tree/Images/zigzig1.png
similarity index 100%
rename from Splay Tree/Images /zigzig1.png
rename to Splay Tree/Images/zigzig1.png
diff --git a/Splay Tree/Images /zigzig2.png b/Splay Tree/Images/zigzig2.png
similarity index 100%
rename from Splay Tree/Images /zigzig2.png
rename to Splay Tree/Images/zigzig2.png

From 5d15f553817310785fc0d5539c01508c86892250 Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Sun, 21 May 2017 22:27:24 +0200
Subject: [PATCH 035/643] Adding images for examples and rotation cases

---
 Splay Tree/readme.md | 26 ++++++++++++++++++++++++--
 1 file changed, 24 insertions(+), 2 deletions(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index aa6bdd4db..89444b2cc 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -8,14 +8,25 @@ Splay tree is a data structure, structurally identitical to a Balanced Binary Se
 
 Given a node *a* if *a* is not the root, and *a* has a child *b*, and both *a* and *b* are left children or right children, a **Zig-Zig** is performed.
 
+![ZigZigCase1](Images/zigzig1.png)
+
+![ZigZigCase2](Images/zigzig2.png)
+
 ### Zig-Zag
 
 Given a node *a* if *a* is not the root, and *a* has a child *b*, and *b* is the left child of *a* being the right child (or the opporsite), a **Zig-Zag** is performed.
 
+![ZigZagCase1](Images/zigzag1.png)
+
+![ZigZagCase2](Images/zigzag2.png)
+
 ### Zig
 
 A **Zig** is performed when the node *a* to be rotated has the root as parent.
 
+![ZigCase](Images/zig.png)
+
+
 ## Splaying
 
 ## Operations
@@ -30,9 +41,20 @@ A **Zig** is performed when the node *a* to be rotated has the root as parent.
 
 ### Example 1
 
+![ZigEx1](Images/examplezigzig1.png)
+
+![ZigEx2](Images/examplezigzig2.png)
+
+![ZigEx3](Images/examplezigzig3.png)
+
+
 ### Example 2
 
-### Example 3
+![ZigEx21](Images/example1-1.png)
+
+![ZigEx22](Images/example1-2.png)
+
+![ZigEx23](Images/example1-3.png)
 
 ## Advantages 
 
@@ -57,4 +79,4 @@ With *n* being the number of items in the tree.
 [Splay Tree on Wikipedia](https://en.wikipedia.org/wiki/Splay_tree)
 [Splay Tree by University of California in Berkeley - CS 61B Lecture 34](https://www.youtube.com/watch?v=G5QIXywcJlY)
 
-*Written for Swift Algorithm Club by Mike Taghavi and Matthijs Hollemans*
+*Written for Swift Algorithm Club by Barbara Martina Rodeker*

From c4268801a9340b1776c6b4e0c452fe8a6388031b Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Tue, 23 May 2017 22:08:14 +0200
Subject: [PATCH 036/643] Update readme.md

---
 Splay Tree/readme.md | 64 +++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 63 insertions(+), 1 deletion(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index 89444b2cc..29f9dede5 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -4,22 +4,36 @@ Splay tree is a data structure, structurally identitical to a Balanced Binary Se
 
 ## Rotations
 
+There are 3 types of rotations that can form an **Splaying**:
+
+- ZigZig
+- ZigZag
+- Zig
+
 ### Zig-Zig
 
 Given a node *a* if *a* is not the root, and *a* has a child *b*, and both *a* and *b* are left children or right children, a **Zig-Zig** is performed.
 
+### Case both nodes right children
 ![ZigZigCase1](Images/zigzig1.png)
 
+### Case both nodes left children
 ![ZigZigCase2](Images/zigzig2.png)
 
+**IMPORTANT** is to note that a *ZigZig* performs first the rotation of the middle node with its parent (call it the grandparent) and later the rotation of the remaining node (grandchild). Doing that helps to keep the trees balanced even if it was first created by inserted a sequence of increasing values (see below worst case scenario).
+
 ### Zig-Zag
 
 Given a node *a* if *a* is not the root, and *a* has a child *b*, and *b* is the left child of *a* being the right child (or the opporsite), a **Zig-Zag** is performed.
 
+### Case right - left
 ![ZigZagCase1](Images/zigzag1.png)
 
+### Case left - right
 ![ZigZagCase2](Images/zigzag2.png)
 
+**IMPORTANT** A *ZigZag* performs first the rotation of the grandchild node and later the same node with its new parent again. 
+
 ### Zig
 
 A **Zig** is performed when the node *a* to be rotated has the root as parent.
@@ -29,7 +43,53 @@ A **Zig** is performed when the node *a* to be rotated has the root as parent.
 
 ## Splaying
 
-## Operations
+A splaying consists in making so many rotations as needed until the node affected by the operation is at the top and becomes the root of the tree.
+
+```
+while (node.parent != nil) {
+            operation(forNode: node).apply(onNode: node)
+}
+```
+
+Where operation returns the required rotation to be applied. 
+
+```
+    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
+        
+        if let parent = node.parent, let _ = parent.parent {
+            if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
+                return .zigZag
+            }
+            return .zigZig
+        }
+        return .zig
+    }
+```
+
+During the applying phase, the algorithms determines which nodes are involved depending on the rotation to be applied and proceeding to re-arrange the node with its parent.
+
+```
+    public func apply<T: Comparable>(onNode node: Node<T>) {
+        switch self {
+        case .zigZag:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node, parent: node.parent!)
+            rotate(child: node, parent: node.parent!)
+
+        case .zigZig:
+            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+            rotate(child: node.parent!, parent: node.parent!.parent!)
+            rotate(child: node, parent: node.parent!)
+        
+        case .zig:
+            assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
+            rotate(child: node, parent: node.parent!)
+        }
+    }
+```
+
+
+## Operations on an Splay Tree
 
 ### Insertion 
 
@@ -73,6 +133,8 @@ Splay tree are not perfectly balanced always, so in case of accessing all the el
 
 With *n* being the number of items in the tree.
 
+# An example of the Worst Case Performance 
+
 
 ## See also
 

From fbd5d6ea149cccd61c93530a772bad148e3a45e1 Mon Sep 17 00:00:00 2001
From: barbara <barbara@komoot.de>
Date: Thu, 25 May 2017 14:04:49 +0200
Subject: [PATCH 037/643] Examples for documentation

---
 .../Images/SplayTreesWorstCaseExamples.svg      |   2 ++
 Splay Tree/Images/example-zigzig-1.png          | Bin 0 -> 32202 bytes
 Splay Tree/Images/example-zigzig-2.png          | Bin 0 -> 34485 bytes
 Splay Tree/Images/example-zigzig-3.png          | Bin 0 -> 29732 bytes
 Splay Tree/Images/example-zigzig-4.png          | Bin 0 -> 28709 bytes
 Splay Tree/Images/example-zigzig-5.png          | Bin 0 -> 25735 bytes
 Splay Tree/Images/worst-case-1.png              | Bin 0 -> 6795 bytes
 Splay Tree/Images/worst-case-2.png              | Bin 0 -> 7076 bytes
 Splay Tree/Images/worst-case-3.png              | Bin 0 -> 9049 bytes
 Splay Tree/Images/worst-case-4.png              | Bin 0 -> 10813 bytes
 Splay Tree/Images/worst-case-5.png              | Bin 0 -> 11827 bytes
 Splay Tree/Images/worst-case-6.png              | Bin 0 -> 35177 bytes
 Splay Tree/Images/zigzig-wrongrotated.png       | Bin 0 -> 38831 bytes
 13 files changed, 2 insertions(+)
 create mode 100644 Splay Tree/Images/SplayTreesWorstCaseExamples.svg
 create mode 100644 Splay Tree/Images/example-zigzig-1.png
 create mode 100644 Splay Tree/Images/example-zigzig-2.png
 create mode 100644 Splay Tree/Images/example-zigzig-3.png
 create mode 100644 Splay Tree/Images/example-zigzig-4.png
 create mode 100644 Splay Tree/Images/example-zigzig-5.png
 create mode 100644 Splay Tree/Images/worst-case-1.png
 create mode 100644 Splay Tree/Images/worst-case-2.png
 create mode 100644 Splay Tree/Images/worst-case-3.png
 create mode 100644 Splay Tree/Images/worst-case-4.png
 create mode 100644 Splay Tree/Images/worst-case-5.png
 create mode 100644 Splay Tree/Images/worst-case-6.png
 create mode 100644 Splay Tree/Images/zigzig-wrongrotated.png

diff --git a/Splay Tree/Images/SplayTreesWorstCaseExamples.svg b/Splay Tree/Images/SplayTreesWorstCaseExamples.svg
new file mode 100644
index 000000000..c07312af2
--- /dev/null
+++ b/Splay Tree/Images/SplayTreesWorstCaseExamples.svg	
@@ -0,0 +1,2 @@
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diff --git a/Splay Tree/Images/example-zigzig-3.png b/Splay Tree/Images/example-zigzig-3.png
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diff --git a/Splay Tree/Images/example-zigzig-4.png b/Splay Tree/Images/example-zigzig-4.png
new file mode 100644
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z+Mf?jDfo))+a?6Q2fJqI4mSQZhCb|ZLK=Ju^;;MiGU7#Ytzi&XvqX;BeVlCm5zFHH
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ztnSSy=S#ulpC;ZFw!3$B)mM-2wIQ{&EfMO>EnfAz!qpSIO4<)a<+Q4@t}Ysg#418n
z`Q*Q;Dj@;h0wUhDs*=e=XX=LEo;~<7XWaj=P{vQ2)a7;@_#btX@y4X}wx|CO+R~YP

literal 0
HcmV?d00001


From 72b6ef68538b5021eae53d507f82a2e1a46a57ed Mon Sep 17 00:00:00 2001
From: Barbara Martina Rodeker <barbararodeker@gmail.com>
Date: Thu, 25 May 2017 14:29:27 +0200
Subject: [PATCH 038/643] Finishing documentation

---
 Splay Tree/readme.md | 144 ++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 137 insertions(+), 7 deletions(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index 29f9dede5..c42cd87fb 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -20,7 +20,7 @@ Given a node *a* if *a* is not the root, and *a* has a child *b*, and both *a* a
 ### Case both nodes left children
 ![ZigZigCase2](Images/zigzig2.png)
 
-**IMPORTANT** is to note that a *ZigZig* performs first the rotation of the middle node with its parent (call it the grandparent) and later the rotation of the remaining node (grandchild). Doing that helps to keep the trees balanced even if it was first created by inserted a sequence of increasing values (see below worst case scenario).
+**IMPORTANT** is to note that a *ZigZig* performs first the rotation of the middle node with its parent (call it the grandparent) and later the rotation of the remaining node (grandchild). Doing that helps to keep the trees balanced even if it was first created by inserted a sequence of increasing values (see below worst case scenario followed by an explanation about why ZigZig rotates first to the grandparent).
 
 ### Zig-Zag
 
@@ -93,28 +93,69 @@ During the applying phase, the algorithms determines which nodes are involved de
 
 ### Insertion 
 
+To insert a value:
+
+- Insert it as in a binary search tree
+- Splay the value to the root
+
 ### Deletion 
 
+To delete a value: 
+
+- Delete it as in a binary search tree 
+- Splay the parent of the removed node to the root 
+
 ### Search 
 
+To search a value: 
+
+- Search for it as in a binary search tree 
+- Splay the node containing the value to the root 
+- If not found splay the node that would had been the parent of the searched value 
+
+### Minimum and maximum 
+
+- Search the tree for the required value 
+- Splay the node to the root 
+
 ## Examples 
 
 ### Example 1
 
-![ZigEx1](Images/examplezigzig1.png)
+Lets suppose a *find(20)* operation was performed and now the values **20** needs to be splayed to the root. 
+The sequence of steps will be the following: 
+
 
-![ZigEx2](Images/examplezigzig2.png)
+1. Since we are in a *ZigZig* case, we need to rotate **9** to **4**
 
-![ZigEx3](Images/examplezigzig3.png)
+![ZiggEx1](Images/examplezigzig1.png)
+
+2. We got the following tree after the first rotation: 
+
+![ZiggEx2](Images/examplezigzig2.png)
+
+3. And finally the **20** is rotated to the **9**
+
+![ZiggEx3](Images/examplezigzig3.png)
 
 
 ### Example 2
 
-![ZigEx21](Images/example1-1.png)
+Now suppose a *insert(7)* operation was performed and we're in a *ZigZag* case.
+
+
+1. First **7** is rotated to **9**
+
+![ZigggEx21](Images/example1-1.png)
+
+2. And the result tree is: 
+
+![ZigggEx22](Images/example1-2.png)
 
-![ZigEx22](Images/example1-2.png)
+3. Finally **7** is rotated to **4**
+
+![ZigggEx23](Images/example1-3.png)
 
-![ZigEx23](Images/example1-3.png)
 
 ## Advantages 
 
@@ -135,10 +176,99 @@ With *n* being the number of items in the tree.
 
 # An example of the Worst Case Performance 
 
+Suppose the a sequence of consecutive values are inserted in an Splay Tree. 
+Let's take for example [1,2,3,4,5,6,7,8].
+
+The tree construction will be like following: 
+
+
+1. Insert the number **1**
+
+2. Insert **2** 
+
+
+![WorstCase1](Images/worst-case-1.png)
+
+
+3. Splay **2** to the root 
+
+
+![WorstCase2](Images/worst-case-2.png)
+
+
+4. Insert **3** 
+
+
+![WorstCase3](Images/worst-case-3.png)
+
+5. Splay **3** to the root 
+
+
+![WorstCase4](Images/worst-case-4.png)
+
+
+6. Insert **4** 
+
+
+![WorstCase5](Images/worst-case-5.png)
+
+
+7. After inserting the rest of the values the tree will look like this: 
+
+
+![WorstCase6](Images/worst-case-6.png)
+
+
+
+If we keep insert number following the same sequence, that tree becomes inbalanced and have a height of **n** with **n** being the numbers of values inserted. 
+After getting this tree, a *find(1)* operation for example will take **O(n)**
+
+## ZigZig rotation order: first grandparent
+
+But thanks to the properties of the **Splay Tree** and the *ZigZig* rotations after the *find(1)* operation the tree becomes balanced again. This only happens if we respect the order of the *ZigZig* rotation, and the rotation to the grandparent happens first. 
+
+The sequence of *ZigZigs* rotations will look like follows: 
+
+1. Rotate **2** to **3**
+
+![ZigZig1](Images/example-zigzig-1.png)
+
+2. Rotate **1** to **2** 
+
+![ZigZig2](Images/example-zigzig-2.png)
+
+3. Rotate **4** to **5**
+
+![ZigZig3](Images/example-zigzig-3.png)
+
+4. Rotate **1** to **4** 
+
+![ZigZig4](Images/example-zigzig-4.png)
+
+5. Finally after splaying **1** to the root the tree will look like this: 
+
+![ZigZig5](Images/example-zigzig-5.png)
+
+
+Based on the example above, we can see why it's important to rotate first to the grandparent. We got a tree of height = 6, from an initial tree of height = 8. If the tree would had been taller, we would have achieved almost half of the initial height after the splaying operation.
+
+## ZigZig wrong rotation order 
+
+If the rotations would had been taking first the parent and not the grandparent we would have finished with the following, yet unbalanced tree, just inverting the side of the elements.
+
+![ZigZigWrong](Images/zigzig-wrongrotated.png)
+
 
 ## See also
 
 [Splay Tree on Wikipedia](https://en.wikipedia.org/wiki/Splay_tree)
+
 [Splay Tree by University of California in Berkeley - CS 61B Lecture 34](https://www.youtube.com/watch?v=G5QIXywcJlY)
 
+
+----------------
+
 *Written for Swift Algorithm Club by Barbara Martina Rodeker*
+
+----------------
+

From 51ee1651fac832478d462396e7e4a82959c60c33 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 24 Jul 2017 17:37:41 -0700
Subject: [PATCH 039/643] Updated for Swift 4 Xcode 9b4

---
 Fizz Buzz/FizzBuzz.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Fizz Buzz/FizzBuzz.playground/Contents.swift b/Fizz Buzz/FizzBuzz.playground/Contents.swift
index ba2f83b15..37acdab61 100644
--- a/Fizz Buzz/FizzBuzz.playground/Contents.swift	
+++ b/Fizz Buzz/FizzBuzz.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func fizzBuzz(_ numberOfTurns: Int) {
   for i in 1...numberOfTurns {
     var result = ""

From d745696bb7b9a8988b079e3e7cdbe8e2a7b28e0c Mon Sep 17 00:00:00 2001
From: Sumit Paul <paulsumit1993@gmail.com>
Date: Tue, 25 Jul 2017 12:05:58 +0530
Subject: [PATCH 040/643] update Stack implementation to Swift 4 with Xcode 9b4

---
 Stack/Stack.playground/Contents.swift | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 1eb705f20..e9e3e9a57 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -1,3 +1,9 @@
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /*
   Stack
 

From 3f0d6971d3edd2cfaf7d69cf906ba0c61db03e37 Mon Sep 17 00:00:00 2001
From: Sumit Paul <paulsumit1993@gmail.com>
Date: Tue, 25 Jul 2017 15:12:09 +0530
Subject: [PATCH 041/643] update palindrome implementation to Swift 4 with
 Xcode 9b4

---
 Palindromes/Palindromes.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index b9e857dd0..44662745a 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 /**

From 679f82ae0b5222caf36ee0aa044696b35fc05bec Mon Sep 17 00:00:00 2001
From: Sumit Paul <paulsumit1993@gmail.com>
Date: Tue, 25 Jul 2017 15:28:12 +0530
Subject: [PATCH 042/643] update gcd implementation to Swift 4 with Xcode 9b4

---
 GCD/GCD.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index 2e264be93..977b80f57 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Recursive version
 func gcd(_ a: Int, _ b: Int) -> Int {
   let r = a % b

From 8073155a0a71665911e54aba21d4cd3ed24f6847 Mon Sep 17 00:00:00 2001
From: Benjamin Hendricks <hendricksbenjamin@gmail.com>
Date: Tue, 25 Jul 2017 13:31:25 +0100
Subject: [PATCH 043/643] claim TwoSum problem

---
 Two-Sum Problem/README.markdown | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index a20666efd..4eeb99dcb 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -1,5 +1,7 @@
 # Two-Sum Problem
 
+### About to be edited for Swift 4 woohoo!
+
 You're given an array `a` with numbers. Write an algorithm that checks if there are any two entries in the array that add up to a given number `k`. In other words, is there any `a[i] + a[j] == k`?
 
 There are a variety of solutions to this problem (some better than others). The following solutions both run in **O(n)** time.

From b3e0dddc22cb26425a2075f67bf339cb1d46fe89 Mon Sep 17 00:00:00 2001
From: Benjamin Hendricks <hendricksbenjamin@gmail.com>
Date: Tue, 25 Jul 2017 18:07:17 +0100
Subject: [PATCH 044/643] no changes needed for twosum for swift 4

---
 Two-Sum Problem/README.markdown                           | 2 --
 Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift | 1 +
 Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift | 1 +
 3 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index 4eeb99dcb..a20666efd 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -1,7 +1,5 @@
 # Two-Sum Problem
 
-### About to be edited for Swift 4 woohoo!
-
 You're given an array `a` with numbers. Write an algorithm that checks if there are any two entries in the array that add up to a given number `k`. In other words, is there any `a[i] + a[j] == k`?
 
 There are a variety of solutions to this problem (some better than others). The following solutions both run in **O(n)** time.
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 00ce05136..9cc83c5ed 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -1,4 +1,5 @@
 //: Playground - noun: a place where people can play
+// Last checked with: Version 9.0 beta 4 (9M189t)
 
 func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var map = [Int: Int]()
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift
index 9a555f0eb..b740dd3e6 100644
--- a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
@@ -1,4 +1,5 @@
 //: Playground - noun: a place where people can play
+// Last checked with: Version 9.0 beta 4 (9M189t)
 
 func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var i = 0

From efbc84a7cdfe979cda9ce2c09a8a05612bb87112 Mon Sep 17 00:00:00 2001
From: Benjamin Hendricks <hendricksbenjamin@gmail.com>
Date: Tue, 25 Jul 2017 18:41:47 +0100
Subject: [PATCH 045/643] add ifdef

---
 Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift   | 3 +++
 Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift   | 3 +++
 .../Solution 2/2Sum.playground/timeline.xctimeline          | 6 ------
 3 files changed, 6 insertions(+), 6 deletions(-)
 delete mode 100644 Two-Sum Problem/Solution 2/2Sum.playground/timeline.xctimeline

diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 9cc83c5ed..4de46128c 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -1,5 +1,8 @@
 //: Playground - noun: a place where people can play
 // Last checked with: Version 9.0 beta 4 (9M189t)
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var map = [Int: Int]()
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift
index b740dd3e6..4cb3d9283 100644
--- a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
@@ -1,5 +1,8 @@
 //: Playground - noun: a place where people can play
 // Last checked with: Version 9.0 beta 4 (9M189t)
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var i = 0
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/timeline.xctimeline b/Two-Sum Problem/Solution 2/2Sum.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Two-Sum Problem/Solution 2/2Sum.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 49569597b19bc2c46277662a525163bd9d1979cd Mon Sep 17 00:00:00 2001
From: Sumit Paul <paulsumit1993@gmail.com>
Date: Tue, 25 Jul 2017 23:49:54 +0530
Subject: [PATCH 046/643] update queue implementation to Swift 4 with Xcode 9b4

---
 Queue/Queue.playground/Contents.swift | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index 08327783f..22d2a84ca 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -1,3 +1,9 @@
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /*
   Queue
 

From e30d68d8112ef069305d93dca33fede27e88e519 Mon Sep 17 00:00:00 2001
From: Vladimir Grigoriev <vladimir.grigoriev@appus.me>
Date: Wed, 26 Jul 2017 11:38:58 +0300
Subject: [PATCH 047/643] Correct typo

Algorithm doesn't work because of usage of incorrect vertices's set.
---
 .../Dijkstra.playground/Sources/Dijkstra.swift              | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
index 9c5961c71..8cda797dd 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
@@ -19,7 +19,7 @@ public class Dijkstra {
         var currentVertex: Vertex? = startVertex
         while let vertex = currentVertex {
             currentVertices.remove(vertex)
-            let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
+            let filteredNeighbors = vertex.neighbors.filter { currentVertices.contains($0.0) }
             for neighbor in filteredNeighbors {
                 let neighborVertex = neighbor.0
                 let weight = neighbor.1
@@ -31,11 +31,11 @@ public class Dijkstra {
                     neighborVertex.pathVerticesFromStart.append(neighborVertex)
                 }
             }
-            if totalVertices.isEmpty {
+            if currentVertices.isEmpty {
                 currentVertex = nil
                 break
             }
-            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
+            currentVertex = currentVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
         }
     }
 }

From acc61b25e3af1f9180f73e49dbf388c1020c9854 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Wed, 26 Jul 2017 11:43:47 -0700
Subject: [PATCH 048/643] Count Occurrences to Swift 4

Tested Count Occurrences with Swift 4 and Xcode 9.0b4
---
 .../CountOccurrences.playground/Contents.swift              | 5 ++++-
 .../CountOccurrences.playground/timeline.xctimeline         | 6 ------
 2 files changed, 4 insertions(+), 7 deletions(-)
 delete mode 100644 Count Occurrences/CountOccurrences.playground/timeline.xctimeline

diff --git a/Count Occurrences/CountOccurrences.playground/Contents.swift b/Count Occurrences/CountOccurrences.playground/Contents.swift
index b4392d501..6138b74ac 100644
--- a/Count Occurrences/CountOccurrences.playground/Contents.swift	
+++ b/Count Occurrences/CountOccurrences.playground/Contents.swift	
@@ -1,4 +1,7 @@
-//: Playground - noun: a place where people can play
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
 
 func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
   func leftBoundary() -> Int {
diff --git a/Count Occurrences/CountOccurrences.playground/timeline.xctimeline b/Count Occurrences/CountOccurrences.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Count Occurrences/CountOccurrences.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From c679dcbd3fc856176f1d62e475110634934056b6 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Wed, 26 Jul 2017 12:24:25 -0700
Subject: [PATCH 049/643] Fixed Size Array to Swift 4

Tested Fixed Size Array with Swift 4 and Xcode 9.0b4
---
 Fixed Size Array/FixedSizeArray.playground/Contents.swift | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
index 8ef545e45..8b5bc1147 100644
--- a/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
+
 /*
  An unordered array with a maximum size.
  
@@ -53,3 +58,4 @@ array.append(2)
 array[1]
 array.removeAt(index: 0)
 array.removeAll()
+

From aff5a595a3c3f8939496f2773995bc7b6ee0cdf8 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Wed, 26 Jul 2017 18:57:45 -0700
Subject: [PATCH 050/643] Boyer Moore to Swift 4

Updated Boyer Moore to Swift 4 and Xcode 9.0b4
---
 .../BoyerMoore.playground/Contents.swift      |  5 ++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 26 +++++++++++++++----
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 ++-
 3 files changed, 29 insertions(+), 6 deletions(-)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore/BoyerMoore.playground/Contents.swift
index f553e1a00..e88a1b93d 100644
--- a/Boyer-Moore/BoyerMoore.playground/Contents.swift
+++ b/Boyer-Moore/BoyerMoore.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+    print("Hello, Swift 4!")
+#endif
+
 /*
   Boyer-Moore string search
 
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
index c4a005163..6fc005d43 100644
--- a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
@@ -16,7 +16,7 @@
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreTests.swift; sourceTree = SOURCE_ROOT; };
-		9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoyerMoore.swift; path = ../../BoyerMoore.swift; sourceTree = "<group>"; };
+		9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoyerMoore.swift; path = ../BoyerMoore.swift; sourceTree = SOURCE_ROOT; };
 		9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreHorspoolTests.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
@@ -87,12 +87,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 0900;
 					};
 				};
 			};
@@ -162,14 +162,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -197,6 +203,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 			};
 			name = Debug;
 		};
@@ -208,14 +215,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -236,6 +249,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 			};
 			name = Release;
 		};
@@ -247,7 +261,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -259,7 +274,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 14f27f777..538a6f4fa 100644
--- a/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,6 +26,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -46,6 +47,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 48eced4ff385e3829848cff2c3c3ad8f1c449638 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sat, 29 Jul 2017 21:04:30 -0700
Subject: [PATCH 051/643] [Swift 4] Update Shuffle to Swift 4

---
 Shuffle/Shuffle.playground/Contents.swift     | 35 ++----------
 .../Shuffle.playground/Sources/Shuffle.swift  | 39 ++++++++++++++
 .../Shuffle.playground/timeline.xctimeline    |  6 ---
 Shuffle/Shuffle.swift                         | 54 +++++++++++--------
 4 files changed, 75 insertions(+), 59 deletions(-)
 create mode 100644 Shuffle/Shuffle.playground/Sources/Shuffle.swift
 delete mode 100644 Shuffle/Shuffle.playground/timeline.xctimeline

diff --git a/Shuffle/Shuffle.playground/Contents.swift b/Shuffle/Shuffle.playground/Contents.swift
index 704a94e7d..ac9181660 100644
--- a/Shuffle/Shuffle.playground/Contents.swift
+++ b/Shuffle/Shuffle.playground/Contents.swift
@@ -1,40 +1,15 @@
 //: Playground - noun: a place where people can play
 
-import Foundation
-
-/* Returns a random integer between 0 and n-1. */
-public func random(_ n: Int) -> Int {
-  return Int(arc4random_uniform(UInt32(n)))
-}
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
-/* Fisher-Yates / Knuth shuffle */
-extension Array {
-  public mutating func shuffle() {
-    for i in stride(from: count - 1, through: 1, by: -1) {
-      let j = random(i + 1)
-      if i != j {
-        swap(&self[i], &self[j])
-      }
-    }
-  }
-}
+import Foundation
 
 var list = [ "a", "b", "c", "d", "e", "f", "g" ]
 list.shuffle()
 list.shuffle()
 list.shuffle()
 
-/* Create a new array of numbers that is already shuffled. */
-public func shuffledArray(_ n: Int) -> [Int] {
-  var a = [Int](repeating: 0, count: n)
-  for i in 0..<n {
-    let j = random(i + 1)
-    if i != j {
-      a[i] = a[j]
-    }
-    a[j] = i
-  }
-  return a
-}
-
 let numbers = shuffledArray(10)
diff --git a/Shuffle/Shuffle.playground/Sources/Shuffle.swift b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
new file mode 100644
index 000000000..63fea2899
--- /dev/null
+++ b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
@@ -0,0 +1,39 @@
+import Foundation
+
+/* Returns a random integer between 0 and n-1. */
+public func random(_ n: Int) -> Int {
+    return Int(arc4random_uniform(UInt32(n)))
+}
+
+extension Array {
+  /*
+    Randomly shuffles the array in-place
+    This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
+    Time complexity: O(n)
+  */
+  public mutating func shuffle() {
+    for i in (1...count-1).reversed() {
+      let j = random(i + 1)
+      if i != j {
+        let t = self[i]
+        self[i] = self[j]
+        self[j] = t
+      }
+    }
+  }
+}
+
+/*
+  Simultaneously initializes an array with the values 0...n-1 and shuffles it.
+*/
+public func shuffledArray(_ n: Int) -> [Int] {
+  var a = Array(repeating: 0, count: n)
+  for i in 0..<n {
+    let j = random(i + 1)
+    if i != j {
+      a[i] = a[j]
+    }
+    a[j] = i  // insert next number from the sequence
+  }
+  return a
+}
diff --git a/Shuffle/Shuffle.playground/timeline.xctimeline b/Shuffle/Shuffle.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Shuffle/Shuffle.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Shuffle/Shuffle.swift b/Shuffle/Shuffle.swift
index 8fe8b4e87..19112fa37 100644
--- a/Shuffle/Shuffle.swift
+++ b/Shuffle/Shuffle.swift
@@ -1,32 +1,40 @@
 import Foundation
 
+/* Returns a random integer between 0 and n-1. */
+public func random(_ n: Int) -> Int {
+    return Int(arc4random_uniform(UInt32(n)))
+}
+
 extension Array {
-  /*
-    Randomly shuffles the array in-place
-    This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
-    Time complexity: O(n)
-  */
-  public mutating func shuffle() {
-    for i in (count - 1).stride(through: 1, by: -1) {
-      let j = random(i + 1)
-      if i != j {
-        swap(&self[i], &self[j])
-      }
+    /*
+     Randomly shuffles the array in-place
+     This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
+     Time complexity: O(n)
+     */
+    public mutating func shuffle() {
+        for i in (1...count-1).reversed() {
+            let j = random(i + 1)
+            if i != j {
+                let t = self[i]
+                self[i] = self[j]
+                self[j] = t
+            }
+        }
     }
-  }
 }
 
 /*
-  Simultaneously initializes an array with the values 0...n-1 and shuffles it.
-*/
-public func shuffledArray(n: Int) -> [Int] {
-  var a = [Int](count: n, repeatedValue: 0)
-  for i in 0..<n {
-    let j = random(i + 1)
-    if i != j {
-      a[i] = a[j]
+ Simultaneously initializes an array with the values 0...n-1 and shuffles it.
+ */
+public func shuffledArray(_ n: Int) -> [Int] {
+    var a = Array(repeating: 0, count: n)
+    for i in 0..<n {
+        let j = random(i + 1)
+        if i != j {
+            a[i] = a[j]
+        }
+        a[j] = i  // insert next number from the sequence
     }
-    a[j] = i  // insert next number from the sequence
-  }
-  return a
+    return a
 }
+

From 088b4347b6bdf84d42b456b2e09099ecf5ff1901 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 07:43:59 -0700
Subject: [PATCH 052/643] [Swift 4] Update Union Find

---
 Union-Find/UnionFind.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index b1f7fb4e1..6ac3b4c4e 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 var dsu = UnionFindQuickUnion<Int>()
 
 for i in 1...10 {

From c18e01c3fd1e8a2444e0967b8ce165926f82d3d7 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 07:50:07 -0700
Subject: [PATCH 053/643] [Swift 4] Update Trie

---
 Trie/Trie/Trie/Trie.swift           | 5 +++++
 Trie/Trie/Trie/ViewController.swift | 5 +++++
 Trie/Trie/TrieTests/TrieTests.swift | 5 +++++
 3 files changed, 15 insertions(+)

diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index 856384fff..1a7017c4c 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -6,6 +6,11 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+    print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 /// A node in the trie
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
index 928b01f4c..9c5e66163 100644
--- a/Trie/Trie/Trie/ViewController.swift
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -6,6 +6,11 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+    print("Hello, Swift 4!")
+#endif
+
 import Cocoa
 
 class ViewController: NSViewController {
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index b69c5666e..45be03aad 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -6,6 +6,11 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+    print("Hello, Swift 4!")
+#endif
+
 import XCTest
 @testable import Trie
 

From e36e7119714e164c0997eb1365334a4fa6979346 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 07:56:08 -0700
Subject: [PATCH 054/643] [Swift 4] Update Tree

---
 Tree/Tree.playground/Contents.swift      | 29 ++-----------
 Tree/Tree.playground/Sources/Tree.swift  | 39 +++++++++++++++++
 Tree/Tree.playground/timeline.xctimeline |  6 ---
 Tree/Tree.swift                          | 53 ++++++++++++------------
 4 files changed, 70 insertions(+), 57 deletions(-)
 create mode 100644 Tree/Tree.playground/Sources/Tree.swift
 delete mode 100644 Tree/Tree.playground/timeline.xctimeline

diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index d59b7eedb..49cf41054 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -1,30 +1,9 @@
 //: Playground - noun: a place where people can play
 
-public class TreeNode<T> {
-  public var value: T
-
-  public weak var parent: TreeNode?
-  public var children = [TreeNode<T>]()
-
-  public init(value: T) {
-    self.value = value
-  }
-
-  public func addChild(_ node: TreeNode<T>) {
-    children.append(node)
-    node.parent = self
-  }
-}
-
-extension TreeNode: CustomStringConvertible {
-  public var description: String {
-    var s = "\(value)"
-    if !children.isEmpty {
-      s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
-    }
-    return s
-  }
-}
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 let tree = TreeNode<String>(value: "beverages")
 
diff --git a/Tree/Tree.playground/Sources/Tree.swift b/Tree/Tree.playground/Sources/Tree.swift
new file mode 100644
index 000000000..fa49f25e9
--- /dev/null
+++ b/Tree/Tree.playground/Sources/Tree.swift
@@ -0,0 +1,39 @@
+public class TreeNode<T> {
+  public var value: T
+
+  public weak var parent: TreeNode?
+  public var children = [TreeNode<T>]()
+
+  public init(value: T) {
+    self.value = value
+  }
+
+  public func addChild(_ node: TreeNode<T>) {
+    children.append(node)
+    node.parent = self
+  }
+}
+
+extension TreeNode: CustomStringConvertible {
+  public var description: String {
+    var s = "\(value)"
+    if !children.isEmpty {
+      s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
+    }
+    return s
+  }
+}
+
+extension TreeNode where T: Equatable {
+  public func search(_ value: T) -> TreeNode? {
+    if value == self.value {
+      return self
+    }
+    for child in children {
+      if let found = child.search(value) {
+        return found
+      }
+    }
+    return nil
+  }
+}
diff --git a/Tree/Tree.playground/timeline.xctimeline b/Tree/Tree.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Tree/Tree.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Tree/Tree.swift b/Tree/Tree.swift
index fa49f25e9..08cb61eb5 100644
--- a/Tree/Tree.swift
+++ b/Tree/Tree.swift
@@ -1,39 +1,40 @@
 public class TreeNode<T> {
-  public var value: T
+    public var value: T
 
-  public weak var parent: TreeNode?
-  public var children = [TreeNode<T>]()
+    public weak var parent: TreeNode?
+    public var children = [TreeNode<T>]()
 
-  public init(value: T) {
-    self.value = value
-  }
+    public init(value: T) {
+        self.value = value
+    }
 
-  public func addChild(_ node: TreeNode<T>) {
-    children.append(node)
-    node.parent = self
-  }
+    public func addChild(_ node: TreeNode<T>) {
+        children.append(node)
+        node.parent = self
+    }
 }
 
 extension TreeNode: CustomStringConvertible {
-  public var description: String {
-    var s = "\(value)"
-    if !children.isEmpty {
-      s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
+    public var description: String {
+        var s = "\(value)"
+        if !children.isEmpty {
+            s += " {" + children.map { $0.description }.joined(separator: ", ") + "}"
+        }
+        return s
     }
-    return s
-  }
 }
 
 extension TreeNode where T: Equatable {
-  public func search(_ value: T) -> TreeNode? {
-    if value == self.value {
-      return self
+    public func search(_ value: T) -> TreeNode? {
+        if value == self.value {
+            return self
+        }
+        for child in children {
+            if let found = child.search(value) {
+                return found
+            }
+        }
+        return nil
     }
-    for child in children {
-      if let found = child.search(value) {
-        return found
-      }
-    }
-    return nil
-  }
 }
+

From 71a78276cdcaab0e1e7b7be57733caaf83757a57 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 07:58:36 -0700
Subject: [PATCH 055/643] [Swift 4] Update Topological Sort

---
 Topological Sort/Topological Sort.playground/Contents.swift | 5 +++++
 .../Topological Sort.playground/timeline.xctimeline         | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Topological Sort/Topological Sort.playground/timeline.xctimeline

diff --git a/Topological Sort/Topological Sort.playground/Contents.swift b/Topological Sort/Topological Sort.playground/Contents.swift
index 8f78c388a..3921d37fc 100644
--- a/Topological Sort/Topological Sort.playground/Contents.swift	
+++ b/Topological Sort/Topological Sort.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import UIKit
 
 let graph = Graph()
diff --git a/Topological Sort/Topological Sort.playground/timeline.xctimeline b/Topological Sort/Topological Sort.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Topological Sort/Topological Sort.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 207d7f916d59f05c9cc16c44bf8fbc7f93795638 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:08:51 -0700
Subject: [PATCH 056/643] [Swift 4] Update Selection Sort

---
 .../SelectionSort.playground/Contents.swift   | 20 +++---------
 .../Sources/SelectionSort.swift               | 21 ++++++++++++
 .../timeline.xctimeline                       |  6 ----
 Selection Sort/SelectionSort.swift            | 32 +++++++++----------
 .../contents.xcworkspacedata                  |  6 ++--
 5 files changed, 44 insertions(+), 41 deletions(-)
 create mode 100644 Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
 delete mode 100644 Selection Sort/SelectionSort.playground/timeline.xctimeline

diff --git a/Selection Sort/SelectionSort.playground/Contents.swift b/Selection Sort/SelectionSort.playground/Contents.swift
index bd8c7cccf..e0bfdf259 100644
--- a/Selection Sort/SelectionSort.playground/Contents.swift	
+++ b/Selection Sort/SelectionSort.playground/Contents.swift	
@@ -1,21 +1,9 @@
 //: Playground - noun: a place where people can play
 
-func selectionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
-  guard array.count > 1 else { return array }
-  var a = array
-  for x in 0 ..< a.count - 1 {
-    var lowest = x
-    for y in x + 1 ..< a.count {
-      if isOrderedBefore(a[y], a[lowest]) {
-        lowest = y
-      }
-    }
-    if x != lowest {
-      swap(&a[x], &a[lowest])
-    }
-  }
-  return a
-}
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
 selectionSort(list, <)
diff --git a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
new file mode 100644
index 000000000..3015fde9b
--- /dev/null
+++ b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
@@ -0,0 +1,21 @@
+public func selectionSort<T: Comparable>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+  guard array.count > 1 else { return array }
+
+  var a = array
+  for x in 0 ..< a.count - 1 {
+
+    // Find the lowest value in the rest of the array.
+    var lowest = x
+    for y in x + 1 ..< a.count {
+      if isOrderedBefore(a[y], a[lowest]) {
+        lowest = y
+      }
+    }
+
+    // Swap the lowest value with the current array index.
+    if x != lowest {
+      a.swapAt(x, lowest)
+    }
+  }
+  return a
+}
diff --git a/Selection Sort/SelectionSort.playground/timeline.xctimeline b/Selection Sort/SelectionSort.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Selection Sort/SelectionSort.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Selection Sort/SelectionSort.swift b/Selection Sort/SelectionSort.swift
index e02c87259..943ae628d 100644
--- a/Selection Sort/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.swift	
@@ -1,21 +1,21 @@
-func selectionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
-  guard array.count > 1 else { return array }
+public func selectionSort<T: Comparable>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+    guard array.count > 1 else { return array }
 
-  var a = array
-  for x in 0 ..< a.count - 1 {
+    var a = array
+    for x in 0 ..< a.count - 1 {
 
-    // Find the lowest value in the rest of the array.
-    var lowest = x
-    for y in x + 1 ..< a.count {
-      if isOrderedBefore(a[y], a[lowest]) {
-        lowest = y
-      }
-    }
+        // Find the lowest value in the rest of the array.
+        var lowest = x
+        for y in x + 1 ..< a.count {
+            if isOrderedBefore(a[y], a[lowest]) {
+                lowest = y
+            }
+        }
 
-    // Swap the lowest value with the current array index.
-    if x != lowest {
-      swap(&a[x], &a[lowest])
+        // Swap the lowest value with the current array index.
+        if x != lowest {
+            a.swapAt(x, lowest)
+        }
     }
-  }
-  return a
+    return a
 }
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7ca193aca..db4691648 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -2058,9 +2058,6 @@
       <FileRef
          location = "group:SelectionSort.playground">
       </FileRef>
-      <FileRef
-         location = "group:SelectionSort.swift">
-      </FileRef>
       <Group
          location = "group:Tests"
          name = "Tests">
@@ -2074,6 +2071,9 @@
             location = "group:Tests.xcodeproj">
          </FileRef>
       </Group>
+      <FileRef
+         location = "group:SelectionSort.swift">
+      </FileRef>
    </Group>
    <Group
       location = "group:Set Cover (Unweighted)"

From fb5c1978dacaad89f4a83ce6dd00dff897e3f7e8 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:11:57 -0700
Subject: [PATCH 057/643] [Swift 4] Update Segment Tree

---
 Segment Tree/SegmentTree.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Segment Tree/SegmentTree.playground/Contents.swift b/Segment Tree/SegmentTree.playground/Contents.swift
index 3a758981f..25116c285 100644
--- a/Segment Tree/SegmentTree.playground/Contents.swift	
+++ b/Segment Tree/SegmentTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public class SegmentTree<T> {
 
 	private var value: T

From a5ca2a8f9e887c61f7559ed7fc75e1e308a73e7f Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:16:03 -0700
Subject: [PATCH 058/643] [Swift 4] Update Merge Sort

---
 Merge Sort/MergeSort.playground/Contents.swift      | 5 +++++
 Merge Sort/MergeSort.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Merge Sort/MergeSort.playground/timeline.xctimeline

diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index f5a1dbbcf..06fa3beaa 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -1,5 +1,10 @@
 /* Top-down recursive version */
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func mergeSort<T: Comparable>(_ array: [T]) -> [T] {
   guard array.count > 1 else { return array }
   let middleIndex = array.count / 2
diff --git a/Merge Sort/MergeSort.playground/timeline.xctimeline b/Merge Sort/MergeSort.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Merge Sort/MergeSort.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From a5dc48eb316405d610c3547eb7c4d31c529065bf Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:34:12 -0700
Subject: [PATCH 059/643] [Swift 4] Update Heap

---
 Heap/Heap.swift                               | 430 ++++++------
 Heap/Tests/HeapTests.swift                    | 615 +++++++++---------
 Heap/Tests/Tests.xcodeproj/project.pbxproj    |   4 +-
 .../xcshareddata/xcschemes/Tests.xcscheme     |   2 +
 4 files changed, 530 insertions(+), 521 deletions(-)

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index 80b40c65f..18a350dca 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -4,224 +4,224 @@
 //
 
 public struct Heap<T> {
-  /** The array that stores the heap's nodes. */
-  var elements = [T]()
-
-  /** Determines whether this is a max-heap (>) or min-heap (<). */
-  fileprivate var isOrderedBefore: (T, T) -> Bool
-
-  /**
-   * Creates an empty heap.
-   * The sort function determines whether this is a min-heap or max-heap.
-   * For integers, > makes a max-heap, < makes a min-heap.
-   */
-  public init(sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
-  }
-
-  /**
-   * Creates a heap from an array. The order of the array does not matter;
-   * the elements are inserted into the heap in the order determined by the
-   * sort function.
-   */
-  public init(array: [T], sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
-    buildHeap(fromArray: array)
-  }
-
-  /*
-  // This version has O(n log n) performance.
-  private mutating func buildHeap(array: [T]) {
-    elements.reserveCapacity(array.count)
-    for value in array {
-      insert(value)
-    }
-  }
-  */
-
-  /**
-   * Converts an array to a max-heap or min-heap in a bottom-up manner.
-   * Performance: This runs pretty much in O(n).
-   */
-  fileprivate mutating func buildHeap(fromArray array: [T]) {
-    elements = array
-    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-      shiftDown(i, heapSize: elements.count)
-    }
-  }
-
-  public var isEmpty: Bool {
-    return elements.isEmpty
-  }
-
-  public var count: Int {
-    return elements.count
-  }
-
-  /**
-   * Returns the index of the parent of the element at index i.
-   * The element at index 0 is the root of the tree and has no parent.
-   */
-  @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
-    return (i - 1) / 2
-  }
-
-  /**
-   * Returns the index of the left child of the element at index i.
-   * Note that this index can be greater than the heap size, in which case
-   * there is no left child.
-   */
-  @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
-    return 2*i + 1
-  }
-
-  /**
-   * Returns the index of the right child of the element at index i.
-   * Note that this index can be greater than the heap size, in which case
-   * there is no right child.
-   */
-  @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
-    return 2*i + 2
-  }
-
-  /**
-   * Returns the maximum value in the heap (for a max-heap) or the minimum
-   * value (for a min-heap).
-   */
-  public func peek() -> T? {
-    return elements.first
-  }
-
-  /**
-   * Adds a new value to the heap. This reorders the heap so that the max-heap
-   * or min-heap property still holds. Performance: O(log n).
-   */
-  public mutating func insert(_ value: T) {
-    elements.append(value)
-    shiftUp(elements.count - 1)
-  }
-
-  public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
-    for value in sequence {
-      insert(value)
-    }
-  }
-
-  /**
-   * Allows you to change an element. In a max-heap, the new element should be
-   * larger than the old one; in a min-heap it should be smaller.
-   */
-  public mutating func replace(index i: Int, value: T) {
-    guard i < elements.count else { return }
-
-    assert(isOrderedBefore(value, elements[i]))
-    elements[i] = value
-    shiftUp(i)
-  }
-
-  /**
-   * Removes the root node from the heap. For a max-heap, this is the maximum
-   * value; for a min-heap it is the minimum value. Performance: O(log n).
-   */
-  @discardableResult public mutating func remove() -> T? {
-    if elements.isEmpty {
-      return nil
-    } else if elements.count == 1 {
-      return elements.removeLast()
-    } else {
-      // Use the last node to replace the first one, then fix the heap by
-      // shifting this new first node into its proper position.
-      let value = elements[0]
-      elements[0] = elements.removeLast()
-      shiftDown()
-      return value
-    }
-  }
-
-  /**
-   * Removes an arbitrary node from the heap. Performance: O(log n). You need
-   * to know the node's index, which may actually take O(n) steps to find.
-   */
-  public mutating func removeAt(_ index: Int) -> T? {
-    guard index < elements.count else { return nil }
-
-    let size = elements.count - 1
-    if index != size {
-      swap(&elements[index], &elements[size])
-      shiftDown(index, heapSize: size)
-      shiftUp(index)
-    }
-    return elements.removeLast()
-  }
-
-  /**
-   * Takes a child node and looks at its parents; if a parent is not larger
-   * (max-heap) or not smaller (min-heap) than the child, we exchange them.
-   */
-  mutating func shiftUp(_ index: Int) {
-    var childIndex = index
-    let child = elements[childIndex]
-    var parentIndex = self.parentIndex(ofIndex: childIndex)
-
-    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
-      elements[childIndex] = elements[parentIndex]
-      childIndex = parentIndex
-      parentIndex = self.parentIndex(ofIndex: childIndex)
-    }
-
-    elements[childIndex] = child
-  }
-
-  mutating func shiftDown() {
-    shiftDown(0, heapSize: elements.count)
-  }
-
-  /**
-   * Looks at a parent node and makes sure it is still larger (max-heap) or
-   * smaller (min-heap) than its childeren.
-   */
-  mutating func shiftDown(_ index: Int, heapSize: Int) {
-    var parentIndex = index
-
-    while true {
-      let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
-      let rightChildIndex = leftChildIndex + 1
-
-      // Figure out which comes first if we order them by the sort function:
-      // the parent, the left child, or the right child. If the parent comes
-      // first, we're done. If not, that element is out-of-place and we make
-      // it "float down" the tree until the heap property is restored.
-      var first = parentIndex
-      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
-        first = leftChildIndex
-      }
-      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
-        first = rightChildIndex
-      }
-      if first == parentIndex { return }
-
-      swap(&elements[parentIndex], &elements[first])
-      parentIndex = first
-    }
-  }
+    /** The array that stores the heap's nodes. */
+    var elements = [T]()
+
+    /** Determines whether this is a max-heap (>) or min-heap (<). */
+    fileprivate var isOrderedBefore: (T, T) -> Bool
+
+    /**
+     * Creates an empty heap.
+     * The sort function determines whether this is a min-heap or max-heap.
+     * For integers, > makes a max-heap, < makes a min-heap.
+     */
+    public init(sort: @escaping (T, T) -> Bool) {
+        self.isOrderedBefore = sort
+    }
+
+    /**
+     * Creates a heap from an array. The order of the array does not matter;
+     * the elements are inserted into the heap in the order determined by the
+     * sort function.
+     */
+    public init(array: [T], sort: @escaping (T, T) -> Bool) {
+        self.isOrderedBefore = sort
+        buildHeap(fromArray: array)
+    }
+
+    /*
+     // This version has O(n log n) performance.
+     private mutating func buildHeap(array: [T]) {
+     elements.reserveCapacity(array.count)
+     for value in array {
+     insert(value)
+     }
+     }
+     */
+
+    /**
+     * Converts an array to a max-heap or min-heap in a bottom-up manner.
+     * Performance: This runs pretty much in O(n).
+     */
+    fileprivate mutating func buildHeap(fromArray array: [T]) {
+        elements = array
+        for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+            shiftDown(i, heapSize: elements.count)
+        }
+    }
+
+    public var isEmpty: Bool {
+        return elements.isEmpty
+    }
+
+    public var count: Int {
+        return elements.count
+    }
+
+    /**
+     * Returns the index of the parent of the element at index i.
+     * The element at index 0 is the root of the tree and has no parent.
+     */
+    @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
+        return (i - 1) / 2
+    }
+
+    /**
+     * Returns the index of the left child of the element at index i.
+     * Note that this index can be greater than the heap size, in which case
+     * there is no left child.
+     */
+    @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 1
+    }
+
+    /**
+     * Returns the index of the right child of the element at index i.
+     * Note that this index can be greater than the heap size, in which case
+     * there is no right child.
+     */
+    @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 2
+    }
+
+    /**
+     * Returns the maximum value in the heap (for a max-heap) or the minimum
+     * value (for a min-heap).
+     */
+    public func peek() -> T? {
+        return elements.first
+    }
+
+    /**
+     * Adds a new value to the heap. This reorders the heap so that the max-heap
+     * or min-heap property still holds. Performance: O(log n).
+     */
+    public mutating func insert(_ value: T) {
+        elements.append(value)
+        shiftUp(elements.count - 1)
+    }
+
+    public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+        for value in sequence {
+            insert(value)
+        }
+    }
+
+    /**
+     * Allows you to change an element. In a max-heap, the new element should be
+     * larger than the old one; in a min-heap it should be smaller.
+     */
+    public mutating func replace(index i: Int, value: T) {
+        guard i < elements.count else { return }
+
+        assert(isOrderedBefore(value, elements[i]))
+        elements[i] = value
+        shiftUp(i)
+    }
+
+    /**
+     * Removes the root node from the heap. For a max-heap, this is the maximum
+     * value; for a min-heap it is the minimum value. Performance: O(log n).
+     */
+    @discardableResult public mutating func remove() -> T? {
+        if elements.isEmpty {
+            return nil
+        } else if elements.count == 1 {
+            return elements.removeLast()
+        } else {
+            // Use the last node to replace the first one, then fix the heap by
+            // shifting this new first node into its proper position.
+            let value = elements[0]
+            elements[0] = elements.removeLast()
+            shiftDown()
+            return value
+        }
+    }
+
+    /**
+     * Removes an arbitrary node from the heap. Performance: O(log n). You need
+     * to know the node's index, which may actually take O(n) steps to find.
+     */
+    public mutating func removeAt(_ index: Int) -> T? {
+        guard index < elements.count else { return nil }
+
+        let size = elements.count - 1
+        if index != size {
+            elements.swapAt(index, size)
+            shiftDown(index, heapSize: size)
+            shiftUp(index)
+        }
+        return elements.removeLast()
+    }
+
+    /**
+     * Takes a child node and looks at its parents; if a parent is not larger
+     * (max-heap) or not smaller (min-heap) than the child, we exchange them.
+     */
+    mutating func shiftUp(_ index: Int) {
+        var childIndex = index
+        let child = elements[childIndex]
+        var parentIndex = self.parentIndex(ofIndex: childIndex)
+
+        while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+            elements[childIndex] = elements[parentIndex]
+            childIndex = parentIndex
+            parentIndex = self.parentIndex(ofIndex: childIndex)
+        }
+
+        elements[childIndex] = child
+    }
+
+    mutating func shiftDown() {
+        shiftDown(0, heapSize: elements.count)
+    }
+
+    /**
+     * Looks at a parent node and makes sure it is still larger (max-heap) or
+     * smaller (min-heap) than its childeren.
+     */
+    mutating func shiftDown(_ index: Int, heapSize: Int) {
+        var parentIndex = index
+
+        while true {
+            let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+            let rightChildIndex = leftChildIndex + 1
+
+            // Figure out which comes first if we order them by the sort function:
+            // the parent, the left child, or the right child. If the parent comes
+            // first, we're done. If not, that element is out-of-place and we make
+            // it "float down" the tree until the heap property is restored.
+            var first = parentIndex
+            if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+                first = leftChildIndex
+            }
+            if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+                first = rightChildIndex
+            }
+            if first == parentIndex { return }
+
+            elements.swapAt(parentIndex, first)
+            parentIndex = first
+        }
+    }
 }
 
 // MARK: - Searching
 
 extension Heap where T: Equatable {
-  /**
-   * Searches the heap for the given element. Performance: O(n).
-   */
-  public func index(of element: T) -> Int? {
-    return index(of: element, 0)
-  }
-
-  fileprivate func index(of element: T, _ i: Int) -> Int? {
-    if i >= count { return nil }
-    if isOrderedBefore(element, elements[i]) { return nil }
-    if element == elements[i] { return i }
-    if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
-    if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
-    return nil
-  }
+    /**
+     * Searches the heap for the given element. Performance: O(n).
+     */
+    public func index(of element: T) -> Int? {
+        return index(of: element, 0)
+    }
+
+    fileprivate func index(of element: T, _ i: Int) -> Int? {
+        if i >= count { return nil }
+        if isOrderedBefore(element, elements[i]) { return nil }
+        if element == elements[i] { return i }
+        if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
+        if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
+        return nil
+    }
 }
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index cac934406..0af3a14e0 100644
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -7,317 +7,324 @@ import XCTest
 
 class HeapTests: XCTestCase {
 
-  fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
-    for i in 0..<h.count {
-      let left = h.leftChildIndex(ofIndex: i)
-      let right = h.rightChildIndex(ofIndex: i)
-      let parent = h.parentIndex(ofIndex: i)
-      if left < h.count && h.elements[i] < h.elements[left] { return false }
-      if right < h.count && h.elements[i] < h.elements[right] { return false }
-      if i > 0 && h.elements[parent] < h.elements[i] { return false }
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
     }
-    return true
-  }
-
-  fileprivate func verifyMinHeap(_ h: Heap<Int>) -> Bool {
-    for i in 0..<h.count {
-      let left = h.leftChildIndex(ofIndex: i)
-      let right = h.rightChildIndex(ofIndex: i)
-      let parent = h.parentIndex(ofIndex: i)
-      if left < h.count && h.elements[i] > h.elements[left] { return false }
-      if right < h.count && h.elements[i] > h.elements[right] { return false }
-      if i > 0 && h.elements[parent] > h.elements[i] { return false }
+
+    fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
+        for i in 0..<h.count {
+            let left = h.leftChildIndex(ofIndex: i)
+            let right = h.rightChildIndex(ofIndex: i)
+            let parent = h.parentIndex(ofIndex: i)
+            if left < h.count && h.elements[i] < h.elements[left] { return false }
+            if right < h.count && h.elements[i] < h.elements[right] { return false }
+            if i > 0 && h.elements[parent] < h.elements[i] { return false }
+        }
+        return true
+    }
+
+    fileprivate func verifyMinHeap(_ h: Heap<Int>) -> Bool {
+        for i in 0..<h.count {
+            let left = h.leftChildIndex(ofIndex: i)
+            let right = h.rightChildIndex(ofIndex: i)
+            let parent = h.parentIndex(ofIndex: i)
+            if left < h.count && h.elements[i] > h.elements[left] { return false }
+            if right < h.count && h.elements[i] > h.elements[right] { return false }
+            if i > 0 && h.elements[parent] > h.elements[i] { return false }
+        }
+        return true
+    }
+
+    fileprivate func isPermutation(_ array1: [Int], _ array2: [Int]) -> Bool {
+        var a1 = array1
+        var a2 = array2
+        if a1.count != a2.count { return false }
+        while a1.count > 0 {
+            if let i = a2.index(of: a1[0]) {
+                a1.remove(at: 0)
+                a2.remove(at: i)
+            } else {
+                return false
+            }
+        }
+        return a2.count == 0
+    }
+
+    func testEmptyHeap() {
+        var heap = Heap<Int>(sort: <)
+        XCTAssertTrue(heap.isEmpty)
+        XCTAssertEqual(heap.count, 0)
+        XCTAssertNil(heap.peek())
+        XCTAssertNil(heap.remove())
+    }
+
+    func testIsEmpty() {
+        var heap = Heap<Int>(sort: >)
+        XCTAssertTrue(heap.isEmpty)
+        heap.insert(1)
+        XCTAssertFalse(heap.isEmpty)
+        heap.remove()
+        XCTAssertTrue(heap.isEmpty)
+    }
+
+    func testCount() {
+        var heap = Heap<Int>(sort: >)
+        XCTAssertEqual(0, heap.count)
+        heap.insert(1)
+        XCTAssertEqual(1, heap.count)
+    }
+
+    func testMaxHeapOneElement() {
+        let heap = Heap<Int>(array: [10], sort: >)
+        XCTAssertTrue(verifyMaxHeap(heap))
+        XCTAssertTrue(verifyMinHeap(heap))
+        XCTAssertFalse(heap.isEmpty)
+        XCTAssertEqual(heap.count, 1)
+        XCTAssertEqual(heap.peek()!, 10)
+    }
+
+    func testCreateMaxHeap() {
+        let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h1))
+        XCTAssertFalse(verifyMinHeap(h1))
+        XCTAssertEqual(h1.elements, [7, 5, 6, 4, 2, 1, 3])
+        XCTAssertFalse(h1.isEmpty)
+        XCTAssertEqual(h1.count, 7)
+        XCTAssertEqual(h1.peek()!, 7)
+
+        let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h2))
+        XCTAssertFalse(verifyMinHeap(h2))
+        XCTAssertEqual(h2.elements, [7, 6, 5, 4, 3, 2, 1])
+        XCTAssertFalse(h2.isEmpty)
+        XCTAssertEqual(h2.count, 7)
+        XCTAssertEqual(h2.peek()!, 7)
+
+        let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h3))
+        XCTAssertFalse(verifyMinHeap(h3))
+        XCTAssertEqual(h3.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
+        XCTAssertFalse(h3.isEmpty)
+        XCTAssertEqual(h3.count, 10)
+        XCTAssertEqual(h3.peek()!, 16)
+
+        let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h4))
+        XCTAssertFalse(verifyMinHeap(h4))
+        XCTAssertEqual(h4.elements, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
+        XCTAssertFalse(h4.isEmpty)
+        XCTAssertEqual(h4.count, 14)
+        XCTAssertEqual(h4.peek()!, 27)
+    }
+
+    func testCreateMinHeap() {
+        let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: <)
+        XCTAssertTrue(verifyMinHeap(h1))
+        XCTAssertFalse(verifyMaxHeap(h1))
+        XCTAssertEqual(h1.elements, [1, 2, 3, 4, 5, 6, 7])
+        XCTAssertFalse(h1.isEmpty)
+        XCTAssertEqual(h1.count, 7)
+        XCTAssertEqual(h1.peek()!, 1)
+
+        let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: <)
+        XCTAssertTrue(verifyMinHeap(h2))
+        XCTAssertFalse(verifyMaxHeap(h2))
+        XCTAssertEqual(h2.elements, [1, 3, 2, 4, 6, 7, 5])
+        XCTAssertFalse(h2.isEmpty)
+        XCTAssertEqual(h2.count, 7)
+        XCTAssertEqual(h2.peek()!, 1)
+
+        let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: <)
+        XCTAssertTrue(verifyMinHeap(h3))
+        XCTAssertFalse(verifyMaxHeap(h3))
+        XCTAssertEqual(h3.elements, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
+        XCTAssertFalse(h3.isEmpty)
+        XCTAssertEqual(h3.count, 10)
+        XCTAssertEqual(h3.peek()!, 1)
+
+        let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: <)
+        XCTAssertTrue(verifyMinHeap(h4))
+        XCTAssertFalse(verifyMaxHeap(h4))
+        XCTAssertEqual(h4.elements, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
+        XCTAssertFalse(h4.isEmpty)
+        XCTAssertEqual(h4.count, 14)
+        XCTAssertEqual(h4.peek()!, 0)
+    }
+
+    func testCreateMaxHeapEqualElements() {
+        let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
+        XCTAssertTrue(verifyMaxHeap(heap))
+        XCTAssertTrue(verifyMinHeap(heap))
+        XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+    }
+
+    func testCreateMinHeapEqualElements() {
+        let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
+        XCTAssertTrue(verifyMinHeap(heap))
+        XCTAssertTrue(verifyMaxHeap(heap))
+        XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+    }
+
+    fileprivate func randomArray(_ n: Int) -> [Int] {
+        var a = [Int]()
+        for _ in 0..<n {
+            a.append(Int(arc4random()))
+        }
+        return a
+    }
+
+    func testCreateRandomMaxHeap() {
+        for n in 1...40 {
+            let a = randomArray(n)
+            let h = Heap(array: a, sort: >)
+            XCTAssertTrue(verifyMaxHeap(h))
+            XCTAssertFalse(h.isEmpty)
+            XCTAssertEqual(h.count, n)
+            XCTAssertTrue(isPermutation(a, h.elements))
+        }
+    }
+
+    func testCreateRandomMinHeap() {
+        for n in 1...40 {
+            let a = randomArray(n)
+            let h = Heap(array: a, sort: <)
+            XCTAssertTrue(verifyMinHeap(h))
+            XCTAssertFalse(h.isEmpty)
+            XCTAssertEqual(h.count, n)
+            XCTAssertTrue(isPermutation(a, h.elements))
+        }
+    }
+
+    func testRemoving() {
+        var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+
+        //test index out of bounds
+        let v = h.removeAt(10)
+        XCTAssertEqual(v, nil)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+
+        let v1 = h.removeAt(5)
+        XCTAssertEqual(v1, 60)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
+
+        let v2 = h.removeAt(4)
+        XCTAssertEqual(v2, 20)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
+
+        let v3 = h.removeAt(4)
+        XCTAssertEqual(v3, 50)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [100, 65, 70, 10])
+
+        let v4 = h.removeAt(0)
+        XCTAssertEqual(v4, 100)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [70, 65, 10])
+
+        XCTAssertEqual(h.peek()!, 70)
+        let v5 = h.remove()
+        XCTAssertEqual(v5, 70)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [65, 10])
+
+        XCTAssertEqual(h.peek()!, 65)
+        let v6 = h.remove()
+        XCTAssertEqual(v6, 65)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [10])
+
+        XCTAssertEqual(h.peek()!, 10)
+        let v7 = h.remove()
+        XCTAssertEqual(v7, 10)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [])
+
+        XCTAssertNil(h.peek())
     }
-    return true
-  }
-
-  fileprivate func isPermutation(_ array1: [Int], _ array2: [Int]) -> Bool {
-    var a1 = array1
-    var a2 = array2
-    if a1.count != a2.count { return false }
-    while a1.count > 0 {
-      if let i = a2.index(of: a1[0]) {
-        a1.remove(at: 0)
-        a2.remove(at: i)
-      } else {
-        return false
-      }
+
+    func testRemoveEmpty() {
+        var heap = Heap<Int>(sort: >)
+        let removed = heap.remove()
+        XCTAssertNil(removed)
     }
-    return a2.count == 0
-  }
-
-  func testEmptyHeap() {
-    var heap = Heap<Int>(sort: <)
-    XCTAssertTrue(heap.isEmpty)
-    XCTAssertEqual(heap.count, 0)
-    XCTAssertNil(heap.peek())
-    XCTAssertNil(heap.remove())
-  }
-
-  func testIsEmpty() {
-    var heap = Heap<Int>(sort: >)
-    XCTAssertTrue(heap.isEmpty)
-    heap.insert(1)
-    XCTAssertFalse(heap.isEmpty)
-    heap.remove()
-    XCTAssertTrue(heap.isEmpty)
-  }
-
-  func testCount() {
-    var heap = Heap<Int>(sort: >)
-    XCTAssertEqual(0, heap.count)
-    heap.insert(1)
-    XCTAssertEqual(1, heap.count)
-  }
-
-  func testMaxHeapOneElement() {
-    let heap = Heap<Int>(array: [10], sort: >)
-    XCTAssertTrue(verifyMaxHeap(heap))
-    XCTAssertTrue(verifyMinHeap(heap))
-    XCTAssertFalse(heap.isEmpty)
-    XCTAssertEqual(heap.count, 1)
-    XCTAssertEqual(heap.peek()!, 10)
-  }
-
-  func testCreateMaxHeap() {
-    let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h1))
-    XCTAssertFalse(verifyMinHeap(h1))
-    XCTAssertEqual(h1.elements, [7, 5, 6, 4, 2, 1, 3])
-    XCTAssertFalse(h1.isEmpty)
-    XCTAssertEqual(h1.count, 7)
-    XCTAssertEqual(h1.peek()!, 7)
-
-    let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h2))
-    XCTAssertFalse(verifyMinHeap(h2))
-    XCTAssertEqual(h2.elements, [7, 6, 5, 4, 3, 2, 1])
-    XCTAssertFalse(h2.isEmpty)
-    XCTAssertEqual(h2.count, 7)
-    XCTAssertEqual(h2.peek()!, 7)
-
-    let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h3))
-    XCTAssertFalse(verifyMinHeap(h3))
-    XCTAssertEqual(h3.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
-    XCTAssertFalse(h3.isEmpty)
-    XCTAssertEqual(h3.count, 10)
-    XCTAssertEqual(h3.peek()!, 16)
-
-    let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h4))
-    XCTAssertFalse(verifyMinHeap(h4))
-    XCTAssertEqual(h4.elements, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
-    XCTAssertFalse(h4.isEmpty)
-    XCTAssertEqual(h4.count, 14)
-    XCTAssertEqual(h4.peek()!, 27)
-  }
-
-  func testCreateMinHeap() {
-    let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: <)
-    XCTAssertTrue(verifyMinHeap(h1))
-    XCTAssertFalse(verifyMaxHeap(h1))
-    XCTAssertEqual(h1.elements, [1, 2, 3, 4, 5, 6, 7])
-    XCTAssertFalse(h1.isEmpty)
-    XCTAssertEqual(h1.count, 7)
-    XCTAssertEqual(h1.peek()!, 1)
-
-    let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: <)
-    XCTAssertTrue(verifyMinHeap(h2))
-    XCTAssertFalse(verifyMaxHeap(h2))
-    XCTAssertEqual(h2.elements, [1, 3, 2, 4, 6, 7, 5])
-    XCTAssertFalse(h2.isEmpty)
-    XCTAssertEqual(h2.count, 7)
-    XCTAssertEqual(h2.peek()!, 1)
-
-    let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: <)
-    XCTAssertTrue(verifyMinHeap(h3))
-    XCTAssertFalse(verifyMaxHeap(h3))
-    XCTAssertEqual(h3.elements, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
-    XCTAssertFalse(h3.isEmpty)
-    XCTAssertEqual(h3.count, 10)
-    XCTAssertEqual(h3.peek()!, 1)
-
-    let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: <)
-    XCTAssertTrue(verifyMinHeap(h4))
-    XCTAssertFalse(verifyMaxHeap(h4))
-    XCTAssertEqual(h4.elements, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
-    XCTAssertFalse(h4.isEmpty)
-    XCTAssertEqual(h4.count, 14)
-    XCTAssertEqual(h4.peek()!, 0)
-  }
-
-  func testCreateMaxHeapEqualElements() {
-    let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(heap))
-    XCTAssertTrue(verifyMinHeap(heap))
-    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
-  }
-
-  func testCreateMinHeapEqualElements() {
-    let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
-    XCTAssertTrue(verifyMinHeap(heap))
-    XCTAssertTrue(verifyMaxHeap(heap))
-    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
-  }
-
-  fileprivate func randomArray(_ n: Int) -> [Int] {
-    var a = [Int]()
-    for _ in 0..<n {
-      a.append(Int(arc4random()))
+
+    func testRemoveRoot() {
+        var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+        XCTAssertEqual(h.peek()!, 15)
+        let v = h.remove()
+        XCTAssertEqual(v, 15)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
     }
-    return a
-  }
-
-  func testCreateRandomMaxHeap() {
-    for n in 1...40 {
-      let a = randomArray(n)
-      let h = Heap(array: a, sort: >)
-      XCTAssertTrue(verifyMaxHeap(h))
-      XCTAssertFalse(h.isEmpty)
-      XCTAssertEqual(h.count, n)
-      XCTAssertTrue(isPermutation(a, h.elements))
+
+    func testRemoveRandomItems() {
+        for n in 1...40 {
+            var a = randomArray(n)
+            var h = Heap(array: a, sort: >)
+            XCTAssertTrue(verifyMaxHeap(h))
+            XCTAssertTrue(isPermutation(a, h.elements))
+
+            let m = (n + 1)/2
+            for k in 1...m {
+                let i = Int(arc4random_uniform(UInt32(n - k + 1)))
+                let v = h.removeAt(i)!
+                let j = a.index(of: v)!
+                a.remove(at: j)
+
+                XCTAssertTrue(verifyMaxHeap(h))
+                XCTAssertEqual(h.count, a.count)
+                XCTAssertEqual(h.count, n - k)
+                XCTAssertTrue(isPermutation(a, h.elements))
+            }
+        }
     }
-  }
-
-  func testCreateRandomMinHeap() {
-    for n in 1...40 {
-      let a = randomArray(n)
-      let h = Heap(array: a, sort: <)
-      XCTAssertTrue(verifyMinHeap(h))
-      XCTAssertFalse(h.isEmpty)
-      XCTAssertEqual(h.count, n)
-      XCTAssertTrue(isPermutation(a, h.elements))
+
+    func testInsert() {
+        var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+
+        h.insert(10)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
+    }
+
+    func testInsertArrayAndRemove() {
+        var heap = Heap<Int>(sort: >)
+        heap.insert([1, 3, 2, 7, 5, 9])
+        XCTAssertEqual(heap.elements, [9, 5, 7, 1, 3, 2])
+
+        XCTAssertEqual(9, heap.remove())
+        XCTAssertEqual(7, heap.remove())
+        XCTAssertEqual(5, heap.remove())
+        XCTAssertEqual(3, heap.remove())
+        XCTAssertEqual(2, heap.remove())
+        XCTAssertEqual(1, heap.remove())
+        XCTAssertNil(heap.remove())
     }
-  }
-
-  func testRemoving() {
-    var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
-
-    //test index out of bounds
-    let v = h.removeAt(10)
-    XCTAssertEqual(v, nil)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
-
-    let v1 = h.removeAt(5)
-    XCTAssertEqual(v1, 60)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
-
-    let v2 = h.removeAt(4)
-    XCTAssertEqual(v2, 20)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
-
-    let v3 = h.removeAt(4)
-    XCTAssertEqual(v3, 50)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 65, 70, 10])
-
-    let v4 = h.removeAt(0)
-    XCTAssertEqual(v4, 100)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [70, 65, 10])
-
-    XCTAssertEqual(h.peek()!, 70)
-    let v5 = h.remove()
-    XCTAssertEqual(v5, 70)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [65, 10])
-
-    XCTAssertEqual(h.peek()!, 65)
-    let v6 = h.remove()
-    XCTAssertEqual(v6, 65)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [10])
-
-    XCTAssertEqual(h.peek()!, 10)
-    let v7 = h.remove()
-    XCTAssertEqual(v7, 10)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [])
-
-    XCTAssertNil(h.peek())
-  }
-
-  func testRemoveEmpty() {
-    var heap = Heap<Int>(sort: >)
-    let removed = heap.remove()
-    XCTAssertNil(removed)
-  }
-
-  func testRemoveRoot() {
-    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
-    XCTAssertEqual(h.peek()!, 15)
-    let v = h.remove()
-    XCTAssertEqual(v, 15)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
-  }
-
-  func testRemoveRandomItems() {
-    for n in 1...40 {
-      var a = randomArray(n)
-      var h = Heap(array: a, sort: >)
-      XCTAssertTrue(verifyMaxHeap(h))
-      XCTAssertTrue(isPermutation(a, h.elements))
-
-      let m = (n + 1)/2
-      for k in 1...m {
-        let i = Int(arc4random_uniform(UInt32(n - k + 1)))
-        let v = h.removeAt(i)!
-        let j = a.index(of: v)!
-        a.remove(at: j)
 
+    func testReplace() {
+        var h = Heap(array: [16, 14, 10, 8, 7, 9, 3, 2, 4, 1], sort: >)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
+
+        h.replace(index: 5, value: 13)
+        XCTAssertTrue(verifyMaxHeap(h))
+        XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
+
+        //test index out of bounds
+        h.replace(index: 20, value: 2)
         XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.count, a.count)
-        XCTAssertEqual(h.count, n - k)
-        XCTAssertTrue(isPermutation(a, h.elements))
-      }
+        XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
     }
-  }
-
-  func testInsert() {
-    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
-
-    h.insert(10)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
-  }
-
-  func testInsertArrayAndRemove() {
-    var heap = Heap<Int>(sort: >)
-    heap.insert([1, 3, 2, 7, 5, 9])
-    XCTAssertEqual(heap.elements, [9, 5, 7, 1, 3, 2])
-
-    XCTAssertEqual(9, heap.remove())
-    XCTAssertEqual(7, heap.remove())
-    XCTAssertEqual(5, heap.remove())
-    XCTAssertEqual(3, heap.remove())
-    XCTAssertEqual(2, heap.remove())
-    XCTAssertEqual(1, heap.remove())
-    XCTAssertNil(heap.remove())
-  }
-
-  func testReplace() {
-    var h = Heap(array: [16, 14, 10, 8, 7, 9, 3, 2, 4, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
-
-    h.replace(index: 5, value: 13)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
-
-    //test index out of bounds
-    h.replace(index: 20, value: 2)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
-  }
 }
diff --git a/Heap/Tests/Tests.xcodeproj/project.pbxproj b/Heap/Tests/Tests.xcodeproj/project.pbxproj
index 22112fa60..617e29f27 100644
--- a/Heap/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Heap/Tests/Tests.xcodeproj/project.pbxproj
@@ -226,7 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -238,7 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 14f27f777..80ed35600 100644
--- a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -26,6 +26,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -46,6 +47,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 33b4078f41776ded597dbce39ff4ddcdf8f67bab Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:37:45 -0700
Subject: [PATCH 060/643] [Swift 4] Update Heap Sort

---
 Heap Sort/HeapSort.swift                      |   2 +-
 Heap Sort/Tests/HeapSortTests.swift           |  41 +-
 .../Tests/Tests.xcodeproj/project.pbxproj     |   4 +-
 Heap/Heap.swift                               | 430 +++++++++---------
 4 files changed, 242 insertions(+), 235 deletions(-)

diff --git a/Heap Sort/HeapSort.swift b/Heap Sort/HeapSort.swift
index 3fbaab14d..1e568f91f 100644
--- a/Heap Sort/HeapSort.swift	
+++ b/Heap Sort/HeapSort.swift	
@@ -1,7 +1,7 @@
 extension Heap {
   public mutating func sort() -> [T] {
     for i in stride(from: (elements.count - 1), through: 1, by: -1) {
-      swap(&elements[0], &elements[i])
+        elements.swapAt(0, i)
       shiftDown(0, heapSize: i)
     }
     return elements
diff --git a/Heap Sort/Tests/HeapSortTests.swift b/Heap Sort/Tests/HeapSortTests.swift
index e5e847a74..55f2f52b4 100644
--- a/Heap Sort/Tests/HeapSortTests.swift	
+++ b/Heap Sort/Tests/HeapSortTests.swift	
@@ -1,26 +1,33 @@
 import XCTest
 
 class HeapSortTests: XCTestCase {
-  func testSort() {
-    var h1 = Heap(array: [5, 13, 2, 25, 7, 17, 20, 8, 4], sort: >)
-    let a1 = h1.sort()
-    XCTAssertEqual(a1, [2, 4, 5, 7, 8, 13, 17, 20, 25])
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
+    
+    func testSort() {
+        var h1 = Heap(array: [5, 13, 2, 25, 7, 17, 20, 8, 4], sort: >)
+        let a1 = h1.sort()
+        XCTAssertEqual(a1, [2, 4, 5, 7, 8, 13, 17, 20, 25])
 
-    let a1_ = heapsort([5, 13, 2, 25, 7, 17, 20, 8, 4], <)
-    XCTAssertEqual(a1_, [2, 4, 5, 7, 8, 13, 17, 20, 25])
+        let a1_ = heapsort([5, 13, 2, 25, 7, 17, 20, 8, 4], <)
+        XCTAssertEqual(a1_, [2, 4, 5, 7, 8, 13, 17, 20, 25])
 
-    var h2 = Heap(array: [16, 14, 10, 8, 7, 8, 3, 2, 4, 1], sort: >)
-    let a2 = h2.sort()
-    XCTAssertEqual(a2, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
+        var h2 = Heap(array: [16, 14, 10, 8, 7, 8, 3, 2, 4, 1], sort: >)
+        let a2 = h2.sort()
+        XCTAssertEqual(a2, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
 
-    let a2_ = heapsort([16, 14, 10, 8, 7, 8, 3, 2, 4, 1], <)
-    XCTAssertEqual(a2_, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
+        let a2_ = heapsort([16, 14, 10, 8, 7, 8, 3, 2, 4, 1], <)
+        XCTAssertEqual(a2_, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
 
-    var h3 = Heap(array: [1, 2, 3, 4, 5, 6], sort: <)
-    let a3 = h3.sort()
-    XCTAssertEqual(a3, [6, 5, 4, 3, 2, 1])
+        var h3 = Heap(array: [1, 2, 3, 4, 5, 6], sort: <)
+        let a3 = h3.sort()
+        XCTAssertEqual(a3, [6, 5, 4, 3, 2, 1])
 
-    let a3_ = heapsort([1, 2, 3, 4, 5, 6], >)
-    XCTAssertEqual(a3_, [6, 5, 4, 3, 2, 1])
-  }
+        let a3_ = heapsort([1, 2, 3, 4, 5, 6], >)
+        XCTAssertEqual(a3_, [6, 5, 4, 3, 2, 1])
+    }
 }
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj
index f7f101cd6..45b3f5821 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -230,7 +230,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -242,7 +242,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index 80b40c65f..18a350dca 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -4,224 +4,224 @@
 //
 
 public struct Heap<T> {
-  /** The array that stores the heap's nodes. */
-  var elements = [T]()
-
-  /** Determines whether this is a max-heap (>) or min-heap (<). */
-  fileprivate var isOrderedBefore: (T, T) -> Bool
-
-  /**
-   * Creates an empty heap.
-   * The sort function determines whether this is a min-heap or max-heap.
-   * For integers, > makes a max-heap, < makes a min-heap.
-   */
-  public init(sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
-  }
-
-  /**
-   * Creates a heap from an array. The order of the array does not matter;
-   * the elements are inserted into the heap in the order determined by the
-   * sort function.
-   */
-  public init(array: [T], sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
-    buildHeap(fromArray: array)
-  }
-
-  /*
-  // This version has O(n log n) performance.
-  private mutating func buildHeap(array: [T]) {
-    elements.reserveCapacity(array.count)
-    for value in array {
-      insert(value)
-    }
-  }
-  */
-
-  /**
-   * Converts an array to a max-heap or min-heap in a bottom-up manner.
-   * Performance: This runs pretty much in O(n).
-   */
-  fileprivate mutating func buildHeap(fromArray array: [T]) {
-    elements = array
-    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-      shiftDown(i, heapSize: elements.count)
-    }
-  }
-
-  public var isEmpty: Bool {
-    return elements.isEmpty
-  }
-
-  public var count: Int {
-    return elements.count
-  }
-
-  /**
-   * Returns the index of the parent of the element at index i.
-   * The element at index 0 is the root of the tree and has no parent.
-   */
-  @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
-    return (i - 1) / 2
-  }
-
-  /**
-   * Returns the index of the left child of the element at index i.
-   * Note that this index can be greater than the heap size, in which case
-   * there is no left child.
-   */
-  @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
-    return 2*i + 1
-  }
-
-  /**
-   * Returns the index of the right child of the element at index i.
-   * Note that this index can be greater than the heap size, in which case
-   * there is no right child.
-   */
-  @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
-    return 2*i + 2
-  }
-
-  /**
-   * Returns the maximum value in the heap (for a max-heap) or the minimum
-   * value (for a min-heap).
-   */
-  public func peek() -> T? {
-    return elements.first
-  }
-
-  /**
-   * Adds a new value to the heap. This reorders the heap so that the max-heap
-   * or min-heap property still holds. Performance: O(log n).
-   */
-  public mutating func insert(_ value: T) {
-    elements.append(value)
-    shiftUp(elements.count - 1)
-  }
-
-  public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
-    for value in sequence {
-      insert(value)
-    }
-  }
-
-  /**
-   * Allows you to change an element. In a max-heap, the new element should be
-   * larger than the old one; in a min-heap it should be smaller.
-   */
-  public mutating func replace(index i: Int, value: T) {
-    guard i < elements.count else { return }
-
-    assert(isOrderedBefore(value, elements[i]))
-    elements[i] = value
-    shiftUp(i)
-  }
-
-  /**
-   * Removes the root node from the heap. For a max-heap, this is the maximum
-   * value; for a min-heap it is the minimum value. Performance: O(log n).
-   */
-  @discardableResult public mutating func remove() -> T? {
-    if elements.isEmpty {
-      return nil
-    } else if elements.count == 1 {
-      return elements.removeLast()
-    } else {
-      // Use the last node to replace the first one, then fix the heap by
-      // shifting this new first node into its proper position.
-      let value = elements[0]
-      elements[0] = elements.removeLast()
-      shiftDown()
-      return value
-    }
-  }
-
-  /**
-   * Removes an arbitrary node from the heap. Performance: O(log n). You need
-   * to know the node's index, which may actually take O(n) steps to find.
-   */
-  public mutating func removeAt(_ index: Int) -> T? {
-    guard index < elements.count else { return nil }
-
-    let size = elements.count - 1
-    if index != size {
-      swap(&elements[index], &elements[size])
-      shiftDown(index, heapSize: size)
-      shiftUp(index)
-    }
-    return elements.removeLast()
-  }
-
-  /**
-   * Takes a child node and looks at its parents; if a parent is not larger
-   * (max-heap) or not smaller (min-heap) than the child, we exchange them.
-   */
-  mutating func shiftUp(_ index: Int) {
-    var childIndex = index
-    let child = elements[childIndex]
-    var parentIndex = self.parentIndex(ofIndex: childIndex)
-
-    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
-      elements[childIndex] = elements[parentIndex]
-      childIndex = parentIndex
-      parentIndex = self.parentIndex(ofIndex: childIndex)
-    }
-
-    elements[childIndex] = child
-  }
-
-  mutating func shiftDown() {
-    shiftDown(0, heapSize: elements.count)
-  }
-
-  /**
-   * Looks at a parent node and makes sure it is still larger (max-heap) or
-   * smaller (min-heap) than its childeren.
-   */
-  mutating func shiftDown(_ index: Int, heapSize: Int) {
-    var parentIndex = index
-
-    while true {
-      let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
-      let rightChildIndex = leftChildIndex + 1
-
-      // Figure out which comes first if we order them by the sort function:
-      // the parent, the left child, or the right child. If the parent comes
-      // first, we're done. If not, that element is out-of-place and we make
-      // it "float down" the tree until the heap property is restored.
-      var first = parentIndex
-      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
-        first = leftChildIndex
-      }
-      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
-        first = rightChildIndex
-      }
-      if first == parentIndex { return }
-
-      swap(&elements[parentIndex], &elements[first])
-      parentIndex = first
-    }
-  }
+    /** The array that stores the heap's nodes. */
+    var elements = [T]()
+
+    /** Determines whether this is a max-heap (>) or min-heap (<). */
+    fileprivate var isOrderedBefore: (T, T) -> Bool
+
+    /**
+     * Creates an empty heap.
+     * The sort function determines whether this is a min-heap or max-heap.
+     * For integers, > makes a max-heap, < makes a min-heap.
+     */
+    public init(sort: @escaping (T, T) -> Bool) {
+        self.isOrderedBefore = sort
+    }
+
+    /**
+     * Creates a heap from an array. The order of the array does not matter;
+     * the elements are inserted into the heap in the order determined by the
+     * sort function.
+     */
+    public init(array: [T], sort: @escaping (T, T) -> Bool) {
+        self.isOrderedBefore = sort
+        buildHeap(fromArray: array)
+    }
+
+    /*
+     // This version has O(n log n) performance.
+     private mutating func buildHeap(array: [T]) {
+     elements.reserveCapacity(array.count)
+     for value in array {
+     insert(value)
+     }
+     }
+     */
+
+    /**
+     * Converts an array to a max-heap or min-heap in a bottom-up manner.
+     * Performance: This runs pretty much in O(n).
+     */
+    fileprivate mutating func buildHeap(fromArray array: [T]) {
+        elements = array
+        for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+            shiftDown(i, heapSize: elements.count)
+        }
+    }
+
+    public var isEmpty: Bool {
+        return elements.isEmpty
+    }
+
+    public var count: Int {
+        return elements.count
+    }
+
+    /**
+     * Returns the index of the parent of the element at index i.
+     * The element at index 0 is the root of the tree and has no parent.
+     */
+    @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
+        return (i - 1) / 2
+    }
+
+    /**
+     * Returns the index of the left child of the element at index i.
+     * Note that this index can be greater than the heap size, in which case
+     * there is no left child.
+     */
+    @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 1
+    }
+
+    /**
+     * Returns the index of the right child of the element at index i.
+     * Note that this index can be greater than the heap size, in which case
+     * there is no right child.
+     */
+    @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 2
+    }
+
+    /**
+     * Returns the maximum value in the heap (for a max-heap) or the minimum
+     * value (for a min-heap).
+     */
+    public func peek() -> T? {
+        return elements.first
+    }
+
+    /**
+     * Adds a new value to the heap. This reorders the heap so that the max-heap
+     * or min-heap property still holds. Performance: O(log n).
+     */
+    public mutating func insert(_ value: T) {
+        elements.append(value)
+        shiftUp(elements.count - 1)
+    }
+
+    public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+        for value in sequence {
+            insert(value)
+        }
+    }
+
+    /**
+     * Allows you to change an element. In a max-heap, the new element should be
+     * larger than the old one; in a min-heap it should be smaller.
+     */
+    public mutating func replace(index i: Int, value: T) {
+        guard i < elements.count else { return }
+
+        assert(isOrderedBefore(value, elements[i]))
+        elements[i] = value
+        shiftUp(i)
+    }
+
+    /**
+     * Removes the root node from the heap. For a max-heap, this is the maximum
+     * value; for a min-heap it is the minimum value. Performance: O(log n).
+     */
+    @discardableResult public mutating func remove() -> T? {
+        if elements.isEmpty {
+            return nil
+        } else if elements.count == 1 {
+            return elements.removeLast()
+        } else {
+            // Use the last node to replace the first one, then fix the heap by
+            // shifting this new first node into its proper position.
+            let value = elements[0]
+            elements[0] = elements.removeLast()
+            shiftDown()
+            return value
+        }
+    }
+
+    /**
+     * Removes an arbitrary node from the heap. Performance: O(log n). You need
+     * to know the node's index, which may actually take O(n) steps to find.
+     */
+    public mutating func removeAt(_ index: Int) -> T? {
+        guard index < elements.count else { return nil }
+
+        let size = elements.count - 1
+        if index != size {
+            elements.swapAt(index, size)
+            shiftDown(index, heapSize: size)
+            shiftUp(index)
+        }
+        return elements.removeLast()
+    }
+
+    /**
+     * Takes a child node and looks at its parents; if a parent is not larger
+     * (max-heap) or not smaller (min-heap) than the child, we exchange them.
+     */
+    mutating func shiftUp(_ index: Int) {
+        var childIndex = index
+        let child = elements[childIndex]
+        var parentIndex = self.parentIndex(ofIndex: childIndex)
+
+        while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+            elements[childIndex] = elements[parentIndex]
+            childIndex = parentIndex
+            parentIndex = self.parentIndex(ofIndex: childIndex)
+        }
+
+        elements[childIndex] = child
+    }
+
+    mutating func shiftDown() {
+        shiftDown(0, heapSize: elements.count)
+    }
+
+    /**
+     * Looks at a parent node and makes sure it is still larger (max-heap) or
+     * smaller (min-heap) than its childeren.
+     */
+    mutating func shiftDown(_ index: Int, heapSize: Int) {
+        var parentIndex = index
+
+        while true {
+            let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+            let rightChildIndex = leftChildIndex + 1
+
+            // Figure out which comes first if we order them by the sort function:
+            // the parent, the left child, or the right child. If the parent comes
+            // first, we're done. If not, that element is out-of-place and we make
+            // it "float down" the tree until the heap property is restored.
+            var first = parentIndex
+            if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+                first = leftChildIndex
+            }
+            if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+                first = rightChildIndex
+            }
+            if first == parentIndex { return }
+
+            elements.swapAt(parentIndex, first)
+            parentIndex = first
+        }
+    }
 }
 
 // MARK: - Searching
 
 extension Heap where T: Equatable {
-  /**
-   * Searches the heap for the given element. Performance: O(n).
-   */
-  public func index(of element: T) -> Int? {
-    return index(of: element, 0)
-  }
-
-  fileprivate func index(of element: T, _ i: Int) -> Int? {
-    if i >= count { return nil }
-    if isOrderedBefore(element, elements[i]) { return nil }
-    if element == elements[i] { return i }
-    if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
-    if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
-    return nil
-  }
+    /**
+     * Searches the heap for the given element. Performance: O(n).
+     */
+    public func index(of element: T) -> Int? {
+        return index(of: element, 0)
+    }
+
+    fileprivate func index(of element: T, _ i: Int) -> Int? {
+        if i >= count { return nil }
+        if isOrderedBefore(element, elements[i]) { return nil }
+        if element == elements[i] { return i }
+        if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
+        if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
+        return nil
+    }
 }

From 028b898af99b0979e0ea0d156f3dcb4ad45b4796 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 31 Jul 2017 16:09:43 +0900
Subject: [PATCH 061/643] Updates the indentation of the code to 2 spaces.

---
 Heap/Heap.swift            | 430 ++++++++++++-------------
 Heap/Tests/HeapTests.swift | 626 ++++++++++++++++++-------------------
 2 files changed, 528 insertions(+), 528 deletions(-)

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index 18a350dca..b0355da5d 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -4,224 +4,224 @@
 //
 
 public struct Heap<T> {
-    /** The array that stores the heap's nodes. */
-    var elements = [T]()
-
-    /** Determines whether this is a max-heap (>) or min-heap (<). */
-    fileprivate var isOrderedBefore: (T, T) -> Bool
-
-    /**
-     * Creates an empty heap.
-     * The sort function determines whether this is a min-heap or max-heap.
-     * For integers, > makes a max-heap, < makes a min-heap.
-     */
-    public init(sort: @escaping (T, T) -> Bool) {
-        self.isOrderedBefore = sort
-    }
-
-    /**
-     * Creates a heap from an array. The order of the array does not matter;
-     * the elements are inserted into the heap in the order determined by the
-     * sort function.
-     */
-    public init(array: [T], sort: @escaping (T, T) -> Bool) {
-        self.isOrderedBefore = sort
-        buildHeap(fromArray: array)
-    }
-
-    /*
-     // This version has O(n log n) performance.
-     private mutating func buildHeap(array: [T]) {
-     elements.reserveCapacity(array.count)
-     for value in array {
-     insert(value)
-     }
-     }
-     */
-
-    /**
-     * Converts an array to a max-heap or min-heap in a bottom-up manner.
-     * Performance: This runs pretty much in O(n).
-     */
-    fileprivate mutating func buildHeap(fromArray array: [T]) {
-        elements = array
-        for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-            shiftDown(i, heapSize: elements.count)
-        }
-    }
-
-    public var isEmpty: Bool {
-        return elements.isEmpty
-    }
-
-    public var count: Int {
-        return elements.count
-    }
-
-    /**
-     * Returns the index of the parent of the element at index i.
-     * The element at index 0 is the root of the tree and has no parent.
-     */
-    @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
-        return (i - 1) / 2
-    }
-
-    /**
-     * Returns the index of the left child of the element at index i.
-     * Note that this index can be greater than the heap size, in which case
-     * there is no left child.
-     */
-    @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
-        return 2*i + 1
-    }
-
-    /**
-     * Returns the index of the right child of the element at index i.
-     * Note that this index can be greater than the heap size, in which case
-     * there is no right child.
-     */
-    @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
-        return 2*i + 2
-    }
-
-    /**
-     * Returns the maximum value in the heap (for a max-heap) or the minimum
-     * value (for a min-heap).
-     */
-    public func peek() -> T? {
-        return elements.first
-    }
-
-    /**
-     * Adds a new value to the heap. This reorders the heap so that the max-heap
-     * or min-heap property still holds. Performance: O(log n).
-     */
-    public mutating func insert(_ value: T) {
-        elements.append(value)
-        shiftUp(elements.count - 1)
-    }
-
-    public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
-        for value in sequence {
-            insert(value)
-        }
-    }
-
-    /**
-     * Allows you to change an element. In a max-heap, the new element should be
-     * larger than the old one; in a min-heap it should be smaller.
-     */
-    public mutating func replace(index i: Int, value: T) {
-        guard i < elements.count else { return }
-
-        assert(isOrderedBefore(value, elements[i]))
-        elements[i] = value
-        shiftUp(i)
-    }
-
-    /**
-     * Removes the root node from the heap. For a max-heap, this is the maximum
-     * value; for a min-heap it is the minimum value. Performance: O(log n).
-     */
-    @discardableResult public mutating func remove() -> T? {
-        if elements.isEmpty {
-            return nil
-        } else if elements.count == 1 {
-            return elements.removeLast()
-        } else {
-            // Use the last node to replace the first one, then fix the heap by
-            // shifting this new first node into its proper position.
-            let value = elements[0]
-            elements[0] = elements.removeLast()
-            shiftDown()
-            return value
-        }
-    }
-
-    /**
-     * Removes an arbitrary node from the heap. Performance: O(log n). You need
-     * to know the node's index, which may actually take O(n) steps to find.
-     */
-    public mutating func removeAt(_ index: Int) -> T? {
-        guard index < elements.count else { return nil }
-
-        let size = elements.count - 1
-        if index != size {
-            elements.swapAt(index, size)
-            shiftDown(index, heapSize: size)
-            shiftUp(index)
-        }
-        return elements.removeLast()
-    }
-
-    /**
-     * Takes a child node and looks at its parents; if a parent is not larger
-     * (max-heap) or not smaller (min-heap) than the child, we exchange them.
-     */
-    mutating func shiftUp(_ index: Int) {
-        var childIndex = index
-        let child = elements[childIndex]
-        var parentIndex = self.parentIndex(ofIndex: childIndex)
-
-        while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
-            elements[childIndex] = elements[parentIndex]
-            childIndex = parentIndex
-            parentIndex = self.parentIndex(ofIndex: childIndex)
-        }
-
-        elements[childIndex] = child
-    }
-
-    mutating func shiftDown() {
-        shiftDown(0, heapSize: elements.count)
-    }
-
-    /**
-     * Looks at a parent node and makes sure it is still larger (max-heap) or
-     * smaller (min-heap) than its childeren.
-     */
-    mutating func shiftDown(_ index: Int, heapSize: Int) {
-        var parentIndex = index
-
-        while true {
-            let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
-            let rightChildIndex = leftChildIndex + 1
-
-            // Figure out which comes first if we order them by the sort function:
-            // the parent, the left child, or the right child. If the parent comes
-            // first, we're done. If not, that element is out-of-place and we make
-            // it "float down" the tree until the heap property is restored.
-            var first = parentIndex
-            if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
-                first = leftChildIndex
-            }
-            if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
-                first = rightChildIndex
-            }
-            if first == parentIndex { return }
-
-            elements.swapAt(parentIndex, first)
-            parentIndex = first
-        }
-    }
+  /** The array that stores the heap's nodes. */
+  var elements = [T]()
+  
+  /** Determines whether this is a max-heap (>) or min-heap (<). */
+  fileprivate var isOrderedBefore: (T, T) -> Bool
+  
+  /**
+   * Creates an empty heap.
+   * The sort function determines whether this is a min-heap or max-heap.
+   * For integers, > makes a max-heap, < makes a min-heap.
+   */
+  public init(sort: @escaping (T, T) -> Bool) {
+    self.isOrderedBefore = sort
+  }
+  
+  /**
+   * Creates a heap from an array. The order of the array does not matter;
+   * the elements are inserted into the heap in the order determined by the
+   * sort function.
+   */
+  public init(array: [T], sort: @escaping (T, T) -> Bool) {
+    self.isOrderedBefore = sort
+    buildHeap(fromArray: array)
+  }
+  
+  /*
+   // This version has O(n log n) performance.
+   private mutating func buildHeap(array: [T]) {
+   elements.reserveCapacity(array.count)
+   for value in array {
+   insert(value)
+   }
+   }
+   */
+  
+  /**
+   * Converts an array to a max-heap or min-heap in a bottom-up manner.
+   * Performance: This runs pretty much in O(n).
+   */
+  fileprivate mutating func buildHeap(fromArray array: [T]) {
+    elements = array
+    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+      shiftDown(i, heapSize: elements.count)
+    }
+  }
+  
+  public var isEmpty: Bool {
+    return elements.isEmpty
+  }
+  
+  public var count: Int {
+    return elements.count
+  }
+  
+  /**
+   * Returns the index of the parent of the element at index i.
+   * The element at index 0 is the root of the tree and has no parent.
+   */
+  @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
+    return (i - 1) / 2
+  }
+  
+  /**
+   * Returns the index of the left child of the element at index i.
+   * Note that this index can be greater than the heap size, in which case
+   * there is no left child.
+   */
+  @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
+    return 2*i + 1
+  }
+  
+  /**
+   * Returns the index of the right child of the element at index i.
+   * Note that this index can be greater than the heap size, in which case
+   * there is no right child.
+   */
+  @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
+    return 2*i + 2
+  }
+  
+  /**
+   * Returns the maximum value in the heap (for a max-heap) or the minimum
+   * value (for a min-heap).
+   */
+  public func peek() -> T? {
+    return elements.first
+  }
+  
+  /**
+   * Adds a new value to the heap. This reorders the heap so that the max-heap
+   * or min-heap property still holds. Performance: O(log n).
+   */
+  public mutating func insert(_ value: T) {
+    elements.append(value)
+    shiftUp(elements.count - 1)
+  }
+  
+  public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+    for value in sequence {
+      insert(value)
+    }
+  }
+  
+  /**
+   * Allows you to change an element. In a max-heap, the new element should be
+   * larger than the old one; in a min-heap it should be smaller.
+   */
+  public mutating func replace(index i: Int, value: T) {
+    guard i < elements.count else { return }
+    
+    assert(isOrderedBefore(value, elements[i]))
+    elements[i] = value
+    shiftUp(i)
+  }
+  
+  /**
+   * Removes the root node from the heap. For a max-heap, this is the maximum
+   * value; for a min-heap it is the minimum value. Performance: O(log n).
+   */
+  @discardableResult public mutating func remove() -> T? {
+    if elements.isEmpty {
+      return nil
+    } else if elements.count == 1 {
+      return elements.removeLast()
+    } else {
+      // Use the last node to replace the first one, then fix the heap by
+      // shifting this new first node into its proper position.
+      let value = elements[0]
+      elements[0] = elements.removeLast()
+      shiftDown()
+      return value
+    }
+  }
+  
+  /**
+   * Removes an arbitrary node from the heap. Performance: O(log n). You need
+   * to know the node's index, which may actually take O(n) steps to find.
+   */
+  public mutating func removeAt(_ index: Int) -> T? {
+    guard index < elements.count else { return nil }
+    
+    let size = elements.count - 1
+    if index != size {
+      elements.swapAt(index, size)
+      shiftDown(index, heapSize: size)
+      shiftUp(index)
+    }
+    return elements.removeLast()
+  }
+  
+  /**
+   * Takes a child node and looks at its parents; if a parent is not larger
+   * (max-heap) or not smaller (min-heap) than the child, we exchange them.
+   */
+  mutating func shiftUp(_ index: Int) {
+    var childIndex = index
+    let child = elements[childIndex]
+    var parentIndex = self.parentIndex(ofIndex: childIndex)
+    
+    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+      elements[childIndex] = elements[parentIndex]
+      childIndex = parentIndex
+      parentIndex = self.parentIndex(ofIndex: childIndex)
+    }
+    
+    elements[childIndex] = child
+  }
+  
+  mutating func shiftDown() {
+    shiftDown(0, heapSize: elements.count)
+  }
+  
+  /**
+   * Looks at a parent node and makes sure it is still larger (max-heap) or
+   * smaller (min-heap) than its childeren.
+   */
+  mutating func shiftDown(_ index: Int, heapSize: Int) {
+    var parentIndex = index
+    
+    while true {
+      let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+      let rightChildIndex = leftChildIndex + 1
+      
+      // Figure out which comes first if we order them by the sort function:
+      // the parent, the left child, or the right child. If the parent comes
+      // first, we're done. If not, that element is out-of-place and we make
+      // it "float down" the tree until the heap property is restored.
+      var first = parentIndex
+      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+        first = leftChildIndex
+      }
+      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+        first = rightChildIndex
+      }
+      if first == parentIndex { return }
+      
+      elements.swapAt(parentIndex, first)
+      parentIndex = first
+    }
+  }
 }
 
 // MARK: - Searching
 
 extension Heap where T: Equatable {
-    /**
-     * Searches the heap for the given element. Performance: O(n).
-     */
-    public func index(of element: T) -> Int? {
-        return index(of: element, 0)
-    }
-
-    fileprivate func index(of element: T, _ i: Int) -> Int? {
-        if i >= count { return nil }
-        if isOrderedBefore(element, elements[i]) { return nil }
-        if element == elements[i] { return i }
-        if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
-        if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
-        return nil
-    }
+  /**
+   * Searches the heap for the given element. Performance: O(n).
+   */
+  public func index(of element: T) -> Int? {
+    return index(of: element, 0)
+  }
+  
+  fileprivate func index(of element: T, _ i: Int) -> Int? {
+    if i >= count { return nil }
+    if isOrderedBefore(element, elements[i]) { return nil }
+    if element == elements[i] { return i }
+    if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
+    if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
+    return nil
+  }
 }
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index 0af3a14e0..66be0931c 100644
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -6,325 +6,325 @@
 import XCTest
 
 class HeapTests: XCTestCase {
-
-    func testSwift4() {
-        // last checked with Xcode 9.0b4
-        #if swift(>=4.0)
-            print("Hello, Swift 4!")
-        #endif
-    }
-
-    fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
-        for i in 0..<h.count {
-            let left = h.leftChildIndex(ofIndex: i)
-            let right = h.rightChildIndex(ofIndex: i)
-            let parent = h.parentIndex(ofIndex: i)
-            if left < h.count && h.elements[i] < h.elements[left] { return false }
-            if right < h.count && h.elements[i] < h.elements[right] { return false }
-            if i > 0 && h.elements[parent] < h.elements[i] { return false }
-        }
-        return true
-    }
-
-    fileprivate func verifyMinHeap(_ h: Heap<Int>) -> Bool {
-        for i in 0..<h.count {
-            let left = h.leftChildIndex(ofIndex: i)
-            let right = h.rightChildIndex(ofIndex: i)
-            let parent = h.parentIndex(ofIndex: i)
-            if left < h.count && h.elements[i] > h.elements[left] { return false }
-            if right < h.count && h.elements[i] > h.elements[right] { return false }
-            if i > 0 && h.elements[parent] > h.elements[i] { return false }
-        }
-        return true
+  
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
+  fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
+    for i in 0..<h.count {
+      let left = h.leftChildIndex(ofIndex: i)
+      let right = h.rightChildIndex(ofIndex: i)
+      let parent = h.parentIndex(ofIndex: i)
+      if left < h.count && h.elements[i] < h.elements[left] { return false }
+      if right < h.count && h.elements[i] < h.elements[right] { return false }
+      if i > 0 && h.elements[parent] < h.elements[i] { return false }
     }
-
-    fileprivate func isPermutation(_ array1: [Int], _ array2: [Int]) -> Bool {
-        var a1 = array1
-        var a2 = array2
-        if a1.count != a2.count { return false }
-        while a1.count > 0 {
-            if let i = a2.index(of: a1[0]) {
-                a1.remove(at: 0)
-                a2.remove(at: i)
-            } else {
-                return false
-            }
-        }
-        return a2.count == 0
+    return true
+  }
+  
+  fileprivate func verifyMinHeap(_ h: Heap<Int>) -> Bool {
+    for i in 0..<h.count {
+      let left = h.leftChildIndex(ofIndex: i)
+      let right = h.rightChildIndex(ofIndex: i)
+      let parent = h.parentIndex(ofIndex: i)
+      if left < h.count && h.elements[i] > h.elements[left] { return false }
+      if right < h.count && h.elements[i] > h.elements[right] { return false }
+      if i > 0 && h.elements[parent] > h.elements[i] { return false }
     }
-
-    func testEmptyHeap() {
-        var heap = Heap<Int>(sort: <)
-        XCTAssertTrue(heap.isEmpty)
-        XCTAssertEqual(heap.count, 0)
-        XCTAssertNil(heap.peek())
-        XCTAssertNil(heap.remove())
+    return true
+  }
+  
+  fileprivate func isPermutation(_ array1: [Int], _ array2: [Int]) -> Bool {
+    var a1 = array1
+    var a2 = array2
+    if a1.count != a2.count { return false }
+    while a1.count > 0 {
+      if let i = a2.index(of: a1[0]) {
+        a1.remove(at: 0)
+        a2.remove(at: i)
+      } else {
+        return false
+      }
     }
-
-    func testIsEmpty() {
-        var heap = Heap<Int>(sort: >)
-        XCTAssertTrue(heap.isEmpty)
-        heap.insert(1)
-        XCTAssertFalse(heap.isEmpty)
-        heap.remove()
-        XCTAssertTrue(heap.isEmpty)
+    return a2.count == 0
+  }
+  
+  func testEmptyHeap() {
+    var heap = Heap<Int>(sort: <)
+    XCTAssertTrue(heap.isEmpty)
+    XCTAssertEqual(heap.count, 0)
+    XCTAssertNil(heap.peek())
+    XCTAssertNil(heap.remove())
+  }
+  
+  func testIsEmpty() {
+    var heap = Heap<Int>(sort: >)
+    XCTAssertTrue(heap.isEmpty)
+    heap.insert(1)
+    XCTAssertFalse(heap.isEmpty)
+    heap.remove()
+    XCTAssertTrue(heap.isEmpty)
+  }
+  
+  func testCount() {
+    var heap = Heap<Int>(sort: >)
+    XCTAssertEqual(0, heap.count)
+    heap.insert(1)
+    XCTAssertEqual(1, heap.count)
+  }
+  
+  func testMaxHeapOneElement() {
+    let heap = Heap<Int>(array: [10], sort: >)
+    XCTAssertTrue(verifyMaxHeap(heap))
+    XCTAssertTrue(verifyMinHeap(heap))
+    XCTAssertFalse(heap.isEmpty)
+    XCTAssertEqual(heap.count, 1)
+    XCTAssertEqual(heap.peek()!, 10)
+  }
+  
+  func testCreateMaxHeap() {
+    let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h1))
+    XCTAssertFalse(verifyMinHeap(h1))
+    XCTAssertEqual(h1.elements, [7, 5, 6, 4, 2, 1, 3])
+    XCTAssertFalse(h1.isEmpty)
+    XCTAssertEqual(h1.count, 7)
+    XCTAssertEqual(h1.peek()!, 7)
+    
+    let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h2))
+    XCTAssertFalse(verifyMinHeap(h2))
+    XCTAssertEqual(h2.elements, [7, 6, 5, 4, 3, 2, 1])
+    XCTAssertFalse(h2.isEmpty)
+    XCTAssertEqual(h2.count, 7)
+    XCTAssertEqual(h2.peek()!, 7)
+    
+    let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h3))
+    XCTAssertFalse(verifyMinHeap(h3))
+    XCTAssertEqual(h3.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
+    XCTAssertFalse(h3.isEmpty)
+    XCTAssertEqual(h3.count, 10)
+    XCTAssertEqual(h3.peek()!, 16)
+    
+    let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h4))
+    XCTAssertFalse(verifyMinHeap(h4))
+    XCTAssertEqual(h4.elements, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
+    XCTAssertFalse(h4.isEmpty)
+    XCTAssertEqual(h4.count, 14)
+    XCTAssertEqual(h4.peek()!, 27)
+  }
+  
+  func testCreateMinHeap() {
+    let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: <)
+    XCTAssertTrue(verifyMinHeap(h1))
+    XCTAssertFalse(verifyMaxHeap(h1))
+    XCTAssertEqual(h1.elements, [1, 2, 3, 4, 5, 6, 7])
+    XCTAssertFalse(h1.isEmpty)
+    XCTAssertEqual(h1.count, 7)
+    XCTAssertEqual(h1.peek()!, 1)
+    
+    let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: <)
+    XCTAssertTrue(verifyMinHeap(h2))
+    XCTAssertFalse(verifyMaxHeap(h2))
+    XCTAssertEqual(h2.elements, [1, 3, 2, 4, 6, 7, 5])
+    XCTAssertFalse(h2.isEmpty)
+    XCTAssertEqual(h2.count, 7)
+    XCTAssertEqual(h2.peek()!, 1)
+    
+    let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: <)
+    XCTAssertTrue(verifyMinHeap(h3))
+    XCTAssertFalse(verifyMaxHeap(h3))
+    XCTAssertEqual(h3.elements, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
+    XCTAssertFalse(h3.isEmpty)
+    XCTAssertEqual(h3.count, 10)
+    XCTAssertEqual(h3.peek()!, 1)
+    
+    let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: <)
+    XCTAssertTrue(verifyMinHeap(h4))
+    XCTAssertFalse(verifyMaxHeap(h4))
+    XCTAssertEqual(h4.elements, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
+    XCTAssertFalse(h4.isEmpty)
+    XCTAssertEqual(h4.count, 14)
+    XCTAssertEqual(h4.peek()!, 0)
+  }
+  
+  func testCreateMaxHeapEqualElements() {
+    let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(heap))
+    XCTAssertTrue(verifyMinHeap(heap))
+    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+  }
+  
+  func testCreateMinHeapEqualElements() {
+    let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
+    XCTAssertTrue(verifyMinHeap(heap))
+    XCTAssertTrue(verifyMaxHeap(heap))
+    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+  }
+  
+  fileprivate func randomArray(_ n: Int) -> [Int] {
+    var a = [Int]()
+    for _ in 0..<n {
+      a.append(Int(arc4random()))
     }
-
-    func testCount() {
-        var heap = Heap<Int>(sort: >)
-        XCTAssertEqual(0, heap.count)
-        heap.insert(1)
-        XCTAssertEqual(1, heap.count)
+    return a
+  }
+  
+  func testCreateRandomMaxHeap() {
+    for n in 1...40 {
+      let a = randomArray(n)
+      let h = Heap(array: a, sort: >)
+      XCTAssertTrue(verifyMaxHeap(h))
+      XCTAssertFalse(h.isEmpty)
+      XCTAssertEqual(h.count, n)
+      XCTAssertTrue(isPermutation(a, h.elements))
     }
-
-    func testMaxHeapOneElement() {
-        let heap = Heap<Int>(array: [10], sort: >)
-        XCTAssertTrue(verifyMaxHeap(heap))
-        XCTAssertTrue(verifyMinHeap(heap))
-        XCTAssertFalse(heap.isEmpty)
-        XCTAssertEqual(heap.count, 1)
-        XCTAssertEqual(heap.peek()!, 10)
+  }
+  
+  func testCreateRandomMinHeap() {
+    for n in 1...40 {
+      let a = randomArray(n)
+      let h = Heap(array: a, sort: <)
+      XCTAssertTrue(verifyMinHeap(h))
+      XCTAssertFalse(h.isEmpty)
+      XCTAssertEqual(h.count, n)
+      XCTAssertTrue(isPermutation(a, h.elements))
     }
-
-    func testCreateMaxHeap() {
-        let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h1))
-        XCTAssertFalse(verifyMinHeap(h1))
-        XCTAssertEqual(h1.elements, [7, 5, 6, 4, 2, 1, 3])
-        XCTAssertFalse(h1.isEmpty)
-        XCTAssertEqual(h1.count, 7)
-        XCTAssertEqual(h1.peek()!, 7)
-
-        let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h2))
-        XCTAssertFalse(verifyMinHeap(h2))
-        XCTAssertEqual(h2.elements, [7, 6, 5, 4, 3, 2, 1])
-        XCTAssertFalse(h2.isEmpty)
-        XCTAssertEqual(h2.count, 7)
-        XCTAssertEqual(h2.peek()!, 7)
-
-        let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h3))
-        XCTAssertFalse(verifyMinHeap(h3))
-        XCTAssertEqual(h3.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
-        XCTAssertFalse(h3.isEmpty)
-        XCTAssertEqual(h3.count, 10)
-        XCTAssertEqual(h3.peek()!, 16)
-
-        let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h4))
-        XCTAssertFalse(verifyMinHeap(h4))
-        XCTAssertEqual(h4.elements, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
-        XCTAssertFalse(h4.isEmpty)
-        XCTAssertEqual(h4.count, 14)
-        XCTAssertEqual(h4.peek()!, 27)
-    }
-
-    func testCreateMinHeap() {
-        let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: <)
-        XCTAssertTrue(verifyMinHeap(h1))
-        XCTAssertFalse(verifyMaxHeap(h1))
-        XCTAssertEqual(h1.elements, [1, 2, 3, 4, 5, 6, 7])
-        XCTAssertFalse(h1.isEmpty)
-        XCTAssertEqual(h1.count, 7)
-        XCTAssertEqual(h1.peek()!, 1)
-
-        let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: <)
-        XCTAssertTrue(verifyMinHeap(h2))
-        XCTAssertFalse(verifyMaxHeap(h2))
-        XCTAssertEqual(h2.elements, [1, 3, 2, 4, 6, 7, 5])
-        XCTAssertFalse(h2.isEmpty)
-        XCTAssertEqual(h2.count, 7)
-        XCTAssertEqual(h2.peek()!, 1)
-
-        let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: <)
-        XCTAssertTrue(verifyMinHeap(h3))
-        XCTAssertFalse(verifyMaxHeap(h3))
-        XCTAssertEqual(h3.elements, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
-        XCTAssertFalse(h3.isEmpty)
-        XCTAssertEqual(h3.count, 10)
-        XCTAssertEqual(h3.peek()!, 1)
-
-        let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: <)
-        XCTAssertTrue(verifyMinHeap(h4))
-        XCTAssertFalse(verifyMaxHeap(h4))
-        XCTAssertEqual(h4.elements, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
-        XCTAssertFalse(h4.isEmpty)
-        XCTAssertEqual(h4.count, 14)
-        XCTAssertEqual(h4.peek()!, 0)
-    }
-
-    func testCreateMaxHeapEqualElements() {
-        let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
-        XCTAssertTrue(verifyMaxHeap(heap))
-        XCTAssertTrue(verifyMinHeap(heap))
-        XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
-    }
-
-    func testCreateMinHeapEqualElements() {
-        let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
-        XCTAssertTrue(verifyMinHeap(heap))
-        XCTAssertTrue(verifyMaxHeap(heap))
-        XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
-    }
-
-    fileprivate func randomArray(_ n: Int) -> [Int] {
-        var a = [Int]()
-        for _ in 0..<n {
-            a.append(Int(arc4random()))
-        }
-        return a
-    }
-
-    func testCreateRandomMaxHeap() {
-        for n in 1...40 {
-            let a = randomArray(n)
-            let h = Heap(array: a, sort: >)
-            XCTAssertTrue(verifyMaxHeap(h))
-            XCTAssertFalse(h.isEmpty)
-            XCTAssertEqual(h.count, n)
-            XCTAssertTrue(isPermutation(a, h.elements))
-        }
-    }
-
-    func testCreateRandomMinHeap() {
-        for n in 1...40 {
-            let a = randomArray(n)
-            let h = Heap(array: a, sort: <)
-            XCTAssertTrue(verifyMinHeap(h))
-            XCTAssertFalse(h.isEmpty)
-            XCTAssertEqual(h.count, n)
-            XCTAssertTrue(isPermutation(a, h.elements))
-        }
-    }
-
-    func testRemoving() {
-        var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
-
-        //test index out of bounds
-        let v = h.removeAt(10)
-        XCTAssertEqual(v, nil)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
-
-        let v1 = h.removeAt(5)
-        XCTAssertEqual(v1, 60)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
-
-        let v2 = h.removeAt(4)
-        XCTAssertEqual(v2, 20)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
-
-        let v3 = h.removeAt(4)
-        XCTAssertEqual(v3, 50)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [100, 65, 70, 10])
-
-        let v4 = h.removeAt(0)
-        XCTAssertEqual(v4, 100)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [70, 65, 10])
-
-        XCTAssertEqual(h.peek()!, 70)
-        let v5 = h.remove()
-        XCTAssertEqual(v5, 70)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [65, 10])
-
-        XCTAssertEqual(h.peek()!, 65)
-        let v6 = h.remove()
-        XCTAssertEqual(v6, 65)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [10])
-
-        XCTAssertEqual(h.peek()!, 10)
-        let v7 = h.remove()
-        XCTAssertEqual(v7, 10)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [])
-
-        XCTAssertNil(h.peek())
-    }
-
-    func testRemoveEmpty() {
-        var heap = Heap<Int>(sort: >)
-        let removed = heap.remove()
-        XCTAssertNil(removed)
-    }
-
-    func testRemoveRoot() {
-        var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
-        XCTAssertEqual(h.peek()!, 15)
-        let v = h.remove()
-        XCTAssertEqual(v, 15)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
-    }
-
-    func testRemoveRandomItems() {
-        for n in 1...40 {
-            var a = randomArray(n)
-            var h = Heap(array: a, sort: >)
-            XCTAssertTrue(verifyMaxHeap(h))
-            XCTAssertTrue(isPermutation(a, h.elements))
-
-            let m = (n + 1)/2
-            for k in 1...m {
-                let i = Int(arc4random_uniform(UInt32(n - k + 1)))
-                let v = h.removeAt(i)!
-                let j = a.index(of: v)!
-                a.remove(at: j)
-
-                XCTAssertTrue(verifyMaxHeap(h))
-                XCTAssertEqual(h.count, a.count)
-                XCTAssertEqual(h.count, n - k)
-                XCTAssertTrue(isPermutation(a, h.elements))
-            }
-        }
-    }
-
-    func testInsert() {
-        var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
-
-        h.insert(10)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
-    }
-
-    func testInsertArrayAndRemove() {
-        var heap = Heap<Int>(sort: >)
-        heap.insert([1, 3, 2, 7, 5, 9])
-        XCTAssertEqual(heap.elements, [9, 5, 7, 1, 3, 2])
-
-        XCTAssertEqual(9, heap.remove())
-        XCTAssertEqual(7, heap.remove())
-        XCTAssertEqual(5, heap.remove())
-        XCTAssertEqual(3, heap.remove())
-        XCTAssertEqual(2, heap.remove())
-        XCTAssertEqual(1, heap.remove())
-        XCTAssertNil(heap.remove())
-    }
-
-    func testReplace() {
-        var h = Heap(array: [16, 14, 10, 8, 7, 9, 3, 2, 4, 1], sort: >)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
-
-        h.replace(index: 5, value: 13)
-        XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
-
-        //test index out of bounds
-        h.replace(index: 20, value: 2)
+  }
+  
+  func testRemoving() {
+    var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+    
+    //test index out of bounds
+    let v = h.removeAt(10)
+    XCTAssertEqual(v, nil)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+    
+    let v1 = h.removeAt(5)
+    XCTAssertEqual(v1, 60)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
+    
+    let v2 = h.removeAt(4)
+    XCTAssertEqual(v2, 20)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
+    
+    let v3 = h.removeAt(4)
+    XCTAssertEqual(v3, 50)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [100, 65, 70, 10])
+    
+    let v4 = h.removeAt(0)
+    XCTAssertEqual(v4, 100)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [70, 65, 10])
+    
+    XCTAssertEqual(h.peek()!, 70)
+    let v5 = h.remove()
+    XCTAssertEqual(v5, 70)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [65, 10])
+    
+    XCTAssertEqual(h.peek()!, 65)
+    let v6 = h.remove()
+    XCTAssertEqual(v6, 65)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [10])
+    
+    XCTAssertEqual(h.peek()!, 10)
+    let v7 = h.remove()
+    XCTAssertEqual(v7, 10)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [])
+    
+    XCTAssertNil(h.peek())
+  }
+  
+  func testRemoveEmpty() {
+    var heap = Heap<Int>(sort: >)
+    let removed = heap.remove()
+    XCTAssertNil(removed)
+  }
+  
+  func testRemoveRoot() {
+    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+    XCTAssertEqual(h.peek()!, 15)
+    let v = h.remove()
+    XCTAssertEqual(v, 15)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
+  }
+  
+  func testRemoveRandomItems() {
+    for n in 1...40 {
+      var a = randomArray(n)
+      var h = Heap(array: a, sort: >)
+      XCTAssertTrue(verifyMaxHeap(h))
+      XCTAssertTrue(isPermutation(a, h.elements))
+      
+      let m = (n + 1)/2
+      for k in 1...m {
+        let i = Int(arc4random_uniform(UInt32(n - k + 1)))
+        let v = h.removeAt(i)!
+        let j = a.index(of: v)!
+        a.remove(at: j)
+        
         XCTAssertTrue(verifyMaxHeap(h))
-        XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
+        XCTAssertEqual(h.count, a.count)
+        XCTAssertEqual(h.count, n - k)
+        XCTAssertTrue(isPermutation(a, h.elements))
+      }
     }
+  }
+  
+  func testInsert() {
+    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+    
+    h.insert(10)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
+  }
+  
+  func testInsertArrayAndRemove() {
+    var heap = Heap<Int>(sort: >)
+    heap.insert([1, 3, 2, 7, 5, 9])
+    XCTAssertEqual(heap.elements, [9, 5, 7, 1, 3, 2])
+    
+    XCTAssertEqual(9, heap.remove())
+    XCTAssertEqual(7, heap.remove())
+    XCTAssertEqual(5, heap.remove())
+    XCTAssertEqual(3, heap.remove())
+    XCTAssertEqual(2, heap.remove())
+    XCTAssertEqual(1, heap.remove())
+    XCTAssertNil(heap.remove())
+  }
+  
+  func testReplace() {
+    var h = Heap(array: [16, 14, 10, 8, 7, 9, 3, 2, 4, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
+    
+    h.replace(index: 5, value: 13)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
+    
+    //test index out of bounds
+    h.replace(index: 20, value: 2)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
+  }
 }

From 7077bc1d6df03c0c3dce224302207ba62f86c02b Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 31 Jul 2017 16:10:56 +0900
Subject: [PATCH 062/643] Updates the indentation of the code and updated
 project settings for Xcode 9

---
 Heap Sort/HeapSort.swift                      |  8 +--
 Heap Sort/Tests/HeapSortTests.swift           | 56 +++++++++----------
 .../Tests/Tests.xcodeproj/project.pbxproj     | 14 ++++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 +-
 4 files changed, 48 insertions(+), 34 deletions(-)

diff --git a/Heap Sort/HeapSort.swift b/Heap Sort/HeapSort.swift
index 1e568f91f..6b5e91dc5 100644
--- a/Heap Sort/HeapSort.swift	
+++ b/Heap Sort/HeapSort.swift	
@@ -1,7 +1,7 @@
 extension Heap {
   public mutating func sort() -> [T] {
     for i in stride(from: (elements.count - 1), through: 1, by: -1) {
-        elements.swapAt(0, i)
+      elements.swapAt(0, i)
       shiftDown(0, heapSize: i)
     }
     return elements
@@ -9,9 +9,9 @@ extension Heap {
 }
 
 /*
-  Sorts an array using a heap.
-  Heapsort can be performed in-place, but it is not a stable sort.
-*/
+ Sorts an array using a heap.
+ Heapsort can be performed in-place, but it is not a stable sort.
+ */
 public func heapsort<T>(_ a: [T], _ sort: @escaping (T, T) -> Bool) -> [T] {
   let reverseOrder = { i1, i2 in sort(i2, i1) }
   var h = Heap(array: a, sort: reverseOrder)
diff --git a/Heap Sort/Tests/HeapSortTests.swift b/Heap Sort/Tests/HeapSortTests.swift
index 55f2f52b4..b36f605e3 100644
--- a/Heap Sort/Tests/HeapSortTests.swift	
+++ b/Heap Sort/Tests/HeapSortTests.swift	
@@ -1,33 +1,33 @@
 import XCTest
 
 class HeapSortTests: XCTestCase {
-    func testSwift4() {
-        // last checked with Xcode 9.0b4
-        #if swift(>=4.0)
-            print("Hello, Swift 4!")
-        #endif
-    }
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
+  func testSort() {
+    var h1 = Heap(array: [5, 13, 2, 25, 7, 17, 20, 8, 4], sort: >)
+    let a1 = h1.sort()
+    XCTAssertEqual(a1, [2, 4, 5, 7, 8, 13, 17, 20, 25])
     
-    func testSort() {
-        var h1 = Heap(array: [5, 13, 2, 25, 7, 17, 20, 8, 4], sort: >)
-        let a1 = h1.sort()
-        XCTAssertEqual(a1, [2, 4, 5, 7, 8, 13, 17, 20, 25])
-
-        let a1_ = heapsort([5, 13, 2, 25, 7, 17, 20, 8, 4], <)
-        XCTAssertEqual(a1_, [2, 4, 5, 7, 8, 13, 17, 20, 25])
-
-        var h2 = Heap(array: [16, 14, 10, 8, 7, 8, 3, 2, 4, 1], sort: >)
-        let a2 = h2.sort()
-        XCTAssertEqual(a2, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
-
-        let a2_ = heapsort([16, 14, 10, 8, 7, 8, 3, 2, 4, 1], <)
-        XCTAssertEqual(a2_, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
-
-        var h3 = Heap(array: [1, 2, 3, 4, 5, 6], sort: <)
-        let a3 = h3.sort()
-        XCTAssertEqual(a3, [6, 5, 4, 3, 2, 1])
-
-        let a3_ = heapsort([1, 2, 3, 4, 5, 6], >)
-        XCTAssertEqual(a3_, [6, 5, 4, 3, 2, 1])
-    }
+    let a1_ = heapsort([5, 13, 2, 25, 7, 17, 20, 8, 4], <)
+    XCTAssertEqual(a1_, [2, 4, 5, 7, 8, 13, 17, 20, 25])
+    
+    var h2 = Heap(array: [16, 14, 10, 8, 7, 8, 3, 2, 4, 1], sort: >)
+    let a2 = h2.sort()
+    XCTAssertEqual(a2, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
+    
+    let a2_ = heapsort([16, 14, 10, 8, 7, 8, 3, 2, 4, 1], <)
+    XCTAssertEqual(a2_, [1, 2, 3, 4, 7, 8, 8, 10, 14, 16])
+    
+    var h3 = Heap(array: [1, 2, 3, 4, 5, 6], sort: <)
+    let a3 = h3.sort()
+    XCTAssertEqual(a3, [6, 5, 4, 3, 2, 1])
+    
+    let a3_ = heapsort([1, 2, 3, 4, 5, 6], >)
+    XCTAssertEqual(a3_, [6, 5, 4, 3, 2, 1])
+  }
 }
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj
index 45b3f5821..ff1f4937f 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,7 +86,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -145,14 +145,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -191,14 +197,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
diff --git a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index dfcf6de42..538a6f4fa 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,6 +26,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -46,6 +47,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 9f7c12a32410dc10f14dfa64f483c50444fb98c7 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 07:46:30 -0700
Subject: [PATCH 063/643] [Swift 4] Update Array2D

---
 Array2D/Array2D.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index d31d77540..77c0b364c 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /*
  Two-dimensional array with a fixed number of rows and columns.
  This is mostly handy for games that are played on a grid, such as chess.

From b49c81322f9d41b81ac1c70f5f452f0e1ebb8b1a Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 07:48:38 -0700
Subject: [PATCH 064/643] [Swift 4] Update Binary Search

---
 Binary Search/BinarySearch.playground/Contents.swift      | 5 +++++
 Binary Search/BinarySearch.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Binary Search/BinarySearch.playground/timeline.xctimeline

diff --git a/Binary Search/BinarySearch.playground/Contents.swift b/Binary Search/BinarySearch.playground/Contents.swift
index f673f25c4..715fb5dc2 100644
--- a/Binary Search/BinarySearch.playground/Contents.swift	
+++ b/Binary Search/BinarySearch.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // An unsorted array of numbers
 let numbers = [11, 59, 3, 2, 53, 17, 31, 7, 19, 67, 47, 13, 37, 61, 29, 43, 5, 41, 23]
 
diff --git a/Binary Search/BinarySearch.playground/timeline.xctimeline b/Binary Search/BinarySearch.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Binary Search/BinarySearch.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 356c2fb881ed54e491a3b4c833dfb6f6d8a72742 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 07:50:34 -0700
Subject: [PATCH 065/643] [Swift 4] Update Binary Search Tree

---
 .../Solution 1/BinarySearchTree.playground/Contents.swift   | 5 +++++
 .../BinarySearchTree.playground/timeline.xctimeline         | 6 ------
 .../Solution 2/BinarySearchTree.playground/Contents.swift   | 5 +++++
 .../BinarySearchTree.playground/timeline.xctimeline         | 6 ------
 4 files changed, 10 insertions(+), 12 deletions(-)
 delete mode 100644 Binary Search Tree/Solution 1/BinarySearchTree.playground/timeline.xctimeline
 delete mode 100644 Binary Search Tree/Solution 2/BinarySearchTree.playground/timeline.xctimeline

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index ec9902283..8c06ae9e1 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let tree = BinarySearchTree<Int>(value: 7)
 tree.insert(value: 2)
 tree.insert(value: 5)
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/timeline.xctimeline b/Binary Search Tree/Solution 1/BinarySearchTree.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index 2b5dcc341..afa4338a9 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Each time you insert something, you get back a completely new tree.
 var tree = BinarySearchTree.leaf(7)
 tree = tree.insert(newValue: 2)
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/timeline.xctimeline b/Binary Search Tree/Solution 2/BinarySearchTree.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From c37d8cb4fcae9add99622b7116a8b13b5fd4753c Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 09:36:07 -0700
Subject: [PATCH 066/643] [Swift 4] Update Binary Tree

---
 Binary Tree/BinaryTree.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Binary Tree/BinaryTree.playground/Contents.swift b/Binary Tree/BinaryTree.playground/Contents.swift
index b0bff577a..9da194fed 100644
--- a/Binary Tree/BinaryTree.playground/Contents.swift	
+++ b/Binary Tree/BinaryTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public indirect enum BinaryTree<T> {
   case node(BinaryTree<T>, T, BinaryTree<T>)
   case empty

From 0b7d673b61934812ac3bbf020b836eb8c6bd20e6 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 09:38:37 -0700
Subject: [PATCH 067/643] [Swift 4] Update DFS

---
 .../Pages/Simple Example.xcplaygroundpage/Contents.swift     | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index 1e32b4bbf..5b1c1b3ee 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var nodesExplored = [source.label]
   source.visited = true

From 3fd8ebecfef9af9a641866d6fd5b3fa75c000d15 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 09:51:41 -0700
Subject: [PATCH 068/643] [Swift 4] Update Huffman Coding

---
 Huffman Coding/Huffman.playground/Contents.swift      | 5 +++++
 Huffman Coding/Huffman.playground/Sources/Heap.swift  | 4 ++--
 Huffman Coding/Huffman.playground/timeline.xctimeline | 4 ++--
 3 files changed, 9 insertions(+), 4 deletions(-)

diff --git a/Huffman Coding/Huffman.playground/Contents.swift b/Huffman Coding/Huffman.playground/Contents.swift
index 2d59908e9..6242ad272 100644
--- a/Huffman Coding/Huffman.playground/Contents.swift	
+++ b/Huffman Coding/Huffman.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 let s1 = "so much words wow many compression"
diff --git a/Huffman Coding/Huffman.playground/Sources/Heap.swift b/Huffman Coding/Huffman.playground/Sources/Heap.swift
index 5ace98a17..b578ef6e4 100644
--- a/Huffman Coding/Huffman.playground/Sources/Heap.swift	
+++ b/Huffman Coding/Huffman.playground/Sources/Heap.swift	
@@ -143,7 +143,7 @@ public struct Heap<T> {
   public mutating func removeAtIndex(i: Int) -> T? {
     let size = elements.count - 1
     if i != size {
-      swap(&elements[i], &elements[size])
+      elements.swapAt(i, size)
       shiftDown(index: i, heapSize: size)
       shiftUp(index: i)
     }
@@ -196,7 +196,7 @@ public struct Heap<T> {
       }
       if first == parentIndex { return }
 
-      swap(&elements[parentIndex], &elements[first])
+      elements.swapAt(parentIndex, first)
       parentIndex = first
     }
   }
diff --git a/Huffman Coding/Huffman.playground/timeline.xctimeline b/Huffman Coding/Huffman.playground/timeline.xctimeline
index 2b2555bb1..5588b0fdd 100644
--- a/Huffman Coding/Huffman.playground/timeline.xctimeline	
+++ b/Huffman Coding/Huffman.playground/timeline.xctimeline	
@@ -3,12 +3,12 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/peter/Programming/iOS/Workspace/swift-algorithm-club/Huffman%20Coding/Huffman.playground#CharacterRangeLen=19&amp;CharacterRangeLoc=678&amp;EndingLineNumber=21&amp;StartingLineNumber=21&amp;Timestamp=505135214.929897"
+         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/Huffman%20Coding/Huffman.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=752&amp;EndingColumnNumber=0&amp;EndingLineNumber=28&amp;StartingColumnNumber=0&amp;StartingLineNumber=28&amp;Timestamp=523212028.643394"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=14&amp;CharacterRangeLoc=350&amp;EndingColumnNumber=21&amp;EndingLineNumber=12&amp;StartingColumnNumber=7&amp;StartingLineNumber=12&amp;Timestamp=505138287.94525"
+         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/Huffman%20Coding/Huffman.playground#CharacterRangeLen=14&amp;CharacterRangeLoc=433&amp;EndingColumnNumber=36&amp;EndingLineNumber=17&amp;StartingColumnNumber=22&amp;StartingLineNumber=17&amp;Timestamp=523212028.643973"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>

From f93b4c583d0401ec898444c58c29d671ed9d9925 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 09:53:46 -0700
Subject: [PATCH 069/643] [Swift 4] Update Deque

---
 Deque/Deque.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Deque/Deque.playground/Contents.swift b/Deque/Deque.playground/Contents.swift
index 9e7b22c02..df9b57a5e 100644
--- a/Deque/Deque.playground/Contents.swift
+++ b/Deque/Deque.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public struct Deque<T> {
   private var array = [T]()
 

From afcfa8028ca28bc37f35b0fccdd6d25a5fa33365 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 09:59:00 -0700
Subject: [PATCH 070/643] [Swift 4] Update Ordered Array

---
 Ordered Array/OrderedArray.playground/Contents.swift      | 5 +++++
 Ordered Array/OrderedArray.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Ordered Array/OrderedArray.playground/timeline.xctimeline

diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index 4fe199f28..5b6be6420 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public struct OrderedArray<T: Comparable> {
   fileprivate var array = [T]()
 
diff --git a/Ordered Array/OrderedArray.playground/timeline.xctimeline b/Ordered Array/OrderedArray.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Ordered Array/OrderedArray.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 9f38465199328cb708996f863492acc600c64498 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:05:59 -0700
Subject: [PATCH 071/643] Update Monty Hall Problem to Swift 4

Updated to work with Swift 4 and Xcode 9.0b4.
---
 Monty Hall Problem/MontyHall.playground/Contents.swift | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/Monty Hall Problem/MontyHall.playground/Contents.swift b/Monty Hall Problem/MontyHall.playground/Contents.swift
index bcdafd137..4bfff2340 100644
--- a/Monty Hall Problem/MontyHall.playground/Contents.swift	
+++ b/Monty Hall Problem/MontyHall.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 func random(_ n: Int) -> Int {
@@ -43,7 +48,7 @@ func playRound() {
 }
 
 // Run the simulation a large number of times.
-for i in 1...5000 {
+for _ in 1...5000 {
   playRound()
 }
 

From 0b097d82979cd624549154b39442860285923441 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:10:24 -0700
Subject: [PATCH 072/643] Update Minimum Edit Distance to Swift 4

Updated to work with Swift 4 and Xcode 9.0b4.
---
 .../MinimumEditDistance.playground/Contents.swift        | 9 ++++++++-
 .../MinimumEditDistance.playground/contents.xcplayground | 0
 Minimum Edit Distance/README.markdown                    | 2 +-
 3 files changed, 9 insertions(+), 2 deletions(-)
 mode change 100755 => 100644 Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
 mode change 100755 => 100644 Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground

diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
old mode 100755
new mode 100644
index 238afeb9b..479815df7
--- a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
@@ -1,3 +1,10 @@
+// Minimum Edit Distance
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 extension String {
 
     public func minimumEditDistance(other: String) -> Int {
@@ -25,7 +32,7 @@ extension String {
                 } else {
                     // minimum of the cost of insertion, deletion, or substitution 
                     // added to the already computed costs in the corresponding cells
-                    matrix[i + 1][j + 1] = min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
+                    matrix[i + 1][j + 1] = Swift.min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
                 }
             }
         }
diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground b/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground
old mode 100755
new mode 100644
diff --git a/Minimum Edit Distance/README.markdown b/Minimum Edit Distance/README.markdown
index 905b358ae..b8880b2d4 100755
--- a/Minimum Edit Distance/README.markdown	
+++ b/Minimum Edit Distance/README.markdown	
@@ -45,7 +45,7 @@ for (i, selfChar) in self.characters.enumerated() {
         } else {
             // minimum of the cost of insertion, deletion, or substitution 
             // added to the already computed costs in the corresponding cells
-            matrix[i + 1][j + 1] = min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
+            matrix[i + 1][j + 1] = Swift.min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
         } 
     }
 }

From 4c340abda42967ada0a272ff5cec4ae2fa065bd5 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:14:08 -0700
Subject: [PATCH 073/643] Update Ring Buffer to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Ring Buffer/RingBuffer.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Ring Buffer/RingBuffer.playground/Contents.swift b/Ring Buffer/RingBuffer.playground/Contents.swift
index 29b9917a0..5c699f191 100644
--- a/Ring Buffer/RingBuffer.playground/Contents.swift	
+++ b/Ring Buffer/RingBuffer.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public struct RingBuffer<T> {
   fileprivate var array: [T?]
   fileprivate var readIndex = 0

From b26a44ccead4c51f0c4b1d31e0a0192bb3cea6d6 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:16:45 -0700
Subject: [PATCH 074/643] Update Run-Length Encoding to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Run-Length Encoding/RLE.playground/Contents.swift      | 5 +++++
 Run-Length Encoding/RLE.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Run-Length Encoding/RLE.playground/timeline.xctimeline

diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
index 26f7dca48..fc2d82505 100644
--- a/Run-Length Encoding/RLE.playground/Contents.swift	
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 let originalString = "aaaaabbbcdeeeeeeef"
diff --git a/Run-Length Encoding/RLE.playground/timeline.xctimeline b/Run-Length Encoding/RLE.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Run-Length Encoding/RLE.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 21dc86c550e0be0155883255809038c522c5e290 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:20:29 -0700
Subject: [PATCH 075/643] Update Linear Search to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Linear Search/LinearSearch.playground/Contents.swift      | 5 +++++
 Linear Search/LinearSearch.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Linear Search/LinearSearch.playground/timeline.xctimeline

diff --git a/Linear Search/LinearSearch.playground/Contents.swift b/Linear Search/LinearSearch.playground/Contents.swift
index 34e859fa3..dad9a77bd 100644
--- a/Linear Search/LinearSearch.playground/Contents.swift	
+++ b/Linear Search/LinearSearch.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
   for (index, obj) in array.enumerated() where obj == object {
     return index
diff --git a/Linear Search/LinearSearch.playground/timeline.xctimeline b/Linear Search/LinearSearch.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Linear Search/LinearSearch.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From f10b1b19c290ce040a9cce25a35ec4974bd68e19 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:23:38 -0700
Subject: [PATCH 076/643] Update Selection Sampling to Swift 4

Update to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 .../SelectionSampling.playground/Contents.swift              | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Selection Sampling/SelectionSampling.playground/Contents.swift b/Selection Sampling/SelectionSampling.playground/Contents.swift
index 4a2484162..f4aace0c7 100644
--- a/Selection Sampling/SelectionSampling.playground/Contents.swift	
+++ b/Selection Sampling/SelectionSampling.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 /* Returns a random integer in the range min...max, inclusive. */

From d3dd6c8b1cf08fc2ecec0ed7039ef40f8236d319 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:26:46 -0700
Subject: [PATCH 077/643] Update Rabin-Karp to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Rabin-Karp/Rabin-Karp.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Rabin-Karp/Rabin-Karp.playground/Contents.swift b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
index 4956fabe3..c0a99339a 100644
--- a/Rabin-Karp/Rabin-Karp.playground/Contents.swift
+++ b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Taking our rabin-karp algorithm for a walk
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import UIKit
 
 struct Constants {

From b6c7f6d922dc0fd35b2c4fdd4b3d90e731adb5bd Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:29:48 -0700
Subject: [PATCH 078/643] Update Radix Tree to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Radix Tree/RadixTree.playground/Contents.swift | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Radix Tree/RadixTree.playground/Contents.swift b/Radix Tree/RadixTree.playground/Contents.swift
index e161e48a2..a5e614849 100644
--- a/Radix Tree/RadixTree.playground/Contents.swift	
+++ b/Radix Tree/RadixTree.playground/Contents.swift	
@@ -1,3 +1,10 @@
+// Radix Tree
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 var radix = RadixTree()
 var radixWiki = RadixTree()
 

From 713bf52f2495203fb2806bd3944028f3e9718519 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:32:04 -0700
Subject: [PATCH 079/643] Updated SetCover to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Set Cover (Unweighted)/SetCover.playground/Contents.swift | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Set Cover (Unweighted)/SetCover.playground/Contents.swift b/Set Cover (Unweighted)/SetCover.playground/Contents.swift
index dcf998a66..d61b9c84a 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
@@ -1,3 +1,10 @@
+// SetCover
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let universe1 = Set(1...7)
 let array1 = randomArrayOfSets(covering: universe1)
 let cover1 = universe1.cover(within: array1)

From db1fc17de22adf7c4cc08117d02686abedb01149 Mon Sep 17 00:00:00 2001
From: Bob DeLaurentis <lists@bobdel.com>
Date: Mon, 31 Jul 2017 12:37:54 -0700
Subject: [PATCH 080/643] Update Naive Bayes Classifier to Swift 4

Updated to Swift 4 and Xcode 9.0b4. No changes necessary.
---
 Naive Bayes Classifier/NaiveBayes.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift
index 66aefaa32..6a2e01aab 100644
--- a/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
+++ b/Naive Bayes Classifier/NaiveBayes.playground/Contents.swift	
@@ -1,5 +1,10 @@
 import Foundation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /*:
  ## Naive Bayes Classifier
 

From b8d324e3309db84e2b0f645d864bccff90f44683 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 12:54:53 -0700
Subject: [PATCH 081/643] [Swift 4] Update All Pairs Shortest Paths

---
 .../APSP/APSP.playground/Contents.swift                    | 5 +++++
 .../APSP/APSP.playground/timeline.xctimeline               | 4 ++--
 .../APSP/APSP.xcodeproj/project.pbxproj                    | 4 ++--
 All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift    | 7 +++++++
 Graph/GraphTests/GraphTests.swift                          | 7 +++++++
 5 files changed, 23 insertions(+), 4 deletions(-)

diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift
index 24c27cac8..b1b499b39 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Graph
 import APSP
 
diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline b/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline
index 2c73a4e3e..c938ca857 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline	
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/timeline.xctimeline	
@@ -3,12 +3,12 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=888&amp;EndingColumnNumber=44&amp;EndingLineNumber=29&amp;StartingColumnNumber=3&amp;StartingLineNumber=28&amp;Timestamp=486844329.035763"
+         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/All-Pairs%20Shortest%20Paths/APSP/APSP.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=971&amp;EndingColumnNumber=68&amp;EndingLineNumber=34&amp;StartingColumnNumber=68&amp;StartingLineNumber=34&amp;Timestamp=523221730.015692"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=4&amp;CharacterRangeLoc=825&amp;EndingColumnNumber=9&amp;EndingLineNumber=29&amp;StartingColumnNumber=5&amp;StartingLineNumber=29&amp;Timestamp=486844329.036018"
+         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/All-Pairs%20Shortest%20Paths/APSP/APSP.playground#CharacterRangeLen=4&amp;CharacterRangeLoc=908&amp;EndingColumnNumber=9&amp;EndingLineNumber=34&amp;StartingColumnNumber=5&amp;StartingLineNumber=34&amp;Timestamp=523221730.015887"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj
index b2d93ea35..78df3fb76 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
@@ -388,7 +388,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -400,7 +400,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift
index 9d026f680..c2f64e239 100644
--- a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
@@ -20,6 +20,13 @@ struct TestCase<T> where T: Hashable {
 
 class APSPTests: XCTestCase {
 
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+
   /**
    See Figure 25.1 of “Introduction to Algorithms” by Cormen et al, 3rd ed., pg 690
    */
diff --git a/Graph/GraphTests/GraphTests.swift b/Graph/GraphTests/GraphTests.swift
index 289d9aa64..92a4ce828 100644
--- a/Graph/GraphTests/GraphTests.swift
+++ b/Graph/GraphTests/GraphTests.swift
@@ -10,6 +10,13 @@ import XCTest
 
 class GraphTests: XCTestCase {
 
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+
   func testAdjacencyMatrixGraphDescription() {
 
     let graph = AdjacencyMatrixGraph<String>()

From 1baaac856e5b3d99ece99594b8c0278f0c5be47b Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 12:58:32 -0700
Subject: [PATCH 082/643] [Swift 4] Update Brute Force String Search

---
 .../BruteForceStringSearch.playground/Contents.swift         | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
index fcee59a7b..003a87e8f 100644
--- a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 extension String {
   func indexOf(_ pattern: String) -> String.Index? {
 

From 52802514df40566b0899dc54272649623da8b2af Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 13:00:14 -0700
Subject: [PATCH 083/643] [Swift 4] Update Insertion Sort

---
 Insertion Sort/InsertionSort.playground/Contents.swift      | 5 +++++
 Insertion Sort/InsertionSort.playground/timeline.xctimeline | 6 ------
 2 files changed, 5 insertions(+), 6 deletions(-)
 delete mode 100644 Insertion Sort/InsertionSort.playground/timeline.xctimeline

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index df1822b8f..91e18640f 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   var a = array
   for x in 1..<a.count {
diff --git a/Insertion Sort/InsertionSort.playground/timeline.xctimeline b/Insertion Sort/InsertionSort.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Insertion Sort/InsertionSort.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From be012cc5df1acd178c770659dafa575d3c0b048d Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 01:43:58 +0500
Subject: [PATCH 084/643] Migrated to Swift 4

---
 AVL Tree/AVLTree.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/AVL Tree/AVLTree.playground/Contents.swift b/AVL Tree/AVLTree.playground/Contents.swift
index 409dfdc49..04ef78d07 100644
--- a/AVL Tree/AVLTree.playground/Contents.swift	
+++ b/AVL Tree/AVLTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let tree = AVLTree<Int, String>()
 
 tree.insert(key: 5, payload: "five")

From 190cc4e9a91a9fc28f14104b484ed72d6bca4136 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 01:51:23 +0500
Subject: [PATCH 085/643] Updated Test for Swift4

---
 AVL Tree/Tests/AVLTreeTests.swift              | 8 ++++++--
 AVL Tree/Tests/Tests.xcodeproj/project.pbxproj | 6 ++++--
 AVL Tree/Tests/TreeNodeTests.swift             | 9 +++++++--
 3 files changed, 17 insertions(+), 6 deletions(-)

diff --git a/AVL Tree/Tests/AVLTreeTests.swift b/AVL Tree/Tests/AVLTreeTests.swift
index 7765c6d29..a9e932117 100644
--- a/AVL Tree/Tests/AVLTreeTests.swift	
+++ b/AVL Tree/Tests/AVLTreeTests.swift	
@@ -7,11 +7,15 @@
 //
 
 import XCTest
-
 class AVLTreeTests: XCTestCase {
-
   var tree: AVLTree<Int, String>?
 
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
   override func setUp() {
     super.setUp()
 
diff --git a/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj b/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj
index 64c244747..e7c6e2989 100644
--- a/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/AVL Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -180,6 +180,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -219,6 +220,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -230,7 +232,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -242,7 +244,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/AVL Tree/Tests/TreeNodeTests.swift b/AVL Tree/Tests/TreeNodeTests.swift
index cac7e549b..dc393232c 100644
--- a/AVL Tree/Tests/TreeNodeTests.swift	
+++ b/AVL Tree/Tests/TreeNodeTests.swift	
@@ -9,11 +9,16 @@
 import XCTest
 
 class TreeNodeTests: XCTestCase {
-
+   
     var root: TreeNode<String, String>?
     var left: TreeNode<String, String>?
     var right: TreeNode<String, String>?
-
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
     override func setUp() {
         super.setUp()
 

From aad5d28451f271dcf4f47e04613fe0e195e37a28 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 01:55:44 +0500
Subject: [PATCH 086/643] B-Tree Playground & Tests updated to Swift 4

---
 B-Tree/BTree.playground/Contents.swift       |  7 +-
 B-Tree/Tests/Tests.xcodeproj/project.pbxproj |  6 +-
 B-Tree/Tests/Tests/BTreeNodeTests.swift      | 87 +++++++++++---------
 B-Tree/Tests/Tests/BTreeTests.swift          |  7 ++
 4 files changed, 63 insertions(+), 44 deletions(-)

diff --git a/B-Tree/BTree.playground/Contents.swift b/B-Tree/BTree.playground/Contents.swift
index 710ace701..a0643586f 100644
--- a/B-Tree/BTree.playground/Contents.swift
+++ b/B-Tree/BTree.playground/Contents.swift
@@ -2,6 +2,11 @@
 
 import Foundation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let bTree = BTree<Int, Int>(order: 1)!
 
 bTree.insert(1, for: 1)
@@ -15,7 +20,7 @@ bTree[3]
 bTree.remove(2)
 
 bTree.traverseKeysInOrder { key in
-  print(key)
+    print(key)
 }
 
 bTree.numberOfKeys
diff --git a/B-Tree/Tests/Tests.xcodeproj/project.pbxproj b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
index 79552bbe5..3e12b9ac3 100644
--- a/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
+++ b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
@@ -179,6 +179,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -219,6 +220,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -232,7 +234,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = viktorsimko.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -245,7 +247,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = viktorsimko.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/B-Tree/Tests/Tests/BTreeNodeTests.swift b/B-Tree/Tests/Tests/BTreeNodeTests.swift
index 8eff926b5..80de8b845 100644
--- a/B-Tree/Tests/Tests/BTreeNodeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeNodeTests.swift
@@ -9,45 +9,50 @@
 import XCTest
 
 class BTreeNodeTests: XCTestCase {
-
-  let owner = BTree<Int, Int>(order: 2)!
-  var root: BTreeNode<Int, Int>!
-  var leftChild: BTreeNode<Int, Int>!
-  var rightChild: BTreeNode<Int, Int>!
-
-  override func setUp() {
-    super.setUp()
-
-    root = BTreeNode(owner: owner)
-    leftChild = BTreeNode(owner: owner)
-    rightChild = BTreeNode(owner: owner)
-
-    root.insert(1, for: 1)
-    root.children = [leftChild, rightChild]
-  }
-
-  func testIsLeafRoot() {
-    XCTAssertFalse(root.isLeaf)
-  }
-
-  func testIsLeafLeaf() {
-    XCTAssertTrue(leftChild.isLeaf)
-    XCTAssertTrue(rightChild.isLeaf)
-  }
-
-  func testOwner() {
-    XCTAssert(root.owner === owner)
-    XCTAssert(leftChild.owner === owner)
-    XCTAssert(rightChild.owner === owner)
-  }
-
-  func testNumberOfKeys() {
-    XCTAssertEqual(root.numberOfKeys, 1)
-    XCTAssertEqual(leftChild.numberOfKeys, 0)
-    XCTAssertEqual(rightChild.numberOfKeys, 0)
-  }
-
-  func testChildren() {
-    XCTAssertEqual(root.children!.count, 2)
-  }
+    
+    let owner = BTree<Int, Int>(order: 2)!
+    var root: BTreeNode<Int, Int>!
+    var leftChild: BTreeNode<Int, Int>!
+    var rightChild: BTreeNode<Int, Int>!
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
+    override func setUp() {
+        super.setUp()
+        
+        root = BTreeNode(owner: owner)
+        leftChild = BTreeNode(owner: owner)
+        rightChild = BTreeNode(owner: owner)
+        
+        root.insert(1, for: 1)
+        root.children = [leftChild, rightChild]
+    }
+    
+    func testIsLeafRoot() {
+        XCTAssertFalse(root.isLeaf)
+    }
+    
+    func testIsLeafLeaf() {
+        XCTAssertTrue(leftChild.isLeaf)
+        XCTAssertTrue(rightChild.isLeaf)
+    }
+    
+    func testOwner() {
+        XCTAssert(root.owner === owner)
+        XCTAssert(leftChild.owner === owner)
+        XCTAssert(rightChild.owner === owner)
+    }
+    
+    func testNumberOfKeys() {
+        XCTAssertEqual(root.numberOfKeys, 1)
+        XCTAssertEqual(leftChild.numberOfKeys, 0)
+        XCTAssertEqual(rightChild.numberOfKeys, 0)
+    }
+    
+    func testChildren() {
+        XCTAssertEqual(root.children!.count, 2)
+    }
 }
diff --git a/B-Tree/Tests/Tests/BTreeTests.swift b/B-Tree/Tests/Tests/BTreeTests.swift
index 1e94bfd7d..69d7ce55d 100644
--- a/B-Tree/Tests/Tests/BTreeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeTests.swift
@@ -11,6 +11,13 @@ import XCTest
 class BTreeTests: XCTestCase {
   var bTree: BTree<Int, Int>!
 
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
+    
   override func setUp() {
     super.setUp()
     bTree = BTree<Int, Int>(order: 3)!

From efa7e4e5d33468b19d56b5aab43b5a215943038f Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 02:17:41 +0500
Subject: [PATCH 087/643] Updated Bloom Filter code & Test to Swift4

---
 Bloom Filter/BloomFilter.playground/Contents.swift | 5 ++++-
 Bloom Filter/Tests/BloomFilterTests.swift          | 7 ++++++-
 Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj | 6 ++++--
 3 files changed, 14 insertions(+), 4 deletions(-)

diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index 3dac76e8e..9e4a89351 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -1,5 +1,8 @@
 //: Playground - noun: a place where people can play
-
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 public class BloomFilter<T> {
   fileprivate var array: [Bool]
   private var hashFunctions: [(T) -> Int]
diff --git a/Bloom Filter/Tests/BloomFilterTests.swift b/Bloom Filter/Tests/BloomFilterTests.swift
index 55db71f3f..30df702a7 100644
--- a/Bloom Filter/Tests/BloomFilterTests.swift	
+++ b/Bloom Filter/Tests/BloomFilterTests.swift	
@@ -24,7 +24,12 @@ func sdbm(_ x: String) -> Int {
 }
 
 class BloomFilterTests: XCTestCase {
-
+    func testSwift4(){
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
   func testSingleHashFunction() {
     let bloom = BloomFilter<String>(hashFunctions: [djb2])
 
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj
index 20998a80e..6493fd153 100644
--- a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
@@ -176,6 +176,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -215,6 +216,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -226,7 +228,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -238,7 +240,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From 85ff254cdda24448c2560aa21303fef603edabf1 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 02:39:03 +0500
Subject: [PATCH 088/643] Migrated Playground and Test to Swift 4

---
 Comb Sort/Comb Sort.playground/Contents.swift          | 4 ++++
 Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift | 2 +-
 Comb Sort/Comb Sort.swift                              | 6 +++---
 Comb Sort/Tests/CombSortTests.swift                    | 5 +++++
 Comb Sort/Tests/Tests.xcodeproj/project.pbxproj        | 6 ++++--
 5 files changed, 17 insertions(+), 6 deletions(-)

diff --git a/Comb Sort/Comb Sort.playground/Contents.swift b/Comb Sort/Comb Sort.playground/Contents.swift
index 40176be9f..39e24248a 100644
--- a/Comb Sort/Comb Sort.playground/Contents.swift	
+++ b/Comb Sort/Comb Sort.playground/Contents.swift	
@@ -3,6 +3,10 @@
 // 7-16-2016
 
 import Cocoa
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 // Test Comb Sort with small array of ten values
 let array = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
diff --git a/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift b/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift
index f7c4eec61..559fe47e8 100644
--- a/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift	
+++ b/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift	
@@ -21,7 +21,7 @@ public func combSort<T: Comparable>(_ input: [T]) -> [T] {
         var index = 0
         while !(index + gap >= copy.count) {
             if copy[index] > copy[index + gap] {
-                swap(&copy[index], &copy[index + gap])
+               copy.swapAt(index, index + gap)
             }
             index += 1
         }
diff --git a/Comb Sort/Comb Sort.swift b/Comb Sort/Comb Sort.swift
index f7c4eec61..bd37fed42 100644
--- a/Comb Sort/Comb Sort.swift	
+++ b/Comb Sort/Comb Sort.swift	
@@ -11,17 +11,17 @@ public func combSort<T: Comparable>(_ input: [T]) -> [T] {
     var copy: [T] = input
     var gap = copy.count
     let shrink = 1.3
-
+    
     while gap > 1 {
         gap = (Int)(Double(gap) / shrink)
         if gap < 1 {
             gap = 1
         }
-
+        
         var index = 0
         while !(index + gap >= copy.count) {
             if copy[index] > copy[index + gap] {
-                swap(&copy[index], &copy[index + gap])
+                copy.swapAt(index, index + gap)
             }
             index += 1
         }
diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
index b9287f84a..e972c0a57 100644
--- a/Comb Sort/Tests/CombSortTests.swift	
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -12,6 +12,11 @@ class CombSortTests: XCTestCase {
     var sequence: [Int]!
     let expectedSequence: [Int] = [-12, -10, -1, 2, 9, 32, 55, 67, 89, 101]
 
+    func testSwift4(){
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
     override func setUp() {
         super.setUp()
         sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
diff --git a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj
index 60039196c..7530acbdc 100644
--- a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -179,6 +179,7 @@
 				SDKROOT = macosx;
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -220,6 +221,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -233,7 +235,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "Swift-Algorithm-Club.Tests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -246,7 +248,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "Swift-Algorithm-Club.Tests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From 05bf739ae9e0810633bcc14f48c4f46019e16c0f Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:04:04 -0700
Subject: [PATCH 089/643] [Swift 4] Update Counting Sort

---
 Counting Sort/CountingSort.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index dc375512a..4d918e384 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 enum CountingSortError: Error {
   case arrayEmpty
 }

From 47358d8ee427a5860a43ab0788045d91a6dcaba9 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:06:33 -0700
Subject: [PATCH 090/643] [Swift 4] Update Bounded PQ

---
 .../BoundedPriorityQueue.playground/Contents.swift           | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift
index d6204abec..f8e219c13 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 struct Message: Comparable, CustomStringConvertible {
   let name: String
   let priority: Int

From 649db39d6f7c1b7e1e080aa252c24a4b218cffd9 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:10:09 -0700
Subject: [PATCH 091/643] [Swift 4] Update BFS

---
 .../Pages/Simple example.xcplaygroundpage/Contents.swift     | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index 675be2203..3986a0cee 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func breadthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
   queue.enqueue(source)

From c9afacb4e3be3ccca28614153b7727be6264e149 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:12:43 -0700
Subject: [PATCH 092/643] [Swift 4] Update Combinatorics

---
 Combinatorics/Combinatorics.playground/Contents.swift    | 9 +++++++--
 .../Combinatorics.playground/timeline.xctimeline         | 6 ------
 2 files changed, 7 insertions(+), 8 deletions(-)
 delete mode 100644 Combinatorics/Combinatorics.playground/timeline.xctimeline

diff --git a/Combinatorics/Combinatorics.playground/Contents.swift b/Combinatorics/Combinatorics.playground/Contents.swift
index 9fbcc1c58..2daa5f22f 100644
--- a/Combinatorics/Combinatorics.playground/Contents.swift
+++ b/Combinatorics/Combinatorics.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /* Calculates n! */
 func factorial(_ n: Int) -> Int {
   var n = n
@@ -44,9 +49,9 @@ func permuteWirth<T>(_ a: [T], _ n: Int) {
     var a = a
     permuteWirth(a, n - 1)
     for i in 0..<n {
-      swap(&a[i], &a[n])
+      a.swapAt(i, n)
       permuteWirth(a, n - 1)
-      swap(&a[i], &a[n])
+      a.swapAt(i, n)
     }
   }
 }
diff --git a/Combinatorics/Combinatorics.playground/timeline.xctimeline b/Combinatorics/Combinatorics.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Combinatorics/Combinatorics.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From b9cbc739e862d847622d77bfbabfa3a09a5bcfa7 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:17:02 -0700
Subject: [PATCH 093/643] [Swift 4] Update Convex Hull

---
 .../Convex Hull.xcodeproj/project.pbxproj     |   5 +-
 Convex Hull/Convex Hull/View.swift            | 255 +++++++++---------
 2 files changed, 133 insertions(+), 127 deletions(-)

diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
index 2f236b013..bb3189d64 100644
--- a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -254,7 +254,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -267,7 +267,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -290,6 +290,7 @@
 				8E6D68CA1E59989400161780 /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index 2f2c3e046..408689a13 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -10,168 +10,173 @@ import UIKit
 
 class View: UIView {
 
-    let MAX_POINTS = 100
-
-    var points = [CGPoint]()
-
-    var convexHull = [CGPoint]()
-
-    override init(frame: CGRect) {
-        super.init(frame: frame)
-
-        generatePoints()
-        quickHull(points: points)
-    }
-
-    required init?(coder aDecoder: NSCoder) {
-        fatalError("init(coder:) has not been implemented")
+  let MAX_POINTS = 100
+
+  var points = [CGPoint]()
+
+  var convexHull = [CGPoint]()
+
+  override init(frame: CGRect) {
+    super.init(frame: frame)
+
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+    
+    generatePoints()
+    quickHull(points: points)
+  }
+
+  required init?(coder aDecoder: NSCoder) {
+    fatalError("init(coder:) has not been implemented")
+  }
+
+  func generatePoints() {
+    for _ in 0..<MAX_POINTS {
+      let offset: CGFloat = 50
+      let xrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.width - offset) + 0.5 * offset
+      let yrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.height - offset) + 0.5 * offset
+      let point = CGPoint(x: xrand, y: yrand)
+      points.append(point)
     }
 
-    func generatePoints() {
-        for _ in 0..<MAX_POINTS {
-            let offset: CGFloat = 50
-            let xrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.width - offset) + 0.5 * offset
-            let yrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.height - offset) + 0.5 * offset
-            let point = CGPoint(x: xrand, y: yrand)
-            points.append(point)
-        }
-
-        points.sort { (a: CGPoint, b: CGPoint) -> Bool in
-            return a.x < b.x
-        }
+    points.sort { (a: CGPoint, b: CGPoint) -> Bool in
+      return a.x < b.x
     }
+  }
 
-    func quickHull(points: [CGPoint]) {
-        var pts = points
+  func quickHull(points: [CGPoint]) {
+    var pts = points
 
-        // Assume points has at least 2 points
-        // Assume list is ordered on x
+    // Assume points has at least 2 points
+    // Assume list is ordered on x
 
-        // left most point
-        let p1 = pts.removeFirst()
-        // right most point
-        let p2 = pts.removeLast()
+    // left most point
+    let p1 = pts.removeFirst()
+    // right most point
+    let p2 = pts.removeLast()
 
-        // p1 and p2 are outer most points and thus are part of the hull
-        convexHull.append(p1)
-        convexHull.append(p2)
+    // p1 and p2 are outer most points and thus are part of the hull
+    convexHull.append(p1)
+    convexHull.append(p2)
 
-        // points to the right of oriented line from p1 to p2
-        var s1 = [CGPoint]()
+    // points to the right of oriented line from p1 to p2
+    var s1 = [CGPoint]()
 
-        // points to the right of oriented line from p2 to p1
-        var s2 = [CGPoint]()
+    // points to the right of oriented line from p2 to p1
+    var s2 = [CGPoint]()
 
-        // p1 to p2 line
-        let lineVec1 = CGPoint(x: p2.x - p1.x, y: p2.y - p1.y)
+    // p1 to p2 line
+    let lineVec1 = CGPoint(x: p2.x - p1.x, y: p2.y - p1.y)
 
-        for p in pts { // per point check if point is to right or left of p1 to p2 line
-            let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y)
-            let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // cross product to check on which side of the line point p is.
+    for p in pts { // per point check if point is to right or left of p1 to p2 line
+      let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y)
+      let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // cross product to check on which side of the line point p is.
 
-            if sign1 > 0 { // right of p1 p2 line (in a normal xy coordinate system this would be < 0 but due to the weird iPhone screen coordinates this is > 0
-                s1.append(p)
-            } else { // right of p2 p1 line
-                s2.append(p)
-            }
-        }
-
-        // find new hull points
-        findHull(s1, p1, p2)
-        findHull(s2, p2, p1)
+      if sign1 > 0 { // right of p1 p2 line (in a normal xy coordinate system this would be < 0 but due to the weird iPhone screen coordinates this is > 0
+        s1.append(p)
+      } else { // right of p2 p1 line
+        s2.append(p)
+      }
     }
 
-    func findHull(_ points: [CGPoint], _ p1: CGPoint, _ p2: CGPoint) {
-        // if set of points is empty there are no points to the right of this line so this line is part of the hull.
-        if points.isEmpty {
-            return
-        }
+    // find new hull points
+    findHull(s1, p1, p2)
+    findHull(s2, p2, p1)
+  }
 
-        var pts = points
+  func findHull(_ points: [CGPoint], _ p1: CGPoint, _ p2: CGPoint) {
+    // if set of points is empty there are no points to the right of this line so this line is part of the hull.
+    if points.isEmpty {
+      return
+    }
 
-        // calculate parameters of general line equation y = a * x + b
-        let a = (p1.y - p2.y) / (p1.x - p2.x)
-        let b = p1.y - a * p1.x
+    var pts = points
 
-        // calculate normal line's growth factor
-        let a1 = -1 / a
+    // calculate parameters of general line equation y = a * x + b
+    let a = (p1.y - p2.y) / (p1.x - p2.x)
+    let b = p1.y - a * p1.x
 
-        var maxDist: CGFloat = -1
-        var maxPoint: CGPoint = pts.first!
+    // calculate normal line's growth factor
+    let a1 = -1 / a
 
-        for p in pts { // for every point check the distance from our line
-            let b1 = p.y - a1 * p.x // calculate offset to line equation for given point p
-            let x = -(b - b1)/(a - a1) // calculate x where the two lines intersect
-            let y = a * x + b // calculate y value of this intersect point
+    var maxDist: CGFloat = -1
+    var maxPoint: CGPoint = pts.first!
 
-            let dist = pow(x - p.x, 2) + pow(y - p.y, 2) // calculate distance squared between intersection point and point p
-            if dist > maxDist { // if distance is larger than current maxDist remember new point p
-                maxDist = dist
-                maxPoint = p
-            }
-        }
+    for p in pts { // for every point check the distance from our line
+      let b1 = p.y - a1 * p.x // calculate offset to line equation for given point p
+      let x = -(b - b1)/(a - a1) // calculate x where the two lines intersect
+      let y = a * x + b // calculate y value of this intersect point
 
-        convexHull.insert(maxPoint, at: convexHull.index(of: p1)! + 1) // insert point with max distance from line in the convexHull after p1
+      let dist = pow(x - p.x, 2) + pow(y - p.y, 2) // calculate distance squared between intersection point and point p
+      if dist > maxDist { // if distance is larger than current maxDist remember new point p
+        maxDist = dist
+        maxPoint = p
+      }
+    }
 
-        pts.remove(at: pts.index(of: maxPoint)!) // remove maxPoint from points array as we are going to split this array in points left and right of the line
+    convexHull.insert(maxPoint, at: convexHull.index(of: p1)! + 1) // insert point with max distance from line in the convexHull after p1
 
-        // points to the right of oriented line from p1 to maxPoint
-        var s1 = [CGPoint]()
+    pts.remove(at: pts.index(of: maxPoint)!) // remove maxPoint from points array as we are going to split this array in points left and right of the line
 
-        // points to the right of oriented line from maxPoint to p2
-        var s2 = [CGPoint]()
+    // points to the right of oriented line from p1 to maxPoint
+    var s1 = [CGPoint]()
 
-        // p1 to maxPoint line
-        let lineVec1 = CGPoint(x: maxPoint.x - p1.x, y: maxPoint.y - p1.y)
-        // maxPoint to p2 line
-        let lineVec2 = CGPoint(x: p2.x - maxPoint.x, y: p2.y - maxPoint.y)
+    // points to the right of oriented line from maxPoint to p2
+    var s2 = [CGPoint]()
 
-        for p in pts {
-            let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y) // vector from p1 to p
-            let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // sign to check is p is to the right or left of lineVec1
+    // p1 to maxPoint line
+    let lineVec1 = CGPoint(x: maxPoint.x - p1.x, y: maxPoint.y - p1.y)
+    // maxPoint to p2 line
+    let lineVec2 = CGPoint(x: p2.x - maxPoint.x, y: p2.y - maxPoint.y)
 
-            let pVec2 = CGPoint(x: p.x - maxPoint.x, y: p.y - maxPoint.y) // vector from p2 to p
-            let sign2 = lineVec2.x * pVec2.y - pVec2.x * lineVec2.y // sign to check is p is to the right or left of lineVec2
+    for p in pts {
+      let pVec1 = CGPoint(x: p.x - p1.x, y: p.y - p1.y) // vector from p1 to p
+      let sign1 = lineVec1.x * pVec1.y - pVec1.x * lineVec1.y // sign to check is p is to the right or left of lineVec1
 
-            if sign1 > 0 { // right of p1 maxPoint line
-                s1.append(p)
-            } else if sign2 > 0 { // right of maxPoint p2 line
-                s2.append(p)
-            }
-        }
+      let pVec2 = CGPoint(x: p.x - maxPoint.x, y: p.y - maxPoint.y) // vector from p2 to p
+      let sign2 = lineVec2.x * pVec2.y - pVec2.x * lineVec2.y // sign to check is p is to the right or left of lineVec2
 
-        // find new hull points
-        findHull(s1, p1, maxPoint)
-        findHull(s2, maxPoint, p2)
+      if sign1 > 0 { // right of p1 maxPoint line
+        s1.append(p)
+      } else if sign2 > 0 { // right of maxPoint p2 line
+        s2.append(p)
+      }
     }
 
-    override func draw(_ rect: CGRect) {
+    // find new hull points
+    findHull(s1, p1, maxPoint)
+    findHull(s2, maxPoint, p2)
+  }
 
-        let context = UIGraphicsGetCurrentContext()
+  override func draw(_ rect: CGRect) {
 
-        // Draw hull
-        let lineWidth: CGFloat = 2.0
+    let context = UIGraphicsGetCurrentContext()
 
-        context!.setFillColor(UIColor.black.cgColor)
-        context!.setLineWidth(lineWidth)
-        context!.setStrokeColor(UIColor.red.cgColor)
-        context!.setFillColor(UIColor.black.cgColor)
+    // Draw hull
+    let lineWidth: CGFloat = 2.0
 
-        let firstPoint = convexHull.first!
-        context!.move(to: firstPoint)
+    context!.setFillColor(UIColor.black.cgColor)
+    context!.setLineWidth(lineWidth)
+    context!.setStrokeColor(UIColor.red.cgColor)
+    context!.setFillColor(UIColor.black.cgColor)
 
-        for p in convexHull.dropFirst() {
-            context!.addLine(to: p)
-        }
-        context!.addLine(to: firstPoint)
+    let firstPoint = convexHull.first!
+    context!.move(to: firstPoint)
+
+    for p in convexHull.dropFirst() {
+      context!.addLine(to: p)
+    }
+    context!.addLine(to: firstPoint)
 
-        context!.strokePath()
+    context!.strokePath()
 
-        // Draw points
-        for p in points {
-            let radius: CGFloat = 5
-            let circleRect = CGRect(x: p.x - radius, y: p.y - radius, width: 2 * radius, height: 2 * radius)
-            context!.fillEllipse(in: circleRect)
-        }
+    // Draw points
+    for p in points {
+      let radius: CGFloat = 5
+      let circleRect = CGRect(x: p.x - radius, y: p.y - radius, width: 2 * radius, height: 2 * radius)
+      context!.fillEllipse(in: circleRect)
     }
+  }
 }

From 892f632c12cf46690a52f74320ff7bee7b8b4b65 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:21:09 -0700
Subject: [PATCH 094/643] [Swift 4] Update Dining Philosophers

---
 .../project.pbxproj                           | 469 +++++++++---------
 DiningPhilosophers/Sources/main.swift         |   5 +
 2 files changed, 227 insertions(+), 247 deletions(-)

diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
index 9743ff7d1..ecb060026 100755
--- a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
@@ -1,250 +1,225 @@
 // !$*UTF8*$!
 {
-   archiveVersion = "1";
-   objectVersion = "46";
-   objects = {
-      OBJ_1 = {
-         isa = "PBXProject";
-         attributes = {
-            LastUpgradeCheck = "9999";
-         };
-         buildConfigurationList = OBJ_2;
-         compatibilityVersion = "Xcode 3.2";
-         developmentRegion = "English";
-         hasScannedForEncodings = "0";
-         knownRegions = (
-            "en",
-         );
-         mainGroup = OBJ_5;
-         productRefGroup = OBJ_11;
-         projectDirPath = ".";
-         targets = (
-            OBJ_13,
-         );
-      };
-      OBJ_10 = {
-         isa = "PBXGroup";
-         children = (
-         );
-         path = "Tests";
-         sourceTree = "<group>";
-      };
-      OBJ_11 = {
-         isa = "PBXGroup";
-         children = (
-            OBJ_12,
-         );
-         name = "Products";
-         path = "";
-         sourceTree = "BUILT_PRODUCTS_DIR";
-      };
-      OBJ_12 = {
-         isa = "PBXFileReference";
-         path = "DiningPhilosophers";
-         sourceTree = "BUILT_PRODUCTS_DIR";
-      };
-      OBJ_13 = {
-         isa = "PBXNativeTarget";
-         buildConfigurationList = OBJ_14;
-         buildPhases = (
-            OBJ_17,
-            OBJ_19,
-         );
-         dependencies = (
-         );
-         name = "DiningPhilosophers";
-         productName = "DiningPhilosophers";
-         productReference = OBJ_12;
-         productType = "com.apple.product-type.tool";
-      };
-      OBJ_14 = {
-         isa = "XCConfigurationList";
-         buildConfigurations = (
-            OBJ_15,
-            OBJ_16,
-         );
-         defaultConfigurationIsVisible = "0";
-         defaultConfigurationName = "Debug";
-      };
-      OBJ_15 = {
-         isa = "XCBuildConfiguration";
-         buildSettings = {
-            FRAMEWORK_SEARCH_PATHS = (
-               "$(PLATFORM_DIR)/Developer/Library/Frameworks",
-            );
-            HEADER_SEARCH_PATHS = (
-            );
-            INFOPLIST_FILE = "DiningPhilosophers.xcodeproj/DiningPhilosophers_Info.plist";
-            LD_RUNPATH_SEARCH_PATHS = (
-               "$(TOOLCHAIN_DIR)/usr/lib/swift/macosx",
-               "@executable_path",
-            );
-            OTHER_LDFLAGS = (
-               "$(inherited)",
-            );
-            OTHER_SWIFT_FLAGS = (
-               "$(inherited)",
-            );
-            SUPPORTED_PLATFORMS = (
-               "macosx",
-            );
-            SWIFT_ACTIVE_COMPILATION_CONDITIONS = "SWIFT_PACKAGE";
-            SWIFT_FORCE_DYNAMIC_LINK_STDLIB = "YES";
-            SWIFT_FORCE_STATIC_LINK_STDLIB = "NO";
-            SWIFT_VERSION = "3.0";
-            TARGET_NAME = "DiningPhilosophers";
-         };
-         name = "Debug";
-      };
-      OBJ_16 = {
-         isa = "XCBuildConfiguration";
-         buildSettings = {
-            FRAMEWORK_SEARCH_PATHS = (
-               "$(PLATFORM_DIR)/Developer/Library/Frameworks",
-            );
-            HEADER_SEARCH_PATHS = (
-            );
-            INFOPLIST_FILE = "DiningPhilosophers.xcodeproj/DiningPhilosophers_Info.plist";
-            LD_RUNPATH_SEARCH_PATHS = (
-               "$(TOOLCHAIN_DIR)/usr/lib/swift/macosx",
-               "@executable_path",
-            );
-            OTHER_LDFLAGS = (
-               "$(inherited)",
-            );
-            OTHER_SWIFT_FLAGS = (
-               "$(inherited)",
-            );
-            SUPPORTED_PLATFORMS = (
-               "macosx",
-            );
-            SWIFT_ACTIVE_COMPILATION_CONDITIONS = "SWIFT_PACKAGE";
-            SWIFT_FORCE_DYNAMIC_LINK_STDLIB = "YES";
-            SWIFT_FORCE_STATIC_LINK_STDLIB = "NO";
-            SWIFT_VERSION = "3.0";
-            TARGET_NAME = "DiningPhilosophers";
-         };
-         name = "Release";
-      };
-      OBJ_17 = {
-         isa = "PBXSourcesBuildPhase";
-         files = (
-            OBJ_18,
-         );
-      };
-      OBJ_18 = {
-         isa = "PBXBuildFile";
-         fileRef = OBJ_9;
-      };
-      OBJ_19 = {
-         isa = "PBXFrameworksBuildPhase";
-         files = (
-         );
-      };
-      OBJ_2 = {
-         isa = "XCConfigurationList";
-         buildConfigurations = (
-            OBJ_3,
-            OBJ_4,
-         );
-         defaultConfigurationIsVisible = "0";
-         defaultConfigurationName = "Debug";
-      };
-      OBJ_3 = {
-         isa = "XCBuildConfiguration";
-         buildSettings = {
-            COMBINE_HIDPI_IMAGES = "YES";
-            COPY_PHASE_STRIP = "NO";
-            DEBUG_INFORMATION_FORMAT = "dwarf";
-            DYLIB_INSTALL_NAME_BASE = "@rpath";
-            ENABLE_NS_ASSERTIONS = "YES";
-            GCC_OPTIMIZATION_LEVEL = "0";
-            MACOSX_DEPLOYMENT_TARGET = "10.10";
-            ONLY_ACTIVE_ARCH = "YES";
-            OTHER_SWIFT_FLAGS = (
-               "-DXcode",
-            );
-            PRODUCT_NAME = "$(TARGET_NAME)";
-            SUPPORTED_PLATFORMS = (
-               "macosx",
-               "iphoneos",
-               "iphonesimulator",
-               "appletvos",
-               "appletvsimulator",
-               "watchos",
-               "watchsimulator",
-            );
-            SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-            USE_HEADERMAP = "NO";
-         };
-         name = "Debug";
-      };
-      OBJ_4 = {
-         isa = "XCBuildConfiguration";
-         buildSettings = {
-            COMBINE_HIDPI_IMAGES = "YES";
-            COPY_PHASE_STRIP = "YES";
-            DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
-            DYLIB_INSTALL_NAME_BASE = "@rpath";
-            GCC_OPTIMIZATION_LEVEL = "s";
-            MACOSX_DEPLOYMENT_TARGET = "10.10";
-            OTHER_SWIFT_FLAGS = (
-               "-DXcode",
-            );
-            PRODUCT_NAME = "$(TARGET_NAME)";
-            SUPPORTED_PLATFORMS = (
-               "macosx",
-               "iphoneos",
-               "iphonesimulator",
-               "appletvos",
-               "appletvsimulator",
-               "watchos",
-               "watchsimulator",
-            );
-            SWIFT_OPTIMIZATION_LEVEL = "-O";
-            USE_HEADERMAP = "NO";
-         };
-         name = "Release";
-      };
-      OBJ_5 = {
-         isa = "PBXGroup";
-         children = (
-            OBJ_6,
-            OBJ_7,
-            OBJ_10,
-            OBJ_11,
-         );
-         path = "";
-         sourceTree = "<group>";
-      };
-      OBJ_6 = {
-         isa = "PBXFileReference";
-         explicitFileType = "sourcecode.swift";
-         path = "Package.swift";
-         sourceTree = "<group>";
-      };
-      OBJ_7 = {
-         isa = "PBXGroup";
-         children = (
-            OBJ_8,
-         );
-         path = "Sources";
-         sourceTree = "<group>";
-      };
-      OBJ_8 = {
-         isa = "PBXGroup";
-         children = (
-            OBJ_9,
-         );
-         name = "DiningPhilosophers";
-         path = "Sources";
-         sourceTree = "SOURCE_ROOT";
-      };
-      OBJ_9 = {
-         isa = "PBXFileReference";
-         path = "main.swift";
-         sourceTree = "<group>";
-      };
-   };
-   rootObject = OBJ_1;
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		OBJ_18 /* main.swift in Sources */ = {isa = PBXBuildFile; fileRef = OBJ_9 /* main.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		OBJ_12 /* DiningPhilosophers */ = {isa = PBXFileReference; explicitFileType = "compiled.mach-o.executable"; path = DiningPhilosophers; sourceTree = BUILT_PRODUCTS_DIR; };
+		OBJ_6 /* Package.swift */ = {isa = PBXFileReference; explicitFileType = sourcecode.swift; path = Package.swift; sourceTree = "<group>"; };
+		OBJ_9 /* main.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = main.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		OBJ_19 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 0;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		OBJ_10 /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+			);
+			path = Tests;
+			sourceTree = "<group>";
+		};
+		OBJ_11 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				OBJ_12 /* DiningPhilosophers */,
+			);
+			name = Products;
+			sourceTree = BUILT_PRODUCTS_DIR;
+		};
+		OBJ_5 /*  */ = {
+			isa = PBXGroup;
+			children = (
+				OBJ_6 /* Package.swift */,
+				OBJ_7 /* Sources */,
+				OBJ_10 /* Tests */,
+				OBJ_11 /* Products */,
+			);
+			name = "";
+			sourceTree = "<group>";
+		};
+		OBJ_7 /* Sources */ = {
+			isa = PBXGroup;
+			children = (
+				OBJ_8 /* DiningPhilosophers */,
+			);
+			path = Sources;
+			sourceTree = "<group>";
+		};
+		OBJ_8 /* DiningPhilosophers */ = {
+			isa = PBXGroup;
+			children = (
+				OBJ_9 /* main.swift */,
+			);
+			name = DiningPhilosophers;
+			path = Sources;
+			sourceTree = SOURCE_ROOT;
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		OBJ_13 /* DiningPhilosophers */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = OBJ_14 /* Build configuration list for PBXNativeTarget "DiningPhilosophers" */;
+			buildPhases = (
+				OBJ_17 /* Sources */,
+				OBJ_19 /* Frameworks */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = DiningPhilosophers;
+			productName = DiningPhilosophers;
+			productReference = OBJ_12 /* DiningPhilosophers */;
+			productType = "com.apple.product-type.tool";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		OBJ_1 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastUpgradeCheck = 9999;
+			};
+			buildConfigurationList = OBJ_2 /* Build configuration list for PBXProject "DiningPhilosophers" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+			);
+			mainGroup = OBJ_5 /*  */;
+			productRefGroup = OBJ_11 /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				OBJ_13 /* DiningPhilosophers */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXSourcesBuildPhase section */
+		OBJ_17 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 0;
+			files = (
+				OBJ_18 /* main.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		OBJ_15 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				FRAMEWORK_SEARCH_PATHS = "$(PLATFORM_DIR)/Developer/Library/Frameworks";
+				HEADER_SEARCH_PATHS = "";
+				INFOPLIST_FILE = DiningPhilosophers.xcodeproj/DiningPhilosophers_Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(TOOLCHAIN_DIR)/usr/lib/swift/macosx @executable_path";
+				OTHER_LDFLAGS = "$(inherited)";
+				OTHER_SWIFT_FLAGS = "$(inherited)";
+				SUPPORTED_PLATFORMS = macosx;
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = SWIFT_PACKAGE;
+				SWIFT_FORCE_DYNAMIC_LINK_STDLIB = YES;
+				SWIFT_FORCE_STATIC_LINK_STDLIB = NO;
+				SWIFT_VERSION = 4.0;
+				TARGET_NAME = DiningPhilosophers;
+			};
+			name = Debug;
+		};
+		OBJ_16 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				FRAMEWORK_SEARCH_PATHS = "$(PLATFORM_DIR)/Developer/Library/Frameworks";
+				HEADER_SEARCH_PATHS = "";
+				INFOPLIST_FILE = DiningPhilosophers.xcodeproj/DiningPhilosophers_Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(TOOLCHAIN_DIR)/usr/lib/swift/macosx @executable_path";
+				OTHER_LDFLAGS = "$(inherited)";
+				OTHER_SWIFT_FLAGS = "$(inherited)";
+				SUPPORTED_PLATFORMS = macosx;
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = SWIFT_PACKAGE;
+				SWIFT_FORCE_DYNAMIC_LINK_STDLIB = YES;
+				SWIFT_FORCE_STATIC_LINK_STDLIB = NO;
+				SWIFT_VERSION = 4.0;
+				TARGET_NAME = DiningPhilosophers;
+			};
+			name = Release;
+		};
+		OBJ_3 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				DYLIB_INSTALL_NAME_BASE = "@rpath";
+				ENABLE_NS_ASSERTIONS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				MACOSX_DEPLOYMENT_TARGET = 10.10;
+				ONLY_ACTIVE_ARCH = YES;
+				OTHER_SWIFT_FLAGS = "-DXcode";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SUPPORTED_PLATFORMS = "macosx iphoneos iphonesimulator appletvos appletvsimulator watchos watchsimulator";
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				USE_HEADERMAP = NO;
+			};
+			name = Debug;
+		};
+		OBJ_4 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = YES;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				DYLIB_INSTALL_NAME_BASE = "@rpath";
+				GCC_OPTIMIZATION_LEVEL = s;
+				MACOSX_DEPLOYMENT_TARGET = 10.10;
+				OTHER_SWIFT_FLAGS = "-DXcode";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SUPPORTED_PLATFORMS = "macosx iphoneos iphonesimulator appletvos appletvsimulator watchos watchsimulator";
+				SWIFT_OPTIMIZATION_LEVEL = "-O";
+				USE_HEADERMAP = NO;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		OBJ_14 /* Build configuration list for PBXNativeTarget "DiningPhilosophers" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				OBJ_15 /* Debug */,
+				OBJ_16 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Debug;
+		};
+		OBJ_2 /* Build configuration list for PBXProject "DiningPhilosophers" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				OBJ_3 /* Debug */,
+				OBJ_4 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Debug;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = OBJ_1 /* Project object */;
 }
diff --git a/DiningPhilosophers/Sources/main.swift b/DiningPhilosophers/Sources/main.swift
index 32c3af979..f473e76fb 100755
--- a/DiningPhilosophers/Sources/main.swift
+++ b/DiningPhilosophers/Sources/main.swift
@@ -6,6 +6,11 @@
 //
 //
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
+
 import Dispatch
 
 let numberOfPhilosophers = 4

From e3e8a34a2f48322c4e567450cd8563460380601e Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:26:43 -0700
Subject: [PATCH 095/643] [Swift 4] Update KMeans

---
 K-Means/Tests/KMeansTests.swift               | 7 +++++++
 K-Means/Tests/Tests.xcodeproj/project.pbxproj | 4 ++--
 2 files changed, 9 insertions(+), 2 deletions(-)

diff --git a/K-Means/Tests/KMeansTests.swift b/K-Means/Tests/KMeansTests.swift
index 7e0c93004..e6f4b08a1 100644
--- a/K-Means/Tests/KMeansTests.swift
+++ b/K-Means/Tests/KMeansTests.swift
@@ -10,6 +10,13 @@ import Foundation
 import XCTest
 
 class KMeansTests: XCTestCase {
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+
   func genPoints(_ numPoints: Int, numDimensions: Int) -> [Vector] {
     var points = [Vector]()
     for _ in 0..<numPoints {
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
index 08b64a8f9..139f6baf5 100644
--- a/K-Means/Tests/Tests.xcodeproj/project.pbxproj
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -229,7 +229,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -271,7 +271,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From b0e6897fff17688018ab50ed3dd402ebff21a509 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 31 Jul 2017 15:35:14 -0700
Subject: [PATCH 096/643] [Swift 4] Update Kth Largest Element

---
 .../kthLargest.playground/Contents.swift      | 72 ++-----------------
 .../Sources}/kthLargest.swift                 | 30 +++-----
 .../contents.xcworkspacedata                  |  3 -
 3 files changed, 14 insertions(+), 91 deletions(-)
 rename Kth Largest Element/{ => kthLargest.playground/Sources}/kthLargest.swift (65%)

diff --git a/Kth Largest Element/kthLargest.playground/Contents.swift b/Kth Largest Element/kthLargest.playground/Contents.swift
index 3e186760c..e6fca2ceb 100644
--- a/Kth Largest Element/kthLargest.playground/Contents.swift	
+++ b/Kth Largest Element/kthLargest.playground/Contents.swift	
@@ -1,14 +1,9 @@
 //: Playground - noun: a place where people can play
 
-func kthLargest(_ a: [Int], _ k: Int) -> Int? {
-  let len = a.count
-  if k > 0 && k <= len {
-    let sorted = a.sorted()
-    return sorted[len - k]
-  } else {
-    return nil
-  }
-}
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 let a = [5, 1, 3, 2, 7, 6, 4]
 
@@ -22,65 +17,6 @@ kthLargest(a, 6)
 kthLargest(a, 7)
 kthLargest(a, 8)
 
-import Foundation
-
-/* Returns a random integer in the range min...max, inclusive. */
-public func random( min: Int, max: Int) -> Int {
-  assert(min < max)
-  return min + Int(arc4random_uniform(UInt32(max - min + 1)))
-}
-
-/*
-  Swift's swap() doesn't like it if the items you're trying to swap refer to
-  the same memory location. This little wrapper simply ignores such swaps.
-*/
-public func swap<T>(_ a:inout [T], _ i: Int, _ j: Int) {
-  if i != j {
-    swap(&a[i], &a[j])
-  }
-}
-
-public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
-  var a = array
-
-  func randomPivot<T: Comparable>(_ a: inout[T], _ low: Int, _ high: Int) -> T {
-    let pivotIndex = random(min: low, max: high)
-    swap(&a, pivotIndex, high)
-    return a[high]
-  }
-
-  func randomizedPartition<T: Comparable>(_ a: inout[T], _ low: Int, _ high: Int) -> Int {
-    let pivot = randomPivot(&a, low, high)
-    var i = low
-    for j in low..<high {
-      if a[j] <= pivot {
-        swap(&a, i, j)
-        i += 1
-      }
-    }
-    swap(&a, i, high)
-    return i
-  }
-
-  func randomizedSelect<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int, _ k: Int) -> T {
-    if low < high {
-      let p = randomizedPartition(&a, low, high)
-      if k == p {
-        return a[p]
-      } else if k < p {
-        return randomizedSelect(&a, low, p - 1, k)
-      } else {
-        return randomizedSelect(&a, p + 1, high, k)
-      }
-    } else {
-      return a[low]
-    }
-  }
-
-  precondition(a.count > 0)
-  return randomizedSelect(&a, 0, a.count - 1, k)
-}
-
 randomizedSelect(a, order: 0)
 randomizedSelect(a, order: 1)
 randomizedSelect(a, order: 2)
diff --git a/Kth Largest Element/kthLargest.swift b/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift
similarity index 65%
rename from Kth Largest Element/kthLargest.swift
rename to Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift
index 16f6caf0c..397c43a38 100644
--- a/Kth Largest Element/kthLargest.swift	
+++ b/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift	
@@ -4,10 +4,10 @@ import Foundation
   Returns the k-th largest value inside of an array a.
   This is an O(n log n) solution since we sort the array.
 */
-func kthLargest(a: [Int], k: Int) -> Int? {
+public func kthLargest(_ a: [Int], _ k: Int) -> Int? {
   let len = a.count
   if k > 0 && k <= len {
-    let sorted = a.sort()
+    let sorted = a.sorted()
     return sorted[len - k]
   } else {
     return nil
@@ -17,21 +17,11 @@ func kthLargest(a: [Int], k: Int) -> Int? {
 // MARK: - Randomized selection
 
 /* Returns a random integer in the range min...max, inclusive. */
-public func random(min min: Int, max: Int) -> Int {
+public func random(min: Int, max: Int) -> Int {
   assert(min < max)
   return min + Int(arc4random_uniform(UInt32(max - min + 1)))
 }
 
-/*
-  Swift's swap() doesn't like it if the items you're trying to swap refer to
-  the same memory location. This little wrapper simply ignores such swaps.
-*/
-public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
-  if i != j {
-    swap(&a[i], &a[j])
-  }
-}
-
 /*
   Returns the i-th smallest element from the array.
 
@@ -45,29 +35,29 @@ public func swap<T>(inout a: [T], _ i: Int, _ j: Int) {
 
   Expected running time: O(n) if the elements are distinct.
 */
-public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
+public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
   var a = array
 
-  func randomPivot<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> T {
+  func randomPivot<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int) -> T {
     let pivotIndex = random(min: low, max: high)
-    swap(&a, pivotIndex, high)
+    a.swapAt(pivotIndex, high)
     return a[high]
   }
 
-  func randomizedPartition<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> Int {
+  func randomizedPartition<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int) -> Int {
     let pivot = randomPivot(&a, low, high)
     var i = low
     for j in low..<high {
       if a[j] <= pivot {
-        swap(&a, i, j)
+        a.swapAt(i, j)
         i += 1
       }
     }
-    swap(&a, i, high)
+    a.swapAt(i, high)
     return i
   }
 
-  func randomizedSelect<T: Comparable>(inout a: [T], _ low: Int, _ high: Int, _ k: Int) -> T {
+  func randomizedSelect<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int, _ k: Int) -> T {
     if low < high {
       let p = randomizedPartition(&a, low, high)
       if k == p {
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7ca193aca..eaa1e1167 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1367,9 +1367,6 @@
       <FileRef
          location = "group:kthLargest.playground">
       </FileRef>
-      <FileRef
-         location = "group:kthLargest.swift">
-      </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>

From 4f4b09dcb465882ceb43dd88ae50a59a2a0da381 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 12:38:49 +0500
Subject: [PATCH 097/643] Updated Code & Test to Swift4

---
 .../Contents.swift                            |   6 +
 .../Tests/DepthFirstSearchTests.swift         | 168 +++++++++---------
 .../Tests/Tests.xcodeproj/project.pbxproj     |   6 +-
 3 files changed, 97 insertions(+), 83 deletions(-)

diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index 1e32b4bbf..dd98e87dc 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,9 @@
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var nodesExplored = [source.label]
   source.visited = true
diff --git a/Depth-First Search/Tests/DepthFirstSearchTests.swift b/Depth-First Search/Tests/DepthFirstSearchTests.swift
index 2cb2556ce..afff5f62f 100755
--- a/Depth-First Search/Tests/DepthFirstSearchTests.swift	
+++ b/Depth-First Search/Tests/DepthFirstSearchTests.swift	
@@ -1,85 +1,91 @@
 import XCTest
 
 class DepthFirstSearchTests: XCTestCase {
-
-  func testExploringTree() {
-    let tree = Graph()
-
-    let nodeA = tree.addNode("a")
-    let nodeB = tree.addNode("b")
-    let nodeC = tree.addNode("c")
-    let nodeD = tree.addNode("d")
-    let nodeE = tree.addNode("e")
-    let nodeF = tree.addNode("f")
-    let nodeG = tree.addNode("g")
-    let nodeH = tree.addNode("h")
-
-    tree.addEdge(nodeA, neighbor: nodeB)
-    tree.addEdge(nodeA, neighbor: nodeC)
-    tree.addEdge(nodeB, neighbor: nodeD)
-    tree.addEdge(nodeB, neighbor: nodeE)
-    tree.addEdge(nodeC, neighbor: nodeF)
-    tree.addEdge(nodeC, neighbor: nodeG)
-    tree.addEdge(nodeE, neighbor: nodeH)
-
-    let nodesExplored = depthFirstSearch(tree, source: nodeA)
-
-    XCTAssertEqual(nodesExplored, ["a", "b", "d", "e", "h", "c", "f", "g"])
-  }
-
-  func testExploringGraph() {
-    let graph = Graph()
-
-    let nodeA = graph.addNode("a")
-    let nodeB = graph.addNode("b")
-    let nodeC = graph.addNode("c")
-    let nodeD = graph.addNode("d")
-    let nodeE = graph.addNode("e")
-    let nodeF = graph.addNode("f")
-    let nodeG = graph.addNode("g")
-    let nodeH = graph.addNode("h")
-    let nodeI = graph.addNode("i")
-
-    graph.addEdge(nodeA, neighbor: nodeB)
-    graph.addEdge(nodeA, neighbor: nodeH)
-    graph.addEdge(nodeB, neighbor: nodeA)
-    graph.addEdge(nodeB, neighbor: nodeC)
-    graph.addEdge(nodeB, neighbor: nodeH)
-    graph.addEdge(nodeC, neighbor: nodeB)
-    graph.addEdge(nodeC, neighbor: nodeD)
-    graph.addEdge(nodeC, neighbor: nodeF)
-    graph.addEdge(nodeC, neighbor: nodeI)
-    graph.addEdge(nodeD, neighbor: nodeC)
-    graph.addEdge(nodeD, neighbor: nodeE)
-    graph.addEdge(nodeD, neighbor: nodeF)
-    graph.addEdge(nodeE, neighbor: nodeD)
-    graph.addEdge(nodeE, neighbor: nodeF)
-    graph.addEdge(nodeF, neighbor: nodeC)
-    graph.addEdge(nodeF, neighbor: nodeD)
-    graph.addEdge(nodeF, neighbor: nodeE)
-    graph.addEdge(nodeF, neighbor: nodeG)
-    graph.addEdge(nodeG, neighbor: nodeF)
-    graph.addEdge(nodeG, neighbor: nodeH)
-    graph.addEdge(nodeG, neighbor: nodeI)
-    graph.addEdge(nodeH, neighbor: nodeA)
-    graph.addEdge(nodeH, neighbor: nodeB)
-    graph.addEdge(nodeH, neighbor: nodeG)
-    graph.addEdge(nodeH, neighbor: nodeI)
-    graph.addEdge(nodeI, neighbor: nodeC)
-    graph.addEdge(nodeI, neighbor: nodeG)
-    graph.addEdge(nodeI, neighbor: nodeH)
-
-    let nodesExplored = depthFirstSearch(graph, source: nodeA)
-
-    XCTAssertEqual(nodesExplored, ["a", "b", "c", "d", "e", "f", "g", "h", "i"])
-  }
-
-  func testExploringGraphWithASingleNode() {
-    let graph = Graph()
-    let node = graph.addNode("a")
-
-    let nodesExplored = depthFirstSearch(graph, source: node)
-
-    XCTAssertEqual(nodesExplored, ["a"])
-  }
+    
+    func testSwift4(){
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
+    }
+    func testExploringTree() {
+        let tree = Graph()
+        
+        let nodeA = tree.addNode("a")
+        let nodeB = tree.addNode("b")
+        let nodeC = tree.addNode("c")
+        let nodeD = tree.addNode("d")
+        let nodeE = tree.addNode("e")
+        let nodeF = tree.addNode("f")
+        let nodeG = tree.addNode("g")
+        let nodeH = tree.addNode("h")
+        
+        tree.addEdge(nodeA, neighbor: nodeB)
+        tree.addEdge(nodeA, neighbor: nodeC)
+        tree.addEdge(nodeB, neighbor: nodeD)
+        tree.addEdge(nodeB, neighbor: nodeE)
+        tree.addEdge(nodeC, neighbor: nodeF)
+        tree.addEdge(nodeC, neighbor: nodeG)
+        tree.addEdge(nodeE, neighbor: nodeH)
+        
+        let nodesExplored = depthFirstSearch(tree, source: nodeA)
+        
+        XCTAssertEqual(nodesExplored, ["a", "b", "d", "e", "h", "c", "f", "g"])
+    }
+    
+    func testExploringGraph() {
+        let graph = Graph()
+        
+        let nodeA = graph.addNode("a")
+        let nodeB = graph.addNode("b")
+        let nodeC = graph.addNode("c")
+        let nodeD = graph.addNode("d")
+        let nodeE = graph.addNode("e")
+        let nodeF = graph.addNode("f")
+        let nodeG = graph.addNode("g")
+        let nodeH = graph.addNode("h")
+        let nodeI = graph.addNode("i")
+        
+        graph.addEdge(nodeA, neighbor: nodeB)
+        graph.addEdge(nodeA, neighbor: nodeH)
+        graph.addEdge(nodeB, neighbor: nodeA)
+        graph.addEdge(nodeB, neighbor: nodeC)
+        graph.addEdge(nodeB, neighbor: nodeH)
+        graph.addEdge(nodeC, neighbor: nodeB)
+        graph.addEdge(nodeC, neighbor: nodeD)
+        graph.addEdge(nodeC, neighbor: nodeF)
+        graph.addEdge(nodeC, neighbor: nodeI)
+        graph.addEdge(nodeD, neighbor: nodeC)
+        graph.addEdge(nodeD, neighbor: nodeE)
+        graph.addEdge(nodeD, neighbor: nodeF)
+        graph.addEdge(nodeE, neighbor: nodeD)
+        graph.addEdge(nodeE, neighbor: nodeF)
+        graph.addEdge(nodeF, neighbor: nodeC)
+        graph.addEdge(nodeF, neighbor: nodeD)
+        graph.addEdge(nodeF, neighbor: nodeE)
+        graph.addEdge(nodeF, neighbor: nodeG)
+        graph.addEdge(nodeG, neighbor: nodeF)
+        graph.addEdge(nodeG, neighbor: nodeH)
+        graph.addEdge(nodeG, neighbor: nodeI)
+        graph.addEdge(nodeH, neighbor: nodeA)
+        graph.addEdge(nodeH, neighbor: nodeB)
+        graph.addEdge(nodeH, neighbor: nodeG)
+        graph.addEdge(nodeH, neighbor: nodeI)
+        graph.addEdge(nodeI, neighbor: nodeC)
+        graph.addEdge(nodeI, neighbor: nodeG)
+        graph.addEdge(nodeI, neighbor: nodeH)
+        
+        let nodesExplored = depthFirstSearch(graph, source: nodeA)
+        
+        XCTAssertEqual(nodesExplored, ["a", "b", "c", "d", "e", "f", "g", "h", "i"])
+    }
+    
+    func testExploringGraphWithASingleNode() {
+        let graph = Graph()
+        let node = graph.addNode("a")
+        
+        let nodesExplored = depthFirstSearch(graph, source: node)
+        
+        XCTAssertEqual(nodesExplored, ["a"])
+    }
 }
diff --git a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index dbc44ecd4..8f6058600 100644
--- a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -180,6 +180,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -219,6 +220,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -232,7 +234,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -245,7 +247,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From e1c0189ad8951acbecb6a71d32a85ef039ea00fc Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 12:44:48 +0500
Subject: [PATCH 098/643] HashSet Code updated to Swift4

---
 Hash Set/HashSet.playground/Contents.swift      | 4 ++++
 Hash Set/HashSet.playground/timeline.xctimeline | 6 ------
 2 files changed, 4 insertions(+), 6 deletions(-)
 delete mode 100644 Hash Set/HashSet.playground/timeline.xctimeline

diff --git a/Hash Set/HashSet.playground/Contents.swift b/Hash Set/HashSet.playground/Contents.swift
index 551c6dc86..5edb76bb4 100644
--- a/Hash Set/HashSet.playground/Contents.swift	
+++ b/Hash Set/HashSet.playground/Contents.swift	
@@ -1,4 +1,8 @@
 //: Playground - noun: a place where people can play
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 var set = HashSet<String>()
 
diff --git a/Hash Set/HashSet.playground/timeline.xctimeline b/Hash Set/HashSet.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Hash Set/HashSet.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 403e11cfcb0f5063415cd24c1df7960afcc8c650 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Tue, 1 Aug 2017 18:04:26 +0900
Subject: [PATCH 099/643] Updated files for 2 spaced-indentations

---
 .../Shuffle.playground/Sources/Shuffle.swift  | 14 +++---
 Shuffle/Shuffle.swift                         | 46 +++++++++----------
 2 files changed, 30 insertions(+), 30 deletions(-)

diff --git a/Shuffle/Shuffle.playground/Sources/Shuffle.swift b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
index 63fea2899..553832d43 100644
--- a/Shuffle/Shuffle.playground/Sources/Shuffle.swift
+++ b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
@@ -2,15 +2,15 @@ import Foundation
 
 /* Returns a random integer between 0 and n-1. */
 public func random(_ n: Int) -> Int {
-    return Int(arc4random_uniform(UInt32(n)))
+  return Int(arc4random_uniform(UInt32(n)))
 }
 
 extension Array {
   /*
-    Randomly shuffles the array in-place
-    This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
-    Time complexity: O(n)
-  */
+   Randomly shuffles the array in-place
+   This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
+   Time complexity: O(n)
+   */
   public mutating func shuffle() {
     for i in (1...count-1).reversed() {
       let j = random(i + 1)
@@ -24,8 +24,8 @@ extension Array {
 }
 
 /*
-  Simultaneously initializes an array with the values 0...n-1 and shuffles it.
-*/
+ Simultaneously initializes an array with the values 0...n-1 and shuffles it.
+ */
 public func shuffledArray(_ n: Int) -> [Int] {
   var a = Array(repeating: 0, count: n)
   for i in 0..<n {
diff --git a/Shuffle/Shuffle.swift b/Shuffle/Shuffle.swift
index 19112fa37..3e4292d56 100644
--- a/Shuffle/Shuffle.swift
+++ b/Shuffle/Shuffle.swift
@@ -2,39 +2,39 @@ import Foundation
 
 /* Returns a random integer between 0 and n-1. */
 public func random(_ n: Int) -> Int {
-    return Int(arc4random_uniform(UInt32(n)))
+  return Int(arc4random_uniform(UInt32(n)))
 }
 
 extension Array {
-    /*
-     Randomly shuffles the array in-place
-     This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
-     Time complexity: O(n)
-     */
-    public mutating func shuffle() {
-        for i in (1...count-1).reversed() {
-            let j = random(i + 1)
-            if i != j {
-                let t = self[i]
-                self[i] = self[j]
-                self[j] = t
-            }
-        }
+  /*
+   Randomly shuffles the array in-place
+   This is the Fisher-Yates algorithm, also known as the Knuth shuffle.
+   Time complexity: O(n)
+   */
+  public mutating func shuffle() {
+    for i in (1...count-1).reversed() {
+      let j = random(i + 1)
+      if i != j {
+        let t = self[i]
+        self[i] = self[j]
+        self[j] = t
+      }
     }
+  }
 }
 
 /*
  Simultaneously initializes an array with the values 0...n-1 and shuffles it.
  */
 public func shuffledArray(_ n: Int) -> [Int] {
-    var a = Array(repeating: 0, count: n)
-    for i in 0..<n {
-        let j = random(i + 1)
-        if i != j {
-            a[i] = a[j]
-        }
-        a[j] = i  // insert next number from the sequence
+  var a = Array(repeating: 0, count: n)
+  for i in 0..<n {
+    let j = random(i + 1)
+    if i != j {
+      a[i] = a[j]
     }
-    return a
+    a[j] = i  // insert next number from the sequence
+  }
+  return a
 }
 

From d6e59a4204f8ea77ca5febfe975adc921282649c Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 07:13:17 -0700
Subject: [PATCH 100/643] [Swift 4] Update Treap

---
 Treap/Treap/Treap.xcodeproj/project.pbxproj | 4 ++--
 Treap/Treap/TreapTests/TreapTests.swift     | 7 +++++++
 2 files changed, 9 insertions(+), 2 deletions(-)

diff --git a/Treap/Treap/Treap.xcodeproj/project.pbxproj b/Treap/Treap/Treap.xcodeproj/project.pbxproj
index df9a0d6ee..d8393e1c5 100644
--- a/Treap/Treap/Treap.xcodeproj/project.pbxproj
+++ b/Treap/Treap/Treap.xcodeproj/project.pbxproj
@@ -243,7 +243,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.TreapTests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -255,7 +255,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.willowtree.TreapTests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Treap/Treap/TreapTests/TreapTests.swift b/Treap/Treap/TreapTests/TreapTests.swift
index d4fc4cfdb..a5d156ec9 100644
--- a/Treap/Treap/TreapTests/TreapTests.swift
+++ b/Treap/Treap/TreapTests/TreapTests.swift
@@ -38,6 +38,13 @@ class TreapTests: XCTestCase {
     super.tearDown()
   }
 
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+
   func testSanity() {
     var treap = Treap<Int, String>.empty
     treap = treap.set(key: 5, val: "a").set(key: 7, val: "b")

From fec536468ce17e1b044296e2957b07ded5b51912 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 07:19:26 -0700
Subject: [PATCH 101/643] [Swift 4] Update Graph

---
 Graph/Graph.playground/Contents.swift      | 6 ++++++
 Graph/Graph.playground/timeline.xctimeline | 2 +-
 Graph/GraphTests/GraphTests.swift          | 8 ++++++++
 3 files changed, 15 insertions(+), 1 deletion(-)

diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph.playground/Contents.swift
index fde396e64..0410942f8 100644
--- a/Graph/Graph.playground/Contents.swift
+++ b/Graph/Graph.playground/Contents.swift
@@ -1,5 +1,11 @@
 import Graph
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+
 for graph in [AdjacencyMatrixGraph<Int>(), AdjacencyListGraph<Int>()] {
 
   let v1 = graph.createVertex(1)
diff --git a/Graph/Graph.playground/timeline.xctimeline b/Graph/Graph.playground/timeline.xctimeline
index 688276d32..6afe06b6f 100644
--- a/Graph/Graph.playground/timeline.xctimeline
+++ b/Graph/Graph.playground/timeline.xctimeline
@@ -3,7 +3,7 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=12&amp;CharacterRangeLoc=1238&amp;EndingColumnNumber=15&amp;EndingLineNumber=38&amp;StartingColumnNumber=3&amp;StartingLineNumber=38&amp;Timestamp=498745868.545441"
+         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/Graph/Graph.playground#CharacterRangeLen=12&amp;CharacterRangeLoc=1322&amp;EndingColumnNumber=4&amp;EndingLineNumber=45&amp;StartingColumnNumber=7&amp;StartingLineNumber=44&amp;Timestamp=523289935.918656"
          selectedRepresentationIndex = "1"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Graph/GraphTests/GraphTests.swift b/Graph/GraphTests/GraphTests.swift
index 289d9aa64..a2f43f9bf 100644
--- a/Graph/GraphTests/GraphTests.swift
+++ b/Graph/GraphTests/GraphTests.swift
@@ -10,6 +10,14 @@ import XCTest
 
 class GraphTests: XCTestCase {
 
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+
+  }
+
   func testAdjacencyMatrixGraphDescription() {
 
     let graph = AdjacencyMatrixGraph<String>()

From e7b8f970b08d2c6df4aaeff129de003ef6a290e4 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:20:38 +0500
Subject: [PATCH 102/643] Hash Table migrated to Swift4

---
 Hash Table/HashTable.playground/Contents.swift | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/Hash Table/HashTable.playground/Contents.swift b/Hash Table/HashTable.playground/Contents.swift
index 121fb6032..67d082094 100644
--- a/Hash Table/HashTable.playground/Contents.swift	
+++ b/Hash Table/HashTable.playground/Contents.swift	
@@ -1,5 +1,8 @@
 //: Playground - noun: a place where people can play
-
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 // Playing with hash values
 
 "firstName".hashValue

From df5b59ea03f3c067890419a84551163052504d71 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:24:54 +0500
Subject: [PATCH 103/643] Hash Table updated to Swift4

---
 Hash Table/HashTable.playground/Contents.swift | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/Hash Table/HashTable.playground/Contents.swift b/Hash Table/HashTable.playground/Contents.swift
index 121fb6032..29cbfd6a9 100644
--- a/Hash Table/HashTable.playground/Contents.swift	
+++ b/Hash Table/HashTable.playground/Contents.swift	
@@ -1,5 +1,7 @@
 //: Playground - noun: a place where people can play
-
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 // Playing with hash values
 
 "firstName".hashValue

From fbcf17b573aa99da235591464c46f4490c85390b Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:29:06 +0500
Subject: [PATCH 104/643] Haversine Distance updated to Swift4

---
 .../HaversineDistance.playground/Contents.swift    | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 deletions(-)

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index 449fa366d..5b3f591d6 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -1,25 +1,29 @@
 import UIKit
+// last checked with Xcode 9.04
+#if swift(>=4)
+print("Hello, Swift 4!")
+#endif
 
 func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
-
+    
     let haversin = { (angle: Double) -> Double in
         return (1 - cos(angle))/2
     }
-
+    
     let ahaversin = { (angle: Double) -> Double in
         return 2*asin(sqrt(angle))
     }
-
+    
     // Converts from degrees to radians
     let dToR = { (angle: Double) -> Double in
         return (angle / 360) * 2 * M_PI
     }
-
+    
     let lat1 = dToR(la1)
     let lon1 = dToR(lo1)
     let lat2 = dToR(la2)
     let lon2 = dToR(lo2)
-
+    
     return radius * ahaversin(haversin(lat2 - lat1) + cos(lat1) * cos(lat2) * haversin(lon2 - lon1))
 }
 

From 8bc4e9a920cf3a1526bf61714fb8c9eac2da73db Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:33:51 +0500
Subject: [PATCH 105/643] Karatsuba Multiplication updated to Swift4

---
 .../Contents.swift                            | 87 ++++++++++---------
 1 file changed, 45 insertions(+), 42 deletions(-)

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 2d327fbac..6b1b0bca2 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -1,60 +1,63 @@
 //: Playground - noun: a place where people can play
 
 import Foundation
-
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4")
+#endif
 precedencegroup ExponentiativePrecedence {
-  higherThan: MultiplicationPrecedence
-  lowerThan: BitwiseShiftPrecedence
-  associativity: left
+    higherThan: MultiplicationPrecedence
+    lowerThan: BitwiseShiftPrecedence
+    associativity: left
 }
 
 infix operator ^^: ExponentiativePrecedence
 func ^^ (radix: Int, power: Int) -> Int {
-  return Int(pow(Double(radix), Double(power)))
+    return Int(pow(Double(radix), Double(power)))
 }
 
 // Long Multiplication - O(n^2)
 func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
-  let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
-  let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
-
-  var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
-
-  for i in num1Array.indices {
-    var carry = 0
-    for j in num2Array.indices {
-      product[i + j] += carry + num1Array[i] * num2Array[j]
-      carry = product[i + j] / base
-      product[i + j] %= base
+    let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
+    let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
+    
+    var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
+    
+    for i in num1Array.indices {
+        var carry = 0
+        for j in num2Array.indices {
+            product[i + j] += carry + num1Array[i] * num2Array[j]
+            carry = product[i + j] / base
+            product[i + j] %= base
+        }
+        product[i + num2Array.count] += carry
     }
-    product[i + num2Array.count] += carry
-  }
-
-  return Int(product.reversed().map { String($0) }.reduce("", +))!
+    
+    return Int(product.reversed().map { String($0) }.reduce("", +))!
 }
 
 // Karatsuba Multiplication - O(n^log2(3))
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
-  let num1Array = String(num1).characters
-  let num2Array = String(num2).characters
-
-  guard num1Array.count > 1 && num2Array.count > 1 else {
-    return multiply(num1, by: num2)
-  }
-
-  let n = max(num1Array.count, num2Array.count)
-  let nBy2 = n / 2
-
-  let a = num1 / 10^^nBy2
-  let b = num1 % 10^^nBy2
-  let c = num2 / 10^^nBy2
-  let d = num2 % 10^^nBy2
-
-  let ac = karatsuba(a, by: c)
-  let bd = karatsuba(b, by: d)
-  let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-
-  let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
-
-  return product
+    let num1Array = String(num1).characters
+    let num2Array = String(num2).characters
+    
+    guard num1Array.count > 1 && num2Array.count > 1 else {
+        return multiply(num1, by: num2)
+    }
+    
+    let n = max(num1Array.count, num2Array.count)
+    let nBy2 = n / 2
+    
+    let a = num1 / 10^^nBy2
+    let b = num1 % 10^^nBy2
+    let c = num2 / 10^^nBy2
+    let d = num2 % 10^^nBy2
+    
+    let ac = karatsuba(a, by: c)
+    let bd = karatsuba(b, by: d)
+    let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
+    
+    let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
+    
+    return product
 }

From be7832327db0b0e20db5c6d829f0bac16ac347bc Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:46:09 +0500
Subject: [PATCH 106/643] Knuth-Morris-Pratt updated to Swift 4

---
 .../Contents.swift                            | 53 ++++++++++---------
 1 file changed, 29 insertions(+), 24 deletions(-)

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
index a27726648..b47cf1257 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -1,34 +1,39 @@
 //: Playground - noun: a place where people can play
 
-func ZetaAlgorithm(ptnr: String) -> [Int]? {
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift4!")
+#endif
 
+func ZetaAlgorithm(ptnr: String) -> [Int]? {
+    
     let pattern = Array(ptnr.characters)
     let patternLength: Int = pattern.count
-
+    
     guard patternLength > 0 else {
         return nil
     }
-
+    
     var zeta: [Int] = [Int](repeating: 0, count: patternLength)
-
+    
     var left: Int = 0
     var right: Int = 0
     var k_1: Int = 0
     var betaLength: Int = 0
     var textIndex: Int = 0
     var patternIndex: Int = 0
-
+    
     for k in 1 ..< patternLength {
         if k > right {
             patternIndex = 0
-
+            
             while k + patternIndex < patternLength  &&
                 pattern[k + patternIndex] == pattern[patternIndex] {
-                patternIndex = patternIndex + 1
+                    patternIndex = patternIndex + 1
             }
-
+            
             zeta[k] = patternIndex
-
+            
             if zeta[k] > 0 {
                 left = k
                 right = k + zeta[k] - 1
@@ -36,13 +41,13 @@ func ZetaAlgorithm(ptnr: String) -> [Int]? {
         } else {
             k_1 = k - left + 1
             betaLength = right - k + 1
-
+            
             if zeta[k_1 - 1] < betaLength {
                 zeta[k] = zeta[k_1 - 1]
             } else if zeta[k_1 - 1] >= betaLength {
                 textIndex = betaLength
                 patternIndex = right + 1
-
+                
                 while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
                     textIndex = textIndex + 1
                     patternIndex = patternIndex + 1
@@ -57,54 +62,54 @@ func ZetaAlgorithm(ptnr: String) -> [Int]? {
 }
 
 extension String {
-
+    
     func indexesOf(ptnr: String) -> [Int]? {
-
+        
         let text = Array(self.characters)
         let pattern = Array(ptnr.characters)
-
+        
         let textLength: Int = text.count
         let patternLength: Int = pattern.count
-
+        
         guard patternLength > 0 else {
             return nil
         }
-
+        
         var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
         var textIndex: Int = 0
         var patternIndex: Int = 0
         var indexes: [Int] = [Int]()
-
+        
         /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
         let zeta = ZetaAlgorithm(ptnr: ptnr)
-
+        
         for patternIndex in (1 ..< patternLength).reversed() {
             textIndex = patternIndex + zeta![patternIndex] - 1
             suffixPrefix[textIndex] = zeta![patternIndex]
         }
-
+        
         /* Search stage: scanning the text for pattern matching */
         textIndex = 0
         patternIndex = 0
-
+        
         while textIndex + (patternLength - patternIndex - 1) < textLength {
-
+            
             while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
                 textIndex = textIndex + 1
                 patternIndex = patternIndex + 1
             }
-
+            
             if patternIndex == patternLength {
                 indexes.append(textIndex - patternIndex)
             }
-
+            
             if patternIndex == 0 {
                 textIndex = textIndex + 1
             } else {
                 patternIndex = suffixPrefix[patternIndex - 1]
             }
         }
-
+        
         guard !indexes.isEmpty else {
             return nil
         }

From 554dfa47a2c1f73415630f79b49c64d145e36f50 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:49:14 +0500
Subject: [PATCH 107/643] Linear Regression updated to Swift 4

---
 Linear Regression/LinearRegression.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 8faf2b738..3e4135794 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -2,6 +2,11 @@
 
 import Foundation
 
+// last checked with Xcode 4.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let carAge: [Double] = [10, 8, 3, 3, 2, 1]
 let carPrice: [Double] = [500, 400, 7000, 8500, 11000, 10500]
 var intercept = 0.0

From e390f5995fd62c27be4c6085dad43b800b381bd3 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:51:44 +0500
Subject: [PATCH 108/643] Linear Search updated to Swift 4

---
 .../LinearSearch.playground/Contents.swift          | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/Linear Search/LinearSearch.playground/Contents.swift b/Linear Search/LinearSearch.playground/Contents.swift
index 34e859fa3..436af2eda 100644
--- a/Linear Search/LinearSearch.playground/Contents.swift	
+++ b/Linear Search/LinearSearch.playground/Contents.swift	
@@ -1,10 +1,15 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 4.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
-  for (index, obj) in array.enumerated() where obj == object {
-    return index
-  }
-  return nil
+    for (index, obj) in array.enumerated() where obj == object {
+        return index
+    }
+    return nil
 }
 
 let array = [5, 2, 4, 7]

From b7b6130e0e062cfbef47cde923c270690cb8b758 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Tue, 1 Aug 2017 23:53:47 +0500
Subject: [PATCH 109/643] code update

---
 Linear Search/LinearSearch.playground/timeline.xctimeline | 6 ------
 1 file changed, 6 deletions(-)
 delete mode 100644 Linear Search/LinearSearch.playground/timeline.xctimeline

diff --git a/Linear Search/LinearSearch.playground/timeline.xctimeline b/Linear Search/LinearSearch.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Linear Search/LinearSearch.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 6cf3900a186c16aa4ab8e8cc17f9474cc9ea4433 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Wed, 2 Aug 2017 00:00:20 +0500
Subject: [PATCH 110/643] Miller-Rabin Primality Test updated to Swift 4

---
 .../MRPrimality.playground/Contents.swift                    | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift
index 98032bd59..d8fd7fad8 100644
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Real primes
 mrPrimalityTest(5)
 mrPrimalityTest(439)

From 99d955a1804fedfcd80c60af7224caceb8b9154b Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Wed, 2 Aug 2017 00:04:23 +0500
Subject: [PATCH 111/643] Minimum Edit Distance updated to Swift 4

---
 .../MinimumEditDistance.playground/Contents.swift | 15 ++++++++++-----
 .../contents.xcplayground                         |  0
 2 files changed, 10 insertions(+), 5 deletions(-)
 mode change 100755 => 100644 Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
 mode change 100755 => 100644 Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground

diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
old mode 100755
new mode 100644
index 238afeb9b..ad4f2dd8d
--- a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
@@ -1,21 +1,26 @@
-extension String {
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
+extension String {
+    
     public func minimumEditDistance(other: String) -> Int {
         let m = self.characters.count
         let n = other.characters.count
         var matrix = [[Int]](repeating: [Int](repeating: 0, count: n + 1), count: m + 1)
-
+        
         // initialize matrix
         for index in 1...m {
             // the distance of any first string to an empty second string
             matrix[index][0] = index
         }
-
+        
         for index in 1...n {
             // the distance of any second string to an empty first string
             matrix[0][index] = index
         }
-
+        
         // compute Levenshtein distance
         for (i, selfChar) in self.characters.enumerated() {
             for (j, otherChar) in other.characters.enumerated() {
@@ -25,7 +30,7 @@ extension String {
                 } else {
                     // minimum of the cost of insertion, deletion, or substitution 
                     // added to the already computed costs in the corresponding cells
-                    matrix[i + 1][j + 1] = min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
+                    matrix[i + 1][j + 1] = Swift.min(matrix[i][j] + 1, matrix[i + 1][j] + 1, matrix[i][j + 1] + 1)
                 }
             }
         }
diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground b/Minimum Edit Distance/MinimumEditDistance.playground/contents.xcplayground
old mode 100755
new mode 100644

From 9bd6c97f3ebf2a00f128fc2e2e41892895d3b337 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Wed, 2 Aug 2017 00:14:50 +0500
Subject: [PATCH 112/643] Minimum Spanning Tree updated to Swift4

---
 .../Contents.swift                            | 107 +++++++++---------
 .../Sources/Heap.swift                        |   4 +-
 2 files changed, 58 insertions(+), 53 deletions(-)

diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift
index 2981d30ea..c4f0a811b 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
@@ -3,65 +3,70 @@
  Kruskal's and Prim's algorithms.
  */
 
-func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
-  var cost: Int = 0
-  var tree = Graph<T>()
-  let sortedEdgeListByWeight = graph.edgeList.sorted(by: { $0.weight < $1.weight })
-
-  var unionFind = UnionFind<T>()
-  for vertex in graph.vertices {
-    unionFind.addSetWith(vertex)
-  }
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
-  for edge in sortedEdgeListByWeight {
-    let v1 = edge.vertex1
-    let v2 = edge.vertex2
-    if !unionFind.inSameSet(v1, and: v2) {
-      cost += edge.weight
-      tree.addEdge(edge)
-      unionFind.unionSetsContaining(v1, and: v2)
+func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
+    var cost: Int = 0
+    var tree = Graph<T>()
+    let sortedEdgeListByWeight = graph.edgeList.sorted(by: { $0.weight < $1.weight })
+    
+    var unionFind = UnionFind<T>()
+    for vertex in graph.vertices {
+        unionFind.addSetWith(vertex)
     }
-  }
-
-  return (cost: cost, tree: tree)
+    
+    for edge in sortedEdgeListByWeight {
+        let v1 = edge.vertex1
+        let v2 = edge.vertex2
+        if !unionFind.inSameSet(v1, and: v2) {
+            cost += edge.weight
+            tree.addEdge(edge)
+            unionFind.unionSetsContaining(v1, and: v2)
+        }
+    }
+    
+    return (cost: cost, tree: tree)
 }
 
 func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
-  var cost: Int = 0
-  var tree = Graph<T>()
-
-  guard let start = graph.vertices.first else {
-    return (cost: cost, tree: tree)
-  }
-
-  var visited = Set<T>()
-  var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
-    sort: { $0.weight < $1.weight })
-
-  priorityQueue.enqueue((vertex: start, weight: 0, parent: nil))
-  while let head = priorityQueue.dequeue() {
-    let vertex = head.vertex
-    if visited.contains(vertex) {
-      continue
+    var cost: Int = 0
+    var tree = Graph<T>()
+    
+    guard let start = graph.vertices.first else {
+        return (cost: cost, tree: tree)
     }
-    visited.insert(vertex)
-
-    cost += head.weight
-    if let prev = head.parent {
-      tree.addEdge(vertex1: prev, vertex2: vertex, weight: head.weight)
-    }
-
-    if let neighbours = graph.adjList[vertex] {
-      for neighbour in neighbours {
-        let nextVertex = neighbour.vertex
-        if !visited.contains(nextVertex) {
-          priorityQueue.enqueue((vertex: nextVertex, weight: neighbour.weight, parent: vertex))
+    
+    var visited = Set<T>()
+    var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
+        sort: { $0.weight < $1.weight })
+    
+    priorityQueue.enqueue((vertex: start, weight: 0, parent: nil))
+    while let head = priorityQueue.dequeue() {
+        let vertex = head.vertex
+        if visited.contains(vertex) {
+            continue
+        }
+        visited.insert(vertex)
+        
+        cost += head.weight
+        if let prev = head.parent {
+            tree.addEdge(vertex1: prev, vertex2: vertex, weight: head.weight)
+        }
+        
+        if let neighbours = graph.adjList[vertex] {
+            for neighbour in neighbours {
+                let nextVertex = neighbour.vertex
+                if !visited.contains(nextVertex) {
+                    priorityQueue.enqueue((vertex: nextVertex, weight: neighbour.weight, parent: vertex))
+                }
+            }
         }
-      }
     }
-  }
-
-  return (cost: cost, tree: tree)
+    
+    return (cost: cost, tree: tree)
 }
 
 /*:
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift
index 80b40c65f..8a2c2aa07 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift	
@@ -147,7 +147,7 @@ public struct Heap<T> {
 
     let size = elements.count - 1
     if index != size {
-      swap(&elements[index], &elements[size])
+      elements.swapAt(index,size)
       shiftDown(index, heapSize: size)
       shiftUp(index)
     }
@@ -200,7 +200,7 @@ public struct Heap<T> {
       }
       if first == parentIndex { return }
 
-      swap(&elements[parentIndex], &elements[first])
+      elements.swapAt(parentIndex,first)
       parentIndex = first
     }
   }

From 9f85804ce36d56e328cc01f07ef58d75368a8496 Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Tue, 1 Aug 2017 22:13:16 -0400
Subject: [PATCH 113/643] Update travis to xcode 9

Update travis to use xcode 9 for swift 4 migration.
---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index d413140fc..1515be04f 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,5 +1,5 @@
 language: objective-c
-osx_image: xcode8.3
+osx_image: xcode9
 # sudo: false
 
 install:

From eb798f2d905c5d5c15555bb47be1854765562cac Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 21:55:11 -0700
Subject: [PATCH 114/643] [Swift 4] Update Z Algorithm

---
 Z-Algorithm/ZetaAlgorithm.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
index b1d49eec7..d057080a1 100644
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
 
   let pattern = Array(ptrn.characters)

From 0b558063e41f37a7ddb7cadb6ae7ac9959d90137 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:01:52 -0700
Subject: [PATCH 115/643] [Swift 4] Update Threaded Binary Tree

---
 .../ThreadedBinaryTree.playground/Contents.swift             | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift
index ece1966e0..4ce9d8157 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Simple little debug function to make testing output pretty
 func check(_ tree: ThreadedBinaryTree<Int>?) {
   if let tree = tree {

From 82d8f3dc7d106ddfada053a0a20b2ff5bcf6ff72 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:05:53 -0700
Subject: [PATCH 116/643] [Swift 4] Update Ternary Search Tree

---
 .../TST.playground/Contents.swift             |  5 +
 .../Tests/TernarySearchTreeTests.swift        | 99 ++++++++++---------
 .../Tests/Tests.xcodeproj/project.pbxproj     |  4 +-
 .../contents.xcworkspacedata                  |  7 ++
 4 files changed, 67 insertions(+), 48 deletions(-)
 create mode 100644 Ternary Search Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata

diff --git a/Ternary Search Tree/TST.playground/Contents.swift b/Ternary Search Tree/TST.playground/Contents.swift
index bacf56aee..0f576835b 100644
--- a/Ternary Search Tree/TST.playground/Contents.swift	
+++ b/Ternary Search Tree/TST.playground/Contents.swift	
@@ -3,6 +3,11 @@
 import Cocoa
 import Foundation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let treeOfStrings = TernarySearchTree<String>()
 
 var testStrings: [(key: String, data: String)] = []
diff --git a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift
index 4a1816412..a595e40a3 100644
--- a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
+++ b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
@@ -10,61 +10,68 @@ import XCTest
 
 class TernarySearchTreeTests: XCTestCase {
 
-    let testCount = 30
+  let testCount = 30
 
-    func testCanFindStringInTree() {
-        var testStrings: [(key: String, data: String)] = []
-        let treeOfStrings = TernarySearchTree<String>()
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
 
-        for _ in (1...testCount) {
-            var randomLength = Int(arc4random_uniform(10))
+  func testCanFindStringInTree() {
+    var testStrings: [(key: String, data: String)] = []
+    let treeOfStrings = TernarySearchTree<String>()
 
-            var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+    for _ in (1...testCount) {
+      var randomLength = Int(arc4random_uniform(10))
 
-            while testStrings.contains(where: { $0.key == key}) {
-                //That key is taken, so we generate a new one with another length
-                randomLength = Int(arc4random_uniform(10))
-                key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
-            }
-            let data = Utils.shared.randomAlphaNumericString(withLength: randomLength)
-            //    print("Key: \(key) Data: \(data)")
+      var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
 
-            if key != "" && data != "" {
-                testStrings.append((key, data))
-                treeOfStrings.insert(data: data, withKey: key)
-            }
-        }
+      while testStrings.contains(where: { $0.key == key}) {
+        //That key is taken, so we generate a new one with another length
+        randomLength = Int(arc4random_uniform(10))
+        key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+      }
+      let data = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+      //    print("Key: \(key) Data: \(data)")
 
-        for aTest in testStrings {
-            let data = treeOfStrings.find(key: aTest.key)
-            XCTAssertNotNil(data)
-            XCTAssertEqual(data, aTest.data)
-        }
+      if key != "" && data != "" {
+        testStrings.append((key, data))
+        treeOfStrings.insert(data: data, withKey: key)
+      }
     }
 
-    func testCanFindNumberInTree() {
-        var testNums: [(key: String, data: Int)] = []
-        let treeOfInts = TernarySearchTree<Int>()
-        for _ in (1...testCount) {
-            let randomNum = Int(arc4random_uniform(UInt32.max))
-            var randomLength = Int(arc4random_uniform(10))
-            var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
-            while testNums.contains(where: { $0.key == key}) {
-                //That key is taken, so we generate a new one with another length
-                randomLength = Int(arc4random_uniform(10))
-                key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
-            }
+    for aTest in testStrings {
+      let data = treeOfStrings.find(key: aTest.key)
+      XCTAssertNotNil(data)
+      XCTAssertEqual(data, aTest.data)
+    }
+  }
+
+  func testCanFindNumberInTree() {
+    var testNums: [(key: String, data: Int)] = []
+    let treeOfInts = TernarySearchTree<Int>()
+    for _ in (1...testCount) {
+      let randomNum = Int(arc4random_uniform(UInt32.max))
+      var randomLength = Int(arc4random_uniform(10))
+      var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+      while testNums.contains(where: { $0.key == key}) {
+        //That key is taken, so we generate a new one with another length
+        randomLength = Int(arc4random_uniform(10))
+        key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
+      }
 
-            if key != "" {
-                testNums.append((key, randomNum))
-                treeOfInts.insert(data: randomNum, withKey: key)
-            }
-        }
+      if key != "" {
+        testNums.append((key, randomNum))
+        treeOfInts.insert(data: randomNum, withKey: key)
+      }
+    }
 
-        for aTest in testNums {
-            let data = treeOfInts.find(key: aTest.key)
-            XCTAssertNotNil(data)
-            XCTAssertEqual(data, aTest.data)
-        }
+    for aTest in testNums {
+      let data = treeOfInts.find(key: aTest.key)
+      XCTAssertNotNil(data)
+      XCTAssertEqual(data, aTest.data)
     }
+  }
 }
diff --git a/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj b/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj
index 7afaca944..1d48e705a 100644
--- a/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Ternary Search Tree/Tests/Tests.xcodeproj/project.pbxproj	
@@ -220,7 +220,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -233,7 +233,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Ternary Search Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Ternary Search Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Ternary Search Tree/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

From fe933ee784f8e25408ead1fdc483b4a4ff9f147a Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:08:54 -0700
Subject: [PATCH 117/643] [Swift 4] Update Strassen Matrix Multiplication

---
 .../StrassensMatrixMultiplication.playground/Contents.swift  | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index 6b9314557..409e28c52 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 var A = Matrix(rows: 2, columns: 4, initialValue: 0)

From 5f9a11c95b1271dac89ed11f3ebdcb819302cfef Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:23:58 -0700
Subject: [PATCH 118/643] [Swift 4] Update Slow Sort

---
 Slow Sort/SlowSort.playground/Contents.swift  |  9 ++++++
 .../Sources/SlowSort.swift                    | 16 ++++++++++
 .../SlowSort.playground/contents.xcplayground |  4 +++
 .../contents.xcworkspacedata                  |  7 +++++
 Slow Sort/SlowSort.swift                      | 31 +++++++++----------
 .../contents.xcworkspacedata                  |  3 ++
 6 files changed, 53 insertions(+), 17 deletions(-)
 create mode 100644 Slow Sort/SlowSort.playground/Contents.swift
 create mode 100644 Slow Sort/SlowSort.playground/Sources/SlowSort.swift
 create mode 100644 Slow Sort/SlowSort.playground/contents.xcplayground
 create mode 100644 Slow Sort/SlowSort.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Slow Sort/SlowSort.playground/Contents.swift b/Slow Sort/SlowSort.playground/Contents.swift
new file mode 100644
index 000000000..95bf80739
--- /dev/null
+++ b/Slow Sort/SlowSort.playground/Contents.swift	
@@ -0,0 +1,9 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+var numberList = [1, 12, 9, 17, 13, 12]
+
+slowsort(0, numberList.count-1, &numberList)
+print(numberList)
diff --git a/Slow Sort/SlowSort.playground/Sources/SlowSort.swift b/Slow Sort/SlowSort.playground/Sources/SlowSort.swift
new file mode 100644
index 000000000..32bb38505
--- /dev/null
+++ b/Slow Sort/SlowSort.playground/Sources/SlowSort.swift	
@@ -0,0 +1,16 @@
+import Foundation
+
+public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+  if i>=j {
+    return
+  }
+  let m = (i+j)/2
+  slowsort(i, m, &numberList)
+  slowsort(m+1, j, &numberList)
+  if numberList[j] < numberList[m] {
+    let temp = numberList[j]
+    numberList[j] = numberList[m]
+    numberList[m] = temp
+  }
+  slowsort(i, j-1, &numberList)
+}
diff --git a/Slow Sort/SlowSort.playground/contents.xcplayground b/Slow Sort/SlowSort.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Slow Sort/SlowSort.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Slow Sort/SlowSort.playground/playground.xcworkspace/contents.xcworkspacedata b/Slow Sort/SlowSort.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Slow Sort/SlowSort.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 6396e8b38..9f264a057 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -6,22 +6,19 @@
 //
 //
 
-var numberList = [1, 12, 9, 17, 13, 12]
+import Foundation
 
-public func slowsort(_ i: Int, _ j: Int) {
-    if i>=j {
-        return
-    }
-    let m = (i+j)/2
-    slowsort(i, m)
-    slowsort(m+1, j)
-    if numberList[j] < numberList[m] {
-        let temp = numberList[j]
-        numberList[j] = numberList[m]
-        numberList[m] = temp
-    }
-    slowsort(i, j-1)
+public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+  if i>=j {
+    return
+  }
+  let m = (i+j)/2
+  slowsort(i, m, &numberList)
+  slowsort(m+1, j, &numberList)
+  if numberList[j] < numberList[m] {
+    let temp = numberList[j]
+    numberList[j] = numberList[m]
+    numberList[m] = temp
+  }
+  slowsort(i, j-1, &numberList)
 }
-
-slowsort(0, numberList.count-1)
-print(numberList)
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7ca193aca..883185e49 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -2293,6 +2293,9 @@
    <Group
       location = "group:Slow Sort"
       name = "Slow Sort">
+      <FileRef
+         location = "group:SlowSort.playground">
+      </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>

From ef52311487a7123cd71c34f9df0af2f2a68a7372 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:33:01 -0700
Subject: [PATCH 119/643] [Swift 4] Update Skip List

---
 Skip-List/SkipList.playground/Contents.swift  |   7 +
 .../Sources/SkipList.swift                    | 270 ++++++++++++++++++
 .../SkipList.playground/contents.xcplayground |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Skip-List/SkipList.swift                      |  13 +-
 .../contents.xcworkspacedata                  |   3 +
 6 files changed, 295 insertions(+), 9 deletions(-)
 create mode 100644 Skip-List/SkipList.playground/Contents.swift
 create mode 100644 Skip-List/SkipList.playground/Sources/SkipList.swift
 create mode 100644 Skip-List/SkipList.playground/contents.xcplayground
 create mode 100644 Skip-List/SkipList.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Skip-List/SkipList.playground/Contents.swift b/Skip-List/SkipList.playground/Contents.swift
new file mode 100644
index 000000000..1b4847c0e
--- /dev/null
+++ b/Skip-List/SkipList.playground/Contents.swift
@@ -0,0 +1,7 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+// SkipList is ready for Swift 4.
+// TODO: Add Test
diff --git a/Skip-List/SkipList.playground/Sources/SkipList.swift b/Skip-List/SkipList.playground/Sources/SkipList.swift
new file mode 100644
index 000000000..f626da0f8
--- /dev/null
+++ b/Skip-List/SkipList.playground/Sources/SkipList.swift
@@ -0,0 +1,270 @@
+// The MIT License (MIT)
+
+// Copyright (c) 2016 Mike Taghavi (mitghi[at]me.com)
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+import Foundation
+
+// Stack from : https://github.com/raywenderlich/swift-algorithm-club/tree/master/Stack
+public struct Stack<T> {
+  fileprivate var array: [T] = []
+
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+
+  public var count: Int {
+    return array.count
+  }
+
+  public mutating func push(_ element: T) {
+    array.append(element)
+  }
+
+  public mutating func pop() -> T? {
+    return array.popLast()
+  }
+
+  public func peek() -> T? {
+    return array.last
+  }
+}
+
+extension Stack: Sequence {
+  public func makeIterator() -> AnyIterator<T> {
+    var curr = self
+    return AnyIterator { curr.pop() }
+  }
+}
+
+private func coinFlip() -> Bool {
+  return arc4random_uniform(2) == 1
+}
+
+public class DataNode<Key: Comparable, Payload> {
+  public typealias Node = DataNode<Key, Payload>
+
+  var data: Payload?
+  fileprivate var key: Key?
+  var next: Node?
+  var down: Node?
+
+  public init(key: Key, data: Payload) {
+    self.key  = key
+    self.data = data
+  }
+
+  public init(asHead head: Bool) {}
+
+}
+
+open class SkipList<Key: Comparable, Payload> {
+  public typealias Node = DataNode<Key, Payload>
+
+  fileprivate(set) var head: Node?
+
+  public init() {}
+
+}
+
+// MARK: - Search lanes for a node with a given key
+
+extension SkipList {
+
+  func findNode(key: Key) -> Node? {
+    var currentNode: Node? = head
+    var isFound: Bool = false
+
+    while !isFound {
+      if let node = currentNode {
+
+        switch node.next {
+        case .none:
+
+          currentNode = node.down
+        case .some(let value) where value.key != nil:
+
+          if value.key == key {
+            isFound = true
+            break
+          } else {
+            if key < value.key! {
+              currentNode = node.down
+            } else {
+              currentNode = node.next
+            }
+          }
+
+        default:
+          continue
+        }
+
+      } else {
+        break
+      }
+    }
+
+    if isFound {
+      return currentNode
+    } else {
+      return nil
+    }
+
+  }
+
+  func search(key: Key) -> Payload? {
+    guard let node = findNode(key: key) else {
+      return nil
+    }
+
+    return node.next!.data
+  }
+
+}
+
+// MARK: - Insert a node into lanes depending on skip list status ( bootstrap base-layer if head is empty / start insertion from current head ).
+
+extension SkipList {
+  private func bootstrapBaseLayer(key: Key, data: Payload) {
+    head       = Node(asHead: true)
+    var node   = Node(key: key, data: data)
+
+    head!.next = node
+
+    var currentTopNode = node
+
+    while coinFlip() {
+      let newHead    = Node(asHead: true)
+      node           = Node(key: key, data: data)
+      node.down      = currentTopNode
+      newHead.next   = node
+      newHead.down   = head
+      head           = newHead
+      currentTopNode = node
+    }
+
+  }
+
+  private func insertItem(key: Key, data: Payload) {
+    var stack              = Stack<Node>()
+    var currentNode: Node? = head
+
+    while currentNode != nil {
+
+      if let nextNode = currentNode!.next {
+        if nextNode.key! > key {
+          stack.push(currentNode!)
+          currentNode = currentNode!.down
+        } else {
+          currentNode = nextNode
+        }
+
+      } else {
+        stack.push(currentNode!)
+        currentNode = currentNode!.down
+      }
+
+    }
+
+    let itemAtLayer    = stack.pop()
+    var node           = Node(key: key, data: data)
+    node.next          = itemAtLayer!.next
+    itemAtLayer!.next  = node
+    var currentTopNode = node
+
+    while coinFlip() {
+      if stack.isEmpty {
+        let newHead    = Node(asHead: true)
+
+        node           = Node(key: key, data: data)
+        node.down      = currentTopNode
+        newHead.next   = node
+        newHead.down   = head
+        head           = newHead
+        currentTopNode = node
+
+      } else {
+        let nextNode  = stack.pop()
+
+        node           = Node(key: key, data: data)
+        node.down      = currentTopNode
+        node.next      = nextNode!.next
+        nextNode!.next = node
+        currentTopNode = node
+      }
+    }
+  }
+
+  func insert(key: Key, data: Payload) {
+    if head != nil {
+      if let node = findNode(key: key) {
+        // replace, in case of key already exists.
+        var currentNode = node.next
+        while currentNode != nil && currentNode!.key == key {
+          currentNode!.data = data
+          currentNode       = currentNode!.down
+        }
+      } else {
+        insertItem(key: key, data: data)
+      }
+
+    } else {
+      bootstrapBaseLayer(key: key, data: data)
+    }
+  }
+
+}
+
+// MARK: - Remove a node with a given key. First, find its position in layers at the top, then remove it from each lane by traversing down to the base layer.
+
+extension SkipList {
+  public func remove(key: Key) {
+    guard let item = findNode(key: key) else {
+      return
+    }
+
+    var currentNode = Optional(item)
+
+    while currentNode != nil {
+      let node   = currentNode!.next
+
+      if node!.key != key {
+        currentNode = node
+        continue
+      }
+
+      let nextNode      = node!.next
+
+      currentNode!.next = nextNode
+      currentNode       = currentNode!.down
+
+    }
+
+  }
+}
+
+// MARK: - Get associated payload from a node with a given key.
+
+extension SkipList {
+
+  public func get(key: Key) -> Payload? {
+    return search(key: key)
+  }
+}
diff --git a/Skip-List/SkipList.playground/contents.xcplayground b/Skip-List/SkipList.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Skip-List/SkipList.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Skip-List/SkipList.playground/playground.xcworkspace/contents.xcworkspacedata b/Skip-List/SkipList.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Skip-List/SkipList.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 43173f236..fc635d0f2 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -50,18 +50,12 @@ public struct Stack<T> {
 extension Stack: Sequence {
   public func makeIterator() -> AnyIterator<T> {
     var curr = self
-    return AnyIterator { _ -> T? in
-      return curr.pop()
-    }
+    return AnyIterator { curr.pop() }
   }
 }
 
 private func coinFlip() -> Bool {
-  #if os(Linux)
-      return random() % 2 == 0
-  #elseif os(OSX)
-      return arc4random_uniform(2) == 1
-  #endif
+  return arc4random_uniform(2) == 1
 }
 
 public class DataNode<Key: Comparable, Payload> {
@@ -221,7 +215,7 @@ extension SkipList {
   func insert(key: Key, data: Payload) {
     if head != nil {
       if let node = findNode(key: key) {
-        // replace, in case of key already exists. 
+        // replace, in case of key already exists.
         var currentNode = node.next
         while currentNode != nil && currentNode!.key == key {
           currentNode!.data = data
@@ -274,3 +268,4 @@ extension SkipList {
     return search(key: key)
   }
 }
+
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7ca193aca..5b78bd25a 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -2237,6 +2237,9 @@
    <Group
       location = "group:Skip-List"
       name = "Skip-List">
+      <FileRef
+         location = "group:SkipList.playground">
+      </FileRef>
       <Group
          location = "group:Images"
          name = "Images">

From 691b5566cf32b55dddd7015d897b769971d37542 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:35:09 -0700
Subject: [PATCH 120/643] [Swift 4] Update Shunting Yard

---
 .../ShuntingYard.playground/Contents.swift    |  5 ++
 .../Sources/Stack.swift                       | 60 +++++++++----------
 2 files changed, 34 insertions(+), 31 deletions(-)

diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index 38431f5e2..ddd73de59 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 internal enum OperatorAssociativity {
   case leftAssociative
   case rightAssociative
diff --git a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift
index c54c5a600..54ffe02ce 100644
--- a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
@@ -1,38 +1,36 @@
 import Foundation
 
 public struct Stack<T> {
-    fileprivate var array = [T]()
-
-    public init() {
-
-    }
-
-    public var isEmpty: Bool {
-        return array.isEmpty
-    }
-
-    public var count: Int {
-        return array.count
-    }
-
-    public mutating func push(_ element: T) {
-        array.append(element)
-    }
-
-    public mutating func pop() -> T? {
-        return array.popLast()
-    }
-
-    public var top: T? {
-        return array.last
-    }
+  fileprivate var array = [T]()
+  
+  public init() {
+    
+  }
+  
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+  
+  public var count: Int {
+    return array.count
+  }
+  
+  public mutating func push(_ element: T) {
+    array.append(element)
+  }
+  
+  public mutating func pop() -> T? {
+    return array.popLast()
+  }
+  
+  public var top: T? {
+    return array.last
+  }
 }
 
 extension Stack: Sequence {
-    public func makeIterator() -> AnyIterator<T> {
-        var curr = self
-        return AnyIterator { _ -> T? in
-            return curr.pop()
-        }
-    }
+  public func makeIterator() -> AnyIterator<T> {
+    var curr = self
+    return AnyIterator { curr.pop() }
+  }
 }

From 4a85e17c6733d9bb27fa8d3d7c29fbd1b1af2470 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Tue, 1 Aug 2017 22:38:19 -0700
Subject: [PATCH 121/643] [Swift 4] Update Rootish Array Stack

---
 .../RootishArrayStack.playground/Contents.swift            | 5 +++++
 Rootish Array Stack/Tests/RootishArrayStackTests.swift     | 7 +++++++
 Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj  | 4 ++--
 3 files changed, 14 insertions(+), 2 deletions(-)

diff --git a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift
index 8b630528d..ade32a3e7 100644
--- a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
+++ b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Darwin
 
 public struct RootishArrayStack<T> {
diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
index 9d5972a41..fc045faf4 100755
--- a/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -205,4 +205,11 @@ class RootishArrayStackTests: XCTestCase {
 		XCTAssertEqual(list.first, 0)
 		XCTAssertTrue(list.equal(toArray: array))
 	}
+
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
 }
diff --git a/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj b/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj
index cdfd35f71..bbc3967e5 100644
--- a/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Rootish Array Stack/Tests/Tests.xcodeproj/project.pbxproj	
@@ -226,7 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -238,7 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From 08cf693ea36bbd313bddc3a649a1dbf6223f7517 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Thu, 3 Aug 2017 09:26:29 +0500
Subject: [PATCH 122/643] Fixed Indent issue

---
 .../Contents.swift                            | 16 +++++++--------
 .../Sources/Edge.swift                        | 12 +++++------
 .../Sources/Graph.swift                       | 20 +++++++++----------
 .../Sources/Node.swift                        | 10 +++++-----
 4 files changed, 29 insertions(+), 29 deletions(-)

diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index dd98e87dc..8a1338dbd 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -5,15 +5,15 @@ print("Hello, Swift 4!")
 #endif
 
 func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
-  var nodesExplored = [source.label]
-  source.visited = true
-
-  for edge in source.neighbors {
-    if !edge.neighbor.visited {
-      nodesExplored += depthFirstSearch(graph, source: edge.neighbor)
+    var nodesExplored = [source.label]
+    source.visited = true
+    
+    for edge in source.neighbors {
+        if !edge.neighbor.visited {
+            nodesExplored += depthFirstSearch(graph, source: edge.neighbor)
+        }
     }
-  }
-  return nodesExplored
+    return nodesExplored
 }
 
 let graph = Graph()
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift
index 7c841be30..40e769aae 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift	
@@ -1,11 +1,11 @@
 public class Edge: Equatable {
-  public var neighbor: Node
-
-  public init(_ neighbor: Node) {
-    self.neighbor = neighbor
-  }
+    public var neighbor: Node
+    
+    public init(_ neighbor: Node) {
+        self.neighbor = neighbor
+    }
 }
 
 public func == (_ lhs: Edge, rhs: Edge) -> Bool {
-  return lhs.neighbor == rhs.neighbor
+    return lhs.neighbor == rhs.neighbor
 }
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift
index 87e21897c..34ee2fa3a 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
@@ -1,24 +1,24 @@
 public class Graph: CustomStringConvertible, Equatable {
   public private(set) var nodes: [Node]
-
+  
   public init() {
     self.nodes = []
   }
-
+  
   public func addNode(_ label: String) -> Node {
     let node = Node(label)
     nodes.append(node)
     return node
   }
-
+  
   public func addEdge(_ source: Node, neighbor: Node) {
     let edge = Edge(neighbor)
     source.neighbors.append(edge)
   }
-
+  
   public var description: String {
     var description = ""
-
+    
     for node in nodes {
       if !node.neighbors.isEmpty {
         description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
@@ -26,18 +26,18 @@ public class Graph: CustomStringConvertible, Equatable {
     }
     return description
   }
-
+  
   public func findNodeWithLabel(_ label: String) -> Node {
     return nodes.filter { $0.label == label }.first!
   }
-
+  
   public func duplicate() -> Graph {
     let duplicated = Graph()
-
+    
     for node in nodes {
       duplicated.addNode(node.label)
     }
-
+    
     for node in nodes {
       for edge in node.neighbors {
         let source = duplicated.findNodeWithLabel(node.label)
@@ -45,7 +45,7 @@ public class Graph: CustomStringConvertible, Equatable {
         duplicated.addEdge(source, neighbor: neighbour)
       }
     }
-
+    
     return duplicated
   }
 }
diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift
index 48fc952e3..bab55c371 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift	
@@ -1,27 +1,27 @@
 public class Node: CustomStringConvertible, Equatable {
   public var neighbors: [Edge]
-
+  
   public private(set) var label: String
   public var distance: Int?
   public var visited: Bool
-
+  
   public init(_ label: String) {
     self.label = label
     neighbors = []
     visited = false
   }
-
+  
   public var description: String {
     if let distance = distance {
       return "Node(label: \(label), distance: \(distance))"
     }
     return "Node(label: \(label), distance: infinity)"
   }
-
+  
   public var hasDistance: Bool {
     return distance != nil
   }
-
+  
   public func remove(_ edge: Edge) {
     neighbors.remove(at: neighbors.index { $0 === edge }!)
   }

From 19433a0d39ddd33a6cc5f3fd617daeeb58629ba8 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Thu, 3 Aug 2017 09:41:50 +0500
Subject: [PATCH 123/643] Fixed Indents

---
 Minimum Spanning Tree/Kruskal.swift |  6 +++---
 Minimum Spanning Tree/Prim.swift    | 12 ++++++------
 2 files changed, 9 insertions(+), 9 deletions(-)

diff --git a/Minimum Spanning Tree/Kruskal.swift b/Minimum Spanning Tree/Kruskal.swift
index 5e6fc5fd2..7db4aeb2d 100644
--- a/Minimum Spanning Tree/Kruskal.swift	
+++ b/Minimum Spanning Tree/Kruskal.swift	
@@ -10,12 +10,12 @@ func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T
   var cost: Int = 0
   var tree = Graph<T>()
   let sortedEdgeListByWeight = graph.edgeList.sorted(by: { $0.weight < $1.weight })
-
+  
   var unionFind = UnionFind<T>()
   for vertex in graph.vertices {
     unionFind.addSetWith(vertex)
   }
-
+  
   for edge in sortedEdgeListByWeight {
     let v1 = edge.vertex1
     let v2 = edge.vertex2
@@ -25,6 +25,6 @@ func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T
       unionFind.unionSetsContaining(v1, and: v2)
     }
   }
-
+  
   return (cost: cost, tree: tree)
 }
diff --git a/Minimum Spanning Tree/Prim.swift b/Minimum Spanning Tree/Prim.swift
index d65d53f29..b05fc1b1f 100644
--- a/Minimum Spanning Tree/Prim.swift	
+++ b/Minimum Spanning Tree/Prim.swift	
@@ -9,15 +9,15 @@
 func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
   var cost: Int = 0
   var tree = Graph<T>()
-
+  
   guard let start = graph.vertices.first else {
     return (cost: cost, tree: tree)
   }
-
+  
   var visited = Set<T>()
   var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
     sort: { $0.weight < $1.weight })
-
+  
   priorityQueue.enqueue((vertex: start, weight: 0, parent: nil))
   while let head = priorityQueue.dequeue() {
     let vertex = head.vertex
@@ -25,12 +25,12 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
       continue
     }
     visited.insert(vertex)
-
+    
     cost += head.weight
     if let prev = head.parent {
       tree.addEdge(vertex1: prev, vertex2: vertex, weight: head.weight)
     }
-
+    
     if let neighbours = graph.adjList[vertex] {
       for neighbour in neighbours {
         let nextVertex = neighbour.vertex
@@ -40,6 +40,6 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
       }
     }
   }
-
+  
   return (cost: cost, tree: tree)
 }

From d54829d5017c0bd193b562338ab4f3cb73d1d223 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 30 Jul 2017 08:14:07 -0700
Subject: [PATCH 124/643] [Swift 4] Update Linked List

---
 Linked List/LinkedList.playground/Contents.swift  | 5 +++++
 Linked List/Tests/LinkedListTests.swift           | 7 +++++++
 Linked List/Tests/Tests.xcodeproj/project.pbxproj | 4 ++--
 3 files changed, 14 insertions(+), 2 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index c7cd6265d..b78ee4809 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -3,6 +3,11 @@
 // For best results, don't forget to select "Show Rendered Markup" from XCode's "Editor" menu
 
 //: Linked List Class Declaration:
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 public final class LinkedList<T> {
 
   /// Linked List's Node Class Declaration
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 7fd31c2c7..0b2b116df 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -11,6 +11,13 @@ class LinkedListTest: XCTestCase {
     return list
   }
 
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+
   func testEmptyList() {
     let list = LinkedList<Int>()
     XCTAssertTrue(list.isEmpty)
diff --git a/Linked List/Tests/Tests.xcodeproj/project.pbxproj b/Linked List/Tests/Tests.xcodeproj/project.pbxproj
index 3a29f5677..388dcd96c 100644
--- a/Linked List/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Linked List/Tests/Tests.xcodeproj/project.pbxproj	
@@ -221,7 +221,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -233,7 +233,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From 449b14b904c6cee06460c3933b7b73f60104593a Mon Sep 17 00:00:00 2001
From: Daniel Stokowski <daniel.stokowski@gmail.com>
Date: Sat, 5 Aug 2017 09:44:55 +0200
Subject: [PATCH 125/643] Update to Swift 4 - applied XCode fixes in
 Quicksort.swift and Quicsort playgrund - renamed "Tests" project to
 "Tests(quicksort)" and recreated scheme - to be easier pickable in schemes
 list - applied swift 4 settings

---
 .travis.yml                                   |  2 +-
 Quicksort/Quicksort.playground/Contents.swift |  9 +++-
 Quicksort/Quicksort.swift                     |  4 +-
 .../project.pbxproj                           | 44 +++++++++++++------
 .../contents.xcworkspacedata                  |  0
 .../xcschemes/Tests(quicksort).xcscheme}      | 44 +++----------------
 .../contents.xcworkspacedata                  |  2 +-
 7 files changed, 47 insertions(+), 58 deletions(-)
 rename Quicksort/Tests/{Tests.xcodeproj => Tests(quicksort).xcodeproj}/project.pbxproj (86%)
 rename Quicksort/Tests/{Tests.xcodeproj => Tests(quicksort).xcodeproj}/project.xcworkspace/contents.xcworkspacedata (100%)
 rename Quicksort/Tests/{Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme => Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme} (53%)

diff --git a/.travis.yml b/.travis.yml
index 1515be04f..6efcbd42b 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -32,7 +32,7 @@ script:
 - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Quicksort/Tests/Tests(quicksort).xcodeproj -scheme Tests(quicksort)
 - xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index 972d0b5e1..94d9f8e45 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 // *** Simple but inefficient version of quicksort ***
@@ -80,7 +85,7 @@ func partitionHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
     repeat { i += 1 } while a[i] < pivot
 
     if i < j {
-      swap(&a[i], &a[j])
+        a.swapAt(i, j)
     } else {
       return j
     }
@@ -132,7 +137,7 @@ list4
 */
 public func swap<T>(_ a: inout [T], _ i: Int, _ j: Int) {
   if i != j {
-    swap(&a[i], &a[j])
+    a.swapAt(i, j)
   }
 }
 
diff --git a/Quicksort/Quicksort.swift b/Quicksort/Quicksort.swift
index 39fa27b66..a67122723 100644
--- a/Quicksort/Quicksort.swift
+++ b/Quicksort/Quicksort.swift
@@ -90,7 +90,7 @@ func partitionHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
     repeat { i += 1 } while a[i] < pivot
 
     if i < j {
-      swap(&a[i], &a[j])
+        a.swapAt(i, j)
     } else {
       return j
     }
@@ -144,7 +144,7 @@ func quicksortRandom<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
 */
 public func swap<T>(_ a: inout [T], _ i: Int, _ j: Int) {
   if i != j {
-    swap(&a[i], &a[j])
+    a.swapAt(i, j)
   }
 }
 
diff --git a/Quicksort/Tests/Tests.xcodeproj/project.pbxproj b/Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj
similarity index 86%
rename from Quicksort/Tests/Tests.xcodeproj/project.pbxproj
rename to Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj
index 2d8ee18ff..70deb0c74 100644
--- a/Quicksort/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj
@@ -13,7 +13,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Tests(quicksort).xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3E51C77A4CA003CECC7 /* Quicksort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Quicksort.swift; path = ../Quicksort.swift; sourceTree = SOURCE_ROOT; };
 		7B80C3E71C77A4D0003CECC7 /* QuicksortTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = QuicksortTests.swift; sourceTree = SOURCE_ROOT; };
@@ -42,7 +42,7 @@
 		7B2BBC721C779D710067B71D /* Products */ = {
 			isa = PBXGroup;
 			children = (
-				7B2BBC801C779D720067B71D /* Tests.xctest */,
+				7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -62,9 +62,9 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		7B2BBC7F1C779D720067B71D /* Tests */ = {
+		7B2BBC7F1C779D720067B71D /* Tests(quicksort) */ = {
 			isa = PBXNativeTarget;
-			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests(quicksort)" */;
 			buildPhases = (
 				7B2BBC7C1C779D720067B71D /* Sources */,
 				7B2BBC7D1C779D720067B71D /* Frameworks */,
@@ -74,9 +74,9 @@
 			);
 			dependencies = (
 			);
-			name = Tests;
+			name = "Tests(quicksort)";
 			productName = TestsTests;
-			productReference = 7B2BBC801C779D720067B71D /* Tests.xctest */;
+			productReference = 7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
@@ -86,16 +86,16 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 0900;
 					};
 				};
 			};
-			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests(quicksort)" */;
 			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
@@ -108,7 +108,7 @@
 			projectDirPath = "";
 			projectRoot = "";
 			targets = (
-				7B2BBC7F1C779D720067B71D /* Tests */,
+				7B2BBC7F1C779D720067B71D /* Tests(quicksort) */,
 			);
 		};
 /* End PBXProject section */
@@ -145,14 +145,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -180,6 +186,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
 			};
 			name = Debug;
 		};
@@ -191,14 +198,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -219,6 +232,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
 			};
 			name = Release;
 		};
@@ -230,7 +244,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -242,14 +257,15 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */ = {
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests(quicksort)" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC871C779D720067B71D /* Debug */,
@@ -258,7 +274,7 @@
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
 		};
-		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests" */ = {
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests(quicksort)" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC8D1C779D720067B71D /* Debug */,
diff --git a/Quicksort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Quicksort/Tests/Tests(quicksort).xcodeproj/project.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Quicksort/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
rename to Quicksort/Tests/Tests(quicksort).xcodeproj/project.xcworkspace/contents.xcworkspacedata
diff --git a/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme
similarity index 53%
rename from Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
rename to Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme
index dfcf6de42..ac3eafc78 100644
--- a/Quicksort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme
@@ -1,31 +1,16 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
       buildImplicitDependencies = "YES">
-      <BuildActionEntries>
-         <BuildActionEntry
-            buildForTesting = "YES"
-            buildForRunning = "YES"
-            buildForProfiling = "NO"
-            buildForArchiving = "NO"
-            buildForAnalyzing = "NO">
-            <BuildableReference
-               BuildableIdentifier = "primary"
-               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "Tests.xctest"
-               BlueprintName = "Tests"
-               ReferencedContainer = "container:Tests.xcodeproj">
-            </BuildableReference>
-         </BuildActionEntry>
-      </BuildActionEntries>
    </BuildAction>
    <TestAction
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -33,9 +18,9 @@
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "Tests.xctest"
-               BlueprintName = "Tests"
-               ReferencedContainer = "container:Tests.xcodeproj">
+               BuildableName = "Tests(quicksort).xctest"
+               BlueprintName = "Tests(quicksort)"
+               ReferencedContainer = "container:Tests(quicksort).xcodeproj">
             </BuildableReference>
          </TestableReference>
       </Testables>
@@ -46,21 +31,13 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"
       debugDocumentVersioning = "YES"
       debugServiceExtension = "internal"
       allowLocationSimulation = "YES">
-      <MacroExpansion>
-         <BuildableReference
-            BuildableIdentifier = "primary"
-            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-            BuildableName = "Tests.xctest"
-            BlueprintName = "Tests"
-            ReferencedContainer = "container:Tests.xcodeproj">
-         </BuildableReference>
-      </MacroExpansion>
       <AdditionalOptions>
       </AdditionalOptions>
    </LaunchAction>
@@ -70,15 +47,6 @@
       savedToolIdentifier = ""
       useCustomWorkingDirectory = "NO"
       debugDocumentVersioning = "YES">
-      <MacroExpansion>
-         <BuildableReference
-            BuildableIdentifier = "primary"
-            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-            BuildableName = "Tests.xctest"
-            BlueprintName = "Tests"
-            ReferencedContainer = "container:Tests.xcodeproj">
-         </BuildableReference>
-      </MacroExpansion>
    </ProfileAction>
    <AnalyzeAction
       buildConfiguration = "Debug">
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index db4691648..3fa8aef62 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1822,7 +1822,7 @@
             location = "group:SortingTestHelpers.swift">
          </FileRef>
          <FileRef
-            location = "group:Tests.xcodeproj">
+            location = "group:/Users/danielstokowski/Documents/GitHub/swift-algorithm-club/Quicksort/Tests/Tests(quicksort).xcodeproj">
          </FileRef>
       </Group>
    </Group>

From 038347d1ce7d72b40c9f7dc4010094068447ee8c Mon Sep 17 00:00:00 2001
From: Alejandro Isaza <al@isaza.ca>
Date: Sat, 5 Aug 2017 14:34:45 -0700
Subject: [PATCH 126/643] Add hashed heap data structure

---
 Hashed Heap/HashedHeap.swift                  | 239 ++++++++++++++++
 Hashed Heap/README.markdown                   |  11 +
 .../project.pbxproj                           | 268 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcschemes/Hashed Heap Tests.xcscheme      |  67 +++++
 Hashed Heap/Tests/HashedHeapTests.swift       |  88 ++++++
 Hashed Heap/Tests/Info.plist                  |  24 ++
 .../contents.xcworkspacedata                  |  23 ++
 8 files changed, 727 insertions(+)
 create mode 100644 Hashed Heap/HashedHeap.swift
 create mode 100644 Hashed Heap/README.markdown
 create mode 100644 Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj
 create mode 100644 Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme
 create mode 100755 Hashed Heap/Tests/HashedHeapTests.swift
 create mode 100644 Hashed Heap/Tests/Info.plist

diff --git a/Hashed Heap/HashedHeap.swift b/Hashed Heap/HashedHeap.swift
new file mode 100644
index 000000000..f123bbc54
--- /dev/null
+++ b/Hashed Heap/HashedHeap.swift	
@@ -0,0 +1,239 @@
+// Written by Alejandro Isaza. Adapted from heap implementation written by Kevin Randrup and Matthijs Hollemans.
+
+/// Heap with an index hash map (dictionary) to speed up lookups by value.
+///
+/// A heap keeps elements ordered in a binary tree without the use of pointers. A hashed heap does that as well as
+/// having amortized constant lookups by value. This is used in the A* and other heuristic search alogirhtms to achieve
+/// optimal perfomrance.
+public struct HashedHeap<T: Hashable> {
+    /// The array that stores the heap's nodes.
+    private(set) var elements = [T]()
+
+    /// Hash mapping from elements to indices in the `elements` array.
+    private(set) var indices = [T: Int]()
+
+    /// Determines whether this is a max-heap (>) or min-heap (<).
+    fileprivate var isOrderedBefore: (T, T) -> Bool
+
+    /// Creates an empty hashed heap.
+    ///
+    /// The sort function determines whether this is a min-heap or max-heap. For integers, > makes a max-heap, < makes
+    /// a min-heap.
+    public init(sort: @escaping (T, T) -> Bool) {
+        isOrderedBefore = sort
+    }
+
+    /// Creates a hashed heap from an array.
+    ///
+    /// The order of the array does not matter; the elements are inserted into the heap in the order determined by the
+    /// sort function.
+    ///
+    /// - Complexity: O(n)
+    public init(array: [T], sort: @escaping (T, T) -> Bool) {
+        isOrderedBefore = sort
+        buildHeap(fromArray: array)
+    }
+
+    /// Converts an array to a max-heap or min-heap in a bottom-up manner.
+    ///
+    /// - Complexity: O(n)
+    private mutating func buildHeap(fromArray array: [T]) {
+        elements = array
+        for index in elements.indices {
+            indices[elements[index]] = index
+        }
+
+        for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+            shiftDown(i, heapSize: elements.count)
+        }
+    }
+
+    /// Whether the heap is empty.
+    public var isEmpty: Bool {
+        return elements.isEmpty
+    }
+
+    /// The number of elements in the heap.
+    public var count: Int {
+        return elements.count
+    }
+
+    /// Returns the index of the given element.
+    ///
+    /// This is the operation that a hashed heap optimizes in compassion with a normal heap. In a normal heap this
+    /// would take O(n), but for the hashed heap this takes amortized constatn time.
+    ///
+    /// - Complexity: Amortized constant
+    public func index(of element: T) -> Int? {
+        return indices[element]
+    }
+
+    /// Returns the maximum value in the heap (for a max-heap) or the minimum value (for a min-heap).
+    ///
+    /// - Complexity: O(1)
+    public func peek() -> T? {
+        return elements.first
+    }
+
+    /// Adds a new value to the heap.
+    ///
+    /// This reorders the heap so that the max-heap or min-heap property still holds.
+    ///
+    /// - Complexity: O(log n)
+    public mutating func insert(_ value: T) {
+        elements.append(value)
+        indices[value] = elements.count - 1
+        shiftUp(elements.count - 1)
+    }
+
+    /// Adds new values to the heap.
+    public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+        for value in sequence {
+            insert(value)
+        }
+    }
+
+    /// Replaces an element in the hash.
+    ///
+    /// In a max-heap, the new element should be larger than the old one; in a min-heap it should be smaller.
+    public mutating func replace(index i: Int, value: T) {
+        guard i < elements.count else { return }
+
+        assert(isOrderedBefore(value, elements[i]))
+        set(value, at: i)
+        shiftUp(i)
+    }
+
+    /// Removes the root node from the heap.
+    ///
+    /// For a max-heap, this is the maximum value; for a min-heap it is the minimum value.
+    ///
+    /// - Complexity: O(log n)
+    @discardableResult
+    public mutating func remove() -> T? {
+        if elements.isEmpty {
+            return nil
+        } else if elements.count == 1 {
+            return removeLast()
+        } else {
+            // Use the last node to replace the first one, then fix the heap by
+            // shifting this new first node into its proper position.
+            let value = elements[0]
+            set(removeLast(), at: 0)
+            shiftDown()
+            return value
+        }
+    }
+
+    /// Removes an arbitrary node from the heap.
+    ///
+    /// You need to know the node's index, which may actually take O(n) steps to find.
+    ///
+    /// - Complexity: O(log n).
+    public mutating func removeAt(_ index: Int) -> T? {
+        guard index < elements.count else { return nil }
+
+        let size = elements.count - 1
+        if index != size {
+            swapAt(index, size)
+            shiftDown(index, heapSize: size)
+            shiftUp(index)
+        }
+        return removeLast()
+    }
+
+    /// Removes the last element from the heap.
+    ///
+    /// - Complexity: O(1)
+    public mutating func removeLast() -> T {
+        guard let value = elements.last else {
+            preconditionFailure("Trying to remove element from empty heap")
+        }
+        indices[value] = nil
+        return elements.removeLast()
+    }
+
+    /// Takes a child node and looks at its parents; if a parent is not larger (max-heap) or not smaller (min-heap)
+    /// than the child, we exchange them.
+    mutating func shiftUp(_ index: Int) {
+        var childIndex = index
+        let child = elements[childIndex]
+        var parentIndex = self.parentIndex(ofIndex: childIndex)
+
+        while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+            set(elements[parentIndex], at: childIndex)
+            childIndex = parentIndex
+            parentIndex = self.parentIndex(ofIndex: childIndex)
+        }
+
+        set(child, at: childIndex)
+    }
+
+    mutating func shiftDown() {
+        shiftDown(0, heapSize: elements.count)
+    }
+
+    /// Looks at a parent node and makes sure it is still larger (max-heap) or smaller (min-heap) than its childeren.
+    mutating func shiftDown(_ index: Int, heapSize: Int) {
+        var parentIndex = index
+
+        while true {
+            let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+            let rightChildIndex = leftChildIndex + 1
+
+            // Figure out which comes first if we order them by the sort function:
+            // the parent, the left child, or the right child. If the parent comes
+            // first, we're done. If not, that element is out-of-place and we make
+            // it "float down" the tree until the heap property is restored.
+            var first = parentIndex
+            if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+                first = leftChildIndex
+            }
+            if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+                first = rightChildIndex
+            }
+            if first == parentIndex { return }
+
+            swapAt(parentIndex, first)
+            parentIndex = first
+        }
+    }
+
+    /// Replaces an element in the heap and updates the indices hash.
+    private mutating func set(_ newValue: T, at index: Int) {
+        indices[elements[index]] = nil
+        elements[index] = newValue
+        indices[newValue] = index
+    }
+
+    /// Swap two elements in the heap and update the indices hash.
+    private mutating func swapAt(_ i: Int, _ j: Int) {
+        swap(&elements[i], &elements[j])
+        indices[elements[i]] = i
+        indices[elements[j]] = j
+    }
+
+    /// Returns the index of the parent of the element at index i.
+    ///
+    /// - Note: The element at index 0 is the root of the tree and has no parent.
+    @inline(__always)
+    func parentIndex(ofIndex i: Int) -> Int {
+        return (i - 1) / 2
+    }
+
+    /// Returns the index of the left child of the element at index i.
+    ///
+    /// - Note: this index can be greater than the heap size, in which case there is no left child.
+    @inline(__always)
+    func leftChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 1
+    }
+
+    /// Returns the index of the right child of the element at index i.
+    ///
+    /// - Note: this index can be greater than the heap size, in which case there is no right child.
+    @inline(__always)
+    func rightChildIndex(ofIndex i: Int) -> Int {
+        return 2*i + 2
+    }
+}
diff --git a/Hashed Heap/README.markdown b/Hashed Heap/README.markdown
new file mode 100644
index 000000000..48fe312ab
--- /dev/null
+++ b/Hashed Heap/README.markdown	
@@ -0,0 +1,11 @@
+# Hashed Heap
+
+A hashed heap is a [heap](../Heap/) with a hash map (also known as a dictionary) to speed up lookup of elements by value. This combination doesn't compromize on time performance but requires extra storage for the hash map. This is mainly used for heuristic search algorihms, in particular A*.
+
+## The code
+
+See [HashedHeap.swift](HashedHeap.swift) for the implementation. See [Heap](../Heap/) for a detailed explanation of the basic heap implementation.
+
+## See also
+
+[Heap on Wikipedia](https://en.wikipedia.org/wiki/Heap_%28data_structure%29)
diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..87791f04d
--- /dev/null
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,268 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		7B80C3FC1C77A658003CECC7 /* HashedHeap.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3FB1C77A658003CECC7 /* HashedHeap.swift */; };
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+			isa = PBXGroup;
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+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Hashed Heap Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
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+			isa = PBXGroup;
+			children = (
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+				7B2BBC941C779E7B0067B71D /* Info.plist */,
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+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
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+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
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+				LastUpgradeCheck = 0800;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
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+			compatibilityVersion = "Xcode 3.2";
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+			targets = (
+				7B2BBC7F1C779D720067B71D /* Hashed Heap Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
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+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
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+		7B2BBC7C1C779D720067B71D /* Sources */ = {
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+			buildActionMask = 2147483647;
+			files = (
+				7B80C3FE1C77A65E003CECC7 /* HashedHeapTests.swift in Sources */,
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+			runOnlyForDeploymentPostprocessing = 0;
+		};
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+
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+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
+				CLANG_CXX_LIBRARY = "libc++";
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+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
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+		};
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+				GCC_NO_COMMON_BLOCKS = YES;
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+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				MACOSX_DEPLOYMENT_TARGET = 10.11;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+			};
+			name = Release;
+		};
+		7B2BBC8D1C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		7B2BBC8E1C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				COMBINE_HIDPI_IMAGES = YES;
+				INFOPLIST_FILE = Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
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+			};
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+		};
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+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Hashed Heap Tests" */ = {
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+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
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+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Hashed Heap Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}
diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme
new file mode 100644
index 000000000..406c8dd2e
--- /dev/null
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme	
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0800"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "Hashed Heap Tests.xctest"
+               BlueprintName = "Hashed Heap Tests"
+               ReferencedContainer = "container:Hashed Heap Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
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+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Hashed Heap/Tests/HashedHeapTests.swift b/Hashed Heap/Tests/HashedHeapTests.swift
new file mode 100755
index 000000000..6badb4ec5
--- /dev/null
+++ b/Hashed Heap/Tests/HashedHeapTests.swift	
@@ -0,0 +1,88 @@
+import Foundation
+import XCTest
+
+private struct Message: Hashable {
+    let text: String
+    let priority: Int
+
+    var hashValue: Int {
+        return text.hashValue
+    }
+
+    static func == (lhs: Message, rhs: Message) -> Bool {
+        return lhs.text == rhs.text
+    }
+
+    static func < (m1: Message, m2: Message) -> Bool {
+        return m1.priority < m2.priority
+    }
+}
+
+class HashedHeapTest: XCTestCase {
+    func testEmpty() {
+        var queue = HashedHeap<Message>(sort: <)
+        XCTAssertTrue(queue.isEmpty)
+        XCTAssertEqual(queue.count, 0)
+        XCTAssertNil(queue.peek())
+        XCTAssertNil(queue.remove())
+    }
+
+    func testOneElement() {
+        var queue = HashedHeap<Message>(sort: <)
+
+        queue.insert(Message(text: "hello", priority: 100))
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 1)
+        XCTAssertEqual(queue.peek()!.priority, 100)
+
+        let result = queue.remove()
+        XCTAssertEqual(result!.priority, 100)
+        XCTAssertTrue(queue.isEmpty)
+        XCTAssertEqual(queue.count, 0)
+        XCTAssertNil(queue.peek())
+    }
+
+    func testTwoElementsInOrder() {
+        var queue = HashedHeap<Message>(sort: <)
+
+        queue.insert(Message(text: "hello", priority: 100))
+        queue.insert(Message(text: "world", priority: 200))
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 2)
+        XCTAssertEqual(queue.peek()!.priority, 100)
+
+        let result1 = queue.remove()
+        XCTAssertEqual(result1!.priority, 100)
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 1)
+        XCTAssertEqual(queue.peek()!.priority, 200)
+
+        let result2 = queue.remove()
+        XCTAssertEqual(result2!.priority, 200)
+        XCTAssertTrue(queue.isEmpty)
+        XCTAssertEqual(queue.count, 0)
+        XCTAssertNil(queue.peek())
+    }
+
+    func testTwoElementsOutOfOrder() {
+        var queue = HashedHeap<Message>(sort: <)
+
+        queue.insert(Message(text: "world", priority: 200))
+        queue.insert(Message(text: "hello", priority: 100))
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 2)
+        XCTAssertEqual(queue.peek()!.priority, 100)
+
+        let result1 = queue.remove()
+        XCTAssertEqual(result1!.priority, 100)
+        XCTAssertFalse(queue.isEmpty)
+        XCTAssertEqual(queue.count, 1)
+        XCTAssertEqual(queue.peek()!.priority, 200)
+
+        let result2 = queue.remove()
+        XCTAssertEqual(result2!.priority, 200)
+        XCTAssertTrue(queue.isEmpty)
+        XCTAssertEqual(queue.count, 0)
+        XCTAssertNil(queue.peek())
+    }
+}
diff --git a/Hashed Heap/Tests/Info.plist b/Hashed Heap/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/Hashed Heap/Tests/Info.plist	
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index db4691648..e2afda53b 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1069,6 +1069,29 @@
          location = "group:README.markdown">
       </FileRef>
    </Group>
+   <Group
+      location = "group:Hashed Heap"
+      name = "Hashed Heap">
+      <FileRef
+         location = "group:HashedHeap.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:HashedHeapTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:/Users/al/dev/swift-algorithm-club/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "group:HaversineDistance"
       name = "HaversineDistance">

From e0b58f68943724a52c0bfd843cb8e2f349bb88c0 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 08:08:27 +0100
Subject: [PATCH 127/643] [Swift 4] Singly Linked List with value semantics,
 copy-on-write and collection protocol conformance.

---
 .travis.yml                                   |   1 +
 .../Images/CopiedIndirectStorage.png          | Bin 0 -> 44765 bytes
 .../Images/SharedIndirectStorage.png          | Bin 0 -> 40994 bytes
 Singly Linked List/KeyValuePair.swift         |  77 ++
 Singly Linked List/Queue.swift                |  28 +
 Singly Linked List/README.markdown            | 140 ++++
 .../Contents.swift                            | 744 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Singly Linked List/SinglyLinkedList.swift     | 581 ++++++++++++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 284 +++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/xcschemes/Tests.xcscheme     |  56 ++
 Singly Linked List/Tests/Tests/Info.plist     |  22 +
 .../Tests/Tests/SinglyLinkedListTests.swift   | 329 ++++++++
 .../contents.xcworkspacedata                  |  46 ++
 16 files changed, 2326 insertions(+)
 create mode 100644 Singly Linked List/Images/CopiedIndirectStorage.png
 create mode 100644 Singly Linked List/Images/SharedIndirectStorage.png
 create mode 100644 Singly Linked List/KeyValuePair.swift
 create mode 100644 Singly Linked List/Queue.swift
 create mode 100644 Singly Linked List/README.markdown
 create mode 100644 Singly Linked List/SinglyLinkedList.playground/Contents.swift
 create mode 100644 Singly Linked List/SinglyLinkedList.playground/contents.xcplayground
 create mode 100644 Singly Linked List/SinglyLinkedList.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Singly Linked List/SinglyLinkedList.swift
 create mode 100644 Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Singly Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Singly Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Singly Linked List/Tests/Tests/Info.plist
 create mode 100644 Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift

diff --git a/.travis.yml b/.travis.yml
index 1515be04f..7954c48b1 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -28,6 +28,7 @@ script:
 - xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Singly\ Linked\ List/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Singly Linked List/Images/CopiedIndirectStorage.png b/Singly Linked List/Images/CopiedIndirectStorage.png
new file mode 100644
index 0000000000000000000000000000000000000000..7a2f7e68cb4cbf1f637c79dbd9177b0efb5fa9fa
GIT binary patch
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diff --git a/Singly Linked List/KeyValuePair.swift b/Singly Linked List/KeyValuePair.swift
new file mode 100644
index 000000000..2751503c2
--- /dev/null
+++ b/Singly Linked List/KeyValuePair.swift	
@@ -0,0 +1,77 @@
+/// Conformers of this protocol represent a pair of comparable values
+/// This can be useful in many data structures and algorithms where items
+/// stored contain a value, but are ordered or retrieved according to a key.
+public protocol KeyValuePair : Comparable {
+    
+    associatedtype K : Comparable, Hashable
+    associatedtype V : Comparable, Hashable
+    
+    // Identifier used in many algorithms to search by, order by, etc
+    var key : K {get set}
+    
+    // A data container
+    var value : V {get set}
+    
+    
+    /// Initializer
+    ///
+    /// - Parameters:
+    ///   - key: Identifier used in many algorithms to search by, order by, etc.
+    ///   - value: A data container.
+    init(key: K, value: V)
+    
+    
+    /// Creates a copy
+    ///
+    /// - Abstract: Conformers of this class can be either value or reference types.
+    ///   Some algorithms might need to guarantee that a conformer instance gets copied.
+    ///   This will perform an innecessary in the case of value types.
+    ///   TODO: is there a better way?
+    /// - Returns: A new instance with the old one's values copied.
+    func copy() -> Self
+}
+
+
+/// Conformance to Equatable and Comparable protocols
+extension KeyValuePair {
+    
+    // MARK: - Equatable protocol
+    public static func ==(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key == rhs.key
+    }
+    
+    
+    
+    // MARK: - Comparable protocol
+    
+    public static func <(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key < rhs.key
+    }
+    
+    public static func <=(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key <= rhs.key
+    }
+    
+    public static func >=(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key >= rhs.key
+    }
+    
+    public static func >(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key > rhs.key
+    }
+}
+
+
+
+/// Concrete impletation of a KeyValuePair where  both the key and the value
+/// are Integers.
+struct IntegerPair : KeyValuePair {
+    
+    // MARK - KeyValuePair protocol
+    var key : Int
+    var value : Int
+    
+    func copy() -> IntegerPair {
+        return IntegerPair(key: self.key, value: self.value)
+    }
+}
diff --git a/Singly Linked List/Queue.swift b/Singly Linked List/Queue.swift
new file mode 100644
index 000000000..68fda9f99
--- /dev/null
+++ b/Singly Linked List/Queue.swift	
@@ -0,0 +1,28 @@
+import Foundation
+
+
+/// Data structure that provides FIFO access
+protocol Queue
+{
+    associatedtype Item
+    
+    
+    /// Adds an element to the queue
+    ///
+    /// - Parameter item: Item to be added
+    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
+    mutating func enqueue(item: Item) throws
+    
+    
+    /// Returns the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue. It does not dequeue it.
+    func getFirst() -> Item?
+    
+    
+    /// Dequeues the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue, which gets removed from it.
+    mutating func dequeue() -> Item?
+    
+}
diff --git a/Singly Linked List/README.markdown b/Singly Linked List/README.markdown
new file mode 100644
index 000000000..b3c8b8b2d
--- /dev/null
+++ b/Singly Linked List/README.markdown	
@@ -0,0 +1,140 @@
+# Singly-Linked List
+
+#### How is this different to the Linked List implementation?
+The existing Linked list implementation represents the same concept. However, the existing implementation has reference semantics and does not conform to the Collection protocol implemented in the Swift's standard Library. What SinglyLinkedList aims to contribute is a more idiomatic Swift implementation, that uses value semantics and copy-on-write as well as conforms to the collection protocol.
+
+#### Conceptual representation
+A Singly linked list is a non-contiguous sequence of data items in memory. Each element links to the next via a memory reference. Additionally, this implementation keeps track of the last element, which can be retrived in order O(1). However, the list can only be traversed from head to tail.
+
+    +--------+    +--------+    +--------+    +--------+
+    |        |    |        |    |        |    |        |
+    | node 0 |--->| node 1 |--->| node 2 |--->| node 3 |---> nil
+    |        |    |        |    |        |    |        |
+    +--------+    +--------+    +--------+    +--------+
+    ^                                         ^
+    |                                         |
+    Head                                      Tail
+
+Each element in the list is represented with an instance of SinglyLinkedListNode class, which basically contains some data and a reference of optional type to the next node, which means that the last node's next reference is `nil`.
+
+#### In-memory representation
+In Swift, data types can have value or reference semantics. This implementation of a singly-linked list uses value semantics. Support for copy-on-write has been added in order to improve performance and delay copying the elements of the array until strictly necessary.
+
+The image below shows how initially, after variable `l2` is assigned `l1`, a new instance of the struct SinglyLinkedList is created. Nevertheless, the indirect storage is still shared as indicated by the references that both l1 and l2 have pointing to a common area in memory.
+
+![alt text](Images/SharedIndirectStorage.png "Two linked lists sharing the indirect storage")
+
+Once a mutating operation happens --for example on `l2` to append a new element--, then the indirect storage and all nodes in the list is actually copied and the references from `l1` and `l2` are updated. This is ilustrated in the following figure.
+
+![alt text](Images/CopiedIndirectStorage.png "A copy is created after editing one of the lists")
+
+#### Implementation details
+1. Direct access to the tail in O(1) by keeping a reference that gets updated only when an operation to the list modifies the tail.
+2. Value semantics. This implementation of a singly-linked list uses a struct. When the list struct is assigned into another variable or passed as an argument to a function, a copy of the struct is made.
+3. Copy-on write. Instances of SinglyLinkedList have an internal reference to an indirect storage allocated in the heap. When a copy of the list is made (according to its value semantics) the indirect storage is initialy shared between the copies. This means that a potentially large list can be accessed to read values in it without an expensive copy having to take place. However, as soon as there is a write access to the indirect storage when there are more than one instances referencing to it, a copy will be performed to guarantee value semantics.
+4. Conformance to the Collection protocol.
+
+
+
+
+
+## Performance of linked lists
+
+EDITION
+- *append*: Appends a new node to the end of the list. This method will modify the list's tail. If the list is empty, it will also modify the head. This operation's time complexity is *O(1)* since there's a reference to the tail node in this implementation.
+- *prepend*: Inserts a new node at the start of the list. If the list is empty, it will also modify the head. This operation's time complexity is *O(1)* since there's a reference to the head node.
+- *delete*: Finds a node in the list and deletes it. This operation's time complexity has an upper bound described by a linear function; O(n).
+
+SEARCH
+- find k-th to last element. Given a list with `n` number of elements and `k` being the passed parameter with `0` <= `k` <= `n`, this method has *O(k)*.
+
+## Conforming to the Collection protocol
+Collections are sequences, therefore the first step is to conform to the Sequence protocol.
+
+```
+extension SinglyLinkedList : Sequence
+{
+    public func makeIterator() -> SinglyLinkedListForwardIterator<T>
+    {
+        return SinglyLinkedListForwardIterator(head: self.storage.head)
+    }
+}
+```
+
+We have used `SinglyLinkedListForwardIterator` an iterator class to keep track of the progress while iterating the structure:
+
+```
+public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
+
+    public typealias Element = T
+
+    private(set) var head: SinglyLinkedListNode<T>?
+
+    mutating public func next() -> T?
+    {
+        let result = self.head?.value
+        self.head = self.head?.next
+        return result
+    }
+}
+```
+
+Next, a collection needs to be indexable. Indexes are implemented by the data structure class. We have encapsulated this knowledge in instances of the class `SinglyLinkedListIndex`. 
+
+```
+public struct SinglyLinkedListIndex<T> : Comparable
+{
+    fileprivate let node: SinglyLinkedListNode<T>?
+    fileprivate let tag: Int
+
+    public static func==<T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag == rhs.tag)
+    }
+
+    public static func< <T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag < rhs.tag)
+    }
+}
+```
+
+Finally, the methods in the collection to manipulate indexes are implemented below:
+- startIndex: Index of the first element. Can be calculated with O(1).
+- endIndex: Index that follows the last valid index in the collection. That is, the index that follows the tail's index. Can be calculated with O(1) if the count of elements is kept internally. However, the implementation below is O(n) with `n` being the number of elements in the list. 
+
+```
+extension SinglyLinkedList : Collection {
+
+    public typealias Index = SinglyLinkedListIndex<T>
+
+    public var startIndex: Index {
+        get {
+            return SinglyLinkedListIndex<T>(node: self.storage.head, tag: 0)
+        }
+    }
+
+public var endIndex: Index {
+    get {
+        if let h = self.storage.head {
+        let (_, numberOfElements) = findTail(in: h)
+            return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
+        } else {
+            return SinglyLinkedListIndex<T>(node: nil, tag: self.startIndex.tag)
+        }
+    }
+}
+
+public subscript(position: Index) -> T {
+    get {
+        return position.node!.value
+    }
+}
+
+public func index(after idx: Index) -> Index {
+    return SinglyLinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+    }
+}
+```
+
+Conforming to the Collection protocol allows our class SinglyLinkedList to take adventage of all the collection methods included in the Stardard Library.
+
+*Written by Borja Arias Drake*
diff --git a/Singly Linked List/SinglyLinkedList.playground/Contents.swift b/Singly Linked List/SinglyLinkedList.playground/Contents.swift
new file mode 100644
index 000000000..fc6acf9dc
--- /dev/null
+++ b/Singly Linked List/SinglyLinkedList.playground/Contents.swift	
@@ -0,0 +1,744 @@
+//: # Linked Lists
+
+// For best results, don't forget to select "Show Rendered Markup" from XCode's "Editor" menu
+
+//: Linked List Class Declaration:
+// last checked with Xcode 9M136h
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+//: We will start by defining a protocol that elements inserted into this implementation of a List will conform to. This is useful, because many algorithms are only interested in a key that all elements have.
+
+/// Conformers of this protocol represent a pair of comparable values
+/// This can be useful in many data structures and algorithms where items
+/// stored contain a value, but are ordered or retrieved according to a key.
+public protocol KeyValuePair : Comparable {
+    
+    associatedtype K : Comparable, Hashable
+    associatedtype V : Comparable, Hashable
+    
+    // Identifier used in many algorithms to search by, order by, etc
+    var key : K {get set}
+    
+    // A data container
+    var value : V {get set}
+    
+    
+    /// Initializer
+    ///
+    /// - Parameters:
+    ///   - key: Identifier used in many algorithms to search by, order by, etc.
+    ///   - value: A data container.
+    init(key: K, value: V)
+    
+    
+    /// Creates a copy
+    ///
+    /// - Abstract: Conformers of this class can be either value or reference types.
+    ///   Some algorithms might need to guarantee that a conformer instance gets copied.
+    ///   This will perform an innecessary in the case of value types.
+    ///   TODO: is there a better way?
+    /// - Returns: A new instance with the old one's values copied.
+    func copy() -> Self
+}
+
+
+/// Conformance to Equatable and Comparable protocols
+extension KeyValuePair {
+    
+    // MARK: - Equatable protocol
+    public static func ==(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key == rhs.key
+    }
+    
+    
+    
+    // MARK: - Comparable protocol
+    
+    public static func <(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key < rhs.key
+    }
+    
+    public static func <=(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key <= rhs.key
+    }
+    
+    public static func >=(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key >= rhs.key
+    }
+    
+    public static func >(lhs: Self, rhs: Self) -> Bool {
+        return lhs.key > rhs.key
+    }
+}
+
+//: Concrete impletation of a KeyValuePair where  both the key and the value that we'll use in the examples in this playground
+
+struct IntegerPair : KeyValuePair {
+    
+    // MARK - KeyValuePair protocol
+    var key : Int
+    var value : Int
+    
+    func copy() -> IntegerPair {
+        return IntegerPair(key: self.key, value: self.value)
+    }
+}
+
+//: Lists are usually used as queues. As an example, we'll define these expectations in a protocol and we'll make the the SinglyLinkedList class conform to it.
+
+/// Data structure that provides FIFO access
+protocol Queue
+{
+    associatedtype Item
+    
+    
+    /// Adds an element to the queue
+    ///
+    /// - Parameter item: Item to be added
+    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
+    mutating func enqueue(item: Item) throws
+    
+    
+    /// Returns the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue. It does not dequeue it.
+    func getFirst() -> Item?
+    
+    
+    /// Dequeues the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue, which gets removed from it.
+    mutating func dequeue() -> Item?
+}
+
+
+//: Next, we are going to implement a list that has value semantics. Value semantics imply that the values will be copied when assigned and passed as a parameter to functions and methods. In order to prevent unnecesasry copies, Swift uses a technique called copy-on-write; copies are only performed when a mutating operation is performed on an instance that is referenced by more than one objects. In Swift, this is ahieved with an additional level of indirection, an internal class instance, therefore with reference semantics, that will be shared, until a mutating operation occurs.
+
+
+/// Helper class to implement copy-on-write
+fileprivate class IndirectStorage<T> {
+    
+    var head: SinglyLinkedListNode<T>?
+    
+    var tail: SinglyLinkedListNode<T>?
+    
+    init(head: SinglyLinkedListNode<T>?, tail: SinglyLinkedListNode<T>?) {
+        self.head = head
+        self.tail = tail
+    }
+    
+    convenience init() {
+        self.init(head: nil, tail: nil)
+    }
+}
+
+
+//: Node of the list
+
+
+// MARK: - NODE -
+
+/// A node is the building block of a linked list.
+/// It can be used on its own to create linked lists. However users of this class,
+/// will need to manipulate references directly.
+public class SinglyLinkedListNode<T> {
+    
+    /// Data container
+    public var value: T
+    
+    /// Link to the next node
+    public var next: SinglyLinkedListNode<T>?
+    
+    /// Designated initializer
+    ///
+    /// - Parameter value: A value
+    public init(value: T) {
+        self.value = value
+    }
+}
+
+//: The list with value semantics
+
+// MARK: - LINKED LIST -
+
+/// Data structure to hold a collection of items.
+/// Each nodes contains a reference to the next node.
+/// The last node does not reference any other node.
+/// This class implements value semantics based on copy-on-write.
+///
+/// However, the elements contained in the list, will be shallow copied if they
+/// implement reference semantics.
+public struct SinglyLinkedList<T>
+{
+    // MARK: PROPERTIES
+    
+    // A level of inderiction, with reference semantics to allow easy
+    // detection of when there are more than one references of the storage.
+    private var storage: IndirectStorage<T>
+    
+    /// Whenever there's a change that potentially can change the value, this reference to the
+    /// storage should be used to guarantee that a new copy is created and written on.
+    private var storageForWritting: IndirectStorage<T> {
+        
+        mutating get {
+            if !isKnownUniquelyReferenced(&self.storage) {
+                self.storage = self.copyStorage()
+            }
+            return self.storage
+        }
+    }
+    
+    /// Returns the last element in the collection
+    public var last: T? {
+        get {
+            return self.storage.tail?.value
+        }
+    }
+    
+    
+    
+    // MARK: INITIALIZERS
+    
+    /// Creates a list with the given node.
+    /// NOTE: This method can break value semantics by accepting a node.
+    ///
+    /// - Parameter head: First node
+    internal init(head: SinglyLinkedListNode<T>)
+    {
+        self.storage = IndirectStorage()
+        self.append(node: head)
+    }
+    
+    
+    /// Creates a list with a single element
+    ///
+    /// - Parameter value: element to populate the list with
+    public init(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.init(head: node)
+    }
+    
+    
+    /// Creates an empty list
+    public init()
+    {
+        self.storage = IndirectStorage()
+    }
+    
+    
+    // MARK: EDITION
+    
+    /// Convenience method to append a value directly to the list
+    ///
+    /// - Parameter value: value to be added
+    public mutating func append(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.append(node: node)
+    }
+    
+    
+    /// Convenience method to prepend a value directly to the list
+    ///
+    /// - Parameter value: value to be added as the new head of the list
+    public mutating func prepend(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.prepend(node: node)
+    }
+    
+    
+    public mutating func deleteItem(at index:Int) -> T
+    {
+        precondition((index >= 0) && (index < self.count))
+        
+        var previous: SinglyLinkedListNode<T>? = nil
+        var current = self.storageForWritting.head
+        var i = 0
+        var elementToDelete: SinglyLinkedListNode<T>
+        
+        while (i < index) {
+            previous = current
+            current = current?.next
+            i += 1
+        }
+        
+        // Current is now the element to delete (at index position.tag)
+        elementToDelete = current!
+        if (self.storage.head === current) {
+            self.storageForWritting.head = current?.next
+        }
+        
+        if (self.storage.tail === current) {
+            self.storageForWritting.tail = previous
+        }
+        
+        previous?.next = current?.next
+        
+        return elementToDelete.value
+    }
+    
+    
+    
+    // MARK: SEARCH
+    
+    /// Returns the node located at the k-th to last position
+    ///
+    /// - Parameter kthToLast: 1 <= k <= N
+    private func find(kthToLast: UInt, startingAt node: SinglyLinkedListNode<T>?, count: UInt) -> SinglyLinkedListNode<T>?
+    {
+        guard kthToLast <= count else {
+            return nil
+        }
+        
+        guard (node != nil) else {
+            return nil
+        }
+        
+        let i = (count - kthToLast)
+        
+        if (i == 0) {
+            return node
+        }
+        
+        return find(kthToLast: kthToLast, startingAt: node?.next, count: (count - 1))
+    }
+    
+    
+    /// Returns the kth-to-last element in the list
+    ///
+    /// - Parameter kthToLast: Reversed ordinal number of the node to fetch.
+    public func find(kthToLast: UInt) -> SinglyLinkedListNode<T>?
+    {
+        return self.find(kthToLast: kthToLast, startingAt: self.storage.head, count: UInt(self.count))
+    }
+    
+    
+    
+    // MARK: LOOP DETECTION
+    
+    /// A singly linked list contains a loop if one node references back to a previous node.
+    ///
+    /// - Returns: Whether the linked list contains a loop
+    public func containsLoop() -> Bool
+    {
+        /// Advances a node at a time
+        var current = self.storage.head
+        
+        /// Advances twice as fast
+        var runner = self.storage.head
+        
+        while (runner != nil) && (runner?.next != nil) {
+            
+            current = current?.next
+            runner = runner?.next?.next
+            
+            if runner === current {
+                return true
+            }
+        }
+        
+        return false
+    }
+    
+}
+
+
+
+// MARK:- Private Methods
+
+private extension SinglyLinkedList {
+    
+    /// Adds a new node to the current head. This method can easily break value semantics. It is left
+    /// for internal use.
+    ///
+    /// - Parameter node: the node that will be the new head of the list.
+    private mutating func prepend(node: SinglyLinkedListNode<T>)
+    {
+        let (tailFromNewNode, _) = findTail(in: node)
+        tailFromNewNode.next = self.storageForWritting.head
+        self.storageForWritting.head = node
+        
+        if self.storage.tail == nil {
+            self.storageForWritting.tail = tailFromNewNode
+        }
+    }
+    
+    /// Appends a new node to the list. This method can easily break value semantics. It is left
+    /// for internal use.
+    /// - Discussion: If the node to be inserted contains a loop, the node is appended but tail is set to nil.
+    ///   This is a private method, therefore this can only happen directly under the control of this class.
+    /// - Parameter node: node to be appended. (It can be a list, even contain loops).
+    private mutating func append(node: SinglyLinkedListNode<T>)
+    {
+        if self.storage.tail != nil
+        {
+            // Copy on write: we are about to modify next a property in
+            // a potentially shared node. Make sure it's new if necessary.
+            self.storageForWritting.tail?.next = node
+            if !self.containsLoop() {
+                let (tail, _) = findTail(in: node)
+                self.storageForWritting.tail = tail // There
+            } else {
+                self.storageForWritting.tail = nil
+            }
+        }
+        else
+        {
+            // This also means that there's no head.
+            // Otherwise the state would be inconsistent.
+            // This will be checked when adding and deleting nodes.
+            self.storageForWritting.head = node
+            if !self.containsLoop() {
+                let (tail, _) = findTail(in: node)
+                self.storageForWritting.tail = tail // There
+            } else {
+                self.storageForWritting.tail = nil
+            }
+        }
+    }
+    
+    /// Creates a copy of the linked list in a diffent memory location.
+    ///
+    /// - Returns: The copy to a new storage or a reference to the old one if no copy was necessary.
+    private func copyStorage() -> IndirectStorage<T> {
+        // If the list is empty, next time an item will be created, it won't affect
+        // other instances of the list that came from copies derived from value types.
+        // like assignments or parameters
+        guard (self.storage.head != nil) && (self.storage.tail != nil) else {
+            return IndirectStorage(head: nil, tail: nil)
+        }
+        
+        // Create a new position in memory.
+        // Note that we are shallow copying the value. If it was reference type
+        // we just make a copy of the reference.
+        let copiedHead = SinglyLinkedListNode<T>(value: self.storage.head!.value)
+        var previousCopied: SinglyLinkedListNode<T> = copiedHead
+        
+        // Iterate through current list of nodes and copy them.
+        var current: SinglyLinkedListNode<T>? = self.storage.head?.next
+        
+        while (current != nil) {
+            // Create a copy
+            let currentCopy = SinglyLinkedListNode<T>(value: current!.value)
+            
+            // Create links
+            previousCopied.next = currentCopy
+            
+            // Update pointers
+            current = current?.next
+            previousCopied = currentCopy
+        }
+        
+        return IndirectStorage(head: copiedHead, tail: previousCopied)
+    }
+}
+
+
+
+// MARK:- Extensions when comparable
+
+extension SinglyLinkedList where T: Comparable
+{
+    /// Deletes node containing a given value
+    ///
+    /// - Parameter v: value of the node to be deleted.
+    public mutating func deleteNode(withValue v: T) {
+        
+        guard self.storage.head != nil else {
+            return
+        }
+        
+        var previous: SinglyLinkedListNode<T>? = nil
+        var current = self.storage.head
+        
+        while (current != nil) && (current?.value != v) {
+            previous = current
+            current = current?.next
+        }
+        
+        if let foundNode = current {
+            
+            if (self.storage.head === foundNode) {
+                self.storageForWritting.head = foundNode.next
+            }
+            
+            if (self.storage.tail === foundNode) {
+                self.storage.tail = previous
+            }
+            
+            previous?.next = foundNode.next
+            foundNode.next = nil
+        }
+    }
+    
+    
+    /// Deletes duplicates without using additional structures like a set to keep track the visited nodes.
+    /// - Complexity: O(N^2)
+    public mutating func deleteDuplicatesInPlace()
+    {
+        // Copy on write: this updates self.storage if necessary.
+        var current = self.storageForWritting.head
+        
+        while (current != nil)
+        {
+            var previous: SinglyLinkedListNode<T>? = current
+            var next = current?.next
+            
+            while (next != nil)
+            {
+                if (current?.value == next?.value) {
+                    
+                    if (self.storage.head === next) {
+                        self.storage.head = next?.next
+                    }
+                    
+                    if (self.storage.tail === next) {
+                        self.storage.tail = previous
+                    }
+                    
+                    // Delete next
+                    previous?.next = next?.next
+                }
+                previous = next
+                next = next?.next
+            }
+            current = current?.next
+        }
+    }
+}
+
+
+
+// MARK: - ITERATOR -
+
+public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
+    
+    public typealias Element = T
+    
+    private(set) var head: SinglyLinkedListNode<T>?
+    
+    mutating public func next() -> T?
+    {
+        let result = self.head?.value
+        self.head = self.head?.next
+        return result
+    }
+}
+
+
+
+// MARK: - SEQUENCE -
+
+extension SinglyLinkedList : Sequence
+{
+    public func makeIterator() -> SinglyLinkedListForwardIterator<T>
+    {
+        return SinglyLinkedListForwardIterator(head: self.storage.head)
+    }
+}
+
+
+
+// MARK: - COLLECTION -
+
+extension SinglyLinkedList : Collection {
+    
+    public typealias Index = SinglyLinkedListIndex<T>
+    
+    public var startIndex: Index {
+        get {
+            return SinglyLinkedListIndex<T>(node: self.storage.head, tag: 0)
+        }
+    }
+    
+    public var endIndex: Index {
+        get {
+            if let h = self.storage.head {
+                let (_, numberOfElements) = findTail(in: h)
+                return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
+            } else {
+                return SinglyLinkedListIndex<T>(node: nil, tag: self.startIndex.tag)
+            }
+        }
+    }
+    
+    public subscript(position: Index) -> T {
+        get {
+            return position.node!.value
+        }
+    }
+    
+    public func index(after idx: Index) -> Index {
+        return SinglyLinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+    }
+}
+
+
+
+// MARK: - QUEUE -
+
+extension SinglyLinkedList : Queue
+{
+    typealias Item = T
+    
+    /// Returns the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue. It does not dequeue it.
+    func getFirst() -> T? {
+        return self.storage.head?.value
+    }
+    
+    /// Adds an element to the queue
+    ///
+    /// - Parameter item: Item to be added
+    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
+    mutating func enqueue(item: T) throws {
+        self.append(node: SinglyLinkedListNode<T>(value: item))
+    }
+    
+    /// Dequeues the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue, which gets removed from it.
+    mutating func dequeue() -> T?
+    {
+        guard self.count > 0 else {
+            return nil
+        }
+        
+        return self.deleteItem(at: 0)
+    }
+}
+
+
+
+// MARK: - EXPRESSIBLE-BY-ARRAY-LITERAL -
+
+extension SinglyLinkedList : ExpressibleByArrayLiteral
+{
+    public typealias Element = T
+    
+    public init(arrayLiteral elements: Element...)
+    {
+        var headSet = false
+        var current : SinglyLinkedListNode<T>?
+        var numberOfElements = 0
+        self.storage = IndirectStorage()
+        
+        for element in elements {
+            
+            numberOfElements += 1
+            
+            if headSet == false {
+                self.storage.head = SinglyLinkedListNode<T>(value: element)
+                current = self.storage.head
+                headSet = true
+            } else {
+                let newNode = SinglyLinkedListNode<T>(value: element)
+                current?.next = newNode
+                current = newNode
+            }
+        }
+        self.storage.tail = current
+    }
+}
+
+
+
+// MARK: - FORWARD-INDEX -
+
+public struct SinglyLinkedListIndex<T> : Comparable
+{
+    fileprivate let node: SinglyLinkedListNode<T>?
+    fileprivate let tag: Int
+    
+    public static func==<T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag == rhs.tag)
+    }
+    
+    public static func< <T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag < rhs.tag)
+    }
+}
+
+
+extension SinglyLinkedList where T : KeyValuePair {
+    
+    public func find(elementWithKey key: T.K) -> T? {
+        let searchResults = self.filter { (keyValuePair) -> Bool in
+            return keyValuePair.key == key
+        }
+        
+        return searchResults.first
+    }
+}
+
+// MARK: - HELPERS -
+
+func findTail<T>(in node: SinglyLinkedListNode<T>) -> (tail: SinglyLinkedListNode<T>, count: Int)
+{
+    // Assign the tail
+    // Note that the passed node can already be linking to other nodes,
+    // so the tail needs to be calculated.
+    var current: SinglyLinkedListNode<T>? = node
+    var count = 1
+    
+    while (current?.next != nil) {
+        current = current?.next
+        count += 1
+    }
+    
+    if current != nil {
+        return (tail: current!, count: count)
+    } else {
+        return (tail: node, count: 1)
+    }
+}
+
+
+
+//: EXAMPLES
+//: Let's create a list
+
+var l1: SinglyLinkedList<Int> = [1,2,3,4,5,6,7]
+
+//: Because it has value semantics, if we assign it, a new value will be created. However, internally the storage is shared.
+
+var l2 = l1
+
+//: If we modify l2, l1 will remain unaffected.
+l2.append(value: 67)
+
+assert(l1.count == 7)
+assert(l1.contains(67) == false)
+
+//: However, as expected, l2 has changed
+assert(l2.count == 8)
+assert(l2.contains(67) == true)
+
+
+//: Notice that becuase our implementation conforms to the Collection protocol, we can use a lot of methods already implemented for us in Swift's standard library, for example, contains, dropLast, etc.
+
+let l3 = l2.dropLast()
+assert(l3.count == 7)
+assert(l3.contains(67) == false)
+
+//: We can use this class as a queue.
+
+func empty<Q: Queue>(queue: inout Q) {
+    while let _ = queue.dequeue() {}
+}
+
+var q: SinglyLinkedList<Int> = [5,1,2,3]
+empty(queue: &q)
+assert(q.count == 0)
+
+try? q.enqueue(item: 1)
+try? q.enqueue(item: 3)
+try? q.enqueue(item: 5)
+assert(q.count == 3)
+
+
diff --git a/Singly Linked List/SinglyLinkedList.playground/contents.xcplayground b/Singly Linked List/SinglyLinkedList.playground/contents.xcplayground
new file mode 100644
index 000000000..fd676d5b4
--- /dev/null
+++ b/Singly Linked List/SinglyLinkedList.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx' display-mode='raw'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Singly Linked List/SinglyLinkedList.playground/playground.xcworkspace/contents.xcworkspacedata b/Singly Linked List/SinglyLinkedList.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Singly Linked List/SinglyLinkedList.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
new file mode 100644
index 000000000..b05526b35
--- /dev/null
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -0,0 +1,581 @@
+import Foundation
+
+
+/// Helper class to implement copy-on-write
+fileprivate class IndirectStorage<T> {
+    
+    var head: SinglyLinkedListNode<T>?
+    
+    var tail: SinglyLinkedListNode<T>?
+    
+    init(head: SinglyLinkedListNode<T>?, tail: SinglyLinkedListNode<T>?) {
+        self.head = head
+        self.tail = tail
+    }
+    
+    convenience init() {
+        self.init(head: nil, tail: nil)
+    }
+}
+
+
+
+// MARK: - NODE -
+
+/// A node is the building block of a linked list.
+/// It can be used on its own to create linked lists. However users of this class,
+/// will need to manipulate references directly.
+public class SinglyLinkedListNode<T> {
+    
+    /// Data container
+    public var value: T
+    
+    /// Link to the next node
+    public var next: SinglyLinkedListNode<T>?
+    
+    /// Designated initializer
+    ///
+    /// - Parameter value: A value
+    public init(value: T) {
+        self.value = value
+    }
+}
+
+
+
+// MARK: - LINKED LIST -
+
+/// Data structure to hold a collection of items.
+/// Each nodes contains a reference to the next node.
+/// The last node does not reference any other node.
+/// This class implements value semantics based on copy-on-write.
+///
+/// However, the elements contained in the list, will be shallow copied if they
+/// implement reference semantics.
+public struct SinglyLinkedList<T>
+{
+    // MARK: PROPERTIES
+    
+    // A level of inderiction, with reference semantics to allow easy
+    // detection of when there are more than one references of the storage.
+    private var storage: IndirectStorage<T>
+    
+    /// Whenever there's a change that potentially can change the value, this reference to the
+    /// storage should be used to guarantee that a new copy is created and written on.
+    private var storageForWritting: IndirectStorage<T> {
+        
+        mutating get {
+            if !isKnownUniquelyReferenced(&self.storage) {
+                self.storage = self.copyStorage()
+            }
+            return self.storage
+        }
+    }
+    
+    /// Returns the last element in the collection
+    public var last: T? {
+        get {
+            return self.storage.tail?.value
+        }
+    }
+    
+    
+    
+    // MARK: INITIALIZERS
+    
+    /// Creates a list with the given node.
+    /// NOTE: This method can break value semantics by accepting a node.
+    ///
+    /// - Parameter head: First node
+    internal init(head: SinglyLinkedListNode<T>)
+    {
+        self.storage = IndirectStorage()
+        self.append(node: head)
+    }
+    
+    
+    /// Creates a list with a single element
+    ///
+    /// - Parameter value: element to populate the list with
+    public init(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.init(head: node)
+    }
+    
+    
+    /// Creates an empty list
+    public init()
+    {
+        self.storage = IndirectStorage()
+    }
+    
+    
+    // MARK: EDITION
+    
+    /// Convenience method to append a value directly to the list
+    ///
+    /// - Parameter value: value to be added
+    public mutating func append(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.append(node: node)
+    }
+    
+    
+    /// Convenience method to prepend a value directly to the list
+    ///
+    /// - Parameter value: value to be added as the new head of the list
+    public mutating func prepend(value: T)
+    {
+        let node = SinglyLinkedListNode<T>(value: value)
+        self.prepend(node: node)
+    }
+    
+    
+    public mutating func deleteItem(at index:Int) -> T
+    {
+        precondition((index >= 0) && (index < self.count))
+        
+        var previous: SinglyLinkedListNode<T>? = nil
+        var current = self.storageForWritting.head
+        var i = 0
+        var elementToDelete: SinglyLinkedListNode<T>
+        
+        while (i < index) {
+            previous = current
+            current = current?.next
+            i += 1
+        }
+        
+        // Current is now the element to delete (at index position.tag)
+        elementToDelete = current!
+        if (self.storage.head === current) {
+            self.storageForWritting.head = current?.next
+        }
+        
+        if (self.storage.tail === current) {
+            self.storageForWritting.tail = previous
+        }
+        
+        previous?.next = current?.next
+        
+        return elementToDelete.value
+    }
+    
+    
+    
+    // MARK: SEARCH
+    
+    /// Returns the node located at the k-th to last position
+    ///
+    /// - Parameter kthToLast: 1 <= k <= N
+    private func find(kthToLast: UInt, startingAt node: SinglyLinkedListNode<T>?, count: UInt) -> SinglyLinkedListNode<T>?
+    {
+        guard kthToLast <= count else {
+            return nil
+        }
+        
+        guard (node != nil) else {
+            return nil
+        }
+        
+        let i = (count - kthToLast)
+        
+        if (i == 0) {
+            return node
+        }
+        
+        return find(kthToLast: kthToLast, startingAt: node?.next, count: (count - 1))
+    }
+    
+    
+    /// Returns the kth-to-last element in the list
+    ///
+    /// - Parameter kthToLast: Reversed ordinal number of the node to fetch.
+    public func find(kthToLast: UInt) -> SinglyLinkedListNode<T>?
+    {
+        return self.find(kthToLast: kthToLast, startingAt: self.storage.head, count: UInt(self.count))
+    }
+    
+    
+    
+    // MARK: LOOP DETECTION
+    
+    /// A singly linked list contains a loop if one node references back to a previous node.
+    ///
+    /// - Returns: Whether the linked list contains a loop
+    public func containsLoop() -> Bool
+    {
+        /// Advances a node at a time
+        var current = self.storage.head
+        
+        /// Advances twice as fast
+        var runner = self.storage.head
+        
+        while (runner != nil) && (runner?.next != nil) {
+            
+            current = current?.next
+            runner = runner?.next?.next
+            
+            if runner === current {
+                return true
+            }
+        }
+        
+        return false
+    }
+    
+}
+
+
+
+// MARK:- Private Methods
+
+private extension SinglyLinkedList {
+    
+    /// Adds a new node to the current head. This method can easily break value semantics. It is left
+    /// for internal use.
+    ///
+    /// - Parameter node: the node that will be the new head of the list.
+    private mutating func prepend(node: SinglyLinkedListNode<T>)
+    {
+        let (tailFromNewNode, _) = findTail(in: node)
+        tailFromNewNode.next = self.storageForWritting.head
+        self.storageForWritting.head = node
+        
+        if self.storage.tail == nil {
+            self.storageForWritting.tail = tailFromNewNode
+        }
+    }
+    
+    /// Appends a new node to the list. This method can easily break value semantics. It is left
+    /// for internal use.
+    /// - Discussion: If the node to be inserted contains a loop, the node is appended but tail is set to nil.
+    ///   This is a private method, therefore this can only happen directly under the control of this class.
+    /// - Parameter node: node to be appended. (It can be a list, even contain loops).
+    private mutating func append(node: SinglyLinkedListNode<T>)
+    {
+        if self.storage.tail != nil
+        {
+            // Copy on write: we are about to modify next a property in
+            // a potentially shared node. Make sure it's new if necessary.
+            self.storageForWritting.tail?.next = node
+            if !self.containsLoop() {
+                let (tail, _) = findTail(in: node)
+                self.storageForWritting.tail = tail // There
+            } else {
+                self.storageForWritting.tail = nil
+            }
+        }
+        else
+        {
+            // This also means that there's no head.
+            // Otherwise the state would be inconsistent.
+            // This will be checked when adding and deleting nodes.
+            self.storageForWritting.head = node
+            if !self.containsLoop() {
+                let (tail, _) = findTail(in: node)
+                self.storageForWritting.tail = tail // There
+            } else {
+                self.storageForWritting.tail = nil
+            }
+        }
+    }
+    
+    /// Creates a copy of the linked list in a diffent memory location.
+    ///
+    /// - Returns: The copy to a new storage or a reference to the old one if no copy was necessary.
+    private func copyStorage() -> IndirectStorage<T> {
+        // If the list is empty, next time an item will be created, it won't affect
+        // other instances of the list that came from copies derived from value types.
+        // like assignments or parameters
+        guard (self.storage.head != nil) && (self.storage.tail != nil) else {
+            return IndirectStorage(head: nil, tail: nil)
+        }
+        
+        // Create a new position in memory.
+        // Note that we are shallow copying the value. If it was reference type
+        // we just make a copy of the reference.
+        let copiedHead = SinglyLinkedListNode<T>(value: self.storage.head!.value)
+        var previousCopied: SinglyLinkedListNode<T> = copiedHead
+        
+        // Iterate through current list of nodes and copy them.
+        var current: SinglyLinkedListNode<T>? = self.storage.head?.next
+        
+        while (current != nil) {
+            // Create a copy
+            let currentCopy = SinglyLinkedListNode<T>(value: current!.value)
+            
+            // Create links
+            previousCopied.next = currentCopy
+            
+            // Update pointers
+            current = current?.next
+            previousCopied = currentCopy
+        }
+        
+        return IndirectStorage(head: copiedHead, tail: previousCopied)
+    }
+}
+
+
+
+// MARK:- Extensions when comparable
+
+extension SinglyLinkedList where T: Comparable
+{
+    /// Deletes node containing a given value
+    ///
+    /// - Parameter v: value of the node to be deleted.
+    public mutating func deleteNode(withValue v: T) {
+        
+        guard self.storage.head != nil else {
+            return
+        }
+        
+        var previous: SinglyLinkedListNode<T>? = nil
+        var current = self.storage.head
+        
+        while (current != nil) && (current?.value != v) {
+            previous = current
+            current = current?.next
+        }
+        
+        if let foundNode = current {
+            
+            if (self.storage.head === foundNode) {
+                self.storageForWritting.head = foundNode.next
+            }
+            
+            if (self.storage.tail === foundNode) {
+                self.storage.tail = previous
+            }
+            
+            previous?.next = foundNode.next
+            foundNode.next = nil
+        }
+    }
+    
+    
+    /// Deletes duplicates without using additional structures like a set to keep track the visited nodes.
+    /// - Complexity: O(N^2)
+    public mutating func deleteDuplicatesInPlace()
+    {
+        // Copy on write: this updates self.storage if necessary.
+        var current = self.storageForWritting.head
+        
+        while (current != nil)
+        {
+            var previous: SinglyLinkedListNode<T>? = current
+            var next = current?.next
+            
+            while (next != nil)
+            {
+                if (current?.value == next?.value) {
+                    
+                    if (self.storage.head === next) {
+                        self.storage.head = next?.next
+                    }
+                    
+                    if (self.storage.tail === next) {
+                        self.storage.tail = previous
+                    }
+                    
+                    // Delete next
+                    previous?.next = next?.next
+                }
+                previous = next
+                next = next?.next
+            }
+            current = current?.next
+        }
+    }
+}
+
+
+
+// MARK: - ITERATOR -
+
+public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
+    
+    public typealias Element = T
+    
+    private(set) var head: SinglyLinkedListNode<T>?
+    
+    mutating public func next() -> T?
+    {
+        let result = self.head?.value
+        self.head = self.head?.next
+        return result
+    }
+}
+
+
+
+// MARK: - SEQUENCE -
+
+extension SinglyLinkedList : Sequence
+{
+    public func makeIterator() -> SinglyLinkedListForwardIterator<T>
+    {
+        return SinglyLinkedListForwardIterator(head: self.storage.head)
+    }
+}
+
+
+
+// MARK: - COLLECTION -
+
+extension SinglyLinkedList : Collection {
+    
+    public typealias Index = SinglyLinkedListIndex<T>
+    
+    public var startIndex: Index {
+        get {
+            return SinglyLinkedListIndex<T>(node: self.storage.head, tag: 0)
+        }
+    }
+    
+    public var endIndex: Index {
+        get {
+            if let h = self.storage.head {
+                let (_, numberOfElements) = findTail(in: h)
+                return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
+            } else {
+                return SinglyLinkedListIndex<T>(node: nil, tag: self.startIndex.tag)
+            }
+        }
+    }
+    
+    public subscript(position: Index) -> T {
+        get {
+            return position.node!.value
+        }
+    }
+    
+    public func index(after idx: Index) -> Index {
+        return SinglyLinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+    }
+}
+
+
+
+// MARK: - QUEUE -
+
+extension SinglyLinkedList : Queue
+{
+    typealias Item = T
+    
+    /// Returns the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue. It does not dequeue it.
+    func getFirst() -> T? {
+        return self.storage.head?.value
+    }
+    
+    /// Adds an element to the queue
+    ///
+    /// - Parameter item: Item to be added
+    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
+    mutating func enqueue(item: T) throws {
+        self.append(node: SinglyLinkedListNode<T>(value: item))
+    }
+    
+    /// Dequeues the oldest element in the queue.
+    ///
+    /// - Returns: The oldest element in the queue, which gets removed from it.
+    mutating func dequeue() -> T?
+    {
+        guard self.count > 0 else {
+            return nil
+        }
+        
+        return self.deleteItem(at: 0)
+    }
+}
+
+
+
+// MARK: - EXPRESSIBLE-BY-ARRAY-LITERAL -
+
+extension SinglyLinkedList : ExpressibleByArrayLiteral
+{
+    public typealias Element = T
+    
+    public init(arrayLiteral elements: Element...)
+    {
+        var headSet = false
+        var current : SinglyLinkedListNode<T>?
+        var numberOfElements = 0
+        self.storage = IndirectStorage()
+        
+        for element in elements {
+            
+            numberOfElements += 1
+            
+            if headSet == false {
+                self.storage.head = SinglyLinkedListNode<T>(value: element)
+                current = self.storage.head
+                headSet = true
+            } else {
+                let newNode = SinglyLinkedListNode<T>(value: element)
+                current?.next = newNode
+                current = newNode
+            }
+        }
+        self.storage.tail = current
+    }
+}
+
+
+
+// MARK: - FORWARD-INDEX -
+
+public struct SinglyLinkedListIndex<T> : Comparable
+{
+    fileprivate let node: SinglyLinkedListNode<T>?
+    fileprivate let tag: Int
+    
+    public static func==<T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag == rhs.tag)
+    }
+    
+    public static func< <T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+        return (lhs.tag < rhs.tag)
+    }
+}
+
+
+extension SinglyLinkedList where T : KeyValuePair {
+    
+    public func find(elementWithKey key: T.K) -> T? {
+        let searchResults = self.filter { (keyValuePair) -> Bool in
+            return keyValuePair.key == key
+        }
+        
+        return searchResults.first
+    }
+}
+
+// MARK: - HELPERS -
+
+func findTail<T>(in node: SinglyLinkedListNode<T>) -> (tail: SinglyLinkedListNode<T>, count: Int)
+{
+    // Assign the tail
+    // Note that the passed node can already be linking to other nodes,
+    // so the tail needs to be calculated.
+    var current: SinglyLinkedListNode<T>? = node
+    var count = 1
+    
+    while (current?.next != nil) {
+        current = current?.next
+        count += 1
+    }
+    
+    if current != nil {
+        return (tail: current!, count: count)
+    } else {
+        return (tail: node, count: 1)
+    }
+}
diff --git a/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj b/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..27d922edf
--- /dev/null
+++ b/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,284 @@
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diff --git a/Singly Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Singly Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/Singly Linked List/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Singly Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Singly Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..a3659d5ab
--- /dev/null
+++ b/Singly Linked List/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0830"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "0061046C1F361359007A6F50"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Singly Linked List/Tests/Tests/Info.plist b/Singly Linked List/Tests/Tests/Info.plist
new file mode 100644
index 000000000..6c6c23c43
--- /dev/null
+++ b/Singly Linked List/Tests/Tests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift
new file mode 100644
index 000000000..11b63f251
--- /dev/null
+++ b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
@@ -0,0 +1,329 @@
+import XCTest
+
+
+class FindTailInNodeTests: XCTestCase {
+    
+    func testExample() {
+        let n1 = SinglyLinkedListNode<Int>(value: 34)
+        let n2 = SinglyLinkedListNode<Int>(value: 35)
+        let n3 = SinglyLinkedListNode<Int>(value: 36)
+        let n4 = SinglyLinkedListNode<Int>(value: 37)
+        
+        n1.next = n2
+        n2.next = n3
+        n3.next = n4
+        
+        XCTAssertTrue(findTail(in: n1).tail === n4)
+        XCTAssertTrue(findTail(in: n2).tail === n4)
+        XCTAssertTrue(findTail(in: n4).tail === n4)
+        XCTAssertTrue(findTail(in: n4).tail === n4)
+    }
+    
+}
+
+class SinglyLinkedListTests: XCTestCase {
+    
+    func testAppendOneNodeFromEmptyList() {
+        var list = SinglyLinkedList<Int>()
+        list.append(value: 34)
+        XCTAssertTrue(list.first == 34)
+        XCTAssertTrue(list.count == 1, "Found \(list.count)")
+    }
+    
+    func testAppendMultipleNodesFromEmptyList() {
+        var list = SinglyLinkedList<Int>()
+        list.append(value: 34)
+        list.append(value: 35)
+        list.append(value: 36)
+        list.append(value: 34)
+        XCTAssertTrue(list.first == 34)
+        let second = list.index(list.startIndex, offsetBy: 1)
+        let third = list.index(list.startIndex, offsetBy: 2)
+        let fouth = list.index(list.startIndex, offsetBy: 3)
+        XCTAssertTrue(list[second] == 35)
+        XCTAssertTrue(list[third] == 36)
+        XCTAssertTrue(list[fouth] == 34)
+        XCTAssertTrue(list.count == 4, "Found \(list.count)")
+    }
+    
+    func testDelete() {
+        var list = SinglyLinkedList<Int>(head: SinglyLinkedListNode<Int>(value: 1))
+        list.append(value: 2)
+        list.append(value: 3)
+        list.append(value: 4)
+        list.append(value: 5)
+        
+        list.deleteNode(withValue: 1)
+        var second = list.index(list.startIndex, offsetBy: 1)
+        var third = list.index(list.startIndex, offsetBy: 2)
+        XCTAssertTrue(list.first == 2)
+        XCTAssertTrue(list[second] == 3)
+        XCTAssertTrue(list[third] == 4)
+        XCTAssertTrue(list.last == 5)
+        XCTAssertTrue(list.count == 4)
+        
+        list.deleteNode(withValue: 5)
+        second = list.index(list.startIndex, offsetBy: 1)
+        third = list.index(list.startIndex, offsetBy: 2)
+        XCTAssertTrue(list.first == 2)
+        XCTAssertTrue(list[second] == 3)
+        XCTAssertTrue(list.last == 4)
+        XCTAssertTrue(list.count == 3)
+        
+        list.deleteNode(withValue: 3)
+        XCTAssertTrue(list.first == 2)
+        XCTAssertTrue(list.last == 4)
+        XCTAssertTrue(list.count == 2)
+        
+        list.deleteNode(withValue: 2)
+        XCTAssertTrue(list.first == 4)
+        XCTAssertTrue(list.last == 4)
+        XCTAssertTrue(list.count == 1)
+        
+        list.deleteNode(withValue: 4)
+        XCTAssertTrue(list.first == nil)
+        XCTAssertTrue(list.last == nil)
+        XCTAssertTrue(list.count == 0)
+    }
+    
+    func testDeleteDuplicatesInPlace() {
+        var list = SinglyLinkedList<Int>(head: SinglyLinkedListNode<Int>(value: 1))
+        list.append(value: 2)
+        list.append(value: 2)
+        list.append(value: 3)
+        list.append(value: 5)
+        list.append(value: 2)
+        list.append(value: 4)
+        list.append(value: 2)
+        list.append(value: 5)
+        
+        list.deleteDuplicatesInPlace()
+        let second = list.index(list.startIndex, offsetBy: 1)
+        let third = list.index(list.startIndex, offsetBy: 2)
+        let fourth = list.index(list.startIndex, offsetBy: 3)
+        XCTAssertTrue(list.first == 1)
+        XCTAssertTrue(list[second] == 2)
+        XCTAssertTrue(list[third] == 3)
+        XCTAssertTrue(list[fourth] == 5)
+        XCTAssertTrue(list.last == 4)
+        XCTAssertTrue(list.count == 5)
+    }
+    
+    func testFindKthToLast() {
+        let list: SinglyLinkedList<Int> = [2,2,3,5,2,4,2,5]
+        XCTAssertTrue(list.find(kthToLast: 1)?.value == 5)
+        XCTAssertTrue(list.find(kthToLast: 2)?.value == 2)
+        XCTAssertTrue(list.find(kthToLast: 3)?.value == 4)
+        XCTAssertTrue(list.find(kthToLast: 4)?.value == 2)
+        XCTAssertTrue(list.find(kthToLast: 5)?.value == 5)
+        XCTAssertTrue(list.find(kthToLast: 6)?.value == 3)
+        XCTAssertTrue(list.find(kthToLast: 7)?.value == 2)
+        XCTAssertTrue(list.find(kthToLast: 8)?.value == 2)
+        XCTAssertTrue(list.find(kthToLast: 9)?.value == nil)
+        XCTAssertFalse(list.containsLoop())
+    }
+    
+    func testContainsLoop() {
+        let n1 = SinglyLinkedListNode<Int>(value: 1)
+        let n2 = SinglyLinkedListNode<Int>(value: 2)
+        let n3 = SinglyLinkedListNode<Int>(value: 3)
+        let n4 = SinglyLinkedListNode<Int>(value: 4)
+        let n5 = SinglyLinkedListNode<Int>(value: 5)
+        let n6 = SinglyLinkedListNode<Int>(value: 6)
+        let n7 = SinglyLinkedListNode<Int>(value: 7)
+        let n8 = SinglyLinkedListNode<Int>(value: 8)
+        n1.next = n2
+        n2.next = n3
+        n3.next = n4
+        n4.next = n5
+        n5.next = n6
+        n6.next = n7
+        n7.next = n8
+        n8.next = n2
+        
+        let list = SinglyLinkedList<Int>(head: n1)
+        XCTAssertTrue(list.containsLoop())
+        XCTAssertTrue(list.last == nil)
+    }
+    
+    func testContainsLoopFalseWithLiterals() {
+        let list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        XCTAssertTrue(list.last == 8, "Found \(String(describing: list.last))")
+        XCTAssertFalse(list.containsLoop())
+    }
+    
+    func testContainsLoopFalseWithNodes() {
+        let n1 = SinglyLinkedListNode<Int>(value: 1)
+        let n2 = SinglyLinkedListNode<Int>(value: 2)
+        let n3 = SinglyLinkedListNode<Int>(value: 3)
+        n1.next = n2
+        n2.next = n3
+        
+        let list = SinglyLinkedList<Int>(head: n1)
+        XCTAssertFalse(list.containsLoop())
+        
+    }
+    
+    func testConstructorFromArrayLiteralWhenEmpty() {
+        let list: SinglyLinkedList<Int> = []
+        XCTAssertTrue(list.first == nil)
+        XCTAssertTrue(list.last == nil)
+        XCTAssertTrue(list.count == 0, "Found \(list.count)")
+    }
+    
+    func testConstructorFromArrayLiteralWithSingleElement() {
+        let list: SinglyLinkedList<Int> = [5]
+        XCTAssertTrue(list.first == 5)
+        XCTAssertTrue(list.last == 5)
+        XCTAssertTrue(list.count == 1, "Found \(list.count)")
+    }
+    
+    
+    func testAppendValue() {
+        var list = SinglyLinkedList<Int>()
+        list.append(value: 1)
+        list.append(value: 1)
+        list.append(value: 2)
+        list.append(value: 2)
+        list.append(value: 4)
+        
+        let result = string(from: list)
+        XCTAssertTrue(result == "11224", "Found \(result)")
+        XCTAssertTrue(list.count == 5, "Found \(list.count)")
+        XCTAssertTrue(list.last == 4, "Found \(String(describing: list.last))")
+    }
+    
+    func testPrependValue() {
+        var list = SinglyLinkedList<Int>()
+        list.prepend(value: 1)
+        list.prepend(value: 2)
+        list.prepend(value: 3)
+        list.prepend(value: 4)
+        list.prepend(value: 5)
+        list.prepend(value: 6)
+        
+        let result = string(from: list)
+        XCTAssertTrue(result == "654321", "Found \(result)")
+        XCTAssertTrue(list.count == 6, "Found \(list.count)")
+        XCTAssertTrue(list.last == 1, "Found \(String(describing: list.last))")
+    }
+    
+    func testDeleteHeadInListWithMultipleItems() {
+        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        
+        let _ = list.deleteItem(at: 0)
+        let result = string(from: list)
+        XCTAssertTrue(result == "2345678", "Found \(result)")
+        XCTAssertTrue(list.first == 2, "Found \(String(describing: list.first))")
+        XCTAssertTrue(list.count == 7, "Found \(list.count)")
+    }
+    
+    func testDeleteTailInListWithMultipleItems() {
+        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        
+        let _ = list.deleteItem(at: 7)
+        let result = string(from: list)
+        XCTAssertTrue(result == "1234567", "Found \(result)")
+        XCTAssertTrue(list.last == 7, "Found \(String(describing: list.last))")
+        XCTAssertTrue(list.count == 7, "Found \(list.count)")
+    }
+    
+    func testDeleteItemInListWithMultipleItems() {
+        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        
+        let _ = list.deleteItem(at: 4)
+        let result = string(from: list)
+        XCTAssertTrue(result == "1234678", "Found \(result)")
+        XCTAssertTrue(list.first == 1, "Found \(String(describing: list.first))")
+        XCTAssertTrue(list.last == 8, "Found \(String(describing: list.last))")
+        XCTAssertTrue(list.count == 7, "Found \(list.count)")
+    }
+    
+    func testDeleteHeadInListWithSingleElement() {
+        var list: SinglyLinkedList<Int> = [1]
+        
+        let _ = list.deleteItem(at: 0)
+        let result = string(from: list)
+        XCTAssertTrue(result == "", "Found \(result)")
+        XCTAssertTrue(list.first == nil, "Found \(String(describing: list.first))")
+        XCTAssertTrue(list.last == nil, "Found \(String(describing: list.last))")
+        XCTAssertTrue(list.count == 0, "Found \(list.count)")
+    }
+    
+    func testDirectIndexAccess() {
+        let list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        let fifthElementIndex = list.index(list.startIndex, offsetBy: 5)
+        XCTAssertTrue(list[fifthElementIndex] == 6 ,  "Found \(list.count)")
+    }
+    
+    
+    func string(from list: SinglyLinkedList<Int>) -> String {
+        var result = ""
+        var iterator = list.makeIterator()
+        while let current = iterator.next() {
+            result += String(describing: current)
+        }
+        
+        return result
+    }
+    
+    func testCopyOnWriteUsingLiterals() {
+        var l1: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+        l1.append(value: 0)
+        var l2 = l1
+        
+        _ = l2.deleteItem(at: 3)
+        XCTAssertTrue(l1.count == 9)
+        XCTAssertTrue(l2.count == 8)
+        
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        _ = l1.deleteItem(at: 0)
+        
+        XCTAssertTrue(l1.count == 0)
+        XCTAssertTrue(l2.count == 8)
+    }
+    
+}
+
+class SinglyLinkedListQueueTests: XCTestCase {
+    
+    func testQueue() {
+        var queue = SinglyLinkedList<Int>()
+        
+        try! queue.enqueue(item: 1)
+        XCTAssertTrue(queue.getFirst()! == 1)
+        XCTAssertTrue(queue.count == 1)
+        
+        try! queue.enqueue(item: 2)
+        XCTAssertTrue(queue.getFirst()! == 1)
+        XCTAssertTrue(queue.count == 2)
+        
+        try! queue.enqueue(item: 3)
+        XCTAssertTrue(queue.getFirst()! == 1)
+        XCTAssertTrue(queue.count == 3)
+        
+        XCTAssertTrue(queue.dequeue() == 1)
+        XCTAssertTrue(queue.count == 2)
+        
+        XCTAssertTrue(queue.dequeue() == 2)
+        XCTAssertTrue(queue.count == 1)
+        
+        XCTAssertTrue(queue.dequeue() == 3)
+        XCTAssertTrue(queue.count == 0)
+        
+        XCTAssertTrue(queue.dequeue() == nil)
+        XCTAssertTrue(queue.count == 0)
+        
+        try! queue.enqueue(item: 9)
+        XCTAssertTrue(queue.getFirst()! == 9)
+        XCTAssertTrue(queue.count == 1)
+        
+    }
+}
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index db4691648..d56db7d12 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1436,6 +1436,52 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Singly Linked List"
+      name = "Singly Linked List">
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:CopiedIndirectStorage.png">
+         </FileRef>
+         <FileRef
+            location = "group:SharedIndirectStorage.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:KeyValuePair.swift">
+      </FileRef>
+      <FileRef
+         location = "group:Queue.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:SinglyLinkedList.playground">
+      </FileRef>
+      <FileRef
+         location = "group:SinglyLinkedList.swift">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <Group
+            location = "group:Tests"
+            name = "Tests">
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:SinglyLinkedListTests.swift">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "group:Longest Common Subsequence"
       name = "Longest Common Subsequence">

From be11f6bcf44cf435b66647faa51a7be07ae0c0e7 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:00:25 +0100
Subject: [PATCH 128/643] Remove loop-detection logic and tests.

---
 Singly Linked List/SinglyLinkedList.swift     | 44 ++-----------------
 .../Tests/Tests/SinglyLinkedListTests.swift   | 43 ------------------
 2 files changed, 4 insertions(+), 83 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index b05526b35..bdc544079 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -198,34 +198,6 @@ public struct SinglyLinkedList<T>
         return self.find(kthToLast: kthToLast, startingAt: self.storage.head, count: UInt(self.count))
     }
     
-    
-    
-    // MARK: LOOP DETECTION
-    
-    /// A singly linked list contains a loop if one node references back to a previous node.
-    ///
-    /// - Returns: Whether the linked list contains a loop
-    public func containsLoop() -> Bool
-    {
-        /// Advances a node at a time
-        var current = self.storage.head
-        
-        /// Advances twice as fast
-        var runner = self.storage.head
-        
-        while (runner != nil) && (runner?.next != nil) {
-            
-            current = current?.next
-            runner = runner?.next?.next
-            
-            if runner === current {
-                return true
-            }
-        }
-        
-        return false
-    }
-    
 }
 
 
@@ -261,12 +233,8 @@ private extension SinglyLinkedList {
             // Copy on write: we are about to modify next a property in
             // a potentially shared node. Make sure it's new if necessary.
             self.storageForWritting.tail?.next = node
-            if !self.containsLoop() {
-                let (tail, _) = findTail(in: node)
-                self.storageForWritting.tail = tail // There
-            } else {
-                self.storageForWritting.tail = nil
-            }
+            let (tail, _) = findTail(in: node)
+            self.storageForWritting.tail = tail // There
         }
         else
         {
@@ -274,12 +242,8 @@ private extension SinglyLinkedList {
             // Otherwise the state would be inconsistent.
             // This will be checked when adding and deleting nodes.
             self.storageForWritting.head = node
-            if !self.containsLoop() {
-                let (tail, _) = findTail(in: node)
-                self.storageForWritting.tail = tail // There
-            } else {
-                self.storageForWritting.tail = nil
-            }
+            let (tail, _) = findTail(in: node)
+            self.storageForWritting.tail = tail // There
         }
     }
     
diff --git a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift
index 11b63f251..2efa7b8d0 100644
--- a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
+++ b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
@@ -120,48 +120,6 @@ class SinglyLinkedListTests: XCTestCase {
         XCTAssertTrue(list.find(kthToLast: 7)?.value == 2)
         XCTAssertTrue(list.find(kthToLast: 8)?.value == 2)
         XCTAssertTrue(list.find(kthToLast: 9)?.value == nil)
-        XCTAssertFalse(list.containsLoop())
-    }
-    
-    func testContainsLoop() {
-        let n1 = SinglyLinkedListNode<Int>(value: 1)
-        let n2 = SinglyLinkedListNode<Int>(value: 2)
-        let n3 = SinglyLinkedListNode<Int>(value: 3)
-        let n4 = SinglyLinkedListNode<Int>(value: 4)
-        let n5 = SinglyLinkedListNode<Int>(value: 5)
-        let n6 = SinglyLinkedListNode<Int>(value: 6)
-        let n7 = SinglyLinkedListNode<Int>(value: 7)
-        let n8 = SinglyLinkedListNode<Int>(value: 8)
-        n1.next = n2
-        n2.next = n3
-        n3.next = n4
-        n4.next = n5
-        n5.next = n6
-        n6.next = n7
-        n7.next = n8
-        n8.next = n2
-        
-        let list = SinglyLinkedList<Int>(head: n1)
-        XCTAssertTrue(list.containsLoop())
-        XCTAssertTrue(list.last == nil)
-    }
-    
-    func testContainsLoopFalseWithLiterals() {
-        let list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        XCTAssertTrue(list.last == 8, "Found \(String(describing: list.last))")
-        XCTAssertFalse(list.containsLoop())
-    }
-    
-    func testContainsLoopFalseWithNodes() {
-        let n1 = SinglyLinkedListNode<Int>(value: 1)
-        let n2 = SinglyLinkedListNode<Int>(value: 2)
-        let n3 = SinglyLinkedListNode<Int>(value: 3)
-        n1.next = n2
-        n2.next = n3
-        
-        let list = SinglyLinkedList<Int>(head: n1)
-        XCTAssertFalse(list.containsLoop())
-        
     }
     
     func testConstructorFromArrayLiteralWhenEmpty() {
@@ -178,7 +136,6 @@ class SinglyLinkedListTests: XCTestCase {
         XCTAssertTrue(list.count == 1, "Found \(list.count)")
     }
     
-    
     func testAppendValue() {
         var list = SinglyLinkedList<Int>()
         list.append(value: 1)

From 0041be6c0bfc54912127add7c4c1168adebe8e41 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:07:15 +0100
Subject: [PATCH 129/643] Remove internal initializer method that takes a node
 as a parameter to prevent misuse that could break value semantics.

---
 Singly Linked List/SinglyLinkedList.swift         | 15 ++-------------
 .../Tests/Tests/SinglyLinkedListTests.swift       |  4 ++--
 2 files changed, 4 insertions(+), 15 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index bdc544079..bdf7d248b 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -83,24 +83,13 @@ public struct SinglyLinkedList<T>
     
     // MARK: INITIALIZERS
     
-    /// Creates a list with the given node.
-    /// NOTE: This method can break value semantics by accepting a node.
-    ///
-    /// - Parameter head: First node
-    internal init(head: SinglyLinkedListNode<T>)
-    {
-        self.storage = IndirectStorage()
-        self.append(node: head)
-    }
-    
-    
     /// Creates a list with a single element
     ///
     /// - Parameter value: element to populate the list with
     public init(value: T)
     {
-        let node = SinglyLinkedListNode<T>(value: value)
-        self.init(head: node)
+        self.init()
+        self.append(value: value)
     }
     
     
diff --git a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift
index 2efa7b8d0..ee8f989c3 100644
--- a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
+++ b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
@@ -47,7 +47,7 @@ class SinglyLinkedListTests: XCTestCase {
     }
     
     func testDelete() {
-        var list = SinglyLinkedList<Int>(head: SinglyLinkedListNode<Int>(value: 1))
+        var list: SinglyLinkedList<Int> = [1]
         list.append(value: 2)
         list.append(value: 3)
         list.append(value: 4)
@@ -87,7 +87,7 @@ class SinglyLinkedListTests: XCTestCase {
     }
     
     func testDeleteDuplicatesInPlace() {
-        var list = SinglyLinkedList<Int>(head: SinglyLinkedListNode<Int>(value: 1))
+        var list: SinglyLinkedList<Int> = [1]
         list.append(value: 2)
         list.append(value: 2)
         list.append(value: 3)

From 74fb0ecb9558a4a26fd8af53f89b3254b6429768 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:11:22 +0100
Subject: [PATCH 130/643] Remove SinglyLinedList's conformance to Queue
 protocol.

---
 Singly Linked List/Queue.swift                | 28 ---------------
 Singly Linked List/SinglyLinkedList.swift     | 36 -------------------
 .../Tests/Tests.xcodeproj/project.pbxproj     |  4 ---
 .../Tests/Tests/SinglyLinkedListTests.swift   | 36 -------------------
 4 files changed, 104 deletions(-)
 delete mode 100644 Singly Linked List/Queue.swift

diff --git a/Singly Linked List/Queue.swift b/Singly Linked List/Queue.swift
deleted file mode 100644
index 68fda9f99..000000000
--- a/Singly Linked List/Queue.swift	
+++ /dev/null
@@ -1,28 +0,0 @@
-import Foundation
-
-
-/// Data structure that provides FIFO access
-protocol Queue
-{
-    associatedtype Item
-    
-    
-    /// Adds an element to the queue
-    ///
-    /// - Parameter item: Item to be added
-    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
-    mutating func enqueue(item: Item) throws
-    
-    
-    /// Returns the oldest element in the queue.
-    ///
-    /// - Returns: The oldest element in the queue. It does not dequeue it.
-    func getFirst() -> Item?
-    
-    
-    /// Dequeues the oldest element in the queue.
-    ///
-    /// - Returns: The oldest element in the queue, which gets removed from it.
-    mutating func dequeue() -> Item?
-    
-}
diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index bdf7d248b..db8cc0229 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -414,42 +414,6 @@ extension SinglyLinkedList : Collection {
 
 
 
-// MARK: - QUEUE -
-
-extension SinglyLinkedList : Queue
-{
-    typealias Item = T
-    
-    /// Returns the oldest element in the queue.
-    ///
-    /// - Returns: The oldest element in the queue. It does not dequeue it.
-    func getFirst() -> T? {
-        return self.storage.head?.value
-    }
-    
-    /// Adds an element to the queue
-    ///
-    /// - Parameter item: Item to be added
-    /// - Throws: There are cases where the operation might fail. For example if there is not enough space.
-    mutating func enqueue(item: T) throws {
-        self.append(node: SinglyLinkedListNode<T>(value: item))
-    }
-    
-    /// Dequeues the oldest element in the queue.
-    ///
-    /// - Returns: The oldest element in the queue, which gets removed from it.
-    mutating func dequeue() -> T?
-    {
-        guard self.count > 0 else {
-            return nil
-        }
-        
-        return self.deleteItem(at: 0)
-    }
-}
-
-
-
 // MARK: - EXPRESSIBLE-BY-ARRAY-LITERAL -
 
 extension SinglyLinkedList : ExpressibleByArrayLiteral
diff --git a/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj b/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj
index 27d922edf..8dddf6498 100644
--- a/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Singly Linked List/Tests/Tests.xcodeproj/project.pbxproj	
@@ -9,7 +9,6 @@
 /* Begin PBXBuildFile section */
 		006104711F361359007A6F50 /* SinglyLinkedListTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 006104701F361359007A6F50 /* SinglyLinkedListTests.swift */; };
 		006104791F36144E007A6F50 /* KeyValuePair.swift in Sources */ = {isa = PBXBuildFile; fileRef = 006104761F36144E007A6F50 /* KeyValuePair.swift */; };
-		0061047A1F36144E007A6F50 /* Queue.swift in Sources */ = {isa = PBXBuildFile; fileRef = 006104771F36144E007A6F50 /* Queue.swift */; };
 		0061047B1F36144E007A6F50 /* SinglyLinkedList.swift in Sources */ = {isa = PBXBuildFile; fileRef = 006104781F36144E007A6F50 /* SinglyLinkedList.swift */; };
 /* End PBXBuildFile section */
 
@@ -18,7 +17,6 @@
 		006104701F361359007A6F50 /* SinglyLinkedListTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = SinglyLinkedListTests.swift; sourceTree = "<group>"; };
 		006104721F361359007A6F50 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 		006104761F36144E007A6F50 /* KeyValuePair.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = KeyValuePair.swift; path = ../../KeyValuePair.swift; sourceTree = "<group>"; };
-		006104771F36144E007A6F50 /* Queue.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Queue.swift; path = ../../Queue.swift; sourceTree = "<group>"; };
 		006104781F36144E007A6F50 /* SinglyLinkedList.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = SinglyLinkedList.swift; path = ../../SinglyLinkedList.swift; sourceTree = "<group>"; };
 /* End PBXFileReference section */
 
@@ -54,7 +52,6 @@
 			children = (
 				006104701F361359007A6F50 /* SinglyLinkedListTests.swift */,
 				006104761F36144E007A6F50 /* KeyValuePair.swift */,
-				006104771F36144E007A6F50 /* Queue.swift */,
 				006104781F36144E007A6F50 /* SinglyLinkedList.swift */,
 				006104721F361359007A6F50 /* Info.plist */,
 			);
@@ -130,7 +127,6 @@
 			buildActionMask = 2147483647;
 			files = (
 				006104711F361359007A6F50 /* SinglyLinkedListTests.swift in Sources */,
-				0061047A1F36144E007A6F50 /* Queue.swift in Sources */,
 				0061047B1F36144E007A6F50 /* SinglyLinkedList.swift in Sources */,
 				006104791F36144E007A6F50 /* KeyValuePair.swift in Sources */,
 			);
diff --git a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift
index ee8f989c3..50d354808 100644
--- a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
+++ b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
@@ -248,39 +248,3 @@ class SinglyLinkedListTests: XCTestCase {
     }
     
 }
-
-class SinglyLinkedListQueueTests: XCTestCase {
-    
-    func testQueue() {
-        var queue = SinglyLinkedList<Int>()
-        
-        try! queue.enqueue(item: 1)
-        XCTAssertTrue(queue.getFirst()! == 1)
-        XCTAssertTrue(queue.count == 1)
-        
-        try! queue.enqueue(item: 2)
-        XCTAssertTrue(queue.getFirst()! == 1)
-        XCTAssertTrue(queue.count == 2)
-        
-        try! queue.enqueue(item: 3)
-        XCTAssertTrue(queue.getFirst()! == 1)
-        XCTAssertTrue(queue.count == 3)
-        
-        XCTAssertTrue(queue.dequeue() == 1)
-        XCTAssertTrue(queue.count == 2)
-        
-        XCTAssertTrue(queue.dequeue() == 2)
-        XCTAssertTrue(queue.count == 1)
-        
-        XCTAssertTrue(queue.dequeue() == 3)
-        XCTAssertTrue(queue.count == 0)
-        
-        XCTAssertTrue(queue.dequeue() == nil)
-        XCTAssertTrue(queue.count == 0)
-        
-        try! queue.enqueue(item: 9)
-        XCTAssertTrue(queue.getFirst()! == 9)
-        XCTAssertTrue(queue.count == 1)
-        
-    }
-}

From 70781ec072f2cf84c40379b6497f1fa2a6eb9e37 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:19:29 +0100
Subject: [PATCH 131/643] Remove needless self references to follow the
 repository's Swift style guidelines.

---
 Singly Linked List/SinglyLinkedList.swift | 96 +++++++++++------------
 1 file changed, 48 insertions(+), 48 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index db8cc0229..cb05914f7 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -65,17 +65,17 @@ public struct SinglyLinkedList<T>
     private var storageForWritting: IndirectStorage<T> {
         
         mutating get {
-            if !isKnownUniquelyReferenced(&self.storage) {
-                self.storage = self.copyStorage()
+            if !isKnownUniquelyReferenced(&storage) {
+                storage = copyStorage()
             }
-            return self.storage
+            return storage
         }
     }
     
     /// Returns the last element in the collection
     public var last: T? {
         get {
-            return self.storage.tail?.value
+            return storage.tail?.value
         }
     }
     
@@ -108,7 +108,7 @@ public struct SinglyLinkedList<T>
     public mutating func append(value: T)
     {
         let node = SinglyLinkedListNode<T>(value: value)
-        self.append(node: node)
+        append(node: node)
     }
     
     
@@ -118,16 +118,16 @@ public struct SinglyLinkedList<T>
     public mutating func prepend(value: T)
     {
         let node = SinglyLinkedListNode<T>(value: value)
-        self.prepend(node: node)
+        prepend(node: node)
     }
     
     
     public mutating func deleteItem(at index:Int) -> T
     {
-        precondition((index >= 0) && (index < self.count))
+        precondition((index >= 0) && (index < count))
         
         var previous: SinglyLinkedListNode<T>? = nil
-        var current = self.storageForWritting.head
+        var current = storageForWritting.head
         var i = 0
         var elementToDelete: SinglyLinkedListNode<T>
         
@@ -139,12 +139,12 @@ public struct SinglyLinkedList<T>
         
         // Current is now the element to delete (at index position.tag)
         elementToDelete = current!
-        if (self.storage.head === current) {
-            self.storageForWritting.head = current?.next
+        if (storage.head === current) {
+            storageForWritting.head = current?.next
         }
         
-        if (self.storage.tail === current) {
-            self.storageForWritting.tail = previous
+        if (storage.tail === current) {
+            storageForWritting.tail = previous
         }
         
         previous?.next = current?.next
@@ -184,7 +184,7 @@ public struct SinglyLinkedList<T>
     /// - Parameter kthToLast: Reversed ordinal number of the node to fetch.
     public func find(kthToLast: UInt) -> SinglyLinkedListNode<T>?
     {
-        return self.find(kthToLast: kthToLast, startingAt: self.storage.head, count: UInt(self.count))
+        return find(kthToLast: kthToLast, startingAt: storage.head, count: UInt(count))
     }
     
 }
@@ -202,11 +202,11 @@ private extension SinglyLinkedList {
     private mutating func prepend(node: SinglyLinkedListNode<T>)
     {
         let (tailFromNewNode, _) = findTail(in: node)
-        tailFromNewNode.next = self.storageForWritting.head
-        self.storageForWritting.head = node
+        tailFromNewNode.next = storageForWritting.head
+        storageForWritting.head = node
         
-        if self.storage.tail == nil {
-            self.storageForWritting.tail = tailFromNewNode
+        if storage.tail == nil {
+            storageForWritting.tail = tailFromNewNode
         }
     }
     
@@ -217,22 +217,22 @@ private extension SinglyLinkedList {
     /// - Parameter node: node to be appended. (It can be a list, even contain loops).
     private mutating func append(node: SinglyLinkedListNode<T>)
     {
-        if self.storage.tail != nil
+        if storage.tail != nil
         {
             // Copy on write: we are about to modify next a property in
             // a potentially shared node. Make sure it's new if necessary.
-            self.storageForWritting.tail?.next = node
+            storageForWritting.tail?.next = node
             let (tail, _) = findTail(in: node)
-            self.storageForWritting.tail = tail // There
+            storageForWritting.tail = tail // There
         }
         else
         {
             // This also means that there's no head.
             // Otherwise the state would be inconsistent.
             // This will be checked when adding and deleting nodes.
-            self.storageForWritting.head = node
+            storageForWritting.head = node
             let (tail, _) = findTail(in: node)
-            self.storageForWritting.tail = tail // There
+            storageForWritting.tail = tail // There
         }
     }
     
@@ -243,18 +243,18 @@ private extension SinglyLinkedList {
         // If the list is empty, next time an item will be created, it won't affect
         // other instances of the list that came from copies derived from value types.
         // like assignments or parameters
-        guard (self.storage.head != nil) && (self.storage.tail != nil) else {
+        guard (storage.head != nil) && (storage.tail != nil) else {
             return IndirectStorage(head: nil, tail: nil)
         }
         
         // Create a new position in memory.
         // Note that we are shallow copying the value. If it was reference type
         // we just make a copy of the reference.
-        let copiedHead = SinglyLinkedListNode<T>(value: self.storage.head!.value)
+        let copiedHead = SinglyLinkedListNode<T>(value: storage.head!.value)
         var previousCopied: SinglyLinkedListNode<T> = copiedHead
         
         // Iterate through current list of nodes and copy them.
-        var current: SinglyLinkedListNode<T>? = self.storage.head?.next
+        var current: SinglyLinkedListNode<T>? = storage.head?.next
         
         while (current != nil) {
             // Create a copy
@@ -283,12 +283,12 @@ extension SinglyLinkedList where T: Comparable
     /// - Parameter v: value of the node to be deleted.
     public mutating func deleteNode(withValue v: T) {
         
-        guard self.storage.head != nil else {
+        guard storage.head != nil else {
             return
         }
         
         var previous: SinglyLinkedListNode<T>? = nil
-        var current = self.storage.head
+        var current = storage.head
         
         while (current != nil) && (current?.value != v) {
             previous = current
@@ -297,12 +297,12 @@ extension SinglyLinkedList where T: Comparable
         
         if let foundNode = current {
             
-            if (self.storage.head === foundNode) {
-                self.storageForWritting.head = foundNode.next
+            if (storage.head === foundNode) {
+                storageForWritting.head = foundNode.next
             }
             
-            if (self.storage.tail === foundNode) {
-                self.storage.tail = previous
+            if (storage.tail === foundNode) {
+                storage.tail = previous
             }
             
             previous?.next = foundNode.next
@@ -315,8 +315,8 @@ extension SinglyLinkedList where T: Comparable
     /// - Complexity: O(N^2)
     public mutating func deleteDuplicatesInPlace()
     {
-        // Copy on write: this updates self.storage if necessary.
-        var current = self.storageForWritting.head
+        // Copy on write: this updates storage if necessary.
+        var current = storageForWritting.head
         
         while (current != nil)
         {
@@ -327,12 +327,12 @@ extension SinglyLinkedList where T: Comparable
             {
                 if (current?.value == next?.value) {
                     
-                    if (self.storage.head === next) {
-                        self.storage.head = next?.next
+                    if (storage.head === next) {
+                        storage.head = next?.next
                     }
                     
-                    if (self.storage.tail === next) {
-                        self.storage.tail = previous
+                    if (storage.tail === next) {
+                        storage.tail = previous
                     }
                     
                     // Delete next
@@ -358,8 +358,8 @@ public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
     
     mutating public func next() -> T?
     {
-        let result = self.head?.value
-        self.head = self.head?.next
+        let result = head?.value
+        head = head?.next
         return result
     }
 }
@@ -372,7 +372,7 @@ extension SinglyLinkedList : Sequence
 {
     public func makeIterator() -> SinglyLinkedListForwardIterator<T>
     {
-        return SinglyLinkedListForwardIterator(head: self.storage.head)
+        return SinglyLinkedListForwardIterator(head: storage.head)
     }
 }
 
@@ -386,17 +386,17 @@ extension SinglyLinkedList : Collection {
     
     public var startIndex: Index {
         get {
-            return SinglyLinkedListIndex<T>(node: self.storage.head, tag: 0)
+            return SinglyLinkedListIndex<T>(node: storage.head, tag: 0)
         }
     }
     
     public var endIndex: Index {
         get {
-            if let h = self.storage.head {
+            if let h = storage.head {
                 let (_, numberOfElements) = findTail(in: h)
                 return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
             } else {
-                return SinglyLinkedListIndex<T>(node: nil, tag: self.startIndex.tag)
+                return SinglyLinkedListIndex<T>(node: nil, tag: startIndex.tag)
             }
         }
     }
@@ -425,15 +425,15 @@ extension SinglyLinkedList : ExpressibleByArrayLiteral
         var headSet = false
         var current : SinglyLinkedListNode<T>?
         var numberOfElements = 0
-        self.storage = IndirectStorage()
+        storage = IndirectStorage()
         
         for element in elements {
             
             numberOfElements += 1
             
             if headSet == false {
-                self.storage.head = SinglyLinkedListNode<T>(value: element)
-                current = self.storage.head
+                storage.head = SinglyLinkedListNode<T>(value: element)
+                current = storage.head
                 headSet = true
             } else {
                 let newNode = SinglyLinkedListNode<T>(value: element)
@@ -441,7 +441,7 @@ extension SinglyLinkedList : ExpressibleByArrayLiteral
                 current = newNode
             }
         }
-        self.storage.tail = current
+        storage.tail = current
     }
 }
 
@@ -467,7 +467,7 @@ public struct SinglyLinkedListIndex<T> : Comparable
 extension SinglyLinkedList where T : KeyValuePair {
     
     public func find(elementWithKey key: T.K) -> T? {
-        let searchResults = self.filter { (keyValuePair) -> Bool in
+        let searchResults = filter { (keyValuePair) -> Bool in
             return keyValuePair.key == key
         }
         

From 11fcad75d64fe194fd7f884b87f2679b043fc060 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:47:22 +0100
Subject: [PATCH 132/643] Replace spacing from 4 to 2 spaces to follow the
 repository's Swift Style guide.

---
 Singly Linked List/KeyValuePair.swift         | 114 +--
 Singly Linked List/SinglyLinkedList.swift     | 736 +++++++++---------
 .../Tests/Tests/SinglyLinkedListTests.swift   | 477 ++++++------
 3 files changed, 651 insertions(+), 676 deletions(-)

diff --git a/Singly Linked List/KeyValuePair.swift b/Singly Linked List/KeyValuePair.swift
index 2751503c2..9c6cacea4 100644
--- a/Singly Linked List/KeyValuePair.swift	
+++ b/Singly Linked List/KeyValuePair.swift	
@@ -3,62 +3,62 @@
 /// stored contain a value, but are ordered or retrieved according to a key.
 public protocol KeyValuePair : Comparable {
     
-    associatedtype K : Comparable, Hashable
-    associatedtype V : Comparable, Hashable
-    
-    // Identifier used in many algorithms to search by, order by, etc
-    var key : K {get set}
-    
-    // A data container
-    var value : V {get set}
-    
-    
-    /// Initializer
-    ///
-    /// - Parameters:
-    ///   - key: Identifier used in many algorithms to search by, order by, etc.
-    ///   - value: A data container.
-    init(key: K, value: V)
-    
-    
-    /// Creates a copy
-    ///
-    /// - Abstract: Conformers of this class can be either value or reference types.
-    ///   Some algorithms might need to guarantee that a conformer instance gets copied.
-    ///   This will perform an innecessary in the case of value types.
-    ///   TODO: is there a better way?
-    /// - Returns: A new instance with the old one's values copied.
-    func copy() -> Self
+  associatedtype K : Comparable, Hashable
+  associatedtype V : Comparable, Hashable
+  
+  // Identifier used in many algorithms to search by, order by, etc
+  var key : K {get set}
+  
+  // A data container
+  var value : V {get set}
+  
+  
+  /// Initializer
+  ///
+  /// - Parameters:
+  ///   - key: Identifier used in many algorithms to search by, order by, etc.
+  ///   - value: A data container.
+  init(key: K, value: V)
+  
+  
+  /// Creates a copy
+  ///
+  /// - Abstract: Conformers of this class can be either value or reference types.
+  ///   Some algorithms might need to guarantee that a conformer instance gets copied.
+  ///   This will perform an innecessary in the case of value types.
+  ///   TODO: is there a better way?
+  /// - Returns: A new instance with the old one's values copied.
+  func copy() -> Self
 }
 
 
 /// Conformance to Equatable and Comparable protocols
 extension KeyValuePair {
     
-    // MARK: - Equatable protocol
-    public static func ==(lhs: Self, rhs: Self) -> Bool {
-        return lhs.key == rhs.key
-    }
-    
-    
-    
-    // MARK: - Comparable protocol
-    
-    public static func <(lhs: Self, rhs: Self) -> Bool {
-        return lhs.key < rhs.key
-    }
-    
-    public static func <=(lhs: Self, rhs: Self) -> Bool {
-        return lhs.key <= rhs.key
-    }
-    
-    public static func >=(lhs: Self, rhs: Self) -> Bool {
-        return lhs.key >= rhs.key
-    }
-    
-    public static func >(lhs: Self, rhs: Self) -> Bool {
-        return lhs.key > rhs.key
-    }
+  // MARK: - Equatable protocol
+  public static func ==(lhs: Self, rhs: Self) -> Bool {
+    return lhs.key == rhs.key
+  }
+  
+  
+  
+  // MARK: - Comparable protocol
+  
+  public static func <(lhs: Self, rhs: Self) -> Bool {
+    return lhs.key < rhs.key
+  }
+  
+  public static func <=(lhs: Self, rhs: Self) -> Bool {
+    return lhs.key <= rhs.key
+  }
+  
+  public static func >=(lhs: Self, rhs: Self) -> Bool {
+    return lhs.key >= rhs.key
+  }
+  
+  public static func >(lhs: Self, rhs: Self) -> Bool {
+    return lhs.key > rhs.key
+  }
 }
 
 
@@ -67,11 +67,11 @@ extension KeyValuePair {
 /// are Integers.
 struct IntegerPair : KeyValuePair {
     
-    // MARK - KeyValuePair protocol
-    var key : Int
-    var value : Int
-    
-    func copy() -> IntegerPair {
-        return IntegerPair(key: self.key, value: self.value)
-    }
+  // MARK - KeyValuePair protocol
+  var key : Int
+  var value : Int
+  
+  func copy() -> IntegerPair {
+    return IntegerPair(key: self.key, value: self.value)
+  }
 }
diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index cb05914f7..4e088e195 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -4,18 +4,18 @@ import Foundation
 /// Helper class to implement copy-on-write
 fileprivate class IndirectStorage<T> {
     
-    var head: SinglyLinkedListNode<T>?
-    
-    var tail: SinglyLinkedListNode<T>?
-    
-    init(head: SinglyLinkedListNode<T>?, tail: SinglyLinkedListNode<T>?) {
-        self.head = head
-        self.tail = tail
-    }
-    
-    convenience init() {
-        self.init(head: nil, tail: nil)
-    }
+  var head: SinglyLinkedListNode<T>?
+    
+  var tail: SinglyLinkedListNode<T>?
+  
+  init(head: SinglyLinkedListNode<T>?, tail: SinglyLinkedListNode<T>?) {
+    self.head = head
+    self.tail = tail
+  }
+  
+  convenience init() {
+    self.init(head: nil, tail: nil)
+  }
 }
 
 
@@ -27,18 +27,18 @@ fileprivate class IndirectStorage<T> {
 /// will need to manipulate references directly.
 public class SinglyLinkedListNode<T> {
     
-    /// Data container
-    public var value: T
-    
-    /// Link to the next node
-    public var next: SinglyLinkedListNode<T>?
-    
-    /// Designated initializer
-    ///
-    /// - Parameter value: A value
-    public init(value: T) {
-        self.value = value
-    }
+  /// Data container
+  public var value: T
+  
+  /// Link to the next node
+  public var next: SinglyLinkedListNode<T>?
+  
+  /// Designated initializer
+  ///
+  /// - Parameter value: A value
+  public init(value: T) {
+    self.value = value
+  }
 }
 
 
@@ -52,140 +52,132 @@ public class SinglyLinkedListNode<T> {
 ///
 /// However, the elements contained in the list, will be shallow copied if they
 /// implement reference semantics.
-public struct SinglyLinkedList<T>
-{
-    // MARK: PROPERTIES
-    
-    // A level of inderiction, with reference semantics to allow easy
-    // detection of when there are more than one references of the storage.
-    private var storage: IndirectStorage<T>
-    
-    /// Whenever there's a change that potentially can change the value, this reference to the
-    /// storage should be used to guarantee that a new copy is created and written on.
-    private var storageForWritting: IndirectStorage<T> {
-        
-        mutating get {
-            if !isKnownUniquelyReferenced(&storage) {
-                storage = copyStorage()
-            }
-            return storage
-        }
+public struct SinglyLinkedList<T> {
+  // MARK: PROPERTIES
+  
+  // A level of inderiction, with reference semantics to allow easy
+  // detection of when there are more than one references of the storage.
+  private var storage: IndirectStorage<T>
+  
+  /// Whenever there's a change that potentially can change the value, this reference to the
+  /// storage should be used to guarantee that a new copy is created and written on.
+  private var storageForWritting: IndirectStorage<T> {
+    
+    mutating get {
+      if !isKnownUniquelyReferenced(&storage) {
+          storage = copyStorage()
+      }
+      return storage
     }
-    
-    /// Returns the last element in the collection
-    public var last: T? {
-        get {
-            return storage.tail?.value
-        }
+  }
+  
+  /// Returns the last element in the collection
+  public var last: T? {
+    get {
+      return storage.tail?.value
     }
-    
-    
-    
-    // MARK: INITIALIZERS
-    
-    /// Creates a list with a single element
-    ///
-    /// - Parameter value: element to populate the list with
-    public init(value: T)
-    {
-        self.init()
-        self.append(value: value)
+  }
+  
+  
+  
+  // MARK: INITIALIZERS
+  
+  /// Creates a list with a single element
+  ///
+  /// - Parameter value: element to populate the list with
+  public init(value: T) {
+    self.init()
+    self.append(value: value)
+  }
+  
+  
+  /// Creates an empty list
+  public init() {
+    self.storage = IndirectStorage()
+  }
+  
+  
+  // MARK: EDITION
+  
+  /// Convenience method to append a value directly to the list
+  ///
+  /// - Parameter value: value to be added
+  public mutating func append(value: T) {
+    let node = SinglyLinkedListNode<T>(value: value)
+    append(node: node)
+  }
+  
+  
+  /// Convenience method to prepend a value directly to the list
+  ///
+  /// - Parameter value: value to be added as the new head of the list
+  public mutating func prepend(value: T) {
+    let node = SinglyLinkedListNode<T>(value: value)
+    prepend(node: node)
+  }
+  
+  
+  public mutating func deleteItem(at index:Int) -> T {
+    precondition((index >= 0) && (index < count))
+    
+    var previous: SinglyLinkedListNode<T>? = nil
+    var current = storageForWritting.head
+    var i = 0
+    var elementToDelete: SinglyLinkedListNode<T>
+    
+    while (i < index) {
+      previous = current
+      current = current?.next
+      i += 1
     }
     
-    
-    /// Creates an empty list
-    public init()
-    {
-        self.storage = IndirectStorage()
+    // Current is now the element to delete (at index position.tag)
+    elementToDelete = current!
+    if (storage.head === current) {
+      storageForWritting.head = current?.next
     }
     
-    
-    // MARK: EDITION
-    
-    /// Convenience method to append a value directly to the list
-    ///
-    /// - Parameter value: value to be added
-    public mutating func append(value: T)
-    {
-        let node = SinglyLinkedListNode<T>(value: value)
-        append(node: node)
+    if (storage.tail === current) {
+      storageForWritting.tail = previous
     }
     
-    
-    /// Convenience method to prepend a value directly to the list
-    ///
-    /// - Parameter value: value to be added as the new head of the list
-    public mutating func prepend(value: T)
-    {
-        let node = SinglyLinkedListNode<T>(value: value)
-        prepend(node: node)
+    previous?.next = current?.next
+    
+    return elementToDelete.value
+  }
+  
+  
+  
+  // MARK: SEARCH
+  
+  /// Returns the node located at the k-th to last position
+  ///
+  /// - Parameter kthToLast: 1 <= k <= N
+  private func find(kthToLast: UInt, startingAt node: SinglyLinkedListNode<T>?, count: UInt) -> SinglyLinkedListNode<T>? {
+    guard kthToLast <= count else {
+      return nil
     }
     
-    
-    public mutating func deleteItem(at index:Int) -> T
-    {
-        precondition((index >= 0) && (index < count))
-        
-        var previous: SinglyLinkedListNode<T>? = nil
-        var current = storageForWritting.head
-        var i = 0
-        var elementToDelete: SinglyLinkedListNode<T>
-        
-        while (i < index) {
-            previous = current
-            current = current?.next
-            i += 1
-        }
-        
-        // Current is now the element to delete (at index position.tag)
-        elementToDelete = current!
-        if (storage.head === current) {
-            storageForWritting.head = current?.next
-        }
-        
-        if (storage.tail === current) {
-            storageForWritting.tail = previous
-        }
-        
-        previous?.next = current?.next
-        
-        return elementToDelete.value
+    guard (node != nil) else {
+      return nil
     }
     
+    let i = (count - kthToLast)
     
-    
-    // MARK: SEARCH
-    
-    /// Returns the node located at the k-th to last position
-    ///
-    /// - Parameter kthToLast: 1 <= k <= N
-    private func find(kthToLast: UInt, startingAt node: SinglyLinkedListNode<T>?, count: UInt) -> SinglyLinkedListNode<T>?
-    {
-        guard kthToLast <= count else {
-            return nil
-        }
-        
-        guard (node != nil) else {
-            return nil
-        }
-        
-        let i = (count - kthToLast)
-        
-        if (i == 0) {
-            return node
-        }
-        
-        return find(kthToLast: kthToLast, startingAt: node?.next, count: (count - 1))
+    if (i == 0) {
+      return node
     }
     
-    
-    /// Returns the kth-to-last element in the list
-    ///
-    /// - Parameter kthToLast: Reversed ordinal number of the node to fetch.
-    public func find(kthToLast: UInt) -> SinglyLinkedListNode<T>?
-    {
-        return find(kthToLast: kthToLast, startingAt: storage.head, count: UInt(count))
-    }
+    return find(kthToLast: kthToLast, startingAt: node?.next, count: (count - 1))
+  }
+  
+  
+  /// Returns the kth-to-last element in the list
+  ///
+  /// - Parameter kthToLast: Reversed ordinal number of the node to fetch.
+  public func find(kthToLast: UInt) -> SinglyLinkedListNode<T>? {
+    return find(kthToLast: kthToLast, startingAt: storage.head, count: UInt(count))
+  }
     
 }
 
@@ -195,155 +187,146 @@ public struct SinglyLinkedList<T>
 
 private extension SinglyLinkedList {
     
-    /// Adds a new node to the current head. This method can easily break value semantics. It is left
-    /// for internal use.
-    ///
-    /// - Parameter node: the node that will be the new head of the list.
-    private mutating func prepend(node: SinglyLinkedListNode<T>)
-    {
-        let (tailFromNewNode, _) = findTail(in: node)
-        tailFromNewNode.next = storageForWritting.head
-        storageForWritting.head = node
-        
-        if storage.tail == nil {
-            storageForWritting.tail = tailFromNewNode
-        }
+  /// Adds a new node to the current head. This method can easily break value semantics. It is left
+  /// for internal use.
+  ///
+  /// - Parameter node: the node that will be the new head of the list.
+  private mutating func prepend(node: SinglyLinkedListNode<T>) {
+    let (tailFromNewNode, _) = findTail(in: node)
+    tailFromNewNode.next = storageForWritting.head
+    storageForWritting.head = node
+    
+    if storage.tail == nil {
+      storageForWritting.tail = tailFromNewNode
     }
-    
-    /// Appends a new node to the list. This method can easily break value semantics. It is left
-    /// for internal use.
-    /// - Discussion: If the node to be inserted contains a loop, the node is appended but tail is set to nil.
-    ///   This is a private method, therefore this can only happen directly under the control of this class.
-    /// - Parameter node: node to be appended. (It can be a list, even contain loops).
-    private mutating func append(node: SinglyLinkedListNode<T>)
-    {
-        if storage.tail != nil
-        {
-            // Copy on write: we are about to modify next a property in
-            // a potentially shared node. Make sure it's new if necessary.
-            storageForWritting.tail?.next = node
-            let (tail, _) = findTail(in: node)
-            storageForWritting.tail = tail // There
-        }
-        else
-        {
-            // This also means that there's no head.
-            // Otherwise the state would be inconsistent.
-            // This will be checked when adding and deleting nodes.
-            storageForWritting.head = node
-            let (tail, _) = findTail(in: node)
-            storageForWritting.tail = tail // There
-        }
+  }
+  
+  /// Appends a new node to the list. This method can easily break value semantics. It is left
+  /// for internal use.
+  /// - Discussion: If the node to be inserted contains a loop, the node is appended but tail is set to nil.
+  ///   This is a private method, therefore this can only happen directly under the control of this class.
+  /// - Parameter node: node to be appended. (It can be a list, even contain loops).
+  private mutating func append(node: SinglyLinkedListNode<T>) {
+    if storage.tail != nil {
+      // Copy on write: we are about to modify next a property in
+      // a potentially shared node. Make sure it's new if necessary.
+      storageForWritting.tail?.next = node
+      let (tail, _) = findTail(in: node)
+      storageForWritting.tail = tail // There
+    } else {
+      // This also means that there's no head.
+      // Otherwise the state would be inconsistent.
+      // This will be checked when adding and deleting nodes.
+      storageForWritting.head = node
+      let (tail, _) = findTail(in: node)
+      storageForWritting.tail = tail // There
+    }
+  }
+  
+  /// Creates a copy of the linked list in a diffent memory location.
+  ///
+  /// - Returns: The copy to a new storage or a reference to the old one if no copy was necessary.
+  private func copyStorage() -> IndirectStorage<T> {
+    // If the list is empty, next time an item will be created, it won't affect
+    // other instances of the list that came from copies derived from value types.
+    // like assignments or parameters
+    guard (storage.head != nil) && (storage.tail != nil) else {
+      return IndirectStorage(head: nil, tail: nil)
     }
     
-    /// Creates a copy of the linked list in a diffent memory location.
-    ///
-    /// - Returns: The copy to a new storage or a reference to the old one if no copy was necessary.
-    private func copyStorage() -> IndirectStorage<T> {
-        // If the list is empty, next time an item will be created, it won't affect
-        // other instances of the list that came from copies derived from value types.
-        // like assignments or parameters
-        guard (storage.head != nil) && (storage.tail != nil) else {
-            return IndirectStorage(head: nil, tail: nil)
-        }
-        
-        // Create a new position in memory.
-        // Note that we are shallow copying the value. If it was reference type
-        // we just make a copy of the reference.
-        let copiedHead = SinglyLinkedListNode<T>(value: storage.head!.value)
-        var previousCopied: SinglyLinkedListNode<T> = copiedHead
-        
-        // Iterate through current list of nodes and copy them.
-        var current: SinglyLinkedListNode<T>? = storage.head?.next
-        
-        while (current != nil) {
-            // Create a copy
-            let currentCopy = SinglyLinkedListNode<T>(value: current!.value)
-            
-            // Create links
-            previousCopied.next = currentCopy
-            
-            // Update pointers
-            current = current?.next
-            previousCopied = currentCopy
-        }
-        
-        return IndirectStorage(head: copiedHead, tail: previousCopied)
+    // Create a new position in memory.
+    // Note that we are shallow copying the value. If it was reference type
+    // we just make a copy of the reference.
+    let copiedHead = SinglyLinkedListNode<T>(value: storage.head!.value)
+    var previousCopied: SinglyLinkedListNode<T> = copiedHead
+    
+    // Iterate through current list of nodes and copy them.
+    var current: SinglyLinkedListNode<T>? = storage.head?.next
+    
+    while (current != nil) {
+      // Create a copy
+      let currentCopy = SinglyLinkedListNode<T>(value: current!.value)
+      
+      // Create links
+      previousCopied.next = currentCopy
+      
+      // Update pointers
+      current = current?.next
+      previousCopied = currentCopy
     }
+    
+    return IndirectStorage(head: copiedHead, tail: previousCopied)
+  }
 }
 
 
 
 // MARK:- Extensions when comparable
 
-extension SinglyLinkedList where T: Comparable
-{
-    /// Deletes node containing a given value
-    ///
-    /// - Parameter v: value of the node to be deleted.
-    public mutating func deleteNode(withValue v: T) {
-        
-        guard storage.head != nil else {
-            return
-        }
-        
-        var previous: SinglyLinkedListNode<T>? = nil
-        var current = storage.head
-        
-        while (current != nil) && (current?.value != v) {
-            previous = current
-            current = current?.next
-        }
-        
-        if let foundNode = current {
-            
-            if (storage.head === foundNode) {
-                storageForWritting.head = foundNode.next
-            }
-            
-            if (storage.tail === foundNode) {
-                storage.tail = previous
-            }
-            
-            previous?.next = foundNode.next
-            foundNode.next = nil
-        }
+extension SinglyLinkedList where T: Comparable {
+  /// Deletes node containing a given value
+  ///
+  /// - Parameter v: value of the node to be deleted.
+  public mutating func deleteNode(withValue v: T) {
+    
+    guard storage.head != nil else {
+      return
     }
     
+    var previous: SinglyLinkedListNode<T>? = nil
+    var current = storage.head
+    
+    while (current != nil) && (current?.value != v) {
+      previous = current
+      current = current?.next
+    }
     
-    /// Deletes duplicates without using additional structures like a set to keep track the visited nodes.
-    /// - Complexity: O(N^2)
-    public mutating func deleteDuplicatesInPlace()
-    {
-        // Copy on write: this updates storage if necessary.
-        var current = storageForWritting.head
-        
-        while (current != nil)
-        {
-            var previous: SinglyLinkedListNode<T>? = current
-            var next = current?.next
-            
-            while (next != nil)
-            {
-                if (current?.value == next?.value) {
-                    
-                    if (storage.head === next) {
-                        storage.head = next?.next
-                    }
-                    
-                    if (storage.tail === next) {
-                        storage.tail = previous
-                    }
-                    
-                    // Delete next
-                    previous?.next = next?.next
-                }
-                previous = next
-                next = next?.next
-            }
-            current = current?.next
+    if let foundNode = current {
+      
+      if (storage.head === foundNode) {
+        storageForWritting.head = foundNode.next
+      }
+      
+      if (storage.tail === foundNode) {
+        storage.tail = previous
+      }
+      
+      previous?.next = foundNode.next
+      foundNode.next = nil
+    }
+  }
+  
+  
+  /// Deletes duplicates without using additional structures like a set to keep track the visited nodes.
+  /// - Complexity: O(N^2)
+  public mutating func deleteDuplicatesInPlace() {
+    // Copy on write: this updates storage if necessary.
+    var current = storageForWritting.head
+    
+    while (current != nil) {
+      var previous: SinglyLinkedListNode<T>? = current
+      var next = current?.next
+      
+      while (next != nil) {
+        if (current?.value == next?.value) {
+          
+          if (storage.head === next) {
+            storage.head = next?.next
+          }
+          
+          if (storage.tail === next) {
+            storage.tail = previous
+          }
+          
+          // Delete next
+          previous?.next = next?.next
         }
+        previous = next
+        next = next?.next
+      }
+      current = current?.next
     }
+  }
 }
 
 
@@ -352,28 +335,25 @@ extension SinglyLinkedList where T: Comparable
 
 public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
     
-    public typealias Element = T
-    
-    private(set) var head: SinglyLinkedListNode<T>?
-    
-    mutating public func next() -> T?
-    {
-        let result = head?.value
-        head = head?.next
-        return result
-    }
+  public typealias Element = T
+  
+  private(set) var head: SinglyLinkedListNode<T>?
+  
+  mutating public func next() -> T? {
+    let result = head?.value
+    head = head?.next
+    return result
+  }
 }
 
 
 
 // MARK: - SEQUENCE -
 
-extension SinglyLinkedList : Sequence
-{
-    public func makeIterator() -> SinglyLinkedListForwardIterator<T>
-    {
-        return SinglyLinkedListForwardIterator(head: storage.head)
-    }
+extension SinglyLinkedList : Sequence {
+  public func makeIterator() -> SinglyLinkedListForwardIterator<T> {
+    return SinglyLinkedListForwardIterator(head: storage.head)
+  }
 }
 
 
@@ -382,117 +362,113 @@ extension SinglyLinkedList : Sequence
 
 extension SinglyLinkedList : Collection {
     
-    public typealias Index = SinglyLinkedListIndex<T>
-    
-    public var startIndex: Index {
-        get {
-            return SinglyLinkedListIndex<T>(node: storage.head, tag: 0)
-        }
-    }
-    
-    public var endIndex: Index {
-        get {
-            if let h = storage.head {
-                let (_, numberOfElements) = findTail(in: h)
-                return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
-            } else {
-                return SinglyLinkedListIndex<T>(node: nil, tag: startIndex.tag)
-            }
-        }
+  public typealias Index = SinglyLinkedListIndex<T>
+  
+  public var startIndex: Index {
+    get {
+      return SinglyLinkedListIndex<T>(node: storage.head, tag: 0)
     }
-    
-    public subscript(position: Index) -> T {
-        get {
-            return position.node!.value
-        }
+  }
+  
+  public var endIndex: Index {
+    get {
+      if let h = storage.head {
+        let (_, numberOfElements) = findTail(in: h)
+        return SinglyLinkedListIndex<T>(node: h, tag: numberOfElements)
+      } else {
+        return SinglyLinkedListIndex<T>(node: nil, tag: startIndex.tag)
+      }
     }
-    
-    public func index(after idx: Index) -> Index {
-        return SinglyLinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+  }
+  
+  public subscript(position: Index) -> T {
+    get {
+      return position.node!.value
     }
+  }
+  
+  public func index(after idx: Index) -> Index {
+    return SinglyLinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+  }
 }
 
 
 
 // MARK: - EXPRESSIBLE-BY-ARRAY-LITERAL -
 
-extension SinglyLinkedList : ExpressibleByArrayLiteral
-{
-    public typealias Element = T
-    
-    public init(arrayLiteral elements: Element...)
-    {
-        var headSet = false
-        var current : SinglyLinkedListNode<T>?
-        var numberOfElements = 0
-        storage = IndirectStorage()
-        
-        for element in elements {
-            
-            numberOfElements += 1
-            
-            if headSet == false {
-                storage.head = SinglyLinkedListNode<T>(value: element)
-                current = storage.head
-                headSet = true
-            } else {
-                let newNode = SinglyLinkedListNode<T>(value: element)
-                current?.next = newNode
-                current = newNode
-            }
-        }
-        storage.tail = current
+extension SinglyLinkedList : ExpressibleByArrayLiteral {
+  public typealias Element = T
+  
+  public init(arrayLiteral elements: Element...) {
+    var headSet = false
+    var current : SinglyLinkedListNode<T>?
+    var numberOfElements = 0
+    storage = IndirectStorage()
+    
+    for element in elements {
+      
+      numberOfElements += 1
+      
+      if headSet == false {
+        storage.head = SinglyLinkedListNode<T>(value: element)
+        current = storage.head
+        headSet = true
+      } else {
+        let newNode = SinglyLinkedListNode<T>(value: element)
+        current?.next = newNode
+        current = newNode
+      }
     }
+    storage.tail = current
+  }
 }
 
 
 
 // MARK: - FORWARD-INDEX -
 
-public struct SinglyLinkedListIndex<T> : Comparable
-{
-    fileprivate let node: SinglyLinkedListNode<T>?
-    fileprivate let tag: Int
-    
-    public static func==<T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
-        return (lhs.tag == rhs.tag)
-    }
-    
-    public static func< <T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
-        return (lhs.tag < rhs.tag)
-    }
+public struct SinglyLinkedListIndex<T> : Comparable {
+  fileprivate let node: SinglyLinkedListNode<T>?
+  fileprivate let tag: Int
+  
+  public static func==<T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+    return (lhs.tag == rhs.tag)
+  }
+  
+  public static func< <T>(lhs: SinglyLinkedListIndex<T>, rhs: SinglyLinkedListIndex<T>) -> Bool {
+    return (lhs.tag < rhs.tag)
+  }
 }
 
 
 extension SinglyLinkedList where T : KeyValuePair {
     
-    public func find(elementWithKey key: T.K) -> T? {
-        let searchResults = filter { (keyValuePair) -> Bool in
-            return keyValuePair.key == key
-        }
-        
-        return searchResults.first
+  public func find(elementWithKey key: T.K) -> T? {
+    let searchResults = filter { (keyValuePair) -> Bool in
+      return keyValuePair.key == key
     }
+    
+    return searchResults.first
+  }
 }
 
 // MARK: - HELPERS -
 
-func findTail<T>(in node: SinglyLinkedListNode<T>) -> (tail: SinglyLinkedListNode<T>, count: Int)
-{
-    // Assign the tail
-    // Note that the passed node can already be linking to other nodes,
-    // so the tail needs to be calculated.
-    var current: SinglyLinkedListNode<T>? = node
-    var count = 1
-    
-    while (current?.next != nil) {
-        current = current?.next
-        count += 1
-    }
-    
-    if current != nil {
-        return (tail: current!, count: count)
-    } else {
-        return (tail: node, count: 1)
-    }
+func findTail<T>(in node: SinglyLinkedListNode<T>) -> (tail: SinglyLinkedListNode<T>, count: Int) {
+  // Assign the tail
+  // Note that the passed node can already be linking to other nodes,
+  // so the tail needs to be calculated.
+  var current: SinglyLinkedListNode<T>? = node
+  var count = 1
+  
+  while (current?.next != nil) {
+    current = current?.next
+    count += 1
+  }
+  
+  if current != nil {
+    return (tail: current!, count: count)
+  } else {
+    return (tail: node, count: 1)
+  }
 }
diff --git a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift
index 50d354808..5ad8ffcc4 100644
--- a/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
+++ b/Singly Linked List/Tests/Tests/SinglyLinkedListTests.swift	
@@ -3,248 +3,247 @@ import XCTest
 
 class FindTailInNodeTests: XCTestCase {
     
-    func testExample() {
-        let n1 = SinglyLinkedListNode<Int>(value: 34)
-        let n2 = SinglyLinkedListNode<Int>(value: 35)
-        let n3 = SinglyLinkedListNode<Int>(value: 36)
-        let n4 = SinglyLinkedListNode<Int>(value: 37)
-        
-        n1.next = n2
-        n2.next = n3
-        n3.next = n4
-        
-        XCTAssertTrue(findTail(in: n1).tail === n4)
-        XCTAssertTrue(findTail(in: n2).tail === n4)
-        XCTAssertTrue(findTail(in: n4).tail === n4)
-        XCTAssertTrue(findTail(in: n4).tail === n4)
-    }
-    
+  func testExample() {
+    let n1 = SinglyLinkedListNode<Int>(value: 34)
+    let n2 = SinglyLinkedListNode<Int>(value: 35)
+    let n3 = SinglyLinkedListNode<Int>(value: 36)
+    let n4 = SinglyLinkedListNode<Int>(value: 37)
+    
+    n1.next = n2
+    n2.next = n3
+    n3.next = n4
+    
+    XCTAssertTrue(findTail(in: n1).tail === n4)
+    XCTAssertTrue(findTail(in: n2).tail === n4)
+    XCTAssertTrue(findTail(in: n4).tail === n4)
+    XCTAssertTrue(findTail(in: n4).tail === n4)
+  }
 }
 
 class SinglyLinkedListTests: XCTestCase {
     
-    func testAppendOneNodeFromEmptyList() {
-        var list = SinglyLinkedList<Int>()
-        list.append(value: 34)
-        XCTAssertTrue(list.first == 34)
-        XCTAssertTrue(list.count == 1, "Found \(list.count)")
-    }
-    
-    func testAppendMultipleNodesFromEmptyList() {
-        var list = SinglyLinkedList<Int>()
-        list.append(value: 34)
-        list.append(value: 35)
-        list.append(value: 36)
-        list.append(value: 34)
-        XCTAssertTrue(list.first == 34)
-        let second = list.index(list.startIndex, offsetBy: 1)
-        let third = list.index(list.startIndex, offsetBy: 2)
-        let fouth = list.index(list.startIndex, offsetBy: 3)
-        XCTAssertTrue(list[second] == 35)
-        XCTAssertTrue(list[third] == 36)
-        XCTAssertTrue(list[fouth] == 34)
-        XCTAssertTrue(list.count == 4, "Found \(list.count)")
-    }
-    
-    func testDelete() {
-        var list: SinglyLinkedList<Int> = [1]
-        list.append(value: 2)
-        list.append(value: 3)
-        list.append(value: 4)
-        list.append(value: 5)
-        
-        list.deleteNode(withValue: 1)
-        var second = list.index(list.startIndex, offsetBy: 1)
-        var third = list.index(list.startIndex, offsetBy: 2)
-        XCTAssertTrue(list.first == 2)
-        XCTAssertTrue(list[second] == 3)
-        XCTAssertTrue(list[third] == 4)
-        XCTAssertTrue(list.last == 5)
-        XCTAssertTrue(list.count == 4)
-        
-        list.deleteNode(withValue: 5)
-        second = list.index(list.startIndex, offsetBy: 1)
-        third = list.index(list.startIndex, offsetBy: 2)
-        XCTAssertTrue(list.first == 2)
-        XCTAssertTrue(list[second] == 3)
-        XCTAssertTrue(list.last == 4)
-        XCTAssertTrue(list.count == 3)
-        
-        list.deleteNode(withValue: 3)
-        XCTAssertTrue(list.first == 2)
-        XCTAssertTrue(list.last == 4)
-        XCTAssertTrue(list.count == 2)
-        
-        list.deleteNode(withValue: 2)
-        XCTAssertTrue(list.first == 4)
-        XCTAssertTrue(list.last == 4)
-        XCTAssertTrue(list.count == 1)
-        
-        list.deleteNode(withValue: 4)
-        XCTAssertTrue(list.first == nil)
-        XCTAssertTrue(list.last == nil)
-        XCTAssertTrue(list.count == 0)
-    }
-    
-    func testDeleteDuplicatesInPlace() {
-        var list: SinglyLinkedList<Int> = [1]
-        list.append(value: 2)
-        list.append(value: 2)
-        list.append(value: 3)
-        list.append(value: 5)
-        list.append(value: 2)
-        list.append(value: 4)
-        list.append(value: 2)
-        list.append(value: 5)
-        
-        list.deleteDuplicatesInPlace()
-        let second = list.index(list.startIndex, offsetBy: 1)
-        let third = list.index(list.startIndex, offsetBy: 2)
-        let fourth = list.index(list.startIndex, offsetBy: 3)
-        XCTAssertTrue(list.first == 1)
-        XCTAssertTrue(list[second] == 2)
-        XCTAssertTrue(list[third] == 3)
-        XCTAssertTrue(list[fourth] == 5)
-        XCTAssertTrue(list.last == 4)
-        XCTAssertTrue(list.count == 5)
-    }
-    
-    func testFindKthToLast() {
-        let list: SinglyLinkedList<Int> = [2,2,3,5,2,4,2,5]
-        XCTAssertTrue(list.find(kthToLast: 1)?.value == 5)
-        XCTAssertTrue(list.find(kthToLast: 2)?.value == 2)
-        XCTAssertTrue(list.find(kthToLast: 3)?.value == 4)
-        XCTAssertTrue(list.find(kthToLast: 4)?.value == 2)
-        XCTAssertTrue(list.find(kthToLast: 5)?.value == 5)
-        XCTAssertTrue(list.find(kthToLast: 6)?.value == 3)
-        XCTAssertTrue(list.find(kthToLast: 7)?.value == 2)
-        XCTAssertTrue(list.find(kthToLast: 8)?.value == 2)
-        XCTAssertTrue(list.find(kthToLast: 9)?.value == nil)
-    }
-    
-    func testConstructorFromArrayLiteralWhenEmpty() {
-        let list: SinglyLinkedList<Int> = []
-        XCTAssertTrue(list.first == nil)
-        XCTAssertTrue(list.last == nil)
-        XCTAssertTrue(list.count == 0, "Found \(list.count)")
-    }
-    
-    func testConstructorFromArrayLiteralWithSingleElement() {
-        let list: SinglyLinkedList<Int> = [5]
-        XCTAssertTrue(list.first == 5)
-        XCTAssertTrue(list.last == 5)
-        XCTAssertTrue(list.count == 1, "Found \(list.count)")
-    }
-    
-    func testAppendValue() {
-        var list = SinglyLinkedList<Int>()
-        list.append(value: 1)
-        list.append(value: 1)
-        list.append(value: 2)
-        list.append(value: 2)
-        list.append(value: 4)
-        
-        let result = string(from: list)
-        XCTAssertTrue(result == "11224", "Found \(result)")
-        XCTAssertTrue(list.count == 5, "Found \(list.count)")
-        XCTAssertTrue(list.last == 4, "Found \(String(describing: list.last))")
-    }
-    
-    func testPrependValue() {
-        var list = SinglyLinkedList<Int>()
-        list.prepend(value: 1)
-        list.prepend(value: 2)
-        list.prepend(value: 3)
-        list.prepend(value: 4)
-        list.prepend(value: 5)
-        list.prepend(value: 6)
-        
-        let result = string(from: list)
-        XCTAssertTrue(result == "654321", "Found \(result)")
-        XCTAssertTrue(list.count == 6, "Found \(list.count)")
-        XCTAssertTrue(list.last == 1, "Found \(String(describing: list.last))")
-    }
-    
-    func testDeleteHeadInListWithMultipleItems() {
-        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        
-        let _ = list.deleteItem(at: 0)
-        let result = string(from: list)
-        XCTAssertTrue(result == "2345678", "Found \(result)")
-        XCTAssertTrue(list.first == 2, "Found \(String(describing: list.first))")
-        XCTAssertTrue(list.count == 7, "Found \(list.count)")
-    }
-    
-    func testDeleteTailInListWithMultipleItems() {
-        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        
-        let _ = list.deleteItem(at: 7)
-        let result = string(from: list)
-        XCTAssertTrue(result == "1234567", "Found \(result)")
-        XCTAssertTrue(list.last == 7, "Found \(String(describing: list.last))")
-        XCTAssertTrue(list.count == 7, "Found \(list.count)")
-    }
-    
-    func testDeleteItemInListWithMultipleItems() {
-        var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        
-        let _ = list.deleteItem(at: 4)
-        let result = string(from: list)
-        XCTAssertTrue(result == "1234678", "Found \(result)")
-        XCTAssertTrue(list.first == 1, "Found \(String(describing: list.first))")
-        XCTAssertTrue(list.last == 8, "Found \(String(describing: list.last))")
-        XCTAssertTrue(list.count == 7, "Found \(list.count)")
-    }
-    
-    func testDeleteHeadInListWithSingleElement() {
-        var list: SinglyLinkedList<Int> = [1]
-        
-        let _ = list.deleteItem(at: 0)
-        let result = string(from: list)
-        XCTAssertTrue(result == "", "Found \(result)")
-        XCTAssertTrue(list.first == nil, "Found \(String(describing: list.first))")
-        XCTAssertTrue(list.last == nil, "Found \(String(describing: list.last))")
-        XCTAssertTrue(list.count == 0, "Found \(list.count)")
-    }
-    
-    func testDirectIndexAccess() {
-        let list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        let fifthElementIndex = list.index(list.startIndex, offsetBy: 5)
-        XCTAssertTrue(list[fifthElementIndex] == 6 ,  "Found \(list.count)")
-    }
-    
-    
-    func string(from list: SinglyLinkedList<Int>) -> String {
-        var result = ""
-        var iterator = list.makeIterator()
-        while let current = iterator.next() {
-            result += String(describing: current)
-        }
-        
-        return result
-    }
-    
-    func testCopyOnWriteUsingLiterals() {
-        var l1: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
-        l1.append(value: 0)
-        var l2 = l1
-        
-        _ = l2.deleteItem(at: 3)
-        XCTAssertTrue(l1.count == 9)
-        XCTAssertTrue(l2.count == 8)
-        
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        _ = l1.deleteItem(at: 0)
-        
-        XCTAssertTrue(l1.count == 0)
-        XCTAssertTrue(l2.count == 8)
-    }
+  func testAppendOneNodeFromEmptyList() {
+    var list = SinglyLinkedList<Int>()
+    list.append(value: 34)
+    XCTAssertTrue(list.first == 34)
+    XCTAssertTrue(list.count == 1, "Found \(list.count)")
+  }
+    
+  func testAppendMultipleNodesFromEmptyList() {
+    var list = SinglyLinkedList<Int>()
+    list.append(value: 34)
+    list.append(value: 35)
+    list.append(value: 36)
+    list.append(value: 34)
+    XCTAssertTrue(list.first == 34)
+    let second = list.index(list.startIndex, offsetBy: 1)
+    let third = list.index(list.startIndex, offsetBy: 2)
+    let fouth = list.index(list.startIndex, offsetBy: 3)
+    XCTAssertTrue(list[second] == 35)
+    XCTAssertTrue(list[third] == 36)
+    XCTAssertTrue(list[fouth] == 34)
+    XCTAssertTrue(list.count == 4, "Found \(list.count)")
+  }
+    
+  func testDelete() {
+    var list: SinglyLinkedList<Int> = [1]
+    list.append(value: 2)
+    list.append(value: 3)
+    list.append(value: 4)
+    list.append(value: 5)
+    
+    list.deleteNode(withValue: 1)
+    var second = list.index(list.startIndex, offsetBy: 1)
+    var third = list.index(list.startIndex, offsetBy: 2)
+    XCTAssertTrue(list.first == 2)
+    XCTAssertTrue(list[second] == 3)
+    XCTAssertTrue(list[third] == 4)
+    XCTAssertTrue(list.last == 5)
+    XCTAssertTrue(list.count == 4)
+    
+    list.deleteNode(withValue: 5)
+    second = list.index(list.startIndex, offsetBy: 1)
+    third = list.index(list.startIndex, offsetBy: 2)
+    XCTAssertTrue(list.first == 2)
+    XCTAssertTrue(list[second] == 3)
+    XCTAssertTrue(list.last == 4)
+    XCTAssertTrue(list.count == 3)
+    
+    list.deleteNode(withValue: 3)
+    XCTAssertTrue(list.first == 2)
+    XCTAssertTrue(list.last == 4)
+    XCTAssertTrue(list.count == 2)
+    
+    list.deleteNode(withValue: 2)
+    XCTAssertTrue(list.first == 4)
+    XCTAssertTrue(list.last == 4)
+    XCTAssertTrue(list.count == 1)
+    
+    list.deleteNode(withValue: 4)
+    XCTAssertTrue(list.first == nil)
+    XCTAssertTrue(list.last == nil)
+    XCTAssertTrue(list.count == 0)
+  }
+    
+  func testDeleteDuplicatesInPlace() {
+    var list: SinglyLinkedList<Int> = [1]
+    list.append(value: 2)
+    list.append(value: 2)
+    list.append(value: 3)
+    list.append(value: 5)
+    list.append(value: 2)
+    list.append(value: 4)
+    list.append(value: 2)
+    list.append(value: 5)
+    
+    list.deleteDuplicatesInPlace()
+    let second = list.index(list.startIndex, offsetBy: 1)
+    let third = list.index(list.startIndex, offsetBy: 2)
+    let fourth = list.index(list.startIndex, offsetBy: 3)
+    XCTAssertTrue(list.first == 1)
+    XCTAssertTrue(list[second] == 2)
+    XCTAssertTrue(list[third] == 3)
+    XCTAssertTrue(list[fourth] == 5)
+    XCTAssertTrue(list.last == 4)
+    XCTAssertTrue(list.count == 5)
+  }
+    
+  func testFindKthToLast() {
+    let list: SinglyLinkedList<Int> = [2,2,3,5,2,4,2,5]
+    XCTAssertTrue(list.find(kthToLast: 1)?.value == 5)
+    XCTAssertTrue(list.find(kthToLast: 2)?.value == 2)
+    XCTAssertTrue(list.find(kthToLast: 3)?.value == 4)
+    XCTAssertTrue(list.find(kthToLast: 4)?.value == 2)
+    XCTAssertTrue(list.find(kthToLast: 5)?.value == 5)
+    XCTAssertTrue(list.find(kthToLast: 6)?.value == 3)
+    XCTAssertTrue(list.find(kthToLast: 7)?.value == 2)
+    XCTAssertTrue(list.find(kthToLast: 8)?.value == 2)
+    XCTAssertTrue(list.find(kthToLast: 9)?.value == nil)
+  }
+    
+  func testConstructorFromArrayLiteralWhenEmpty() {
+    let list: SinglyLinkedList<Int> = []
+    XCTAssertTrue(list.first == nil)
+    XCTAssertTrue(list.last == nil)
+    XCTAssertTrue(list.count == 0, "Found \(list.count)")
+  }
+    
+  func testConstructorFromArrayLiteralWithSingleElement() {
+    let list: SinglyLinkedList<Int> = [5]
+    XCTAssertTrue(list.first == 5)
+    XCTAssertTrue(list.last == 5)
+    XCTAssertTrue(list.count == 1, "Found \(list.count)")
+  }
+  
+  func testAppendValue() {
+    var list = SinglyLinkedList<Int>()
+    list.append(value: 1)
+    list.append(value: 1)
+    list.append(value: 2)
+    list.append(value: 2)
+    list.append(value: 4)
+    
+    let result = string(from: list)
+    XCTAssertTrue(result == "11224", "Found \(result)")
+    XCTAssertTrue(list.count == 5, "Found \(list.count)")
+    XCTAssertTrue(list.last == 4, "Found \(String(describing: list.last))")
+  }
+    
+  func testPrependValue() {
+    var list = SinglyLinkedList<Int>()
+    list.prepend(value: 1)
+    list.prepend(value: 2)
+    list.prepend(value: 3)
+    list.prepend(value: 4)
+    list.prepend(value: 5)
+    list.prepend(value: 6)
+    
+    let result = string(from: list)
+    XCTAssertTrue(result == "654321", "Found \(result)")
+    XCTAssertTrue(list.count == 6, "Found \(list.count)")
+    XCTAssertTrue(list.last == 1, "Found \(String(describing: list.last))")
+  }
+    
+  func testDeleteHeadInListWithMultipleItems() {
+    var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+    
+    let _ = list.deleteItem(at: 0)
+    let result = string(from: list)
+    XCTAssertTrue(result == "2345678", "Found \(result)")
+    XCTAssertTrue(list.first == 2, "Found \(String(describing: list.first))")
+    XCTAssertTrue(list.count == 7, "Found \(list.count)")
+  }
+    
+  func testDeleteTailInListWithMultipleItems() {
+    var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+    
+    let _ = list.deleteItem(at: 7)
+    let result = string(from: list)
+    XCTAssertTrue(result == "1234567", "Found \(result)")
+    XCTAssertTrue(list.last == 7, "Found \(String(describing: list.last))")
+    XCTAssertTrue(list.count == 7, "Found \(list.count)")
+  }
+    
+  func testDeleteItemInListWithMultipleItems() {
+    var list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+    
+    let _ = list.deleteItem(at: 4)
+    let result = string(from: list)
+    XCTAssertTrue(result == "1234678", "Found \(result)")
+    XCTAssertTrue(list.first == 1, "Found \(String(describing: list.first))")
+    XCTAssertTrue(list.last == 8, "Found \(String(describing: list.last))")
+    XCTAssertTrue(list.count == 7, "Found \(list.count)")
+  }
+    
+  func testDeleteHeadInListWithSingleElement() {
+    var list: SinglyLinkedList<Int> = [1]
+    
+    let _ = list.deleteItem(at: 0)
+    let result = string(from: list)
+    XCTAssertTrue(result == "", "Found \(result)")
+    XCTAssertTrue(list.first == nil, "Found \(String(describing: list.first))")
+    XCTAssertTrue(list.last == nil, "Found \(String(describing: list.last))")
+    XCTAssertTrue(list.count == 0, "Found \(list.count)")
+  }
+    
+  func testDirectIndexAccess() {
+    let list: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+    let fifthElementIndex = list.index(list.startIndex, offsetBy: 5)
+    XCTAssertTrue(list[fifthElementIndex] == 6 ,  "Found \(list.count)")
+  }
+  
+  
+  func string(from list: SinglyLinkedList<Int>) -> String {
+    var result = ""
+    var iterator = list.makeIterator()
+    while let current = iterator.next() {
+        result += String(describing: current)
+    }
+    
+    return result
+  }
+  
+  func testCopyOnWriteUsingLiterals() {
+    var l1: SinglyLinkedList<Int> = [1,2,3,4,5,6,7,8]
+    l1.append(value: 0)
+    var l2 = l1
+  
+    _ = l2.deleteItem(at: 3)
+    XCTAssertTrue(l1.count == 9)
+    XCTAssertTrue(l2.count == 8)
+  
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+    _ = l1.deleteItem(at: 0)
+  
+    XCTAssertTrue(l1.count == 0)
+    XCTAssertTrue(l2.count == 8)
+  }
     
 }

From 15d277849385433a0cfdd2dff71eaaee5e0a9bda Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:50:27 +0100
Subject: [PATCH 133/643] Remove needless parenthesis in conditional statements
 to follow the repository's Swift Style Guide.

---
 Singly Linked List/SinglyLinkedList.swift | 26 +++++++++++------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index 4e088e195..e8fdfa32c 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -125,7 +125,7 @@ public struct SinglyLinkedList<T> {
     var i = 0
     var elementToDelete: SinglyLinkedListNode<T>
     
-    while (i < index) {
+    while i < index {
       previous = current
       current = current?.next
       i += 1
@@ -133,11 +133,11 @@ public struct SinglyLinkedList<T> {
     
     // Current is now the element to delete (at index position.tag)
     elementToDelete = current!
-    if (storage.head === current) {
+    if storage.head === current {
       storageForWritting.head = current?.next
     }
     
-    if (storage.tail === current) {
+    if storage.tail === current {
       storageForWritting.tail = previous
     }
     
@@ -164,7 +164,7 @@ public struct SinglyLinkedList<T> {
     
     let i = (count - kthToLast)
     
-    if (i == 0) {
+    if i == 0 {
       return node
     }
     
@@ -243,7 +243,7 @@ private extension SinglyLinkedList {
     // Iterate through current list of nodes and copy them.
     var current: SinglyLinkedListNode<T>? = storage.head?.next
     
-    while (current != nil) {
+    while current != nil {
       // Create a copy
       let currentCopy = SinglyLinkedListNode<T>(value: current!.value)
       
@@ -283,11 +283,11 @@ extension SinglyLinkedList where T: Comparable {
     
     if let foundNode = current {
       
-      if (storage.head === foundNode) {
+      if storage.head === foundNode {
         storageForWritting.head = foundNode.next
       }
       
-      if (storage.tail === foundNode) {
+      if storage.tail === foundNode {
         storage.tail = previous
       }
       
@@ -303,18 +303,18 @@ extension SinglyLinkedList where T: Comparable {
     // Copy on write: this updates storage if necessary.
     var current = storageForWritting.head
     
-    while (current != nil) {
+    while current != nil {
       var previous: SinglyLinkedListNode<T>? = current
       var next = current?.next
       
-      while (next != nil) {
-        if (current?.value == next?.value) {
+      while next != nil {
+        if current?.value == next?.value {
           
-          if (storage.head === next) {
+          if storage.head === next {
             storage.head = next?.next
           }
           
-          if (storage.tail === next) {
+          if storage.tail === next {
             storage.tail = previous
           }
           
@@ -461,7 +461,7 @@ func findTail<T>(in node: SinglyLinkedListNode<T>) -> (tail: SinglyLinkedListNod
   var current: SinglyLinkedListNode<T>? = node
   var count = 1
   
-  while (current?.next != nil) {
+  while current?.next != nil {
     current = current?.next
     count += 1
   }

From 06d29b77f9399c813e08bc7ae2d65514779c37fc Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:53:38 +0100
Subject: [PATCH 134/643] Remove custom iterator
 SinglyLinkedListForwardIterator to rely on the default implementation
 provided by Collection.

---
 Singly Linked List/SinglyLinkedList.swift | 27 -----------------------
 1 file changed, 27 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index e8fdfa32c..faf25b255 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -331,33 +331,6 @@ extension SinglyLinkedList where T: Comparable {
 
 
 
-// MARK: - ITERATOR -
-
-public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
-    
-  public typealias Element = T
-  
-  private(set) var head: SinglyLinkedListNode<T>?
-  
-  mutating public func next() -> T? {
-    let result = head?.value
-    head = head?.next
-    return result
-  }
-}
-
-
-
-// MARK: - SEQUENCE -
-
-extension SinglyLinkedList : Sequence {
-  public func makeIterator() -> SinglyLinkedListForwardIterator<T> {
-    return SinglyLinkedListForwardIterator(head: storage.head)
-  }
-}
-
-
-
 // MARK: - COLLECTION -
 
 extension SinglyLinkedList : Collection {

From 745cc1a87adc21fc99de34b4c19a0f5ad2cc24e6 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 11:56:24 +0100
Subject: [PATCH 135/643] Remove SinglyLinkedList's initializer that takes a
 value as an argument, to rely exclusively on mutating methods to edit the
 list.

---
 Singly Linked List/SinglyLinkedList.swift | 9 ---------
 1 file changed, 9 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.swift b/Singly Linked List/SinglyLinkedList.swift
index faf25b255..67e30eb7d 100644
--- a/Singly Linked List/SinglyLinkedList.swift	
+++ b/Singly Linked List/SinglyLinkedList.swift	
@@ -82,15 +82,6 @@ public struct SinglyLinkedList<T> {
   
   // MARK: INITIALIZERS
   
-  /// Creates a list with a single element
-  ///
-  /// - Parameter value: element to populate the list with
-  public init(value: T) {
-    self.init()
-    self.append(value: value)
-  }
-  
-  
   /// Creates an empty list
   public init() {
     self.storage = IndirectStorage()

From d01e3b312fcbafc26f6ac96b6ee9d80fad00a948 Mon Sep 17 00:00:00 2001
From: Alejandro Isaza <al@isaza.ca>
Date: Sun, 6 Aug 2017 10:45:25 -0700
Subject: [PATCH 136/643] Style fixes

---
 Hashed Heap/HashedHeap.swift | 36 ++++++++++++++++++------------------
 1 file changed, 18 insertions(+), 18 deletions(-)

diff --git a/Hashed Heap/HashedHeap.swift b/Hashed Heap/HashedHeap.swift
index f123bbc54..db4278a36 100644
--- a/Hashed Heap/HashedHeap.swift	
+++ b/Hashed Heap/HashedHeap.swift	
@@ -31,13 +31,13 @@ public struct HashedHeap<T: Hashable> {
     /// - Complexity: O(n)
     public init(array: [T], sort: @escaping (T, T) -> Bool) {
         isOrderedBefore = sort
-        buildHeap(fromArray: array)
+        build(from: array)
     }
 
     /// Converts an array to a max-heap or min-heap in a bottom-up manner.
     ///
     /// - Complexity: O(n)
-    private mutating func buildHeap(fromArray array: [T]) {
+    private mutating func build(from array: [T]) {
         elements = array
         for index in elements.indices {
             indices[elements[index]] = index
@@ -96,12 +96,12 @@ public struct HashedHeap<T: Hashable> {
     /// Replaces an element in the hash.
     ///
     /// In a max-heap, the new element should be larger than the old one; in a min-heap it should be smaller.
-    public mutating func replace(index i: Int, value: T) {
-        guard i < elements.count else { return }
+    public mutating func replace(_ value: T, at index: Int) {
+        guard index < elements.count else { return }
 
-        assert(isOrderedBefore(value, elements[i]))
-        set(value, at: i)
-        shiftUp(i)
+        assert(isOrderedBefore(value, elements[index]))
+        set(value, at: index)
+        shiftUp(index)
     }
 
     /// Removes the root node from the heap.
@@ -130,7 +130,7 @@ public struct HashedHeap<T: Hashable> {
     /// You need to know the node's index, which may actually take O(n) steps to find.
     ///
     /// - Complexity: O(log n).
-    public mutating func removeAt(_ index: Int) -> T? {
+    public mutating func remove(at index: Int) -> T? {
         guard index < elements.count else { return nil }
 
         let size = elements.count - 1
@@ -158,12 +158,12 @@ public struct HashedHeap<T: Hashable> {
     mutating func shiftUp(_ index: Int) {
         var childIndex = index
         let child = elements[childIndex]
-        var parentIndex = self.parentIndex(ofIndex: childIndex)
+        var parentIndex = self.parentIndex(of: childIndex)
 
         while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
             set(elements[parentIndex], at: childIndex)
             childIndex = parentIndex
-            parentIndex = self.parentIndex(ofIndex: childIndex)
+            parentIndex = self.parentIndex(of: childIndex)
         }
 
         set(child, at: childIndex)
@@ -178,7 +178,7 @@ public struct HashedHeap<T: Hashable> {
         var parentIndex = index
 
         while true {
-            let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
+            let leftChildIndex = self.leftChildIndex(of: parentIndex)
             let rightChildIndex = leftChildIndex + 1
 
             // Figure out which comes first if we order them by the sort function:
@@ -208,7 +208,7 @@ public struct HashedHeap<T: Hashable> {
 
     /// Swap two elements in the heap and update the indices hash.
     private mutating func swapAt(_ i: Int, _ j: Int) {
-        swap(&elements[i], &elements[j])
+        elements.swapAt(i, j)
         indices[elements[i]] = i
         indices[elements[j]] = j
     }
@@ -217,23 +217,23 @@ public struct HashedHeap<T: Hashable> {
     ///
     /// - Note: The element at index 0 is the root of the tree and has no parent.
     @inline(__always)
-    func parentIndex(ofIndex i: Int) -> Int {
-        return (i - 1) / 2
+    func parentIndex(of index: Int) -> Int {
+        return (index - 1) / 2
     }
 
     /// Returns the index of the left child of the element at index i.
     ///
     /// - Note: this index can be greater than the heap size, in which case there is no left child.
     @inline(__always)
-    func leftChildIndex(ofIndex i: Int) -> Int {
-        return 2*i + 1
+    func leftChildIndex(of index: Int) -> Int {
+        return 2*index + 1
     }
 
     /// Returns the index of the right child of the element at index i.
     ///
     /// - Note: this index can be greater than the heap size, in which case there is no right child.
     @inline(__always)
-    func rightChildIndex(ofIndex i: Int) -> Int {
-        return 2*i + 2
+    func rightChildIndex(of index: Int) -> Int {
+        return 2*index + 2
     }
 }

From 3ef6ef4a520b62bea0aa713be96eba0eb1d490b2 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 20:14:49 +0100
Subject: [PATCH 137/643] Add conformance to Collection protocol for LinkedList
 class.

---
 .../LinkedList.playground/Contents.swift      | 63 ++++++++++++++++++
 Linked List/LinkedList.swift                  | 54 +++++++++++++++
 Linked List/README.markdown                   | 66 +++++++++++++++++++
 Linked List/Tests/LinkedListTests.swift       |  8 +++
 4 files changed, 191 insertions(+)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index b78ee4809..ed3de41be 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -317,6 +317,61 @@ extension LinkedList: ExpressibleByArrayLiteral {
   }
 }
 
+// MARK: - Collection
+extension LinkedList : Collection {
+  
+  public typealias Index = LinkedListIndex<T>
+  
+  /// The position of the first element in a nonempty collection.
+  ///
+  /// If the collection is empty, `startIndex` is equal to `endIndex`.
+  /// - Complexity: O(1)
+  public var startIndex: Index {
+    get {
+      return LinkedListIndex<T>(node: head, tag: 0)
+    }
+  }
+  
+  /// The collection's "past the end" position---that is, the position one
+  /// greater than the last valid subscript argument.
+  /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
+  ///   to the last node in the collection.
+  public var endIndex: Index {
+    get {
+      if let h = self.head {
+        return LinkedListIndex<T>(node: h, tag: count)
+      } else {
+        return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
+      }
+    }
+  }
+  
+  public subscript(position: Index) -> T {
+    get {
+      return position.node!.value
+    }
+  }
+  
+  public func index(after idx: Index) -> Index {
+    return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+  }
+}
+
+// MARK: - Collection Index
+/// Custom index type that contains a reference to the node at index 'tag'
+public struct LinkedListIndex<T> : Comparable
+{
+  fileprivate let node: LinkedList<T>.LinkedListNode<T>?
+  fileprivate let tag: Int
+  
+  public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag == rhs.tag)
+  }
+  
+  public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag < rhs.tag)
+  }
+}
 //: Ok, now that the declarations are done, let's see our Linked List in action:
 let list = LinkedList<String>()
 list.isEmpty                  // true
@@ -392,3 +447,11 @@ let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
 listArrayLiteral2.count        // 3
 listArrayLiteral2[0]           // "Swift"
 listArrayLiteral2.removeLast()  // "Club"
+
+
+// Conformance to the Collection protocol
+let collection: LinkedList<Int> = [1, 2, 3, 4, 5]
+let index2 = collection.index(collection.startIndex, offsetBy: 2)
+let value = collection[index2] // 3
+
+
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 94e978c07..f51064e01 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -244,3 +244,57 @@ extension LinkedList: ExpressibleByArrayLiteral {
     }
   }
 }
+
+extension LinkedList : Collection {
+  
+  public typealias Index = LinkedListIndex<T>
+  
+  /// The position of the first element in a nonempty collection.
+  ///
+  /// If the collection is empty, `startIndex` is equal to `endIndex`.
+  /// - Complexity: O(1)
+  public var startIndex: Index {
+    get {
+      return LinkedListIndex<T>(node: head, tag: 0)
+    }
+  }
+  
+  /// The collection's "past the end" position---that is, the position one
+  /// greater than the last valid subscript argument.
+  /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
+  ///   to the last node in the collection.
+  public var endIndex: Index {
+    get {
+      if let h = self.head {
+        return LinkedListIndex<T>(node: h, tag: count)
+      } else {
+        return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
+      }
+    }
+  }
+  
+  public subscript(position: Index) -> T {
+    get {
+      return position.node!.value
+    }
+  }
+  
+  public func index(after idx: Index) -> Index {
+    return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+  }
+}
+
+/// Custom index type that contains a reference to the node at index 'tag'
+public struct LinkedListIndex<T> : Comparable
+{
+  fileprivate let node: LinkedList<T>.LinkedListNode<T>?
+  fileprivate let tag: Int
+  
+  public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag == rhs.tag)
+  }
+  
+  public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag < rhs.tag)
+  }
+}
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index c03023c42..f1b1a2480 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -535,6 +535,72 @@ The big difference with the class-based version is that any modification you mak
 
 [I might fill out this section in more detail if there's a demand for it.]
 
+## Conforming to the Collection protocol
+Types that conform to the Sequence protocol, whose elements can be traversed multiple times, nondestructively, and accessed by indexed subscript should conform to the Collection protocol defined in Swift's Standard Library.
+
+Doing so grants access to a very large number of properties and operations that are common when dealing collections of data. In addition to this, it lets custom types follow the patterns that are common to Swift developers.
+
+In order to conform to this protocol, classes need to provide:
+  1 `startIndex` and `endIndex` properties.
+  2 Subscript access to elements as O(1). Diversions of this time complexity need to be documented.
+  
+```swift
+/// The position of the first element in a nonempty collection.
+public var startIndex: Index {
+  get {
+    return LinkedListIndex<T>(node: head, tag: 0)
+  }
+}
+  
+/// The collection's "past the end" position---that is, the position one
+/// greater than the last valid subscript argument.
+/// - Complexity: O(n), where n is the number of elements in the list.
+///   This diverts from the protocol's expectation.
+public var endIndex: Index {
+  get {
+    if let h = self.head {
+      return LinkedListIndex<T>(node: h, tag: count)
+    } else {
+      return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
+    }
+  }
+}
+```
+
+```swift
+public subscript(position: Index) -> T {
+  get {
+    return position.node!.value
+  }
+}
+```
+
+Becuase collections are responsible for managing their own indexes, the implementation below keeps a reference to a node in the list. A tag property in the index represents the position of the node in the list.
+
+```swift
+/// Custom index type that contains a reference to the node at index 'tag'
+public struct LinkedListIndex<T> : Comparable
+{
+  fileprivate let node: LinkedList<T>.LinkedListNode<T>?
+  fileprivate let tag: Int
+
+  public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag == rhs.tag)
+  }
+
+  public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+    return (lhs.tag < rhs.tag)
+  }
+}
+```
+
+Finally, the linked is is able to calculate the index after a given one with the following implementation.
+```swift
+public func index(after idx: Index) -> Index {
+  return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
+}
+```
+
 ## Some things to keep in mind
 
 Linked lists are flexible but many operations are **O(n)**.
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 0b2b116df..bc9831a41 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -337,4 +337,12 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(arrayLiteralInitExplicit.removeLast(), 3)
     XCTAssertEqual(arrayLiteralInitExplicit.count, 2)
   }
+  
+  func testConformanceToCollectionProtocol() {
+    let collection: LinkedList<Int> = [1, 2, 3, 4, 5]
+    let index2 = collection.index(collection.startIndex, offsetBy: 2)
+    let value = collection[index2]
+    
+    XCTAssertTrue(value == 3)
+  }
 }

From c76252a5b5dfeccaf7f96bbbf99583e2a08b3980 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 20:17:21 +0100
Subject: [PATCH 138/643] Remove queue example from playground as
 implementation was removed.

---
 .../SinglyLinkedList.playground/Contents.swift  | 17 -----------------
 1 file changed, 17 deletions(-)

diff --git a/Singly Linked List/SinglyLinkedList.playground/Contents.swift b/Singly Linked List/SinglyLinkedList.playground/Contents.swift
index fc6acf9dc..d9104ebe7 100644
--- a/Singly Linked List/SinglyLinkedList.playground/Contents.swift	
+++ b/Singly Linked List/SinglyLinkedList.playground/Contents.swift	
@@ -725,20 +725,3 @@ assert(l2.contains(67) == true)
 let l3 = l2.dropLast()
 assert(l3.count == 7)
 assert(l3.contains(67) == false)
-
-//: We can use this class as a queue.
-
-func empty<Q: Queue>(queue: inout Q) {
-    while let _ = queue.dequeue() {}
-}
-
-var q: SinglyLinkedList<Int> = [5,1,2,3]
-empty(queue: &q)
-assert(q.count == 0)
-
-try? q.enqueue(item: 1)
-try? q.enqueue(item: 3)
-try? q.enqueue(item: 5)
-assert(q.count == 3)
-
-

From f5678857ca24a9c1403a5f721d62e73ef90e64c3 Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 20:23:17 +0100
Subject: [PATCH 139/643] Fix styling issue; Parentheses on new line.

---
 Linked List/LinkedList.playground/Contents.swift | 3 +--
 Linked List/LinkedList.swift                     | 3 +--
 2 files changed, 2 insertions(+), 4 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index ed3de41be..7805d4a37 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -359,8 +359,7 @@ extension LinkedList : Collection {
 
 // MARK: - Collection Index
 /// Custom index type that contains a reference to the node at index 'tag'
-public struct LinkedListIndex<T> : Comparable
-{
+public struct LinkedListIndex<T> : Comparable {
   fileprivate let node: LinkedList<T>.LinkedListNode<T>?
   fileprivate let tag: Int
   
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index f51064e01..e7e2c714e 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -285,8 +285,7 @@ extension LinkedList : Collection {
 }
 
 /// Custom index type that contains a reference to the node at index 'tag'
-public struct LinkedListIndex<T> : Comparable
-{
+public struct LinkedListIndex<T> : Comparable {
   fileprivate let node: LinkedList<T>.LinkedListNode<T>?
   fileprivate let tag: Int
   

From 5570a711df3d1bc79ce921bd94fe2b9365e141ad Mon Sep 17 00:00:00 2001
From: Borja Arias Drake <borja.arias@gmail.com>
Date: Sun, 6 Aug 2017 20:32:55 +0100
Subject: [PATCH 140/643] Add two examples of Sequence methods gained through
 the conformance to Collection protocol.

---
 Linked List/LinkedList.playground/Contents.swift | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 7805d4a37..ef70c561b 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -453,4 +453,16 @@ let collection: LinkedList<Int> = [1, 2, 3, 4, 5]
 let index2 = collection.index(collection.startIndex, offsetBy: 2)
 let value = collection[index2] // 3
 
+// Iterating in a for loop, since the Sequence protocol allows this.
+var sum = 0
+for element in collection {
+  sum += element
+}
+// sum is 15
+
+// Another way of achieving the same result though 'reduce', another method defined in an extension of Sequence. Collections are Sequences.
+let result = collection.reduce(0) {$0 + $1} // 15
+
+
+
 

From 18a46e78b7e8cb37bf9643368ac5cb5173565832 Mon Sep 17 00:00:00 2001
From: Alessandro Martin <martin.acg@gmail.com>
Date: Sun, 6 Aug 2017 21:28:31 +0100
Subject: [PATCH 141/643] Added array private extension to wrap indexes, added
 Sequence conformance, simplified read and write implementations, nilling out
 value when reading.

---
 .../RingBuffer.playground/Contents.swift      | 48 +++++++++++++------
 Ring Buffer/RingBuffer.swift                  | 48 ++++++++++++-------
 2 files changed, 65 insertions(+), 31 deletions(-)

diff --git a/Ring Buffer/RingBuffer.playground/Contents.swift b/Ring Buffer/RingBuffer.playground/Contents.swift
index 29b9917a0..d1195e102 100644
--- a/Ring Buffer/RingBuffer.playground/Contents.swift	
+++ b/Ring Buffer/RingBuffer.playground/Contents.swift	
@@ -9,24 +9,20 @@ public struct RingBuffer<T> {
     array = [T?](repeating: nil, count: count)
   }
 
+  /* Returns false if out of space. */
+  @discardableResult
   public mutating func write(_ element: T) -> Bool {
-    if !isFull {
-      array[writeIndex % array.count] = element
-      writeIndex += 1
-      return true
-    } else {
-      return false
-    }
+    guard !isFull else { return false }
+    defer { writeIndex += 1 }
+    array[wrapped: writeIndex] = element
+    return true
   }
-
+    
+  /* Returns nil if the buffer is empty. */
   public mutating func read() -> T? {
-    if !isEmpty {
-      let element = array[readIndex % array.count]
-      readIndex += 1
-      return element
-    } else {
-      return nil
-    }
+    guard !isEmpty else { return nil }
+    defer { array[wrapped: readIndex] = nil ; readIndex += 1 }
+    return array[wrapped: readIndex]
   }
 
   fileprivate var availableSpaceForReading: Int {
@@ -46,6 +42,28 @@ public struct RingBuffer<T> {
   }
 }
 
+extension RingBuffer: Sequence {
+  public func makeIterator() -> AnyIterator<T> {
+    var index = readIndex
+    return AnyIterator {
+      guard index < self.writeIndex else { return nil }
+      defer { index += 1 }
+      return self.array[wrapped: index]
+    }
+  }
+}
+
+private extension Array {
+  subscript (wrapped index: Int) -> Element {
+    get {
+      return self[index % count]
+    }
+    set {
+      self[index % count] = newValue
+    }
+  }
+}
+
 var buffer = RingBuffer<Int>(count: 5)
 buffer.array          // [nil, nil, nil, nil, nil]
 buffer.readIndex      // 0
diff --git a/Ring Buffer/RingBuffer.swift b/Ring Buffer/RingBuffer.swift
index 7e845aa74..7dd0d6fc3 100644
--- a/Ring Buffer/RingBuffer.swift	
+++ b/Ring Buffer/RingBuffer.swift	
@@ -16,29 +16,23 @@ public struct RingBuffer<T> {
   private var writeIndex = 0
 
   public init(count: Int) {
-    array = [T?](count: count, repeatedValue: nil)
+    array = [T?](repeating: nil, count: count)
   }
 
   /* Returns false if out of space. */
-  public mutating func write(element: T) -> Bool {
-    if !isFull {
-      array[writeIndex % array.count] = element
-      writeIndex += 1
-      return true
-    } else {
-      return false
-    }
+  @discardableResult
+  public mutating func write(_ element: T) -> Bool {
+    guard !isFull else { return false }
+    defer { writeIndex += 1 }
+    array[wrapped: writeIndex] = element
+    return true
   }
 
   /* Returns nil if the buffer is empty. */
   public mutating func read() -> T? {
-    if !isEmpty {
-      let element = array[readIndex % array.count]
-      readIndex += 1
-      return element
-    } else {
-      return nil
-    }
+    guard !isEmpty else { return nil }
+    defer { array[wrapped: readIndex] = nil ; readIndex += 1 }
+    return array[wrapped: readIndex]
   }
 
   private var availableSpaceForReading: Int {
@@ -57,3 +51,25 @@ public struct RingBuffer<T> {
     return availableSpaceForWriting == 0
   }
 }
+
+public extension RingBuffer: Sequence {
+  public func makeIterator() -> AnyIterator<T> {
+    var index = readIndex
+    return AnyIterator {
+        guard index < self.writeIndex else { return nil }
+        defer { index += 1 }
+        return self.array[wrapped: index]
+    }
+  }
+}
+
+private extension Array {
+  subscript (wrapped index: Int) -> Element {
+    get {
+      return self[index % count]
+    }
+    set {
+      self[index % count] = newValue
+    }
+  }
+}

From a40da8c0424635da3f8ea393668fe08f44cc268e Mon Sep 17 00:00:00 2001
From: Ishaan Sejwal <ishaan211991@gmail.com>
Date: Tue, 8 Aug 2017 17:23:05 +0530
Subject: [PATCH 142/643] Improved description [skip ci]

---
 Array2D/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index 88f25c99a..cf00638e1 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -33,7 +33,7 @@ You can also create the array in a single line of code:
 var cookies = [[Int]](repeating: [Int](repeating: 0, count: 7), count: 9)
 ```
 
-This looks complicated, but can simplfy it in a helper function:
+This looks complicated, but you can simplify it with a helper function:
 
 ```swift
 func dim<T>(_ count: Int, _ value: T) -> [T] {

From f5a8485b5fb3f4588306e7efb5c95cd9957c9931 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:19:46 +0900
Subject: [PATCH 143/643] Applies Xcode 9 b4 changes to Hashed Heap test
 xcodeproj

---
 .../project.pbxproj                           | 22 +++++++++++++++----
 .../xcschemes/Hashed Heap Tests.xcscheme      |  2 +-
 2 files changed, 19 insertions(+), 5 deletions(-)

diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj
index 87791f04d..ae1904884 100644
--- a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj	
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj	
@@ -82,12 +82,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 0900;
 					};
 				};
 			};
@@ -140,14 +140,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -186,14 +192,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -225,7 +237,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -237,7 +250,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme
index 406c8dd2e..3f298101d 100644
--- a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme	
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/xcshareddata/xcschemes/Hashed Heap Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 15ca8aff43cde029018a70675059ba26e6966398 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:27:40 +0900
Subject: [PATCH 144/643] Turns automatic objc inference to default (off) for
 the Hashed Heap.

---
 .../Tests/Hashed Heap Tests.xcodeproj/project.pbxproj       | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj
index ae1904884..01f5fae50 100644
--- a/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj	
+++ b/Hashed Heap/Tests/Hashed Heap Tests.xcodeproj/project.pbxproj	
@@ -181,6 +181,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 			};
 			name = Debug;
 		};
@@ -226,6 +227,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 			};
 			name = Release;
 		};
@@ -237,7 +239,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
@@ -250,7 +252,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.0;
 			};
 			name = Release;

From 864c16cd6a79877fda59440109ab190432f132bd Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:28:38 +0900
Subject: [PATCH 145/643] Fixes some spelling errors.

---
 Hashed Heap/HashedHeap.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Hashed Heap/HashedHeap.swift b/Hashed Heap/HashedHeap.swift
index db4278a36..ac8035057 100644
--- a/Hashed Heap/HashedHeap.swift	
+++ b/Hashed Heap/HashedHeap.swift	
@@ -3,8 +3,8 @@
 /// Heap with an index hash map (dictionary) to speed up lookups by value.
 ///
 /// A heap keeps elements ordered in a binary tree without the use of pointers. A hashed heap does that as well as
-/// having amortized constant lookups by value. This is used in the A* and other heuristic search alogirhtms to achieve
-/// optimal perfomrance.
+/// having amortized constant lookups by value. This is used in the A* and other heuristic search algorithms to achieve
+/// optimal performance.
 public struct HashedHeap<T: Hashable> {
     /// The array that stores the heap's nodes.
     private(set) var elements = [T]()

From 0a73a1402a3675f6268a0e0eaf3c19b64f30ce6c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:31:19 +0900
Subject: [PATCH 146/643] Adds credit footer.

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

diff --git a/Hashed Heap/README.markdown b/Hashed Heap/README.markdown
index 48fe312ab..8a4fece02 100644
--- a/Hashed Heap/README.markdown	
+++ b/Hashed Heap/README.markdown	
@@ -9,3 +9,5 @@ See [HashedHeap.swift](HashedHeap.swift) for the implementation. See [Heap](../H
 ## See also
 
 [Heap on Wikipedia](https://en.wikipedia.org/wiki/Heap_%28data_structure%29)
+
+*Written for the Swift Algorithm Club by [Alejandro Isaza](https://github.com/aleph7)*

From 0055ab0e88e95200ba45c8b07f9e0946c3e7bdd3 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:33:34 +0900
Subject: [PATCH 147/643] Added if check for Swift 4

---
 Hashed Heap/Tests/HashedHeapTests.swift | 168 +++++++++++++-----------
 1 file changed, 88 insertions(+), 80 deletions(-)

diff --git a/Hashed Heap/Tests/HashedHeapTests.swift b/Hashed Heap/Tests/HashedHeapTests.swift
index 6badb4ec5..895a21c63 100755
--- a/Hashed Heap/Tests/HashedHeapTests.swift	
+++ b/Hashed Heap/Tests/HashedHeapTests.swift	
@@ -2,87 +2,95 @@ import Foundation
 import XCTest
 
 private struct Message: Hashable {
-    let text: String
-    let priority: Int
-
-    var hashValue: Int {
-        return text.hashValue
-    }
-
-    static func == (lhs: Message, rhs: Message) -> Bool {
-        return lhs.text == rhs.text
-    }
-
-    static func < (m1: Message, m2: Message) -> Bool {
-        return m1.priority < m2.priority
-    }
+  let text: String
+  let priority: Int
+  
+  var hashValue: Int {
+    return text.hashValue
+  }
+  
+  static func == (lhs: Message, rhs: Message) -> Bool {
+    return lhs.text == rhs.text
+  }
+  
+  static func < (m1: Message, m2: Message) -> Bool {
+    return m1.priority < m2.priority
+  }
 }
 
 class HashedHeapTest: XCTestCase {
-    func testEmpty() {
-        var queue = HashedHeap<Message>(sort: <)
-        XCTAssertTrue(queue.isEmpty)
-        XCTAssertEqual(queue.count, 0)
-        XCTAssertNil(queue.peek())
-        XCTAssertNil(queue.remove())
-    }
-
-    func testOneElement() {
-        var queue = HashedHeap<Message>(sort: <)
-
-        queue.insert(Message(text: "hello", priority: 100))
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 1)
-        XCTAssertEqual(queue.peek()!.priority, 100)
-
-        let result = queue.remove()
-        XCTAssertEqual(result!.priority, 100)
-        XCTAssertTrue(queue.isEmpty)
-        XCTAssertEqual(queue.count, 0)
-        XCTAssertNil(queue.peek())
-    }
-
-    func testTwoElementsInOrder() {
-        var queue = HashedHeap<Message>(sort: <)
-
-        queue.insert(Message(text: "hello", priority: 100))
-        queue.insert(Message(text: "world", priority: 200))
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 2)
-        XCTAssertEqual(queue.peek()!.priority, 100)
-
-        let result1 = queue.remove()
-        XCTAssertEqual(result1!.priority, 100)
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 1)
-        XCTAssertEqual(queue.peek()!.priority, 200)
-
-        let result2 = queue.remove()
-        XCTAssertEqual(result2!.priority, 200)
-        XCTAssertTrue(queue.isEmpty)
-        XCTAssertEqual(queue.count, 0)
-        XCTAssertNil(queue.peek())
-    }
-
-    func testTwoElementsOutOfOrder() {
-        var queue = HashedHeap<Message>(sort: <)
-
-        queue.insert(Message(text: "world", priority: 200))
-        queue.insert(Message(text: "hello", priority: 100))
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 2)
-        XCTAssertEqual(queue.peek()!.priority, 100)
-
-        let result1 = queue.remove()
-        XCTAssertEqual(result1!.priority, 100)
-        XCTAssertFalse(queue.isEmpty)
-        XCTAssertEqual(queue.count, 1)
-        XCTAssertEqual(queue.peek()!.priority, 200)
-
-        let result2 = queue.remove()
-        XCTAssertEqual(result2!.priority, 200)
-        XCTAssertTrue(queue.isEmpty)
-        XCTAssertEqual(queue.count, 0)
-        XCTAssertNil(queue.peek())
-    }
+  override func setUp() {
+    super.setUp()
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
+  func testEmpty() {
+    var queue = HashedHeap<Message>(sort: <)
+    XCTAssertTrue(queue.isEmpty)
+    XCTAssertEqual(queue.count, 0)
+    XCTAssertNil(queue.peek())
+    XCTAssertNil(queue.remove())
+  }
+  
+  func testOneElement() {
+    var queue = HashedHeap<Message>(sort: <)
+    
+    queue.insert(Message(text: "hello", priority: 100))
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 1)
+    XCTAssertEqual(queue.peek()!.priority, 100)
+    
+    let result = queue.remove()
+    XCTAssertEqual(result!.priority, 100)
+    XCTAssertTrue(queue.isEmpty)
+    XCTAssertEqual(queue.count, 0)
+    XCTAssertNil(queue.peek())
+  }
+  
+  func testTwoElementsInOrder() {
+    var queue = HashedHeap<Message>(sort: <)
+    
+    queue.insert(Message(text: "hello", priority: 100))
+    queue.insert(Message(text: "world", priority: 200))
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 2)
+    XCTAssertEqual(queue.peek()!.priority, 100)
+    
+    let result1 = queue.remove()
+    XCTAssertEqual(result1!.priority, 100)
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 1)
+    XCTAssertEqual(queue.peek()!.priority, 200)
+    
+    let result2 = queue.remove()
+    XCTAssertEqual(result2!.priority, 200)
+    XCTAssertTrue(queue.isEmpty)
+    XCTAssertEqual(queue.count, 0)
+    XCTAssertNil(queue.peek())
+  }
+  
+  func testTwoElementsOutOfOrder() {
+    var queue = HashedHeap<Message>(sort: <)
+    
+    queue.insert(Message(text: "world", priority: 200))
+    queue.insert(Message(text: "hello", priority: 100))
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 2)
+    XCTAssertEqual(queue.peek()!.priority, 100)
+    
+    let result1 = queue.remove()
+    XCTAssertEqual(result1!.priority, 100)
+    XCTAssertFalse(queue.isEmpty)
+    XCTAssertEqual(queue.count, 1)
+    XCTAssertEqual(queue.peek()!.priority, 200)
+    
+    let result2 = queue.remove()
+    XCTAssertEqual(result2!.priority, 200)
+    XCTAssertTrue(queue.isEmpty)
+    XCTAssertEqual(queue.count, 0)
+    XCTAssertNil(queue.peek())
+  }
 }

From 9971ae6f22f0690e7565001ec3969cd42566ae79 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 9 Aug 2017 11:33:56 +0900
Subject: [PATCH 148/643] Fixes indentation to 2 spaces.

---
 Hashed Heap/HashedHeap.swift | 460 +++++++++++++++++------------------
 1 file changed, 230 insertions(+), 230 deletions(-)

diff --git a/Hashed Heap/HashedHeap.swift b/Hashed Heap/HashedHeap.swift
index ac8035057..be7d9ab78 100644
--- a/Hashed Heap/HashedHeap.swift	
+++ b/Hashed Heap/HashedHeap.swift	
@@ -6,234 +6,234 @@
 /// having amortized constant lookups by value. This is used in the A* and other heuristic search algorithms to achieve
 /// optimal performance.
 public struct HashedHeap<T: Hashable> {
-    /// The array that stores the heap's nodes.
-    private(set) var elements = [T]()
-
-    /// Hash mapping from elements to indices in the `elements` array.
-    private(set) var indices = [T: Int]()
-
-    /// Determines whether this is a max-heap (>) or min-heap (<).
-    fileprivate var isOrderedBefore: (T, T) -> Bool
-
-    /// Creates an empty hashed heap.
-    ///
-    /// The sort function determines whether this is a min-heap or max-heap. For integers, > makes a max-heap, < makes
-    /// a min-heap.
-    public init(sort: @escaping (T, T) -> Bool) {
-        isOrderedBefore = sort
-    }
-
-    /// Creates a hashed heap from an array.
-    ///
-    /// The order of the array does not matter; the elements are inserted into the heap in the order determined by the
-    /// sort function.
-    ///
-    /// - Complexity: O(n)
-    public init(array: [T], sort: @escaping (T, T) -> Bool) {
-        isOrderedBefore = sort
-        build(from: array)
-    }
-
-    /// Converts an array to a max-heap or min-heap in a bottom-up manner.
-    ///
-    /// - Complexity: O(n)
-    private mutating func build(from array: [T]) {
-        elements = array
-        for index in elements.indices {
-            indices[elements[index]] = index
-        }
-
-        for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-            shiftDown(i, heapSize: elements.count)
-        }
-    }
-
-    /// Whether the heap is empty.
-    public var isEmpty: Bool {
-        return elements.isEmpty
-    }
-
-    /// The number of elements in the heap.
-    public var count: Int {
-        return elements.count
-    }
-
-    /// Returns the index of the given element.
-    ///
-    /// This is the operation that a hashed heap optimizes in compassion with a normal heap. In a normal heap this
-    /// would take O(n), but for the hashed heap this takes amortized constatn time.
-    ///
-    /// - Complexity: Amortized constant
-    public func index(of element: T) -> Int? {
-        return indices[element]
-    }
-
-    /// Returns the maximum value in the heap (for a max-heap) or the minimum value (for a min-heap).
-    ///
-    /// - Complexity: O(1)
-    public func peek() -> T? {
-        return elements.first
-    }
-
-    /// Adds a new value to the heap.
-    ///
-    /// This reorders the heap so that the max-heap or min-heap property still holds.
-    ///
-    /// - Complexity: O(log n)
-    public mutating func insert(_ value: T) {
-        elements.append(value)
-        indices[value] = elements.count - 1
-        shiftUp(elements.count - 1)
-    }
-
-    /// Adds new values to the heap.
-    public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
-        for value in sequence {
-            insert(value)
-        }
-    }
-
-    /// Replaces an element in the hash.
-    ///
-    /// In a max-heap, the new element should be larger than the old one; in a min-heap it should be smaller.
-    public mutating func replace(_ value: T, at index: Int) {
-        guard index < elements.count else { return }
-
-        assert(isOrderedBefore(value, elements[index]))
-        set(value, at: index)
-        shiftUp(index)
-    }
-
-    /// Removes the root node from the heap.
-    ///
-    /// For a max-heap, this is the maximum value; for a min-heap it is the minimum value.
-    ///
-    /// - Complexity: O(log n)
-    @discardableResult
-    public mutating func remove() -> T? {
-        if elements.isEmpty {
-            return nil
-        } else if elements.count == 1 {
-            return removeLast()
-        } else {
-            // Use the last node to replace the first one, then fix the heap by
-            // shifting this new first node into its proper position.
-            let value = elements[0]
-            set(removeLast(), at: 0)
-            shiftDown()
-            return value
-        }
-    }
-
-    /// Removes an arbitrary node from the heap.
-    ///
-    /// You need to know the node's index, which may actually take O(n) steps to find.
-    ///
-    /// - Complexity: O(log n).
-    public mutating func remove(at index: Int) -> T? {
-        guard index < elements.count else { return nil }
-
-        let size = elements.count - 1
-        if index != size {
-            swapAt(index, size)
-            shiftDown(index, heapSize: size)
-            shiftUp(index)
-        }
-        return removeLast()
-    }
-
-    /// Removes the last element from the heap.
-    ///
-    /// - Complexity: O(1)
-    public mutating func removeLast() -> T {
-        guard let value = elements.last else {
-            preconditionFailure("Trying to remove element from empty heap")
-        }
-        indices[value] = nil
-        return elements.removeLast()
-    }
-
-    /// Takes a child node and looks at its parents; if a parent is not larger (max-heap) or not smaller (min-heap)
-    /// than the child, we exchange them.
-    mutating func shiftUp(_ index: Int) {
-        var childIndex = index
-        let child = elements[childIndex]
-        var parentIndex = self.parentIndex(of: childIndex)
-
-        while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
-            set(elements[parentIndex], at: childIndex)
-            childIndex = parentIndex
-            parentIndex = self.parentIndex(of: childIndex)
-        }
-
-        set(child, at: childIndex)
-    }
-
-    mutating func shiftDown() {
-        shiftDown(0, heapSize: elements.count)
-    }
-
-    /// Looks at a parent node and makes sure it is still larger (max-heap) or smaller (min-heap) than its childeren.
-    mutating func shiftDown(_ index: Int, heapSize: Int) {
-        var parentIndex = index
-
-        while true {
-            let leftChildIndex = self.leftChildIndex(of: parentIndex)
-            let rightChildIndex = leftChildIndex + 1
-
-            // Figure out which comes first if we order them by the sort function:
-            // the parent, the left child, or the right child. If the parent comes
-            // first, we're done. If not, that element is out-of-place and we make
-            // it "float down" the tree until the heap property is restored.
-            var first = parentIndex
-            if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
-                first = leftChildIndex
-            }
-            if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
-                first = rightChildIndex
-            }
-            if first == parentIndex { return }
-
-            swapAt(parentIndex, first)
-            parentIndex = first
-        }
-    }
-
-    /// Replaces an element in the heap and updates the indices hash.
-    private mutating func set(_ newValue: T, at index: Int) {
-        indices[elements[index]] = nil
-        elements[index] = newValue
-        indices[newValue] = index
-    }
-
-    /// Swap two elements in the heap and update the indices hash.
-    private mutating func swapAt(_ i: Int, _ j: Int) {
-        elements.swapAt(i, j)
-        indices[elements[i]] = i
-        indices[elements[j]] = j
-    }
-
-    /// Returns the index of the parent of the element at index i.
-    ///
-    /// - Note: The element at index 0 is the root of the tree and has no parent.
-    @inline(__always)
-    func parentIndex(of index: Int) -> Int {
-        return (index - 1) / 2
-    }
-
-    /// Returns the index of the left child of the element at index i.
-    ///
-    /// - Note: this index can be greater than the heap size, in which case there is no left child.
-    @inline(__always)
-    func leftChildIndex(of index: Int) -> Int {
-        return 2*index + 1
-    }
-
-    /// Returns the index of the right child of the element at index i.
-    ///
-    /// - Note: this index can be greater than the heap size, in which case there is no right child.
-    @inline(__always)
-    func rightChildIndex(of index: Int) -> Int {
-        return 2*index + 2
-    }
+  /// The array that stores the heap's nodes.
+  private(set) var elements = [T]()
+  
+  /// Hash mapping from elements to indices in the `elements` array.
+  private(set) var indices = [T: Int]()
+  
+  /// Determines whether this is a max-heap (>) or min-heap (<).
+  fileprivate var isOrderedBefore: (T, T) -> Bool
+  
+  /// Creates an empty hashed heap.
+  ///
+  /// The sort function determines whether this is a min-heap or max-heap. For integers, > makes a max-heap, < makes
+  /// a min-heap.
+  public init(sort: @escaping (T, T) -> Bool) {
+    isOrderedBefore = sort
+  }
+  
+  /// Creates a hashed heap from an array.
+  ///
+  /// The order of the array does not matter; the elements are inserted into the heap in the order determined by the
+  /// sort function.
+  ///
+  /// - Complexity: O(n)
+  public init(array: [T], sort: @escaping (T, T) -> Bool) {
+    isOrderedBefore = sort
+    build(from: array)
+  }
+  
+  /// Converts an array to a max-heap or min-heap in a bottom-up manner.
+  ///
+  /// - Complexity: O(n)
+  private mutating func build(from array: [T]) {
+    elements = array
+    for index in elements.indices {
+      indices[elements[index]] = index
+    }
+    
+    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
+      shiftDown(i, heapSize: elements.count)
+    }
+  }
+  
+  /// Whether the heap is empty.
+  public var isEmpty: Bool {
+    return elements.isEmpty
+  }
+  
+  /// The number of elements in the heap.
+  public var count: Int {
+    return elements.count
+  }
+  
+  /// Returns the index of the given element.
+  ///
+  /// This is the operation that a hashed heap optimizes in compassion with a normal heap. In a normal heap this
+  /// would take O(n), but for the hashed heap this takes amortized constatn time.
+  ///
+  /// - Complexity: Amortized constant
+  public func index(of element: T) -> Int? {
+    return indices[element]
+  }
+  
+  /// Returns the maximum value in the heap (for a max-heap) or the minimum value (for a min-heap).
+  ///
+  /// - Complexity: O(1)
+  public func peek() -> T? {
+    return elements.first
+  }
+  
+  /// Adds a new value to the heap.
+  ///
+  /// This reorders the heap so that the max-heap or min-heap property still holds.
+  ///
+  /// - Complexity: O(log n)
+  public mutating func insert(_ value: T) {
+    elements.append(value)
+    indices[value] = elements.count - 1
+    shiftUp(elements.count - 1)
+  }
+  
+  /// Adds new values to the heap.
+  public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
+    for value in sequence {
+      insert(value)
+    }
+  }
+  
+  /// Replaces an element in the hash.
+  ///
+  /// In a max-heap, the new element should be larger than the old one; in a min-heap it should be smaller.
+  public mutating func replace(_ value: T, at index: Int) {
+    guard index < elements.count else { return }
+    
+    assert(isOrderedBefore(value, elements[index]))
+    set(value, at: index)
+    shiftUp(index)
+  }
+  
+  /// Removes the root node from the heap.
+  ///
+  /// For a max-heap, this is the maximum value; for a min-heap it is the minimum value.
+  ///
+  /// - Complexity: O(log n)
+  @discardableResult
+  public mutating func remove() -> T? {
+    if elements.isEmpty {
+      return nil
+    } else if elements.count == 1 {
+      return removeLast()
+    } else {
+      // Use the last node to replace the first one, then fix the heap by
+      // shifting this new first node into its proper position.
+      let value = elements[0]
+      set(removeLast(), at: 0)
+      shiftDown()
+      return value
+    }
+  }
+  
+  /// Removes an arbitrary node from the heap.
+  ///
+  /// You need to know the node's index, which may actually take O(n) steps to find.
+  ///
+  /// - Complexity: O(log n).
+  public mutating func remove(at index: Int) -> T? {
+    guard index < elements.count else { return nil }
+    
+    let size = elements.count - 1
+    if index != size {
+      swapAt(index, size)
+      shiftDown(index, heapSize: size)
+      shiftUp(index)
+    }
+    return removeLast()
+  }
+  
+  /// Removes the last element from the heap.
+  ///
+  /// - Complexity: O(1)
+  public mutating func removeLast() -> T {
+    guard let value = elements.last else {
+      preconditionFailure("Trying to remove element from empty heap")
+    }
+    indices[value] = nil
+    return elements.removeLast()
+  }
+  
+  /// Takes a child node and looks at its parents; if a parent is not larger (max-heap) or not smaller (min-heap)
+  /// than the child, we exchange them.
+  mutating func shiftUp(_ index: Int) {
+    var childIndex = index
+    let child = elements[childIndex]
+    var parentIndex = self.parentIndex(of: childIndex)
+    
+    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
+      set(elements[parentIndex], at: childIndex)
+      childIndex = parentIndex
+      parentIndex = self.parentIndex(of: childIndex)
+    }
+    
+    set(child, at: childIndex)
+  }
+  
+  mutating func shiftDown() {
+    shiftDown(0, heapSize: elements.count)
+  }
+  
+  /// Looks at a parent node and makes sure it is still larger (max-heap) or smaller (min-heap) than its childeren.
+  mutating func shiftDown(_ index: Int, heapSize: Int) {
+    var parentIndex = index
+    
+    while true {
+      let leftChildIndex = self.leftChildIndex(of: parentIndex)
+      let rightChildIndex = leftChildIndex + 1
+      
+      // Figure out which comes first if we order them by the sort function:
+      // the parent, the left child, or the right child. If the parent comes
+      // first, we're done. If not, that element is out-of-place and we make
+      // it "float down" the tree until the heap property is restored.
+      var first = parentIndex
+      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
+        first = leftChildIndex
+      }
+      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
+        first = rightChildIndex
+      }
+      if first == parentIndex { return }
+      
+      swapAt(parentIndex, first)
+      parentIndex = first
+    }
+  }
+  
+  /// Replaces an element in the heap and updates the indices hash.
+  private mutating func set(_ newValue: T, at index: Int) {
+    indices[elements[index]] = nil
+    elements[index] = newValue
+    indices[newValue] = index
+  }
+  
+  /// Swap two elements in the heap and update the indices hash.
+  private mutating func swapAt(_ i: Int, _ j: Int) {
+    elements.swapAt(i, j)
+    indices[elements[i]] = i
+    indices[elements[j]] = j
+  }
+  
+  /// Returns the index of the parent of the element at index i.
+  ///
+  /// - Note: The element at index 0 is the root of the tree and has no parent.
+  @inline(__always)
+  func parentIndex(of index: Int) -> Int {
+    return (index - 1) / 2
+  }
+  
+  /// Returns the index of the left child of the element at index i.
+  ///
+  /// - Note: this index can be greater than the heap size, in which case there is no left child.
+  @inline(__always)
+  func leftChildIndex(of index: Int) -> Int {
+    return 2*index + 1
+  }
+  
+  /// Returns the index of the right child of the element at index i.
+  ///
+  /// - Note: this index can be greater than the heap size, in which case there is no right child.
+  @inline(__always)
+  func rightChildIndex(of index: Int) -> Int {
+    return 2*index + 2
+  }
 }

From aa8081e56c66499fce86c55116a16abc7359fd43 Mon Sep 17 00:00:00 2001
From: Vui Nguyen <vui_engineer@yahoo.com>
Date: Wed, 9 Aug 2017 14:55:29 -0600
Subject: [PATCH 149/643] Updated to Swift 4 & Xcode 9.0b5.No code changes
 needed,only minor spelling change to README

---
 QuadTree/QuadTree.playground/Contents.swift | 5 +++++
 QuadTree/README.md                          | 2 +-
 2 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/QuadTree/QuadTree.playground/Contents.swift b/QuadTree/QuadTree.playground/Contents.swift
index ad8ee31f8..f0d8cb2ef 100644
--- a/QuadTree/QuadTree.playground/Contents.swift
+++ b/QuadTree/QuadTree.playground/Contents.swift
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b5
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 import Foundation
 
 let tree = QuadTree(rect: Rect(origin: Point(0, 0), size: Size(xLength: 10, yLength: 10)))
diff --git a/QuadTree/README.md b/QuadTree/README.md
index 3fc682547..ff71a66f0 100644
--- a/QuadTree/README.md
+++ b/QuadTree/README.md
@@ -152,7 +152,7 @@ Both adding a point and searching can still take up to O(n) in the worst case, s
 
 ### See also
 
-Displaying a large amount of objects in a MapView - a great use case for a Quadtree ([Thoughtbot Atricle](https://robots.thoughtbot.com/how-to-handle-large-amounts-of-data-on-maps))
+Displaying a large amount of objects in a MapView - a great use case for a Quadtree ([Thoughtbot Article](https://robots.thoughtbot.com/how-to-handle-large-amounts-of-data-on-maps))
 
 More info on [Wiki](https://en.wikipedia.org/wiki/Quadtree)
 

From aa900e36d75cd669ab85cb5afd64c4388252f12b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=82=B8=E3=83=A5=E3=83=A9=E3=82=AD=E3=83=A5=E3=83=BC?=
 =?UTF-8?q?=E3=83=AB=E3=83=BB=E3=83=9F=E3=83=9B=E3=83=BC=E3=82=AF?=
 <dkhuong291@gmail.com>
Date: Thu, 17 Aug 2017 23:05:21 +0700
Subject: [PATCH 150/643] Update reverse function in LinkedList

Add `tail = node` to update tail.
---
 Linked List/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index c03023c42..9aaecc206 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -451,6 +451,7 @@ How about reversing a list, so that the head becomes the tail and vice versa? Th
 ```swift
   public func reverse() {
     var node = head
+    tail = node // If you had a tail pointer
     while let currentNode = node {
       node = currentNode.next
       swap(&currentNode.next, &currentNode.previous)

From 06d3ef364bde2462e2ee31055124f69e466ab9b5 Mon Sep 17 00:00:00 2001
From: Yeral <YYamil24@gmail.com>
Date: Thu, 17 Aug 2017 18:07:08 -0400
Subject: [PATCH 151/643] [Swift 4] Update Bucket Search

---
 Bucket Sort/BucketSort.swift                  | 47 ++++++++++++++-----
 Bucket Sort/Tests/Tests.swift                 |  9 ++--
 .../Tests/Tests.xcodeproj/project.pbxproj     | 24 +++++++++-
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 +-
 4 files changed, 64 insertions(+), 20 deletions(-)

diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index 8363fd867..108073288 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -21,12 +21,34 @@
 //
 
 import Foundation
+// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
+// Consider refactoring the code to use the non-optional operators.
+fileprivate func < <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
+  switch (lhs, rhs) {
+  case let (l?, r?):
+    return l < r
+  case (nil, _?):
+    return true
+  default:
+    return false
+  }
+}
+
+// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
+// Consider refactoring the code to use the non-optional operators.
+fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
+  switch (lhs, rhs) {
+  case let (l?, r?):
+    return l >= r
+  default:
+    return !(lhs < rhs)
+  }
+}
 
 //////////////////////////////////////
 // MARK: Main algorithm
 //////////////////////////////////////
 
-
 /**
     Performs bucket sort algorithm on the given input elements.
     [Bucket Sort Algorithm Reference](https://en.wikipedia.org/wiki/Bucket_sort)
@@ -39,7 +61,7 @@ import Foundation
     - Returns: A new array with sorted elements
  */
 
-public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
+public func bucketSort<T>(_ elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
     precondition(allPositiveNumbers(elements))
     precondition(enoughSpaceInBuckets(buckets, elements: elements))
 
@@ -57,12 +79,12 @@ public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sor
     return results
 }
 
-private func allPositiveNumbers<T: Sortable>(array: [T]) -> Bool {
+private func allPositiveNumbers<T: Sortable>(_ array: [T]) -> Bool {
     return array.filter { $0.toInt() >= 0 }.count > 0
 }
 
-private func enoughSpaceInBuckets<T: Sortable>(buckets: [Bucket<T>], elements: [T]) -> Bool {
-    let maximumValue = elements.maxElement()?.toInt()
+private func enoughSpaceInBuckets<T>(_ buckets: [Bucket<T>], elements: [T]) -> Bool {
+    let maximumValue = elements.max()?.toInt()
     let totalCapacity = buckets.count * (buckets.first?.capacity)!
 
     return totalCapacity >= maximumValue
@@ -72,9 +94,8 @@ private func enoughSpaceInBuckets<T: Sortable>(buckets: [Bucket<T>], elements: [
 // MARK: Distributor
 //////////////////////////////////////
 
-
 public protocol Distributor {
-    func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>])
+    func distribute<T>(_ element: T, buckets: inout [Bucket<T>])
 }
 
 /*
@@ -96,7 +117,7 @@ public struct RangeDistributor: Distributor {
 
     public init() {}
 
-    public func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>]) {
+    public func distribute<T>(_ element: T, buckets: inout [Bucket<T>]) {
         let value = element.toInt()
         let bucketCapacity = buckets.first!.capacity
 
@@ -121,14 +142,14 @@ public protocol Sortable: IntConvertible, Comparable {
 //////////////////////////////////////
 
 public protocol Sorter {
-    func sort<T: Sortable>(items: [T]) -> [T]
+    func sort<T: Sortable>(_ items: [T]) -> [T]
 }
 
 public struct InsertionSorter: Sorter {
 
     public init() {}
 
-    public func sort<T: Sortable>(items: [T]) -> [T] {
+    public func sort<T: Sortable>(_ items: [T]) -> [T] {
         var results = items
         for i in 0 ..< results.count {
             var j = i
@@ -149,7 +170,7 @@ public struct InsertionSorter: Sorter {
 // MARK: Bucket
 //////////////////////////////////////
 
-public struct Bucket<T:Sortable> {
+public struct Bucket<T: Sortable> {
     var elements: [T]
     let capacity: Int
 
@@ -158,13 +179,13 @@ public struct Bucket<T:Sortable> {
         elements = [T]()
     }
 
-    public mutating func add(item: T) {
+    public mutating func add(_ item: T) {
         if elements.count < capacity {
             elements.append(item)
         }
     }
 
-    public func sort(algorithm: Sorter) -> [T] {
+    public func sort(_ algorithm: Sorter) -> [T] {
         return algorithm.sort(elements)
     }
 }
diff --git a/Bucket Sort/Tests/Tests.swift b/Bucket Sort/Tests/Tests.swift
index 22ac751de..1a06c92b5 100644
--- a/Bucket Sort/Tests/Tests.swift	
+++ b/Bucket Sort/Tests/Tests.swift	
@@ -25,7 +25,7 @@ class TestTests: XCTestCase {
 
         largeArray = [Int]()
         for _ in 0..<total {
-            largeArray!.append( random() % maximum )
+            largeArray!.append( Int(arc4random_uniform( UInt32( maximum ) ) ) )
         }
 
         sparsedArray = [Int]()
@@ -57,9 +57,9 @@ class TestTests: XCTestCase {
 
     // MARK: Private functions
 
-    private func performBucketSort(elements: [Int], totalBuckets: Int) -> [Int] {
+    fileprivate func performBucketSort(_ elements: [Int], totalBuckets: Int) -> [Int] {
 
-        let value = (elements.maxElement()?.toInt())! + 1
+        let value = (elements.max()?.toInt())! + 1
         let capacityRequired = Int( ceil( Double(value) / Double(totalBuckets) ) )
 
         var buckets = [Bucket<Int>]()
@@ -71,7 +71,7 @@ class TestTests: XCTestCase {
         return results
     }
 
-    func isSorted(array: [Int]) -> Bool {
+    func isSorted(_ array: [Int]) -> Bool {
 
         var index = 0
         var sorted = true
@@ -86,7 +86,6 @@ class TestTests: XCTestCase {
     }
 }
 
-
 //////////////////////////////////////
 // MARK: Extensions
 //////////////////////////////////////
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj
index 9a42afa4b..84a305784 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,11 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0900;
 					};
 				};
 			};
@@ -140,13 +141,21 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -184,13 +193,21 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -209,6 +226,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 			};
 			name = Release;
 		};
@@ -222,6 +240,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -234,6 +254,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..538a6f4fa 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,6 +26,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -46,6 +47,7 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 689efb386ed0e227659cc7363da4efb8b11f6cc0 Mon Sep 17 00:00:00 2001
From: Yeral <YYamil24@gmail.com>
Date: Thu, 17 Aug 2017 22:59:41 -0400
Subject: [PATCH 152/643] [Swift 4] Update Bucket Search

---
 .../Sources/BucketSort.swift                  | 166 +++++++++++-------
 1 file changed, 107 insertions(+), 59 deletions(-)

diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
index c93b96cb2..bafd216fa 100644
--- a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -21,34 +21,81 @@
 //
 
 import Foundation
+// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
+// Consider refactoring the code to use the non-optional operators.
+fileprivate func < <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
+    switch (lhs, rhs) {
+    case let (l?, r?):
+        return l < r
+    case (nil, _?):
+        return true
+    default:
+        return false
+    }
+}
+
+// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
+// Consider refactoring the code to use the non-optional operators.
+fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
+    switch (lhs, rhs) {
+    case let (l?, r?):
+        return l >= r
+    default:
+        return !(lhs < rhs)
+    }
+}
 
 //////////////////////////////////////
 // MARK: Main algorithm
 //////////////////////////////////////
 
+/**
+ Performs bucket sort algorithm on the given input elements.
+ [Bucket Sort Algorithm Reference](https://en.wikipedia.org/wiki/Bucket_sort)
+ 
+ - Parameter elements:     Array of Sortable elements
+ - Parameter distributor:  Performs the distribution of each element of a bucket
+ - Parameter sorter:       Performs the sorting inside each bucket, after all the elements are distributed
+ - Parameter buckets:      An array of buckets
+ 
+ - Returns: A new array with sorted elements
+ */
 
-public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
-  var bucketsCopy = buckets
-  for elem in elements {
-    distributor.distribute(elem, buckets: &bucketsCopy)
-  }
-
-  var results = [T]()
+public func bucketSort<T>(_ elements: [T], distributor: Distributor, sorter: Sorter, buckets: [Bucket<T>]) -> [T] {
+    precondition(allPositiveNumbers(elements))
+    precondition(enoughSpaceInBuckets(buckets, elements: elements))
+    
+    var bucketsCopy = buckets
+    for elem in elements {
+        distributor.distribute(elem, buckets: &bucketsCopy)
+    }
+    
+    var results = [T]()
+    
+    for bucket in bucketsCopy {
+        results += bucket.sort(sorter)
+    }
+    
+    return results
+}
 
-  for bucket in buckets {
-    results += bucket.sort(sorter)
-  }
+private func allPositiveNumbers<T: Sortable>(_ array: [T]) -> Bool {
+    return array.filter { $0.toInt() >= 0 }.count > 0
+}
 
-  return results
+private func enoughSpaceInBuckets<T>(_ buckets: [Bucket<T>], elements: [T]) -> Bool {
+    let maximumValue = elements.max()?.toInt()
+    let totalCapacity = buckets.count * (buckets.first?.capacity)!
+    
+    return totalCapacity >= maximumValue
 }
 
 //////////////////////////////////////
 // MARK: Distributor
 //////////////////////////////////////
 
-
 public protocol Distributor {
-  func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>])
+    func distribute<T>(_ element: T, buckets: inout [Bucket<T>])
 }
 
 /*
@@ -67,16 +114,16 @@ public protocol Distributor {
  * By following the formula: element / capacity = #ofBucket
  */
 public struct RangeDistributor: Distributor {
-
-  public init() {}
-
-  public func distribute<T: Sortable>(element: T, inout buckets: [Bucket<T>]) {
-    let value = element.toInt()
-    let bucketCapacity = buckets.first!.capacity
-
-    let bucketIndex = value / bucketCapacity
-    buckets[bucketIndex].add(element)
-  }
+    
+    public init() {}
+    
+    public func distribute<T>(_ element: T, buckets: inout [Bucket<T>]) {
+        let value = element.toInt()
+        let bucketCapacity = buckets.first!.capacity
+        
+        let bucketIndex = value / bucketCapacity
+        buckets[bucketIndex].add(element)
+    }
 }
 
 //////////////////////////////////////
@@ -84,7 +131,7 @@ public struct RangeDistributor: Distributor {
 //////////////////////////////////////
 
 public protocol IntConvertible {
-  func toInt() -> Int
+    func toInt() -> Int
 }
 
 public protocol Sortable: IntConvertible, Comparable {
@@ -95,50 +142,51 @@ public protocol Sortable: IntConvertible, Comparable {
 //////////////////////////////////////
 
 public protocol Sorter {
-  func sort<T: Sortable>(items: [T]) -> [T]
+    func sort<T: Sortable>(_ items: [T]) -> [T]
 }
 
 public struct InsertionSorter: Sorter {
-
-  public init() {}
-
-  public func sort<T: Sortable>(items: [T]) -> [T] {
-    var results = items
-    for i in 0 ..< results.count {
-      var j = i
-      while j > 0 && results[j-i] > results[j] {
-
-        let auxiliar = results[i]
-        results[i] = results[j]
-        results[j] = auxiliar
-
-        j -= 1
-      }
+    
+    public init() {}
+    
+    public func sort<T: Sortable>(_ items: [T]) -> [T] {
+        var results = items
+        for i in 0 ..< results.count {
+            var j = i
+            while j > 0 && results[j-1] > results[j] {
+                
+                let auxiliar = results[j-1]
+                results[j-1] = results[j]
+                results[j] = auxiliar
+                
+                j -= 1
+            }
+        }
+        return results
     }
-    return results
-  }
 }
 
 //////////////////////////////////////
 // MARK: Bucket
 //////////////////////////////////////
 
-public struct Bucket<T:Sortable> {
-  var elements: [T]
-  let capacity: Int
-
-  public init(capacity: Int) {
-    self.capacity = capacity
-    elements = [T]()
-  }
-
-  public mutating func add(item: T) {
-    if elements.count < capacity {
-      elements.append(item)
+public struct Bucket<T: Sortable> {
+    var elements: [T]
+    let capacity: Int
+    
+    public init(capacity: Int) {
+        self.capacity = capacity
+        elements = [T]()
+    }
+    
+    public mutating func add(_ item: T) {
+        if elements.count < capacity {
+            elements.append(item)
+        }
+    }
+    
+    public func sort(_ algorithm: Sorter) -> [T] {
+        return algorithm.sort(elements)
     }
-  }
-
-  public func sort(algorithm: Sorter) -> [T] {
-    return algorithm.sort(elements)
-  }
 }
+

From 69edcb4830ead3e51fd21b1a3c65998413670588 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Sat, 19 Aug 2017 11:27:59 +0500
Subject: [PATCH 153/643] Fix indentation to 2 spaces

---
 .../Contents.swift                            | 82 +++++++++----------
 .../KaratsubaMultiplication.swift             | 12 +--
 2 files changed, 47 insertions(+), 47 deletions(-)

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 6b1b0bca2..04aff1ec4 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -6,58 +6,58 @@ import Foundation
 print("Hello, Swift 4")
 #endif
 precedencegroup ExponentiativePrecedence {
-    higherThan: MultiplicationPrecedence
-    lowerThan: BitwiseShiftPrecedence
-    associativity: left
+  higherThan: MultiplicationPrecedence
+  lowerThan: BitwiseShiftPrecedence
+  associativity: left
 }
 
 infix operator ^^: ExponentiativePrecedence
 func ^^ (radix: Int, power: Int) -> Int {
-    return Int(pow(Double(radix), Double(power)))
+  return Int(pow(Double(radix), Double(power)))
 }
 
 // Long Multiplication - O(n^2)
 func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
-    let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
-    let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
-    
-    var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
-    
-    for i in num1Array.indices {
-        var carry = 0
-        for j in num2Array.indices {
-            product[i + j] += carry + num1Array[i] * num2Array[j]
-            carry = product[i + j] / base
-            product[i + j] %= base
-        }
-        product[i + num2Array.count] += carry
+  let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
+  let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
+  
+  var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
+  
+  for i in num1Array.indices {
+    var carry = 0
+    for j in num2Array.indices {
+      product[i + j] += carry + num1Array[i] * num2Array[j]
+      carry = product[i + j] / base
+      product[i + j] %= base
     }
-    
-    return Int(product.reversed().map { String($0) }.reduce("", +))!
+    product[i + num2Array.count] += carry
+  }
+  
+  return Int(product.reversed().map { String($0) }.reduce("", +))!
 }
 
 // Karatsuba Multiplication - O(n^log2(3))
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
-    let num1Array = String(num1).characters
-    let num2Array = String(num2).characters
-    
-    guard num1Array.count > 1 && num2Array.count > 1 else {
-        return multiply(num1, by: num2)
-    }
-    
-    let n = max(num1Array.count, num2Array.count)
-    let nBy2 = n / 2
-    
-    let a = num1 / 10^^nBy2
-    let b = num1 % 10^^nBy2
-    let c = num2 / 10^^nBy2
-    let d = num2 % 10^^nBy2
-    
-    let ac = karatsuba(a, by: c)
-    let bd = karatsuba(b, by: d)
-    let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-    
-    let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
-    
-    return product
+  let num1Array = String(num1).characters
+  let num2Array = String(num2).characters
+  
+  guard num1Array.count > 1 && num2Array.count > 1 else {
+    return multiply(num1, by: num2)
+  }
+  
+  let n = max(num1Array.count, num2Array.count)
+  let nBy2 = n / 2
+  
+  let a = num1 / 10^^nBy2
+  let b = num1 % 10^^nBy2
+  let c = num2 / 10^^nBy2
+  let d = num2 % 10^^nBy2
+  
+  let ac = karatsuba(a, by: c)
+  let bd = karatsuba(b, by: d)
+  let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
+  
+  let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
+  
+  return product
 }
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
index 0f0e8ed12..fb20a667d 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -22,24 +22,24 @@ func ^^ (radix: Int, power: Int) -> Int {
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1Array = String(num1).characters
   let num2Array = String(num2).characters
-
+  
   guard num1Array.count > 1 && num2Array.count > 1 else {
     return num1 * num2
   }
-
+  
   let n = max(num1Array.count, num2Array.count)
   let nBy2 = n / 2
-
+  
   let a = num1 / 10^^nBy2
   let b = num1 % 10^^nBy2
   let c = num2 / 10^^nBy2
   let d = num2 % 10^^nBy2
-
+  
   let ac = karatsuba(a, by: c)
   let bd = karatsuba(b, by: d)
   let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-
+  
   let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
-
+  
   return product
 }

From a6c3e9f32d68c595150db11b274e4908cee20928 Mon Sep 17 00:00:00 2001
From: Shabir Jan <iam.shabir@yahoo.com>
Date: Sat, 19 Aug 2017 11:33:45 +0500
Subject: [PATCH 154/643] Fix indentation to 2 spaces

---
 .../Contents.swift                            | 192 +++++++++---------
 Knuth-Morris-Pratt/KnuthMorrisPratt.swift     | 116 +++++------
 2 files changed, 154 insertions(+), 154 deletions(-)

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
index b47cf1257..6609c9abe 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -6,115 +6,115 @@ print("Hello, Swift4!")
 #endif
 
 func ZetaAlgorithm(ptnr: String) -> [Int]? {
+  
+  let pattern = Array(ptnr.characters)
+  let patternLength: Int = pattern.count
+  
+  guard patternLength > 0 else {
+    return nil
+  }
+  
+  var zeta: [Int] = [Int](repeating: 0, count: patternLength)
+  
+  var left: Int = 0
+  var right: Int = 0
+  var k_1: Int = 0
+  var betaLength: Int = 0
+  var textIndex: Int = 0
+  var patternIndex: Int = 0
+  
+  for k in 1 ..< patternLength {
+    if k > right {
+      patternIndex = 0
+      
+      while k + patternIndex < patternLength  &&
+        pattern[k + patternIndex] == pattern[patternIndex] {
+          patternIndex = patternIndex + 1
+      }
+      
+      zeta[k] = patternIndex
+      
+      if zeta[k] > 0 {
+        left = k
+        right = k + zeta[k] - 1
+      }
+    } else {
+      k_1 = k - left + 1
+      betaLength = right - k + 1
+      
+      if zeta[k_1 - 1] < betaLength {
+        zeta[k] = zeta[k_1 - 1]
+      } else if zeta[k_1 - 1] >= betaLength {
+        textIndex = betaLength
+        patternIndex = right + 1
+        
+        while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
+          textIndex = textIndex + 1
+          patternIndex = patternIndex + 1
+        }
+        zeta[k] = patternIndex - k
+        left = k
+        right = patternIndex - 1
+      }
+    }
+  }
+  return zeta
+}
+
+extension String {
+  
+  func indexesOf(ptnr: String) -> [Int]? {
     
+    let text = Array(self.characters)
     let pattern = Array(ptnr.characters)
+    
+    let textLength: Int = text.count
     let patternLength: Int = pattern.count
     
     guard patternLength > 0 else {
-        return nil
+      return nil
     }
     
-    var zeta: [Int] = [Int](repeating: 0, count: patternLength)
-    
-    var left: Int = 0
-    var right: Int = 0
-    var k_1: Int = 0
-    var betaLength: Int = 0
+    var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
     var textIndex: Int = 0
     var patternIndex: Int = 0
+    var indexes: [Int] = [Int]()
     
-    for k in 1 ..< patternLength {
-        if k > right {
-            patternIndex = 0
-            
-            while k + patternIndex < patternLength  &&
-                pattern[k + patternIndex] == pattern[patternIndex] {
-                    patternIndex = patternIndex + 1
-            }
-            
-            zeta[k] = patternIndex
-            
-            if zeta[k] > 0 {
-                left = k
-                right = k + zeta[k] - 1
-            }
-        } else {
-            k_1 = k - left + 1
-            betaLength = right - k + 1
-            
-            if zeta[k_1 - 1] < betaLength {
-                zeta[k] = zeta[k_1 - 1]
-            } else if zeta[k_1 - 1] >= betaLength {
-                textIndex = betaLength
-                patternIndex = right + 1
-                
-                while patternIndex < patternLength && pattern[textIndex] == pattern[patternIndex] {
-                    textIndex = textIndex + 1
-                    patternIndex = patternIndex + 1
-                }
-                zeta[k] = patternIndex - k
-                left = k
-                right = patternIndex - 1
-            }
-        }
+    /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
+    let zeta = ZetaAlgorithm(ptnr: ptnr)
+    
+    for patternIndex in (1 ..< patternLength).reversed() {
+      textIndex = patternIndex + zeta![patternIndex] - 1
+      suffixPrefix[textIndex] = zeta![patternIndex]
     }
-    return zeta
-}
-
-extension String {
     
-    func indexesOf(ptnr: String) -> [Int]? {
-        
-        let text = Array(self.characters)
-        let pattern = Array(ptnr.characters)
-        
-        let textLength: Int = text.count
-        let patternLength: Int = pattern.count
-        
-        guard patternLength > 0 else {
-            return nil
-        }
-        
-        var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
-        var textIndex: Int = 0
-        var patternIndex: Int = 0
-        var indexes: [Int] = [Int]()
-        
-        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
-        let zeta = ZetaAlgorithm(ptnr: ptnr)
-        
-        for patternIndex in (1 ..< patternLength).reversed() {
-            textIndex = patternIndex + zeta![patternIndex] - 1
-            suffixPrefix[textIndex] = zeta![patternIndex]
-        }
-        
-        /* Search stage: scanning the text for pattern matching */
-        textIndex = 0
-        patternIndex = 0
-        
-        while textIndex + (patternLength - patternIndex - 1) < textLength {
-            
-            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
-                textIndex = textIndex + 1
-                patternIndex = patternIndex + 1
-            }
-            
-            if patternIndex == patternLength {
-                indexes.append(textIndex - patternIndex)
-            }
-            
-            if patternIndex == 0 {
-                textIndex = textIndex + 1
-            } else {
-                patternIndex = suffixPrefix[patternIndex - 1]
-            }
-        }
-        
-        guard !indexes.isEmpty else {
-            return nil
-        }
-        return indexes
+    /* Search stage: scanning the text for pattern matching */
+    textIndex = 0
+    patternIndex = 0
+    
+    while textIndex + (patternLength - patternIndex - 1) < textLength {
+      
+      while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
+        textIndex = textIndex + 1
+        patternIndex = patternIndex + 1
+      }
+      
+      if patternIndex == patternLength {
+        indexes.append(textIndex - patternIndex)
+      }
+      
+      if patternIndex == 0 {
+        textIndex = textIndex + 1
+      } else {
+        patternIndex = suffixPrefix[patternIndex - 1]
+      }
+    }
+    
+    guard !indexes.isEmpty else {
+      return nil
     }
+    return indexes
+  }
 }
 
 /* Examples */
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
index 45d9812b7..81bc65278 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
@@ -1,65 +1,65 @@
 /*  Knuth-Morris-Pratt algorithm for pattern/string matching
-
-    The code is based on the book:
-    "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
-    by Dan Gusfield
-    Cambridge University Press, 1997
-*/
+ 
+ The code is based on the book:
+ "Algorithms on String, Trees and Sequences: Computer Science and Computational Biology"
+ by Dan Gusfield
+ Cambridge University Press, 1997
+ */
 
 import Foundation
 
 extension String {
-
-    func indexesOf(ptnr: String) -> [Int]? {
-
-        let text = Array(self.characters)
-        let pattern = Array(ptnr.characters)
-
-        let textLength: Int = text.count
-        let patternLength: Int = pattern.count
-
-        guard patternLength > 0 else {
-            return nil
-        }
-
-        var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
-        var textIndex: Int = 0
-        var patternIndex: Int = 0
-        var indexes: [Int] = [Int]()
-
-        /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
-        let zeta = ZetaAlgorithm(ptnr: ptnr)
-
-        for patternIndex in (1 ..< patternLength).reversed() {
-            textIndex = patternIndex + zeta![patternIndex] - 1
-            suffixPrefix[textIndex] = zeta![patternIndex]
-        }
-
-        /* Search stage: scanning the text for pattern matching */
-        textIndex = 0
-        patternIndex = 0
-
-        while textIndex + (patternLength - patternIndex - 1) < textLength {
-
-            while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
-                textIndex = textIndex + 1
-                patternIndex = patternIndex + 1
-            }
-
-            if patternIndex == patternLength {
-                indexes.append(textIndex - patternIndex)
-            }
-
-            if patternIndex == 0 {
-                textIndex = textIndex + 1
-            } else {
-                patternIndex = suffixPrefix[patternIndex - 1]
-            }
-        }
-
-        guard !indexes.isEmpty else {
-            return nil
-        }
-        return indexes
+  
+  func indexesOf(ptnr: String) -> [Int]? {
+    
+    let text = Array(self.characters)
+    let pattern = Array(ptnr.characters)
+    
+    let textLength: Int = text.count
+    let patternLength: Int = pattern.count
+    
+    guard patternLength > 0 else {
+      return nil
+    }
+    
+    var suffixPrefix: [Int] = [Int](repeating: 0, count: patternLength)
+    var textIndex: Int = 0
+    var patternIndex: Int = 0
+    var indexes: [Int] = [Int]()
+    
+    /* Pre-processing stage: computing the table for the shifts (through Z-Algorithm) */
+    let zeta = ZetaAlgorithm(ptnr: ptnr)
+    
+    for patternIndex in (1 ..< patternLength).reversed() {
+      textIndex = patternIndex + zeta![patternIndex] - 1
+      suffixPrefix[textIndex] = zeta![patternIndex]
+    }
+    
+    /* Search stage: scanning the text for pattern matching */
+    textIndex = 0
+    patternIndex = 0
+    
+    while textIndex + (patternLength - patternIndex - 1) < textLength {
+      
+      while patternIndex < patternLength && text[textIndex] == pattern[patternIndex] {
+        textIndex = textIndex + 1
+        patternIndex = patternIndex + 1
+      }
+      
+      if patternIndex == patternLength {
+        indexes.append(textIndex - patternIndex)
+      }
+      
+      if patternIndex == 0 {
+        textIndex = textIndex + 1
+      } else {
+        patternIndex = suffixPrefix[patternIndex - 1]
+      }
+    }
+    
+    guard !indexes.isEmpty else {
+      return nil
     }
+    return indexes
+  }
 }

From dd1ed39fca150d4fa2905b902736f12a49f3efb1 Mon Sep 17 00:00:00 2001
From: Alessandro Martin <martin.acg@gmail.com>
Date: Thu, 24 Aug 2017 22:19:06 +0100
Subject: [PATCH 155/643] Code Review comments addressed

---
 Ring Buffer/RingBuffer.playground/Contents.swift | 13 ++++++++++---
 Ring Buffer/RingBuffer.swift                     | 13 ++++++++++---
 2 files changed, 20 insertions(+), 6 deletions(-)

diff --git a/Ring Buffer/RingBuffer.playground/Contents.swift b/Ring Buffer/RingBuffer.playground/Contents.swift
index d1195e102..adcf146b4 100644
--- a/Ring Buffer/RingBuffer.playground/Contents.swift	
+++ b/Ring Buffer/RingBuffer.playground/Contents.swift	
@@ -13,7 +13,9 @@ public struct RingBuffer<T> {
   @discardableResult
   public mutating func write(_ element: T) -> Bool {
     guard !isFull else { return false }
-    defer { writeIndex += 1 }
+    defer {
+        writeIndex += 1
+    }
     array[wrapped: writeIndex] = element
     return true
   }
@@ -21,7 +23,10 @@ public struct RingBuffer<T> {
   /* Returns nil if the buffer is empty. */
   public mutating func read() -> T? {
     guard !isEmpty else { return nil }
-    defer { array[wrapped: readIndex] = nil ; readIndex += 1 }
+    defer {
+        array[wrapped: readIndex] = nil
+        readIndex += 1
+    }
     return array[wrapped: readIndex]
   }
 
@@ -47,7 +52,9 @@ extension RingBuffer: Sequence {
     var index = readIndex
     return AnyIterator {
       guard index < self.writeIndex else { return nil }
-      defer { index += 1 }
+      defer {
+        index += 1
+        }
       return self.array[wrapped: index]
     }
   }
diff --git a/Ring Buffer/RingBuffer.swift b/Ring Buffer/RingBuffer.swift
index 7dd0d6fc3..0006afea6 100644
--- a/Ring Buffer/RingBuffer.swift	
+++ b/Ring Buffer/RingBuffer.swift	
@@ -23,7 +23,9 @@ public struct RingBuffer<T> {
   @discardableResult
   public mutating func write(_ element: T) -> Bool {
     guard !isFull else { return false }
-    defer { writeIndex += 1 }
+    defer {
+        writeIndex += 1
+    }
     array[wrapped: writeIndex] = element
     return true
   }
@@ -31,7 +33,10 @@ public struct RingBuffer<T> {
   /* Returns nil if the buffer is empty. */
   public mutating func read() -> T? {
     guard !isEmpty else { return nil }
-    defer { array[wrapped: readIndex] = nil ; readIndex += 1 }
+    defer {
+        array[wrapped: readIndex] = nil
+        readIndex += 1
+    }
     return array[wrapped: readIndex]
   }
 
@@ -57,7 +62,9 @@ public extension RingBuffer: Sequence {
     var index = readIndex
     return AnyIterator {
         guard index < self.writeIndex else { return nil }
-        defer { index += 1 }
+        defer {
+            index += 1
+        }
         return self.array[wrapped: index]
     }
   }

From 9b6ca04034f7dfc2c5eec2ba885a88d828d46468 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Thu, 24 Aug 2017 22:55:19 -0700
Subject: [PATCH 156/643] [Swift 4] Update LRU Cache

---
 LRU Cache/LRUCache.playground/Contents.swift | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/LRU Cache/LRUCache.playground/Contents.swift b/LRU Cache/LRUCache.playground/Contents.swift
index 35dcc5d59..2ebc03242 100644
--- a/LRU Cache/LRUCache.playground/Contents.swift	
+++ b/LRU Cache/LRUCache.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let cache = LRUCache<String>(2)
 cache.set("a", val: 1)
 cache.set("b", val: 2)

From 975709d99f1304d66c1d7b3b7c98734aeac83ee0 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Thu, 24 Aug 2017 22:57:23 -0700
Subject: [PATCH 157/643] [Swift 4] Update Ordered Set

---
 .../Pages/Example 1.xcplaygroundpage/Contents.swift         | 5 +++++
 .../Pages/Example 1.xcplaygroundpage/timeline.xctimeline    | 6 +++---
 2 files changed, 8 insertions(+), 3 deletions(-)

diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
index 2420019fc..c12dadf0f 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 //: # Example 1 with type Int
 
 var mySet = OrderedSet<Int>()
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline
index 454d1011b..53114d22e 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline	
+++ b/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline	
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=21&amp;CharacterRangeLoc=288&amp;EndingColumnNumber=22&amp;EndingLineNumber=18&amp;StartingColumnNumber=1&amp;StartingLineNumber=18&amp;Timestamp=496197876.557751"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=21&amp;CharacterRangeLoc=371&amp;EndingColumnNumber=0&amp;EndingLineNumber=24&amp;StartingColumnNumber=1&amp;StartingLineNumber=23&amp;Timestamp=525333424.593074"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=24&amp;CharacterRangeLoc=329&amp;EndingColumnNumber=27&amp;EndingLineNumber=20&amp;StartingColumnNumber=3&amp;StartingLineNumber=20&amp;Timestamp=496197876.557751"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=24&amp;CharacterRangeLoc=412&amp;EndingColumnNumber=0&amp;EndingLineNumber=26&amp;StartingColumnNumber=3&amp;StartingLineNumber=25&amp;Timestamp=525333424.593234"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=25&amp;CharacterRangeLoc=428&amp;EndingColumnNumber=28&amp;EndingLineNumber=26&amp;StartingColumnNumber=3&amp;StartingLineNumber=26&amp;Timestamp=496197876.557751"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=25&amp;CharacterRangeLoc=511&amp;EndingColumnNumber=0&amp;EndingLineNumber=32&amp;StartingColumnNumber=3&amp;StartingLineNumber=31&amp;Timestamp=525333424.593352"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>

From c03c0a558e12156b543be7482e649e571e89c6ac Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 08:33:30 -0700
Subject: [PATCH 158/643] [Swift 4] Update Longest Common Subsequence

---
 .../LongestCommonSubsequence.playground/Contents.swift       | 5 +++++
 .../contents.xcplayground                                    | 2 +-
 2 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift
index 0fc9ec325..c8d413e7f 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 extension String {
   public func longestCommonSubsequence(_ other: String) -> String {
 
diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground b/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground
index fc5b4ab70..5da2641c9 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
 <playground version='5.0' target-platform='ios'>
     <timeline fileName='timeline.xctimeline'/>
-</playground>
+</playground>
\ No newline at end of file

From c7d25842a6eb11d8fee32d6ebfddb0a9fb4d53ed Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 08:36:59 -0700
Subject: [PATCH 159/643] [Swift 4] Update Minimum Spanning Tree(unweighted)

---
 .../Contents.swift                                           | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
index 8ad04379c..65aa9fbc4 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func breadthFirstSearchMinimumSpanningTree(_ graph: Graph, source: Node) -> Graph {
   let minimumSpanningTree = graph.duplicate()
 

From c66f3c361b47c263b4bde9cbf076129fa5fb64bd Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 08:42:58 -0700
Subject: [PATCH 160/643] [Swift 4] Update Minimum Coin Change

---
 .../MinimumCoinChangeTests.swift              | 47 +++++++++++--------
 1 file changed, 27 insertions(+), 20 deletions(-)

diff --git a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
index 7c106eeb9..45beff775 100644
--- a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
+++ b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
@@ -2,27 +2,34 @@ import XCTest
 @testable import MinimumCoinChange
 
 class MinimumCoinChangeTests: XCTestCase {
-    func testExample() {
-        let mcc = MinimumCoinChange(coinSet: [1, 2, 5, 10, 20, 25])
-        print("Coin set: \(mcc.sortedCoinSet)")
-
-        do {
-            for i in 0..<100 {
-                let greedy = try mcc.changeGreedy(i)
-                let dynamic = try mcc.changeDynamic(i)
-
-                XCTAssertEqual(greedy.reduce(0, +), dynamic.reduce(0, +), "Greedy and Dynamic return two different changes")
-
-                if greedy.count != dynamic.count {
-                    print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
-                }
-            }
-        } catch {
-            XCTFail("Test Failed: impossible to change with the given coin set")
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
+  func testExample() {
+    let mcc = MinimumCoinChange(coinSet: [1, 2, 5, 10, 20, 25])
+    print("Coin set: \(mcc.sortedCoinSet)")
+    
+    do {
+      for i in 0..<100 {
+        let greedy = try mcc.changeGreedy(i)
+        let dynamic = try mcc.changeDynamic(i)
+        
+        XCTAssertEqual(greedy.reduce(0, +), dynamic.reduce(0, +), "Greedy and Dynamic return two different changes")
+        
+        if greedy.count != dynamic.count {
+          print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
         }
+      }
+    } catch {
+      XCTFail("Test Failed: impossible to change with the given coin set")
     }
-
-    static var allTests = [
-        ("testExample", testExample),
+  }
+  
+  static var allTests = [
+    ("testExample", testExample),
     ]
 }

From d8e0bf5eb18a6ac9e4bd281c6b3fc207afeb4b56 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 08:52:25 -0700
Subject: [PATCH 161/643] [Swift 4] Update Priority Queue

---
 Priority Queue/Tests/PriorityQueueTests.swift        | 7 +++++++
 Priority Queue/Tests/Tests.xcodeproj/project.pbxproj | 6 ++++--
 2 files changed, 11 insertions(+), 2 deletions(-)

diff --git a/Priority Queue/Tests/PriorityQueueTests.swift b/Priority Queue/Tests/PriorityQueueTests.swift
index 56536310d..e31fa3d07 100755
--- a/Priority Queue/Tests/PriorityQueueTests.swift	
+++ b/Priority Queue/Tests/PriorityQueueTests.swift	
@@ -11,6 +11,13 @@ private func < (m1: Message, m2: Message) -> Bool {
 }
 
 class PriorityQueueTest: XCTestCase {
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
   func testEmpty() {
     var queue = PriorityQueue<Message>(sort: <)
     XCTAssertTrue(queue.isEmpty)
diff --git a/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj b/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
index 0f7d84be9..5ddfd574d 100644
--- a/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
@@ -180,6 +180,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -219,6 +220,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -230,7 +232,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -242,7 +244,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From b85438e81864b29acce71a49186475c69719f2ac Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 08:56:36 -0700
Subject: [PATCH 162/643] [Swift 4] Update Radix Sort

---
 Radix Sort/RadixSort.playground/Contents.swift   | 5 +++++
 Radix Sort/Tests/RadixSortTests.swift            | 7 +++++++
 Radix Sort/Tests/Tests.xcodeproj/project.pbxproj | 6 ++++--
 3 files changed, 16 insertions(+), 2 deletions(-)

diff --git a/Radix Sort/RadixSort.playground/Contents.swift b/Radix Sort/RadixSort.playground/Contents.swift
index a4f7e3527..941723c37 100644
--- a/Radix Sort/RadixSort.playground/Contents.swift	
+++ b/Radix Sort/RadixSort.playground/Contents.swift	
@@ -2,6 +2,11 @@
 
 import Cocoa
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Test Radix Sort with small array of ten values
 var array: [Int] = [19, 4242, 2, 9, 912, 101, 55, 67, 89, 32]
 radixSort(&array)
diff --git a/Radix Sort/Tests/RadixSortTests.swift b/Radix Sort/Tests/RadixSortTests.swift
index 688bcdcb8..9b881318a 100644
--- a/Radix Sort/Tests/RadixSortTests.swift	
+++ b/Radix Sort/Tests/RadixSortTests.swift	
@@ -9,6 +9,13 @@
 import XCTest
 
 class RadixSortTests: XCTestCase {
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
   func testCombSort() {
     let expectedSequence: [Int] = [2, 9, 19, 32, 55, 67, 89, 101, 912, 4242]
     var sequence = [19, 4242, 2, 9, 912, 101, 55, 67, 89, 32]
diff --git a/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj b/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj
index 4b32f71b5..bef4ead9b 100644
--- a/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Radix Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -179,6 +179,7 @@
 				SDKROOT = macosx;
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -220,6 +221,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -233,7 +235,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = Swift.Algorithm.Club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -246,7 +248,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = Swift.Algorithm.Club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From acd52410739a05bf63c7773e1397170fb566e7b0 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 09:00:31 -0700
Subject: [PATCH 163/643] [Swift 4] Update Red Black Tree

---
 Red-Black Tree/RedBlackTree.playground/Contents.swift     | 7 ++++++-
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata | 4 ++--
 2 files changed, 8 insertions(+), 3 deletions(-)

diff --git a/Red-Black Tree/RedBlackTree.playground/Contents.swift b/Red-Black Tree/RedBlackTree.playground/Contents.swift
index 50d61167d..f14f18e58 100644
--- a/Red-Black Tree/RedBlackTree.playground/Contents.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Contents.swift	
@@ -2,6 +2,11 @@
 // Test for  the RedBlackTree implementation provided in the Source folder of this Playground
 import Foundation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let redBlackTree = RedBlackTree<Double>()
 
 let randomMax = Double(0x10000000)
@@ -27,4 +32,4 @@ for i in 0..<1000 {
     redBlackTree.verify()
   }
 }
-redBlackTree.verify()
\ No newline at end of file
+redBlackTree.verify()
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7fd89d5f2..f8f58fd7c 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1912,10 +1912,10 @@
       location = "group:Red-Black Tree"
       name = "Red-Black Tree">
       <FileRef
-         location = "group:README.markdown">
+         location = "group:RedBlackTree.playground">
       </FileRef>
       <FileRef
-         location = "group:Red-Black Tree 2.playground">
+         location = "group:README.markdown">
       </FileRef>
    </Group>
    <Group

From f03f5ecc42b7fa5a4c37b6f43b8429a40c849986 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 17:43:39 -0700
Subject: [PATCH 164/643] [Swift 4] Update Select Minimum Maximum

---
 .../SelectMinimumMaximum.playground/Contents.swift           | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift
index c30bf2fa4..e1101a864 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
+++ b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Compare each item to find minimum
 func minimum<T: Comparable>(_ array: [T]) -> T? {
   guard var minimum = array.first else {

From 5286469928e5c24de3a05404060e11f5473278b2 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 17:46:46 -0700
Subject: [PATCH 165/643] [Swift 4] Update Shell Sort

---
 Shell Sort/Tests/ShellSortTests.swift            | 7 +++++++
 Shell Sort/Tests/Tests.xcodeproj/project.pbxproj | 6 ++++--
 2 files changed, 11 insertions(+), 2 deletions(-)

diff --git a/Shell Sort/Tests/ShellSortTests.swift b/Shell Sort/Tests/ShellSortTests.swift
index f9404b781..494d6841e 100644
--- a/Shell Sort/Tests/ShellSortTests.swift	
+++ b/Shell Sort/Tests/ShellSortTests.swift	
@@ -1,6 +1,13 @@
 import XCTest
 
 class ShellSortTests: XCTestCase {
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
   func testShellSort() {
     checkSortAlgorithm { (a: [Int]) -> [Int] in
       var b = a
diff --git a/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj b/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj
index 1de1c7213..c2966af46 100644
--- a/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Shell Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -178,6 +178,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -214,6 +215,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -225,7 +227,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -237,7 +239,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From d1542eb5b57c87545a98d17b9edbbb961e8a54d8 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 17:54:35 -0700
Subject: [PATCH 166/643] [Swift 4] Update Shortest Path (Unweighted)

---
 .../Shortest path example.xcplaygroundpage/Contents.swift  | 5 +++++
 Shortest Path (Unweighted)/Tests/ShortestPathTests.swift   | 7 +++++++
 .../Tests/Tests.xcodeproj/project.pbxproj                  | 6 ++++--
 3 files changed, 16 insertions(+), 2 deletions(-)

diff --git a/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift
index 9f2eda4f3..2404f5b8c 100644
--- a/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
+++ b/Shortest Path (Unweighted)/ShortestPath.playground/Pages/Shortest path example.xcplaygroundpage/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   let shortestPathGraph = graph.duplicate()
 
diff --git a/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift b/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift
index 71b9f88ab..4d79eeaa7 100644
--- a/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift	
+++ b/Shortest Path (Unweighted)/Tests/ShortestPathTests.swift	
@@ -1,6 +1,13 @@
 import XCTest
 
 class ShortestPathTests: XCTestCase {
+  
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
 
   func testShortestPathWhenGivenTree() {
     let tree = Graph()
diff --git a/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj
index f1744fcf1..b601a1665 100644
--- a/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Shortest Path (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
@@ -182,6 +182,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -218,6 +219,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -231,7 +233,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -244,7 +246,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};

From 23ff396398e9ea3f4985c3bac25348c3a33c501e Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 18:00:40 -0700
Subject: [PATCH 167/643] [Swift 4] Update Single-Source Shortest Paths
 (Weighted)

---
 Graph/Graph.xcodeproj/project.pbxproj                |  2 ++
 .../SSSP.playground/Contents.swift                   |  5 +++++
 .../SSSP.xcodeproj/project.pbxproj                   | 12 ++++++------
 .../SSSPTests/SSSPTests.swift                        |  7 +++++++
 4 files changed, 20 insertions(+), 6 deletions(-)

diff --git a/Graph/Graph.xcodeproj/project.pbxproj b/Graph/Graph.xcodeproj/project.pbxproj
index 4822d80bb..17a5a7d6b 100644
--- a/Graph/Graph.xcodeproj/project.pbxproj
+++ b/Graph/Graph.xcodeproj/project.pbxproj
@@ -289,6 +289,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -338,6 +339,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_VERSION = 4.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift b/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift
index 652b558b1..e897ada4a 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift	
@@ -1,6 +1,11 @@
 import Graph
 import SSSP
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let graph = AdjacencyMatrixGraph<String>()
 let s = graph.createVertex("s")
 let t = graph.createVertex("t")
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj
index fb425a73e..44365e5aa 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj	
@@ -334,7 +334,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -378,7 +378,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -401,7 +401,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -421,7 +421,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -433,7 +433,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -445,7 +445,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.SSSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift b/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift
index 04584dfeb..924a487f5 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift	
@@ -10,6 +10,13 @@ import XCTest
 @testable import SSSP
 
 class SSSPTests: XCTestCase {
+  
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
 
   /**
    See Figure 24.4 of “Introduction to Algorithms” by Cormen et al, 3rd ed., pg 652

From 4c796cca9566e888ac6c3871f068c00f0a3a2b5e Mon Sep 17 00:00:00 2001
From: "Carlos A. King" <carlos.king70@gmail.com>
Date: Sat, 26 Aug 2017 22:22:54 -0400
Subject: [PATCH 168/643] [Swift 4] Update Shell Sort

---
 .../Shell Sort.playground/Contents.swift      | 34 +++++++++++++++++++
 .../contents.xcplayground                     |  4 +++
 2 files changed, 38 insertions(+)
 create mode 100644 Shell Sort/Shell Sort.playground/Contents.swift
 create mode 100644 Shell Sort/Shell Sort.playground/contents.xcplayground

diff --git a/Shell Sort/Shell Sort.playground/Contents.swift b/Shell Sort/Shell Sort.playground/Contents.swift
new file mode 100644
index 000000000..9e2153f88
--- /dev/null
+++ b/Shell Sort/Shell Sort.playground/Contents.swift	
@@ -0,0 +1,34 @@
+//: Playground - noun: a place where people can play
+
+import UIKit
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+    print("Hello, Swift 4!")
+#endif
+
+public func insertionSort(_ list: inout [Int], start: Int, gap: Int) {
+    for i in stride(from: (start + gap), to: list.count, by: gap) {
+        let currentValue = list[i]
+        var pos = i
+        while pos >= gap && list[pos - gap] > currentValue {
+            list[pos] = list[pos - gap]
+            pos -= gap
+        }
+        list[pos] = currentValue
+    }
+}
+
+public func shellSort(_ list: inout [Int]) {
+    var sublistCount = list.count / 2
+    while sublistCount > 0 {
+        for pos in 0..<sublistCount {
+            insertionSort(&list, start: pos, gap: sublistCount)
+        }
+        sublistCount = sublistCount / 2
+    }
+}
+
+var arr = [64, 20, 50, 33, 72, 10, 23, -1, 4, 5]
+
+shellSort(&arr)
diff --git a/Shell Sort/Shell Sort.playground/contents.xcplayground b/Shell Sort/Shell Sort.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Shell Sort/Shell Sort.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file

From 1df06b2a962c63e44cf90aae513c149511d69a19 Mon Sep 17 00:00:00 2001
From: "Carlos A. King" <carlos.king70@gmail.com>
Date: Sat, 26 Aug 2017 22:55:08 -0400
Subject: [PATCH 169/643] Update README.markdown

---
 Shell Sort/README.markdown | 18 ++----------------
 1 file changed, 2 insertions(+), 16 deletions(-)

diff --git a/Shell Sort/README.markdown b/Shell Sort/README.markdown
index c21c29685..72375e51b 100644
--- a/Shell Sort/README.markdown	
+++ b/Shell Sort/README.markdown	
@@ -117,24 +117,10 @@ Here is an implementation of Shell Sort in Swift:
 var arr = [64, 20, 50, 33, 72, 10, 23, -1, 4, 5]
 
 public func shellSort(_ list: inout [Int]) {
-    
     var sublistCount = list.count / 2
-   
     while sublistCount > 0 {
-        
-        for index in 0..<list.count {
-           
-            guard index + sublistCount < list.count else { break }
-            
-            if list[index] > list[index + sublistCount] {
-                swap(&list[index], &list[index + sublistCount])
-            }
-            
-            guard sublistCount == 1 && index > 0 else { continue }
-            
-            if list[index - 1] > list[index] {
-                swap(&list[index - 1], &list[index])
-            }
+        for pos in 0..<sublistCount {
+            insertionSort(&list, start: pos, gap: sublistCount)
         }
         sublistCount = sublistCount / 2
     }

From da7b056a139cff811a607dff953d3e51718fc3ed Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 26 Aug 2017 18:31:49 -0700
Subject: [PATCH 170/643] [Bug] Fix build error

---
 .travis.yml                                   |  2 +-
 Quicksort/Tests/QuicksortTests.swift          |  7 ++++++
 .../project.pbxproj                           | 22 ++++++++++---------
 .../contents.xcworkspacedata                  |  2 +-
 .../xcschemes/Tests-Quicksort.xcscheme}       |  6 ++---
 .../contents.xcworkspacedata                  |  3 ---
 6 files changed, 24 insertions(+), 18 deletions(-)
 rename Quicksort/Tests/{Tests(quicksort).xcodeproj => Tests-Quicksort.xcodeproj}/project.pbxproj (93%)
 rename Quicksort/Tests/{Tests(quicksort).xcodeproj => Tests-Quicksort.xcodeproj}/project.xcworkspace/contents.xcworkspacedata (50%)
 rename Quicksort/Tests/{Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme => Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme} (90%)

diff --git a/.travis.yml b/.travis.yml
index 6efcbd42b..244b8819d 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -32,7 +32,7 @@ script:
 - xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Quicksort/Tests/Tests(quicksort).xcodeproj -scheme Tests(quicksort)
+- xcodebuild test -project ./Quicksort/Tests/Tests-Quicksort.xcodeproj -scheme Tests-Quicksort
 - xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
diff --git a/Quicksort/Tests/QuicksortTests.swift b/Quicksort/Tests/QuicksortTests.swift
index c8d9a62e6..0a8f1a2a8 100644
--- a/Quicksort/Tests/QuicksortTests.swift
+++ b/Quicksort/Tests/QuicksortTests.swift
@@ -1,6 +1,13 @@
 import XCTest
 
 class QuicksortTests: XCTestCase {
+  func testSwift4() {
+    // last checked with Xcode 9.0b4
+    #if swift(>=4.0)
+      print("Hello, Swift 4!")
+    #endif
+  }
+  
   func testQuicksort() {
     checkSortAlgorithm(quicksort)
   }
diff --git a/Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
similarity index 93%
rename from Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj
rename to Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
index 70deb0c74..c1b14e727 100644
--- a/Quicksort/Tests/Tests(quicksort).xcodeproj/project.pbxproj
+++ b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
@@ -13,7 +13,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Tests(quicksort).xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC801C779D720067B71D /* Tests-Quicksort.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Tests-Quicksort.xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3E51C77A4CA003CECC7 /* Quicksort.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = Quicksort.swift; path = ../Quicksort.swift; sourceTree = SOURCE_ROOT; };
 		7B80C3E71C77A4D0003CECC7 /* QuicksortTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = QuicksortTests.swift; sourceTree = SOURCE_ROOT; };
@@ -42,7 +42,7 @@
 		7B2BBC721C779D710067B71D /* Products */ = {
 			isa = PBXGroup;
 			children = (
-				7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */,
+				7B2BBC801C779D720067B71D /* Tests-Quicksort.xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -62,9 +62,9 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		7B2BBC7F1C779D720067B71D /* Tests(quicksort) */ = {
+		7B2BBC7F1C779D720067B71D /* Tests-Quicksort */ = {
 			isa = PBXNativeTarget;
-			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests(quicksort)" */;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests-Quicksort" */;
 			buildPhases = (
 				7B2BBC7C1C779D720067B71D /* Sources */,
 				7B2BBC7D1C779D720067B71D /* Frameworks */,
@@ -74,9 +74,9 @@
 			);
 			dependencies = (
 			);
-			name = "Tests(quicksort)";
+			name = "Tests-Quicksort";
 			productName = TestsTests;
-			productReference = 7B2BBC801C779D720067B71D /* Tests(quicksort).xctest */;
+			productReference = 7B2BBC801C779D720067B71D /* Tests-Quicksort.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 /* End PBXNativeTarget section */
@@ -95,7 +95,7 @@
 					};
 				};
 			};
-			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests(quicksort)" */;
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests-Quicksort" */;
 			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
@@ -108,7 +108,7 @@
 			projectDirPath = "";
 			projectRoot = "";
 			targets = (
-				7B2BBC7F1C779D720067B71D /* Tests(quicksort) */,
+				7B2BBC7F1C779D720067B71D /* Tests-Quicksort */,
 			);
 		};
 /* End PBXProject section */
@@ -187,6 +187,7 @@
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -233,6 +234,7 @@
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
@@ -265,7 +267,7 @@
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests(quicksort)" */ = {
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests-Quicksort" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC871C779D720067B71D /* Debug */,
@@ -274,7 +276,7 @@
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
 		};
-		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests(quicksort)" */ = {
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Tests-Quicksort" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
 				7B2BBC8D1C779D720067B71D /* Debug */,
diff --git a/Quicksort/Tests/Tests(quicksort).xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.xcworkspace/contents.xcworkspacedata
similarity index 50%
rename from Quicksort/Tests/Tests(quicksort).xcodeproj/project.xcworkspace/contents.xcworkspacedata
rename to Quicksort/Tests/Tests-Quicksort.xcodeproj/project.xcworkspace/contents.xcworkspacedata
index 6c0ea8493..c948249d9 100644
--- a/Quicksort/Tests/Tests(quicksort).xcodeproj/project.xcworkspace/contents.xcworkspacedata
+++ b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -2,6 +2,6 @@
 <Workspace
    version = "1.0">
    <FileRef
-      location = "self:Tests.xcodeproj">
+      location = "self:/Users/kaichen/src/swift-algorithm-club/Quicksort/Tests/Tests-Quicksort.xcodeproj">
    </FileRef>
 </Workspace>
diff --git a/Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme b/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
similarity index 90%
rename from Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme
rename to Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
index ac3eafc78..5b67c6f70 100644
--- a/Quicksort/Tests/Tests(quicksort).xcodeproj/xcshareddata/xcschemes/Tests(quicksort).xcscheme
+++ b/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
@@ -18,9 +18,9 @@
             <BuildableReference
                BuildableIdentifier = "primary"
                BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
-               BuildableName = "Tests(quicksort).xctest"
-               BlueprintName = "Tests(quicksort)"
-               ReferencedContainer = "container:Tests(quicksort).xcodeproj">
+               BuildableName = "Tests-Quicksort.xctest"
+               BlueprintName = "Tests-Quicksort"
+               ReferencedContainer = "container:Tests-Quicksort.xcodeproj">
             </BuildableReference>
          </TestableReference>
       </Testables>
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 7fd89d5f2..e1b09e0b2 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1841,9 +1841,6 @@
          <FileRef
             location = "group:SortingTestHelpers.swift">
          </FileRef>
-         <FileRef
-            location = "group:/Users/danielstokowski/Documents/GitHub/swift-algorithm-club/Quicksort/Tests/Tests(quicksort).xcodeproj">
-         </FileRef>
       </Group>
    </Group>
    <Group

From a5cf6b71c4dab7f6e1dfbf8c28687eb8b0b563f3 Mon Sep 17 00:00:00 2001
From: Mac Bellingrath <mbellingrath@weddingwire.com>
Date: Tue, 29 Aug 2017 09:19:42 -0400
Subject: [PATCH 171/643] removes redundant case let ? statements from
 workspace

---
 Binary Search Tree/README.markdown                   | 12 ++++++------
 .../Sources/BinarySearchTree.swift                   | 12 ++++++------
 .../LRUCache.playground/Sources/LinkedList.swift     |  4 ++--
 Linked List/LinkedList.swift                         |  4 ++--
 Linked List/README.markdown                          |  6 +++---
 .../Sources/ThreadedBinaryTree.swift                 |  8 ++++----
 6 files changed, 23 insertions(+), 23 deletions(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 80c2df7df..340a58655 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -267,7 +267,7 @@ Searching is a recursive process, but you can also implement it with a simple lo
 ```swift
   public func search(value: T) -> BinarySearchTree? {
     var node: BinarySearchTree? = self
-    while case let n? = node {
+    while let n = node {
       if value < n.value {
         node = n.left
       } else if value > n.value {
@@ -391,7 +391,7 @@ We also need a function that returns the minimum and maximum of a node:
 ```swift
   public func minimum() -> BinarySearchTree {
     var node = self
-    while case let next? = node.left {
+    while let next = node.left {
       node = next
     }
     return node
@@ -399,7 +399,7 @@ We also need a function that returns the minimum and maximum of a node:
 
   public func maximum() -> BinarySearchTree {
     var node = self
-    while case let next? = node.right {
+    while let next = node.right {
       node = next
     }
     return node
@@ -471,7 +471,7 @@ You can also calculate the *depth* of a node, which is the distance to the root.
   public func depth() -> Int {
     var node = self
     var edges = 0
-    while case let parent? = node.parent {
+    while let parent = node.parent {
       node = parent
       edges += 1
     }
@@ -503,7 +503,7 @@ The `predecessor()` function returns the node whose value precedes the current v
       return left.maximum()
     } else {
       var node = self
-      while case let parent? = node.parent {
+      while let parent = node.parent {
         if parent.value < value { return parent }
         node = parent
       }
@@ -524,7 +524,7 @@ The code for `successor()` works the same way but mirrored:
       return right.minimum()
     } else {
       var node = self
-      while case let parent? = node.parent {
+      while let parent = node.parent {
         if parent.value > value { return parent }
         node = parent
       }
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index 8a126e950..34ade3896 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -155,7 +155,7 @@ extension BinarySearchTree {
   */
   public func search(value: T) -> BinarySearchTree? {
     var node: BinarySearchTree? = self
-    while case let n? = node {
+    while let n = node {
       if value < n.value {
         node = n.left
       } else if value > n.value {
@@ -189,7 +189,7 @@ extension BinarySearchTree {
   */
   public func minimum() -> BinarySearchTree {
     var node = self
-    while case let next? = node.left {
+    while let next = node.left {
       node = next
     }
     return node
@@ -200,7 +200,7 @@ extension BinarySearchTree {
   */
   public func maximum() -> BinarySearchTree {
     var node = self
-    while case let next? = node.right {
+    while let next = node.right {
       node = next
     }
     return node
@@ -213,7 +213,7 @@ extension BinarySearchTree {
   public func depth() -> Int {
     var node = self
     var edges = 0
-    while case let parent? = node.parent {
+    while let parent = node.parent {
       node = parent
       edges += 1
     }
@@ -240,7 +240,7 @@ extension BinarySearchTree {
       return left.maximum()
     } else {
       var node = self
-      while case let parent? = node.parent {
+      while let parent = node.parent {
         if parent.value < value { return parent }
         node = parent
       }
@@ -256,7 +256,7 @@ extension BinarySearchTree {
       return right.minimum()
     } else {
       var node = self
-      while case let parent? = node.parent {
+      while let parent = node.parent {
         if parent.value > value { return parent }
         node = parent
       }
diff --git a/LRU Cache/LRUCache.playground/Sources/LinkedList.swift b/LRU Cache/LRUCache.playground/Sources/LinkedList.swift
index 94e978c07..a5594eb31 100755
--- a/LRU Cache/LRUCache.playground/Sources/LinkedList.swift	
+++ b/LRU Cache/LRUCache.playground/Sources/LinkedList.swift	
@@ -26,7 +26,7 @@ public final class LinkedList<T> {
 
     public var last: Node? {
         if var node = head {
-            while case let next? = node.next {
+            while let next = node.next {
                 node = next
             }
             return node
@@ -38,7 +38,7 @@ public final class LinkedList<T> {
     public var count: Int {
         if var node = head {
             var c = 1
-            while case let next? = node.next {
+            while let next = node.next {
                 node = next
                 c += 1
             }
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 94e978c07..a5594eb31 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -26,7 +26,7 @@ public final class LinkedList<T> {
 
     public var last: Node? {
         if var node = head {
-            while case let next? = node.next {
+            while let next = node.next {
                 node = next
             }
             return node
@@ -38,7 +38,7 @@ public final class LinkedList<T> {
     public var count: Int {
         if var node = head {
             var c = 1
-            while case let next? = node.next {
+            while let next = node.next {
                 node = next
                 c += 1
             }
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 9aaecc206..240d3fbba 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -109,7 +109,7 @@ Let's also add a property that gives you the last node in the list. This is wher
 ```swift
   public var last: Node? {
     if var node = head {
-      while case let next? = node.next {
+      while let next = node.next {
         node = next
       }
       return node
@@ -121,7 +121,7 @@ Let's also add a property that gives you the last node in the list. This is wher
 
 If you're new to Swift, you've probably seen `if let` but maybe not `if var`. It does the same thing -- it unwraps the `head` optional and puts the result in a new local variable named `node`. The difference is that `node` is not a constant but an actual variable, so we can change it inside the loop.
 
-The loop also does some Swift magic. The `while case let next? = node.next` bit keeps looping until `node.next` is nil. You could have written this as follows:
+The loop also does some Swift magic. The `while let next = node.next` bit keeps looping until `node.next` is nil. You could have written this as follows:
 
 ```swift
       var node: Node? = head
@@ -198,7 +198,7 @@ Let's add a method to count how many nodes are in the list. This will look very
   public var count: Int {
     if var node = head {
       var c = 1
-      while case let next? = node.next {
+      while let next = node.next {
         node = next
         c += 1
       }
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift
index c85f56a68..5c7671688 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
@@ -217,7 +217,7 @@ extension ThreadedBinaryTree {
   */
   public func search(_ value: T) -> ThreadedBinaryTree? {
     var node: ThreadedBinaryTree? = self
-    while case let n? = node {
+    while let n = node {
       if value < n.value {
         node = n.left
       } else if value > n.value {
@@ -252,7 +252,7 @@ extension ThreadedBinaryTree {
   */
   public func minimum() -> ThreadedBinaryTree {
     var node = self
-    while case let next? = node.left {
+    while let next = node.left {
       node = next
     }
     return node
@@ -263,7 +263,7 @@ extension ThreadedBinaryTree {
   */
   public func maximum() -> ThreadedBinaryTree {
     var node = self
-    while case let next? = node.right {
+    while let next = node.right {
       node = next
     }
     return node
@@ -276,7 +276,7 @@ extension ThreadedBinaryTree {
   public func depth() -> Int {
     var node = self
     var edges = 0
-    while case let parent? = node.parent {
+    while let parent = node.parent {
       node = parent
       edges += 1
     }

From 23770dd5dc49948534961b93c4dbdecc72d14e7c Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Mon, 4 Sep 2017 18:16:29 +0100
Subject: [PATCH 172/643] Add Multiset

---
 Multiset/Multiset.playground/Contents.swift   | 19 +++++
 .../Sources/Multiset.swift                    | 82 +++++++++++++++++++
 .../Multiset.playground/contents.xcplayground |  4 +
 Multiset/README.markdown                      | 12 +++
 README.markdown                               |  2 +-
 .../contents.xcworkspacedata                  | 10 +++
 6 files changed, 128 insertions(+), 1 deletion(-)
 create mode 100644 Multiset/Multiset.playground/Contents.swift
 create mode 100644 Multiset/Multiset.playground/Sources/Multiset.swift
 create mode 100644 Multiset/Multiset.playground/contents.xcplayground
 create mode 100644 Multiset/README.markdown

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
new file mode 100644
index 000000000..e99d12b01
--- /dev/null
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -0,0 +1,19 @@
+//: Playground - noun: a place where people can play
+
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
+
+import Cocoa
+
+var set = Multiset<String>()
+
+set.add("Foo")
+set.add("Foo")
+set.add("Bar")
+set.add("Baz")
+
+set.count
+set.count(for: "Foo")
+
+set.allItems()
\ No newline at end of file
diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
new file mode 100644
index 000000000..ac393e8dd
--- /dev/null
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -0,0 +1,82 @@
+//
+//  Multiset.swift
+//  Multiset
+//
+//  Created by Simon Whitaker on 28/08/2017.
+//
+
+import Foundation
+
+public struct Multiset<T: Hashable> {
+  fileprivate var storage: Dictionary<T, Int>
+  private var _count: Int = 0
+
+  public init() {
+    storage = Dictionary<T, Int>()
+  }
+
+  public mutating func add (_ elem: T) {
+    if let currentCount = self.storage[elem] {
+      self.storage[elem] = currentCount + 1;
+    } else {
+      self.storage[elem] = 1
+    }
+    _count += 1
+  }
+
+  public mutating func remove (_ elem: T) {
+    if let currentCount = self.storage[elem] {
+      if currentCount > 1 {
+        self.storage[elem] = currentCount - 1
+      } else {
+        self.storage.removeValue(forKey: elem)
+      }
+      _count -= 1
+    }
+  }
+
+  public func isSubSet (of superset: Multiset<T>) -> Bool {
+    for (key, count) in self.storage {
+      let supersetcount = superset.storage[key] ?? 0
+      if count > supersetcount {
+        return false
+      }
+    }
+    return true
+  }
+
+  public var count: Int {
+    get {
+      return _count
+    }
+  }
+
+  public func count(for key: T) -> Int {
+    return self.storage[key] ?? 0
+  }
+
+  public func allItems() -> [T] {
+    var result = Array<T>()
+    for (key, count) in self.storage {
+      for _ in 0 ..< count {
+        result.append(key)
+      }
+    }
+    return result
+  }
+}
+
+extension Multiset: Equatable {
+  public static func == (lhs: Multiset<T>, rhs: Multiset<T>) -> Bool {
+    if lhs.storage.count != rhs.storage.count {
+      return false
+    }
+    for (lkey, lcount) in lhs.storage {
+      let rcount = rhs.storage[lkey] ?? 0
+      if lcount != rcount {
+        return false
+      }
+    }
+    return true
+  }
+}
diff --git a/Multiset/Multiset.playground/contents.xcplayground b/Multiset/Multiset.playground/contents.xcplayground
new file mode 100644
index 000000000..63b6dd8df
--- /dev/null
+++ b/Multiset/Multiset.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Multiset/README.markdown b/Multiset/README.markdown
new file mode 100644
index 000000000..a6e7c7391
--- /dev/null
+++ b/Multiset/README.markdown
@@ -0,0 +1,12 @@
+# An implementation of the multiset data stucture
+
+## Usage
+
+``` swift
+var b = Multiset<Character>();
+for c in "hello".characters {
+    b.add(c)
+}
+let count = b.count // count is 5
+let lcount = b.count(for: "l") // lcount is 2
+```
diff --git a/README.markdown b/README.markdown
index 3c25a4bb3..464c6b199 100644
--- a/README.markdown
+++ b/README.markdown
@@ -172,7 +172,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 - [Bloom Filter](Bloom%20Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
 - [Hash Set](Hash%20Set/). A set implemented using a hash table.
-- Multiset
+- [Multiset](Multiset/). A set where the number of times an element is added matters. (Also known as a bag.)
 - [Ordered Set](Ordered%20Set/). A set where the order of items matters.
 
 ### Graphs
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index e1b09e0b2..d27e01804 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1656,6 +1656,16 @@
          location = "group:README.markdown">
       </FileRef>
    </Group>
+   <Group
+      location = "container:"
+      name = "Multiset">
+      <FileRef
+         location = "group:Multiset/Multiset.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Multiset/README.markdown">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Ordered Array"
       name = "Ordered Array">

From 8fcb7e4cd9fbf68a3d2afec558ad816428f7dcca Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Mon, 4 Sep 2017 18:22:47 +0100
Subject: [PATCH 173/643] Make allItems a var

---
 Multiset/Multiset.playground/Contents.swift        |  3 ++-
 .../Multiset.playground/Sources/Multiset.swift     | 14 ++++++++------
 2 files changed, 10 insertions(+), 7 deletions(-)

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
index e99d12b01..59abb7f30 100644
--- a/Multiset/Multiset.playground/Contents.swift
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -16,4 +16,5 @@ set.add("Baz")
 set.count
 set.count(for: "Foo")
 
-set.allItems()
\ No newline at end of file
+set.allItems
+
diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index ac393e8dd..32bc0db92 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -55,14 +55,16 @@ public struct Multiset<T: Hashable> {
     return self.storage[key] ?? 0
   }
 
-  public func allItems() -> [T] {
-    var result = Array<T>()
-    for (key, count) in self.storage {
-      for _ in 0 ..< count {
-        result.append(key)
+  public var allItems: [T] {
+    get {
+      var result = Array<T>()
+      for (key, count) in self.storage {
+        for _ in 0 ..< count {
+          result.append(key)
+        }
       }
+      return result
     }
-    return result
   }
 }
 

From 4fbe62b0f0511b9c7a7f2c250d57c962d532ca8b Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Mon, 4 Sep 2017 18:38:40 +0100
Subject: [PATCH 174/643] Adopt Ray Wenderlich Swift coding style

https://github.com/raywenderlich/swift-style-guide
---
 .../Sources/Multiset.swift                    | 53 +++++++++----------
 1 file changed, 25 insertions(+), 28 deletions(-)

diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index 32bc0db92..67a8851c6 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -7,36 +7,36 @@
 
 import Foundation
 
-public struct Multiset<T: Hashable> {
-  fileprivate var storage: Dictionary<T, Int>
-  private var _count: Int = 0
+public struct Multiset<Element: Hashable> {
+  fileprivate var storage: [Element: Int]
+  private var _count = 0
 
   public init() {
-    storage = Dictionary<T, Int>()
+    storage = [:]
   }
 
-  public mutating func add (_ elem: T) {
-    if let currentCount = self.storage[elem] {
-      self.storage[elem] = currentCount + 1;
+  public mutating func add (_ elem: Element) {
+    if let currentCount = storage[elem] {
+      storage[elem] = currentCount + 1;
     } else {
-      self.storage[elem] = 1
+      storage[elem] = 1
     }
     _count += 1
   }
 
-  public mutating func remove (_ elem: T) {
-    if let currentCount = self.storage[elem] {
+  public mutating func remove (_ elem: Element) {
+    if let currentCount = storage[elem] {
       if currentCount > 1 {
-        self.storage[elem] = currentCount - 1
+        storage[elem] = currentCount - 1
       } else {
-        self.storage.removeValue(forKey: elem)
+        storage.removeValue(forKey: elem)
       }
       _count -= 1
     }
   }
 
-  public func isSubSet (of superset: Multiset<T>) -> Bool {
-    for (key, count) in self.storage {
+  public func isSubSet (of superset: Multiset<Element>) -> Bool {
+    for (key, count) in storage {
       let supersetcount = superset.storage[key] ?? 0
       if count > supersetcount {
         return false
@@ -46,30 +46,27 @@ public struct Multiset<T: Hashable> {
   }
 
   public var count: Int {
-    get {
-      return _count
-    }
+    return _count
   }
 
-  public func count(for key: T) -> Int {
-    return self.storage[key] ?? 0
+  public func count(for key: Element) -> Int {
+    return storage[key] ?? 0
   }
 
-  public var allItems: [T] {
-    get {
-      var result = Array<T>()
-      for (key, count) in self.storage {
-        for _ in 0 ..< count {
-          result.append(key)
-        }
+  public var allItems: [Element] {
+    var result = Array<Element>()
+    for (key, count) in storage {
+      for _ in 0 ..< count {
+        result.append(key)
       }
-      return result
     }
+    return result
   }
 }
 
+// MARK: - Equatable
 extension Multiset: Equatable {
-  public static func == (lhs: Multiset<T>, rhs: Multiset<T>) -> Bool {
+  public static func == (lhs: Multiset<Element>, rhs: Multiset<Element>) -> Bool {
     if lhs.storage.count != rhs.storage.count {
       return false
     }

From 6fda1b763408c4ba35977e3f8f9cfea28d96802d Mon Sep 17 00:00:00 2001
From: Simon Whitaker <sw@netcetera.org>
Date: Mon, 4 Sep 2017 21:41:09 +0100
Subject: [PATCH 175/643] Add isSubSet examples

---
 Multiset/Multiset.playground/Contents.swift | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
index 59abb7f30..e9c64a74b 100644
--- a/Multiset/Multiset.playground/Contents.swift
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -18,3 +18,9 @@ set.count(for: "Foo")
 
 set.allItems
 
+var set2 = Multiset<String>()
+set2.add("Foo")
+set2.add("Foo")
+
+set2.isSubSet(of: set) // true
+set.isSubSet(of: set2) // false

From 0490426d16ca4a52e798674f873a36d5dd7332cf Mon Sep 17 00:00:00 2001
From: Simon Whitaker <sw@netcetera.org>
Date: Mon, 4 Sep 2017 21:41:52 +0100
Subject: [PATCH 176/643] Make count type UInt

---
 Multiset/Multiset.playground/Sources/Multiset.swift | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index 67a8851c6..b4d309e24 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -8,8 +8,8 @@
 import Foundation
 
 public struct Multiset<Element: Hashable> {
-  fileprivate var storage: [Element: Int]
-  private var _count = 0
+  fileprivate var storage: [Element: UInt]
+  private var _count: UInt = 0
 
   public init() {
     storage = [:]
@@ -45,16 +45,16 @@ public struct Multiset<Element: Hashable> {
     return true
   }
 
-  public var count: Int {
+  public var count: UInt {
     return _count
   }
 
-  public func count(for key: Element) -> Int {
+  public func count(for key: Element) -> UInt {
     return storage[key] ?? 0
   }
 
   public var allItems: [Element] {
-    var result = Array<Element>()
+    var result = [Element]()
     for (key, count) in storage {
       for _ in 0 ..< count {
         result.append(key)

From d5c14d3735882e8ee3ca46696ec6d30757a0bf79 Mon Sep 17 00:00:00 2001
From: Simon Whitaker <sw@netcetera.org>
Date: Mon, 4 Sep 2017 21:42:02 +0100
Subject: [PATCH 177/643] Improve README

---
 Multiset/README.markdown | 91 ++++++++++++++++++++++++++++++++++++----
 1 file changed, 84 insertions(+), 7 deletions(-)

diff --git a/Multiset/README.markdown b/Multiset/README.markdown
index a6e7c7391..eb28e3eea 100644
--- a/Multiset/README.markdown
+++ b/Multiset/README.markdown
@@ -1,12 +1,89 @@
-# An implementation of the multiset data stucture
+# Multiset
 
-## Usage
+A multiset (also known as a bag) is a data structure similar to a regular set, but it can store multiple instances of the same element.
+
+The following all represent the same *set*, but do not represent the same *multiset*.
+
+```
+[1, 3, 2]
+[1, 3, 2, 2]
+```
+
+In this multiset implementation, ordering is unimportant. So these two multisets are identical:
+
+```
+[1, 2, 2]
+[2, 1, 2]
+```
+
+Typical operations on a multiset are:
+
+- Add an element
+- Remove an element
+- Get the count for an element (the number of times it's been added)
+- Get the count for the whole set (the number of items that have been added)
+- Check whether it is a subset of another multiset
+
+## Implementation
+
+Under the hood, this implementation of Multiset uses a dictionary to store a mapping of elements to the number of times they've been added.
+
+Here's the essence of it:
+
+``` swift
+public struct Multiset<Element: Hashable> {
+  fileprivate var storage: [Element: UInt]
+  
+  public init() {
+    storage = [:]
+  }
+```
+
+And here's how you'd use this class to create a multiset of strings:
+
+``` swift
+var set = Multiset<String>()
+```
+
+Adding an element is a case of incrementing the counter for that element, or setting it to 1 if it doesn't already exist:
+
+``` swift
+public mutating func add (_ elem: Element) {
+  if let currentCount = storage[elem] {
+    storage[elem] = currentCount + 1;
+  } else {
+    storage[elem] = 1
+  }
+}
+```
+
+Here's how you'd use this method to add to the set we created earlier:
+
+```swift
+set.add("foo")
+set.add("foo") 
+```
+
+Our set now contains two elements, both the string "foo".
+
+Removing an element works much the same way as adding; decrement the counter for the element, or remove it from the underlying dictionary if its value is 1 before removal.
+
+``` swift
+public mutating func remove (_ elem: Element) {
+  if let currentCount = storage[elem] {
+    if currentCount > 1 {
+      storage[elem] = currentCount - 1
+    } else {
+      storage.removeValue(forKey: elem)
+    }
+  }
+}
+```
+
+Getting the count for an item is simple: we just return the value for the given item in the internal dictionary.
 
 ``` swift
-var b = Multiset<Character>();
-for c in "hello".characters {
-    b.add(c)
+public func count(for key: Element) -> UInt {
+  return storage[key] ?? 0
 }
-let count = b.count // count is 5
-let lcount = b.count(for: "l") // lcount is 2
 ```

From 6c7eb0c3f1936dfe782da74a4ab325eed5ac92cd Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Tue, 5 Sep 2017 06:19:31 +0100
Subject: [PATCH 178/643] Address review comments

---
 .../Sources/Multiset.swift                    | 22 +++++--------------
 Multiset/README.markdown                      |  2 ++
 2 files changed, 8 insertions(+), 16 deletions(-)

diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index b4d309e24..71bc78fa9 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -8,20 +8,14 @@
 import Foundation
 
 public struct Multiset<Element: Hashable> {
-  fileprivate var storage: [Element: UInt]
-  private var _count: UInt = 0
+  private var storage: [Element: UInt] = [:]
+  public private(set) var count: UInt = 0
 
-  public init() {
-    storage = [:]
-  }
+  public init() {}
 
   public mutating func add (_ elem: Element) {
-    if let currentCount = storage[elem] {
-      storage[elem] = currentCount + 1;
-    } else {
-      storage[elem] = 1
-    }
-    _count += 1
+    storage[elem, default: 0] += 1
+    count += 1
   }
 
   public mutating func remove (_ elem: Element) {
@@ -31,7 +25,7 @@ public struct Multiset<Element: Hashable> {
       } else {
         storage.removeValue(forKey: elem)
       }
-      _count -= 1
+      count -= 1
     }
   }
 
@@ -45,10 +39,6 @@ public struct Multiset<Element: Hashable> {
     return true
   }
 
-  public var count: UInt {
-    return _count
-  }
-
   public func count(for key: Element) -> UInt {
     return storage[key] ?? 0
   }
diff --git a/Multiset/README.markdown b/Multiset/README.markdown
index eb28e3eea..fd72d269c 100644
--- a/Multiset/README.markdown
+++ b/Multiset/README.markdown
@@ -87,3 +87,5 @@ public func count(for key: Element) -> UInt {
   return storage[key] ?? 0
 }
 ```
+
+*Written for the Swift Algorithm Club by Simon Whitaker*

From ecaf749467a2966474ab94bca7bf8e386fb53f4c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 4 Sep 2017 22:36:45 -0700
Subject: [PATCH 179/643] Fixed readme to match code.

---
 Multiset/README.markdown | 12 +++---------
 1 file changed, 3 insertions(+), 9 deletions(-)

diff --git a/Multiset/README.markdown b/Multiset/README.markdown
index fd72d269c..85538d870 100644
--- a/Multiset/README.markdown
+++ b/Multiset/README.markdown
@@ -32,11 +32,9 @@ Here's the essence of it:
 
 ``` swift
 public struct Multiset<Element: Hashable> {
-  fileprivate var storage: [Element: UInt]
+  public private(set) var storage: [Element: UInt] = [:]
   
-  public init() {
-    storage = [:]
-  }
+  public init() {}
 ```
 
 And here's how you'd use this class to create a multiset of strings:
@@ -49,11 +47,7 @@ Adding an element is a case of incrementing the counter for that element, or set
 
 ``` swift
 public mutating func add (_ elem: Element) {
-  if let currentCount = storage[elem] {
-    storage[elem] = currentCount + 1;
-  } else {
-    storage[elem] = 1
-  }
+  storage[elem, default: 0] += 1
 }
 ```
 

From fb523d64407e9f2e51cec1dbf48aaf4634255c88 Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Tue, 5 Sep 2017 08:03:57 +0100
Subject: [PATCH 180/643] Add ctor for instantiating with a collection of
 Hashables

---
 Multiset/Multiset.playground/Contents.swift   |  5 +++
 .../Sources/Multiset.swift                    | 24 +++++++----
 Multiset/README.markdown                      | 43 ++++++++++++-------
 3 files changed, 47 insertions(+), 25 deletions(-)

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
index e9c64a74b..f8b05d2b0 100644
--- a/Multiset/Multiset.playground/Contents.swift
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -24,3 +24,8 @@ set2.add("Foo")
 
 set2.isSubSet(of: set) // true
 set.isSubSet(of: set2) // false
+
+var cacti = Multiset<Character>("cacti")
+var tactical = Multiset<Character>("tactical")
+cacti.isSubSet(of: tactical) // true
+tactical.isSubSet(of: cacti) // false
diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index 71bc78fa9..f77983f8c 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -7,18 +7,24 @@
 
 import Foundation
 
-public struct Multiset<Element: Hashable> {
-  private var storage: [Element: UInt] = [:]
+public struct Multiset<T: Hashable> {
+  private var storage: [T: UInt] = [:]
   public private(set) var count: UInt = 0
 
   public init() {}
 
-  public mutating func add (_ elem: Element) {
+  public init<C: Collection>(_ collection: C) where C.Element == T {
+    for element in collection {
+      self.add(element)
+    }
+  }
+
+  public mutating func add (_ elem: T) {
     storage[elem, default: 0] += 1
     count += 1
   }
 
-  public mutating func remove (_ elem: Element) {
+  public mutating func remove (_ elem: T) {
     if let currentCount = storage[elem] {
       if currentCount > 1 {
         storage[elem] = currentCount - 1
@@ -29,7 +35,7 @@ public struct Multiset<Element: Hashable> {
     }
   }
 
-  public func isSubSet (of superset: Multiset<Element>) -> Bool {
+  public func isSubSet (of superset: Multiset<T>) -> Bool {
     for (key, count) in storage {
       let supersetcount = superset.storage[key] ?? 0
       if count > supersetcount {
@@ -39,12 +45,12 @@ public struct Multiset<Element: Hashable> {
     return true
   }
 
-  public func count(for key: Element) -> UInt {
+  public func count(for key: T) -> UInt {
     return storage[key] ?? 0
   }
 
-  public var allItems: [Element] {
-    var result = [Element]()
+  public var allItems: [T] {
+    var result = [T]()
     for (key, count) in storage {
       for _ in 0 ..< count {
         result.append(key)
@@ -56,7 +62,7 @@ public struct Multiset<Element: Hashable> {
 
 // MARK: - Equatable
 extension Multiset: Equatable {
-  public static func == (lhs: Multiset<Element>, rhs: Multiset<Element>) -> Bool {
+  public static func == (lhs: Multiset<T>, rhs: Multiset<T>) -> Bool {
     if lhs.storage.count != rhs.storage.count {
       return false
     }
diff --git a/Multiset/README.markdown b/Multiset/README.markdown
index fd72d269c..6296a1538 100644
--- a/Multiset/README.markdown
+++ b/Multiset/README.markdown
@@ -2,20 +2,30 @@
 
 A multiset (also known as a bag) is a data structure similar to a regular set, but it can store multiple instances of the same element.
 
-The following all represent the same *set*, but do not represent the same *multiset*.
+For example, if I added the elements 1, 2, 2 to a regular set, the set would only contain two items, since adding 2 a second time has no effect.
 
 ```
-[1, 3, 2]
-[1, 3, 2, 2]
+var set = Set<Int>()
+set.add(1) // set is now [1]
+set.add(2) // set is now [1, 2]
+set.add(2) // set is still [1, 2]
 ```
 
-In this multiset implementation, ordering is unimportant. So these two multisets are identical:
+By comparison, after adding the elements 1, 2, 2 to a multiset, it would contain three items.
 
 ```
-[1, 2, 2]
-[2, 1, 2]
+var set = Multiset<Int>()
+set.add(1) // set is now [1]
+set.add(2) // set is now [1, 2]
+set.add(2) // set is now [1, 2, 2]
 ```
 
+You might be thinking that this looks an awful lot like an array. So why would you use a multiset? Let's consider the differences between the two…
+
+- Ordering: arrays maintain the order of items added to them, multisets do not
+- Testing for membership: testing whether an element is a member of the collection is O(N) for arrays, O(1) for multisets.
+- Testing for subset: testing whether collection X is a subset of collection Y is a simple operation for a multiset, but complex for arrays
+
 Typical operations on a multiset are:
 
 - Add an element
@@ -24,6 +34,14 @@ Typical operations on a multiset are:
 - Get the count for the whole set (the number of items that have been added)
 - Check whether it is a subset of another multiset
 
+One real-world use of multisets is to determine whether one string is a partial anagram of another. For example, the word "cacti" is a partial anagrams of "tactical". (In other words, I can rearrange the letters of "tactical" to make "cacti", with some letters left over.)
+
+``` swift
+var cacti = Multiset<Character>("cacti")
+var tactical = Multiset<Character>("tactical")
+cacti.isSubSet(of: tactical) // true!
+```
+
 ## Implementation
 
 Under the hood, this implementation of Multiset uses a dictionary to store a mapping of elements to the number of times they've been added.
@@ -32,11 +50,7 @@ Here's the essence of it:
 
 ``` swift
 public struct Multiset<Element: Hashable> {
-  fileprivate var storage: [Element: UInt]
-  
-  public init() {
-    storage = [:]
-  }
+  private var storage: [Element: UInt] = [:]
 ```
 
 And here's how you'd use this class to create a multiset of strings:
@@ -49,11 +63,7 @@ Adding an element is a case of incrementing the counter for that element, or set
 
 ``` swift
 public mutating func add (_ elem: Element) {
-  if let currentCount = storage[elem] {
-    storage[elem] = currentCount + 1;
-  } else {
-    storage[elem] = 1
-  }
+  storage[elem, default: 0] += 1
 }
 ```
 
@@ -62,6 +72,7 @@ Here's how you'd use this method to add to the set we created earlier:
 ```swift
 set.add("foo")
 set.add("foo") 
+set.allItems // returns ["foo", "foo"]
 ```
 
 Our set now contains two elements, both the string "foo".

From b4533bffdf2537773deb2c0edbba6a69c283fdf2 Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Tue, 5 Sep 2017 19:34:18 +0100
Subject: [PATCH 181/643] Implement ExpressibleByArrayLiteral protocol

---
 Multiset/Multiset.playground/Sources/Multiset.swift | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Multiset/Multiset.playground/Sources/Multiset.swift b/Multiset/Multiset.playground/Sources/Multiset.swift
index f77983f8c..5dba5d32c 100644
--- a/Multiset/Multiset.playground/Sources/Multiset.swift
+++ b/Multiset/Multiset.playground/Sources/Multiset.swift
@@ -75,3 +75,10 @@ extension Multiset: Equatable {
     return true
   }
 }
+
+// MARK: - ExpressibleByArrayLiteral
+extension Multiset: ExpressibleByArrayLiteral {
+  public init(arrayLiteral elements: T...) {
+    self.init(elements)
+  }
+}

From e7bce0ddcc03ac933f69f18b1115bb242cd2ddd3 Mon Sep 17 00:00:00 2001
From: Simon Whitaker <swhitaker@fb.com>
Date: Tue, 5 Sep 2017 19:34:47 +0100
Subject: [PATCH 182/643] Add more toys to the playground

---
 Multiset/Multiset.playground/Contents.swift | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
index f8b05d2b0..b4f64ee1f 100644
--- a/Multiset/Multiset.playground/Contents.swift
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -25,7 +25,18 @@ set2.add("Foo")
 set2.isSubSet(of: set) // true
 set.isSubSet(of: set2) // false
 
+// Convenience constructor: pass a Collection of Hashables to the constructor
 var cacti = Multiset<Character>("cacti")
+cacti.allItems
 var tactical = Multiset<Character>("tactical")
 cacti.isSubSet(of: tactical) // true
 tactical.isSubSet(of: cacti) // false
+
+// Test ExpressibleByArrayLiteral protocol
+let set3: Multiset<String> = ["foo", "bar"]
+set3.count(for: "foo")
+
+// Test Equatable protocol
+let set4 = Multiset<String>(set3.allItems)
+set4 == set3 // true
+set4 == set // false

From 10d90da2d16a46bb5183448be7c39a5720d50c23 Mon Sep 17 00:00:00 2001
From: Harry Twan <gua@desgard.com>
Date: Wed, 6 Sep 2017 15:40:57 +0800
Subject: [PATCH 183/643] Update the Segment Tree: add Lazy Propagation for
 interval update

Signed-off-by: Harry Twan <gua@desgard.com>
---
 .../LazyPropagation/Images/Segment-tree.png   | Bin 0 -> 34257 bytes
 .../LazyPropagation/Images/lazy-sample-2.png  | Bin 0 -> 80206 bytes
 .../LazyPropagation/Images/pushUp.png         | Bin 0 -> 30566 bytes
 .../LazyPropagation/Images/pushdown.png       | Bin 0 -> 32410 bytes
 .../LazyPropagation.playground/Contents.swift | 147 ++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Segment Tree/LazyPropagation/README.markdown  | 269 ++++++++++++++++++
 8 files changed, 427 insertions(+)
 create mode 100644 Segment Tree/LazyPropagation/Images/Segment-tree.png
 create mode 100644 Segment Tree/LazyPropagation/Images/lazy-sample-2.png
 create mode 100644 Segment Tree/LazyPropagation/Images/pushUp.png
 create mode 100644 Segment Tree/LazyPropagation/Images/pushdown.png
 create mode 100644 Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift
 create mode 100644 Segment Tree/LazyPropagation/LazyPropagation.playground/contents.xcplayground
 create mode 100644 Segment Tree/LazyPropagation/LazyPropagation.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Segment Tree/LazyPropagation/README.markdown

diff --git a/Segment Tree/LazyPropagation/Images/Segment-tree.png b/Segment Tree/LazyPropagation/Images/Segment-tree.png
new file mode 100644
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diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift
new file mode 100644
index 000000000..d576be254
--- /dev/null
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
@@ -0,0 +1,147 @@
+//: Playground - noun: a place where people can play
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+//protocol SegmentTree<T> {
+//    func pushUp(lson: T, rson: T)
+//    func pushDown(round: Int, lson: T, rson: T)
+//}
+
+public class LazySegmentTree {
+    
+    private var value: Int
+    
+    private var leftBound: Int
+    
+    private var rightBound: Int
+    
+    private var leftChild: LazySegmentTree?
+    
+    private var rightChild: LazySegmentTree?
+    
+    // Interval Update Lazy Element
+    private var lazyValue: Int
+    
+    // MARK: - Push Up Operation
+    // Description: 这里是 push up 操作，用来对 Segment Tree 向上更新
+    private func pushUp(lson: LazySegmentTree, rson: LazySegmentTree) {
+        self.value = lson.value + rson.value
+    }
+    
+    // MARK: - Push Down Operation
+    // Description: 这里是 push down 操作，用来对 Segment Tree 向下更新
+    // Open Interface Function: 此处应该开放方法对齐进行 Override
+    private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
+        if lazyValue != 0 {
+            lson.lazyValue += lazyValue
+            rson.lazyValue += lazyValue
+            lson.value += lazyValue * (round - (round >> 1))
+            rson.value += lazyValue * (round >> 1)
+            lazyValue = 0
+        }
+    }
+    
+    public init(array: [Int], leftBound: Int, rightBound: Int) {
+        self.leftBound = leftBound
+        self.rightBound = rightBound
+        self.value = 0
+        self.lazyValue = 0
+        
+        if leftBound == rightBound {
+            value = array[leftBound]
+            return
+        }
+        
+        let middle = (leftBound + rightBound) / 2
+        leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
+        rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
+        pushUp(lson: leftChild!, rson: rightChild!)
+        
+    }
+    
+    public convenience init(array: [Int]) {
+        self.init(array: array, leftBound: 0, rightBound: array.count - 1)
+    }
+    
+    public func query(leftBound: Int, rightBound: Int) -> Int {
+        if leftBound <= self.leftBound && self.rightBound <= rightBound {
+            return value
+        }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+        
+        pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
+        
+        let middle = (self.leftBound + self.rightBound) / 2
+        var result: Int = 0
+        
+        if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
+        if rightBound > middle { result += rightChild.query(leftBound: leftBound, rightBound: rightBound) }
+        
+        return result
+    }
+    
+    // MARK: - One Item Update
+    public func update(index: Int, incremental: Int) {
+        if self.leftBound == self.rightBound {
+            self.value += incremental
+            return
+        }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+        
+        let middle = (self.leftBound + self.rightBound) / 2
+        
+        if index <= middle { leftChild.update(index: index, incremental: incremental) }
+        else { rightChild.update(index: index, incremental: incremental) }
+        pushUp(lson: leftChild, rson: rightChild)
+    }
+    
+    // MARK: - Interval Item Update
+    public func update(leftBound: Int, rightBound: Int, incremental: Int) {
+        if leftBound <= self.leftBound && self.rightBound <= rightBound {
+            self.lazyValue += incremental
+            self.value += incremental * (self.rightBound - self.leftBound + 1)
+            return 
+        }
+        
+        guard let leftChild = leftChild else { fatalError() }
+        guard let rightChild = rightChild else { fatalError() }
+        
+        pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
+        
+        let middle = (self.leftBound + self.rightBound) / 2
+        
+        if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
+        if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
+        
+        pushUp(lson: leftChild, rson: rightChild)
+    }
+    
+}
+
+let array = [1, 2, 3, 4, 1, 3, 2]
+
+let sumSegmentTree = LazySegmentTree(array: array)
+
+print(sumSegmentTree.query(leftBound: 0, rightBound: 3)) // 10 = 1 + 2 + 3 + 4
+sumSegmentTree.update(index: 1, incremental: 2)
+print(sumSegmentTree.query(leftBound: 0, rightBound: 3)) // 12 = 1 + 4 + 3 + 4
+sumSegmentTree.update(leftBound: 0, rightBound: 2, incremental: 2)
+print(sumSegmentTree.query(leftBound: 0, rightBound: 3)) // 18 = 3 + 6 + 5 + 4
+
+for index in 2 ... 5 {
+    sumSegmentTree.update(index: index, incremental: 3)
+}
+
+
+sumSegmentTree.update(leftBound: 0, rightBound: 5, incremental: 2)
+print(sumSegmentTree.query(leftBound: 0, rightBound: 2))
+
+
+
+
+
diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/contents.xcplayground b/Segment Tree/LazyPropagation/LazyPropagation.playground/contents.xcplayground
new file mode 100644
index 000000000..16f9952aa
--- /dev/null
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx' last-migration='0800'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/playground.xcworkspace/contents.xcworkspacedata b/Segment Tree/LazyPropagation/LazyPropagation.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
new file mode 100644
index 000000000..49987c14e
--- /dev/null
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -0,0 +1,269 @@
+# Lazy Propagation in Segment Tree
+
+In previous implement about the Segment Tree by **Artur Antonov**, it's a strong data structure with *Generic* `<T>`. And we can pass a closure parameter `function: (T, T) -> T` to reflect the relationship between parent and child node. And in particular, Generic can solve multiple strings stitching problem. It's just like the sample in Playground:
+
+```swift
+stringSegmentTree.replaceItem(at: 0, withItem: "I")
+stringSegmentTree.replaceItem(at: 1, withItem: " like")
+stringSegmentTree.replaceItem(at: 2, withItem: " algorithms")
+stringSegmentTree.replaceItem(at: 3, withItem: " and")
+stringSegmentTree.replaceItem(at: 4, withItem: " swift")
+stringSegmentTree.replaceItem(at: 5, withItem: "!")
+print(stringSegmentTree.query(leftBound: 0, rightBound: 5))
+// "I like algorithms and swift!"
+```
+
+The use of `<T>` is so exciting. But we seldom use the Segment Tree to solve string problem instead of *Suffix Array*. And the Segment Tree is a kind of *Interval Tree* to solve the Interval Problem in mathemtics and statistics, which is a structure for storing intervals, or segments, and allows querying which of the stored segments contain a given point. A segment tree for a set *I* of n intervals uses `O(nlogn)` storage and can be built in `O(nlogn)` time. Segment trees support searching for all the intervals that contain a query point in O(log n+k), k being the number of retrieved intervals or segments.
+
+But that is common Segment Tree. By **Lazy Propagation**, we can implement to modify an interval in `O(nlogn)` time. Let's explore together in following:
+
+## `PushUp` - update to the top
+
+At first, we reference the implement of **Artur Antonov** about Segment Tree. This code contained *build*, *single update* and *interval query* three operation. The implement of *build* and *single update* operation is following:
+
+```swift
+public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
+	self.leftBound = leftBound
+	self.rightBound = rightBound
+	self.function = function
+	// ①
+	if leftBound == rightBound {
+		value = array[leftBound]
+	} 
+	// ②
+	else {
+		let middle = (leftBound + rightBound) / 2
+		leftChild = SegmentTree<T>(array: array, leftBound: leftBound, rightBound: middle, function: function)
+		rightChild = SegmentTree<T>(array: array, leftBound: middle+1, rightBound: rightBound, function: function)
+		value = function(leftChild!.value, rightChild!.value)
+	}
+}
+```
+
+In position ①, it means the current node is *leaf* because its left bound data is equal to the right. So we assign a value to it directly. In position ②, it means the current node is *parent* (which has one or more children), and we need to recursion down and update current node's data in the follow-up process.
+
+And then, we have a look for *interval query* operation:
+
+```swift
+public func query(leftBound: Int, rightBound: Int) -> T {
+	if self.leftBound == leftBound && self.rightBound == rightBound {
+		return self.value
+	}
+	guard let leftChild = leftChild else { fatalError("leftChild should not be nil") }
+	guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+	// ①
+	if leftChild.rightBound < leftBound {
+		return rightChild.query(leftBound: leftBound, rightBound: rightBound)
+	} 
+	// ②
+	else if rightChild.leftBound > rightBound {
+		return leftChild.query(leftBound: leftBound, rightBound: rightBound)
+	}
+	// ③ 
+	else {
+		let leftResult = leftChild.query(leftBound: leftBound, rightBound: leftChild.rightBound)
+		let rightResult = rightChild.query(leftBound:rightChild.leftBound, rightBound: rightBound)
+		return function(leftResult, rightResult)
+	}
+}
+```
+
+Position ① means that the left bound of current query interval is on the  right of this right bound, so recurs to right direction. Position ② is opposite of position ①, recurs to left direction. Position ③ means our check interval is included the interval we need, so recurs deeply.
+
+![pushUp](Images/pushUp.png)
+There are common part from the two parts of code above - **recurs deeply below, and update data up**. So we can decouple this operation named `func pushUp(lson: LazySegmentTree, rson: LazySegmentTree)`:
+
+```swift
+// MARK: - Push Up Operation
+private func pushUp(lson: LazySegmentTree, rson: LazySegmentTree) {
+    self.value = lson.value + rson.value
+}
+```
+
+(This code only describe the *Sum Segment Tree*)
+
+And then, we can update the implement before:
+
+```swift
+public init(array: [Int], leftBound: Int, rightBound: Int) {
+    self.leftBound = leftBound
+    self.rightBound = rightBound
+    self.value = 0
+    self.lazyValue = 0
+    if leftBound == rightBound {
+        value = array[leftBound]
+        return
+    }
+    let middle = (leftBound + rightBound) / 2
+    leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
+    rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
+    pushUp(lson: leftChild!, rson: rightChild!)
+}
+// MARK: - One Item Update
+public func update(index: Int, newValue: Int) {
+    if self.leftBound == self.rightBound {
+        self.value = newValue
+        return
+    }
+    guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+    guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+    let middle = (self.leftBound + self.rightBound) / 2
+    if index <= middle { leftChild.update(index: index, newValue: newValue) }
+    else { rightChild.update(index: index, newValue: newValue) }
+    pushUp(lson: leftChild, rson: rightChild)
+}
+```
+
+## `PushDown` - Lazy Propagation 
+
+You may feel that the `pushUp` is so simple. In fact, this's just to lead `pushDown` this function.
+
+Before this, I want to talk about the topic about **interval operation**. The interval operation is a way to update all elements of a continuous subset. But these isn't in the version of **Artur Antonov**. You might disdain with this, because it's solved with a `for` loop:
+
+```swift
+// Sample: update the elements with subscript [2, 5] 
+for index in 2 ... 5 {
+    sumSegmentTree.update(index: index, incremental: 3)
+}
+```
+
+It is a `O(n)` time operation, which make the interval operation uses `O(nlogn)` time to update these elements. We need a `O(logn)` way to maintain the elegance of Segment Tree. 
+
+ Check the data structure of Segment Tree again:
+ 
+ ![Segment-tree](Images/Segment-tree.png)
+We only catch the root node in programming. If we want to explore the bottom of the tree, and use `pushUp` to update every node, the task will be reached. So it asked us to traverse the tree, that spent `O(n)` time to do this with any way. This can't conform our expectations.  
+
+Then we started to think about `pushDown` to update down from the root. **After we update the parent, the data continued to distributed to its children according to law.** But it still need `O(n)` time to do this. Keep thinking, we **only update the parent, and to update the children when `query` time**. Yeah, that's the key of **lazy propagation**. Because the recursing direct of the `query` and `update interval` is same. So we got it! 😁 Let's check this sample:
+
+![lazy-sample-2](Images/lazy-sample-2.png)
+`update` make the subscript 1...3 elements plus 2, so we make the 1st node in 2 depth and 3rd in 3 depth get a *lazy mark*, which means these node need to be updated. And we shouldn't add a *lazy mark* for root node, because it was updated before the `pushDown` in the first recursing. 
+
+In `query` operation, we accord to the original method to recurs the tree, and find the 1st node held *lazy mark* in 2 depth, so to update it. It's the same situation about the 1st node in 3 depth.
+
+Do you understand the **lazy propagation**? **In short, we only update the wide range node data and add it a lazy mark. Then they will be update when we need to query them.** And the *Update Down* operation is the function of `pushDown`.
+
+This is the complete implementation about the Sum Segment Tree with interval update operation:
+
+```swift
+public class LazySegmentTree {
+    private var value: Int
+    private var leftBound: Int
+    private var rightBound: Int
+    private var leftChild: LazySegmentTree?
+    private var rightChild: LazySegmentTree?
+    // Interval Update Lazy Element
+    private var lazyValue: Int
+    // MARK: - Push Up Operation
+    private func pushUp(lson: LazySegmentTree, rson: LazySegmentTree) {
+        self.value = lson.value + rson.value
+    }
+    // MARK: - Push Down Operation
+    private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
+        if lazyValue != 0 {
+            lson.lazyValue += lazyValue
+            rson.lazyValue += lazyValue
+            lson.value += lazyValue * (round - (round >> 1))
+            rson.value += lazyValue * (round >> 1)
+            lazyValue = 0
+        }
+    }
+    public init(array: [Int], leftBound: Int, rightBound: Int) {
+        self.leftBound = leftBound
+        self.rightBound = rightBound
+        self.value = 0
+        self.lazyValue = 0
+        if leftBound == rightBound {
+            value = array[leftBound]
+            return
+        }
+        let middle = (leftBound + rightBound) / 2
+        leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
+        rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
+        pushUp(lson: leftChild!, rson: rightChild!)
+    }
+    public convenience init(array: [Int]) {
+        self.init(array: array, leftBound: 0, rightBound: array.count - 1)
+    }
+    public func query(leftBound: Int, rightBound: Int) -> Int {
+        if leftBound <= self.leftBound && self.rightBound <= rightBound {
+            return value
+        }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+        pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
+        let middle = (self.leftBound + self.rightBound) / 2
+        var result: Int = 0
+        if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
+        if rightBound > middle { result += rightChild.query(leftBound: leftBound, rightBound: rightBound) }
+        return result
+    }
+    // MARK: - One Item Update
+    public func update(index: Int, incremental: Int) {
+        if self.leftBound == self.rightBound {
+            self.value += incremental
+            return
+        }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+        let middle = (self.leftBound + self.rightBound) / 2
+        if index <= middle { leftChild.update(index: index, incremental: incremental) }
+        else { rightChild.update(index: index, incremental: incremental) }
+        pushUp(lson: leftChild, rson: rightChild)
+    }
+    // MARK: - Interval Item Update
+    public func update(leftBound: Int, rightBound: Int, incremental: Int) {
+        if leftBound <= self.leftBound && self.rightBound <= rightBound {
+            self.lazyValue += incremental
+            self.value += incremental * (self.rightBound - self.leftBound + 1)
+            return 
+        }
+        guard let leftChild = leftChild else { fatalError() }
+        guard let rightChild = rightChild else { fatalError() }
+        pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
+        let middle = (self.leftBound + self.rightBound) / 2
+        if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
+        if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
+        pushUp(lson: leftChild, rson: rightChild)
+    }
+}
+```
+
+Explain some sample snippets:
+
+```swift
+private var lazyValue: Int
+```
+
+Here we add a new property for Segment Tree to represent *lazy mark*. And it is a incremental value for Sum Segment Tree. If the `lazyValue` isn't equal to zero, the current node need to be updated. And its real value is equal to `value + lazyValue * (rightBound - leftBound + 1)`.
+
+```swift
+// MARK: - Push Down Operation
+private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
+    if lazyValue != 0 {
+        lson.lazyValue += lazyValue
+        rson.lazyValue += lazyValue
+        lson.value += lazyValue * (round - (round >> 1))
+        rson.value += lazyValue * (round >> 1)
+        lazyValue = 0
+    }
+}
+```
+
+![pushdown](Images/pushdown.png)
+
+At first we check whether the node needs to be updated. If the `lazyValue` isn't equal to zero, we need to `pushDown`. And the update rules are the `lazyValue * (rightBound - leftBound + 1)`. At last, reset the `lazyValue` to zero.
+
+## Conclusion
+
+This is the introduce of the Lazy Propagation in Segment Tree. You can also learn **Functional Segment Tree** to understand the Lazy Propagation deeply. In addition, I learn from the *notonlysuccess*'s code about Segment Tree described by C, this is the [link](http://www.cnblogs.com/Destiny-Gem/articles/3875243.html).
+
+In fact, the operation of Segment Tree is far more than that. It can also be used to handle problems between collections. I want to implement it with Swift in the future and make the Swift Segment Tree stronger and stronger. 😁
+
+---
+
+*Written for Swift Algorithm Club by [Desgard_Duan](https://github.com/desgard)*
+
+
+
+

From 891a700361267067f0db4d9ba6b828119230edc3 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 9 Sep 2017 08:04:31 -0700
Subject: [PATCH 184/643] [Swift 4] Update Bit Set

---
 Bit Set/BitSet.playground/Contents.swift      |  5 ++
 .../BitSet.playground/Sources/BitSet.swift    |  4 +-
 Bit Set/BitSet.playground/timeline.xctimeline |  6 --
 Bit Set/BitSet.swift                          | 75 ++++++++++---------
 4 files changed, 45 insertions(+), 45 deletions(-)
 delete mode 100644 Bit Set/BitSet.playground/timeline.xctimeline

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index d11b36e8c..95253ea27 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Create a bit set that stores 140 bits
 var bits = BitSet(size: 140)
 
diff --git a/Bit Set/BitSet.playground/Sources/BitSet.swift b/Bit Set/BitSet.playground/Sources/BitSet.swift
index d8985bd13..59306f5a5 100644
--- a/Bit Set/BitSet.playground/Sources/BitSet.swift	
+++ b/Bit Set/BitSet.playground/Sources/BitSet.swift	
@@ -41,7 +41,7 @@ public struct BitSet {
       // Set the highest bit that's still valid.
       let mask = 1 << Word(63 - diff)
       // Subtract 1 to turn it into a mask, and add the high bit back in.
-      return mask | (mask - 1)
+      return (Word)(mask | (mask - 1))
     } else {
       return allOnes
     }
@@ -167,7 +167,7 @@ extension BitSet: Hashable {
 
 // MARK: - Bitwise operations
 
-extension BitSet: BitwiseOperations {
+extension BitSet {
   public static var allZeros: BitSet {
     return BitSet(size: 64)
   }
diff --git a/Bit Set/BitSet.playground/timeline.xctimeline b/Bit Set/BitSet.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Bit Set/BitSet.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Bit Set/BitSet.swift b/Bit Set/BitSet.swift
index d8985bd13..cfe8517b5 100644
--- a/Bit Set/BitSet.swift	
+++ b/Bit Set/BitSet.swift	
@@ -1,30 +1,30 @@
 /*
-  A fixed-size sequence of n bits. Bits have indices 0 to n-1.
-*/
+ A fixed-size sequence of n bits. Bits have indices 0 to n-1.
+ */
 public struct BitSet {
   /* How many bits this object can hold. */
   private(set) public var size: Int
-
+  
   /*
-    We store the bits in a list of unsigned 64-bit integers.
-    The first entry, `words[0]`, is the least significant word.
-  */
+   We store the bits in a list of unsigned 64-bit integers.
+   The first entry, `words[0]`, is the least significant word.
+   */
   private let N = 64
   public typealias Word = UInt64
   fileprivate(set) public var words: [Word]
-
+  
   private let allOnes = ~Word()
-
+  
   /* Creates a bit set that can hold `size` bits. All bits are initially 0. */
   public init(size: Int) {
     precondition(size > 0)
     self.size = size
-
+    
     // Round up the count to the next multiple of 64.
     let n = (size + (N-1)) / N
     words = [Word](repeating: 0, count: n)
   }
-
+  
   /* Converts a bit index into an array index and a mask inside the word. */
   private func indexOf(_ i: Int) -> (Int, Word) {
     precondition(i >= 0)
@@ -33,7 +33,7 @@ public struct BitSet {
     let m = Word(i - o*N)
     return (o, 1 << m)
   }
-
+  
   /* Returns a mask that has 1s for all bits that are in the last word. */
   private func lastWordMask() -> Word {
     let diff = words.count*N - size
@@ -41,33 +41,33 @@ public struct BitSet {
       // Set the highest bit that's still valid.
       let mask = 1 << Word(63 - diff)
       // Subtract 1 to turn it into a mask, and add the high bit back in.
-      return mask | (mask - 1)
+      return (Word)(mask | (mask - 1))
     } else {
       return allOnes
     }
   }
-
+  
   /*
-    If the size is not a multiple of N, then we have to clear out the bits
-    that we're not using, or bitwise operations between two differently sized
-    BitSets will go wrong.
-  */
+   If the size is not a multiple of N, then we have to clear out the bits
+   that we're not using, or bitwise operations between two differently sized
+   BitSets will go wrong.
+   */
   fileprivate mutating func clearUnusedBits() {
     words[words.count - 1] &= lastWordMask()
   }
-
+  
   /* So you can write bitset[99] = ... */
   public subscript(i: Int) -> Bool {
     get { return isSet(i) }
     set { if newValue { set(i) } else { clear(i) } }
   }
-
+  
   /* Sets the bit at the specified index to 1. */
   public mutating func set(_ i: Int) {
     let (j, m) = indexOf(i)
     words[j] |= m
   }
-
+  
   /* Sets all the bits to 1. */
   public mutating func setAll() {
     for i in 0..<words.count {
@@ -75,37 +75,37 @@ public struct BitSet {
     }
     clearUnusedBits()
   }
-
+  
   /* Sets the bit at the specified index to 0. */
   public mutating func clear(_ i: Int) {
     let (j, m) = indexOf(i)
     words[j] &= ~m
   }
-
+  
   /* Sets all the bits to 0. */
   public mutating func clearAll() {
     for i in 0..<words.count {
       words[i] = 0
     }
   }
-
+  
   /* Changes 0 into 1 and 1 into 0. Returns the new value of the bit. */
   public mutating func flip(_ i: Int) -> Bool {
     let (j, m) = indexOf(i)
     words[j] ^= m
     return (words[j] & m) != 0
   }
-
+  
   /* Determines whether the bit at the specific index is 1 (true) or 0 (false). */
   public func isSet(_ i: Int) -> Bool {
     let (j, m) = indexOf(i)
     return (words[j] & m) != 0
   }
-
+  
   /*
-    Returns the number of bits that are 1. Time complexity is O(s) where s is
-    the number of 1-bits.
-  */
+   Returns the number of bits that are 1. Time complexity is O(s) where s is
+   the number of 1-bits.
+   */
   public var cardinality: Int {
     var count = 0
     for var x in words {
@@ -117,7 +117,7 @@ public struct BitSet {
     }
     return count
   }
-
+  
   /* Checks if all the bits are set. */
   public func all1() -> Bool {
     for i in 0..<words.count - 1 {
@@ -125,7 +125,7 @@ public struct BitSet {
     }
     return words[words.count - 1] == lastWordMask()
   }
-
+  
   /* Checks if any of the bits are set. */
   public func any1() -> Bool {
     for x in words {
@@ -133,7 +133,7 @@ public struct BitSet {
     }
     return false
   }
-
+  
   /* Checks if none of the bits are set. */
   public func all0() -> Bool {
     for x in words {
@@ -167,7 +167,7 @@ extension BitSet: Hashable {
 
 // MARK: - Bitwise operations
 
-extension BitSet: BitwiseOperations {
+extension BitSet {
   public static var allZeros: BitSet {
     return BitSet(size: 64)
   }
@@ -178,11 +178,11 @@ private func copyLargest(_ lhs: BitSet, _ rhs: BitSet) -> BitSet {
 }
 
 /*
-  Note: In all of these bitwise operations, lhs and rhs are allowed to have a
-  different number of bits. The new BitSet always has the larger size.
-  The extra bits that get added to the smaller BitSet are considered to be 0.
-  That will strip off the higher bits from the larger BitSet when doing &.
-*/
+ Note: In all of these bitwise operations, lhs and rhs are allowed to have a
+ different number of bits. The new BitSet always has the larger size.
+ The extra bits that get added to the smaller BitSet are considered to be 0.
+ That will strip off the higher bits from the larger BitSet when doing &.
+ */
 
 public func & (lhs: BitSet, rhs: BitSet) -> BitSet {
   let m = max(lhs.size, rhs.size)
@@ -245,3 +245,4 @@ extension BitSet: CustomStringConvertible {
     return s
   }
 }
+

From 557d208a90873cfb0fc8dcaa90a2ed2c26c3ff31 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 9 Sep 2017 08:14:39 -0700
Subject: [PATCH 185/643] [Swift 4] Update Dijkstra

---
 .../Dijkstra.playground/Contents.swift        |  5 ++
 .../Contents.swift                            |  6 +++
 .../timeline.xctimeline                       |  6 ---
 .../contents.xcworkspacedata                  | 53 +++++++++++++++++++
 4 files changed, 64 insertions(+), 6 deletions(-)
 delete mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index 7c7f1a4b0..1cd1254b1 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -1,6 +1,11 @@
 //: Playground - noun: a place where people can play
 import Foundation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 var vertices: Set<Vertex> = Set()
 
 func createNotConnectedVertices() {
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift
index e4b3e6732..8e61ef49b 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift	
@@ -8,6 +8,12 @@
  */
 import UIKit
 import PlaygroundSupport
+
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 /*:
  First of all, let's set up colors for our window and graph. The visited color will be applied to visited vertices. The checking color will be applied to an edge and an edge neighbor every time the algorithm is checking some vertex neighbors. And default colors are just initial colors for elements.
  */
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline b/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index dfa422074..975e8e21c 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -25,6 +25,59 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "container:"
+      name = "Dijkstra">
+      <Group
+         location = "group:Dijkstra Algorithm/Images"
+         name = "Images">
+         <FileRef
+            location = "group:DirectedGraph.png">
+         </FileRef>
+         <FileRef
+            location = "group:image1.png">
+         </FileRef>
+         <FileRef
+            location = "group:image2.png">
+         </FileRef>
+         <FileRef
+            location = "group:image3.png">
+         </FileRef>
+         <FileRef
+            location = "group:image4.png">
+         </FileRef>
+         <FileRef
+            location = "group:image5.png">
+         </FileRef>
+         <FileRef
+            location = "group:image6.png">
+         </FileRef>
+         <FileRef
+            location = "group:image7.png">
+         </FileRef>
+         <FileRef
+            location = "group:Vertices.png">
+         </FileRef>
+         <FileRef
+            location = "group:WeightedDirectedGraph.png">
+         </FileRef>
+         <FileRef
+            location = "group:WeightedDirectedGraphFinal.png">
+         </FileRef>
+         <FileRef
+            location = "group:WeightedUndirectedGraph.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:Dijkstra Algorithm/README.md">
+      </FileRef>
+      <FileRef
+         location = "group:Dijkstra Algorithm/VisualizedDijkstra.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Dijkstra Algorithm/Dijkstra.playground">
+      </FileRef>
+   </Group>
    <Group
       location = "container:"
       name = "LRU Cache">

From 5bdfb5d034d770d12d60dc070d3da394e03157cb Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Sat, 9 Sep 2017 23:30:28 +0800
Subject: [PATCH 186/643] Update README.markdown

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

diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
index 49987c14e..6f85f47bd 100644
--- a/Segment Tree/LazyPropagation/README.markdown	
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -15,7 +15,7 @@ print(stringSegmentTree.query(leftBound: 0, rightBound: 5))
 
 The use of `<T>` is so exciting. But we seldom use the Segment Tree to solve string problem instead of *Suffix Array*. And the Segment Tree is a kind of *Interval Tree* to solve the Interval Problem in mathemtics and statistics, which is a structure for storing intervals, or segments, and allows querying which of the stored segments contain a given point. A segment tree for a set *I* of n intervals uses `O(nlogn)` storage and can be built in `O(nlogn)` time. Segment trees support searching for all the intervals that contain a query point in O(log n+k), k being the number of retrieved intervals or segments.
 
-But that is common Segment Tree. By **Lazy Propagation**, we can implement to modify an interval in `O(nlogn)` time. Let's explore together in following:
+But that is common Segment Tree. By **Lazy Propagation**, we can implement to modify an interval in `O(logn)` time. Let's explore together in following:
 
 ## `PushUp` - update to the top
 

From 22984bbad346431d7887f939ea4f1fb353fe0873 Mon Sep 17 00:00:00 2001
From: Yeral <YYamil24@gmail.com>
Date: Sat, 9 Sep 2017 11:51:39 -0400
Subject: [PATCH 187/643] Fix playground compilation error

---
 Bucket Sort/BucketSort.playground/Contents.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Bucket Sort/BucketSort.playground/Contents.swift b/Bucket Sort/BucketSort.playground/Contents.swift
index c111c3961..e862f8bb1 100644
--- a/Bucket Sort/BucketSort.playground/Contents.swift	
+++ b/Bucket Sort/BucketSort.playground/Contents.swift	
@@ -34,9 +34,9 @@ extension Int: IntConvertible, Sortable {
 // MARK: Playing code
 //////////////////////////////////////
 
-let input = [1, 2, 4, 6, 10]
+let input = [1, 2, 4, 6, 10, 5]
 var buckets = [Bucket<Int>(capacity: 15), Bucket<Int>(capacity: 15), Bucket<Int>(capacity: 15)]
 
-let sortedElements = bucketSort(elements: input, distributor: RangeDistributor(), sorter: InsertionSorter(), buckets: &buckets)
+let sortedElements = bucketSort(input, distributor: RangeDistributor(), sorter: InsertionSorter(), buckets: buckets)
 
 print(sortedElements)

From 433d1f909846f168307830cf0f1e982eaf5daf99 Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Mon, 11 Sep 2017 09:08:56 +0800
Subject: [PATCH 188/643] Update Contents.swift

---
 .../LazyPropagation.playground/Contents.swift | 52 ++++++-------------
 1 file changed, 17 insertions(+), 35 deletions(-)

diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift
index d576be254..79b791431 100644
--- a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
@@ -1,15 +1,3 @@
-//: Playground - noun: a place where people can play
-
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
-//protocol SegmentTree<T> {
-//    func pushUp(lson: T, rson: T)
-//    func pushDown(round: Int, lson: T, rson: T)
-//}
-
 public class LazySegmentTree {
     
     private var value: Int
@@ -26,22 +14,20 @@ public class LazySegmentTree {
     private var lazyValue: Int
     
     // MARK: - Push Up Operation
-    // Description: 这里是 push up 操作，用来对 Segment Tree 向上更新
+    // Description: pushUp() - update items to the top
     private func pushUp(lson: LazySegmentTree, rson: LazySegmentTree) {
         self.value = lson.value + rson.value
     }
     
     // MARK: - Push Down Operation
-    // Description: 这里是 push down 操作，用来对 Segment Tree 向下更新
-    // Open Interface Function: 此处应该开放方法对齐进行 Override
+    // Description: pushDown() - update items to the bottom
     private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
-        if lazyValue != 0 {
-            lson.lazyValue += lazyValue
-            rson.lazyValue += lazyValue
-            lson.value += lazyValue * (round - (round >> 1))
-            rson.value += lazyValue * (round >> 1)
-            lazyValue = 0
-        }
+        guard lazyValue != 0 else { return }
+        lson.lazyValue += lazyValue
+        rson.lazyValue += lazyValue
+        lson.value += lazyValue * (round - (round >> 1))
+        rson.value += lazyValue * (round >> 1)
+        lazyValue = 0
     }
     
     public init(array: [Int], leftBound: Int, rightBound: Int) {
@@ -50,16 +36,17 @@ public class LazySegmentTree {
         self.value = 0
         self.lazyValue = 0
         
-        if leftBound == rightBound {
+        guard leftBound != rightBound else {
             value = array[leftBound]
             return
         }
         
-        let middle = (leftBound + rightBound) / 2
+        let middle = leftBound + (rightBound - leftBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
-        pushUp(lson: leftChild!, rson: rightChild!)
-        
+        if let leftChild = leftChild, let rightChild = rightChild {
+            pushUp(lson: leftChild, rson: rightChild)
+        }
     }
     
     public convenience init(array: [Int]) {
@@ -75,7 +62,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         var result: Int = 0
         
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
@@ -86,14 +73,14 @@ public class LazySegmentTree {
     
     // MARK: - One Item Update
     public func update(index: Int, incremental: Int) {
-        if self.leftBound == self.rightBound {
+        guard self.leftBound != self.rightBound else {
             self.value += incremental
             return
         }
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
         
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
@@ -113,7 +100,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
         
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
@@ -140,8 +127,3 @@ for index in 2 ... 5 {
 
 sumSegmentTree.update(leftBound: 0, rightBound: 5, incremental: 2)
 print(sumSegmentTree.query(leftBound: 0, rightBound: 2))
-
-
-
-
-

From a9fa8db3a017bd6ad2c680e7d99c9ea1cfe32fd4 Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Mon, 11 Sep 2017 09:14:54 +0800
Subject: [PATCH 189/643] Update README.markdown

After code review to update readme.md
---
 Segment Tree/LazyPropagation/README.markdown | 101 +++++++++++++------
 1 file changed, 70 insertions(+), 31 deletions(-)

diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
index 6f85f47bd..4aaa41d93 100644
--- a/Segment Tree/LazyPropagation/README.markdown	
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -71,6 +71,7 @@ public func query(leftBound: Int, rightBound: Int) -> T {
 Position ① means that the left bound of current query interval is on the  right of this right bound, so recurs to right direction. Position ② is opposite of position ①, recurs to left direction. Position ③ means our check interval is included the interval we need, so recurs deeply.
 
 ![pushUp](Images/pushUp.png)
+
 There are common part from the two parts of code above - **recurs deeply below, and update data up**. So we can decouple this operation named `func pushUp(lson: LazySegmentTree, rson: LazySegmentTree)`:
 
 ```swift
@@ -90,26 +91,32 @@ public init(array: [Int], leftBound: Int, rightBound: Int) {
     self.rightBound = rightBound
     self.value = 0
     self.lazyValue = 0
-    if leftBound == rightBound {
+    
+    guard leftBound != rightBound else {
         value = array[leftBound]
         return
     }
-    let middle = (leftBound + rightBound) / 2
+    
+    let middle = leftBound + (rightBound - leftBound) / 2
     leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
     rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
-    pushUp(lson: leftChild!, rson: rightChild!)
+    if let leftChild = leftChild, let rightChild = rightChild {
+        pushUp(lson: leftChild, rson: rightChild)
+    }
 }
 // MARK: - One Item Update
-public func update(index: Int, newValue: Int) {
-    if self.leftBound == self.rightBound {
-        self.value = newValue
+public func update(index: Int, incremental: Int) {
+    guard self.leftBound != self.rightBound else {
+        self.value += incremental
         return
     }
     guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
     guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-    let middle = (self.leftBound + self.rightBound) / 2
-    if index <= middle { leftChild.update(index: index, newValue: newValue) }
-    else { rightChild.update(index: index, newValue: newValue) }
+    
+    let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+    
+    if index <= middle { leftChild.update(index: index, incremental: incremental) }
+    else { rightChild.update(index: index, incremental: incremental) }
     pushUp(lson: leftChild, rson: rightChild)
 }
 ```
@@ -132,11 +139,13 @@ It is a `O(n)` time operation, which make the interval operation uses `O(nlogn)`
  Check the data structure of Segment Tree again:
  
  ![Segment-tree](Images/Segment-tree.png)
+ 
 We only catch the root node in programming. If we want to explore the bottom of the tree, and use `pushUp` to update every node, the task will be reached. So it asked us to traverse the tree, that spent `O(n)` time to do this with any way. This can't conform our expectations.  
 
 Then we started to think about `pushDown` to update down from the root. **After we update the parent, the data continued to distributed to its children according to law.** But it still need `O(n)` time to do this. Keep thinking, we **only update the parent, and to update the children when `query` time**. Yeah, that's the key of **lazy propagation**. Because the recursing direct of the `query` and `update interval` is same. So we got it! 😁 Let's check this sample:
 
 ![lazy-sample-2](Images/lazy-sample-2.png)
+
 `update` make the subscript 1...3 elements plus 2, so we make the 1st node in 2 depth and 3rd in 3 depth get a *lazy mark*, which means these node need to be updated. And we shouldn't add a *lazy mark* for root node, because it was updated before the `pushDown` in the first recursing. 
 
 In `query` operation, we accord to the original method to recurs the tree, and find the 1st node held *lazy mark* in 2 depth, so to update it. It's the same situation about the 1st node in 3 depth.
@@ -147,70 +156,94 @@ This is the complete implementation about the Sum Segment Tree with interval upd
 
 ```swift
 public class LazySegmentTree {
+    
     private var value: Int
+    
     private var leftBound: Int
+    
     private var rightBound: Int
+    
     private var leftChild: LazySegmentTree?
+    
     private var rightChild: LazySegmentTree?
+    
     // Interval Update Lazy Element
     private var lazyValue: Int
+    
     // MARK: - Push Up Operation
+    // Description: pushUp() - update items to the top
     private func pushUp(lson: LazySegmentTree, rson: LazySegmentTree) {
         self.value = lson.value + rson.value
     }
+    
     // MARK: - Push Down Operation
+    // Description: pushDown() - update items to the bottom
     private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
-        if lazyValue != 0 {
-            lson.lazyValue += lazyValue
-            rson.lazyValue += lazyValue
-            lson.value += lazyValue * (round - (round >> 1))
-            rson.value += lazyValue * (round >> 1)
-            lazyValue = 0
-        }
+        guard lazyValue != 0 else { return }
+        lson.lazyValue += lazyValue
+        rson.lazyValue += lazyValue
+        lson.value += lazyValue * (round - (round >> 1))
+        rson.value += lazyValue * (round >> 1)
+        lazyValue = 0
     }
+    
     public init(array: [Int], leftBound: Int, rightBound: Int) {
         self.leftBound = leftBound
         self.rightBound = rightBound
         self.value = 0
         self.lazyValue = 0
-        if leftBound == rightBound {
+        
+        guard leftBound != rightBound else {
             value = array[leftBound]
             return
         }
-        let middle = (leftBound + rightBound) / 2
+        
+        let middle = leftBound + (rightBound - leftBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
-        pushUp(lson: leftChild!, rson: rightChild!)
+        if let leftChild = leftChild, let rightChild = rightChild {
+            pushUp(lson: leftChild, rson: rightChild)
+        }
     }
+    
     public convenience init(array: [Int]) {
         self.init(array: array, leftBound: 0, rightBound: array.count - 1)
     }
+    
     public func query(leftBound: Int, rightBound: Int) -> Int {
         if leftBound <= self.leftBound && self.rightBound <= rightBound {
             return value
         }
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
+        
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
-        let middle = (self.leftBound + self.rightBound) / 2
+        
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         var result: Int = 0
+        
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
         if rightBound > middle { result += rightChild.query(leftBound: leftBound, rightBound: rightBound) }
+        
         return result
     }
+    
     // MARK: - One Item Update
     public func update(index: Int, incremental: Int) {
-        if self.leftBound == self.rightBound {
+        guard self.leftBound != self.rightBound else {
             self.value += incremental
             return
         }
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
-        let middle = (self.leftBound + self.rightBound) / 2
+        
+        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
         pushUp(lson: leftChild, rson: rightChild)
     }
+    
     // MARK: - Interval Item Update
     public func update(leftBound: Int, rightBound: Int, incremental: Int) {
         if leftBound <= self.leftBound && self.rightBound <= rightBound {
@@ -218,14 +251,20 @@ public class LazySegmentTree {
             self.value += incremental * (self.rightBound - self.leftBound + 1)
             return 
         }
+        
         guard let leftChild = leftChild else { fatalError() }
         guard let rightChild = rightChild else { fatalError() }
+        
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
-        let middle = (self.leftBound + self.rightBound) / 2
+        
+        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
+        
         pushUp(lson: leftChild, rson: rightChild)
     }
+    
 }
 ```
 
@@ -238,15 +277,15 @@ private var lazyValue: Int
 Here we add a new property for Segment Tree to represent *lazy mark*. And it is a incremental value for Sum Segment Tree. If the `lazyValue` isn't equal to zero, the current node need to be updated. And its real value is equal to `value + lazyValue * (rightBound - leftBound + 1)`.
 
 ```swift
-// MARK: - Push Down Operation
+    // MARK: - Push Down Operation
+    // Description: pushDown() - update items to the bottom
 private func pushDown(round: Int, lson: LazySegmentTree, rson: LazySegmentTree) {
-    if lazyValue != 0 {
-        lson.lazyValue += lazyValue
-        rson.lazyValue += lazyValue
-        lson.value += lazyValue * (round - (round >> 1))
-        rson.value += lazyValue * (round >> 1)
-        lazyValue = 0
-    }
+    guard lazyValue != 0 else { return }
+    lson.lazyValue += lazyValue
+    rson.lazyValue += lazyValue
+    lson.value += lazyValue * (round - (round >> 1))
+    rson.value += lazyValue * (round >> 1)
+    lazyValue = 0
 }
 ```
 

From 643828a6f3087c180f5a52663d129744200fd623 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 11 Sep 2017 17:02:55 -0700
Subject: [PATCH 190/643] Updates Splay tree to Swift 4

---
 Splay Tree/SplayTree.playground/Contents.swift         |  4 ++++
 .../SplayTree.playground/Sources/SplayTree.swift       | 10 +++++-----
 2 files changed, 9 insertions(+), 5 deletions(-)

diff --git a/Splay Tree/SplayTree.playground/Contents.swift b/Splay Tree/SplayTree.playground/Contents.swift
index 4406a759d..a8a0bc5c6 100644
--- a/Splay Tree/SplayTree.playground/Contents.swift	
+++ b/Splay Tree/SplayTree.playground/Contents.swift	
@@ -1,5 +1,9 @@
 //: Playground - Splay Tree Implementation
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 let splayTree = SplayTree(value: 1)
 splayTree.insert(value: 2)
diff --git a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift
index a4feda7ef..9e484129c 100644
--- a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
+++ b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
@@ -28,7 +28,7 @@ public enum SplayOperation {
      - Parameters:
      - node      SplayTree node to move up to the root
      */
-    public static func splay<T: Comparable>(node: Node<T>) {
+    public static func splay<T>(node: Node<T>) {
         
         while (node.parent != nil) {
             operation(forNode: node).apply(onNode: node)
@@ -44,7 +44,7 @@ public enum SplayOperation {
      - Returns
      - Operation     Case zigZag - zigZig - zig
      */
-    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
+    public static func operation<T>(forNode node: Node<T>) -> SplayOperation {
         
         if let parent = node.parent, let _ = parent.parent {
             if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
@@ -62,7 +62,7 @@ public enum SplayOperation {
      - Parameters:
      - onNode    Node to splay up. Should be alwayas the node that needs to be splayed, neither its parent neither it's grandparent
      */
-    public func apply<T: Comparable>(onNode node: Node<T>) {
+    public func apply<T>(onNode node: Node<T>) {
         switch self {
         case .zigZag:
             assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
@@ -84,7 +84,7 @@ public enum SplayOperation {
      Performs a single rotation from a node to its parent
      re-arranging the children properly
      */
-    public func rotate<T: Comparable>(child: Node<T>, parent: Node<T>) {
+    public func rotate<T>(child: Node<T>, parent: Node<T>) {
         
         assert(child.parent != nil && child.parent!.value == parent.value, "Parent and child.parent should match here")
         
@@ -610,7 +610,7 @@ extension SplayTree: CustomStringConvertible {
 
 extension Node: CustomDebugStringConvertible {
     public var debugDescription: String {
-        var s = "value: \(value)"
+      var s = "value: \(String(describing: value))"
         if let parent = parent, let v = parent.value {
             s += ", parent: \(v)"
         }

From bedaaac782478eddeff7ede9fde6957fcf6c9999 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 11 Sep 2017 17:06:40 -0700
Subject: [PATCH 191/643] Updated readme for splay trees for Swift 4.

---
 Splay Tree/readme.md | 56 ++++++++++++++++++++++----------------------
 1 file changed, 28 insertions(+), 28 deletions(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index c42cd87fb..2c5e87ed7 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -1,5 +1,5 @@
 # Splay Tree
-Splay tree is a data structure, structurally identitical to a Balanced Binary Search Tree. Every operation performed on a Splay Tree causes a readjustment in order to provide fast access to recently operated values. On every access, the tree is rearranged and the node accessed is moved to the root of the tree using a set of specific rotations, which together are referred to as **Splaying**.
+Splay tree is a data structure, structurally identitical to a balanced binary search tree. Every operation performed on a Splay Tree causes a readjustment in order to provide fast access to recently operated values. On every access, the tree is rearranged and the node accessed is moved to the root of the tree using a set of specific rotations, which together are referred to as **Splaying**.
 
 
 ## Rotations
@@ -24,7 +24,7 @@ Given a node *a* if *a* is not the root, and *a* has a child *b*, and both *a* a
 
 ### Zig-Zag
 
-Given a node *a* if *a* is not the root, and *a* has a child *b*, and *b* is the left child of *a* being the right child (or the opporsite), a **Zig-Zag** is performed.
+Given a node *a* if *a* is not the root, and *a* has a child *b*, and *b* is the left child of *a* being the right child (or the opposite), a **Zig-Zag** is performed.
 
 ### Case right - left
 ![ZigZagCase1](Images/zigzag1.png)
@@ -43,49 +43,49 @@ A **Zig** is performed when the node *a* to be rotated has the root as parent.
 
 ## Splaying
 
-A splaying consists in making so many rotations as needed until the node affected by the operation is at the top and becomes the root of the tree.
+Splaying consists in making so many rotations as needed until the node affected by the operation is at the top and becomes the root of the tree.
 
 ```
 while (node.parent != nil) {
-            operation(forNode: node).apply(onNode: node)
+    operation(forNode: node).apply(onNode: node)
 }
 ```
 
 Where operation returns the required rotation to be applied. 
 
 ```
-    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
-        
-        if let parent = node.parent, let _ = parent.parent {
-            if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
-                return .zigZag
-            }
-            return .zigZig
+public static func operation<T>(forNode node: Node<T>) -> SplayOperation {
+    
+    if let parent = node.parent, let _ = parent.parent {
+        if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
+            return .zigZag
         }
-        return .zig
+        return .zigZig
     }
+    return .zig
+}
 ```
 
 During the applying phase, the algorithms determines which nodes are involved depending on the rotation to be applied and proceeding to re-arrange the node with its parent.
 
 ```
-    public func apply<T: Comparable>(onNode node: Node<T>) {
-        switch self {
-        case .zigZag:
-            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
-            rotate(child: node, parent: node.parent!)
-            rotate(child: node, parent: node.parent!)
-
-        case .zigZig:
-            assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
-            rotate(child: node.parent!, parent: node.parent!.parent!)
-            rotate(child: node, parent: node.parent!)
-        
-        case .zig:
-            assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
-            rotate(child: node, parent: node.parent!)
-        }
+public func apply<T>(onNode node: Node<T>) {
+    switch self {
+    case .zigZag:
+        assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+        rotate(child: node, parent: node.parent!)
+        rotate(child: node, parent: node.parent!)
+
+    case .zigZig:
+        assert(node.parent != nil && node.parent!.parent != nil, "Should be at least 2 nodes up in the tree")
+        rotate(child: node.parent!, parent: node.parent!.parent!)
+        rotate(child: node, parent: node.parent!)
+    
+    case .zig:
+        assert(node.parent != nil && node.parent!.parent == nil, "There should be a parent which is the root")
+        rotate(child: node, parent: node.parent!)
     }
+}
 ```
 
 

From 08abb81fc0616f29d5064145597e2a3558eca523 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 11 Sep 2017 17:08:10 -0700
Subject: [PATCH 192/643] Added splay trees to main readme.

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

diff --git a/README.markdown b/README.markdown
index 464c6b199..0494e749d 100644
--- a/README.markdown
+++ b/README.markdown
@@ -153,7 +153,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Binary Tree](Binary%20Tree/). A tree where each node has at most two children.
 - [Binary Search Tree (BST)](Binary%20Search%20Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
 - [Red-Black Tree](Red-Black%20Tree/). A self balancing binary search tree.
-- Splay Tree
+- [Splay Tree](Splay%20Tree/). A self balancing binary search tree that enables fast retrieval of recently updated elements.
 - [Threaded Binary Tree](Threaded%20Binary%20Tree/). A binary tree that maintains a few extra variables for cheap and fast in-order traversals.
 - [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
 - kd-Tree

From 45889d79c0aac7d1889aeb6839041f518e6d5247 Mon Sep 17 00:00:00 2001
From: Mark Rabins <markrabins@gmail.com>
Date: Sun, 17 Sep 2017 12:05:36 -0700
Subject: [PATCH 193/643] Syntax Updates

Minor update due to Swift changed in the makeIterator function.
---
 Stack/Stack.swift | 51 +++++++++++++++++++++++------------------------
 1 file changed, 25 insertions(+), 26 deletions(-)

diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index c3f42ea44..a9e8fb7a4 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -1,36 +1,35 @@
 /*
-  Last-in first-out stack (LIFO)
-
-  Push and pop are O(1) operations.
-*/
+ Last-in first-out stack (LIFO)
+ Push and pop are O(1) operations.
+ */
 public struct Stack<T> {
-  fileprivate var array = [T]()
-
-  public var isEmpty: Bool {
-    return array.isEmpty
-  }
-
-  public var count: Int {
-    return array.count
-  }
-
-  public mutating func push(_ element: T) {
-    array.append(element)
-  }
-
-  public mutating func pop() -> T? {
-    return array.popLast()
-  }
-
-  public var top: T? {
-    return array.last
-  }
+    fileprivate var array = [T]()
+    
+    public var isEmpty: Bool {
+        return array.isEmpty
+    }
+    
+    public var count: Int {
+        return array.count
+    }
+    
+    public mutating func push(_ element: T) {
+        array.append(element)
+    }
+    
+    public mutating func pop() -> T? {
+        return array.popLast()
+    }
+    
+    public var top: T? {
+        return array.last
+    }
 }
 
 extension Stack: Sequence {
     public func makeIterator() -> AnyIterator<T> {
         var curr = self
-        return AnyIterator { _ -> T? in
+        return AnyIterator {
             return curr.pop()
         }
     }

From 0d5d8d38ed681a18d2951875545a5882df686a71 Mon Sep 17 00:00:00 2001
From: Mark Rabins <markrabins@gmail.com>
Date: Sun, 17 Sep 2017 12:09:21 -0700
Subject: [PATCH 194/643] Swap changes

Swap changed from swap(&a[y - 1], &a[y])  ->  a.swapAt(y - 1, y)
---
 Insertion Sort/README.markdown | 16 +++++++++++++++-
 1 file changed, 15 insertions(+), 1 deletion(-)

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index 286d92ed1..91dfd18ad 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -91,7 +91,7 @@ Here is an implementation of insertion sort in Swift:
 
 ```swift
 func insertionSort(_ array: [Int]) -> [Int] {
-  var a = array                             // 1
+  var a = array                            
   for x in 1..<a.count {                    // 2
     var y = x
     while y > 0 && a[y] < a[y - 1] {        // 3
@@ -101,6 +101,20 @@ func insertionSort(_ array: [Int]) -> [Int] {
   }
   return a
 }
+
+func insertionSort(_ array: [Int]) -> [Int] {
+    var a = array			 // 1
+    for x in 1..<a.count {		 // 2
+        var y = x
+        while y > 0 && a[y] < a[y - 1] { // 3
+            a.swapAt(y - 1, y)
+            y -= 1
+        }
+    }
+    return a
+}
+
+
 ```
 
 Put this code in a playground and test it like so:

From 28f1fc3d70c318394a3944a4e206d25149160450 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 17 Sep 2017 20:19:44 -0700
Subject: [PATCH 195/643] Reverts indentation to 2 spaces.

---
 Stack/Stack.swift | 52 +++++++++++++++++++++++------------------------
 1 file changed, 26 insertions(+), 26 deletions(-)

diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index a9e8fb7a4..b12f713f5 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -3,34 +3,34 @@
  Push and pop are O(1) operations.
  */
 public struct Stack<T> {
-    fileprivate var array = [T]()
-    
-    public var isEmpty: Bool {
-        return array.isEmpty
-    }
-    
-    public var count: Int {
-        return array.count
-    }
-    
-    public mutating func push(_ element: T) {
-        array.append(element)
-    }
-    
-    public mutating func pop() -> T? {
-        return array.popLast()
-    }
-    
-    public var top: T? {
-        return array.last
-    }
+  fileprivate var array = [T]()
+  
+  public var isEmpty: Bool {
+    return array.isEmpty
+  }
+  
+  public var count: Int {
+    return array.count
+  }
+  
+  public mutating func push(_ element: T) {
+    array.append(element)
+  }
+  
+  public mutating func pop() -> T? {
+    return array.popLast()
+  }
+  
+  public var top: T? {
+    return array.last
+  }
 }
 
 extension Stack: Sequence {
-    public func makeIterator() -> AnyIterator<T> {
-        var curr = self
-        return AnyIterator {
-            return curr.pop()
-        }
+  public func makeIterator() -> AnyIterator<T> {
+    var curr = self
+    return AnyIterator {
+      return curr.pop()
     }
+  }
 }

From d27354e096f73c9a078fc956099eefbf80e0468b Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Mon, 18 Sep 2017 11:26:05 +0800
Subject: [PATCH 196/643] Update Contents.swift

---
 .../LazyPropagation.playground/Contents.swift      | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift
index 79b791431..5def3df33 100644
--- a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
@@ -41,7 +41,7 @@ public class LazySegmentTree {
             return
         }
         
-        let middle = leftBound + (rightBound - leftBound) / 2
+        let middle = (leftBound + rightBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
         if let leftChild = leftChild, let rightChild = rightChild {
@@ -62,8 +62,8 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
-        var result: Int = 0
+        let middle = (self.leftBound + self.rightBound) / 2
+        var result = 0
         
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
         if rightBound > middle { result += rightChild.query(leftBound: leftBound, rightBound: rightBound) }
@@ -80,7 +80,7 @@ public class LazySegmentTree {
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
-        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        let middle = (self.leftBound + self.rightBound) / 2
         
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
@@ -95,12 +95,12 @@ public class LazySegmentTree {
             return 
         }
         
-        guard let leftChild = leftChild else { fatalError() }
-        guard let rightChild = rightChild else { fatalError() }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        let middle = (self.leftBound + self.rightBound) / 2
         
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }

From 5e8840787066ede9bcdbf32b338c5a50b8d4a3a2 Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Mon, 18 Sep 2017 12:46:02 +0800
Subject: [PATCH 197/643] Update README.markdown

---
 Segment Tree/LazyPropagation/README.markdown | 22 ++++++++------------
 1 file changed, 9 insertions(+), 13 deletions(-)

diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
index 4aaa41d93..bcfb890fd 100644
--- a/Segment Tree/LazyPropagation/README.markdown	
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -97,7 +97,7 @@ public init(array: [Int], leftBound: Int, rightBound: Int) {
         return
     }
     
-    let middle = leftBound + (rightBound - leftBound) / 2
+    let middle = (leftBound + rightBound) / 2
     leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
     rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
     if let leftChild = leftChild, let rightChild = rightChild {
@@ -113,7 +113,7 @@ public func update(index: Int, incremental: Int) {
     guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
     guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
     
-    let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+    let middle = (self.leftBound + self.rightBound) / 2
     
     if index <= middle { leftChild.update(index: index, incremental: incremental) }
     else { rightChild.update(index: index, incremental: incremental) }
@@ -198,7 +198,7 @@ public class LazySegmentTree {
             return
         }
         
-        let middle = leftBound + (rightBound - leftBound) / 2
+        let middle = (leftBound + rightBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
         if let leftChild = leftChild, let rightChild = rightChild {
@@ -219,8 +219,8 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
-        var result: Int = 0
+        let middle = (self.leftBound + self.rightBound) / 2
+        var result = 0
         
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
         if rightBound > middle { result += rightChild.query(leftBound: leftBound, rightBound: rightBound) }
@@ -237,7 +237,7 @@ public class LazySegmentTree {
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
-        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        let middle = (self.leftBound + self.rightBound) / 2
         
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
@@ -252,12 +252,12 @@ public class LazySegmentTree {
             return 
         }
         
-        guard let leftChild = leftChild else { fatalError() }
-        guard let rightChild = rightChild else { fatalError() }
+        guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
+        guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = self.rightBound + (self.leftBound - self.rightBound) / 2
+        let middle = (self.leftBound + self.rightBound) / 2
         
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
@@ -302,7 +302,3 @@ In fact, the operation of Segment Tree is far more than that. It can also be use
 ---
 
 *Written for Swift Algorithm Club by [Desgard_Duan](https://github.com/desgard)*
-
-
-
-

From c4952f9fbdcb00801167ac28327a56ab7cd97aee Mon Sep 17 00:00:00 2001
From: Harry Twan <gua@desgard.com>
Date: Mon, 18 Sep 2017 12:54:18 +0800
Subject: [PATCH 198/643] Update the pushUp image

---
 .../LazyPropagation/Images/pushUp.png         | Bin 30566 -> 28125 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/Segment Tree/LazyPropagation/Images/pushUp.png b/Segment Tree/LazyPropagation/Images/pushUp.png
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GIT binary patch
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From aef1bb7092e6dd05190fb32b66d148792385ebca Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 19 Sep 2017 20:42:45 -0700
Subject: [PATCH 199/643] Removes old implementation

---
 Insertion Sort/README.markdown | 12 ------------
 1 file changed, 12 deletions(-)

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index 91dfd18ad..4bad29aa1 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -90,18 +90,6 @@ This was a description of the inner loop of the insertion sort algorithm, which
 Here is an implementation of insertion sort in Swift:
 
 ```swift
-func insertionSort(_ array: [Int]) -> [Int] {
-  var a = array                            
-  for x in 1..<a.count {                    // 2
-    var y = x
-    while y > 0 && a[y] < a[y - 1] {        // 3
-      swap(&a[y - 1], &a[y])
-      y -= 1
-    }
-  }
-  return a
-}
-
 func insertionSort(_ array: [Int]) -> [Int] {
     var a = array			 // 1
     for x in 1..<a.count {		 // 2

From ba27b0bd6624234d42dd60c36115a7b6f9933607 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Wed, 20 Sep 2017 00:21:27 -0700
Subject: [PATCH 200/643] Updates the preamble and description of the readme

---
 Egg Drop Problem/README.markdown | 23 ++++++++++++++++-------
 1 file changed, 16 insertions(+), 7 deletions(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 82543502d..7c15bcf62 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -1,18 +1,27 @@
-# Egg Drop Dynamic Problem
+# Egg Drop
 
-## Problem Description 
+The *egg drop* problem is an interview question popularized by Google. The premise is simple; You're given a task to evaluate the *shatter resistance* of unknown objects by dropping them at a certain height. For simplicity, you test this by going inside a multi-story building and performing tests by dropping the objects out the window and onto the ground:
 
-Given some number of floors and some number of eggs, what is the minimum number of attempts it will take to find out from which floor egg will break.
+![building with eggs being dropped](images/eggdrop.png)
 
-Suppose that we wish to know which stories in a 36-story building are safe to drop eggs from, and which will cause the eggs to break on landing. We make a few assumptions:
+Your goal is to find out the **minimum** height that causes the object to shatter. Consider the trivial case you're given **1** object to obtain the results with. Since you've only got one sample for testing, you need to play it safe by performing drop tests starting with the bottom floor and working your way up:
+
+![dropping from first floor](images/eggdrop2.png)
+
+If the object is incredibly resilient, and you may need to do the testing on the world's tallest building - the [Burj Khalifa](https://en.wikipedia.org/wiki/Burj_Khalifa). With **163** floors, that's a lot of climbing. Let's assume you complain, and your employer hears your plight. You are now given *several* samples to work with. How can you make use of these extra samples to expedite your testing process? The problem for this situation is popularized as the **egg drop** problem.
+
+## Description
+
+You're in a building with **m** floors and you are given **n** eggs. What is the minimum number attempts it will take to find out the lowest floor that breaks the egg?
+
+For convenience, here are a few rules to keep in mind:
 
 - An egg that survives a fall can be used again.
 - A broken egg must be discarded.
 - The effect of a fall is the same for all eggs.
-- If an egg breaks when dropped, then it would break if dropped from a higher floor.
-- If an egg survives a fall then it would survive a shorter fall.
+- If an egg breaks, then it would break if dropped from a higher floor.
+- If an egg survives, then it would survive a shorter fall.
 
-If only one egg is available and we wish to be sure of obtaining the right result, the experiment can be carried out in only one way. Drop the egg from the first-floor window; if it survives, drop it from the second floor window. Continue upward until it breaks. In the worst case, this method may require 36 droppings. Suppose 2 eggs are available. What is the least number of egg-droppings that is guaranteed to work in all cases?
 The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
 
 ## Solution

From 4ace4c5c9b35fcc0839eaf00ba0ec388a23767eb Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 20 Sep 2017 00:23:42 -0700
Subject: [PATCH 201/643] Adds images to egg drop problem

---
 Egg Drop Problem/images/eggdrop.png  | Bin 0 -> 312712 bytes
 Egg Drop Problem/images/eggdrop2.png | Bin 0 -> 368811 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 Egg Drop Problem/images/eggdrop.png
 create mode 100644 Egg Drop Problem/images/eggdrop2.png

diff --git a/Egg Drop Problem/images/eggdrop.png b/Egg Drop Problem/images/eggdrop.png
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HcmV?d00001


From ea4b20857955ae00d425604a159ee0ab67dd4fa3 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 20 Sep 2017 01:24:45 -0700
Subject: [PATCH 202/643] Updates code to Swift 4. Refactored a bit of the
 readme.

---
 .../EggDrop.playground/Contents.swift         | 17 +++---
 .../EggDrop.playground/Sources/EggDrop.swift  | 60 ++++++++-----------
 .../contents.xcworkspacedata                  |  7 +++
 Egg Drop Problem/README.markdown              |  5 +-
 4 files changed, 43 insertions(+), 46 deletions(-)
 create mode 100644 Egg Drop Problem/EggDrop.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Egg Drop Problem/EggDrop.playground/Contents.swift b/Egg Drop Problem/EggDrop.playground/Contents.swift
index d452e7f9f..0b707da98 100644
--- a/Egg Drop Problem/EggDrop.playground/Contents.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Contents.swift	
@@ -1,9 +1,12 @@
- //: Playground - noun: a place where people can play
+#if swift(>=4.0)
+  print("Hello, Swift 4!")
+#endif
 
-import Cocoa
+drop(numberOfEggs: 2, numberOfFloors: 2) //expected answer: 2
+drop(numberOfEggs: 2, numberOfFloors: 4) //expected answer: 3
+drop(numberOfEggs: 2, numberOfFloors: 6) //expected answer: 3
+drop(numberOfEggs: 5, numberOfFloors: 5) //expected answer: 2
+drop(numberOfEggs: 5, numberOfFloors: 20) //expected answer: 4
 
-eggDrop(numberOfEggs: 2, numberOfFloors: 2) //expected answer: 2
-eggDrop(numberOfEggs: 2, numberOfFloors: 4) //expected answer: 3
-eggDrop(numberOfEggs: 2, numberOfFloors: 6) //expected answer: 3
-eggDrop(numberOfEggs: 5, numberOfFloors: 5) //expected answer: 2
-eggDrop(numberOfEggs: 5, numberOfFloors: 20) //expected answer: 4
\ No newline at end of file
+drop(numberOfEggs: 2, numberOfFloors: 36)
+drop(numberOfEggs: 2, numberOfFloors: 10)
diff --git a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift
index db1e48b95..f8bb0a420 100644
--- a/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Sources/EggDrop.swift	
@@ -1,39 +1,27 @@
-public func eggDrop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
-    if numberOfEggs == 0 || numberOfFloors == 0{ //edge case: When either number of eggs or number of floors is 0, answer is 0
-        return 0
-    }
-    if numberOfEggs == 1 || numberOfFloors == 1{ //edge case: When either number of eggs or number of floors is 1, answer is 1
-        return 1
-    }
-    
-    var eggFloor = [[Int]](repeating: [Int](repeating: 0, count: numberOfFloors+1), count: numberOfEggs+1) //egg(rows) floor(cols) array to store the solutions
-    var attempts: Int = 0
-    
-    for var floorNumber in (0..<(numberOfFloors+1)){
-        eggFloor[1][floorNumber] = floorNumber      //base case: if there's only one egg, it takes 'numberOfFloors' attempts
-    }
-    eggFloor[2][1] = 1 //base case: if there are two eggs and one floor, it takes one attempt
-    
-    for var eggNumber in (2..<(numberOfEggs+1)){
-        for var floorNumber in (2..<(numberOfFloors+1)){
-            eggFloor[eggNumber][floorNumber] = Int.max   //setting the final result a high number to find out minimum
-            for var visitingFloor in (1..<(floorNumber+1)){
-                //there are two cases
-                //case 1: egg breaks. meaning we'll have one less egg, and we'll have to go downstairs -> visitingFloor-1
-                //case 2: egg doesn't break. meaning we'll still have 'eggs' number of eggs, and we'll go upstairs -> floorNumber-visitingFloor
-                attempts = 1 + max(eggFloor[eggNumber-1][visitingFloor-1], eggFloor[eggNumber][floorNumber-visitingFloor])//we add one taking into account the attempt we're taking at the moment
-                
-                if attempts < eggFloor[eggNumber][floorNumber]{ //finding the min
-                    eggFloor[eggNumber][floorNumber] = attempts;
-                }
-            }
+public func drop(numberOfEggs: Int, numberOfFloors: Int) -> Int {
+  guard numberOfEggs != 0 && numberOfFloors != 0 else { return 0 }
+  guard numberOfEggs != 1 && numberOfFloors != 1 else { return 1 }
+  
+  var eggFloor: [[Int]] = .init(repeating: .init(repeating: 0, count: numberOfFloors + 1), count: numberOfEggs + 1)
+  var attempts = 0
+  
+  for floorNumber in stride(from: 0, through: numberOfFloors, by: 1) {
+    eggFloor[1][floorNumber] = floorNumber
+  }
+  eggFloor[2][1] = 1
+  
+  for eggNumber in stride(from: 2, through: numberOfEggs, by: 1) {
+    for floorNumber in stride(from: 2, through: numberOfFloors, by: 1) {
+      eggFloor[eggNumber][floorNumber] = Int.max
+      for visitingFloor in stride(from: 1, through: floorNumber, by: 1) {
+        attempts = 1 + max(eggFloor[eggNumber - 1][visitingFloor - 1], eggFloor[eggNumber][floorNumber - visitingFloor])
+        
+        if attempts < eggFloor[eggNumber][floorNumber] {
+          eggFloor[eggNumber][floorNumber] = attempts
         }
+      }
     }
-    
-    return eggFloor[numberOfEggs][numberOfFloors]
-}
-
-//Helper function to find max of two integers
-public func max(_ x1: Int, _ x2: Int) -> Int{
-    return x1 > x2 ? x1 : x2
+  }
+  
+  return eggFloor[numberOfEggs][numberOfFloors]
 }
diff --git a/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/contents.xcworkspacedata b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index 7c15bcf62..dd7ed4104 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -12,7 +12,7 @@ If the object is incredibly resilient, and you may need to do the testing on the
 
 ## Description
 
-You're in a building with **m** floors and you are given **n** eggs. What is the minimum number attempts it will take to find out the lowest floor that breaks the egg?
+You're in a building with **m** floors and you are given **n** eggs. What is the maximum number of attempts it will take to find out the floor that breaks the egg?
 
 For convenience, here are a few rules to keep in mind:
 
@@ -22,9 +22,8 @@ For convenience, here are a few rules to keep in mind:
 - If an egg breaks, then it would break if dropped from a higher floor.
 - If an egg survives, then it would survive a shorter fall.
 
-The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.
-
 ## Solution
+
 - eggNumber -> Number of eggs at the moment
 - floorNumber -> Floor number at the moment
 - visitingFloor -> Floor being visited at the moment

From 19acc0096a4d106b06dcd6fc8f240f96990ba6e5 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 20 Sep 2017 01:26:06 -0700
Subject: [PATCH 203/643] Added credits footer.

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

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index dd7ed4104..b2f45d09e 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -69,4 +69,4 @@ Let's assume we have 2 eggs and 2 floors.
 3) Finding the minimum of 2 and 2 gives us 2, so the answer is 2. 
    2 is the minimum number of attempts it will take to find out from which floor egg will break.
 
-
+*Written for the Swift Algorithm Club by Arkalyk Akash. Revisions and additions by Kelvin Lau*

From eb8edb19c446070806ae335b3b3522f97d9003be Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Wed, 20 Sep 2017 01:28:23 -0700
Subject: [PATCH 204/643] Adds egg drop problem to the main README file.

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

diff --git a/README.markdown b/README.markdown
index 0494e749d..c28d37f7a 100644
--- a/README.markdown
+++ b/README.markdown
@@ -196,7 +196,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 - [Monty Hall Problem](Monty%20Hall%20Problem/)
 - [Finding Palindromes](Palindromes/)
 - [Dining Philosophers](DiningPhilosophers/)
-
+- [Egg Drop Problem](Egg%20Drop%20Problem/)
 ## Learn more!
 
 For more information, check out these great books:

From 16775c6b7b26a838d4b7a5d42bf231bb983607fc Mon Sep 17 00:00:00 2001
From: Mark Rabins <markrabins@gmail.com>
Date: Wed, 20 Sep 2017 11:48:46 -0700
Subject: [PATCH 205/643] Minor Change

Updated the sort() function to sorted() based on Swift syntax changes.
---
 Kth Largest Element/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Kth Largest Element/README.markdown b/Kth Largest Element/README.markdown
index 53bec1c1c..aba2d9c29 100644
--- a/Kth Largest Element/README.markdown	
+++ b/Kth Largest Element/README.markdown	
@@ -12,7 +12,7 @@ The following solution is semi-naive. Its time complexity is **O(n log n)** sinc
 func kthLargest(a: [Int], k: Int) -> Int? {
   let len = a.count
   if k > 0 && k <= len {
-    let sorted = a.sort()
+    let sorted = a.sorted()
     return sorted[len - k]
   } else {
     return nil

From 37594584bdadf5290dd11afe2e0f56090f05130f Mon Sep 17 00:00:00 2001
From: Harry Twan <gua@desgard.com>
Date: Thu, 21 Sep 2017 09:23:17 +0800
Subject: [PATCH 206/643] Update mid is `l + (r + l) / 2`

---
 .../LazyPropagation.playground/Contents.swift    | 10 +++++-----
 Segment Tree/LazyPropagation/README.markdown     | 16 ++++++++++------
 2 files changed, 15 insertions(+), 11 deletions(-)

diff --git a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift
index 5def3df33..38dd51859 100644
--- a/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
+++ b/Segment Tree/LazyPropagation/LazyPropagation.playground/Contents.swift	
@@ -41,7 +41,7 @@ public class LazySegmentTree {
             return
         }
         
-        let middle = (leftBound + rightBound) / 2
+        let middle = leftBound + (rightBound - leftBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
         if let leftChild = leftChild, let rightChild = rightChild {
@@ -62,7 +62,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         var result = 0
         
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
@@ -80,7 +80,7 @@ public class LazySegmentTree {
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
@@ -100,7 +100,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
@@ -126,4 +126,4 @@ for index in 2 ... 5 {
 
 
 sumSegmentTree.update(leftBound: 0, rightBound: 5, incremental: 2)
-print(sumSegmentTree.query(leftBound: 0, rightBound: 2))
+print(sumSegmentTree.query(leftBound: 0, rightBound: 2))
\ No newline at end of file
diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
index bcfb890fd..21f6a7868 100644
--- a/Segment Tree/LazyPropagation/README.markdown	
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -22,6 +22,7 @@ But that is common Segment Tree. By **Lazy Propagation**, we can implement to mo
 At first, we reference the implement of **Artur Antonov** about Segment Tree. This code contained *build*, *single update* and *interval query* three operation. The implement of *build* and *single update* operation is following:
 
 ```swift
+// Author: Artur Antonov
 public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
 	self.leftBound = leftBound
 	self.rightBound = rightBound
@@ -45,6 +46,7 @@ In position ①, it means the current node is *leaf* because its left bound data
 And then, we have a look for *interval query* operation:
 
 ```swift
+// Author: Artur Antonov
 public func query(leftBound: Int, rightBound: Int) -> T {
 	if self.leftBound == leftBound && self.rightBound == rightBound {
 		return self.value
@@ -97,7 +99,7 @@ public init(array: [Int], leftBound: Int, rightBound: Int) {
         return
     }
     
-    let middle = (leftBound + rightBound) / 2
+    let middle = leftBound + (rightBound - leftBound) / 2
     leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
     rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
     if let leftChild = leftChild, let rightChild = rightChild {
@@ -113,7 +115,7 @@ public func update(index: Int, incremental: Int) {
     guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
     guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
     
-    let middle = (self.leftBound + self.rightBound) / 2
+    let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
     
     if index <= middle { leftChild.update(index: index, incremental: incremental) }
     else { rightChild.update(index: index, incremental: incremental) }
@@ -198,7 +200,7 @@ public class LazySegmentTree {
             return
         }
         
-        let middle = (leftBound + rightBound) / 2
+        let middle = leftBound + (rightBound - leftBound) / 2
         leftChild = LazySegmentTree(array: array, leftBound: leftBound, rightBound: middle)
         rightChild = LazySegmentTree(array: array, leftBound: middle + 1, rightBound: rightBound)
         if let leftChild = leftChild, let rightChild = rightChild {
@@ -219,7 +221,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         var result = 0
         
         if leftBound <= middle { result +=  leftChild.query(leftBound: leftBound, rightBound: rightBound) }
@@ -237,7 +239,7 @@ public class LazySegmentTree {
         guard let leftChild  = leftChild  else { fatalError("leftChild should not be nil") }
         guard let rightChild = rightChild else { fatalError("rightChild should not be nil") }
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         
         if index <= middle { leftChild.update(index: index, incremental: incremental) }
         else { rightChild.update(index: index, incremental: incremental) }
@@ -257,7 +259,7 @@ public class LazySegmentTree {
         
         pushDown(round: self.rightBound - self.leftBound + 1, lson: leftChild, rson: rightChild)
         
-        let middle = (self.leftBound + self.rightBound) / 2
+        let middle = self.leftBound + (self.rightBound - self.leftBound) / 2
         
         if leftBound <= middle { leftChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
         if middle < rightBound { rightChild.update(leftBound: leftBound, rightBound: rightBound, incremental: incremental) }
@@ -302,3 +304,5 @@ In fact, the operation of Segment Tree is far more than that. It can also be use
 ---
 
 *Written for Swift Algorithm Club by [Desgard_Duan](https://github.com/desgard)*
+
+

From bf50772cec8a64eab3e219994046f3d15cb29b5c Mon Sep 17 00:00:00 2001
From: Desgard_Duan <desgard_duan@foxmail.com>
Date: Thu, 21 Sep 2017 09:24:46 +0800
Subject: [PATCH 207/643] Update README.markdown

---
 Segment Tree/LazyPropagation/README.markdown | 2 --
 1 file changed, 2 deletions(-)

diff --git a/Segment Tree/LazyPropagation/README.markdown b/Segment Tree/LazyPropagation/README.markdown
index 21f6a7868..c625a7dc8 100644
--- a/Segment Tree/LazyPropagation/README.markdown	
+++ b/Segment Tree/LazyPropagation/README.markdown	
@@ -304,5 +304,3 @@ In fact, the operation of Segment Tree is far more than that. It can also be use
 ---
 
 *Written for Swift Algorithm Club by [Desgard_Duan](https://github.com/desgard)*
-
-

From 7f7270dc5c25dae5251e7914c10fa2ef18b96c44 Mon Sep 17 00:00:00 2001
From: Mark Rabins <markrabins@gmail.com>
Date: Wed, 20 Sep 2017 21:13:30 -0700
Subject: [PATCH 208/643] Missing a curly Brace, opps.

Missing a curly Brace, opps.
---
 Run-Length Encoding/README.markdown | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Run-Length Encoding/README.markdown b/Run-Length Encoding/README.markdown
index f7d196161..b29a49dd1 100644
--- a/Run-Length Encoding/README.markdown	
+++ b/Run-Length Encoding/README.markdown	
@@ -51,6 +51,7 @@ extension Data {
         }
         return data
     }
+ }
 ```
 
 How it works:

From 9f1f467648a84f0997d69757fb0b03e5cd6461de Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 21 Sep 2017 03:39:36 -0700
Subject: [PATCH 209/643] Updated solution 1 for clarity.

---
 Two-Sum Problem/README.markdown               | 20 +++++++-------
 .../Solution 1/2Sum.playground/Contents.swift | 27 ++++++++-----------
 2 files changed, 21 insertions(+), 26 deletions(-)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index a20666efd..e99902167 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -1,24 +1,24 @@
 # Two-Sum Problem
 
-You're given an array `a` with numbers. Write an algorithm that checks if there are any two entries in the array that add up to a given number `k`. In other words, is there any `a[i] + a[j] == k`?
+You're given an array of numbers. Write an algorithm that checks if there are any two elements in the array that add up to a given number.
 
 There are a variety of solutions to this problem (some better than others). The following solutions both run in **O(n)** time.
 
 # Solution 1
 
-This solution uses a dictionary to store differences between each element in the array and the sum `k` that we're looking for. The dictionary also stores the indices of each element.
+This solution uses a dictionary to store differences between each element in the array and the sum that we're looking for. The dictionary also stores the indices of each element.
 
-With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum to `k`.
+With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum.
 
 ```swift
-func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
-  var dict = [Int: Int]()
-
-  for i in 0 ..< a.count {
-    if let newK = dict[a[i]] {
-      return (newK, i)
+func twoSumProblem(_ numbers: [Int], sum: Int) -> (Int, Int)? {
+  var dict: [Int: Int] = [:]
+  
+  for (index, number) in numbers.enumerated() {
+    if let otherIndex = dict[number] {
+      return (index, otherIndex)
     } else {
-      dict[k - a[i]] =  i
+      dict[sum - number] = index
     }
   }
 
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 4de46128c..4b6db5d51 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -4,26 +4,21 @@
 print("Hello, Swift 4!")
 #endif
 
-func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
-  var map = [Int: Int]()
-
-  for i in 0 ..< a.count {
-    if let newK = map[a[i]] {
-      return (newK, i)
+func twoSum(_ numbers: [Int], target: Int) -> (Int, Int)? {
+  var dict: [Int: Int] = [:]
+  
+  for (index, number) in numbers.enumerated() {
+    if let otherIndex = dict[number] {
+      return (index, otherIndex)
     } else {
-      map[k - a[i]] =  i
+      dict[target - number] = index
     }
   }
+  
   return nil
 }
 
-let a = [7, 100, 2, 21, 12, 10, 22, 14, 3, 4, 8, 4, 9]
-if let (i, j) = twoSumProblem(a, k: 33) {
-  i            // 3
-  a[i]         // 21
-  j            // 4
-  a[j]         // 12
-  a[i] + a[j]  // 33
-}
+let numbers = [3, 2, 4]
+let target = 6
 
-twoSumProblem(a, k: 37)  // nil
+twoSum(numbers, target: target) // expected output: indices 2 and 1

From d757cbe04c88ab9ef8065ac240fd04db0e5d0e4a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 21 Sep 2017 03:40:58 -0700
Subject: [PATCH 210/643] Fixes a typo.

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

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index e99902167..6fb05d316 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -11,14 +11,14 @@ This solution uses a dictionary to store differences between each element in the
 With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum.
 
 ```swift
-func twoSumProblem(_ numbers: [Int], sum: Int) -> (Int, Int)? {
+func twoSumProblem(_ numbers: [Int], target: Int) -> (Int, Int)? {
   var dict: [Int: Int] = [:]
   
   for (index, number) in numbers.enumerated() {
     if let otherIndex = dict[number] {
       return (index, otherIndex)
     } else {
-      dict[sum - number] = index
+      dict[target - number] = index
     }
   }
 

From c93cc36debd8f0965575a330a3d531fa6e09a954 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 21 Sep 2017 03:46:05 -0700
Subject: [PATCH 211/643] Fixes the explanation to match the code.

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

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index 6fb05d316..dacf5a40a 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -26,7 +26,7 @@ func twoSumProblem(_ numbers: [Int], target: Int) -> (Int, Int)? {
 }
 ```
 
-The `twoSumProblem()` function takes two parameters: the array `a` with the numbers, and `k`, the sum we're looking for. It returns the first set of indices `(i, j)` where `a[i] + a[j] == k`, or `nil` if no two numbers add up to `k`.
+The `twoSumProble` function takes two parameters: the `numbers` array and the target sum you're looking for. It returns the 2 indices with elements that sums up to the target, or `nil` if it can't be found.
 
 Let's take a look at an example and run through the algorithm to see how it works. Given is the array:
 
@@ -38,7 +38,7 @@ Let's find out if there exist two entries whose sum is equal to 10.
 
 Initially, our dictionary is empty. We begin looping through each element:
 
-- **i = 0**: Is `7` in the dictionary? No. We add the difference between the target `k` and the current number to the dictionary. The difference is `10 - 7 = 3`, so the dictionary key is `3`. The value for that key is the current index, `0`. The dictionary now looks like this:
+- **i = 0**: Is `7` in the dictionary? No. We add the difference between the `target` and the current number to the dictionary. The difference is `10 - 7 = 3`, so the dictionary key is `3`. The value for that key is the current index, `0`. The dictionary now looks like this:
 
 ```swift
 [ 3: 0 ]

From a75e7047a92005649f547d2e3d212318473e0c71 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 23 Sep 2017 23:14:14 -0700
Subject: [PATCH 212/643] Update readme for swift 4 and Xcode 9

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

diff --git a/README.markdown b/README.markdown
index c28d37f7a..48e1a90f0 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,7 +8,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-Most code is compatible with **Xcode 8.3** and **Swift 3**. We'll keep this updated with the latest version of Swift.
+All code are compatible with **Xcode 9** and **Swift 4**. We'll keep this updated with the latest version of Swift.
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 

From b521470d82f9c9fbb54d3ec9ccfc7a84dea6dc34 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 24 Sep 2017 07:45:19 -0700
Subject: [PATCH 213/643] Updated readme for Swift 4

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

diff --git a/README.markdown b/README.markdown
index 48e1a90f0..dd001f75a 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,7 +8,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-All code are compatible with **Xcode 9** and **Swift 4**. We'll keep this updated with the latest version of Swift.
+Code is compatible with **Xcode 9** and **Swift 4**. We'll keep this updated with the latest version of Swift.
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 

From 0d17a67abfa28dd093189ad1af581ffb2a6d5c7d Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Mon, 25 Sep 2017 17:09:08 +0900
Subject: [PATCH 214/643] Code Refactoring

Modifying the merge method in Merge Sort:
* empty array definition.
* unifying the while loop.
---
 .../MergeSort.playground/Contents.swift       | 27 +++++-------
 Merge Sort/MergeSort.swift                    | 41 ++++++++-----------
 2 files changed, 28 insertions(+), 40 deletions(-)

diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index 06fa3beaa..b05332bfe 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -21,31 +21,24 @@ func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
     orderedPile.reserveCapacity(leftPile.count + rightPile.count)
   }
 
-  while leftIndex < leftPile.count && rightIndex < rightPile.count {
+  while true {
+    guard leftIndex < leftPile.endIndex else {
+      orderedPile.append(contentsOf: rightPile[rightIndex..<rightPile.endIndex])
+      break
+    }
+    guard rightIndex < rightPile.endIndex else {
+      orderedPile.append(contentsOf: leftPile[leftIndex..<leftPile.endIndex])
+      break
+    }
+    
     if leftPile[leftIndex] < rightPile[rightIndex] {
       orderedPile.append(leftPile[leftIndex])
       leftIndex += 1
-    } else if leftPile[leftIndex] > rightPile[rightIndex] {
-      orderedPile.append(rightPile[rightIndex])
-      rightIndex += 1
     } else {
-      orderedPile.append(leftPile[leftIndex])
-      leftIndex += 1
       orderedPile.append(rightPile[rightIndex])
       rightIndex += 1
     }
   }
-
-  while leftIndex < leftPile.count {
-    orderedPile.append(leftPile[leftIndex])
-    leftIndex += 1
-  }
-
-  while rightIndex < rightPile.count {
-    orderedPile.append(rightPile[rightIndex])
-    rightIndex += 1
-  }
-
   return orderedPile
 }
 
diff --git a/Merge Sort/MergeSort.swift b/Merge Sort/MergeSort.swift
index 990c432fa..00e35f498 100644
--- a/Merge Sort/MergeSort.swift	
+++ b/Merge Sort/MergeSort.swift	
@@ -17,35 +17,30 @@ func mergeSort<T: Comparable>(_ array: [T]) -> [T] {
 func merge<T: Comparable>(leftPile: [T], rightPile: [T]) -> [T] {
   var leftIndex = 0
   var rightIndex = 0
-  var orderedPile = [T]()
+  var orderedPile: [T] = []
   if orderedPile.capacity < leftPile.count + rightPile.count {
     orderedPile.reserveCapacity(leftPile.count + rightPile.count)
   }
 
-  while leftIndex < leftPile.count && rightIndex < rightPile.count {
-    if leftPile[leftIndex] < rightPile[rightIndex] {
-      orderedPile.append(leftPile[leftIndex])
-      leftIndex += 1
-    } else if leftPile[leftIndex] > rightPile[rightIndex] {
-      orderedPile.append(rightPile[rightIndex])
-      rightIndex += 1
-    } else {
-      orderedPile.append(leftPile[leftIndex])
-      leftIndex += 1
-      orderedPile.append(rightPile[rightIndex])
-      rightIndex += 1
-    }
-  }
-
-  while leftIndex < leftPile.count {
-    orderedPile.append(leftPile[leftIndex])
-    leftIndex += 1
+  while true {
+      guard leftIndex < leftPile.endIndex else {
+          orderedPile.append(contentsOf: rightPile[rightIndex..<rightPile.endIndex])
+          break
+      }
+      guard rightIndex < rightPile.endIndex else {
+          orderedPile.append(contentsOf: leftPile[leftIndex..<leftPile.endIndex])
+          break
+      }
+      
+      if leftPile[leftIndex] < rightPile[rightIndex] {
+          orderedPile.append(leftPile[leftIndex])
+          leftIndex += 1
+      } else {
+          orderedPile.append(rightPile[rightIndex])
+          rightIndex += 1
+      }
   }
 
-  while rightIndex < rightPile.count {
-    orderedPile.append(rightPile[rightIndex])
-    rightIndex += 1
-  }
 
   return orderedPile
 }

From 71ab3f8eb62bea0886536f2fd12b7b703ea0cb2e Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine@appirio.com>
Date: Tue, 26 Sep 2017 15:34:03 -0700
Subject: [PATCH 215/643] algorithm proposal

---
 Genetic/README.markdown |   2 +
 Genetic/gen.swift       | 179 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 181 insertions(+)
 create mode 100644 Genetic/README.markdown
 create mode 100644 Genetic/gen.swift

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
new file mode 100644
index 000000000..7cad649cb
--- /dev/null
+++ b/Genetic/README.markdown
@@ -0,0 +1,2 @@
+# todo
+refactoring https://gist.github.com/blainerothrock/efda6e12fe10792c99c990f8ff3daeba for swift 4. Creating a tutorial and writing in more playground friendly format
diff --git a/Genetic/gen.swift b/Genetic/gen.swift
new file mode 100644
index 000000000..72830b8a7
--- /dev/null
+++ b/Genetic/gen.swift
@@ -0,0 +1,179 @@
+/*
+  base .. to be refactored
+*/
+
+import Foundation
+
+// HELPERS
+/*
+    String extension to convert a string to ascii value
+*/
+extension String {
+    var asciiArray: [UInt8] {
+        return unicodeScalars.filter{$0.isASCII}.map{UInt8($0.value)}
+    }
+}
+
+/*
+    helper function to return a random character string
+*/
+func randomChar() -> UInt8 {
+    
+    let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+    let len = UInt32(letters.count-1)
+    
+    let rand = Int(arc4random_uniform(len))
+    return letters[rand]
+}
+
+// END HELPERS
+
+let OPTIMAL:[UInt8] = "Hello, World".asciiArray
+let DNA_SIZE = OPTIMAL.count
+let POP_SIZE = 50
+let GENERATIONS = 5000
+let MUTATION_CHANCE = 100
+
+/*
+    calculated the fitness based on approximate string matching
+    compares each character ascii value difference and adds that to a total fitness
+    optimal string comparsion = 0
+*/
+func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
+    
+    var fitness = 0
+    for c in 0...dna.count-1 {
+        fitness += abs(Int(dna[c]) - Int(optimal[c]))
+    }
+    return fitness
+}
+
+/*
+    randomly mutate the string
+*/
+func mutate(dna:[UInt8], mutationChance:Int, dnaSize:Int) -> [UInt8] {
+    var outputDna = dna
+    
+    for i in 0..<dnaSize {
+        let rand = Int(arc4random_uniform(UInt32(mutationChance)))
+        if rand == 1 {
+            outputDna[i] = randomChar()
+        }
+    }
+
+    return outputDna
+}
+
+/*
+    combine two parents to create an offspring
+    parent = xy & yx, offspring = xx, yy
+*/
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+    let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
+    
+    let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
+    let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
+    
+    return (
+        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
+        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
+    )
+}
+
+
+/*
+returns a random population, used to start the evolution
+*/
+func randomPopulation(populationSize: Int, dnaSize: Int) -> [[UInt8]] {
+    
+    let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+    let len = UInt32(letters.count)
+
+    var pop = [[UInt8]]()
+    
+    for _ in 0..<populationSize {
+        var dna = [UInt8]()
+        for _ in 0..<dnaSize {
+            let rand = arc4random_uniform(len)
+            let nextChar = letters[Int(rand)]
+            dna.append(nextChar)
+        }
+        pop.append(dna)
+    }
+    return pop
+}
+
+
+/*
+function to return random canidate of a population randomally, but weight on fitness.
+*/
+func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+    var weightTotal = 0.0
+    for itemTuple in items {
+        weightTotal += itemTuple.weight;
+    }
+    
+    var n = Double(arc4random_uniform(UInt32(weightTotal * 1000000.0))) / 1000000.0
+
+    for itemTuple in items {
+        if n < itemTuple.weight {
+            return itemTuple
+        }
+        n = n - itemTuple.weight
+    }
+    return items[1]
+}
+
+func main() {
+
+    // generate the starting random population
+    var population:[[UInt8]] = randomPopulation(populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+    // print("population: \(population), dnaSize: \(DNA_SIZE) ")
+    var fittest = [UInt8]()
+
+    for generation in 0...GENERATIONS {
+        print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
+        
+        var weightedPopulation = [(item:[UInt8], weight:Double)]()
+        
+        // calulcated the fitness of each individual in the population
+        // and add it to the weight population (weighted = 1.0/fitness)
+        for individual in population {
+            let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
+            
+            let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
+            
+            weightedPopulation.append(pair)
+        }
+        
+        population = []
+        
+        // create a new generation using the individuals in the origional population
+        for _ in 0...POP_SIZE/2 {
+            let ind1 = weightedChoice(items: weightedPopulation)
+            let ind2 = weightedChoice(items: weightedPopulation)
+            
+            let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+
+            // append to the population and mutate
+            population.append(mutate(dna: offspring.dna1, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
+            population.append(mutate(dna: offspring.dna2, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
+        }
+        
+        fittest = population[0]
+        var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
+        
+        // parse the population for the fittest string
+        for indv in population {
+            let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
+            if indvFitness < minFitness {
+                fittest = indv
+                minFitness = indvFitness
+            }
+        }
+        if minFitness == 0 { break; }
+    }
+    print("fittest string: \(String(bytes: fittest, encoding: .ascii)!)")
+}
+
+main()

From 08543ed89a5b2e2275f037f01970544199b66397 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Tue, 3 Oct 2017 18:40:21 -0300
Subject: [PATCH 216/643] Aditions to AVLTree

---
 AVL Tree/AVLTree.swift | 704 ++++++++++++++++++++++-------------------
 1 file changed, 384 insertions(+), 320 deletions(-)

diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index 52ea082ce..ddc8e7892 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -21,379 +21,443 @@
 // SOFTWARE.
 
 public class TreeNode<Key: Comparable, Payload> {
-  public typealias Node = TreeNode<Key, Payload>
-
-  var payload: Payload?
-
-  fileprivate var key: Key
-  internal var leftChild: Node?
-  internal var rightChild: Node?
-  fileprivate var height: Int
-  fileprivate weak var parent: Node?
-
-  public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
-    self.key = key
-    self.payload = payload
-    self.leftChild = leftChild
-    self.rightChild = rightChild
-    self.parent = parent
-    self.height = height
-
-    self.leftChild?.parent = self
-    self.rightChild?.parent = self
-  }
-
-  public convenience init(key: Key, payload: Payload?) {
-    self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil, height: 1)
-  }
-
-  public convenience init(key: Key) {
-    self.init(key: key, payload: nil)
-  }
-
-  var isRoot: Bool {
-    return parent == nil
-  }
-
-  var isLeaf: Bool {
-    return rightChild == nil && leftChild == nil
-  }
-
-  var isLeftChild: Bool {
-    return parent?.leftChild === self
-  }
-
-  var isRightChild: Bool {
-    return parent?.rightChild === self
-  }
-
-  var hasLeftChild: Bool {
-    return leftChild != nil
-  }
-
-  var hasRightChild: Bool {
-    return rightChild != nil
-  }
-
-  var hasAnyChild: Bool {
-    return leftChild != nil || rightChild != nil
-  }
-
-  var hasBothChildren: Bool {
-    return leftChild != nil && rightChild != nil
-  }
+    public typealias Node = TreeNode<Key, Payload>
+    
+    var payload: Payload?   // Value held by the node
+    
+    fileprivate var key: Key    // Node's name
+    internal var leftChild: Node?
+    internal var rightChild: Node?
+    fileprivate var height: Int
+    weak fileprivate var parent: Node?
+    
+    public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
+        self.key = key
+        self.payload = payload
+        self.leftChild = leftChild
+        self.rightChild = rightChild
+        self.parent = parent
+        self.height = height
+        
+        self.leftChild?.parent = self
+        self.rightChild?.parent = self
+    }
+    
+    public convenience init(key: Key, payload: Payload?) {
+        self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil, height: 1)
+    }
+    
+    public convenience init(key: Key) {
+        self.init(key: key, payload: nil)
+    }
+    
+    var isRoot: Bool {
+        return parent == nil
+    }
+    
+    var isLeaf: Bool {
+        return rightChild == nil && leftChild == nil
+    }
+    
+    var isLeftChild: Bool {
+        return parent?.leftChild === self
+    }
+    
+    var isRightChild: Bool {
+        return parent?.rightChild === self
+    }
+    
+    var hasLeftChild: Bool {
+        return leftChild != nil
+    }
+    
+    var hasRightChild: Bool {
+        return rightChild != nil
+    }
+    
+    var hasAnyChild: Bool {
+        return leftChild != nil || rightChild != nil
+    }
+    
+    var hasBothChildren: Bool {
+        return leftChild != nil && rightChild != nil
+    }
 }
 
 // MARK: - The AVL tree
 
 open class AVLTree<Key: Comparable, Payload> {
-  public typealias Node = TreeNode<Key, Payload>
-
-  fileprivate(set) var root: Node?
-  fileprivate(set) var size = 0
-
-  public init() { }
+    public typealias Node = TreeNode<Key, Payload>
+    
+    fileprivate(set) var root: Node?
+    fileprivate(set) var size = 0
+    
+    public init() { }
 }
 
 // MARK: - Searching
 
 extension TreeNode {
-  public func minimum() -> TreeNode? {
-    return leftChild?.minimum() ?? self
-  }
-
-  public func maximum() -> TreeNode? {
-    return rightChild?.maximum() ?? self
-  }
+    public func minimum() -> TreeNode? {
+        return leftChild?.minimum() ?? self
+    }
+    
+    public func maximum() -> TreeNode? {
+        return rightChild?.maximum() ?? self
+    }
 }
 
 extension AVLTree {
-  subscript(key: Key) -> Payload? {
-    get { return search(input: key) }
-    set { insert(key: key, payload: newValue) }
-  }
-
-  public func search(input: Key) -> Payload? {
-    return search(key: input, node: root)?.payload
-  }
-
-  fileprivate func search(key: Key, node: Node?) -> Node? {
-    if let node = node {
-      if key == node.key {
-        return node
-      } else if key < node.key {
-        return search(key: key, node: node.leftChild)
-      } else {
-        return search(key: key, node: node.rightChild)
-      }
-    }
-    return nil
-  }
+    subscript(key: Key) -> Payload? {
+        get { return search(input: key) }
+        set { insert(key: key, payload: newValue) }
+    }
+    
+    public func search(input: Key) -> Payload? {
+        return search(key: input, node: root)?.payload
+    }
+    
+    fileprivate func search(key: Key, node: Node?) -> Node? {
+        if let node = node {
+            if key == node.key {
+                return node
+            } else if key < node.key {
+                return search(key: key, node: node.leftChild)
+            } else {
+                return search(key: key, node: node.rightChild)
+            }
+        }
+        return nil
+    }
 }
 
 // MARK: - Inserting new items
 
 extension AVLTree {
-  public func insert(key: Key, payload: Payload? = nil) {
-    if let root = root {
-      insert(input: key, payload: payload, node: root)
-    } else {
-      root = Node(key: key, payload: payload)
-    }
-    size += 1
-  }
-
-  private func insert(input: Key, payload: Payload?, node: Node) {
-    if input < node.key {
-      if let child = node.leftChild {
-        insert(input: input, payload: payload, node: child)
-      } else {
-        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
-        node.leftChild = child
-        balance(node: child)
-      }
-    } else {
-      if let child = node.rightChild {
-        insert(input: input, payload: payload, node: child)
-      } else {
-        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
-        node.rightChild = child
-        balance(node: child)
-      }
-    }
-  }
+    public func insert(key: Key, payload: Payload? = nil) {
+        if let root = root {
+            insert(input: key, payload: payload, node: root)
+        } else {
+            root = Node(key: key, payload: payload)
+        }
+        size += 1
+    }
+    
+    private func insert(input: Key, payload: Payload?, node: Node) {
+        if input < node.key {
+            if let child = node.leftChild {
+                insert(input: input, payload: payload, node: child)
+            } else {
+                let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
+                node.leftChild = child
+                balance(node: child)
+            }
+        } else if input != node.key {
+            if let child = node.rightChild {
+                insert(input: input, payload: payload, node: child)
+            } else {
+                let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
+                node.rightChild = child
+                balance(node: child)
+            }
+        }
+    }
 }
 
 // MARK: - Balancing tree
 
 extension AVLTree {
-  fileprivate func updateHeightUpwards(node: Node?) {
-    if let node = node {
-      let lHeight = node.leftChild?.height ?? 0
-      let rHeight = node.rightChild?.height ?? 0
-      node.height = max(lHeight, rHeight) + 1
-      updateHeightUpwards(node: node.parent)
-    }
-  }
-
-  fileprivate func lrDifference(node: Node?) -> Int {
-    let lHeight = node?.leftChild?.height ?? 0
-    let rHeight = node?.rightChild?.height ?? 0
-    return lHeight - rHeight
-  }
-
-  fileprivate func balance(node: Node?) {
-    guard let node = node else {
-      return
+    fileprivate func updateHeightUpwards(node: Node?) {
+        if let node = node {
+            let lHeight = node.leftChild?.height ?? 0
+            let rHeight = node.rightChild?.height ?? 0
+            node.height = max(lHeight, rHeight) + 1
+            updateHeightUpwards(node: node.parent)
+        }
     }
-
-    updateHeightUpwards(node: node.leftChild)
-    updateHeightUpwards(node: node.rightChild)
-
-    var nodes = [Node?](repeating: nil, count: 3)
-    var subtrees = [Node?](repeating: nil, count: 4)
-    let nodeParent = node.parent
-
-    let lrFactor = lrDifference(node: node)
-    if lrFactor > 1 {
-      // left-left or left-right
-      if lrDifference(node: node.leftChild) > 0 {
-        // left-left
-        nodes[0] = node
-        nodes[2] = node.leftChild
-        nodes[1] = nodes[2]?.leftChild
-
-        subtrees[0] = nodes[1]?.leftChild
-        subtrees[1] = nodes[1]?.rightChild
-        subtrees[2] = nodes[2]?.rightChild
-        subtrees[3] = nodes[0]?.rightChild
-      } else {
-        // left-right
-        nodes[0] = node
-        nodes[1] = node.leftChild
-        nodes[2] = nodes[1]?.rightChild
-
-        subtrees[0] = nodes[1]?.leftChild
-        subtrees[1] = nodes[2]?.leftChild
-        subtrees[2] = nodes[2]?.rightChild
-        subtrees[3] = nodes[0]?.rightChild
-      }
-    } else if lrFactor < -1 {
-      // right-left or right-right
-      if lrDifference(node: node.rightChild) < 0 {
-        // right-right
-        nodes[1] = node
-        nodes[2] = node.rightChild
-        nodes[0] = nodes[2]?.rightChild
-
-        subtrees[0] = nodes[1]?.leftChild
-        subtrees[1] = nodes[2]?.leftChild
-        subtrees[2] = nodes[0]?.leftChild
-        subtrees[3] = nodes[0]?.rightChild
-      } else {
-        // right-left
-        nodes[1] = node
-        nodes[0] = node.rightChild
-        nodes[2] = nodes[0]?.leftChild
-
-        subtrees[0] = nodes[1]?.leftChild
-        subtrees[1] = nodes[2]?.leftChild
-        subtrees[2] = nodes[2]?.rightChild
-        subtrees[3] = nodes[0]?.rightChild
-      }
-    } else {
-      // Don't need to balance 'node', go for parent
-      balance(node: node.parent)
-      return
+    
+    fileprivate func lrDifference(node: Node?) -> Int {
+        let lHeight = node?.leftChild?.height ?? 0
+        let rHeight = node?.rightChild?.height ?? 0
+        return lHeight - rHeight
     }
-
-    // nodes[2] is always the head
-
-    if node.isRoot {
-      root = nodes[2]
-      root?.parent = nil
-    } else if node.isLeftChild {
-      nodeParent?.leftChild = nodes[2]
-      nodes[2]?.parent = nodeParent
-    } else if node.isRightChild {
-      nodeParent?.rightChild = nodes[2]
-      nodes[2]?.parent = nodeParent
+    
+    fileprivate func balance(node: Node?) {
+        guard let node = node else {
+            return
+        }
+        
+        updateHeightUpwards(node: node.leftChild)
+        updateHeightUpwards(node: node.rightChild)
+        
+        var nodes = [Node?](repeating: nil, count: 3)
+        var subtrees = [Node?](repeating: nil, count: 4)
+        let nodeParent = node.parent
+        
+        let lrFactor = lrDifference(node: node)
+        if lrFactor > 1 {
+            // left-left or left-right
+            if lrDifference(node: node.leftChild) > 0 {
+                // left-left
+                nodes[0] = node
+                nodes[2] = node.leftChild
+                nodes[1] = nodes[2]?.leftChild
+                
+                subtrees[0] = nodes[1]?.leftChild
+                subtrees[1] = nodes[1]?.rightChild
+                subtrees[2] = nodes[2]?.rightChild
+                subtrees[3] = nodes[0]?.rightChild
+            } else {
+                // left-right
+                nodes[0] = node
+                nodes[1] = node.leftChild
+                nodes[2] = nodes[1]?.rightChild
+                
+                subtrees[0] = nodes[1]?.leftChild
+                subtrees[1] = nodes[2]?.leftChild
+                subtrees[2] = nodes[2]?.rightChild
+                subtrees[3] = nodes[0]?.rightChild
+            }
+        } else if lrFactor < -1 {
+            // right-left or right-right
+            if lrDifference(node: node.rightChild) < 0 {
+                // right-right
+                nodes[1] = node
+                nodes[2] = node.rightChild
+                nodes[0] = nodes[2]?.rightChild
+                
+                subtrees[0] = nodes[1]?.leftChild
+                subtrees[1] = nodes[2]?.leftChild
+                subtrees[2] = nodes[0]?.leftChild
+                subtrees[3] = nodes[0]?.rightChild
+            } else {
+                // right-left
+                nodes[1] = node
+                nodes[0] = node.rightChild
+                nodes[2] = nodes[0]?.leftChild
+                
+                subtrees[0] = nodes[1]?.leftChild
+                subtrees[1] = nodes[2]?.leftChild
+                subtrees[2] = nodes[2]?.rightChild
+                subtrees[3] = nodes[0]?.rightChild
+            }
+        } else {
+            // Don't need to balance 'node', go for parent
+            balance(node: node.parent)
+            return
+        }
+        
+        // nodes[2] is always the head
+        
+        if node.isRoot {
+            root = nodes[2]
+            root?.parent = nil
+        } else if node.isLeftChild {
+            nodeParent?.leftChild = nodes[2]
+            nodes[2]?.parent = nodeParent
+        } else if node.isRightChild {
+            nodeParent?.rightChild = nodes[2]
+            nodes[2]?.parent = nodeParent
+        }
+        
+        nodes[2]?.leftChild = nodes[1]
+        nodes[1]?.parent = nodes[2]
+        nodes[2]?.rightChild = nodes[0]
+        nodes[0]?.parent = nodes[2]
+        
+        nodes[1]?.leftChild = subtrees[0]
+        subtrees[0]?.parent = nodes[1]
+        nodes[1]?.rightChild = subtrees[1]
+        subtrees[1]?.parent = nodes[1]
+        
+        nodes[0]?.leftChild = subtrees[2]
+        subtrees[2]?.parent = nodes[0]
+        nodes[0]?.rightChild = subtrees[3]
+        subtrees[3]?.parent = nodes[0]
+        
+        updateHeightUpwards(node: nodes[1])    // Update height from left
+        updateHeightUpwards(node: nodes[0])    // Update height from right
+        
+        balance(node: nodes[2]?.parent)
     }
-
-    nodes[2]?.leftChild = nodes[1]
-    nodes[1]?.parent = nodes[2]
-    nodes[2]?.rightChild = nodes[0]
-    nodes[0]?.parent = nodes[2]
-
-    nodes[1]?.leftChild = subtrees[0]
-    subtrees[0]?.parent = nodes[1]
-    nodes[1]?.rightChild = subtrees[1]
-    subtrees[1]?.parent = nodes[1]
-
-    nodes[0]?.leftChild = subtrees[2]
-    subtrees[2]?.parent = nodes[0]
-    nodes[0]?.rightChild = subtrees[3]
-    subtrees[3]?.parent = nodes[0]
-
-    updateHeightUpwards(node: nodes[1])    // Update height from left
-    updateHeightUpwards(node: nodes[0])    // Update height from right
-
-    balance(node: nodes[2]?.parent)
-  }
 }
 
 // MARK: - Displaying tree
 
 extension AVLTree {
-  fileprivate func display(node: Node?, level: Int) {
-    if let node = node {
-      display(node: node.rightChild, level: level + 1)
-      print("")
-      if node.isRoot {
-        print("Root -> ", terminator: "")
-      }
-      for _ in 0..<level {
-        print("        ", terminator:  "")
-      }
-      print("(\(node.key):\(node.height))", terminator: "")
-      display(node: node.leftChild, level: level + 1)
-    }
-  }
-
-  public func display(node: Node) {
-    display(node: node, level: 0)
-    print("")
-  }
+    fileprivate func display(node: Node?, level: Int) {
+        if let node = node {
+            display(node: node.rightChild, level: level + 1)
+            print("")
+            if node.isRoot {
+                print("Root -> ", terminator: "")
+            }
+            for _ in 0..<level {
+                print("        ", terminator:  "")
+            }
+            print("(\(node.key):\(node.height))", terminator: "")
+            display(node: node.leftChild, level: level + 1)
+        }
+    }
+    
+    public func display(node: Node) {
+        display(node: node, level: 0)
+        print("")
+    }
+    
+    public func inorder(node: Node?) -> String {
+        var output = ""
+        if let node = node {
+            output = "\(inorder(node: node.leftChild)) \(print("\(node.key) ")) \(inorder(node: node.rightChild))"
+        }
+        return output
+    }
+    
+    public func preorder(node: Node?) -> String {
+        var output = ""
+        if let node = node {
+            output = "\(preorder(node: node.leftChild)) \(print("\(node.key) ")) \(preorder(node: node.rightChild))"
+        }
+        return output
+    }
+    
+    public func postorder(node: Node?) -> String {
+        var output = ""
+        if let node = node {
+            output = "\(postorder(node: node.leftChild)) \(print("\(node.key) ")) \(postorder(node: node.rightChild))"
+        }
+        return output
+    }
 }
 
 // MARK: - Delete node
 
 extension AVLTree {
-  public func delete(key: Key) {
-    if size == 1 {
-      root = nil
-      size -= 1
-    } else if let node = search(key: key, node: root) {
-      delete(node: node)
-      size -= 1
-    }
-  }
-
-  private func delete(node: Node) {
-    if node.isLeaf {
-      // Just remove and balance up
-      if let parent = node.parent {
-        guard node.isLeftChild || node.isRightChild else {
-          // just in case
-          fatalError("Error: tree is invalid.")
+    public func delete(key: Key) {
+        if size == 1 {
+            root = nil
+            size -= 1
+        } else if let node = search(key: key, node: root) {
+            delete(node: node)
+            size -= 1
         }
-
-        if node.isLeftChild {
-          parent.leftChild = nil
-        } else if node.isRightChild {
-          parent.rightChild = nil
+    }
+    
+    private func delete(node: Node) {
+        if node.isLeaf {
+            // Just remove and balance up
+            if let parent = node.parent {
+                guard node.isLeftChild || node.isRightChild else {
+                    // just in case
+                    fatalError("Error: tree is invalid.")
+                }
+                
+                if node.isLeftChild {
+                    parent.leftChild = nil
+                } else if node.isRightChild {
+                    parent.rightChild = nil
+                }
+                
+                balance(node: parent)
+            } else {
+                // at root
+                root = nil
+            }
+        } else {
+            // Handle stem cases
+            if let replacement = node.leftChild?.maximum(), replacement !== node {
+                node.key = replacement.key
+                node.payload = replacement.payload
+                delete(node: replacement)
+            } else if let replacement = node.rightChild?.minimum(), replacement !== node {
+                node.key = replacement.key
+                node.payload = replacement.payload
+                delete(node: replacement)
+            }
         }
+    }
+}
 
-        balance(node: parent)
-      } else {
-        // at root
-        root = nil
-      }
-    } else {
-      // Handle stem cases
-      if let replacement = node.leftChild?.maximum(), replacement !== node {
-        node.key = replacement.key
-        node.payload = replacement.payload
-        delete(node: replacement)
-      } else if let replacement = node.rightChild?.minimum(), replacement !== node {
-        node.key = replacement.key
-        node.payload = replacement.payload
-        delete(node: replacement)
-      }
-    }
-  }
+// MARK: - Advanced Stuff
+
+extension AVLTree {
+    public func doInOrder(node: Node?, _ completion: (Node) -> Void) {
+        if let node = node {
+            doInOrder(node: node.leftChild) { lnode in
+                completion(lnode)
+            }
+            completion(node)
+            doInOrder(node: node.rightChild) { rnode in
+                completion(rnode)
+            }
+        }
+    }
+    
+    public func doInPreOrder(node: Node?, _ completion: (Node) -> Void) {
+        if let node = node {
+            completion(node)
+            doInPreOrder(node: node.leftChild) { lnode in
+                completion(lnode)
+            }
+            doInPreOrder(node: node.rightChild) { rnode in
+                completion(rnode)
+            }
+        }
+    }
+    
+    public func doInPostOrder(node: Node?, _ completion: (Node) -> Void) {
+        if let node = node {
+            doInPostOrder(node: node.leftChild) { lnode in
+                completion(lnode)
+            }
+            doInPostOrder(node: node.rightChild) { rnode in
+                completion(rnode)
+            }
+            completion(node)
+        }
+    }
 }
 
 // MARK: - Debugging
 
 extension TreeNode: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    var s = "key: \(key), payload: \(payload), height: \(height)"
-    if let parent = parent {
-      s += ", parent: \(parent.key)"
-    }
-    if let left = leftChild {
-      s += ", left = [" + left.debugDescription + "]"
-    }
-    if let right = rightChild {
-      s += ", right = [" + right.debugDescription + "]"
+    public var debugDescription: String {
+        var s = "key: \(key), payload: \(payload), height: \(height)"
+        if let parent = parent {
+            s += ", parent: \(parent.key)"
+        }
+        if let left = leftChild {
+            s += ", left = [" + left.debugDescription + "]"
+        }
+        if let right = rightChild {
+            s += ", right = [" + right.debugDescription + "]"
+        }
+        return s
     }
-    return s
-  }
 }
 
 extension AVLTree: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    return root?.debugDescription ?? "[]"
-  }
+    public var debugDescription: String {
+        return root?.debugDescription ?? "[]"
+    }
 }
 
 extension TreeNode: CustomStringConvertible {
-  public var description: String {
-    var s = ""
-    if let left = leftChild {
-      s += "(\(left.description)) <- "
-    }
-    s += "\(key)"
-    if let right = rightChild {
-      s += " -> (\(right.description))"
+    public var description: String {
+        var s = ""
+        if let left = leftChild {
+            s += "(\(left.description)) <- "
+        }
+        s += "\(key)"
+        if let right = rightChild {
+            s += " -> (\(right.description))"
+        }
+        return s
     }
-    return s
-  }
 }
 
 extension AVLTree: CustomStringConvertible {
-  public var description: String {
-    return root?.description ?? "[]"
-  }
+    public var description: String {
+        return root?.description ?? "[]"
+    }
 }

From fbfd2062cd53b51effc66b414121f1818e217a3d Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Fri, 6 Oct 2017 20:23:19 -0700
Subject: [PATCH 217/643] Added a note concerning brevity in CONTRIBUTING

---
 .github/CONTRIBUTING.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index 3bd5a1a91..e5d00c17b 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -4,7 +4,9 @@ Want to help out with the Swift Algorithm Club? Great! While we don't have stric
 
 **Readability**
 
-The `README` file is the cake, and the sample code is the cherry on top. Readablity is really important for us. A good contribution has succinct explanations supported by diagrams. Code is best introduced in chunks, weaved into the explanations where relevant. 
+Our repo is all about learning. The `README` file is the cake, and the sample code is the cherry on top. A good contribution has succinct explanations supported by diagrams. Code is best introduced in chunks, weaved into the explanations where relevant. 
+
+> When choosing between brievity and performance, err to the side of brievity as long as the time complexity of the particular implementation is the same. You can make a note afterwards suggesting a more performant way of doing things. 
 
 **API Design Guidelines**
 

From d32c5e7476cdc77d84c13d79cae37e3d63131c5b Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Tue, 21 Mar 2017 11:23:37 +0100
Subject: [PATCH 218/643] Deleted old version

---
 t.txt | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 t.txt

diff --git a/t.txt b/t.txt
new file mode 100644
index 000000000..d5f75df13
--- /dev/null
+++ b/t.txt
@@ -0,0 +1 @@
+wer

From a792197665757a73fea960d9ef739375c5dcfe65 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 15 Jul 2017 20:35:33 -0700
Subject: [PATCH 219/643] 3Sum and 4Sum
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Follow up 2Sum problem. How to solve 3Sum and 4Sum problem? What’s their relationships? Could we get some generic idea to solve this kind of problems? I give the explanation here.
---
 3Sum and 4Sum/3Sum.playground/Contents.swift  | 53 ++++++++++++++++
 .../3Sum.playground/contents.xcplayground     |  4 ++
 3Sum and 4Sum/4Sum.playground/Contents.swift  | 61 +++++++++++++++++++
 .../4Sum.playground/contents.xcplayground     |  4 ++
 3Sum and 4Sum/README.md                       | 48 +++++++++++++++
 .../contents.xcworkspacedata                  |  9 +++
 6 files changed, 179 insertions(+)
 create mode 100644 3Sum and 4Sum/3Sum.playground/Contents.swift
 create mode 100644 3Sum and 4Sum/3Sum.playground/contents.xcplayground
 create mode 100644 3Sum and 4Sum/4Sum.playground/Contents.swift
 create mode 100644 3Sum and 4Sum/4Sum.playground/contents.xcplayground
 create mode 100644 3Sum and 4Sum/README.md

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
new file mode 100644
index 000000000..7091ab789
--- /dev/null
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -0,0 +1,53 @@
+func ThreeSum(_ nums: [Int], targetSum: Int) -> [[Int]] {
+    var a = nums.sorted()
+    var ret: [[Int]] = []
+    
+    for i in 0..<a.count {
+        if i != 0 && a[i] == a[i-1] {
+            continue
+        }
+        
+        var j = i + 1
+        var k = nums.count - 1
+        
+        while j < k {
+            let sum = a[i] + a[j] + a[k]
+            
+            if sum == targetSum {
+                ret.append([a[i], a[j], a[k]])
+                j += 1
+            } else if sum < targetSum {
+                j += 1
+            } else {
+                k -= 1
+            }
+            
+            if sum == targetSum {
+                while j < k {
+                    var flag = false
+                    if j != 0 && a[j] == a[j-1] {
+                        j += 1
+                        flag = true
+                    }
+                    
+                    if (k != a.count - 1) && a[k] == a[k+1] {
+                        k -= 1
+                        flag = true
+                    }
+                    
+                    if (!flag) {
+                        break
+                    }
+                }
+            }
+        }
+    }
+    
+    return ret
+}
+
+// Answer: [[-1, 0, 1], [-1, -1, 2]]
+ThreeSum([-1, 0, 1, 2, -1, -4], targetSum: 0)
+
+// Answer: [[-1, -1, 1]]
+ThreeSum([-1, 1, 1, -1], targetSum: 1)
diff --git a/3Sum and 4Sum/3Sum.playground/contents.xcplayground b/3Sum and 4Sum/3Sum.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/3Sum and 4Sum/3Sum.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/3Sum and 4Sum/4Sum.playground/Contents.swift b/3Sum and 4Sum/4Sum.playground/Contents.swift
new file mode 100644
index 000000000..b86dd42f5
--- /dev/null
+++ b/3Sum and 4Sum/4Sum.playground/Contents.swift	
@@ -0,0 +1,61 @@
+func FourSum(_ nums: [Int], target: Int) -> [[Int]] {
+    let a = nums.sorted()
+    var ret: [[Int]] = []
+    
+    for i in 0..<nums.count {
+        if i != 0 && a[i] == a[i-1] {
+            continue
+        }
+        for j in i+1..<nums.count {
+            if j != i+1 && a[j] == a[j-1] {
+                continue
+            }
+            
+            var k = j + 1
+            var t = nums.count - 1
+            
+            while k < t {
+                let sum = a[i] + a[j] + a[k] + a[t]
+                
+                if sum == target {
+                    ret.append([a[i], a[j], a[k], a[t]])
+                    k += 1
+                } else if sum < target {
+                    k += 1
+                } else {
+                    t -= 1
+                }
+                
+                if sum == target {
+                    while k < t {
+                        var flag = true
+                        if k != j + 1 && a[k] == a[k-1] {
+                            k += 1
+                            flag = false
+                        }
+                        
+                        if t != nums.count - 1 && a[t] == a[t+1] {
+                            t -= 1
+                            flag = false
+                        }
+                        
+                        if flag {
+                            break
+                        }
+                    }
+                }
+            }
+        }
+    }
+    
+    return ret
+}
+
+/* Answer
+[
+    [-1,  0, 0, 1],
+    [-2, -1, 1, 2],
+    [-2,  0, 0, 2]
+]
+*/
+FourSum([1, 0, -1, 0, -2, 2], target: 0)
diff --git a/3Sum and 4Sum/4Sum.playground/contents.xcplayground b/3Sum and 4Sum/4Sum.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/3Sum and 4Sum/4Sum.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
new file mode 100644
index 000000000..e8ae4f2e1
--- /dev/null
+++ b/3Sum and 4Sum/README.md	
@@ -0,0 +1,48 @@
+# 3Sum and 4Sum
+
+## 3Sum
+Given an array S of n integers, are there elements a, b, c in S such that a + b + c = 0? 
+Find all unique triplets in the array which gives the sum of zero.
+
+**Note**: The solution set must not contain duplicate triplets.
+
+> For example, given array S = [-1, 0, 1, 2, -1, -4](),
+> A solution set is:
+> [
+> ]()>  [-1, 0, 1](),
+>  [-1, -1, 2]()
+> ]
+
+### Solution
+Like [2Sum][5], we can sort the array first, then use 2 pointers method to solve the problem. But here, we need 3 numbers, so we need add one more pointer. But how to play with 3 pointers?
+
+The key idea here is we split the array into 2 parts, if we have a pointer `i`, let’s assume we got `i` position already. What’ next? Actually, next is just a 2Sum problem right? We can just apply 2 pointers method in 2Sum. But what’s 2Sum’s target sum? Is it `target2Sum = target3Sum - nums[i]` ? That’s awesome! 
+
+How we figure out `i`? We can loop i from `0` to `nums.count - 1`.
+
+How we avoid duplicate triplets? Since the array has been sorted, we just need to check if `a[i] == a[i-1]`. Why? Because if `a[i] == a[i-1]`, it means that `a[i-1]` already covers all `a[i]` solutions, we should not do it, otherwise it will have duplicate answers. The same for `j` and `k` which runs for 2Sum.
+
+So, we successfully downgrade 3Sum to 2Sum problem with some tricks. Next, you will see how we downgrade 4Sum to 3Sum.
+
+## 4Sum
+Given an array S of n integers, are there elements a, b, c, and d in S such that a + b + c + d = target? Find all unique quadruplets in the array which gives the sum of target.
+
+**Note**: The solution set must not contain duplicate quadruplets.
+
+### Solution
+After 3Sum, you should have feeling actually we just need a same idea to downgrade it to 3Sum, and then 2Sum, and then solve it.
+
+How? I will leave it as a challenge for you to figure out first and see if you really master the idea behind this kind of problems.
+
+Feel free to check out the solution if you are blocked.
+
+## Where to go next?
+If it’s a KSum, and `K` is a big number, do we need to create `K` pointers and solve it?
+
+I will write another topic to present how we will solve this KSum problem with a generic way soon.
+
+
+
+
+
+[5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem
\ No newline at end of file
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 1e3c20224..2d9123248 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -103,6 +103,15 @@
       <FileRef
          location = "group:LRU Cache/Readme.md">
       </FileRef>
+      <FileRef
+         location = "group:3Sum and 4Sum/README.md">
+      </FileRef>
+      <FileRef
+         location = "group:3Sum and 4Sum/3Sum.playground">
+      </FileRef>
+      <FileRef
+         location = "group:3Sum and 4Sum/4Sum.playground">
+      </FileRef>
    </Group>
    <Group
       location = "group:Miller-Rabin Primality Test"

From 936bf5bfc115c79cff4bb667a4aa1820b88d2bb2 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 15 Jul 2017 20:35:33 -0700
Subject: [PATCH 220/643] 3Sum and 4Sum
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Follow up 2Sum problem. How to solve 3Sum and 4Sum problem? What’s their relationships? Could we get some generic idea to solve this kind of problems? I give the explanation here.
---
 3Sum and 4Sum/README.md | 10 +++-------
 1 file changed, 3 insertions(+), 7 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index e8ae4f2e1..caac3f37e 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -6,12 +6,8 @@ Find all unique triplets in the array which gives the sum of zero.
 
 **Note**: The solution set must not contain duplicate triplets.
 
-> For example, given array S = [-1, 0, 1, 2, -1, -4](),
-> A solution set is:
-> [
-> ]()>  [-1, 0, 1](),
->  [-1, -1, 2]()
-> ]
+> For example, given array S = [-1, 0, 1, 2, -1, -4],
+> A solution set is: [[-1, 0, 1], [-1, -1, 2]]
 
 ### Solution
 Like [2Sum][5], we can sort the array first, then use 2 pointers method to solve the problem. But here, we need 3 numbers, so we need add one more pointer. But how to play with 3 pointers?
@@ -45,4 +41,4 @@ I will write another topic to present how we will solve this KSum problem with a
 
 
 
-[5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem
\ No newline at end of file
+[5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem

From 00994544ebbf59a27876b3d8ec21c02ef1645e64 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 28 Sep 2017 01:47:37 -0700
Subject: [PATCH 221/643] Update README.md

Work in progress, not done yet!
---
 3Sum and 4Sum/README.md | 125 ++++++++++++++++++++++++++++++++++++----
 1 file changed, 114 insertions(+), 11 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index caac3f37e..3d311f650 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -1,24 +1,127 @@
 # 3Sum and 4Sum
 
+3Sum and 4Sum are extensions of a popular algorithm question, the [2Sum][5]. This article will talk about the problem and describe possible solutions.
+
 ## 3Sum
-Given an array S of n integers, are there elements a, b, c in S such that a + b + c = 0? 
-Find all unique triplets in the array which gives the sum of zero.
 
-**Note**: The solution set must not contain duplicate triplets.
+Given an array of integers, find all subsets of the array with 3 values where the 3 values sum up to a target number. 
 
-> For example, given array S = [-1, 0, 1, 2, -1, -4],
-> A solution set is: [[-1, 0, 1], [-1, -1, 2]]
+**Note**: The solution subsets must not contain duplicate triplets. (Each element in the array can only be used once)
 
-### Solution
-Like [2Sum][5], we can sort the array first, then use 2 pointers method to solve the problem. But here, we need 3 numbers, so we need add one more pointer. But how to play with 3 pointers?
+> For example, given the array [-1, 0, 1, 2, -1, -4], and the target **0**:
+> The solution set is: [[-1, 0, 1], [-1, -1, 2]] // The two **-1** values in the array are considered to be distinct
+
+### Example
+
+Consider the following array of integers, and a target sum of **0**:
+
+```
+[-1, 0, 1, 2, -1, -4]
+```
+
+#### 1. Sorting
+
+You'll first sort the array in ascending order:
+
+```
+[-4, -1, -1, 0, 1, 2]
+```
+
+#### 2. Two Sum's Methodology
+
+The 3Sum problem can be solved by augmenting the 2Sum solution, so let's begin by doing a quick explanation on how 2Sum handles the solution. 2Sum begins by comparing the left and right most values:
+
+```
+[-4, -1, -1, 0, 1, 2]
+  l                r
+```
+
+Your target sum is **0**. Given the current left and right values, you won't be able to make the target number. However, you've gained a valuable hint for your next step. 
+
+```
+-4 + 2 = -2 // too small!
+```
+
+The result of `l + r` gave you a value that is smaller than the target number. Thus, you have two options:
+
+1. Increase the lower number. 
+2. Increase the higher number.
+
+Because your array is sorted, you can quickly identify that you cannot pick option **2**, since the rightmost number is already the biggest number. Thus, you have no choice but to try for a different number from the left end of the array:
+
+```
+[-4, -1, -1, 0, 1, 2]
+      l            r
+```
+
+This time, you'll get the following result from summing `l` and `r`:
+
+```
+-1 + 2 = 1 // too big!
+```
+
+This time, the value is too big! I hope you see where it goes from here. Since the array is already sorted, you can only decrease the value on the right side in an attempt to balance things out. Hence, the next iteration of your algorithm will look like this:
+
+```
+[-4, -1, -1, 0, 1, 2]
+      l         r 
+```
+
+And then you've found a match :]
+
+```
+-1 + 1 = 0
+```
+
+#### Augmenting 2Sum
+
+Let's start from scratch and consider the same problem where you've sorted your input and you're target sum is **0**:
+
+```
+[-4, -1, -1, 0, 1, 2]
+  l                r
+```
+
+Your goal this time is the following equation:
+
+```
+l + r + m = 0
+```
+
+You have the values of `l` and `r`:
+
+```
+-4 + 2 + m = 0
+
+// in other words
+m = 4 - 2 = 2
+```
+
+For the current values of `l` and `r`, you need to find a value of **2** in the array to satisfy your target sum...
+
+#### Finding `m`
+
+```
+         m -- where?
+[-4, -1, -1, 0, 1, 2]
+  l                r 
+```
+
+There are slight optimizations you can do to find `m`, but to keep things simple, you'll just iterate through the array from `l` index to the `r` index. Once you find a value where `l + r + m = target`, you've found your first match! 
+
+#### Avoiding Duplicates
+
+// TODO: Work in progress
 
-The key idea here is we split the array into 2 parts, if we have a pointer `i`, let’s assume we got `i` position already. What’ next? Actually, next is just a 2Sum problem right? We can just apply 2 pointers method in 2Sum. But what’s 2Sum’s target sum? Is it `target2Sum = target3Sum - nums[i]` ? That’s awesome! 
+Avoiding duplicate values is fairly straightforward if you've understood everything so far. Let's consider a sample array that has a few duplicates:
 
-How we figure out `i`? We can loop i from `0` to `nums.count - 1`.
+```
+target = 0
 
-How we avoid duplicate triplets? Since the array has been sorted, we just need to check if `a[i] == a[i-1]`. Why? Because if `a[i] == a[i-1]`, it means that `a[i-1]` already covers all `a[i]` solutions, we should not do it, otherwise it will have duplicate answers. The same for `j` and `k` which runs for 2Sum.
+[-1, -1, -1, -1, 0, 1, 1, 1]
+```
 
-So, we successfully downgrade 3Sum to 2Sum problem with some tricks. Next, you will see how we downgrade 4Sum to 3Sum.
+One possible subset is `[-1, 0, 1]`, and in fact is the only subset for 3Sum. 
 
 ## 4Sum
 Given an array S of n integers, are there elements a, b, c, and d in S such that a + b + c + d = target? Find all unique quadruplets in the array which gives the sum of target.

From 5632cae5ed1d7255c799252ccc5a2fd8a0f1f741 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 30 Sep 2017 08:56:22 -0700
Subject: [PATCH 222/643] address comment

---
 3Sum and 4Sum/README.md                       | 41 +++++++++++++------
 .../contents.xcworkspacedata                  | 22 ++++++----
 t.txt                                         |  1 -
 3 files changed, 42 insertions(+), 22 deletions(-)
 delete mode 100644 t.txt

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 3d311f650..486c45c92 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -111,8 +111,6 @@ There are slight optimizations you can do to find `m`, but to keep things simple
 
 #### Avoiding Duplicates
 
-// TODO: Work in progress
-
 Avoiding duplicate values is fairly straightforward if you've understood everything so far. Let's consider a sample array that has a few duplicates:
 
 ```
@@ -123,25 +121,44 @@ target = 0
 
 One possible subset is `[-1, 0, 1]`, and in fact is the only subset for 3Sum. 
 
-## 4Sum
-Given an array S of n integers, are there elements a, b, c, and d in S such that a + b + c + d = target? Find all unique quadruplets in the array which gives the sum of target.
+The easiet way is using set. We can maintain a solution set, then we can check if the triplets is in the set or not to determine whether it's duplicate.
 
-**Note**: The solution set must not contain duplicate quadruplets.
+Set introduces space complexity. So we still want to avoid extra space using. Let's change an angle consider, we can loop the array first find `m` then next thing is to find `l` and `r`. 
 
-### Solution
-After 3Sum, you should have feeling actually we just need a same idea to downgrade it to 3Sum, and then 2Sum, and then solve it.
+For example
 
-How? I will leave it as a challenge for you to figure out first and see if you really master the idea behind this kind of problems.
+```
+​```
+[-1, 0, 1, 2, -1, -4] // unsorted
 
-Feel free to check out the solution if you are blocked.
+1)
+[-4, -1, -1, 0, 1, 2]
+      m   l        r
 
-## Where to go next?
-If it’s a KSum, and `K` is a big number, do we need to create `K` pointers and solve it?
+2)
+[-4, -1, -1, 0, 1, 2]
+          m  l     r
 
-I will write another topic to present how we will solve this KSum problem with a generic way soon.
+3)
+[-4, -1, -1, 0, 1, 2]
+      m      l     r
+​```
+
+We loop `m` in `0..<n`. We will do another inner loop at the same time, `l..r` loops in `i+1..<n`. 
+In 1), we will check if `a[i] == a[i-1]`? It's not in this case, then the problem is 2sum (`l..r`).
+In 2), Since `a[i] == a[i-1]`, it means `a[i-1]` covers `a[i]` case. Because case 3) contains case 2) solutions.
+```
 
 
 
+## 4Sum
+Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
+
+**Note**: The solution set must not contain duplicate quadruplets.
+
+### Solution
+After 3Sum, we already have the idea to change to a problem to a familiar problem we solved before. So, the idea here is straightforward. We just need to downgrade 4Sum to 3Sum. Then we can solve 4Sum.
 
+It's easy to think that we loop the array and get the first the element, then the rest array is 3Sum problem. Since the code is pretty simple, I will avoid duplicate introducation here.
 
 [5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 2d9123248..4cab8e2d4 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -38,6 +38,19 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "container:"
+      name = "3Sum and 4Sum">
+      <FileRef
+         location = "group:3Sum and 4Sum/README.md">
+      </FileRef>
+      <FileRef
+         location = "group:3Sum and 4Sum/3Sum.playground">
+      </FileRef>
+      <FileRef
+         location = "group:3Sum and 4Sum/4Sum.playground">
+      </FileRef>
+   </Group>
    <Group
       location = "container:"
       name = "Dijkstra">
@@ -103,15 +116,6 @@
       <FileRef
          location = "group:LRU Cache/Readme.md">
       </FileRef>
-      <FileRef
-         location = "group:3Sum and 4Sum/README.md">
-      </FileRef>
-      <FileRef
-         location = "group:3Sum and 4Sum/3Sum.playground">
-      </FileRef>
-      <FileRef
-         location = "group:3Sum and 4Sum/4Sum.playground">
-      </FileRef>
    </Group>
    <Group
       location = "group:Miller-Rabin Primality Test"
diff --git a/t.txt b/t.txt
deleted file mode 100644
index d5f75df13..000000000
--- a/t.txt
+++ /dev/null
@@ -1 +0,0 @@
-wer

From ca6bd9f1c0c851e0561443c9b5bffdb926f38929 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Fri, 6 Oct 2017 22:51:55 -0700
Subject: [PATCH 223/643] address comments

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 36 ++++++++++++--------
 1 file changed, 21 insertions(+), 15 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index 7091ab789..ec79ba787 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -2,36 +2,36 @@ func ThreeSum(_ nums: [Int], targetSum: Int) -> [[Int]] {
     var a = nums.sorted()
     var ret: [[Int]] = []
     
-    for i in 0..<a.count {
-        if i != 0 && a[i] == a[i-1] {
+    for m in 0..<a.count {
+        if m != 0 && a[m] == a[m-1] {
             continue
         }
         
-        var j = i + 1
-        var k = nums.count - 1
+        var l = m + 1
+        var r = nums.count - 1
         
-        while j < k {
-            let sum = a[i] + a[j] + a[k]
+        while l < r {
+            let sum = a[m] + a[l] + a[r]
             
             if sum == targetSum {
-                ret.append([a[i], a[j], a[k]])
-                j += 1
+                ret.append([a[m], a[l], a[r]])
+                l += 1
             } else if sum < targetSum {
-                j += 1
+                l += 1
             } else {
-                k -= 1
+                r -= 1
             }
             
             if sum == targetSum {
-                while j < k {
+                while l < r {
                     var flag = false
-                    if j != 0 && a[j] == a[j-1] {
-                        j += 1
+                    if l != 0 && a[l] == a[l-1] {
+                        l += 1
                         flag = true
                     }
                     
-                    if (k != a.count - 1) && a[k] == a[k+1] {
-                        k -= 1
+                    if (r != a.count - 1) && a[r] == a[r+1] {
+                        r -= 1
                         flag = true
                     }
                     
@@ -51,3 +51,9 @@ ThreeSum([-1, 0, 1, 2, -1, -4], targetSum: 0)
 
 // Answer: [[-1, -1, 1]]
 ThreeSum([-1, 1, 1, -1], targetSum: 1)
+
+// Answer: [[-1, -1, 2], [-1, 0, 1]]
+ThreeSum([-1, -1, -1, -1, 2, 1, -4, 0], targetSum: 0)
+
+// Answer: [[-1, -1, 2]]
+ThreeSum([-1, -1, -1, -1, -1, -1, 2], targetSum: 0)

From a47ddd704b70b6a4e7e93fedf8d4b1032c0f70a2 Mon Sep 17 00:00:00 2001
From: mnespor <mnespor@gmail.com>
Date: Sat, 7 Oct 2017 12:15:39 -0500
Subject: [PATCH 224/643] fix: convex hull no longer produces concave shapes

- removed a division by zero in the point-to-line distance formula
---
 .../Convex Hull.xcodeproj/project.pbxproj     | 146 +++++++++++++++++-
 Convex Hull/Convex Hull/View.swift            |  30 ++--
 .../Convex HullTests/Convex_HullTests.swift   |  34 ++++
 Convex Hull/Convex HullTests/Info.plist       |  22 +++
 4 files changed, 218 insertions(+), 14 deletions(-)
 create mode 100644 Convex Hull/Convex HullTests/Convex_HullTests.swift
 create mode 100644 Convex Hull/Convex HullTests/Info.plist

diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
index bb3189d64..4eec69f7d 100644
--- a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -7,13 +7,28 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
+		1CB614211F893A3800A14493 /* Convex_HullTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 1CB614201F893A3800A14493 /* Convex_HullTests.swift */; };
+		1CB614281F893ACA00A14493 /* View.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68CB1E599CF100161780 /* View.swift */; };
 		8E6D68BA1E59989400161780 /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68B91E59989400161780 /* AppDelegate.swift */; };
 		8E6D68C11E59989400161780 /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = 8E6D68C01E59989400161780 /* Assets.xcassets */; };
 		8E6D68C41E59989400161780 /* LaunchScreen.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = 8E6D68C21E59989400161780 /* LaunchScreen.storyboard */; };
 		8E6D68CC1E599CF100161780 /* View.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68CB1E599CF100161780 /* View.swift */; };
 /* End PBXBuildFile section */
 
+/* Begin PBXContainerItemProxy section */
+		1CB614231F893A3800A14493 /* PBXContainerItemProxy */ = {
+			isa = PBXContainerItemProxy;
+			containerPortal = 8E6D68AE1E59989400161780 /* Project object */;
+			proxyType = 1;
+			remoteGlobalIDString = 8E6D68B51E59989400161780;
+			remoteInfo = "Convex Hull";
+		};
+/* End PBXContainerItemProxy section */
+
 /* Begin PBXFileReference section */
+		1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Convex HullTests.xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
+		1CB614201F893A3800A14493 /* Convex_HullTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Convex_HullTests.swift; sourceTree = "<group>"; };
+		1CB614221F893A3800A14493 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 		8E6D68B61E59989400161780 /* Convex Hull.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = "Convex Hull.app"; sourceTree = BUILT_PRODUCTS_DIR; };
 		8E6D68B91E59989400161780 /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
 		8E6D68C01E59989400161780 /* Assets.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Assets.xcassets; sourceTree = "<group>"; };
@@ -23,6 +38,13 @@
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
+		1CB6141B1F893A3800A14493 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
 		8E6D68B31E59989400161780 /* Frameworks */ = {
 			isa = PBXFrameworksBuildPhase;
 			buildActionMask = 2147483647;
@@ -33,10 +55,20 @@
 /* End PBXFrameworksBuildPhase section */
 
 /* Begin PBXGroup section */
+		1CB6141F1F893A3800A14493 /* Convex HullTests */ = {
+			isa = PBXGroup;
+			children = (
+				1CB614201F893A3800A14493 /* Convex_HullTests.swift */,
+				1CB614221F893A3800A14493 /* Info.plist */,
+			);
+			path = "Convex HullTests";
+			sourceTree = "<group>";
+		};
 		8E6D68AD1E59989400161780 = {
 			isa = PBXGroup;
 			children = (
 				8E6D68B81E59989400161780 /* Convex Hull */,
+				1CB6141F1F893A3800A14493 /* Convex HullTests */,
 				8E6D68B71E59989400161780 /* Products */,
 			);
 			sourceTree = "<group>";
@@ -45,6 +77,7 @@
 			isa = PBXGroup;
 			children = (
 				8E6D68B61E59989400161780 /* Convex Hull.app */,
+				1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -64,6 +97,24 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
+		1CB6141D1F893A3800A14493 /* Convex HullTests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 1CB614271F893A3800A14493 /* Build configuration list for PBXNativeTarget "Convex HullTests" */;
+			buildPhases = (
+				1CB6141A1F893A3800A14493 /* Sources */,
+				1CB6141B1F893A3800A14493 /* Frameworks */,
+				1CB6141C1F893A3800A14493 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+				1CB614241F893A3800A14493 /* PBXTargetDependency */,
+			);
+			name = "Convex HullTests";
+			productName = "Convex HullTests";
+			productReference = 1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
 		8E6D68B51E59989400161780 /* Convex Hull */ = {
 			isa = PBXNativeTarget;
 			buildConfigurationList = 8E6D68C81E59989400161780 /* Build configuration list for PBXNativeTarget "Convex Hull" */;
@@ -87,10 +138,15 @@
 		8E6D68AE1E59989400161780 /* Project object */ = {
 			isa = PBXProject;
 			attributes = {
-				LastSwiftUpdateCheck = 0820;
+				LastSwiftUpdateCheck = 0900;
 				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = Workmoose;
 				TargetAttributes = {
+					1CB6141D1F893A3800A14493 = {
+						CreatedOnToolsVersion = 9.0;
+						ProvisioningStyle = Automatic;
+						TestTargetID = 8E6D68B51E59989400161780;
+					};
 					8E6D68B51E59989400161780 = {
 						CreatedOnToolsVersion = 8.2.1;
 						DevelopmentTeam = 7C4LVS3ZVC;
@@ -112,11 +168,19 @@
 			projectRoot = "";
 			targets = (
 				8E6D68B51E59989400161780 /* Convex Hull */,
+				1CB6141D1F893A3800A14493 /* Convex HullTests */,
 			);
 		};
 /* End PBXProject section */
 
 /* Begin PBXResourcesBuildPhase section */
+		1CB6141C1F893A3800A14493 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
 		8E6D68B41E59989400161780 /* Resources */ = {
 			isa = PBXResourcesBuildPhase;
 			buildActionMask = 2147483647;
@@ -129,6 +193,15 @@
 /* End PBXResourcesBuildPhase section */
 
 /* Begin PBXSourcesBuildPhase section */
+		1CB6141A1F893A3800A14493 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				1CB614281F893ACA00A14493 /* View.swift in Sources */,
+				1CB614211F893A3800A14493 /* Convex_HullTests.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
 		8E6D68B21E59989400161780 /* Sources */ = {
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
@@ -140,6 +213,14 @@
 		};
 /* End PBXSourcesBuildPhase section */
 
+/* Begin PBXTargetDependency section */
+		1CB614241F893A3800A14493 /* PBXTargetDependency */ = {
+			isa = PBXTargetDependency;
+			target = 8E6D68B51E59989400161780 /* Convex Hull */;
+			targetProxy = 1CB614231F893A3800A14493 /* PBXContainerItemProxy */;
+		};
+/* End PBXTargetDependency section */
+
 /* Begin PBXVariantGroup section */
 		8E6D68C21E59989400161780 /* LaunchScreen.storyboard */ = {
 			isa = PBXVariantGroup;
@@ -152,6 +233,60 @@
 /* End PBXVariantGroup section */
 
 /* Begin XCBuildConfiguration section */
+		1CB614251F893A3800A14493 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "$(TEST_HOST)";
+				CLANG_ANALYZER_NUMBER_OBJECT_CONVERSION = YES_AGGRESSIVE;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++14";
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
+				CLANG_WARN_COMMA = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_UNGUARDED_AVAILABILITY = YES_AGGRESSIVE;
+				CODE_SIGN_IDENTITY = "iPhone Developer";
+				CODE_SIGN_STYLE = Automatic;
+				GCC_C_LANGUAGE_STANDARD = gnu11;
+				INFOPLIST_FILE = "Convex HullTests/Info.plist";
+				IPHONEOS_DEPLOYMENT_TARGET = 11.0;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.mnespor.Convex-HullTests";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 4.0;
+				TARGETED_DEVICE_FAMILY = "1,2";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Convex Hull.app/Convex Hull";
+			};
+			name = Debug;
+		};
+		1CB614261F893A3800A14493 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				BUNDLE_LOADER = "$(TEST_HOST)";
+				CLANG_ANALYZER_NUMBER_OBJECT_CONVERSION = YES_AGGRESSIVE;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++14";
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
+				CLANG_WARN_COMMA = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_UNGUARDED_AVAILABILITY = YES_AGGRESSIVE;
+				CODE_SIGN_IDENTITY = "iPhone Developer";
+				CODE_SIGN_STYLE = Automatic;
+				GCC_C_LANGUAGE_STANDARD = gnu11;
+				INFOPLIST_FILE = "Convex HullTests/Info.plist";
+				IPHONEOS_DEPLOYMENT_TARGET = 11.0;
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "com.mnespor.Convex-HullTests";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 4.0;
+				TARGETED_DEVICE_FAMILY = "1,2";
+				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Convex Hull.app/Convex Hull";
+			};
+			name = Release;
+		};
 		8E6D68C61E59989400161780 /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
@@ -274,6 +409,15 @@
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
+		1CB614271F893A3800A14493 /* Build configuration list for PBXNativeTarget "Convex HullTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				1CB614251F893A3800A14493 /* Debug */,
+				1CB614261F893A3800A14493 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
 		8E6D68B11E59989400161780 /* Build configuration list for PBXProject "Convex Hull" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index 408689a13..a50cc247a 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -93,23 +93,11 @@ class View: UIView {
     }
 
     var pts = points
-
-    // calculate parameters of general line equation y = a * x + b
-    let a = (p1.y - p2.y) / (p1.x - p2.x)
-    let b = p1.y - a * p1.x
-
-    // calculate normal line's growth factor
-    let a1 = -1 / a
-
     var maxDist: CGFloat = -1
     var maxPoint: CGPoint = pts.first!
 
     for p in pts { // for every point check the distance from our line
-      let b1 = p.y - a1 * p.x // calculate offset to line equation for given point p
-      let x = -(b - b1)/(a - a1) // calculate x where the two lines intersect
-      let y = a * x + b // calculate y value of this intersect point
-
-      let dist = pow(x - p.x, 2) + pow(y - p.y, 2) // calculate distance squared between intersection point and point p
+      let dist = distance(from: p, to: (p1, p2))
       if dist > maxDist { // if distance is larger than current maxDist remember new point p
         maxDist = dist
         maxPoint = p
@@ -150,6 +138,22 @@ class View: UIView {
     findHull(s2, maxPoint, p2)
   }
 
+  func distance(from p: CGPoint, to line: (CGPoint, CGPoint)) -> CGFloat {
+    // If line.0 and line.1 are the same point, they don't define a line (and, besides,
+    // would cause division by zero in the distance formula). Return the distance between
+    // line.0 and point p instead.
+    if line.0 == line.1 {
+      return sqrt(pow(p.x - line.0.x, 2) + pow(p.y - line.0.y, 2))
+    }
+
+    // from Deza, Michel Marie; Deza, Elena (2013), Encyclopedia of Distances (2nd ed.), Springer, p. 86, ISBN 9783642309588
+    return abs((line.1.y - line.0.y) * p.x
+      - (line.1.x - line.0.x) * p.y
+      + line.1.x * line.0.y
+      - line.1.y * line.0.x)
+      / sqrt(pow(line.1.y - line.0.y, 2) + pow(line.1.x - line.0.x, 2))
+  }
+
   override func draw(_ rect: CGRect) {
 
     let context = UIGraphicsGetCurrentContext()
diff --git a/Convex Hull/Convex HullTests/Convex_HullTests.swift b/Convex Hull/Convex HullTests/Convex_HullTests.swift
new file mode 100644
index 000000000..40f6def07
--- /dev/null
+++ b/Convex Hull/Convex HullTests/Convex_HullTests.swift	
@@ -0,0 +1,34 @@
+//
+//  Convex_HullTests.swift
+//  Convex HullTests
+//
+//  Created by Matthew Nespor on 10/7/17.
+//  Copyright © 2017 Workmoose. All rights reserved.
+//
+
+import XCTest
+
+class Convex_HullTests: XCTestCase {
+  func testHorizontalInitialLine() {
+    let view = View()
+    let excludedPoint = CGPoint(x: 146, y: 284)
+    let includedPoints = [
+      CGPoint(x: 353, y: 22),
+      CGPoint(x: 22, y: 22),
+      CGPoint(x: 157, y: 447),
+    ]
+
+    view.points.append(contentsOf: includedPoints)
+    view.points.append(excludedPoint)
+    view.points.sort { (a: CGPoint, b: CGPoint) -> Bool in
+      return a.x < b.x
+    }
+
+    view.quickHull(points: view.points)
+
+    assert(includedPoints.filter({ view.convexHull.contains($0) }).count == 3,
+           "\(includedPoints) should have been included")
+    assert(!view.convexHull.contains(excludedPoint),
+           "\(excludedPoint) should have been excluded")
+    }
+}
diff --git a/Convex Hull/Convex HullTests/Info.plist b/Convex Hull/Convex HullTests/Info.plist
new file mode 100644
index 000000000..6c40a6cd0
--- /dev/null
+++ b/Convex Hull/Convex HullTests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>$(DEVELOPMENT_LANGUAGE)</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>

From dad84159ddd2af73945b8a2da85c987151042007 Mon Sep 17 00:00:00 2001
From: mnespor <mnespor@gmail.com>
Date: Sat, 7 Oct 2017 12:34:10 -0500
Subject: [PATCH 225/643] test: configure convex hull tests for travis ci

---
 .travis.yml                                   |  1 +
 .../Convex Hull.xcodeproj/project.pbxproj     | 78 +++++++++----------
 .../xcshareddata/xcschemes/Tests.xcscheme     | 58 ++++++++++++++
 .../{Convex HullTests => Tests}/Info.plist    |  0
 .../Tests.swift}                              |  8 +-
 5 files changed, 103 insertions(+), 42 deletions(-)
 create mode 100644 Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 rename Convex Hull/{Convex HullTests => Tests}/Info.plist (100%)
 rename Convex Hull/{Convex HullTests/Convex_HullTests.swift => Tests/Tests.swift} (87%)

diff --git a/.travis.yml b/.travis.yml
index 16f1934d1..977ff6774 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -20,6 +20,7 @@ script:
 - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests
 - xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
index 4eec69f7d..651a5bed3 100644
--- a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -7,8 +7,8 @@
 	objects = {
 
 /* Begin PBXBuildFile section */
-		1CB614211F893A3800A14493 /* Convex_HullTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 1CB614201F893A3800A14493 /* Convex_HullTests.swift */; };
-		1CB614281F893ACA00A14493 /* View.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68CB1E599CF100161780 /* View.swift */; };
+		1CB614301F89456C00A14493 /* Tests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 1CB6142F1F89456C00A14493 /* Tests.swift */; };
+		1CB614371F8945B300A14493 /* View.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68CB1E599CF100161780 /* View.swift */; };
 		8E6D68BA1E59989400161780 /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8E6D68B91E59989400161780 /* AppDelegate.swift */; };
 		8E6D68C11E59989400161780 /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = 8E6D68C01E59989400161780 /* Assets.xcassets */; };
 		8E6D68C41E59989400161780 /* LaunchScreen.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = 8E6D68C21E59989400161780 /* LaunchScreen.storyboard */; };
@@ -16,7 +16,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXContainerItemProxy section */
-		1CB614231F893A3800A14493 /* PBXContainerItemProxy */ = {
+		1CB614321F89456C00A14493 /* PBXContainerItemProxy */ = {
 			isa = PBXContainerItemProxy;
 			containerPortal = 8E6D68AE1E59989400161780 /* Project object */;
 			proxyType = 1;
@@ -26,9 +26,9 @@
 /* End PBXContainerItemProxy section */
 
 /* Begin PBXFileReference section */
-		1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Convex HullTests.xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
-		1CB614201F893A3800A14493 /* Convex_HullTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Convex_HullTests.swift; sourceTree = "<group>"; };
-		1CB614221F893A3800A14493 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		1CB6142D1F89456C00A14493 /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		1CB6142F1F89456C00A14493 /* Tests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Tests.swift; sourceTree = "<group>"; };
+		1CB614311F89456C00A14493 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 		8E6D68B61E59989400161780 /* Convex Hull.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = "Convex Hull.app"; sourceTree = BUILT_PRODUCTS_DIR; };
 		8E6D68B91E59989400161780 /* AppDelegate.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = AppDelegate.swift; sourceTree = "<group>"; };
 		8E6D68C01E59989400161780 /* Assets.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Assets.xcassets; sourceTree = "<group>"; };
@@ -38,7 +38,7 @@
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
-		1CB6141B1F893A3800A14493 /* Frameworks */ = {
+		1CB6142A1F89456C00A14493 /* Frameworks */ = {
 			isa = PBXFrameworksBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
@@ -55,20 +55,20 @@
 /* End PBXFrameworksBuildPhase section */
 
 /* Begin PBXGroup section */
-		1CB6141F1F893A3800A14493 /* Convex HullTests */ = {
+		1CB6142E1F89456C00A14493 /* Tests */ = {
 			isa = PBXGroup;
 			children = (
-				1CB614201F893A3800A14493 /* Convex_HullTests.swift */,
-				1CB614221F893A3800A14493 /* Info.plist */,
+				1CB6142F1F89456C00A14493 /* Tests.swift */,
+				1CB614311F89456C00A14493 /* Info.plist */,
 			);
-			path = "Convex HullTests";
+			path = Tests;
 			sourceTree = "<group>";
 		};
 		8E6D68AD1E59989400161780 = {
 			isa = PBXGroup;
 			children = (
 				8E6D68B81E59989400161780 /* Convex Hull */,
-				1CB6141F1F893A3800A14493 /* Convex HullTests */,
+				1CB6142E1F89456C00A14493 /* Tests */,
 				8E6D68B71E59989400161780 /* Products */,
 			);
 			sourceTree = "<group>";
@@ -77,7 +77,7 @@
 			isa = PBXGroup;
 			children = (
 				8E6D68B61E59989400161780 /* Convex Hull.app */,
-				1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */,
+				1CB6142D1F89456C00A14493 /* Tests.xctest */,
 			);
 			name = Products;
 			sourceTree = "<group>";
@@ -97,22 +97,22 @@
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
-		1CB6141D1F893A3800A14493 /* Convex HullTests */ = {
+		1CB6142C1F89456C00A14493 /* Tests */ = {
 			isa = PBXNativeTarget;
-			buildConfigurationList = 1CB614271F893A3800A14493 /* Build configuration list for PBXNativeTarget "Convex HullTests" */;
+			buildConfigurationList = 1CB614341F89456C00A14493 /* Build configuration list for PBXNativeTarget "Tests" */;
 			buildPhases = (
-				1CB6141A1F893A3800A14493 /* Sources */,
-				1CB6141B1F893A3800A14493 /* Frameworks */,
-				1CB6141C1F893A3800A14493 /* Resources */,
+				1CB614291F89456C00A14493 /* Sources */,
+				1CB6142A1F89456C00A14493 /* Frameworks */,
+				1CB6142B1F89456C00A14493 /* Resources */,
 			);
 			buildRules = (
 			);
 			dependencies = (
-				1CB614241F893A3800A14493 /* PBXTargetDependency */,
+				1CB614331F89456C00A14493 /* PBXTargetDependency */,
 			);
-			name = "Convex HullTests";
-			productName = "Convex HullTests";
-			productReference = 1CB6141E1F893A3800A14493 /* Convex HullTests.xctest */;
+			name = Tests;
+			productName = Tests;
+			productReference = 1CB6142D1F89456C00A14493 /* Tests.xctest */;
 			productType = "com.apple.product-type.bundle.unit-test";
 		};
 		8E6D68B51E59989400161780 /* Convex Hull */ = {
@@ -142,7 +142,7 @@
 				LastUpgradeCheck = 0820;
 				ORGANIZATIONNAME = Workmoose;
 				TargetAttributes = {
-					1CB6141D1F893A3800A14493 = {
+					1CB6142C1F89456C00A14493 = {
 						CreatedOnToolsVersion = 9.0;
 						ProvisioningStyle = Automatic;
 						TestTargetID = 8E6D68B51E59989400161780;
@@ -168,13 +168,13 @@
 			projectRoot = "";
 			targets = (
 				8E6D68B51E59989400161780 /* Convex Hull */,
-				1CB6141D1F893A3800A14493 /* Convex HullTests */,
+				1CB6142C1F89456C00A14493 /* Tests */,
 			);
 		};
 /* End PBXProject section */
 
 /* Begin PBXResourcesBuildPhase section */
-		1CB6141C1F893A3800A14493 /* Resources */ = {
+		1CB6142B1F89456C00A14493 /* Resources */ = {
 			isa = PBXResourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
@@ -193,12 +193,12 @@
 /* End PBXResourcesBuildPhase section */
 
 /* Begin PBXSourcesBuildPhase section */
-		1CB6141A1F893A3800A14493 /* Sources */ = {
+		1CB614291F89456C00A14493 /* Sources */ = {
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				1CB614281F893ACA00A14493 /* View.swift in Sources */,
-				1CB614211F893A3800A14493 /* Convex_HullTests.swift in Sources */,
+				1CB614371F8945B300A14493 /* View.swift in Sources */,
+				1CB614301F89456C00A14493 /* Tests.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
@@ -214,10 +214,10 @@
 /* End PBXSourcesBuildPhase section */
 
 /* Begin PBXTargetDependency section */
-		1CB614241F893A3800A14493 /* PBXTargetDependency */ = {
+		1CB614331F89456C00A14493 /* PBXTargetDependency */ = {
 			isa = PBXTargetDependency;
 			target = 8E6D68B51E59989400161780 /* Convex Hull */;
-			targetProxy = 1CB614231F893A3800A14493 /* PBXContainerItemProxy */;
+			targetProxy = 1CB614321F89456C00A14493 /* PBXContainerItemProxy */;
 		};
 /* End PBXTargetDependency section */
 
@@ -233,7 +233,7 @@
 /* End PBXVariantGroup section */
 
 /* Begin XCBuildConfiguration section */
-		1CB614251F893A3800A14493 /* Debug */ = {
+		1CB614351F89456C00A14493 /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				BUNDLE_LOADER = "$(TEST_HOST)";
@@ -249,10 +249,10 @@
 				CODE_SIGN_IDENTITY = "iPhone Developer";
 				CODE_SIGN_STYLE = Automatic;
 				GCC_C_LANGUAGE_STANDARD = gnu11;
-				INFOPLIST_FILE = "Convex HullTests/Info.plist";
+				INFOPLIST_FILE = Tests/Info.plist;
 				IPHONEOS_DEPLOYMENT_TARGET = 11.0;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = "com.mnespor.Convex-HullTests";
+				PRODUCT_BUNDLE_IDENTIFIER = com.mnespor.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_VERSION = 4.0;
 				TARGETED_DEVICE_FAMILY = "1,2";
@@ -260,7 +260,7 @@
 			};
 			name = Debug;
 		};
-		1CB614261F893A3800A14493 /* Release */ = {
+		1CB614361F89456C00A14493 /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				BUNDLE_LOADER = "$(TEST_HOST)";
@@ -276,10 +276,10 @@
 				CODE_SIGN_IDENTITY = "iPhone Developer";
 				CODE_SIGN_STYLE = Automatic;
 				GCC_C_LANGUAGE_STANDARD = gnu11;
-				INFOPLIST_FILE = "Convex HullTests/Info.plist";
+				INFOPLIST_FILE = Tests/Info.plist;
 				IPHONEOS_DEPLOYMENT_TARGET = 11.0;
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
-				PRODUCT_BUNDLE_IDENTIFIER = "com.mnespor.Convex-HullTests";
+				PRODUCT_BUNDLE_IDENTIFIER = com.mnespor.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_VERSION = 4.0;
 				TARGETED_DEVICE_FAMILY = "1,2";
@@ -409,11 +409,11 @@
 /* End XCBuildConfiguration section */
 
 /* Begin XCConfigurationList section */
-		1CB614271F893A3800A14493 /* Build configuration list for PBXNativeTarget "Convex HullTests" */ = {
+		1CB614341F89456C00A14493 /* Build configuration list for PBXNativeTarget "Tests" */ = {
 			isa = XCConfigurationList;
 			buildConfigurations = (
-				1CB614251F893A3800A14493 /* Debug */,
-				1CB614261F893A3800A14493 /* Release */,
+				1CB614351F89456C00A14493 /* Debug */,
+				1CB614361F89456C00A14493 /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
 			defaultConfigurationName = Release;
diff --git a/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..1f93a0c4f
--- /dev/null
+++ b/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,58 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0900"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "1CB6142C1F89456C00A14493"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Convex Hull.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Convex Hull/Convex HullTests/Info.plist b/Convex Hull/Tests/Info.plist
similarity index 100%
rename from Convex Hull/Convex HullTests/Info.plist
rename to Convex Hull/Tests/Info.plist
diff --git a/Convex Hull/Convex HullTests/Convex_HullTests.swift b/Convex Hull/Tests/Tests.swift
similarity index 87%
rename from Convex Hull/Convex HullTests/Convex_HullTests.swift
rename to Convex Hull/Tests/Tests.swift
index 40f6def07..411424479 100644
--- a/Convex Hull/Convex HullTests/Convex_HullTests.swift	
+++ b/Convex Hull/Tests/Tests.swift	
@@ -1,6 +1,6 @@
 //
-//  Convex_HullTests.swift
-//  Convex HullTests
+//  Tests.swift
+//  Tests
 //
 //  Created by Matthew Nespor on 10/7/17.
 //  Copyright © 2017 Workmoose. All rights reserved.
@@ -8,7 +8,7 @@
 
 import XCTest
 
-class Convex_HullTests: XCTestCase {
+class Tests: XCTestCase {
   func testHorizontalInitialLine() {
     let view = View()
     let excludedPoint = CGPoint(x: 146, y: 284)
@@ -18,6 +18,8 @@ class Convex_HullTests: XCTestCase {
       CGPoint(x: 157, y: 447),
     ]
 
+    view.points = [CGPoint]()
+    view.convexHull = [CGPoint]()
     view.points.append(contentsOf: includedPoints)
     view.points.append(excludedPoint)
     view.points.sort { (a: CGPoint, b: CGPoint) -> Bool in

From a1d0e3fd3008d1c17c37aee32d3d8ab39bab669c Mon Sep 17 00:00:00 2001
From: mnespor <mnespor@gmail.com>
Date: Sat, 7 Oct 2017 12:48:13 -0500
Subject: [PATCH 226/643] edit Selection Sampling for clarity as described in
 #475

---
 .../SelectionSampling.playground/Contents.swift           | 8 ++++----
 Selection Sampling/SelectionSampling.swift                | 8 ++++----
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/Selection Sampling/SelectionSampling.playground/Contents.swift b/Selection Sampling/SelectionSampling.playground/Contents.swift
index f4aace0c7..7443db67c 100644
--- a/Selection Sampling/SelectionSampling.playground/Contents.swift	
+++ b/Selection Sampling/SelectionSampling.playground/Contents.swift	
@@ -32,19 +32,19 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
   var b = [T]()
 
   while selected < requested {
-    examined += 1
-
     // Calculate random variable 0.0 <= r < 1.0 (exclusive!).
     let r = Double(arc4random()) / 0x100000000
 
-    let leftToExamine = a.count - examined + 1
+    let leftToExamine = a.count - examined
     let leftToAdd = requested - selected
 
     // Decide whether to use the next record from the input.
     if Double(leftToExamine) * r < Double(leftToAdd) {
       selected += 1
-      b.append(a[examined - 1])
+      b.append(a[examined])
     }
+
+    examined += 1
   }
   return b
 }
diff --git a/Selection Sampling/SelectionSampling.swift b/Selection Sampling/SelectionSampling.swift
index 1e6257908..52aa5988b 100644
--- a/Selection Sampling/SelectionSampling.swift	
+++ b/Selection Sampling/SelectionSampling.swift	
@@ -61,19 +61,19 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
   var b = [T]()
 
   while selected < requested {
-    examined += 1
-
     // Calculate random variable 0.0 <= r < 1.0 (exclusive!).
     let r = Double(arc4random()) / 0x100000000
 
-    let leftToExamine = a.count - examined + 1
+    let leftToExamine = a.count - examined
     let leftToAdd = requested - selected
 
     // Decide whether to use the next record from the input.
     if Double(leftToExamine) * r < Double(leftToAdd) {
       selected += 1
-      b.append(a[examined - 1])
+      b.append(a[examined])
     }
+
+    examined += 1
   }
   return b
 }

From 6d816c24b159b591ddbe11d9ececa1e1ac8b2c42 Mon Sep 17 00:00:00 2001
From: mnespor <mnespor@gmail.com>
Date: Sat, 7 Oct 2017 14:08:34 -0500
Subject: [PATCH 227/643] specify simulator for convex hull tests on travis

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 977ff6774..d70eb74b6 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -20,7 +20,7 @@ script:
 - xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests
+- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests -destination 'platform=iOS Simulator,name=iPhone 7,OS=11.0'
 - xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests

From cc32ec58d921793b97d203bc60994b406ea91bb3 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 7 Oct 2017 13:29:39 -0700
Subject: [PATCH 228/643] Deleted the checkboxes in favour of using labels

---
 .github/ISSUE_TEMPLATE.md | 8 +-------
 1 file changed, 1 insertion(+), 7 deletions(-)

diff --git a/.github/ISSUE_TEMPLATE.md b/.github/ISSUE_TEMPLATE.md
index 416641261..5c72ed5a5 100644
--- a/.github/ISSUE_TEMPLATE.md
+++ b/.github/ISSUE_TEMPLATE.md
@@ -1,13 +1,7 @@
-### Category
-
-- [ ] Bug
-- [ ] Feature Request
-- [ ] Question
-
 ### Brief Intro
 
 <!-- Describe the issue briefly.-->
 
 ### More Details
 
-<!-- If necessary, start off with the code snippet. Put the code in between ``` to format them into code blocks.-->
\ No newline at end of file
+<!-- If necessary, start off with the code snippet. Put the code in between ``` to format them into code blocks.-->

From bed042cc2e8ceec0fa1ca1aa592038e050b3eea7 Mon Sep 17 00:00:00 2001
From: mnespor <mnespor@gmail.com>
Date: Sat, 7 Oct 2017 15:44:30 -0500
Subject: [PATCH 229/643] update Selection Sampling readme to match code

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

diff --git a/Selection Sampling/README.markdown b/Selection Sampling/README.markdown
index bf17d93bd..ff80791e1 100644
--- a/Selection Sampling/README.markdown	
+++ b/Selection Sampling/README.markdown	
@@ -89,17 +89,17 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
   var b = [T]()
   
   while selected < requested {                          // 1
-    examined += 1
-    
     let r = Double(arc4random()) / 0x100000000          // 2
     
-    let leftToExamine = a.count - examined + 1          // 3
+    let leftToExamine = a.count - examined              // 3
     let leftToAdd = requested - selected
 
     if Double(leftToExamine) * r < Double(leftToAdd) {  // 4
       selected += 1
-      b.append(a[examined - 1])
+      b.append(a[examined])
     }
+
+    examined += 1
   }
   return b
 }

From be2785025b67b813bd1afc3a7d6aeda87c816ca9 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 7 Oct 2017 16:25:16 -0700
Subject: [PATCH 230/643] Fixed a section header to emphasize 3Sum

---
 3Sum and 4Sum/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 486c45c92..129555061 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -73,7 +73,7 @@ And then you've found a match :]
 -1 + 1 = 0
 ```
 
-#### Augmenting 2Sum
+# Augmenting 2Sum
 
 Let's start from scratch and consider the same problem where you've sorted your input and you're target sum is **0**:
 

From 4567dd1e49d079b5761d8349cbef3966e8231f05 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 7 Oct 2017 16:25:47 -0700
Subject: [PATCH 231/643] Fixed a typo

---
 3Sum and 4Sum/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 129555061..a34d2f49e 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -73,7 +73,7 @@ And then you've found a match :]
 -1 + 1 = 0
 ```
 
-# Augmenting 2Sum
+# 3Sum
 
 Let's start from scratch and consider the same problem where you've sorted your input and you're target sum is **0**:
 

From d7ebac3d898e931719de3611fbcf410552fbd8fa Mon Sep 17 00:00:00 2001
From: Nishtha Bhatia <nbhatia329@gmail.com>
Date: Sun, 8 Oct 2017 09:52:50 +0530
Subject: [PATCH 232/643] Updated Big-O Notation.markdown

---
 Big-O Notation.markdown | 108 +++++++++++++++++++++++++++++++++++++++-
 1 file changed, 107 insertions(+), 1 deletion(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 746cba8a3..2bb0d77db 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -15,8 +15,114 @@ Big-O | Name | Description
 **O(n^2)** | quadratic | **Kinda slow.** If you have 100 items, this does 100^2 = 10,000 units of work. Doubling the number of items makes it four times slower (because 2 squared equals 4). Example: algorithms using nested loops, such as insertion sort.
 **O(n^3)** | cubic | **Poor performance.** If you have 100 items, this does 100^3 = 1,000,000 units of work. Doubling the input size makes it eight times slower. Example: matrix multiplication.
 **O(2^n)** | exponential | **Very poor performance.** You want to avoid these kinds of algorithms, but sometimes you have no choice. Adding just one bit to the input doubles the running time. Example: traveling salesperson problem.
-**O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.
+**O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.  
+  
 
+Some examples to better understand the Big(O) notation:
+
+**O(1)**
+
+  The most common example with O(1) complexity is accessing an array index.
+  
+  ```c++
+  int i = a[5];
+  ```
+    
+  Another example of O(1) is Pushing and Popping from Stack.
+  
+ 
+**O(log n)**
+
+  ```c++
+  for(int i=0; i<n; i *= 2){
+      cout<<i<<endl;  // instead of simply incrementing, 'i' is increased by 2 times itself in each run.
+  }
+  ```
+  Binary Search Algorithm is an example of O(log n) complexity.
+  
+  
+**O(n)**
+
+  ```c++
+  for(int i=0; i<n; i++){
+      cout<<a[i]<<endl;
+  } 
+  ```
+  
+  Array Traversal and Linear Search are examples of O(n) complexity.  
+  
+  
+**O(n log n)**
+
+  ```c++
+  for(int i = 0; i < n; i++) { //linear
+    for(int j = 1; j < n; j *= 2){ // log (n)
+        //do constant time stuff
+    }
+  }
+```
+  
+  Merge Sort and Heap Sort are examples of O(n log n) complexity.  
+  
+  
+**O(n^2)**
+
+  ```c++
+  for(int i = 0; i < n; i++) { 
+    for(int j = 1; j < n; j++){ 
+        //do constant time stuff
+    }
+  }  
+  ```
+  
+  Traversing a simple 2-D array and Bubble Sort are examples of O(n^2) complexity.
+  
+  
+**O(n^3)**
+
+  ```c++
+  for(int i = 0; i < n; i++) { 
+    for(int j = 1; j < n; j++){ 
+      for(int k = 1; k < n; k++){
+        //do constant time stuff
+      }
+    }
+  }  
+  ```  
+  
+**O(2^n)**
+
+  Algorithms with running time O(2^N) are often recursive algorithms that solve a problem of size N by recursively solving two smaller problems of size N-1.
+  The following example prints all the moves necessary to solve the famous "Towers of Hanoi" problem for N disks.
+
+  ```c++
+  void solve_hanoi(int N, string from, string to, string spare) {
+    if (N<1) {
+        return;
+    }
+    if (N>1) {
+        solve_hanoi(N-1, from, spare, to);
+    }
+    print "move from " + from + " to " + to;
+    if (N>1) {
+        solve_hanoi(N-1, spare, to, from);
+    }
+  } 
+  ```
+  
+  
+**O(n!)**
+
+  The most trivial example of function that takes O(n!) time is given below.
+
+  ```c++
+    void nFacFunc(int n) {
+      for(int i=0; i<n; i++) {
+        nFacFunc(n-1);
+      }
+    } 
+  ``` 
+  
 Often you don't need math to figure out what the Big-O of an algorithm is but you can simply use your intuition. If your code uses a single loop that looks at all **n** elements of your input, the algorithm is **O(n)**. If the code has two nested loops, it is **O(n^2)**. Three nested loops gives **O(n^3)**, and so on.
 
 Note that Big-O notation is an estimate and is only really useful for large values of **n**. For example, the worst-case running time for the [insertion sort](Insertion%20Sort/) algorithm is **O(n^2)**. In theory that is worse than the running time for [merge sort](Merge%20Sort/), which is **O(n log n)**. But for small amounts of data, insertion sort is actually faster, especially if the array is partially sorted already!

From d7589aa68e46d1bdc4402dce754fab5a5b654744 Mon Sep 17 00:00:00 2001
From: Nishtha Bhatia <nbhatia329@gmail.com>
Date: Sun, 8 Oct 2017 10:50:00 +0530
Subject: [PATCH 233/643] Replaces the code snippets with swift equivalents

---
 Big-O Notation.markdown | 104 +++++++++++++++++++++++-----------------
 1 file changed, 60 insertions(+), 44 deletions(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 2bb0d77db..6819e17de 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -24,8 +24,8 @@ Some examples to better understand the Big(O) notation:
 
   The most common example with O(1) complexity is accessing an array index.
   
-  ```c++
-  int i = a[5];
+  ```swift
+  let value = array[5]
   ```
     
   Another example of O(1) is Pushing and Popping from Stack.
@@ -33,20 +33,25 @@ Some examples to better understand the Big(O) notation:
  
 **O(log n)**
 
-  ```c++
-  for(int i=0; i<n; i *= 2){
-      cout<<i<<endl;  // instead of simply incrementing, 'i' is increased by 2 times itself in each run.
+  ```swift
+  var j = 1
+  while j < n {
+    // do constant time stuff
+    j *= 2
   }
-  ```
+  ```  
+  
+  Instead of simply incrementing, 'j' is increased by 2 times itself in each run.
+  
   Binary Search Algorithm is an example of O(log n) complexity.
   
   
 **O(n)**
 
-  ```c++
-  for(int i=0; i<n; i++){
-      cout<<a[i]<<endl;
-  } 
+  ```swift
+  for i in stride(from: 0, to: n, by: 1) {
+    print(array[i])
+  }
   ```
   
   Array Traversal and Linear Search are examples of O(n) complexity.  
@@ -54,25 +59,40 @@ Some examples to better understand the Big(O) notation:
   
 **O(n log n)**
 
-  ```c++
-  for(int i = 0; i < n; i++) { //linear
-    for(int j = 1; j < n; j *= 2){ // log (n)
-        //do constant time stuff
+  ```swift
+  for i in stride(from: 0, to: n, by: 1) {
+  var j = 1
+    while j < n {
+      j *= 2
+      // do constant time stuff
+    }
+  }
+  ```
+  
+  OR
+  
+  ```swift
+  for i in stride(from: 0, to: n, by: 1) {
+    func index(after i: Int) -> Int? { // multiplies `i` by 2 until `i` >= `n`
+      return i < n ? i * 2 : nil 
+    }
+    for j in sequence(first: 1, next: index(after:)) {
+      // do constant time stuff
     }
   }
-```
+  ```
   
   Merge Sort and Heap Sort are examples of O(n log n) complexity.  
   
   
 **O(n^2)**
 
-  ```c++
-  for(int i = 0; i < n; i++) { 
-    for(int j = 1; j < n; j++){ 
-        //do constant time stuff
+  ```swift
+  for i  in stride(from: 0, to: n, by: 1) {
+    for j in stride(from: 1, to: n, by: 1) {
+      // do constant time stuff
     }
-  }  
+  }
   ```
   
   Traversing a simple 2-D array and Bubble Sort are examples of O(n^2) complexity.
@@ -80,14 +100,14 @@ Some examples to better understand the Big(O) notation:
   
 **O(n^3)**
 
-  ```c++
-  for(int i = 0; i < n; i++) { 
-    for(int j = 1; j < n; j++){ 
-      for(int k = 1; k < n; k++){
-        //do constant time stuff
+  ```swift
+  for i in stride(from: 0, to: n, by: 1) {
+    for j in stride(from: 1, to: n, by: 1) {
+      for k in stride(from: 1, to: n, by: 1) {
+        // do constant time stuff
       }
     }
-  }  
+  }
   ```  
   
 **O(2^n)**
@@ -95,19 +115,15 @@ Some examples to better understand the Big(O) notation:
   Algorithms with running time O(2^N) are often recursive algorithms that solve a problem of size N by recursively solving two smaller problems of size N-1.
   The following example prints all the moves necessary to solve the famous "Towers of Hanoi" problem for N disks.
 
-  ```c++
-  void solve_hanoi(int N, string from, string to, string spare) {
-    if (N<1) {
-        return;
-    }
-    if (N>1) {
-        solve_hanoi(N-1, from, spare, to);
+  ```swift
+  func solveHanoi(N: Int, from: String, to: String, spare: String) {
+    guard n >= 1 else { return }
+    if N > 1 {
+      solveHanoi(N: N - 1, from: from, to: spare, spare: to)
+    } else {
+      solveHanoi(N: N-1, from: spare, to: to, spare: from)
     }
-    print "move from " + from + " to " + to;
-    if (N>1) {
-        solve_hanoi(N-1, spare, to, from);
-    }
-  } 
+  }
   ```
   
   
@@ -115,12 +131,12 @@ Some examples to better understand the Big(O) notation:
 
   The most trivial example of function that takes O(n!) time is given below.
 
-  ```c++
-    void nFacFunc(int n) {
-      for(int i=0; i<n; i++) {
-        nFacFunc(n-1);
-      }
-    } 
+  ```swift
+  func nFacFunc(n: Int) {
+    for i in stride(from: 0, to: n, by: 1) {
+      nFactFunc(n - 1)
+    }
+  }
   ``` 
   
 Often you don't need math to figure out what the Big-O of an algorithm is but you can simply use your intuition. If your code uses a single loop that looks at all **n** elements of your input, the algorithm is **O(n)**. If the code has two nested loops, it is **O(n^2)**. Three nested loops gives **O(n^3)**, and so on.

From 8ea6fb23654c44fc9d5f5accac9d091bf220a142 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 7 Oct 2017 22:40:10 -0700
Subject: [PATCH 234/643] Fixes grammar.

---
 Big-O Notation.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 6819e17de..acb9b0a36 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -28,7 +28,7 @@ Some examples to better understand the Big(O) notation:
   let value = array[5]
   ```
     
-  Another example of O(1) is Pushing and Popping from Stack.
+  Another example of O(1) is pushing and popping from Stack.
   
  
 **O(log n)**

From 6cfff2fa0b8cfcdf8bd8ed889423236340eaf951 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 7 Oct 2017 22:42:02 -0700
Subject: [PATCH 235/643] Grammar fixes.

---
 Big-O Notation.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index acb9b0a36..78b1808e6 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -18,7 +18,7 @@ Big-O | Name | Description
 **O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.  
   
 
-Some examples to better understand the Big(O) notation:
+Below are some examples for each category of performance:
 
 **O(1)**
 

From 69b7eeed4e29313e0e1b9e4af0b34ba620e0db0b Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 9 Oct 2017 09:50:41 -0300
Subject: [PATCH 236/643] Changed tabs width

changed it back to two spaces
---
 AVL Tree/AVLTree.swift | 748 ++++++++++++++++++++---------------------
 1 file changed, 374 insertions(+), 374 deletions(-)

diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index ddc8e7892..04763f03b 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -21,443 +21,443 @@
 // SOFTWARE.
 
 public class TreeNode<Key: Comparable, Payload> {
-    public typealias Node = TreeNode<Key, Payload>
+  public typealias Node = TreeNode<Key, Payload>
+  
+  var payload: Payload?   // Value held by the node
+  
+  fileprivate var key: Key    // Node's name
+  internal var leftChild: Node?
+  internal var rightChild: Node?
+  fileprivate var height: Int
+  weak fileprivate var parent: Node?
+  
+  public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
+    self.key = key
+    self.payload = payload
+    self.leftChild = leftChild
+    self.rightChild = rightChild
+    self.parent = parent
+    self.height = height
     
-    var payload: Payload?   // Value held by the node
-    
-    fileprivate var key: Key    // Node's name
-    internal var leftChild: Node?
-    internal var rightChild: Node?
-    fileprivate var height: Int
-    weak fileprivate var parent: Node?
-    
-    public init(key: Key, payload: Payload?, leftChild: Node?, rightChild: Node?, parent: Node?, height: Int) {
-        self.key = key
-        self.payload = payload
-        self.leftChild = leftChild
-        self.rightChild = rightChild
-        self.parent = parent
-        self.height = height
-        
-        self.leftChild?.parent = self
-        self.rightChild?.parent = self
-    }
-    
-    public convenience init(key: Key, payload: Payload?) {
-        self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil, height: 1)
-    }
-    
-    public convenience init(key: Key) {
-        self.init(key: key, payload: nil)
-    }
-    
-    var isRoot: Bool {
-        return parent == nil
-    }
-    
-    var isLeaf: Bool {
-        return rightChild == nil && leftChild == nil
-    }
-    
-    var isLeftChild: Bool {
-        return parent?.leftChild === self
-    }
-    
-    var isRightChild: Bool {
-        return parent?.rightChild === self
-    }
-    
-    var hasLeftChild: Bool {
-        return leftChild != nil
-    }
-    
-    var hasRightChild: Bool {
-        return rightChild != nil
-    }
-    
-    var hasAnyChild: Bool {
-        return leftChild != nil || rightChild != nil
-    }
-    
-    var hasBothChildren: Bool {
-        return leftChild != nil && rightChild != nil
-    }
+    self.leftChild?.parent = self
+    self.rightChild?.parent = self
+  }
+  
+  public convenience init(key: Key, payload: Payload?) {
+    self.init(key: key, payload: payload, leftChild: nil, rightChild: nil, parent: nil, height: 1)
+  }
+  
+  public convenience init(key: Key) {
+    self.init(key: key, payload: nil)
+  }
+  
+  var isRoot: Bool {
+    return parent == nil
+  }
+  
+  var isLeaf: Bool {
+    return rightChild == nil && leftChild == nil
+  }
+  
+  var isLeftChild: Bool {
+    return parent?.leftChild === self
+  }
+  
+  var isRightChild: Bool {
+    return parent?.rightChild === self
+  }
+  
+  var hasLeftChild: Bool {
+    return leftChild != nil
+  }
+  
+  var hasRightChild: Bool {
+    return rightChild != nil
+  }
+  
+  var hasAnyChild: Bool {
+    return leftChild != nil || rightChild != nil
+  }
+  
+  var hasBothChildren: Bool {
+    return leftChild != nil && rightChild != nil
+  }
 }
 
 // MARK: - The AVL tree
 
 open class AVLTree<Key: Comparable, Payload> {
-    public typealias Node = TreeNode<Key, Payload>
-    
-    fileprivate(set) var root: Node?
-    fileprivate(set) var size = 0
-    
-    public init() { }
+  public typealias Node = TreeNode<Key, Payload>
+  
+  fileprivate(set) var root: Node?
+  fileprivate(set) var size = 0
+  
+  public init() { }
 }
 
 // MARK: - Searching
 
 extension TreeNode {
-    public func minimum() -> TreeNode? {
-        return leftChild?.minimum() ?? self
-    }
-    
-    public func maximum() -> TreeNode? {
-        return rightChild?.maximum() ?? self
-    }
+  public func minimum() -> TreeNode? {
+    return leftChild?.minimum() ?? self
+  }
+  
+  public func maximum() -> TreeNode? {
+    return rightChild?.maximum() ?? self
+  }
 }
 
 extension AVLTree {
-    subscript(key: Key) -> Payload? {
-        get { return search(input: key) }
-        set { insert(key: key, payload: newValue) }
-    }
-    
-    public func search(input: Key) -> Payload? {
-        return search(key: input, node: root)?.payload
-    }
-    
-    fileprivate func search(key: Key, node: Node?) -> Node? {
-        if let node = node {
-            if key == node.key {
-                return node
-            } else if key < node.key {
-                return search(key: key, node: node.leftChild)
-            } else {
-                return search(key: key, node: node.rightChild)
-            }
-        }
-        return nil
-    }
+  subscript(key: Key) -> Payload? {
+    get { return search(input: key) }
+    set { insert(key: key, payload: newValue) }
+  }
+  
+  public func search(input: Key) -> Payload? {
+    return search(key: input, node: root)?.payload
+  }
+  
+  fileprivate func search(key: Key, node: Node?) -> Node? {
+    if let node = node {
+      if key == node.key {
+        return node
+      } else if key < node.key {
+        return search(key: key, node: node.leftChild)
+      } else {
+        return search(key: key, node: node.rightChild)
+      }
+    }
+    return nil
+  }
 }
 
 // MARK: - Inserting new items
 
 extension AVLTree {
-    public func insert(key: Key, payload: Payload? = nil) {
-        if let root = root {
-            insert(input: key, payload: payload, node: root)
-        } else {
-            root = Node(key: key, payload: payload)
-        }
-        size += 1
-    }
-    
-    private func insert(input: Key, payload: Payload?, node: Node) {
-        if input < node.key {
-            if let child = node.leftChild {
-                insert(input: input, payload: payload, node: child)
-            } else {
-                let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
-                node.leftChild = child
-                balance(node: child)
-            }
-        } else if input != node.key {
-            if let child = node.rightChild {
-                insert(input: input, payload: payload, node: child)
-            } else {
-                let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
-                node.rightChild = child
-                balance(node: child)
-            }
-        }
-    }
+  public func insert(key: Key, payload: Payload? = nil) {
+    if let root = root {
+      insert(input: key, payload: payload, node: root)
+    } else {
+      root = Node(key: key, payload: payload)
+    }
+    size += 1
+  }
+  
+  private func insert(input: Key, payload: Payload?, node: Node) {
+    if input < node.key {
+      if let child = node.leftChild {
+        insert(input: input, payload: payload, node: child)
+      } else {
+        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
+        node.leftChild = child
+        balance(node: child)
+      }
+    } else if input != node.key {
+      if let child = node.rightChild {
+        insert(input: input, payload: payload, node: child)
+      } else {
+        let child = Node(key: input, payload: payload, leftChild: nil, rightChild: nil, parent: node, height: 1)
+        node.rightChild = child
+        balance(node: child)
+      }
+    }
+  }
 }
 
 // MARK: - Balancing tree
 
 extension AVLTree {
-    fileprivate func updateHeightUpwards(node: Node?) {
-        if let node = node {
-            let lHeight = node.leftChild?.height ?? 0
-            let rHeight = node.rightChild?.height ?? 0
-            node.height = max(lHeight, rHeight) + 1
-            updateHeightUpwards(node: node.parent)
-        }
+  fileprivate func updateHeightUpwards(node: Node?) {
+    if let node = node {
+      let lHeight = node.leftChild?.height ?? 0
+      let rHeight = node.rightChild?.height ?? 0
+      node.height = max(lHeight, rHeight) + 1
+      updateHeightUpwards(node: node.parent)
+    }
+  }
+  
+  fileprivate func lrDifference(node: Node?) -> Int {
+    let lHeight = node?.leftChild?.height ?? 0
+    let rHeight = node?.rightChild?.height ?? 0
+    return lHeight - rHeight
+  }
+  
+  fileprivate func balance(node: Node?) {
+    guard let node = node else {
+      return
     }
     
-    fileprivate func lrDifference(node: Node?) -> Int {
-        let lHeight = node?.leftChild?.height ?? 0
-        let rHeight = node?.rightChild?.height ?? 0
-        return lHeight - rHeight
-    }
+    updateHeightUpwards(node: node.leftChild)
+    updateHeightUpwards(node: node.rightChild)
     
-    fileprivate func balance(node: Node?) {
-        guard let node = node else {
-            return
-        }
-        
-        updateHeightUpwards(node: node.leftChild)
-        updateHeightUpwards(node: node.rightChild)
-        
-        var nodes = [Node?](repeating: nil, count: 3)
-        var subtrees = [Node?](repeating: nil, count: 4)
-        let nodeParent = node.parent
-        
-        let lrFactor = lrDifference(node: node)
-        if lrFactor > 1 {
-            // left-left or left-right
-            if lrDifference(node: node.leftChild) > 0 {
-                // left-left
-                nodes[0] = node
-                nodes[2] = node.leftChild
-                nodes[1] = nodes[2]?.leftChild
-                
-                subtrees[0] = nodes[1]?.leftChild
-                subtrees[1] = nodes[1]?.rightChild
-                subtrees[2] = nodes[2]?.rightChild
-                subtrees[3] = nodes[0]?.rightChild
-            } else {
-                // left-right
-                nodes[0] = node
-                nodes[1] = node.leftChild
-                nodes[2] = nodes[1]?.rightChild
-                
-                subtrees[0] = nodes[1]?.leftChild
-                subtrees[1] = nodes[2]?.leftChild
-                subtrees[2] = nodes[2]?.rightChild
-                subtrees[3] = nodes[0]?.rightChild
-            }
-        } else if lrFactor < -1 {
-            // right-left or right-right
-            if lrDifference(node: node.rightChild) < 0 {
-                // right-right
-                nodes[1] = node
-                nodes[2] = node.rightChild
-                nodes[0] = nodes[2]?.rightChild
-                
-                subtrees[0] = nodes[1]?.leftChild
-                subtrees[1] = nodes[2]?.leftChild
-                subtrees[2] = nodes[0]?.leftChild
-                subtrees[3] = nodes[0]?.rightChild
-            } else {
-                // right-left
-                nodes[1] = node
-                nodes[0] = node.rightChild
-                nodes[2] = nodes[0]?.leftChild
-                
-                subtrees[0] = nodes[1]?.leftChild
-                subtrees[1] = nodes[2]?.leftChild
-                subtrees[2] = nodes[2]?.rightChild
-                subtrees[3] = nodes[0]?.rightChild
-            }
-        } else {
-            // Don't need to balance 'node', go for parent
-            balance(node: node.parent)
-            return
-        }
-        
-        // nodes[2] is always the head
-        
-        if node.isRoot {
-            root = nodes[2]
-            root?.parent = nil
-        } else if node.isLeftChild {
-            nodeParent?.leftChild = nodes[2]
-            nodes[2]?.parent = nodeParent
-        } else if node.isRightChild {
-            nodeParent?.rightChild = nodes[2]
-            nodes[2]?.parent = nodeParent
-        }
-        
-        nodes[2]?.leftChild = nodes[1]
-        nodes[1]?.parent = nodes[2]
-        nodes[2]?.rightChild = nodes[0]
-        nodes[0]?.parent = nodes[2]
+    var nodes = [Node?](repeating: nil, count: 3)
+    var subtrees = [Node?](repeating: nil, count: 4)
+    let nodeParent = node.parent
+    
+    let lrFactor = lrDifference(node: node)
+    if lrFactor > 1 {
+      // left-left or left-right
+      if lrDifference(node: node.leftChild) > 0 {
+        // left-left
+        nodes[0] = node
+        nodes[2] = node.leftChild
+        nodes[1] = nodes[2]?.leftChild
         
-        nodes[1]?.leftChild = subtrees[0]
-        subtrees[0]?.parent = nodes[1]
-        nodes[1]?.rightChild = subtrees[1]
-        subtrees[1]?.parent = nodes[1]
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[1]?.rightChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
+      } else {
+        // left-right
+        nodes[0] = node
+        nodes[1] = node.leftChild
+        nodes[2] = nodes[1]?.rightChild
         
-        nodes[0]?.leftChild = subtrees[2]
-        subtrees[2]?.parent = nodes[0]
-        nodes[0]?.rightChild = subtrees[3]
-        subtrees[3]?.parent = nodes[0]
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
+      }
+    } else if lrFactor < -1 {
+      // right-left or right-right
+      if lrDifference(node: node.rightChild) < 0 {
+        // right-right
+        nodes[1] = node
+        nodes[2] = node.rightChild
+        nodes[0] = nodes[2]?.rightChild
         
-        updateHeightUpwards(node: nodes[1])    // Update height from left
-        updateHeightUpwards(node: nodes[0])    // Update height from right
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[0]?.leftChild
+        subtrees[3] = nodes[0]?.rightChild
+      } else {
+        // right-left
+        nodes[1] = node
+        nodes[0] = node.rightChild
+        nodes[2] = nodes[0]?.leftChild
         
-        balance(node: nodes[2]?.parent)
-    }
-}
-
-// MARK: - Displaying tree
-
-extension AVLTree {
-    fileprivate func display(node: Node?, level: Int) {
-        if let node = node {
-            display(node: node.rightChild, level: level + 1)
-            print("")
-            if node.isRoot {
-                print("Root -> ", terminator: "")
-            }
-            for _ in 0..<level {
-                print("        ", terminator:  "")
-            }
-            print("(\(node.key):\(node.height))", terminator: "")
-            display(node: node.leftChild, level: level + 1)
-        }
+        subtrees[0] = nodes[1]?.leftChild
+        subtrees[1] = nodes[2]?.leftChild
+        subtrees[2] = nodes[2]?.rightChild
+        subtrees[3] = nodes[0]?.rightChild
+      }
+    } else {
+      // Don't need to balance 'node', go for parent
+      balance(node: node.parent)
+      return
     }
     
-    public func display(node: Node) {
-        display(node: node, level: 0)
-        print("")
-    }
+    // nodes[2] is always the head
     
-    public func inorder(node: Node?) -> String {
-        var output = ""
-        if let node = node {
-            output = "\(inorder(node: node.leftChild)) \(print("\(node.key) ")) \(inorder(node: node.rightChild))"
-        }
-        return output
+    if node.isRoot {
+      root = nodes[2]
+      root?.parent = nil
+    } else if node.isLeftChild {
+      nodeParent?.leftChild = nodes[2]
+      nodes[2]?.parent = nodeParent
+    } else if node.isRightChild {
+      nodeParent?.rightChild = nodes[2]
+      nodes[2]?.parent = nodeParent
     }
     
-    public func preorder(node: Node?) -> String {
-        var output = ""
-        if let node = node {
-            output = "\(preorder(node: node.leftChild)) \(print("\(node.key) ")) \(preorder(node: node.rightChild))"
-        }
-        return output
-    }
+    nodes[2]?.leftChild = nodes[1]
+    nodes[1]?.parent = nodes[2]
+    nodes[2]?.rightChild = nodes[0]
+    nodes[0]?.parent = nodes[2]
     
-    public func postorder(node: Node?) -> String {
-        var output = ""
-        if let node = node {
-            output = "\(postorder(node: node.leftChild)) \(print("\(node.key) ")) \(postorder(node: node.rightChild))"
-        }
-        return output
-    }
+    nodes[1]?.leftChild = subtrees[0]
+    subtrees[0]?.parent = nodes[1]
+    nodes[1]?.rightChild = subtrees[1]
+    subtrees[1]?.parent = nodes[1]
+    
+    nodes[0]?.leftChild = subtrees[2]
+    subtrees[2]?.parent = nodes[0]
+    nodes[0]?.rightChild = subtrees[3]
+    subtrees[3]?.parent = nodes[0]
+    
+    updateHeightUpwards(node: nodes[1])    // Update height from left
+    updateHeightUpwards(node: nodes[0])    // Update height from right
+    
+    balance(node: nodes[2]?.parent)
+  }
+}
+
+// MARK: - Displaying tree
+
+extension AVLTree {
+  fileprivate func display(node: Node?, level: Int) {
+    if let node = node {
+      display(node: node.rightChild, level: level + 1)
+      print("")
+      if node.isRoot {
+        print("Root -> ", terminator: "")
+      }
+      for _ in 0..<level {
+        print("        ", terminator:  "")
+      }
+      print("(\(node.key):\(node.height))", terminator: "")
+      display(node: node.leftChild, level: level + 1)
+    }
+  }
+  
+  public func display(node: Node) {
+    display(node: node, level: 0)
+    print("")
+  }
+  
+  public func inorder(node: Node?) -> String {
+    var output = ""
+    if let node = node {
+      output = "\(inorder(node: node.leftChild)) \(print("\(node.key) ")) \(inorder(node: node.rightChild))"
+    }
+    return output
+  }
+  
+  public func preorder(node: Node?) -> String {
+    var output = ""
+    if let node = node {
+      output = "\(preorder(node: node.leftChild)) \(print("\(node.key) ")) \(preorder(node: node.rightChild))"
+    }
+    return output
+  }
+  
+  public func postorder(node: Node?) -> String {
+    var output = ""
+    if let node = node {
+      output = "\(postorder(node: node.leftChild)) \(print("\(node.key) ")) \(postorder(node: node.rightChild))"
+    }
+    return output
+  }
 }
 
 // MARK: - Delete node
 
 extension AVLTree {
-    public func delete(key: Key) {
-        if size == 1 {
-            root = nil
-            size -= 1
-        } else if let node = search(key: key, node: root) {
-            delete(node: node)
-            size -= 1
+  public func delete(key: Key) {
+    if size == 1 {
+      root = nil
+      size -= 1
+    } else if let node = search(key: key, node: root) {
+      delete(node: node)
+      size -= 1
+    }
+  }
+  
+  private func delete(node: Node) {
+    if node.isLeaf {
+      // Just remove and balance up
+      if let parent = node.parent {
+        guard node.isLeftChild || node.isRightChild else {
+          // just in case
+          fatalError("Error: tree is invalid.")
         }
-    }
-    
-    private func delete(node: Node) {
-        if node.isLeaf {
-            // Just remove and balance up
-            if let parent = node.parent {
-                guard node.isLeftChild || node.isRightChild else {
-                    // just in case
-                    fatalError("Error: tree is invalid.")
-                }
-                
-                if node.isLeftChild {
-                    parent.leftChild = nil
-                } else if node.isRightChild {
-                    parent.rightChild = nil
-                }
-                
-                balance(node: parent)
-            } else {
-                // at root
-                root = nil
-            }
-        } else {
-            // Handle stem cases
-            if let replacement = node.leftChild?.maximum(), replacement !== node {
-                node.key = replacement.key
-                node.payload = replacement.payload
-                delete(node: replacement)
-            } else if let replacement = node.rightChild?.minimum(), replacement !== node {
-                node.key = replacement.key
-                node.payload = replacement.payload
-                delete(node: replacement)
-            }
+        
+        if node.isLeftChild {
+          parent.leftChild = nil
+        } else if node.isRightChild {
+          parent.rightChild = nil
         }
-    }
+        
+        balance(node: parent)
+      } else {
+        // at root
+        root = nil
+      }
+    } else {
+      // Handle stem cases
+      if let replacement = node.leftChild?.maximum(), replacement !== node {
+        node.key = replacement.key
+        node.payload = replacement.payload
+        delete(node: replacement)
+      } else if let replacement = node.rightChild?.minimum(), replacement !== node {
+        node.key = replacement.key
+        node.payload = replacement.payload
+        delete(node: replacement)
+      }
+    }
+  }
 }
 
 // MARK: - Advanced Stuff
 
 extension AVLTree {
-    public func doInOrder(node: Node?, _ completion: (Node) -> Void) {
-        if let node = node {
-            doInOrder(node: node.leftChild) { lnode in
-                completion(lnode)
-            }
-            completion(node)
-            doInOrder(node: node.rightChild) { rnode in
-                completion(rnode)
-            }
-        }
-    }
-    
-    public func doInPreOrder(node: Node?, _ completion: (Node) -> Void) {
-        if let node = node {
-            completion(node)
-            doInPreOrder(node: node.leftChild) { lnode in
-                completion(lnode)
-            }
-            doInPreOrder(node: node.rightChild) { rnode in
-                completion(rnode)
-            }
-        }
-    }
-    
-    public func doInPostOrder(node: Node?, _ completion: (Node) -> Void) {
-        if let node = node {
-            doInPostOrder(node: node.leftChild) { lnode in
-                completion(lnode)
-            }
-            doInPostOrder(node: node.rightChild) { rnode in
-                completion(rnode)
-            }
-            completion(node)
-        }
-    }
+  public func doInOrder(node: Node?, _ completion: (Node) -> Void) {
+    if let node = node {
+      doInOrder(node: node.leftChild) { lnode in
+        completion(lnode)
+      }
+      completion(node)
+      doInOrder(node: node.rightChild) { rnode in
+        completion(rnode)
+      }
+    }
+  }
+  
+  public func doInPreOrder(node: Node?, _ completion: (Node) -> Void) {
+    if let node = node {
+      completion(node)
+      doInPreOrder(node: node.leftChild) { lnode in
+        completion(lnode)
+      }
+      doInPreOrder(node: node.rightChild) { rnode in
+        completion(rnode)
+      }
+    }
+  }
+  
+  public func doInPostOrder(node: Node?, _ completion: (Node) -> Void) {
+    if let node = node {
+      doInPostOrder(node: node.leftChild) { lnode in
+        completion(lnode)
+      }
+      doInPostOrder(node: node.rightChild) { rnode in
+        completion(rnode)
+      }
+      completion(node)
+    }
+  }
 }
 
 // MARK: - Debugging
 
 extension TreeNode: CustomDebugStringConvertible {
-    public var debugDescription: String {
-        var s = "key: \(key), payload: \(payload), height: \(height)"
-        if let parent = parent {
-            s += ", parent: \(parent.key)"
-        }
-        if let left = leftChild {
-            s += ", left = [" + left.debugDescription + "]"
-        }
-        if let right = rightChild {
-            s += ", right = [" + right.debugDescription + "]"
-        }
-        return s
+  public var debugDescription: String {
+    var s = "key: \(key), payload: \(payload), height: \(height)"
+    if let parent = parent {
+      s += ", parent: \(parent.key)"
+    }
+    if let left = leftChild {
+      s += ", left = [" + left.debugDescription + "]"
     }
+    if let right = rightChild {
+      s += ", right = [" + right.debugDescription + "]"
+    }
+    return s
+  }
 }
 
 extension AVLTree: CustomDebugStringConvertible {
-    public var debugDescription: String {
-        return root?.debugDescription ?? "[]"
-    }
+  public var debugDescription: String {
+    return root?.debugDescription ?? "[]"
+  }
 }
 
 extension TreeNode: CustomStringConvertible {
-    public var description: String {
-        var s = ""
-        if let left = leftChild {
-            s += "(\(left.description)) <- "
-        }
-        s += "\(key)"
-        if let right = rightChild {
-            s += " -> (\(right.description))"
-        }
-        return s
+  public var description: String {
+    var s = ""
+    if let left = leftChild {
+      s += "(\(left.description)) <- "
+    }
+    s += "\(key)"
+    if let right = rightChild {
+      s += " -> (\(right.description))"
     }
+    return s
+  }
 }
 
 extension AVLTree: CustomStringConvertible {
-    public var description: String {
-        return root?.description ?? "[]"
-    }
+  public var description: String {
+    return root?.description ?? "[]"
+  }
 }

From 952a064d4acf96c452169e4d1c4634e895432db6 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 9 Oct 2017 10:38:10 -0300
Subject: [PATCH 237/643] further corrections

---
 .../Tests/DepthFirstSearchTests.swift         | 90 +++++++++----------
 1 file changed, 45 insertions(+), 45 deletions(-)

diff --git a/Depth-First Search/Tests/DepthFirstSearchTests.swift b/Depth-First Search/Tests/DepthFirstSearchTests.swift
index afff5f62f..abf1c19c6 100755
--- a/Depth-First Search/Tests/DepthFirstSearchTests.swift	
+++ b/Depth-First Search/Tests/DepthFirstSearchTests.swift	
@@ -9,7 +9,7 @@ class DepthFirstSearchTests: XCTestCase {
         #endif
     }
     func testExploringTree() {
-        let tree = Graph()
+        let tree = Digraph()
         
         let nodeA = tree.addNode("a")
         let nodeB = tree.addNode("b")
@@ -33,58 +33,58 @@ class DepthFirstSearchTests: XCTestCase {
         XCTAssertEqual(nodesExplored, ["a", "b", "d", "e", "h", "c", "f", "g"])
     }
     
-    func testExploringGraph() {
-        let graph = Graph()
+    func testExploringDigraph() {
+        let digraph = Digraph()
         
-        let nodeA = graph.addNode("a")
-        let nodeB = graph.addNode("b")
-        let nodeC = graph.addNode("c")
-        let nodeD = graph.addNode("d")
-        let nodeE = graph.addNode("e")
-        let nodeF = graph.addNode("f")
-        let nodeG = graph.addNode("g")
-        let nodeH = graph.addNode("h")
-        let nodeI = graph.addNode("i")
+        let nodeA = digraph.addNode("a")
+        let nodeB = digraph.addNode("b")
+        let nodeC = digraph.addNode("c")
+        let nodeD = digraph.addNode("d")
+        let nodeE = digraph.addNode("e")
+        let nodeF = digraph.addNode("f")
+        let nodeG = digraph.addNode("g")
+        let nodeH = digraph.addNode("h")
+        let nodeI = digraph.addNode("i")
         
-        graph.addEdge(nodeA, neighbor: nodeB)
-        graph.addEdge(nodeA, neighbor: nodeH)
-        graph.addEdge(nodeB, neighbor: nodeA)
-        graph.addEdge(nodeB, neighbor: nodeC)
-        graph.addEdge(nodeB, neighbor: nodeH)
-        graph.addEdge(nodeC, neighbor: nodeB)
-        graph.addEdge(nodeC, neighbor: nodeD)
-        graph.addEdge(nodeC, neighbor: nodeF)
-        graph.addEdge(nodeC, neighbor: nodeI)
-        graph.addEdge(nodeD, neighbor: nodeC)
-        graph.addEdge(nodeD, neighbor: nodeE)
-        graph.addEdge(nodeD, neighbor: nodeF)
-        graph.addEdge(nodeE, neighbor: nodeD)
-        graph.addEdge(nodeE, neighbor: nodeF)
-        graph.addEdge(nodeF, neighbor: nodeC)
-        graph.addEdge(nodeF, neighbor: nodeD)
-        graph.addEdge(nodeF, neighbor: nodeE)
-        graph.addEdge(nodeF, neighbor: nodeG)
-        graph.addEdge(nodeG, neighbor: nodeF)
-        graph.addEdge(nodeG, neighbor: nodeH)
-        graph.addEdge(nodeG, neighbor: nodeI)
-        graph.addEdge(nodeH, neighbor: nodeA)
-        graph.addEdge(nodeH, neighbor: nodeB)
-        graph.addEdge(nodeH, neighbor: nodeG)
-        graph.addEdge(nodeH, neighbor: nodeI)
-        graph.addEdge(nodeI, neighbor: nodeC)
-        graph.addEdge(nodeI, neighbor: nodeG)
-        graph.addEdge(nodeI, neighbor: nodeH)
+        digraph.addEdge(nodeA, neighbor: nodeB)
+        digraph.addEdge(nodeA, neighbor: nodeH)
+        digraph.addEdge(nodeB, neighbor: nodeA)
+        digraph.addEdge(nodeB, neighbor: nodeC)
+        digraph.addEdge(nodeB, neighbor: nodeH)
+        digraph.addEdge(nodeC, neighbor: nodeB)
+        digraph.addEdge(nodeC, neighbor: nodeD)
+        digraph.addEdge(nodeC, neighbor: nodeF)
+        digraph.addEdge(nodeC, neighbor: nodeI)
+        digraph.addEdge(nodeD, neighbor: nodeC)
+        digraph.addEdge(nodeD, neighbor: nodeE)
+        digraph.addEdge(nodeD, neighbor: nodeF)
+        digraph.addEdge(nodeE, neighbor: nodeD)
+        digraph.addEdge(nodeE, neighbor: nodeF)
+        digraph.addEdge(nodeF, neighbor: nodeC)
+        digraph.addEdge(nodeF, neighbor: nodeD)
+        digraph.addEdge(nodeF, neighbor: nodeE)
+        digraph.addEdge(nodeF, neighbor: nodeG)
+        digraph.addEdge(nodeG, neighbor: nodeF)
+        digraph.addEdge(nodeG, neighbor: nodeH)
+        digraph.addEdge(nodeG, neighbor: nodeI)
+        digraph.addEdge(nodeH, neighbor: nodeA)
+        digraph.addEdge(nodeH, neighbor: nodeB)
+        digraph.addEdge(nodeH, neighbor: nodeG)
+        digraph.addEdge(nodeH, neighbor: nodeI)
+        digraph.addEdge(nodeI, neighbor: nodeC)
+        digraph.addEdge(nodeI, neighbor: nodeG)
+        digraph.addEdge(nodeI, neighbor: nodeH)
         
-        let nodesExplored = depthFirstSearch(graph, source: nodeA)
+        let nodesExplored = depthFirstSearch(digraph, source: nodeA)
         
         XCTAssertEqual(nodesExplored, ["a", "b", "c", "d", "e", "f", "g", "h", "i"])
     }
     
-    func testExploringGraphWithASingleNode() {
-        let graph = Graph()
-        let node = graph.addNode("a")
+    func testExploringDigraphWithASingleNode() {
+        let digraph = Digraph()
+        let node = digraph.addNode("a")
         
-        let nodesExplored = depthFirstSearch(graph, source: node)
+        let nodesExplored = depthFirstSearch(digraph, source: node)
         
         XCTAssertEqual(nodesExplored, ["a"])
     }

From f71c10d104247d239a9d4fb238ed195e687f0eac Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Mon, 9 Oct 2017 17:30:42 +0200
Subject: [PATCH 238/643] create octree algorithm

---
 Octree/Octree.playground/Contents.swift       |  33 ++
 Octree/Octree.playground/Sources/Octree.swift | 372 ++++++++++++++++++
 .../Octree.playground/contents.xcplayground   |   4 +
 Octree/Octree.playground/timeline.xctimeline  |  16 +
 4 files changed, 425 insertions(+)
 create mode 100644 Octree/Octree.playground/Contents.swift
 create mode 100644 Octree/Octree.playground/Sources/Octree.swift
 create mode 100644 Octree/Octree.playground/contents.xcplayground
 create mode 100644 Octree/Octree.playground/timeline.xctimeline

diff --git a/Octree/Octree.playground/Contents.swift b/Octree/Octree.playground/Contents.swift
new file mode 100644
index 000000000..cdcd2df0f
--- /dev/null
+++ b/Octree/Octree.playground/Contents.swift
@@ -0,0 +1,33 @@
+//: Playground - noun: a place where people can play
+
+import UIKit
+import simd
+
+let boxMin = vector_double3(0, 2, 6)
+let boxMax = vector_double3(5, 10, 9)
+let box = Box(boxMin: boxMin, boxMax: boxMax)
+var octree = Octree<Int>(boundingBox: box, minimumCellSize: 5.0)
+var five = octree.add(5, at: vector_double3(3,4,8))
+octree.add(8, at: vector_double3(3,4,8.2))
+octree.add(10, at: vector_double3(3,4,8.2))
+octree.add(7, at: vector_double3(2,5,8))
+octree.add(2, at: vector_double3(1,6,7))
+
+var cont = octree.elements(at: vector_double3(3,4,8.2))
+octree.remove(8)
+octree.elements(at: vector_double3(3,4,8))
+
+let boxMin2 = vector_double3(1,3,7)
+let boxMax2 = vector_double3(4,9,8)
+let box2 = Box(boxMin: boxMin2, boxMax: boxMax2)
+box.isContained(in: box2)
+box.intersects(box2)
+
+let boxMin3 = vector_double3(3,8,8)
+let boxMax3 = vector_double3(10,12,20)
+let box3 = Box(boxMin: boxMin3, boxMax: boxMax3)
+box3.intersects(box3)
+
+octree.elements(in: box)
+octree.elements(in: box2)
+print(octree)
diff --git a/Octree/Octree.playground/Sources/Octree.swift b/Octree/Octree.playground/Sources/Octree.swift
new file mode 100644
index 000000000..72863fb7c
--- /dev/null
+++ b/Octree/Octree.playground/Sources/Octree.swift
@@ -0,0 +1,372 @@
+import Foundation
+import simd
+
+public struct Box: CustomStringConvertible {
+    public var boxMin: vector_double3
+    public var boxMax: vector_double3
+    
+    public init(boxMin: vector_double3, boxMax: vector_double3) {
+        self.boxMin = boxMin
+        self.boxMax = boxMax
+    }
+    
+    public var boxSize: vector_double3 {
+        return boxMax - boxMin
+    }
+    
+    var halfBoxSize: vector_double3 {
+        return boxSize/2
+    }
+    
+    var frontLeftTop: Box {
+        let boxMin = self.boxMin + vector_double3(0, halfBoxSize.y, halfBoxSize.z)
+        let boxMax = self.boxMax - vector_double3(halfBoxSize.x, 0, 0)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var frontLeftBottom: Box {
+        let boxMin = self.boxMin + vector_double3(0, 0, halfBoxSize.z)
+        let boxMax = self.boxMax - vector_double3(halfBoxSize.x, halfBoxSize.y, 0)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var frontRightTop: Box {
+        let boxMin = self.boxMin + vector_double3(halfBoxSize.x, halfBoxSize.y, halfBoxSize.z)
+        let boxMax = self.boxMax - vector_double3(0, 0, 0)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var frontRightBottom: Box {
+        let boxMin = self.boxMin + vector_double3(halfBoxSize.x, 0, halfBoxSize.z)
+        let boxMax = self.boxMax - vector_double3(0, halfBoxSize.y, 0)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var backLeftTop: Box {
+        let boxMin = self.boxMin + vector_double3(0, halfBoxSize.y, 0)
+        let boxMax = self.boxMax - vector_double3(halfBoxSize.x, 0, halfBoxSize.z)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var backLeftBottom: Box {
+        let boxMin = self.boxMin + vector_double3(0, 0, 0)
+        let boxMax = self.boxMax - vector_double3(halfBoxSize.x, halfBoxSize.y, halfBoxSize.z)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var backRightTop: Box {
+        let boxMin = self.boxMin + vector_double3(halfBoxSize.x, halfBoxSize.y, 0)
+        let boxMax = self.boxMax - vector_double3(0, 0, halfBoxSize.z)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    var backRightBottom: Box {
+        let boxMin = self.boxMin + vector_double3(halfBoxSize.x, 0, 0)
+        let boxMax = self.boxMax - vector_double3(0, halfBoxSize.y, halfBoxSize.z)
+        return Box(boxMin: boxMin, boxMax: boxMax)
+    }
+    
+    public func contains(_ point: vector_double3) -> Bool {
+        return (boxMin.x <= point.x && point.x <= boxMax.x) && (boxMin.y <= point.y && point.y <= boxMax.y) && (boxMin.z <= point.z && point.z <= boxMax.z)
+    }
+    
+    public func contains(_ box: Box) -> Bool {
+        return
+            self.boxMin.x <= box.boxMin.x &&
+                self.boxMin.y <= box.boxMin.y &&
+                self.boxMin.z <= box.boxMin.z &&
+                self.boxMax.x >= box.boxMax.x &&
+                self.boxMax.y >= box.boxMax.y &&
+                self.boxMax.z >= box.boxMax.z
+    }
+    
+    public func isContained(in box: Box) -> Bool {
+        return
+            self.boxMin.x >= box.boxMin.x &&
+                self.boxMin.y >= box.boxMin.y &&
+                self.boxMin.z >= box.boxMin.z &&
+                self.boxMax.x <= box.boxMax.x &&
+                self.boxMax.y <= box.boxMax.y &&
+                self.boxMax.z <= box.boxMax.z
+    }
+    
+    /* This intersect function does not handle all possibilities such as two beams
+     of different diameter crossing each other half way. But it does cover all cases
+     needed for an octree as the bounding box has to contain the given intersect box */
+    public func intersects(_ box: Box) -> Bool {
+        let corners = [
+            vector_double3(boxMin.x, boxMax.y, boxMax.z), //frontLeftTop
+            vector_double3(boxMin.x, boxMin.y, boxMax.z), //frontLeftBottom
+            vector_double3(boxMax.x, boxMax.y, boxMax.z), //frontRightTop
+            vector_double3(boxMax.x, boxMin.y, boxMax.z), //frontRightBottom
+            vector_double3(boxMin.x, boxMax.y, boxMin.z), //backLeftTop
+            vector_double3(boxMin.x, boxMin.y, boxMin.z), //backLeftBottom
+            vector_double3(boxMax.x, boxMax.y, boxMin.z), //backRightTop
+            vector_double3(boxMax.x, boxMin.y, boxMin.z)  //backRightBottom
+        ]
+        for corner in corners {
+            if box.contains(corner) {
+                return true
+            }
+        }
+        return false
+    }
+    
+    public var description: String {
+        return "Box from:\(boxMin) to:\(boxMax)"
+    }
+}
+
+public class OctreeNode<T: Equatable>: CustomStringConvertible {
+    let box: Box
+    var point: vector_double3!
+    var elements: [T]!
+    var type: NodeType = .leaf
+    
+    enum NodeType {
+        case leaf
+        case `internal`(children: Children)
+    }
+    
+    public var description: String {
+        switch type {
+        case .leaf:
+            return "leaf node with \(box) elements: \(elements)"
+        case .internal:
+            return "internal node with \(box)"
+        }
+    }
+    
+    var recursiveDescription: String {
+        return recursiveDescription(withTabCount: 0)
+    }
+    
+    private func recursiveDescription(withTabCount count: Int) -> String {
+        let indent = String(repeating: "\t", count: count)
+        var result = "\(indent)" + description + "\n"
+        switch type {
+        case .internal(let children):
+            for child in children {
+                result += child.recursiveDescription(withTabCount: count + 1)
+            }
+        default:
+            break
+        }
+        return result
+    }
+    
+    struct Children: Sequence {
+        let frontLeftTop: OctreeNode
+        let frontLeftBottom: OctreeNode
+        let frontRightTop: OctreeNode
+        let frontRightBottom: OctreeNode
+        let backLeftTop: OctreeNode
+        let backLeftBottom: OctreeNode
+        let backRightTop: OctreeNode
+        let backRightBottom: OctreeNode
+        
+        init(parentNode: OctreeNode) {
+            frontLeftTop = OctreeNode(box: parentNode.box.frontLeftTop)
+            frontLeftBottom = OctreeNode(box: parentNode.box.frontLeftBottom)
+            frontRightTop = OctreeNode(box: parentNode.box.frontRightTop)
+            frontRightBottom = OctreeNode(box: parentNode.box.frontRightBottom)
+            backLeftTop = OctreeNode(box: parentNode.box.backLeftTop)
+            backLeftBottom = OctreeNode(box: parentNode.box.backLeftBottom)
+            backRightTop = OctreeNode(box: parentNode.box.backRightTop)
+            backRightBottom = OctreeNode(box: parentNode.box.backRightBottom)
+        }
+        
+        struct ChildrenIterator: IteratorProtocol {
+            var index = 0
+            let children: Children
+            
+            init(children: Children) {
+                self.children = children
+            }
+            
+            mutating func next() -> OctreeNode? {
+                defer { index += 1 }
+                switch index {
+                case 0: return children.frontLeftTop
+                case 1: return children.frontLeftBottom
+                case 2: return children.frontRightTop
+                case 3: return children.frontRightBottom
+                case 4: return children.backLeftTop
+                case 5: return children.backLeftBottom
+                case 6: return children.backRightTop
+                case 7: return children.backRightBottom
+                default: return nil
+                }
+            }
+        }
+        
+        func makeIterator() -> ChildrenIterator {
+            return ChildrenIterator(children: self)
+        }
+    }
+    
+    init(box: Box) {
+        self.box = box
+    }
+    
+    @discardableResult
+    func add(_ element: T, at point: vector_double3) -> OctreeNode {
+        return tryAdd(element, at: point)!
+    }
+    
+    private func tryAdd(_ element: T, at point: vector_double3) -> OctreeNode? {
+        if !box.contains(point) {
+            return nil
+        }
+        
+        switch type {
+        case .internal(let children):
+            // pass the point to one of the children
+            for child in children {
+                if let child = child.tryAdd(element, at: point) {
+                    return child
+                }
+            }
+            
+            fatalError("box.contains evaluted to true, but none of the children added the point")
+        case .leaf:
+            if self.point != nil {
+                // leaf already has an asigned point
+                if self.point == point {
+                    self.elements.append(element)
+                    return self
+                } else {
+                    return subdivide(adding: element, at: point)
+                }
+            } else {
+                self.elements = [element]
+                self.point = point
+                return self
+            }
+        }
+    }
+    
+    func add(_ elements: [T], at point: vector_double3) {
+        for element in elements {
+            self.add(element, at: point)
+        }
+    }
+    
+    @discardableResult
+    func remove(_ element: T) -> Bool {
+        switch type {
+        case .leaf:
+            if let elements = self.elements {
+                // leaf contains one ore more elements
+                if let index = elements.index(of: element) {
+                    // leaf contains the element we want to remove
+                    self.elements.remove(at: index)
+                    // if elements is now empty remove it
+                    if self.elements.isEmpty {
+                        self.elements = nil
+                    }
+                    return true
+                }
+            }
+            return false
+        case .internal(let children):
+            for child in children  {
+                if child.remove(element) {
+                    return true
+                }
+            }
+            return false
+        }
+    }
+    
+    func elements(at point: vector_double3) -> [T]? {
+        switch type {
+        case .leaf:
+            if self.point == point {
+                return self.elements
+            }
+        case .internal(let children):
+            for child in children {
+                if child.box.contains(point) {
+                    return child.elements(at: point)
+                }
+            }
+        }
+        // tree does not contain given point
+        return nil
+    }
+    
+    func elements(in box: Box) -> [T]? {
+        var values: [T] = []
+        switch type {
+        case .leaf:
+            // check if leaf has an assigned point
+            if let point = self.point {
+                // check if point is inside given box
+                if box.contains(point) {
+                    values += elements ?? []
+                }
+            }
+        case .internal(let children):
+            for child in children {
+                if child.box.isContained(in: box) {
+                    // child is contained in box
+                    // add all children of child
+                    values += child.elements(in: child.box) ?? []
+                } else if child.box.contains(box) || child.box.intersects(box) {
+                    // child contains at least part of box
+                    values += child.elements(in: box) ?? []
+                }
+                // child does not contain any part of given box
+            }
+        }
+        if values.isEmpty { return nil }
+        return values
+    }
+    
+    private func subdivide(adding element: T, at point: vector_double3) -> OctreeNode? {
+        precondition(self.elements != nil, "Subdividing while leaf does not contain a element")
+        precondition(self.point != nil, "Subdividing while leaf does not contain a point")
+        switch type {
+        case .leaf:
+            type = .internal(children: Children(parentNode: self))
+            // add element previously contained in leaf to children
+            self.add(self.elements, at: self.point)
+            self.elements = nil
+            self.point = nil
+            // add new element to children
+            return self.add(element, at: point)
+        case .internal:
+            preconditionFailure("Calling subdivide on an internal node")
+        }
+    }
+}
+
+public class Octree<T: Equatable>: CustomStringConvertible {
+    var root: OctreeNode<T>
+    
+    public var description: String {
+        return "Octree\n" + root.recursiveDescription
+    }
+    
+    public init(boundingBox: Box, minimumCellSize: Double) {
+        root = OctreeNode<T>(box: boundingBox)
+    }
+    
+    @discardableResult
+    public func add(_ element: T, at point: vector_double3) -> OctreeNode<T> {
+        return root.add(element, at: point)
+    }
+    
+    @discardableResult
+    public func remove(_ element: T, using node: OctreeNode<T>) -> Bool {
+        return node.remove(element)
+    }
+    
+    @discardableResult
+    public func remove(_ element: T) -> Bool {
+        return root.remove(element)
+    }
+    
+    public func elements(at point: vector_double3) -> [T]? {
+        return root.elements(at: point)
+    }
+    
+    public func elements(in box: Box) -> [T]? {
+        precondition(root.box.contains(box), "box is outside of octree bounds")
+        return root.elements(in: box)
+    }
+}
diff --git a/Octree/Octree.playground/contents.xcplayground b/Octree/Octree.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Octree/Octree.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Octree/Octree.playground/timeline.xctimeline b/Octree/Octree.playground/timeline.xctimeline
new file mode 100644
index 000000000..783cc6694
--- /dev/null
+++ b/Octree/Octree.playground/timeline.xctimeline
@@ -0,0 +1,16 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "file:///Users/jaap/code/swift-algorithm-club/Octree/Octree.playground#CharacterRangeLen=17&amp;CharacterRangeLoc=968&amp;EndingColumnNumber=13&amp;EndingLineNumber=32&amp;StartingColumnNumber=22&amp;StartingLineNumber=31&amp;Timestamp=529255572.908338"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+      <LoggerValueHistoryTimelineItem
+         documentLocation = "file:///Users/jaap/code/swift-algorithm-club/Octree/Octree.playground#CharacterRangeLen=32&amp;CharacterRangeLoc=455&amp;EndingColumnNumber=0&amp;EndingLineNumber=14&amp;StartingColumnNumber=9&amp;StartingLineNumber=13&amp;Timestamp=529255572.908505"
+         selectedRepresentationIndex = "0"
+         shouldTrackSuperviewWidth = "NO">
+      </LoggerValueHistoryTimelineItem>
+   </TimelineItems>
+</Timeline>

From 33e5572b5f3891bb600724d32b8ec5079ffaeba6 Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Mon, 9 Oct 2017 17:42:54 +0200
Subject: [PATCH 239/643] add readme

---
 Octree/README.md | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 Octree/README.md

diff --git a/Octree/README.md b/Octree/README.md
new file mode 100644
index 000000000..12b8cff39
--- /dev/null
+++ b/Octree/README.md
@@ -0,0 +1,27 @@
+# OcTree
+
+An octree is a [tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Tree) in which each internal (not leaf) node has eight children. Often used for collision detection in games for example.
+
+### Problem
+
+Consider the following problem: your need to store a number of objects in 3D space (each at a certain location with `X`, `Y` and `Z` coordinates) and then you need to answer which objects lie in a certain 3D region. A naive solution would be to store the points inside an array and then iterate over the points and check each one individually. This solution runs in O(n) though.
+
+### A Better Approach
+
+Octrees are most commonly used to partition a three-dimensional space by recursively subdividing it into 8 regions. Let's see how we can use an Octree to store some values.
+
+Each node in the tree represents a box-like region. Leaf nodes store a single point in that region with an array of objects assigned to that point.
+
+Once an object within the same region (but at a different point) is added the leaf node turns into an internal node and 8 child nodes (leaves) are added to it. All points previously contained in the node are passed to its corresponding children and stored. Thus only leaves contain actual points and values.
+
+To find the points that lie in a given region we can now traverse the tree from top to bottom and collect the suitable points from nodes.
+
+Both adding a point and searching can still take up to O(n) in the worst case, since the tree isn't balanced in any way. However, on average it runs significantly faster (something comparable to O(log n)).
+
+### See also
+
+More info on [Wiki](https://en.wikipedia.org/wiki/Octree)
+Apple's implementation of [GKOctree](https://developer.apple.com/documentation/gameplaykit/gkoctree)
+
+*Written for Swift Algorithm Club by Jaap Wijnen*
+*Heavily inspired by Timur Galimov's Quadtree implementation and Apple's GKOctree implementation

From d7cc4b6a625427271ce8c744369e6eedbcab4c31 Mon Sep 17 00:00:00 2001
From: Paige Sun <paige.sun.dev@gmail.com>
Date: Mon, 9 Oct 2017 16:42:03 -0400
Subject: [PATCH 240/643] Simplify twoSum logic by using (n) instead of the
 (target - n) as the dictionary key.

---
 .../Solution 1/2Sum.playground/Contents.swift | 28 ++++++++++---------
 1 file changed, 15 insertions(+), 13 deletions(-)

diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 4b6db5d51..7ce0ba07d 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -4,21 +4,23 @@
 print("Hello, Swift 4!")
 #endif
 
-func twoSum(_ numbers: [Int], target: Int) -> (Int, Int)? {
-  var dict: [Int: Int] = [:]
-  
-  for (index, number) in numbers.enumerated() {
-    if let otherIndex = dict[number] {
-      return (index, otherIndex)
-    } else {
-      dict[target - number] = index
+func twoSum(_ nums: [Int], target: Int) -> (Int, Int)? {
+    var dict = [Int: Int]()
+    
+    for (currentIndex, n) in nums.enumerated() {
+        let complement = target - n
+        
+        if let complementIndex = dict[complement] {
+            return (complementIndex, currentIndex)
+        }
+        
+        dict[n] = currentIndex
     }
-  }
-  
-  return nil
+    
+    return nil
 }
 
-let numbers = [3, 2, 4]
+let numbers = [3, 2, 8, 4]
 let target = 6
 
-twoSum(numbers, target: target) // expected output: indices 2 and 1
+twoSum(numbers, target: target) // expected output: indices 1 and 3

From 5eb53e0479061402f35cd9bcf3a9ecab98183206 Mon Sep 17 00:00:00 2001
From: Paige Sun <paige.sun.dev@gmail.com>
Date: Mon, 9 Oct 2017 16:48:58 -0400
Subject: [PATCH 241/643] Update title, Xcode version. Minor refactor.

---
 .../Solution 1/2Sum.playground/Contents.swift            | 9 +++------
 .../Solution 1/2Sum.playground/contents.xcplayground     | 2 +-
 2 files changed, 4 insertions(+), 7 deletions(-)

diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 7ce0ba07d..e89e52c94 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -1,5 +1,5 @@
-//: Playground - noun: a place where people can play
-// Last checked with: Version 9.0 beta 4 (9M189t)
+//: Two Sum
+// Last checked with: Version 9.0 (9A235)
 #if swift(>=4.0)
 print("Hello, Swift 4!")
 #endif
@@ -20,7 +20,4 @@ func twoSum(_ nums: [Int], target: Int) -> (Int, Int)? {
     return nil
 }
 
-let numbers = [3, 2, 8, 4]
-let target = 6
-
-twoSum(numbers, target: target) // expected output: indices 1 and 3
+twoSum([3, 2, 8, 4], target: 6) // expected output: indices 1 and 3
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/contents.xcplayground b/Two-Sum Problem/Solution 1/2Sum.playground/contents.xcplayground
index 06828af92..3de2b51ba 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/contents.xcplayground	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' display-mode='rendered'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 38e284f12cd61a0b6ad87196778b005ab9cbb7fe Mon Sep 17 00:00:00 2001
From: Paige Sun <paige.sun.dev@gmail.com>
Date: Mon, 9 Oct 2017 17:55:55 -0400
Subject: [PATCH 242/643] =?UTF-8?q?Update=20twoSum=E2=80=99s=20README=20wi?=
 =?UTF-8?q?th=20a=20simpler=20dictionary.?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 Two-Sum Problem/README.markdown               | 70 ++++++++++++-------
 .../Solution 1/2Sum.playground/Contents.swift |  2 +-
 2 files changed, 44 insertions(+), 28 deletions(-)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index dacf5a40a..b2f126595 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -1,66 +1,82 @@
 # Two-Sum Problem
 
-You're given an array of numbers. Write an algorithm that checks if there are any two elements in the array that add up to a given number.
+Given an array of integers and an integer target, return the indices of two numbers that add up to the target.
 
 There are a variety of solutions to this problem (some better than others). The following solutions both run in **O(n)** time.
 
 # Solution 1
 
-This solution uses a dictionary to store differences between each element in the array and the sum that we're looking for. The dictionary also stores the indices of each element.
+This solution looks at one number at a time, storing each number in the dictionary. It uses the number as the key and the number's index in the array as the value.
 
-With this approach, each key in the dictionary corresponds to a new target value. If one of the successive numbers from the array is equal to one of the dictionary's keys, then we know there exist two numbers that sum.
+For each number n, we know the complementing number to sum up to the target is `target - n`. By looking up the complement in the dictionary, we'd know whether we've seen the complement before and what its index is.
 
 ```swift
-func twoSumProblem(_ numbers: [Int], target: Int) -> (Int, Int)? {
-  var dict: [Int: Int] = [:]
-  
-  for (index, number) in numbers.enumerated() {
-    if let otherIndex = dict[number] {
-      return (index, otherIndex)
-    } else {
-      dict[target - number] = index
+func twoSum(_ nums: [Int], target: Int) -> (Int, Int)? {
+    var dict = [Int: Int]()
+    
+    // For every number n,
+    for (currentIndex, n) in nums.enumerated() {
+        // Find the complement to n that would sum up to the target.
+        let complement = target - n
+        
+        // Check if the complement is in the dictionary.
+        if let complementIndex = dict[complement] {
+            return (complementIndex, currentIndex)
+        }
+        
+        // Store n and its index into the dictionary.
+        dict[n] = currentIndex
     }
-  }
-
-  return nil  // if empty array or no entries sum to target k
+    
+    return nil
 }
 ```
 
-The `twoSumProble` function takes two parameters: the `numbers` array and the target sum you're looking for. It returns the 2 indices with elements that sums up to the target, or `nil` if it can't be found.
+The `twoSum` function takes two parameters: the `numbers` array and the target sum. It returns the two indicies of the pair of elements that sums up to the target, or `nil` if they can't be found.
 
-Let's take a look at an example and run through the algorithm to see how it works. Given is the array:
+Let's run through the algorithm to see how it works. Given the array:
 
 ```swift
-[ 7, 2, 23, 8, -1, 0, 11, 6  ]
+[3, 2, 9, 8]
 ```
 
-Let's find out if there exist two entries whose sum is equal to 10.
+Let's find out if there exist two entries whose sum is 10.
 
 Initially, our dictionary is empty. We begin looping through each element:
 
-- **i = 0**: Is `7` in the dictionary? No. We add the difference between the `target` and the current number to the dictionary. The difference is `10 - 7 = 3`, so the dictionary key is `3`. The value for that key is the current index, `0`. The dictionary now looks like this:
+- **currentIndex = 0** | n = nums[0] = 3 | complement = 10 - 3 = 7
+
+Is the complement `7` in the dictionary? No, so we add `3` and its index `0` to the dictionary.
 
 ```swift
-[ 3: 0 ]
+[3: 0]
 ```
 
-- **i = 1:** Is `2` in the dictionary? No. Let's do as above and add the difference (`10 - 2 = 8`) and the array index (`1`). The dictionary is:
+- **currentIndex = 1** | n = 2 | complement = 10 - 2 = 8
+
+Is the complement `8` in the dictionary? No, so we add `2` and its index `1` to the dictionary.
 
 ```swift
-[ 3: 0, 8: 1 ]
+[3: 0, 2: 1]
 ```
 
-- **i = 2:** Is `23` in the dictionary? No. Again, we add it to the dictionary. The difference is `10 - 23 = -13` and the index is `2`:
+- **currentIndex = 2** | n = 9 | complement = 10 - 9 = 1
+
+Is the complement `1` in the dictionary? No, so we add `9` and its index `2` to the dictionary.:
 
 ```swift
-[ 3: 0, 8: 1, -13: 2 ]
+[3: 0, 2: 1, 9: 2]
 ```
 
-- **i = 3:** Is `8` in the dictionary? Yes! That means that we have found a pair of entries that sum to our target. Namely the current number `8` and `array[dict[8]]` because `dict[8] = 1`, `array[1] = 2`, and `8 + 2 = 10`. Therefore, we return the corresponding indices of these numbers. For `8` that is the current loop index, `3`. For `2` that is `dict[8]` or `1`. The tuple we return is `(1, 3)`.
+- **currentIndex = 3** | n = 8 | complement = 10 - 8 = 2
+
+Is the complement `2` in the dictionary? Yes! That means that we have found a pair of entries that sum to the target!
+
+Therefore, the `complementIndex = dict[2] = 1` and the `currentIndex = 3`. The tuple we return is `(1, 3)`.
 
-The given array actually has multiple solutions: `(1, 3)` and `(4, 6)`. However, only the first solution is returned.
+If the given array has multiple solutions, only the first solution is returned.
 
-The running time of this algorithm is **O(n)** because it potentially may need to look at all array elements. It also requires **O(n)** additional storage space for the dictionary.
+The running time of this algorithm is **O(n)** because it may look at every element in the array. It also requires **O(n)** additional storage space for the dictionary.
 
 # Solution 2
 
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index e89e52c94..26bfae449 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -20,4 +20,4 @@ func twoSum(_ nums: [Int], target: Int) -> (Int, Int)? {
     return nil
 }
 
-twoSum([3, 2, 8, 4], target: 6) // expected output: indices 1 and 3
+twoSum([3, 2, 9, 8], target: 10) // expected output: indices 1 and 3

From eca6517dc5dafd3d39901160d8ae9c3589652a87 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 9 Oct 2017 16:33:09 -0700
Subject: [PATCH 243/643] Added links to the topic on Lazy Propagation

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

diff --git a/Segment Tree/README.markdown b/Segment Tree/README.markdown
index 9897c9c3b..97d7f7d92 100644
--- a/Segment Tree/README.markdown	
+++ b/Segment Tree/README.markdown	
@@ -1,5 +1,7 @@
 # Segment Tree
 
+> For an example on lazy propagation, see this [article](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation).
+
 I'm pleased to present to you Segment Tree. It's actually one of my favorite data structures because it's very flexible and simple in realization.
 
 Let's suppose that you have an array **a** of some type and some associative function **f**. For example, the function can be sum, multiplication, min, max, [gcd](../GCD/), and so on.
@@ -199,6 +201,7 @@ See the playground for more examples of how to use the segment tree.
 
 ## See also
 
+[Lazy Propagation]((https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
 [Segment tree at PEGWiki](http://wcipeg.com/wiki/Segment_tree)
 
 *Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*

From cfb4f9bc05a6f7a8c50c42ae97bb116e5cd2ce4e Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 9 Oct 2017 16:33:28 -0700
Subject: [PATCH 244/643] Fixed formatting

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

diff --git a/Segment Tree/README.markdown b/Segment Tree/README.markdown
index 97d7f7d92..e3010b1fe 100644
--- a/Segment Tree/README.markdown	
+++ b/Segment Tree/README.markdown	
@@ -201,7 +201,7 @@ See the playground for more examples of how to use the segment tree.
 
 ## See also
 
-[Lazy Propagation]((https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
+[Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
 [Segment tree at PEGWiki](http://wcipeg.com/wiki/Segment_tree)
 
 *Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*

From cefb1c1ea2e9e998a5c12a95c789345e500a7a51 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 9 Oct 2017 16:34:25 -0700
Subject: [PATCH 245/643] Added a few extra words describing lazy propagation.

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

diff --git a/Segment Tree/README.markdown b/Segment Tree/README.markdown
index e3010b1fe..99ec85cd8 100644
--- a/Segment Tree/README.markdown	
+++ b/Segment Tree/README.markdown	
@@ -201,7 +201,8 @@ See the playground for more examples of how to use the segment tree.
 
 ## See also
 
-[Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
+[Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation) implementation and explanation.
+
 [Segment tree at PEGWiki](http://wcipeg.com/wiki/Segment_tree)
 
 *Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*

From 70bae5bee70aaea80dd5fe7d74824098f8107f4b Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 9 Oct 2017 16:35:33 -0700
Subject: [PATCH 246/643] Added lazy propagation to main README.

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

diff --git a/README.markdown b/README.markdown
index dd001f75a..fa3483657 100644
--- a/README.markdown
+++ b/README.markdown
@@ -156,6 +156,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Splay Tree](Splay%20Tree/). A self balancing binary search tree that enables fast retrieval of recently updated elements.
 - [Threaded Binary Tree](Threaded%20Binary%20Tree/). A binary tree that maintains a few extra variables for cheap and fast in-order traversals.
 - [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
+  - [Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation) 
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap

From 4d92bfc5fd05c72fc5e35f45c17dbadb637b9db1 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 01:36:00 -0700
Subject: [PATCH 247/643] Updates the avoiding duplicates section.

---
 3Sum and 4Sum/README.md | 82 ++++++++++++++++++++++-------------------
 1 file changed, 44 insertions(+), 38 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index a34d2f49e..f9a121fab 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -111,45 +111,51 @@ There are slight optimizations you can do to find `m`, but to keep things simple
 
 #### Avoiding Duplicates
 
-Avoiding duplicate values is fairly straightforward if you've understood everything so far. Let's consider a sample array that has a few duplicates:
-
-```
-target = 0
-
-[-1, -1, -1, -1, 0, 1, 1, 1]
-```
-
-One possible subset is `[-1, 0, 1]`, and in fact is the only subset for 3Sum. 
-
-The easiet way is using set. We can maintain a solution set, then we can check if the triplets is in the set or not to determine whether it's duplicate.
-
-Set introduces space complexity. So we still want to avoid extra space using. Let's change an angle consider, we can loop the array first find `m` then next thing is to find `l` and `r`. 
-
-For example
-
+Since you pre-sort the array, duplicates will be adjacent to each other. You just need to skip over duplicates by comparing adjacent values:
+
+```
+extension Collection where Element: Equatable {
+  
+  /// Returns next index with unique value. Works only on sorted arrays.
+  ///
+  /// - Parameter index: The current `Int` index.
+  /// - Returns: The new `Int` index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
+  func uniqueIndex(after index: Index) -> Index? {
+    guard index < endIndex else { return nil }
+    var index = index
+    var nextIndex = self.index(after: index)
+    while nextIndex < endIndex && self[index] == self[nextIndex] {
+      formIndex(after: &index)
+      formIndex(after: &nextIndex)
+    }
+    
+    if nextIndex == endIndex {
+      return nil
+    } else {
+      return nextIndex
+    }
+  }
+}
+```
+
+A similar implementation is used to get the unique index *before* a given index:
+
+```
+extension BidirectionalCollection where Element: Equatable {
+  
+  /// Returns next index with unique value. Works only on sorted arrays.
+  ///
+  /// - Parameter index: The current `Int` index.
+  /// - Returns: The new `Int` index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
+  func uniqueIndex(before index: Index) -> Index? {
+    return indices[..<index].reversed().first { index -> Bool in
+      let nextIndex = self.index(after: index)
+      guard nextIndex >= startIndex && self[index] != self[nextIndex] else { return false }
+      return true
+    }
+  }
+}
 ```
-​```
-[-1, 0, 1, 2, -1, -4] // unsorted
-
-1)
-[-4, -1, -1, 0, 1, 2]
-      m   l        r
-
-2)
-[-4, -1, -1, 0, 1, 2]
-          m  l     r
-
-3)
-[-4, -1, -1, 0, 1, 2]
-      m      l     r
-​```
-
-We loop `m` in `0..<n`. We will do another inner loop at the same time, `l..r` loops in `i+1..<n`. 
-In 1), we will check if `a[i] == a[i-1]`? It's not in this case, then the problem is 2sum (`l..r`).
-In 2), Since `a[i] == a[i-1]`, it means `a[i-1]` covers `a[i]` case. Because case 3) contains case 2) solutions.
-```
-
-
 
 ## 4Sum
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 

From 8a51e9730e31b8d1e824a18c663e949df46b406d Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 01:45:25 -0700
Subject: [PATCH 248/643] Removes unnecessary explanations.

---
 3Sum and 4Sum/README.md | 104 ++++------------------------------------
 1 file changed, 8 insertions(+), 96 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index f9a121fab..c808e5e26 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -4,110 +4,20 @@
 
 ## 3Sum
 
-Given an array of integers, find all subsets of the array with 3 values where the 3 values sum up to a target number. 
+> Given an array of integers, find all subsets of the array with 3 values where the 3 values sum up to a target number. 
 
-**Note**: The solution subsets must not contain duplicate triplets. (Each element in the array can only be used once)
+> **Note**: The solution subsets must not contain duplicate triplets.
 
 > For example, given the array [-1, 0, 1, 2, -1, -4], and the target **0**:
 > The solution set is: [[-1, 0, 1], [-1, -1, 2]] // The two **-1** values in the array are considered to be distinct
 
-### Example
+There are 3 key procedures in solving this algorithm:
 
-Consider the following array of integers, and a target sum of **0**:
+1. Sort the array in ascending order. This allows you to make smart decisions when moving indexes around (since duplicates will be adjacent to each other).
 
-```
-[-1, 0, 1, 2, -1, -4]
-```
-
-#### 1. Sorting
-
-You'll first sort the array in ascending order:
-
-```
-[-4, -1, -1, 0, 1, 2]
-```
-
-#### 2. Two Sum's Methodology
-
-The 3Sum problem can be solved by augmenting the 2Sum solution, so let's begin by doing a quick explanation on how 2Sum handles the solution. 2Sum begins by comparing the left and right most values:
-
-```
-[-4, -1, -1, 0, 1, 2]
-  l                r
-```
-
-Your target sum is **0**. Given the current left and right values, you won't be able to make the target number. However, you've gained a valuable hint for your next step. 
-
-```
--4 + 2 = -2 // too small!
-```
-
-The result of `l + r` gave you a value that is smaller than the target number. Thus, you have two options:
-
-1. Increase the lower number. 
-2. Increase the higher number.
-
-Because your array is sorted, you can quickly identify that you cannot pick option **2**, since the rightmost number is already the biggest number. Thus, you have no choice but to try for a different number from the left end of the array:
-
-```
-[-4, -1, -1, 0, 1, 2]
-      l            r
-```
-
-This time, you'll get the following result from summing `l` and `r`:
-
-```
--1 + 2 = 1 // too big!
-```
-
-This time, the value is too big! I hope you see where it goes from here. Since the array is already sorted, you can only decrease the value on the right side in an attempt to balance things out. Hence, the next iteration of your algorithm will look like this:
+2. Ignoring duplicate values
 
-```
-[-4, -1, -1, 0, 1, 2]
-      l         r 
-```
-
-And then you've found a match :]
-
-```
--1 + 1 = 0
-```
-
-# 3Sum
-
-Let's start from scratch and consider the same problem where you've sorted your input and you're target sum is **0**:
-
-```
-[-4, -1, -1, 0, 1, 2]
-  l                r
-```
-
-Your goal this time is the following equation:
-
-```
-l + r + m = 0
-```
-
-You have the values of `l` and `r`:
-
-```
--4 + 2 + m = 0
-
-// in other words
-m = 4 - 2 = 2
-```
-
-For the current values of `l` and `r`, you need to find a value of **2** in the array to satisfy your target sum...
-
-#### Finding `m`
-
-```
-         m -- where?
-[-4, -1, -1, 0, 1, 2]
-  l                r 
-```
-
-There are slight optimizations you can do to find `m`, but to keep things simple, you'll just iterate through the array from `l` index to the `r` index. Once you find a value where `l + r + m = target`, you've found your first match! 
+3. Clever adjustment of indices for each pass. 
 
 #### Avoiding Duplicates
 
@@ -157,6 +67,8 @@ extension BidirectionalCollection where Element: Equatable {
 }
 ```
 
+### 
+
 ## 4Sum
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
 

From 63cae2538e12b358f7b0c514d2b5a2df7bb1fcf1 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 01:56:55 -0700
Subject: [PATCH 249/643] Summarizes technique for solving the problem.

---
 3Sum and 4Sum/README.md | 17 +++++++++--------
 1 file changed, 9 insertions(+), 8 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index c808e5e26..26b007668 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -5,19 +5,22 @@
 ## 3Sum
 
 > Given an array of integers, find all subsets of the array with 3 values where the 3 values sum up to a target number. 
-
+>
 > **Note**: The solution subsets must not contain duplicate triplets.
-
+>
 > For example, given the array [-1, 0, 1, 2, -1, -4], and the target **0**:
 > The solution set is: [[-1, 0, 1], [-1, -1, 2]] // The two **-1** values in the array are considered to be distinct
 
-There are 3 key procedures in solving this algorithm:
+There are 2 key procedures in solving this algorithm. Sorting the array, and avoiding duplicates.
 
-1. Sort the array in ascending order. This allows you to make smart decisions when moving indexes around (since duplicates will be adjacent to each other).
+### Pre-sorting
 
-2. Ignoring duplicate values
+Sorting your input array allows for powerful assumptions:
 
-3. Clever adjustment of indices for each pass. 
+* duplicates are always adjacent to each other
+* moving an index to the right increases the value, while moving an index to the left decreases the value
+
+You'll make use of these two rules to create an efficient algorithm.
 
 #### Avoiding Duplicates
 
@@ -67,8 +70,6 @@ extension BidirectionalCollection where Element: Equatable {
 }
 ```
 
-### 
-
 ## 4Sum
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
 

From a7ab5dae00c799d292845169940653a26070eb40 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 01:57:28 -0700
Subject: [PATCH 250/643] Removes a pointless sentence.

---
 3Sum and 4Sum/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 26b007668..f37d18d9c 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -1,6 +1,6 @@
 # 3Sum and 4Sum
 
-3Sum and 4Sum are extensions of a popular algorithm question, the [2Sum][5]. This article will talk about the problem and describe possible solutions.
+3Sum and 4Sum are extensions of a popular algorithm question, the [2Sum][5]. 
 
 ## 3Sum
 

From 0bf83f16b7eafcb5dea84fe97cb4cbc10755bb14 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 01:58:09 -0700
Subject: [PATCH 251/643] Updates a header.

---
 3Sum and 4Sum/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index f37d18d9c..9a5124637 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -13,7 +13,7 @@
 
 There are 2 key procedures in solving this algorithm. Sorting the array, and avoiding duplicates.
 
-### Pre-sorting
+### Sorting
 
 Sorting your input array allows for powerful assumptions:
 
@@ -22,7 +22,7 @@ Sorting your input array allows for powerful assumptions:
 
 You'll make use of these two rules to create an efficient algorithm.
 
-#### Avoiding Duplicates
+### Avoiding Duplicates
 
 Since you pre-sort the array, duplicates will be adjacent to each other. You just need to skip over duplicates by comparing adjacent values:
 

From 1fc26da0fa18a6134428dc14bef7a767fbd3c5c0 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 02:12:20 -0700
Subject: [PATCH 252/643] Added solution to 3Sum

---
 3Sum and 4Sum/README.md | 47 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 9a5124637..42732fda9 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -70,6 +70,53 @@ extension BidirectionalCollection where Element: Equatable {
 }
 ```
 
+### Assembling the Subsets
+
+You'll keep track of 3 indices to represent the 3 numbers. The sum at any given moment is `array[l] + array[m] + array[r]`:
+
+```
+      m ->      <- r
+[-4, -1, -1, 0, 1, 2]
+  l   
+```
+
+The premise is quite straightforward (given that you're familiar with 2Sum). You'll iterate `l` through the array. For every iteration, you also apply the 2Sum algorithm to elements after `l`. You'll check the sum every time you moving the indices to check if you found match. Here's the algorithm:
+
+```
+func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: BinaryInteger & Comparable {
+  let sorted = collection.sorted()
+  var ret: [[T.Element]] = []
+  
+  for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
+    var m = sorted.index(after: l)
+    var r = sorted.index(before: sorted.endIndex)
+
+    while m < r {
+      let sum = sorted[l] + sorted[m] + sorted[r]
+      switch target {
+      case sum:
+        ret.append([sorted[l], sorted[m], sorted[r]])
+        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break }
+        m = nextMid
+        r = nextRight
+      case ..<target:
+        guard let nextMid = sorted.uniqueIndex(after: m) else { break }
+        m = nextMid
+      case target...:
+        guard let nextRight = sorted.uniqueIndex(before: r) else { break }
+        r = nextRight
+      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
+      }
+    }
+  }
+  
+  return ret
+}
+```
+
+
+
+
 ## 4Sum
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
 

From 1279b3791e37c3531c9400524420cd3befd055cd Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 02:13:48 -0700
Subject: [PATCH 253/643] Updates implementation.

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 117 +++++++++++--------
 1 file changed, 67 insertions(+), 50 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index ec79ba787..fad2bf76d 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -1,59 +1,76 @@
-func ThreeSum(_ nums: [Int], targetSum: Int) -> [[Int]] {
-    var a = nums.sorted()
-    var ret: [[Int]] = []
-    
-    for m in 0..<a.count {
-        if m != 0 && a[m] == a[m-1] {
-            continue
-        }
-        
-        var l = m + 1
-        var r = nums.count - 1
-        
-        while l < r {
-            let sum = a[m] + a[l] + a[r]
-            
-            if sum == targetSum {
-                ret.append([a[m], a[l], a[r]])
-                l += 1
-            } else if sum < targetSum {
-                l += 1
-            } else {
-                r -= 1
-            }
-            
-            if sum == targetSum {
-                while l < r {
-                    var flag = false
-                    if l != 0 && a[l] == a[l-1] {
-                        l += 1
-                        flag = true
-                    }
-                    
-                    if (r != a.count - 1) && a[r] == a[r+1] {
-                        r -= 1
-                        flag = true
-                    }
-                    
-                    if (!flag) {
-                        break
-                    }
-                }
-            }
-        }
+extension Collection where Element: Equatable {
+  
+  /// Returns next index with unique value. Works only on sorted arrays.
+  ///
+  /// - Parameter index: The current `Int` index.
+  /// - Returns: The new `Int` index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
+  func uniqueIndex(after index: Index) -> Index? {
+    guard index < endIndex else { return nil }
+    var index = index
+    var nextIndex = self.index(after: index)
+    while nextIndex < endIndex && self[index] == self[nextIndex] {
+      formIndex(after: &index)
+      formIndex(after: &nextIndex)
     }
     
-    return ret
+    if nextIndex == endIndex {
+      return nil
+    } else {
+      return nextIndex
+    }
+  }
 }
 
-// Answer: [[-1, 0, 1], [-1, -1, 2]]
-ThreeSum([-1, 0, 1, 2, -1, -4], targetSum: 0)
+extension BidirectionalCollection where Element: Equatable {
+  
+  /// Returns next index with unique value. Works only on sorted arrays.
+  ///
+  /// - Parameter index: The current `Int` index.
+  /// - Returns: The new `Int` index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
+  func uniqueIndex(before index: Index) -> Index? {
+    return indices[..<index].reversed().first { index -> Bool in
+      let nextIndex = self.index(after: index)
+      guard nextIndex >= startIndex && self[index] != self[nextIndex] else { return false }
+      return true
+    }
+  }
+}
 
-// Answer: [[-1, -1, 1]]
-ThreeSum([-1, 1, 1, -1], targetSum: 1)
+func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: BinaryInteger & Comparable {
+  let sorted = collection.sorted()
+  var ret: [[T.Element]] = []
+  
+  for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
+    var m = sorted.index(after: l)
+    var r = sorted.index(before: sorted.endIndex)
+
+    while m < r {
+      let sum = sorted[l] + sorted[m] + sorted[r]
+      switch target {
+      case sum:
+        ret.append([sorted[l], sorted[m], sorted[r]])
+        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break }
+        m = nextMid
+        r = nextRight
+      case ..<target:
+        guard let nextMid = sorted.uniqueIndex(after: m) else { break }
+        m = nextMid
+      case target...:
+        guard let nextRight = sorted.uniqueIndex(before: r) else { break }
+        r = nextRight
+      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
+      }
+    }
+  }
+  
+  return ret
+}
+
+// Answer: [[-1, 0, 1], [-1, -1, 2]]
+threeSum([-1, 0, 1, 2, -1, -4], target: 0)
 
 // Answer: [[-1, -1, 2], [-1, 0, 1]]
-ThreeSum([-1, -1, -1, -1, 2, 1, -4, 0], targetSum: 0)
+threeSum([-1, -1, -1, -1, 2, 1, -4, 0], target: 0)
 
 // Answer: [[-1, -1, 2]]
-ThreeSum([-1, -1, -1, -1, -1, -1, 2], targetSum: 0)
+threeSum([-1, -1, -1, -1, -1, -1, 2], target: 0)

From 5aa6e17acc7224857ff5b5e27b55b6daf1ef56e6 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 14:53:22 -0700
Subject: [PATCH 254/643] Downgraded from BinaryInteger to Numeric. Fixes
 documentation.

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 14 +++++---------
 1 file changed, 5 insertions(+), 9 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index fad2bf76d..1a2f2933f 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -3,7 +3,7 @@ extension Collection where Element: Equatable {
   /// Returns next index with unique value. Works only on sorted arrays.
   ///
   /// - Parameter index: The current `Int` index.
-  /// - Returns: The new `Int` index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
+  /// - Returns: The new index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
   func uniqueIndex(after index: Index) -> Index? {
     guard index < endIndex else { return nil }
     var index = index
@@ -13,11 +13,7 @@ extension Collection where Element: Equatable {
       formIndex(after: &nextIndex)
     }
     
-    if nextIndex == endIndex {
-      return nil
-    } else {
-      return nextIndex
-    }
+    return nextIndex != endIndex ? nextIndex : nil
   }
 }
 
@@ -25,8 +21,8 @@ extension BidirectionalCollection where Element: Equatable {
   
   /// Returns next index with unique value. Works only on sorted arrays.
   ///
-  /// - Parameter index: The current `Int` index.
-  /// - Returns: The new `Int` index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
+  /// - Parameter index: The current index.
+  /// - Returns: The new index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
   func uniqueIndex(before index: Index) -> Index? {
     return indices[..<index].reversed().first { index -> Bool in
       let nextIndex = self.index(after: index)
@@ -36,7 +32,7 @@ extension BidirectionalCollection where Element: Equatable {
   }
 }
 
-func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: BinaryInteger & Comparable {
+func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
   let sorted = collection.sorted()
   var ret: [[T.Element]] = []
   

From 7d1d83ee2c74b3dded13e191ba23ed08d155d544 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 14:57:38 -0700
Subject: [PATCH 255/643] Adds loop labeling for better visibility

Easier to understand which parts of the code is borrowed using TwoSum.
---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index 1a2f2933f..8730a9b39 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -36,23 +36,23 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   let sorted = collection.sorted()
   var ret: [[T.Element]] = []
   
-  for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
+  ThreeSum: for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
 
-    while m < r {
+    TwoSum: while m < r {
       let sum = sorted[l] + sorted[m] + sorted[r]
       switch target {
       case sum:
         ret.append([sorted[l], sorted[m], sorted[r]])
-        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break }
+        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break TwoSum }
         m = nextMid
         r = nextRight
       case ..<target:
-        guard let nextMid = sorted.uniqueIndex(after: m) else { break }
+        guard let nextMid = sorted.uniqueIndex(after: m) else { break TwoSum }
         m = nextMid
       case target...:
-        guard let nextRight = sorted.uniqueIndex(before: r) else { break }
+        guard let nextRight = sorted.uniqueIndex(before: r) else { break TwoSum }
         r = nextRight
       default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }

From 26052e77e4747eb060780cfa369648c1885e736a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 14:58:03 -0700
Subject: [PATCH 256/643] Removes extra line.

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 1 -
 1 file changed, 1 deletion(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index 8730a9b39..c5680d345 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -12,7 +12,6 @@ extension Collection where Element: Equatable {
       formIndex(after: &index)
       formIndex(after: &nextIndex)
     }
-    
     return nextIndex != endIndex ? nextIndex : nil
   }
 }

From 48d83f2cbe1d813adb5519de31990b54a0c65e20 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 12 Oct 2017 15:00:10 -0700
Subject: [PATCH 257/643] Updates readme based on changes to playground code.

---
 3Sum and 4Sum/README.md | 41 ++++++++++++++++++-----------------------
 1 file changed, 18 insertions(+), 23 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 42732fda9..9fdc0277a 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -31,8 +31,8 @@ extension Collection where Element: Equatable {
   
   /// Returns next index with unique value. Works only on sorted arrays.
   ///
-  /// - Parameter index: The current `Int` index.
-  /// - Returns: The new `Int` index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
+  /// - Parameter index: The current index.
+  /// - Returns: The new index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
   func uniqueIndex(after index: Index) -> Index? {
     guard index < endIndex else { return nil }
     var index = index
@@ -41,12 +41,7 @@ extension Collection where Element: Equatable {
       formIndex(after: &index)
       formIndex(after: &nextIndex)
     }
-    
-    if nextIndex == endIndex {
-      return nil
-    } else {
-      return nextIndex
-    }
+    return nextIndex != endIndex ? nextIndex : nil
   }
 }
 ```
@@ -58,8 +53,8 @@ extension BidirectionalCollection where Element: Equatable {
   
   /// Returns next index with unique value. Works only on sorted arrays.
   ///
-  /// - Parameter index: The current `Int` index.
-  /// - Returns: The new `Int` index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
+  /// - Parameter index: The current index.
+  /// - Returns: The new index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
   func uniqueIndex(before index: Index) -> Index? {
     return indices[..<index].reversed().first { index -> Bool in
       let nextIndex = self.index(after: index)
@@ -83,29 +78,29 @@ You'll keep track of 3 indices to represent the 3 numbers. The sum at any given
 The premise is quite straightforward (given that you're familiar with 2Sum). You'll iterate `l` through the array. For every iteration, you also apply the 2Sum algorithm to elements after `l`. You'll check the sum every time you moving the indices to check if you found match. Here's the algorithm:
 
 ```
-func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: BinaryInteger & Comparable {
-  let sorted = collection.sorted()
+func threeSum<T: BidirectionalCollection>(_ c: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
+  let sorted = c.sorted()
   var ret: [[T.Element]] = []
   
   for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
-
+    
     while m < r {
       let sum = sorted[l] + sorted[m] + sorted[r]
-      switch target {
-      case sum:
+      switch sum {
+      case target:
         ret.append([sorted[l], sorted[m], sorted[r]])
-        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break }
-        m = nextMid
-        r = nextRight
+        guard let nextM = sorted.uniqueIndex(after: m), let nextR = sorted.uniqueIndex(before: r) else { break }
+        m = nextM
+        r = nextR
       case ..<target:
-        guard let nextMid = sorted.uniqueIndex(after: m) else { break }
-        m = nextMid
+        guard let nextM = sorted.uniqueIndex(after: m) else { break }
+        m = nextM
       case target...:
-        guard let nextRight = sorted.uniqueIndex(before: r) else { break }
-        r = nextRight
-      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
+        guard let nextR = sorted.uniqueIndex(before: m) else { break }
+        r = nextR
+      default: fatalError()
       }
     }
   }

From f9b6a2f3059b258ffeff1fa11342d1652cd8a5a0 Mon Sep 17 00:00:00 2001
From: Semen Zhydenko <simeon.zhidenko@gmail.com>
Date: Sat, 14 Oct 2017 21:27:16 +0200
Subject: [PATCH 258/643] becuase -> because

---
 Singly Linked List/SinglyLinkedList.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Singly Linked List/SinglyLinkedList.playground/Contents.swift b/Singly Linked List/SinglyLinkedList.playground/Contents.swift
index d9104ebe7..8c62f9e78 100644
--- a/Singly Linked List/SinglyLinkedList.playground/Contents.swift	
+++ b/Singly Linked List/SinglyLinkedList.playground/Contents.swift	
@@ -720,7 +720,7 @@ assert(l2.count == 8)
 assert(l2.contains(67) == true)
 
 
-//: Notice that becuase our implementation conforms to the Collection protocol, we can use a lot of methods already implemented for us in Swift's standard library, for example, contains, dropLast, etc.
+//: Notice that because our implementation conforms to the Collection protocol, we can use a lot of methods already implemented for us in Swift's standard library, for example, contains, dropLast, etc.
 
 let l3 = l2.dropLast()
 assert(l3.count == 7)

From 3402103956c96bfd03af5a1345aa8cfce05fda3c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 21:38:08 -0700
Subject: [PATCH 259/643] Simplifies algorithm via in-place index traversals

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 57 +++++++++-----------
 1 file changed, 26 insertions(+), 31 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index c5680d345..d16492689 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -1,61 +1,56 @@
+
 extension Collection where Element: Equatable {
   
-  /// Returns next index with unique value. Works only on sorted arrays.
+  /// In a sorted collection, replaces the given index with a successor mapping to a unique element.
   ///
-  /// - Parameter index: The current `Int` index.
-  /// - Returns: The new index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
-  func uniqueIndex(after index: Index) -> Index? {
-    guard index < endIndex else { return nil }
-    var index = index
-    var nextIndex = self.index(after: index)
-    while nextIndex < endIndex && self[index] == self[nextIndex] {
+  /// - Parameter index: A valid index of the collection. `index` must be less than `endIndex`
+  func formUniqueIndex(after index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
       formIndex(after: &index)
-      formIndex(after: &nextIndex)
-    }
-    return nextIndex != endIndex ? nextIndex : nil
+    } while index < endIndex && self[prev] == self[index]
   }
 }
 
 extension BidirectionalCollection where Element: Equatable {
   
-  /// Returns next index with unique value. Works only on sorted arrays.
+  /// In a sorted collection, replaces the given index with a predecessor that maps to a unique element.
   ///
-  /// - Parameter index: The current index.
-  /// - Returns: The new index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
-  func uniqueIndex(before index: Index) -> Index? {
-    return indices[..<index].reversed().first { index -> Bool in
-      let nextIndex = self.index(after: index)
-      guard nextIndex >= startIndex && self[index] != self[nextIndex] else { return false }
-      return true
-    }
+  /// - Parameter index: A valid index of the collection. `index` must be greater than `startIndex`.
+  func formUniqueIndex(before index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
+      formIndex(before: &index)
+    } while index > startIndex && self[prev] == self[index]
   }
 }
 
 func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
   let sorted = collection.sorted()
   var ret: [[T.Element]] = []
+  var l = sorted.startIndex
   
-  ThreeSum: for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
+  while l < sorted.endIndex {
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
-
-    TwoSum: while m < r {
+    
+    while m < r && r < sorted.endIndex {
       let sum = sorted[l] + sorted[m] + sorted[r]
       switch target {
       case sum:
         ret.append([sorted[l], sorted[m], sorted[r]])
-        guard let nextMid = sorted.uniqueIndex(after: m), let nextRight = sorted.uniqueIndex(before: r) else { break TwoSum }
-        m = nextMid
-        r = nextRight
+        sorted.formUniqueIndex(after: &m)
+        sorted.formUniqueIndex(before: &r)
       case ..<target:
-        guard let nextMid = sorted.uniqueIndex(after: m) else { break TwoSum }
-        m = nextMid
+        sorted.formUniqueIndex(after: &m)
       case target...:
-        guard let nextRight = sorted.uniqueIndex(before: r) else { break TwoSum }
-        r = nextRight
-      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
+        sorted.formUniqueIndex(before: &r)
+      default: fatalError("Sw ift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
+    sorted.formUniqueIndex(after: &l)
   }
   
   return ret

From e4d1faec77b123b60cb975302fcc5701f54484e0 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 21:38:57 -0700
Subject: [PATCH 260/643] Removes a needless whitespace in string.

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index d16492689..dfc4d12f8 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -47,7 +47,7 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
         sorted.formUniqueIndex(after: &m)
       case target...:
         sorted.formUniqueIndex(before: &r)
-      default: fatalError("Sw ift isn't smart enough to detect that this switch statement is exhausive")
+      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
     sorted.formUniqueIndex(after: &l)

From 1c4ce41440cfd34f38993dfb82853130c953c07b Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 21:42:19 -0700
Subject: [PATCH 261/643] Updated readme based on code changes.

---
 3Sum and 4Sum/README.md | 65 ++++++++++++++++++-----------------------
 1 file changed, 28 insertions(+), 37 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 9fdc0277a..781c1f52b 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -29,19 +29,15 @@ Since you pre-sort the array, duplicates will be adjacent to each other. You jus
 ```
 extension Collection where Element: Equatable {
   
-  /// Returns next index with unique value. Works only on sorted arrays.
+  /// In a sorted collection, replaces the given index with a successor mapping to a unique element.
   ///
-  /// - Parameter index: The current index.
-  /// - Returns: The new index. Will return `nil` if new index happens to be the `endIndex` (out of bounds)
-  func uniqueIndex(after index: Index) -> Index? {
-    guard index < endIndex else { return nil }
-    var index = index
-    var nextIndex = self.index(after: index)
-    while nextIndex < endIndex && self[index] == self[nextIndex] {
+  /// - Parameter index: A valid index of the collection. `index` must be less than `endIndex`
+  func formUniqueIndex(after index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
       formIndex(after: &index)
-      formIndex(after: &nextIndex)
-    }
-    return nextIndex != endIndex ? nextIndex : nil
+    } while index < endIndex && self[prev] == self[index]
   }
 }
 ```
@@ -51,16 +47,15 @@ A similar implementation is used to get the unique index *before* a given index:
 ```
 extension BidirectionalCollection where Element: Equatable {
   
-  /// Returns next index with unique value. Works only on sorted arrays.
+  /// In a sorted collection, replaces the given index with a predecessor that maps to a unique element.
   ///
-  /// - Parameter index: The current index.
-  /// - Returns: The new index. Will return `nil` if new index happens to come before the `startIndex` (out of bounds)
-  func uniqueIndex(before index: Index) -> Index? {
-    return indices[..<index].reversed().first { index -> Bool in
-      let nextIndex = self.index(after: index)
-      guard nextIndex >= startIndex && self[index] != self[nextIndex] else { return false }
-      return true
-    }
+  /// - Parameter index: A valid index of the collection. `index` must be greater than `startIndex`.
+  func formUniqueIndex(before index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
+      formIndex(before: &index)
+    } while index > startIndex && self[prev] == self[index]
   }
 }
 ```
@@ -78,40 +73,36 @@ You'll keep track of 3 indices to represent the 3 numbers. The sum at any given
 The premise is quite straightforward (given that you're familiar with 2Sum). You'll iterate `l` through the array. For every iteration, you also apply the 2Sum algorithm to elements after `l`. You'll check the sum every time you moving the indices to check if you found match. Here's the algorithm:
 
 ```
-func threeSum<T: BidirectionalCollection>(_ c: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
-  let sorted = c.sorted()
+func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
+  let sorted = collection.sorted()
   var ret: [[T.Element]] = []
+  var l = sorted.startIndex
   
-  for l in sequence(first: sorted.startIndex, next: sorted.uniqueIndex(after:)) {
+  while l < sorted.endIndex {
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
-    while m < r {
+    while m < r && r < sorted.endIndex {
       let sum = sorted[l] + sorted[m] + sorted[r]
-      switch sum {
-      case target:
+      switch target {
+      case sum:
         ret.append([sorted[l], sorted[m], sorted[r]])
-        guard let nextM = sorted.uniqueIndex(after: m), let nextR = sorted.uniqueIndex(before: r) else { break }
-        m = nextM
-        r = nextR
+        sorted.formUniqueIndex(after: &m)
+        sorted.formUniqueIndex(before: &r)
       case ..<target:
-        guard let nextM = sorted.uniqueIndex(after: m) else { break }
-        m = nextM
+        sorted.formUniqueIndex(after: &m)
       case target...:
-        guard let nextR = sorted.uniqueIndex(before: m) else { break }
-        r = nextR
-      default: fatalError()
+        sorted.formUniqueIndex(before: &r)
+      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
+    sorted.formUniqueIndex(after: &l)
   }
   
   return ret
 }
 ```
 
-
-
-
 ## 4Sum
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
 

From 8c10fbddd1c44b4ecfeb13a666a6a17ab5f1d762 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 21:48:31 -0700
Subject: [PATCH 262/643] Repositions index traversal of `l`

Seems like a good use case for `defer`... giving the index traversal more visibility by putting it next to the `while` loop. Reads a bit more like for loops now, where exit condition and traversal procedure can be understood in 1 line.
---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index dfc4d12f8..ec021a75c 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -32,11 +32,11 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var ret: [[T.Element]] = []
   var l = sorted.startIndex
   
-  while l < sorted.endIndex {
+  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
-    while m < r && r < sorted.endIndex {
+    while m < r && r < sorted.endIndex { 
       let sum = sorted[l] + sorted[m] + sorted[r]
       switch target {
       case sum:
@@ -50,7 +50,6 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
       default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
-    sorted.formUniqueIndex(after: &l)
   }
   
   return ret

From 676fbbe9d096daa6916504e36acbfce60fdc73c7 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 21:49:02 -0700
Subject: [PATCH 263/643] Updates README based on code updates

---
 3Sum and 4Sum/README.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 781c1f52b..c2374507f 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -78,7 +78,7 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var ret: [[T.Element]] = []
   var l = sorted.startIndex
   
-  while l < sorted.endIndex {
+  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
@@ -96,7 +96,6 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
       default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
-    sorted.formUniqueIndex(after: &l)
   }
   
   return ret

From da9e823f7b486c088a7d5f0134abe008b794b0f6 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 22:07:09 -0700
Subject: [PATCH 264/643] Simplified switch statement to if-else loop

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index ec021a75c..6c9a81f50 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -38,16 +38,14 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
     
     while m < r && r < sorted.endIndex { 
       let sum = sorted[l] + sorted[m] + sorted[r]
-      switch target {
-      case sum:
+      if sum == target {
         ret.append([sorted[l], sorted[m], sorted[r]])
         sorted.formUniqueIndex(after: &m)
         sorted.formUniqueIndex(before: &r)
-      case ..<target:
+      } else if sum < target {
         sorted.formUniqueIndex(after: &m)
-      case target...:
+      } else {
         sorted.formUniqueIndex(before: &r)
-      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
   }

From c76072464c603b348ffa183de4ee36ae060ffece Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 14 Oct 2017 22:08:12 -0700
Subject: [PATCH 265/643] Updated readme for new code.

---
 3Sum and 4Sum/README.md | 10 ++++------
 1 file changed, 4 insertions(+), 6 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index c2374507f..77e7ff854 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -82,18 +82,16 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
-    while m < r && r < sorted.endIndex {
+    while m < r && r < sorted.endIndex { 
       let sum = sorted[l] + sorted[m] + sorted[r]
-      switch target {
-      case sum:
+      if sum == target {
         ret.append([sorted[l], sorted[m], sorted[r]])
         sorted.formUniqueIndex(after: &m)
         sorted.formUniqueIndex(before: &r)
-      case ..<target:
+      } else if sum < target {
         sorted.formUniqueIndex(after: &m)
-      case target...:
+      } else {
         sorted.formUniqueIndex(before: &r)
-      default: fatalError("Swift isn't smart enough to detect that this switch statement is exhausive")
       }
     }
   }

From 30d168445a17ec1b16b24f9ccbb1fc8c3fd35c5c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:24:31 -0700
Subject: [PATCH 266/643] Updated implementation of 4Sum

---
 3Sum and 4Sum/4Sum.playground/Contents.swift | 111 +++++++++----------
 1 file changed, 54 insertions(+), 57 deletions(-)

diff --git a/3Sum and 4Sum/4Sum.playground/Contents.swift b/3Sum and 4Sum/4Sum.playground/Contents.swift
index b86dd42f5..4c26bbf07 100644
--- a/3Sum and 4Sum/4Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/4Sum.playground/Contents.swift	
@@ -1,61 +1,58 @@
-func FourSum(_ nums: [Int], target: Int) -> [[Int]] {
-    let a = nums.sorted()
-    var ret: [[Int]] = []
-    
-    for i in 0..<nums.count {
-        if i != 0 && a[i] == a[i-1] {
-            continue
-        }
-        for j in i+1..<nums.count {
-            if j != i+1 && a[j] == a[j-1] {
-                continue
-            }
-            
-            var k = j + 1
-            var t = nums.count - 1
-            
-            while k < t {
-                let sum = a[i] + a[j] + a[k] + a[t]
-                
-                if sum == target {
-                    ret.append([a[i], a[j], a[k], a[t]])
-                    k += 1
-                } else if sum < target {
-                    k += 1
-                } else {
-                    t -= 1
-                }
-                
-                if sum == target {
-                    while k < t {
-                        var flag = true
-                        if k != j + 1 && a[k] == a[k-1] {
-                            k += 1
-                            flag = false
-                        }
-                        
-                        if t != nums.count - 1 && a[t] == a[t+1] {
-                            t -= 1
-                            flag = false
-                        }
-                        
-                        if flag {
-                            break
-                        }
-                    }
-                }
-            }
+extension Collection where Element: Equatable {
+  
+  /// In a sorted collection, replaces the given index with a successor mapping to a unique element.
+  ///
+  /// - Parameter index: A valid index of the collection. `index` must be less than `endIndex`
+  func formUniqueIndex(after index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
+      formIndex(after: &index)
+    } while index < endIndex && self[prev] == self[index]
+  }
+}
+
+extension BidirectionalCollection where Element: Equatable {
+  
+  /// In a sorted collection, replaces the given index with a predecessor that maps to a unique element.
+  ///
+  /// - Parameter index: A valid index of the collection. `index` must be greater than `startIndex`.
+  func formUniqueIndex(before index: inout Index) {
+    var prev = index
+    repeat {
+      prev = index
+      formIndex(before: &index)
+    } while index > startIndex && self[prev] == self[index]
+  }
+}
+
+func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
+  let sorted = collection.sorted()
+  var ret: [[T.Element]] = []
+  
+  var l = sorted.startIndex
+  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
+    var ml = sorted.index(after: l)
+    while ml < sorted.endIndex { defer { sorted.formUniqueIndex(after: &ml) }
+      var mr = sorted.index(after: ml)
+      var r = sorted.index(before: sorted.endIndex)
+      
+      while mr < r && r < sorted.endIndex {
+        let sum = sorted[l] + sorted[ml] + sorted[mr] + sorted[r]
+        if sum == target {
+          ret.append([sorted[l], sorted[ml], sorted[mr], sorted[r]])
+          sorted.formUniqueIndex(after: &mr)
+          sorted.formUniqueIndex(before: &r)
+        } else if sum < target {
+          sorted.formUniqueIndex(after: &mr)
+        } else {
+          sorted.formUniqueIndex(before: &r)
         }
+      }
     }
-    
-    return ret
+  }
+  return ret
 }
 
-/* Answer
-[
-    [-1,  0, 0, 1],
-    [-2, -1, 1, 2],
-    [-2,  0, 0, 2]
-]
-*/
-FourSum([1, 0, -1, 0, -2, 2], target: 0)
+// answer: [[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]
+fourSum([1, 0, -1, 0, -2, 2], target: 0)

From d7b2c1a60e03970cb998cce5ad5e44c6865565f9 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:25:03 -0700
Subject: [PATCH 267/643] Labeled while loops for clarity.

---
 3Sum and 4Sum/3Sum.playground/Contents.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index 6c9a81f50..2581da6e7 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -32,11 +32,11 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var ret: [[T.Element]] = []
   var l = sorted.startIndex
   
-  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
+  ThreeSum: while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
-    while m < r && r < sorted.endIndex { 
+    TwoSum: while m < r && r < sorted.endIndex { 
       let sum = sorted[l] + sorted[m] + sorted[r]
       if sum == target {
         ret.append([sorted[l], sorted[m], sorted[r]])

From 67d4c9d306719e79612875c36759c9c9e19a3ef1 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:25:35 -0700
Subject: [PATCH 268/643] Labelled while loops for clarity.

---
 3Sum and 4Sum/4Sum.playground/Contents.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/3Sum and 4Sum/4Sum.playground/Contents.swift b/3Sum and 4Sum/4Sum.playground/Contents.swift
index 4c26bbf07..100534b28 100644
--- a/3Sum and 4Sum/4Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/4Sum.playground/Contents.swift	
@@ -31,13 +31,13 @@ func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var ret: [[T.Element]] = []
   
   var l = sorted.startIndex
-  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
+  FourSum: while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var ml = sorted.index(after: l)
-    while ml < sorted.endIndex { defer { sorted.formUniqueIndex(after: &ml) }
+    ThreeSum: while ml < sorted.endIndex { defer { sorted.formUniqueIndex(after: &ml) }
       var mr = sorted.index(after: ml)
       var r = sorted.index(before: sorted.endIndex)
       
-      while mr < r && r < sorted.endIndex {
+      TwoSum: while mr < r && r < sorted.endIndex {
         let sum = sorted[l] + sorted[ml] + sorted[mr] + sorted[r]
         if sum == target {
           ret.append([sorted[l], sorted[ml], sorted[mr], sorted[r]])

From 97911efc8216f439df075c3842d57340a7a972ee Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:26:11 -0700
Subject: [PATCH 269/643] Added new line between loops

---
 3Sum and 4Sum/4Sum.playground/Contents.swift | 1 +
 1 file changed, 1 insertion(+)

diff --git a/3Sum and 4Sum/4Sum.playground/Contents.swift b/3Sum and 4Sum/4Sum.playground/Contents.swift
index 100534b28..86b530224 100644
--- a/3Sum and 4Sum/4Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/4Sum.playground/Contents.swift	
@@ -33,6 +33,7 @@ func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var l = sorted.startIndex
   FourSum: while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var ml = sorted.index(after: l)
+                                      
     ThreeSum: while ml < sorted.endIndex { defer { sorted.formUniqueIndex(after: &ml) }
       var mr = sorted.index(after: ml)
       var r = sorted.index(before: sorted.endIndex)

From 38b32d28c2f61e8ec3eb3e75516ee2bad2d0c3fb Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:31:58 -0700
Subject: [PATCH 270/643] Updated for FourSum.

---
 3Sum and 4Sum/README.md | 55 ++++++++++++++++++++++++++++++++++++++---
 1 file changed, 51 insertions(+), 4 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 77e7ff854..af998a4a7 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -78,11 +78,11 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
   var ret: [[T.Element]] = []
   var l = sorted.startIndex
   
-  while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
+  ThreeSum: while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
     var m = sorted.index(after: l)
     var r = sorted.index(before: sorted.endIndex)
     
-    while m < r && r < sorted.endIndex { 
+    TwoSum: while m < r && r < sorted.endIndex { 
       let sum = sorted[l] + sorted[m] + sorted[r]
       if sum == target {
         ret.append([sorted[l], sorted[m], sorted[r]])
@@ -101,13 +101,60 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
 ```
 
 ## 4Sum
+
 Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
 
 **Note**: The solution set must not contain duplicate quadruplets.
 
 ### Solution
-After 3Sum, we already have the idea to change to a problem to a familiar problem we solved before. So, the idea here is straightforward. We just need to downgrade 4Sum to 3Sum. Then we can solve 4Sum.
 
-It's easy to think that we loop the array and get the first the element, then the rest array is 3Sum problem. Since the code is pretty simple, I will avoid duplicate introducation here.
+Foursum is a very straightforward extension to the threeSum algorithm. In threeSum, you kept track of 3 indices:
+
+```
+      m ->      <- r
+[-4, -1, -1, 0, 1, 2]
+  l   
+```
+
+For fourSum, you'll keep track of 4:
+
+```
+         mr ->  <- r
+[-4, -1, -1, 0, 1, 2]
+  l  ml -> 
+```
+
+Here's the code for it (notice it is very similar to 3Sum):
+
+```
+func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
+  let sorted = collection.sorted()
+  var ret: [[T.Element]] = []
+  
+  var l = sorted.startIndex
+  FourSum: while l < sorted.endIndex { defer { sorted.formUniqueIndex(after: &l) }
+    var ml = sorted.index(after: l)
+    
+    ThreeSum: while ml < sorted.endIndex { defer { sorted.formUniqueIndex(after: &ml) }
+      var mr = sorted.index(after: ml)
+      var r = sorted.index(before: sorted.endIndex)
+      
+      TwoSum: while mr < r && r < sorted.endIndex {
+        let sum = sorted[l] + sorted[ml] + sorted[mr] + sorted[r]
+        if sum == target {
+          ret.append([sorted[l], sorted[ml], sorted[mr], sorted[r]])
+          sorted.formUniqueIndex(after: &mr)
+          sorted.formUniqueIndex(before: &r)
+        } else if sum < target {
+          sorted.formUniqueIndex(after: &mr)
+        } else {
+          sorted.formUniqueIndex(before: &r)
+        }
+      }
+    }
+  }
+  return ret
+}
+```
 
 [5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem

From 3c0612a467c362a6ef882a6b39f91b7f8375dce7 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:46:46 -0700
Subject: [PATCH 271/643] Fixes a bit of formatting.

---
 3Sum and 4Sum/README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index af998a4a7..4a51b00f0 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -102,9 +102,9 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
 
 ## 4Sum
 
-Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
-
-**Note**: The solution set must not contain duplicate quadruplets.
+> Given an array S of n integers, find all subsets of the array with 4 values where the 4 values sum up to a target number. 
+>
+> **Note**: The solution set must not contain duplicate quadruplets.
 
 ### Solution
 

From 7dcfdf41cccb5c7ea1ede852cebf72a2c9f4a503 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:51:15 -0700
Subject: [PATCH 272/643] Added link to 3sum/4sum

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

diff --git a/README.markdown b/README.markdown
index fa3483657..e874a8190 100644
--- a/README.markdown
+++ b/README.markdown
@@ -193,6 +193,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 A lot of software developer interview questions consist of algorithmic puzzles. Here is a small selection of fun ones. For more puzzles (with answers), see [here](http://elementsofprogramminginterviews.com/) and [here](http://www.crackingthecodinginterview.com).
 
 - [Two-Sum Problem](Two-Sum%20Problem/)
+- [Three-Sum/Four-Sum Problem](3Sum%20and%204Sum/)
 - [Fizz Buzz](Fizz%20Buzz/)
 - [Monty Hall Problem](Monty%20Hall%20Problem/)
 - [Finding Palindromes](Palindromes/)

From 4213b0892ec878609b114d0f34f9417164f56e1e Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:51:58 -0700
Subject: [PATCH 273/643] Added credits.

---
 3Sum and 4Sum/README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 4a51b00f0..5547789c7 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -158,3 +158,5 @@ func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
 ```
 
 [5]:	https://github.com/raywenderlich/swift-algorithm-club/tree/master/Two-Sum%20Problem
+
+*Written for the Swift Algorithm Club by Kai Chen and Kelvin Lau*

From dfc1246b4f5a489f8e5bf76fb208e2684c9f7fc5 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 00:52:49 -0700
Subject: [PATCH 274/643] Added reference to 3sum/4sum

---
 Two-Sum Problem/README.markdown | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index b2f126595..4d8ffcd95 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -164,4 +164,8 @@ It's possible, of course, that there are no values for `a[i] + a[j]` that sum to
 
 I'm quite enamored by this little algorithm. It shows that with some basic preprocessing on the input data -- sorting it from low to high -- you can turn a tricky problem into a very simple and beautiful algorithm.
 
+## Additional Reading
+
+* [3Sum / 4Sum](https://github.com/raywenderlich/swift-algorithm-club/tree/master/3Sum%20and%204Sum)
+
 *Written for Swift Algorithm Club by Matthijs Hollemans and Daniel Speiser*

From 829cf17379477f4ac085f8d80ecb4b68ca020e51 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 15 Oct 2017 18:50:28 -0700
Subject: [PATCH 275/643] Adds Octree to the main toc

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

diff --git a/README.markdown b/README.markdown
index e874a8190..42cd23739 100644
--- a/README.markdown
+++ b/README.markdown
@@ -163,6 +163,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Trie](Trie/). A special type of tree used to store associative data structures.
 - [B-Tree](B-Tree/). A self-balancing search tree, in which nodes can have more than two children.
 - [QuadTree](QuadTree/). A tree with 4 children.
+- [Octree](Octree/). A tree with 8 children. 
 
 ### Hashing
 

From 97acdd38f33fdf682a2c56a52501b738054e8a85 Mon Sep 17 00:00:00 2001
From: Hai Nguyen <aquarchitecture@gmail.com>
Date: Sun, 15 Oct 2017 21:32:04 -0700
Subject: [PATCH 276/643] Fix typos

---
 All-Pairs Shortest Paths/README.markdown | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/All-Pairs Shortest Paths/README.markdown b/All-Pairs Shortest Paths/README.markdown
index 8a75c8b73..bbef6c64e 100644
--- a/All-Pairs Shortest Paths/README.markdown	
+++ b/All-Pairs Shortest Paths/README.markdown	
@@ -1,14 +1,14 @@
 # All-Pairs Shortest Paths
 
-The All-Pairs shortest path problem simultaneously computes the shortest path from each node in the graph to each other node, provded a path exists for each pair. In the naive approach, we could simply compute a single-source shortest path from each node to each other node. The number of shortest paths computed is then bound by `O(V^2)`, where `V` is the number of vertices in the graph. Because SSSP is also bounded by `O(V^2)`, the total running time for the naive approach would be `O(V^4)`.
+The All-Pairs shortest path problem simultaneously computes the shortest path from each node in the graph to each other node, provided a path exists for each pair. In the naive approach, we could simply compute a single-source shortest path from each node to each other node. The number of shortest paths computed is then bound by `O(V^2)`, where `V` is the number of vertices in the graph. Because SSSP is also bounded by `O(V^2)`, the total running time for the naive approach would be `O(V^4)`.
 
-However, by applying a dynamic approach on the adjacency matrix of the graph, a running time of `Θ(V^3)` is achievable, using the `Floyd-Warshall` algorithm. Floyd-Warshall iterates through an adjacency matrix, and for each pair of start(`i`) and end(`j`) vertices it considers if the current distance between them is greater than a path taken through another vertex(`k`) in the graph (if paths `i` ~> `k` and `k` ~> `j` exist). It moves through an adjacency matrix for every vertex `k` applying its comparison for each pair (`i`, `j`), so for each `k` a new adjacency matrix `D(k)` is derived, where each value `d(k)[i][j]` is defined as:
+However, by applying a dynamic approach on the adjacency matrix of the graph, a running time of `O(V^3)` is achievable, using the `Floyd-Warshall` algorithm. Floyd-Warshall iterates through an adjacency matrix, and for each pair of start(`i`) and end(`j`) vertices it considers if the current distance between them is greater than a path taken through another vertex(`k`) in the graph (if paths `i` ~> `k` and `k` ~> `j` exist). It moves through an adjacency matrix for every vertex `k` applying its comparison for each pair (`i`, `j`), so for each `k` a new adjacency matrix `D(k)` is derived, where each value `d(k)[i][j]` is defined as:
 
 <img src="img/weight_comparison_formula.png" width="400px" />
 
-where `w[i][j]` is the weight of the edge connecting vertex `i` to vertex `j` in the graph's original adjacency matrix. 
+where `w[i][j]` is the weight of the edge connecting vertex `i` to vertex `j` in the graph's original adjacency matrix.
 
-When the algorithm memoizes each refined adjacency and predecessor matrix, its space complexity is `Θ(V^3)`, which can be optimised to `Θ(V^2)` by only memoizing the latest refinements. Reconstructing paths is a recursive procedure which requires `Θ(V)` time and `Θ(V^2)` space.
+When the algorithm memoizes each refined adjacency and predecessor matrix, its space complexity is `O(V^3)`, which can be optimised to `O(V^2)` by only memoizing the latest refinements. Reconstructing paths is a recursive procedure which requires `O(V)` time and `O(V^2)` space.
 
 # Example
 
@@ -22,9 +22,9 @@ the adjacency matrix representation `w` is
 
 ### Calculating shortest paths' weights
 
-At the beginning of the algorithm, `D(0)` is the same as `w`, with the following exceptions to accomodate the comparison function:
+At the beginning of the algorithm, `D(0)` is the same as `w`, with the following exceptions to accommodate the comparison function:
 
-1. vertices with no path connecting them have the `ø` replaced with `∞` 
+1. vertices with no path connecting them have the `ø` replaced with `∞`
 2. the diagonal has all `0`s
 
 Here are all the adjacency matrices derived when perform Floyd-Warshall on the above graph:
@@ -56,7 +56,7 @@ This algorithm finds only the lengths of the shortest paths between all pairs of
 
 # Project Structure
 
-The provided xcworkspace allows working in the playground, which imports the APSP framework target from the xcodeproj. Build the framework target and rerun the playground to get started. There is also a test target in the xcodeproj. 
+The provided xcworkspace allows working in the playground, which imports the APSP framework target from the xcodeproj. Build the framework target and rerun the playground to get started. There is also a test target in the xcodeproj.
 
 In the framework:
 
@@ -65,7 +65,7 @@ In the framework:
 
 # TODO
 
-- Implement naive `Θ(V^4)` method for comparison
+- Implement naive `O(V^4)` method for comparison
 - Implement Johnson's algorithm for sparse graphs
 - Implement other cool optimized versions
 
@@ -73,4 +73,4 @@ In the framework:
 
 Chapter 25 of Introduction to Algorithms, Third Edition by Cormen, Leiserson, Rivest and Stein [https://mitpress.mit.edu/books/introduction-algorithms](https://mitpress.mit.edu/books/introduction-algorithms)
 
-*Written for Swift Algorithm Club by [Andrew McKnight](https://github.com/armcknight)*
\ No newline at end of file
+*Written for Swift Algorithm Club by [Andrew McKnight](https://github.com/armcknight)*

From 07563e0cdb87bd0efc1e359bdaae5f13ac932075 Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Thu, 19 Oct 2017 00:22:35 +0200
Subject: [PATCH 277/643] add astar reference in readme

---
 Dijkstra Algorithm/README.md | 58 +++++++++++++++++++-----------------
 1 file changed, 30 insertions(+), 28 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 5f8a0ce07..4bc719598 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,6 +1,6 @@
 # Weighted graph general concepts
 
-Every weighted graph should contain: 
+Every weighted graph should contain:
 1. Vertices/Nodes (I will use "vertex" in this readme).
 
 <img src="Images/Vertices.png" height="250" />
@@ -11,11 +11,11 @@ Every weighted graph should contain:
 
 <img src="Images/DirectedGraph.png" height="250" />
 
-3. Weights for every edge. 
+3. Weights for every edge.
 
 <img src="Images/WeightedDirectedGraph.png" height="250" />
 
-Final result. 
+Final result.
 Directed weighted graph:
 
 <img src="Images/WeightedDirectedGraphFinal.png" height="250" />
@@ -44,7 +44,9 @@ When all vertices are marked as visited, the algorithm's job is done. Now, you c
 
 I have created **VisualizedDijkstra.playground** game/tutorial to improve your understanding of the algorithm's flow. Besides, below is step by step algorithm's description.
 
-## Example 
+A short sidenote. The Swift Algorithm Club also contains the A* algorithm, which essentially is a faster version of Dijkstra's algorithm for which the only extra prerequisite is you have to know where the destination is located.
+
+## Example
 Let's imagine that you want to go to the shop. Your house is A vertex and there are 4 possible stores around your house. How to find the closest one/ones? Luckily, you have a graph that connects your house with all these stores. So, you know what to do :)
 
 ### Initialisation
@@ -95,7 +97,7 @@ After this step graph has this state:
 
 ### Step 1
 
-Then we check all of its neighbours. 
+Then we check all of its neighbours.
 If checking vertex path length from start + edge weight is smaller than neighbour's path length from start then we set neighbour's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
 
 for clarity:
@@ -120,7 +122,7 @@ And its state is here:
 
 ### Step 2
 
-From now we repeat all actions again and fill our table with new info! 
+From now we repeat all actions again and fill our table with new info!
 
 <img src="Images/image4.png" height="250" />
 
@@ -161,7 +163,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
 
-## Code implementation 
+## Code implementation
 First of all, let’s create class that will describe any Vertex in the graph.
 It is pretty simple
 ```swift
@@ -169,12 +171,12 @@ open class Vertex {
 
     //Every vertex should be unique that's why we set up identifier
     open var identifier: String
-	
-    //For Dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some usecases 
+
+    //For Dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some usecases
     //when you firstly initialize all vertices without neighbours. And then on next iteration you set up their neighbours. So, initially neighbours is an empty array.
     //Array contains tuples (Vertex, Double). Vertex is a neighbour and Double is as edge weight to that neighbour.
     open var neighbours: [(Vertex, Double)] = []
-	
+
     //As it was mentioned in the algorithm description, default path length from start for all vertices should be as much as possible.
     //It is var because we will update it during the algorithm execution.
     open var pathLengthFromStart = Double.infinity
@@ -215,7 +217,7 @@ We've created a base for our algorithm. Now let's create a house :)
 Dijkstra's realisation is really straightforward.
 ```swift
 public class Dijkstra {
-    //This is a storage for vertices in the graph. 
+    //This is a storage for vertices in the graph.
     //Assuming that our vertices are unique we can use Set instead of array. This approach will bring some benefits later.
     private var totalVertices: Set<Vertex>
 
@@ -223,69 +225,69 @@ public class Dijkstra {
         totalVertices = vertices
     }
 
-    //Remember clearCache function in the Vertex class implementation? 
+    //Remember clearCache function in the Vertex class implementation?
     //This is just a wrapper that cleans cache for all stored vertices.
     private func clearCache() {
         totalVertices.forEach { $0.clearCache() }
     }
 
     public func findShortestPaths(from startVertex: Vertex) {
-	//Before we start searching the shortest path from startVertex, 
+	//Before we start searching the shortest path from startVertex,
 	//we need to clear vertices cache just to be sure that out graph is clean.
-	//Remember that every Vertex is a class and classes are passed by reference. 
+	//Remember that every Vertex is a class and classes are passed by reference.
 	//So whenever you change vertex outside of this class it will affect this vertex inside totalVertices Set
         clearCache()
 	//Now all our vertices have Double.infinity pathLengthFromStart and an empty pathVerticesFromStart array.
-		
+
 	//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
-		
+
 	//Here starts the main part. We will use while loop to iterate through all vertices in the graph.
 	//For this purpose we define currentVertex variable which we will change in the end of each while cycle.
         var currentVertex: Vertex? = startVertex
-		
+
         while let vertex = currentVertex {
-    			
+
     	    //Next line of code is an implementation of setting vertex as visited.
     	    //As it has been said, we should check only unvisited vertices in the graph,
 	    //So why don't just delete it from the set? This approach let us skip checking for *"if !vertex.visited then"*
             totalVertices.remove(vertex)
-			
+
 	    //filteredNeighbours is an array that contains current vertex neighbours which aren't yet visited
             let filteredNeighbours = vertex.neighbours.filter { totalVertices.contains($0.0) }
-			
+
 	    //Let's iterate through them
             for neighbour in filteredNeighbours {
 		//These variable are more representative, than neighbour.0 or neighbour.1
                 let neighbourVertex = neighbour.0
                 let weight = neighbour.1
-				
-		//Here we calculate new weight, that we can offer to neighbour. 
+
+		//Here we calculate new weight, that we can offer to neighbour.
                 let theoreticNewWeight = vertex.pathLengthFromStart + weight
-				
+
 		//If it is smaller than neighbour's current pathLengthFromStart
 		//Then we perform this code
                 if theoreticNewWeight < neighbourVertex.pathLengthFromStart {
-					
+
 		    //set new pathLengthFromStart
                     neighbourVertex.pathLengthFromStart = theoreticNewWeight
-					
+
 		    //set new pathVerticesFromStart
                     neighbourVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
-					
+
 		    //append current vertex to neighbour's pathVerticesFromStart
                     neighbourVertex.pathVerticesFromStart.append(neighbourVertex)
                 }
             }
-			
+
 	    //If totalVertices is empty, i.e. all vertices are visited
 	    //Than break the loop
             if totalVertices.isEmpty {
                 currentVertex = nil
                 break
             }
-			
+
 	    //If loop is not broken, than pick next vertex for checkin from not visited.
 	    //Next vertex pathLengthFromStart should be the smallest one.
             currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }

From 54d4ef15ed6d624e2028795ab3214060e897f380 Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Thu, 19 Oct 2017 03:28:12 +0200
Subject: [PATCH 278/643] rename boyer-moore to boyer-moore-horspool

---
 .../BoyerMooreHorspool.playground}/Contents.swift                 | 0
 .../BoyerMooreHorspool.playground}/contents.xcplayground          | 0
 .../playground.xcworkspace/contents.xcworkspacedata               | 0
 .../BoyerMooreHorspool.playground}/timeline.xctimeline            | 0
 .../BoyerMooreHorspool.swift                                      | 0
 {Boyer-Moore => Boyer-Moore-Horspool}/README.markdown             | 0
 .../Tests/BoyerMooreHorspoolTests.swift                           | 0
 {Boyer-Moore => Boyer-Moore-Horspool}/Tests/BoyerMooreTests.swift | 0
 {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Info.plist            | 0
 .../Tests/Tests.xcodeproj/project.pbxproj                         | 0
 .../Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata  | 0
 .../project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings | 0
 .../Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme   | 0
 13 files changed, 0 insertions(+), 0 deletions(-)
 rename {Boyer-Moore/BoyerMoore.playground => Boyer-Moore-Horspool/BoyerMooreHorspool.playground}/Contents.swift (100%)
 rename {Boyer-Moore/BoyerMoore.playground => Boyer-Moore-Horspool/BoyerMooreHorspool.playground}/contents.xcplayground (100%)
 rename {Boyer-Moore/BoyerMoore.playground => Boyer-Moore-Horspool/BoyerMooreHorspool.playground}/playground.xcworkspace/contents.xcworkspacedata (100%)
 rename {Boyer-Moore/BoyerMoore.playground => Boyer-Moore-Horspool/BoyerMooreHorspool.playground}/timeline.xctimeline (100%)
 rename Boyer-Moore/BoyerMoore.swift => Boyer-Moore-Horspool/BoyerMooreHorspool.swift (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/README.markdown (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/BoyerMooreHorspoolTests.swift (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/BoyerMooreTests.swift (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Info.plist (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Tests.xcodeproj/project.pbxproj (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings (100%)
 rename {Boyer-Moore => Boyer-Moore-Horspool}/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme (100%)

diff --git a/Boyer-Moore/BoyerMoore.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
similarity index 100%
rename from Boyer-Moore/BoyerMoore.playground/Contents.swift
rename to Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
diff --git a/Boyer-Moore/BoyerMoore.playground/contents.xcplayground b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/contents.xcplayground
similarity index 100%
rename from Boyer-Moore/BoyerMoore.playground/contents.xcplayground
rename to Boyer-Moore-Horspool/BoyerMooreHorspool.playground/contents.xcplayground
diff --git a/Boyer-Moore/BoyerMoore.playground/playground.xcworkspace/contents.xcworkspacedata b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Boyer-Moore/BoyerMoore.playground/playground.xcworkspace/contents.xcworkspacedata
rename to Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/contents.xcworkspacedata
diff --git a/Boyer-Moore/BoyerMoore.playground/timeline.xctimeline b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
similarity index 100%
rename from Boyer-Moore/BoyerMoore.playground/timeline.xctimeline
rename to Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
diff --git a/Boyer-Moore/BoyerMoore.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
similarity index 100%
rename from Boyer-Moore/BoyerMoore.swift
rename to Boyer-Moore-Horspool/BoyerMooreHorspool.swift
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore-Horspool/README.markdown
similarity index 100%
rename from Boyer-Moore/README.markdown
rename to Boyer-Moore-Horspool/README.markdown
diff --git a/Boyer-Moore/Tests/BoyerMooreHorspoolTests.swift b/Boyer-Moore-Horspool/Tests/BoyerMooreHorspoolTests.swift
similarity index 100%
rename from Boyer-Moore/Tests/BoyerMooreHorspoolTests.swift
rename to Boyer-Moore-Horspool/Tests/BoyerMooreHorspoolTests.swift
diff --git a/Boyer-Moore/Tests/BoyerMooreTests.swift b/Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift
similarity index 100%
rename from Boyer-Moore/Tests/BoyerMooreTests.swift
rename to Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift
diff --git a/Boyer-Moore/Tests/Info.plist b/Boyer-Moore-Horspool/Tests/Info.plist
similarity index 100%
rename from Boyer-Moore/Tests/Info.plist
rename to Boyer-Moore-Horspool/Tests/Info.plist
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
similarity index 100%
rename from Boyer-Moore/Tests/Tests.xcodeproj/project.pbxproj
rename to Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
rename to Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
similarity index 100%
rename from Boyer-Moore/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
rename to Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
diff --git a/Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
similarity index 100%
rename from Boyer-Moore/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
rename to Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

From 453dcba01ef0c10212ae70f4b02607a258d84f6f Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Fri, 20 Oct 2017 12:26:07 +0200
Subject: [PATCH 279/643] fix tests

---
 .../Tests/Tests.xcodeproj/project.pbxproj     | 23 ++++++-------------
 1 file changed, 7 insertions(+), 16 deletions(-)

diff --git a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
index 6fc005d43..ab93d46a0 100644
--- a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
@@ -8,7 +8,7 @@
 
 /* Begin PBXBuildFile section */
 		7B80C3CE1C77A256003CECC7 /* BoyerMooreTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */; };
-		9AED567C1E0ED6DE00958DCC /* BoyerMoore.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */; };
+		8ED7591C1F9A064A00440D89 /* BoyerMooreHorspool.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8ED7591B1F9A064A00440D89 /* BoyerMooreHorspool.swift */; };
 		9AED56801E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */; };
 /* End PBXBuildFile section */
 
@@ -16,7 +16,7 @@
 		7B2BBC801C779D720067B71D /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
 		7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreTests.swift; sourceTree = SOURCE_ROOT; };
-		9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoyerMoore.swift; path = ../BoyerMoore.swift; sourceTree = SOURCE_ROOT; };
+		8ED7591B1F9A064A00440D89 /* BoyerMooreHorspool.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = BoyerMooreHorspool.swift; path = ../BoyerMooreHorspool.swift; sourceTree = "<group>"; };
 		9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BoyerMooreHorspoolTests.swift; sourceTree = SOURCE_ROOT; };
 /* End PBXFileReference section */
 
@@ -34,7 +34,10 @@
 		7B2BBC681C779D710067B71D = {
 			isa = PBXGroup;
 			children = (
-				7B2BBC831C779D720067B71D /* Tests */,
+				8ED7591B1F9A064A00440D89 /* BoyerMooreHorspool.swift */,
+				7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+				9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */,
 				7B2BBC721C779D710067B71D /* Products */,
 			);
 			sourceTree = "<group>";
@@ -47,18 +50,6 @@
 			name = Products;
 			sourceTree = "<group>";
 		};
-		7B2BBC831C779D720067B71D /* Tests */ = {
-			isa = PBXGroup;
-			children = (
-				9AED567B1E0ED6DE00958DCC /* BoyerMoore.swift */,
-				7B80C3CD1C77A256003CECC7 /* BoyerMooreTests.swift */,
-				7B2BBC941C779E7B0067B71D /* Info.plist */,
-				9AED567F1E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift */,
-			);
-			name = Tests;
-			path = TestsTests;
-			sourceTree = "<group>";
-		};
 /* End PBXGroup section */
 
 /* Begin PBXNativeTarget section */
@@ -145,8 +136,8 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				8ED7591C1F9A064A00440D89 /* BoyerMooreHorspool.swift in Sources */,
 				9AED56801E0EE60B00958DCC /* BoyerMooreHorspoolTests.swift in Sources */,
-				9AED567C1E0ED6DE00958DCC /* BoyerMoore.swift in Sources */,
 				7B80C3CE1C77A256003CECC7 /* BoyerMooreTests.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;

From 1376007baed57cf196abf92b239f12bcca44869d Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Fri, 20 Oct 2017 13:30:44 +0200
Subject: [PATCH 280/643] change test command for boyer-moore-horspool

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index d70eb74b6..5d2a05848 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -12,7 +12,7 @@ script:
 - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Boyer-Moore/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Boyer-Moore-Horspool/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
 - xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests

From 4c9c04e9686c2147fe6a6ff3fafacd488406a758 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sat, 21 Oct 2017 08:52:25 -0700
Subject: [PATCH 281/643] Add syntax color for code

---
 3Sum and 4Sum/README.md | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/3Sum and 4Sum/README.md b/3Sum and 4Sum/README.md
index 5547789c7..188f89109 100644
--- a/3Sum and 4Sum/README.md	
+++ b/3Sum and 4Sum/README.md	
@@ -26,7 +26,7 @@ You'll make use of these two rules to create an efficient algorithm.
 
 Since you pre-sort the array, duplicates will be adjacent to each other. You just need to skip over duplicates by comparing adjacent values:
 
-```
+```swift
 extension Collection where Element: Equatable {
   
   /// In a sorted collection, replaces the given index with a successor mapping to a unique element.
@@ -44,7 +44,7 @@ extension Collection where Element: Equatable {
 
 A similar implementation is used to get the unique index *before* a given index:
 
-```
+```swift
 extension BidirectionalCollection where Element: Equatable {
   
   /// In a sorted collection, replaces the given index with a predecessor that maps to a unique element.
@@ -64,7 +64,7 @@ extension BidirectionalCollection where Element: Equatable {
 
 You'll keep track of 3 indices to represent the 3 numbers. The sum at any given moment is `array[l] + array[m] + array[r]`:
 
-```
+```swift
       m ->      <- r
 [-4, -1, -1, 0, 1, 2]
   l   
@@ -72,7 +72,7 @@ You'll keep track of 3 indices to represent the 3 numbers. The sum at any given
 
 The premise is quite straightforward (given that you're familiar with 2Sum). You'll iterate `l` through the array. For every iteration, you also apply the 2Sum algorithm to elements after `l`. You'll check the sum every time you moving the indices to check if you found match. Here's the algorithm:
 
-```
+```swift
 func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
   let sorted = collection.sorted()
   var ret: [[T.Element]] = []
@@ -110,7 +110,7 @@ func threeSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) ->
 
 Foursum is a very straightforward extension to the threeSum algorithm. In threeSum, you kept track of 3 indices:
 
-```
+```swift
       m ->      <- r
 [-4, -1, -1, 0, 1, 2]
   l   
@@ -118,7 +118,7 @@ Foursum is a very straightforward extension to the threeSum algorithm. In threeS
 
 For fourSum, you'll keep track of 4:
 
-```
+```swift
          mr ->  <- r
 [-4, -1, -1, 0, 1, 2]
   l  ml -> 
@@ -126,7 +126,7 @@ For fourSum, you'll keep track of 4:
 
 Here's the code for it (notice it is very similar to 3Sum):
 
-```
+```swift
 func fourSum<T: BidirectionalCollection>(_ collection: T, target: T.Element) -> [[T.Element]] where T.Element: Numeric & Comparable {
   let sorted = collection.sorted()
   var ret: [[T.Element]] = []

From 2be222849f4dfeb35fd69335fa120965d7dec227 Mon Sep 17 00:00:00 2001
From: Egor Zhdan <egor.zhdan@gmail.com>
Date: Sun, 22 Oct 2017 00:50:15 +0300
Subject: [PATCH 282/643] Fix integer overflow in LCM algorithm

---
 GCD/GCD.playground/Contents.swift | 2 +-
 GCD/GCD.swift                     | 2 +-
 GCD/README.markdown               | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index 977b80f57..f0fceb0da 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -32,7 +32,7 @@ func gcd(m: Int, _ n: Int) -> Int {
 */
 
 func lcm(_ m: Int, _ n: Int) -> Int {
-  return m*n / gcd(m, n)
+  return m / gcd(m, n) * n // we divide before multiplying to avoid integer overflow
 }
 
 gcd(52, 39)       // 13
diff --git a/GCD/GCD.swift b/GCD/GCD.swift
index ce7e7fa78..bd903e58a 100644
--- a/GCD/GCD.swift
+++ b/GCD/GCD.swift
@@ -30,5 +30,5 @@ func gcd(_ a: Int, _ b: Int) -> Int {
   Returns the least common multiple of two numbers.
 */
 func lcm(_ m: Int, _ n: Int) -> Int {
-  return m*n / gcd(m, n)
+  return m / gcd(m, n) * n
 }
diff --git a/GCD/README.markdown b/GCD/README.markdown
index 07d2de1ca..d7e9304bd 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -102,7 +102,7 @@ In code:
 
 ```swift
 func lcm(_ m: Int, _ n: Int) -> Int {
-  return m*n / gcd(m, n)
+  return m / gcd(m, n) * n
 }
 ```
 

From b8d20e6287e25cc9f60acc50c93266f437834fd2 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sat, 21 Oct 2017 22:06:09 -0700
Subject: [PATCH 283/643] Adds links to written tutorials on raywenderlich.com

---
 Binary Search Tree/README.markdown    | 3 +++
 Boyer-Moore-Horspool/README.markdown  | 3 +++
 Breadth-First Search/README.markdown  | 3 +++
 Depth-First Search/README.markdown    | 2 ++
 Graph/README.markdown                 | 3 +++
 Heap/README.markdown                  | 2 ++
 Linked List/README.markdown           | 2 ++
 Merge Sort/README.markdown            | 2 ++
 Minimum Spanning Tree/README.markdown | 2 ++
 Queue/README.markdown                 | 2 ++
 Stack/README.markdown                 | 2 ++
 Tree/README.markdown                  | 3 +++
 Trie/ReadMe.md                        | 2 ++
 13 files changed, 31 insertions(+)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 340a58655..1d9321591 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -1,5 +1,8 @@
 # Binary Search Tree (BST)
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/139821/swift-algorithm-club-swift-binary-search-tree-data-structure)
+
+
 A binary search tree is a special kind of [binary tree](../Binary%20Tree/) (a tree in which each node has at most two children) that performs insertions and deletions such that the tree is always sorted.
 
 For more information about a tree, [read this first](../Tree/).
diff --git a/Boyer-Moore-Horspool/README.markdown b/Boyer-Moore-Horspool/README.markdown
index 5b3841eca..f5e21ea41 100644
--- a/Boyer-Moore-Horspool/README.markdown
+++ b/Boyer-Moore-Horspool/README.markdown
@@ -1,5 +1,8 @@
 # Boyer-Moore String Search
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/163964/swift-algorithm-club-booyer-moore-string-search-algorithm)
+
+
 Goal: Write a string search algorithm in pure Swift without importing Foundation or using `NSString`'s `rangeOfString()` method.
 
 In other words, we want to implement an `indexOf(pattern: String)` extension on `String` that returns the `String.Index` of the first occurrence of the search pattern, or `nil` if the pattern could not be found inside the string.
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 2ef92fd73..b2298822f 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -1,5 +1,8 @@
 # Breadth-First Search
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/155801/swift-algorithm-club-swift-breadth-first-search)
+
+
 Breadth-first search (BFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at a source node and explores the immediate neighbor nodes first, before moving to the next level neighbors.
 
 Breadth-first search can be used on both directed and undirected graphs.
diff --git a/Depth-First Search/README.markdown b/Depth-First Search/README.markdown
index 98a19e0cb..67030346b 100644
--- a/Depth-First Search/README.markdown	
+++ b/Depth-First Search/README.markdown	
@@ -1,5 +1,7 @@
 # Depth-First Search
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/157949/swift-algorithm-club-depth-first-search)
+
 Depth-first search (DFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at a source node and explores as far as possible along each branch before backtracking.
 
 Depth-first search can be used on both directed and undirected graphs.
diff --git a/Graph/README.markdown b/Graph/README.markdown
index d3c8b89e5..1331a07d3 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -1,5 +1,8 @@
 # Graph
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/152046/swift-algorithm-club-graphs-adjacency-list)
+
+
 A graph looks like the following picture:
 
 ![A graph](Images/Graph.png)
diff --git a/Heap/README.markdown b/Heap/README.markdown
index bb7a785a5..49031dcc3 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -1,5 +1,7 @@
 # Heap
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/160631/swift-algorithm-club-heap-and-priority-queue-data-structure)
+
 A heap is a [binary tree](../Binary%20Tree/) inside an array, so it does not use parent/child pointers. A heap is sorted based on the "heap property" that determines the order of the nodes in the tree.
 
 Common uses for heap:
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 240d3fbba..2e1f03ece 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -1,5 +1,7 @@
 # Linked List
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/144083/swift-algorithm-club-swift-linked-list-data-structure)
+
 A linked list is a sequence of data items, just like an array. But where an array allocates a big block of memory to store the objects, the elements in a linked list are totally separate objects in memory and are connected through links:
 
 	+--------+    +--------+    +--------+    +--------+
diff --git a/Merge Sort/README.markdown b/Merge Sort/README.markdown
index 05b90f166..140cfe48f 100644
--- a/Merge Sort/README.markdown	
+++ b/Merge Sort/README.markdown	
@@ -1,5 +1,7 @@
 # Merge Sort
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/154256/swift-algorithm-club-swift-merge-sort)
+
 Goal: Sort an array from low to high (or high to low)
 
 Invented in 1945 by John von Neumann, merge-sort is an efficient algorithm with a best, worst, and average time complexity of **O(n log n)**.
diff --git a/Minimum Spanning Tree/README.markdown b/Minimum Spanning Tree/README.markdown
index c47713701..6ae7a89d9 100644
--- a/Minimum Spanning Tree/README.markdown	
+++ b/Minimum Spanning Tree/README.markdown	
@@ -1,5 +1,7 @@
 # Minimum Spanning Tree (Weighted Graph)
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/169392/swift-algorithm-club-minimum-spanning-tree-with-prims-algorithm)
+
 A [minimum spanning tree](https://en.wikipedia.org/wiki/Minimum_spanning_tree) (MST) of a connected undirected weighted graph has a subset of the edges from the original graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. There can be more than one MSTs of a graph.
 
 There are two popular algorithms to calculate MST of a graph - [Kruskal's algorithm](https://en.wikipedia.org/wiki/Kruskal's_algorithm) and [Prim's algorithm](https://en.wikipedia.org/wiki/Prim's_algorithm). Both algorithms have a total time complexity of `O(ElogE)` where `E` is the number of edges from the original graph.
diff --git a/Queue/README.markdown b/Queue/README.markdown
index 8938e0cf1..ca55f0f28 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -1,5 +1,7 @@
 # Queue
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/148141/swift-algorithm-club-swift-queue-data-structure)
+
 A queue is a list where you can only insert new items at the back and remove items from the front. This ensures that the first item you enqueue is also the first item you dequeue. First come, first serve!
 
 Why would you need this? Well, in many algorithms you want to add objects to a temporary list and pull them off this list later. Often the order in which you add and remove these objects matters.
diff --git a/Stack/README.markdown b/Stack/README.markdown
index 1a3ca2638..b84b585df 100644
--- a/Stack/README.markdown
+++ b/Stack/README.markdown
@@ -1,5 +1,7 @@
 # Stack
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/149213/swift-algorithm-club-swift-stack-data-structure)
+
 A stack is like an array but with limited functionality. You can only *push* to add a new element to the top of the stack, *pop* to remove the element from the top, and *peek* at the top element without popping it off.
 
 Why would you want to do this? Well, in many algorithms you want to add objects to a temporary list at some point and then pull them off this list again at a later time. Often the order in which you add and remove these objects matters.
diff --git a/Tree/README.markdown b/Tree/README.markdown
index 566864a8f..40129cab5 100644
--- a/Tree/README.markdown
+++ b/Tree/README.markdown
@@ -1,5 +1,8 @@
 # Trees
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/138190/swift-algorithm-club-swift-tree-data-structure)
+
+
 A tree represents hierarchical relationships between objects. This is a tree:
 
 ![A tree](Images/Tree.png)
diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 356f6887e..34b9beb9c 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -1,5 +1,7 @@
 # Trie
 
+> This topic has been tutorialized [here](https://www.raywenderlich.com/139410/swift-algorithm-club-swift-trie-data-structure)
+
 ## What is a Trie?
 
 A `Trie`, (also known as a prefix tree, or radix tree in some other implementations) is a special type of tree used to store associative data structures. A `Trie` for a dictionary might look like this:

From 575bacaa6176f0edc84fac83e935c02a627fa677 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Wed, 25 Oct 2017 13:24:30 -0700
Subject: [PATCH 284/643] Fixes the tests.

---
 Depth-First Search/Tests/DepthFirstSearchTests.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Depth-First Search/Tests/DepthFirstSearchTests.swift b/Depth-First Search/Tests/DepthFirstSearchTests.swift
index abf1c19c6..5fb450190 100755
--- a/Depth-First Search/Tests/DepthFirstSearchTests.swift	
+++ b/Depth-First Search/Tests/DepthFirstSearchTests.swift	
@@ -9,7 +9,7 @@ class DepthFirstSearchTests: XCTestCase {
         #endif
     }
     func testExploringTree() {
-        let tree = Digraph()
+        let tree = Graph()
         
         let nodeA = tree.addNode("a")
         let nodeB = tree.addNode("b")
@@ -34,7 +34,7 @@ class DepthFirstSearchTests: XCTestCase {
     }
     
     func testExploringDigraph() {
-        let digraph = Digraph()
+        let digraph = Graph()
         
         let nodeA = digraph.addNode("a")
         let nodeB = digraph.addNode("b")
@@ -81,7 +81,7 @@ class DepthFirstSearchTests: XCTestCase {
     }
     
     func testExploringDigraphWithASingleNode() {
-        let digraph = Digraph()
+        let digraph = Graph()
         let node = digraph.addNode("a")
         
         let nodesExplored = depthFirstSearch(digraph, source: node)

From 4b73295140df7cb645431aeb01b867f944725ef8 Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Thu, 26 Oct 2017 02:21:17 +0200
Subject: [PATCH 285/643] initial points lines planes commit

---
 .../project.pbxproj                           | 296 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../Points Lines Planes/2D/Line2D.swift       | 161 ++++++++++
 .../Points Lines Planes/2D/Point2D.swift      |  40 +++
 .../Points Lines Planes/main.swift            |  24 ++
 Points Lines Planes/README.md                 |  34 ++
 6 files changed, 562 insertions(+)
 create mode 100644 Points Lines Planes/Points Lines Planes.xcodeproj/project.pbxproj
 create mode 100644 Points Lines Planes/Points Lines Planes.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Points Lines Planes/Points Lines Planes/2D/Line2D.swift
 create mode 100644 Points Lines Planes/Points Lines Planes/2D/Point2D.swift
 create mode 100644 Points Lines Planes/Points Lines Planes/main.swift
 create mode 100644 Points Lines Planes/README.md

diff --git a/Points Lines Planes/Points Lines Planes.xcodeproj/project.pbxproj b/Points Lines Planes/Points Lines Planes.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..aeba4777b
--- /dev/null
+++ b/Points Lines Planes/Points Lines Planes.xcodeproj/project.pbxproj	
@@ -0,0 +1,296 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 48;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		8EA8A3BB1F9F7B6300FD8BC0 /* Point2D.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8EA8A3BA1F9F7B6300FD8BC0 /* Point2D.swift */; };
+		8EA8A3BD1F9F7B7100FD8BC0 /* Line2D.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8EA8A3BC1F9F7B7100FD8BC0 /* Line2D.swift */; };
+		8EF612481F9E00E000267358 /* main.swift in Sources */ = {isa = PBXBuildFile; fileRef = 8EF612471F9E00E000267358 /* main.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXCopyFilesBuildPhase section */
+		8EF612421F9E00E000267358 /* CopyFiles */ = {
+			isa = PBXCopyFilesBuildPhase;
+			buildActionMask = 2147483647;
+			dstPath = /usr/share/man/man1/;
+			dstSubfolderSpec = 0;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 1;
+		};
+/* End PBXCopyFilesBuildPhase section */
+
+/* Begin PBXFileReference section */
+		8EA8A3BA1F9F7B6300FD8BC0 /* Point2D.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Point2D.swift; sourceTree = "<group>"; };
+		8EA8A3BC1F9F7B7100FD8BC0 /* Line2D.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Line2D.swift; sourceTree = "<group>"; };
+		8EF612441F9E00E000267358 /* Points Lines Planes */ = {isa = PBXFileReference; explicitFileType = "compiled.mach-o.executable"; includeInIndex = 0; path = "Points Lines Planes"; sourceTree = BUILT_PRODUCTS_DIR; };
+		8EF612471F9E00E000267358 /* main.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = main.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		8EF612411F9E00E000267358 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		8EA8A3C21F9F7C9000FD8BC0 /* 2D */ = {
+			isa = PBXGroup;
+			children = (
+				8EA8A3BA1F9F7B6300FD8BC0 /* Point2D.swift */,
+				8EA8A3BC1F9F7B7100FD8BC0 /* Line2D.swift */,
+			);
+			path = 2D;
+			sourceTree = "<group>";
+		};
+		8EF6123B1F9E00DF00267358 = {
+			isa = PBXGroup;
+			children = (
+				8EF612461F9E00E000267358 /* Points Lines Planes */,
+				8EF612451F9E00E000267358 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		8EF612451F9E00E000267358 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				8EF612441F9E00E000267358 /* Points Lines Planes */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		8EF612461F9E00E000267358 /* Points Lines Planes */ = {
+			isa = PBXGroup;
+			children = (
+				8EF612471F9E00E000267358 /* main.swift */,
+				8EA8A3C21F9F7C9000FD8BC0 /* 2D */,
+			);
+			path = "Points Lines Planes";
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		8EF612431F9E00E000267358 /* Points Lines Planes */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 8EF6124B1F9E00E000267358 /* Build configuration list for PBXNativeTarget "Points Lines Planes" */;
+			buildPhases = (
+				8EF612401F9E00E000267358 /* Sources */,
+				8EF612411F9E00E000267358 /* Frameworks */,
+				8EF612421F9E00E000267358 /* CopyFiles */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = "Points Lines Planes";
+			productName = "Points Lines Planes";
+			productReference = 8EF612441F9E00E000267358 /* Points Lines Planes */;
+			productType = "com.apple.product-type.tool";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		8EF6123C1F9E00DF00267358 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0900;
+				LastUpgradeCheck = 0900;
+				ORGANIZATIONNAME = Workmoose;
+				TargetAttributes = {
+					8EF612431F9E00E000267358 = {
+						CreatedOnToolsVersion = 9.0.1;
+						ProvisioningStyle = Automatic;
+					};
+				};
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+		};
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+			defaultConfigurationName = Release;
+		};
+		8EF6124B1F9E00E000267358 /* Build configuration list for PBXNativeTarget "Points Lines Planes" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				8EF6124C1F9E00E000267358 /* Debug */,
+				8EF6124D1F9E00E000267358 /* Release */,
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+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 8EF6123C1F9E00DF00267358 /* Project object */;
+}
diff --git a/Points Lines Planes/Points Lines Planes.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Points Lines Planes/Points Lines Planes.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..82bfe2b7d
--- /dev/null
+++ b/Points Lines Planes/Points Lines Planes.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Points Lines Planes.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Points Lines Planes/Points Lines Planes/2D/Line2D.swift b/Points Lines Planes/Points Lines Planes/2D/Line2D.swift
new file mode 100644
index 000000000..c92cbdbed
--- /dev/null
+++ b/Points Lines Planes/Points Lines Planes/2D/Line2D.swift	
@@ -0,0 +1,161 @@
+//
+//  Line2D.swift
+//  Points Lines Planes
+//
+//  Created by Jaap Wijnen on 24-10-17.
+//
+
+struct Line2D: Equatable {
+    
+    var slope: Slope
+    var offset: Double
+    var direction: Direction
+    
+    enum Slope: Equatable {
+        case finite(slope: Double)
+        case infinite(offset: Double)
+        
+        static func ==(lhs: Slope, rhs: Slope) -> Bool {
+            switch (lhs, rhs) {
+            case (.finite(let slope1), .finite(let slope2)): return slope1 == slope2
+            case (.infinite(let offset1), .infinite(let offset2)): return offset1 == offset2
+            default: return false
+            }
+        }
+    }
+    
+    enum Direction: Equatable {
+        case increasing
+        case decreasing
+        
+        static func ==(lhs: Direction, rhs: Direction) -> Bool {
+            switch (lhs, rhs) {
+            case (.increasing, .increasing): return true
+            case (.decreasing, .decreasing): return true
+            default: return false
+            }
+        }
+    }
+    
+    init(from p1: Point2D, to p2: Point2D) {
+        if p1 == p2 { fatalError("Points can not be equal when creating a line between them") }
+        if p1.x == p2.x {
+            self.slope = .infinite(offset: p1.x)
+            self.offset = 0
+            self.direction = p1.y < p2.y ? .increasing : .decreasing
+            
+            return
+        }
+        
+        let slope = (p1.y - p2.y)/(p1.x - p2.x)
+        self.slope = .finite(slope: slope)
+        offset = (p1.y + p2.y - slope * (p1.x + p2.x))/2
+        if slope >= 0 {
+            // so a horizontal line going left to right is called increasing
+            self.direction = p1.x < p2.x ? .increasing : .decreasing
+        } else {
+            self.direction = p1.x < p2.x ? .decreasing : .increasing
+        }
+    }
+    
+    fileprivate init(slope: Slope, offset: Double, direction: Direction) {
+        self.slope = slope
+        self.offset = offset
+        self.direction = direction
+    }
+    
+    // returns y coordinate on line for given x
+    func y(at x: Double) -> Double {
+        switch self.slope {
+        case .finite(let slope):
+            return slope * x + self.offset
+        case .infinite:
+            fatalError("y can be anywhere on vertical line")
+        }
+    }
+    
+    // returns x coordinate on line for given y
+    func x(at y: Double) -> Double {
+        switch self.slope {
+        case .finite(let slope):
+            if slope == 0 {
+                fatalError("x can be anywhere on horizontal line")
+            }
+            return (y - self.offset)/slope
+        case .infinite(let offset):
+            return offset
+        }
+    }
+    
+    // finds intersection point between two lines. returns nil when lines don't intersect or lie on top of each other.
+    func intersect(with line: Line2D) -> Point2D? {
+        if self == line { return nil }
+        switch (self.slope, line.slope) {
+        case (.infinite, .infinite):
+            // lines are either parallel or on top of each other.
+            return nil
+        case (.finite(let slope1), .finite(let slope2)):
+            if slope1 == slope2 { return nil } // lines are parallel
+            // lines are not parallel calculate intersection point
+            let x = (line.offset - self.offset)/(slope1 - slope2)
+            let y = (slope1 + slope2) * x + self.offset + line.offset
+            return Point2D(x: x, y: y)
+        case (.infinite(let offset), .finite):
+            // one line is vertical so we only check what y value the other line has at that point
+            let x = offset
+            let y = line.y(at: x)
+            return Point2D(x: x, y: y)
+        case (.finite, .infinite(let offset)):
+            // one line is vertical so we only check what y value the other line has at that point
+            // lines are switched with respect to case above this one
+            let x = offset
+            let y = self.y(at: x)
+            return Point2D(x: x, y: y)
+        }
+    }
+    
+    // returns a line perpendicular to self at the given y coordinate
+    // direction of perpendicular lines always changes clockwise
+    func perpendicularLineAt(y: Double) -> Line2D {
+        return perpendicularLineAt(p: Point2D(x: self.x(at: y), y: y))
+    }
+    
+    // returns a line perpendicular to self at the given x coordinate
+    // direction of perpendicular lines always changes clockwise
+    func perpendicularLineAt(x: Double) -> Line2D {
+        return perpendicularLineAt(p: Point2D(x: x, y: self.y(at: x)))
+    }
+    
+    private func perpendicularLineAt(p: Point2D) -> Line2D {
+        switch self.slope {
+        case .finite(let slope):
+            if slope == 0 {
+                // line is horizontal so new line will be vertical
+                let dir: Direction = self.direction == .increasing ? .decreasing : .increasing
+                return Line2D(slope: .infinite(offset: p.x), offset: 0, direction: dir)
+            }
+            
+            // line is neither horizontal nor vertical
+            // we make a new line through the point p with new slope -1/slope
+            let offset = (slope + 1/slope)*p.x + self.offset
+            
+            // determine direction of new line based on direction of the old line and its slope
+            let dir: Direction
+            switch self.direction {
+            case .increasing:
+                dir = slope > 0 ? .decreasing : .increasing
+            case .decreasing:
+                dir = slope > 0 ? .increasing : .decreasing
+            }
+            return Line2D(slope: .finite(slope: -1/slope), offset: offset, direction: dir)
+        case .infinite:
+            // line is vertical so new line will be horizontal
+            let dir: Direction = self.direction == .increasing ? .increasing : .decreasing
+            return Line2D(slope: .finite(slope: 0), offset: p.y, direction: dir)
+        }
+    }
+    
+    static func ==(lhs: Line2D, rhs: Line2D) -> Bool {
+        return lhs.slope == rhs.slope && lhs.offset == rhs.offset && lhs.direction == rhs.direction
+    }
+}
diff --git a/Points Lines Planes/Points Lines Planes/2D/Point2D.swift b/Points Lines Planes/Points Lines Planes/2D/Point2D.swift
new file mode 100644
index 000000000..f51ffd64d
--- /dev/null
+++ b/Points Lines Planes/Points Lines Planes/2D/Point2D.swift	
@@ -0,0 +1,40 @@
+//
+//  Point2D.swift
+//  Points Lines Planes
+//
+//  Created by Jaap Wijnen on 24-10-17.
+//
+
+struct Point2D: Equatable {
+    var x: Double
+    var y: Double
+    
+    static func ==(lhs: Point2D, rhs: Point2D) -> Bool {
+        return lhs.x == rhs.x && lhs.y == rhs.y
+    }
+    
+    // returns true if point is on or right of line
+    func isRight(of line: Line2D) -> Bool {
+        switch line.slope {
+        case .finite:
+            let y = line.y(at: self.x)
+            switch line.direction {
+            case .increasing:
+                return y >= self.y
+            case .decreasing:
+                return y <= self.y
+            }
+        case .infinite(let offset):
+            switch line.direction {
+            case .increasing:
+                return self.x >= offset
+            case .decreasing:
+                return self.x <= offset
+            }
+        }
+    }
+    
+    func isLeft(of line: Line2D) -> Bool {
+        return !self.isRight(of: line)
+    }
+}
diff --git a/Points Lines Planes/Points Lines Planes/main.swift b/Points Lines Planes/Points Lines Planes/main.swift
new file mode 100644
index 000000000..02137fc9d
--- /dev/null
+++ b/Points Lines Planes/Points Lines Planes/main.swift	
@@ -0,0 +1,24 @@
+//
+//  main.swift
+//  Points Lines Planes
+//
+//  Created by Jaap Wijnen on 23-10-17.
+//
+
+let p0 = Point2D(x: 0, y: 2)
+let p1 = Point2D(x: 1, y: 1)
+let p2 = Point2D(x: 1, y: 3)
+let p3 = Point2D(x: 3, y: 1)
+let p4 = Point2D(x: 3, y: 3)
+
+let horLine = Line2D(from: p1, to: p3)
+let verLine = Line2D(from: p1, to: p2)
+let line45 = Line2D(from: p1, to: p4)
+
+print(horLine.intersect(with: verLine))
+print(p0.isRight(of: line45))
+print(p0.isRight(of: horLine))
+print(p0.isRight(of: verLine))
+let lineperp = horLine.perpendicularLineAt(x: 2)
+print(lineperp)
+
diff --git a/Points Lines Planes/README.md b/Points Lines Planes/README.md
new file mode 100644
index 000000000..23c965978
--- /dev/null
+++ b/Points Lines Planes/README.md	
@@ -0,0 +1,34 @@
+# Points Lines (Planes)
+This implements data structures for points lines and planes(not yet) in (for now) 2D space and a few functions to play around with them. This was originally written to improve on the Convex Hull algorithm but I thought it might be a nice addition in itself. Im planning to add 3D implementations as well.
+
+# implementation
+Two `struct`s are implemented the `Point2D` and `Line2D`.
+
+```
+struct Point2D: {
+  var x: Double
+  var y: double
+}
+```
+
+```
+struct Line2D {
+  var slope: Slope
+  var offset: Double
+  var direction: Direction
+}
+```
+Here `Slope` is an enum to account for vertical lines.
+slope is infinite for vertical lines, offset is the x coordinate where the line crosses the line `y=0`.
+slope is finite for any other line and contains a double with the actual value of the slope.
+```
+enum Slope {
+  case finite(slope: Double)
+  case infinite(offset: Double)
+}
+```
+`Line2D` also contains a `Direction` enum. This is introduced in order to make lines directional in order to be able to determine what is left and right of a certain line. It is `.increasing` if the line points in positive y direction and `.decreasing` if it points in the negative y direction.
+
+`Line2D`'s offset is the the y-coordinate where the line crosses the vertical x=0 line
+
+*Written for the Swift Algorithm Club by Jaap Wijnen.*

From 7f6f5a5a56baa1a1bb6854dd2a29699f1be2c558 Mon Sep 17 00:00:00 2001
From: Jaap Wijnen <wijnen.jaap@gmail.com>
Date: Thu, 26 Oct 2017 02:40:29 +0200
Subject: [PATCH 286/643] typo

---
 Points Lines Planes/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Points Lines Planes/README.md b/Points Lines Planes/README.md
index 23c965978..2d36667ec 100644
--- a/Points Lines Planes/README.md	
+++ b/Points Lines Planes/README.md	
@@ -29,6 +29,6 @@ enum Slope {
 ```
 `Line2D` also contains a `Direction` enum. This is introduced in order to make lines directional in order to be able to determine what is left and right of a certain line. It is `.increasing` if the line points in positive y direction and `.decreasing` if it points in the negative y direction.
 
-`Line2D`'s offset is the the y-coordinate where the line crosses the vertical x=0 line
+`Line2D`'s offset is the the y-coordinate where the line crosses the vertical `x=0` line.
 
 *Written for the Swift Algorithm Club by Jaap Wijnen.*

From 6ca1ad1da1e6c629e164a23c6b5759225f61962e Mon Sep 17 00:00:00 2001
From: Hai Nguyen <aquarchitecture@gmail.com>
Date: Sat, 21 Oct 2017 10:02:08 -0700
Subject: [PATCH 287/643] Add .gfm-render.sh

---
 .travis.yml   |  82 +++++++++++++++++++-------------------
 gfm-render.sh | 106 ++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 149 insertions(+), 39 deletions(-)
 create mode 100755 gfm-render.sh

diff --git a/.travis.yml b/.travis.yml
index 5d2a05848..7cd02c9bc 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,46 +4,50 @@ osx_image: xcode9
 
 install:
 
+- gem install xcpretty-travis-formatter
 # - ./install_swiftlint.sh
 
 script:
 
-- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
-- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Boyer-Moore-Horspool/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests -destination 'platform=iOS Simulator,name=iPhone 7,OS=11.0'
-- xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests
-- xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Singly\ Linked\ List/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Quicksort/Tests/Tests-Quicksort.xcodeproj -scheme Tests-Quicksort
-- xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
-- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests
-- xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests
-- xcodebuild test -project ./Palindromes/Test/Test.xcodeproj -scheme Test
-- xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests
+- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Boyer-Moore-Horspool/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests -destination 'platform=iOS Simulator,name=iPhone 7,OS=11.0' | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Singly\ Linked\ List/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Quicksort/Tests/Tests-Quicksort.xcodeproj -scheme Test-Quicksort | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Palindromes/Test/Test.xcodeproj -scheme Test | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+
+after_success:
+- if [[ "$TRAVIS_BRANCH" == "master" ]]; then ./gfm-render.sh; fi
diff --git a/gfm-render.sh b/gfm-render.sh
new file mode 100755
index 000000000..09c026d55
--- /dev/null
+++ b/gfm-render.sh
@@ -0,0 +1,106 @@
+#!/usr/bin/env bash
+
+# $1 - readme
+function render_markdown_to_html {
+  # escape escaping characters
+  if [[ $(uname) == "Darwin" ]]; then
+    content=$(
+      cat "$1"                                          \
+        | sed 's/\\/\\\\/g'                             \
+        | sed 's/"/\\"/g'                               \
+        | sed $'s/\t/\\\\t/g'                           \
+        | sed -e ':a' -e 'N' -e '$!ba' -e 's/\n/\\\n/g' \
+    )
+  else
+    content=$(
+      cat "$1"                          \
+        | sed 's/\\/\\\\/g'             \
+        | sed 's/"/\\"/g'               \
+        | sed 's/\t/\\t/g'              \
+        | sed ':a;N;$!ba;s/\n/\\n/g'    \
+    )
+  fi
+
+  # network call to GitHub API
+  json="{\"text\":\"$content\",\"mode\":\"gfm\",\"context\":\"$USERNAME/swift-algorithm-club\"}"
+  echo -e "$(curl -s --data "$json" -u $USERNAME:$TOKEN https://api.github.com/markdown)"
+}
+
+# $1 - comment
+function push_to_gh_pages {
+  git checkout -b gh-pages
+  git add .
+  git commit -m "$1"
+  git push -f https://$TOKEN@github.com/$USERNAME/swift-algorithm-club.git gh-pages
+}
+
+# download github systax highlight stylesheet
+echo "> Downloading github-light.css..."
+curl -s -O https://raw.githubusercontent.com/primer/github-syntax-light/master/lib/github-light.css
+
+# if index.html does not exist, create one;
+# otherwise, empty its content.
+if [[ -z index.html ]]; then
+  touch index.html
+else
+  > index.html
+fi
+
+# iterate immediate directories
+find . -maxdepth 1 -type d | while read folder; do
+  readme=''
+
+  # get the right extension for the README file if there is one
+  if [[ -f $folder/README.md ]]; then readme="$folder/README.md"; fi
+  if [[ -f $folder/README.markdown ]]; then readme="$folder/README.markdown"; fi
+
+  # exclude the repository's README
+  if [[ !(-z $readme) && ($readme != "./README.markdown") ]]; then
+    name=$(basename "$folder")
+    echo "> Generating $name/index.html..."
+
+    cat > "$folder/index.html" << EOF
+<!DOCTYPE html>
+<head>
+  <link rel="stylesheet" type="text/css" href="../github-light.css">
+  <style>
+    body {
+      font-size: 18px;
+    }
+    code {
+        padding: 0.2em;
+        margin: 0;
+        font-size: 85%;
+        background-color: #f6f8fa;
+        line-height: 1.45;
+        border-radius: 3px
+    }
+    pre code {
+        padding: 0px;
+        background-color: transparent;
+    }
+    .highlight {
+      margin: 0px;
+      padding: 0px 16px;
+      font-size: 85%;
+      line-height: 1.45;
+      overflow: auto;
+      background-color: #f6f8fa;
+      border-radius: 3px;
+    }
+  </style>
+</head>
+<body>
+    $(render_markdown_to_html "$readme")
+</body>
+</html>
+EOF
+    # temporarily write the list of HTML filenames to the main index.html
+    echo "$lists<li><a href=\"$name/index.html\">$name</a></li>" >> index.html
+  fi
+done
+
+echo "<!DOCTYPE html><body><h1>Swift Algorithm</h1><ul>$(echo -n $(cat index.html))</ul></body></html>" > index.html
+
+# push to gh-pages
+if [[ $CI = true ]]; then push_to_gh_pages "Generated by TravisCI on $(date +%D)"; fi

From b687ab17a53a08bfd5b7cc9814c655be094acef5 Mon Sep 17 00:00:00 2001
From: Volkan Bicer <vlknbcr@gmail.com>
Date: Tue, 31 Oct 2017 23:47:18 +0200
Subject: [PATCH 288/643] Update README.markdown

Boyer-Moore path is wrong.
---
 README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.markdown b/README.markdown
index 42cd23739..b15bd1527 100644
--- a/README.markdown
+++ b/README.markdown
@@ -33,7 +33,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 - [Insertion Sort](Insertion%20Sort/)
 - [Binary Search](Binary%20Search/) and [Binary Search Tree](Binary%20Search%20Tree/)
 - [Merge Sort](Merge%20Sort/)
-- [Boyer-Moore string search](Boyer-Moore/)
+- [Boyer-Moore string search](Boyer-Moore-Horspool/)
 
 ## The algorithms
 
@@ -51,7 +51,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 ### String Search
 
 - [Brute-Force String Search](Brute-Force%20String%20Search/). A naive method.
-- [Boyer-Moore](Boyer-Moore/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
+- [Boyer-Moore](Boyer-Moore-Horspool/). A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
 - [Knuth-Morris-Pratt](Knuth-Morris-Pratt/). A linear-time string algorithm that returns indexes of all occurrencies of a given pattern.
 - [Rabin-Karp](Rabin-Karp/)  Faster search by using hashing.
 - [Longest Common Subsequence](Longest%20Common%20Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.

From e466249391a1b7c8e4a009593eefc45fc14bf5ca Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 9 Nov 2017 00:21:30 +0500
Subject: [PATCH 289/643] Fix the position of the opening brace to conform to
 the style guide

---
 Singly Linked List/README.markdown | 12 ++++--------
 1 file changed, 4 insertions(+), 8 deletions(-)

diff --git a/Singly Linked List/README.markdown b/Singly Linked List/README.markdown
index b3c8b8b2d..6d896db88 100644
--- a/Singly Linked List/README.markdown	
+++ b/Singly Linked List/README.markdown	
@@ -52,10 +52,8 @@ SEARCH
 Collections are sequences, therefore the first step is to conform to the Sequence protocol.
 
 ```
-extension SinglyLinkedList : Sequence
-{
-    public func makeIterator() -> SinglyLinkedListForwardIterator<T>
-    {
+extension SinglyLinkedList: Sequence {
+    public func makeIterator() -> SinglyLinkedListForwardIterator<T> {
         return SinglyLinkedListForwardIterator(head: self.storage.head)
     }
 }
@@ -70,8 +68,7 @@ public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
 
     private(set) var head: SinglyLinkedListNode<T>?
 
-    mutating public func next() -> T?
-    {
+    mutating public func next() -> T? {
         let result = self.head?.value
         self.head = self.head?.next
         return result
@@ -82,8 +79,7 @@ public struct SinglyLinkedListForwardIterator<T> : IteratorProtocol {
 Next, a collection needs to be indexable. Indexes are implemented by the data structure class. We have encapsulated this knowledge in instances of the class `SinglyLinkedListIndex`. 
 
 ```
-public struct SinglyLinkedListIndex<T> : Comparable
-{
+public struct SinglyLinkedListIndex<T>: Comparable {
     fileprivate let node: SinglyLinkedListNode<T>?
     fileprivate let tag: Int
 

From 02395b8cc0a32b7b11dd0cddfc8c4c74360edaff Mon Sep 17 00:00:00 2001
From: Artem Kirillov <artemkirillov@gmail.com>
Date: Fri, 10 Nov 2017 10:27:30 +0400
Subject: [PATCH 290/643] Fix nonconventional parameter naming in Big-O
 notation article

---
 Big-O Notation.markdown | 60 ++++++++++++++++++++---------------------
 1 file changed, 30 insertions(+), 30 deletions(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 78b1808e6..33cdf9465 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -16,21 +16,21 @@ Big-O | Name | Description
 **O(n^3)** | cubic | **Poor performance.** If you have 100 items, this does 100^3 = 1,000,000 units of work. Doubling the input size makes it eight times slower. Example: matrix multiplication.
 **O(2^n)** | exponential | **Very poor performance.** You want to avoid these kinds of algorithms, but sometimes you have no choice. Adding just one bit to the input doubles the running time. Example: traveling salesperson problem.
 **O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.  
-  
+
 
 Below are some examples for each category of performance:
 
 **O(1)**
 
   The most common example with O(1) complexity is accessing an array index.
-  
+
   ```swift
   let value = array[5]
   ```
-    
+
   Another example of O(1) is pushing and popping from Stack.
-  
- 
+
+
 **O(log n)**
 
   ```swift
@@ -40,12 +40,12 @@ Below are some examples for each category of performance:
     j *= 2
   }
   ```  
-  
+
   Instead of simply incrementing, 'j' is increased by 2 times itself in each run.
-  
+
   Binary Search Algorithm is an example of O(log n) complexity.
-  
-  
+
+
 **O(n)**
 
   ```swift
@@ -53,10 +53,10 @@ Below are some examples for each category of performance:
     print(array[i])
   }
   ```
-  
+
   Array Traversal and Linear Search are examples of O(n) complexity.  
-  
-  
+
+
 **O(n log n)**
 
   ```swift
@@ -68,23 +68,23 @@ Below are some examples for each category of performance:
     }
   }
   ```
-  
+
   OR
-  
+
   ```swift
   for i in stride(from: 0, to: n, by: 1) {
     func index(after i: Int) -> Int? { // multiplies `i` by 2 until `i` >= `n`
-      return i < n ? i * 2 : nil 
+      return i < n ? i * 2 : nil
     }
     for j in sequence(first: 1, next: index(after:)) {
       // do constant time stuff
     }
   }
   ```
-  
+
   Merge Sort and Heap Sort are examples of O(n log n) complexity.  
-  
-  
+
+
 **O(n^2)**
 
   ```swift
@@ -94,10 +94,10 @@ Below are some examples for each category of performance:
     }
   }
   ```
-  
+
   Traversing a simple 2-D array and Bubble Sort are examples of O(n^2) complexity.
-  
-  
+
+
 **O(n^3)**
 
   ```swift
@@ -109,24 +109,24 @@ Below are some examples for each category of performance:
     }
   }
   ```  
-  
+
 **O(2^n)**
 
   Algorithms with running time O(2^N) are often recursive algorithms that solve a problem of size N by recursively solving two smaller problems of size N-1.
   The following example prints all the moves necessary to solve the famous "Towers of Hanoi" problem for N disks.
 
   ```swift
-  func solveHanoi(N: Int, from: String, to: String, spare: String) {
+  func solveHanoi(n: Int, from: String, to: String, spare: String) {
     guard n >= 1 else { return }
-    if N > 1 {
-      solveHanoi(N: N - 1, from: from, to: spare, spare: to)
+    if n > 1 {
+      solveHanoi(n: n - 1, from: from, to: spare, spare: to)
     } else {
-      solveHanoi(N: N-1, from: spare, to: to, spare: from)
+      solveHanoi(n: n-1, from: spare, to: to, spare: from)
     }
   }
   ```
-  
-  
+
+
 **O(n!)**
 
   The most trivial example of function that takes O(n!) time is given below.
@@ -137,8 +137,8 @@ Below are some examples for each category of performance:
       nFactFunc(n - 1)
     }
   }
-  ``` 
-  
+  ```
+
 Often you don't need math to figure out what the Big-O of an algorithm is but you can simply use your intuition. If your code uses a single loop that looks at all **n** elements of your input, the algorithm is **O(n)**. If the code has two nested loops, it is **O(n^2)**. Three nested loops gives **O(n^3)**, and so on.
 
 Note that Big-O notation is an estimate and is only really useful for large values of **n**. For example, the worst-case running time for the [insertion sort](Insertion%20Sort/) algorithm is **O(n^2)**. In theory that is worse than the running time for [merge sort](Merge%20Sort/), which is **O(n log n)**. But for small amounts of data, insertion sort is actually faster, especially if the array is partially sorted already!

From d38c428e7f10010562af5500322ca843ddd54e25 Mon Sep 17 00:00:00 2001
From: Artem Kirillov <artemkirillov@gmail.com>
Date: Fri, 10 Nov 2017 10:38:25 +0400
Subject: [PATCH 291/643] Fix spacing in Big-O notation article

---
 Big-O Notation.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 33cdf9465..19a1ddbde 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -121,7 +121,7 @@ Below are some examples for each category of performance:
     if n > 1 {
       solveHanoi(n: n - 1, from: from, to: spare, spare: to)
     } else {
-      solveHanoi(n: n-1, from: spare, to: to, spare: from)
+      solveHanoi(n: n - 1, from: spare, to: to, spare: from)
     }
   }
   ```

From b49331f0d8e387cf21b6be2e4f1e6ebd023c8248 Mon Sep 17 00:00:00 2001
From: Artem Kirillov <artemkirillov@gmail.com>
Date: Fri, 10 Nov 2017 15:06:25 +0400
Subject: [PATCH 292/643] Fix typos in Merge Sort article

---
 Merge Sort/README.markdown | 38 +++++++++++++++++++-------------------
 1 file changed, 19 insertions(+), 19 deletions(-)

diff --git a/Merge Sort/README.markdown b/Merge Sort/README.markdown
index 140cfe48f..7ad6fd95e 100644
--- a/Merge Sort/README.markdown	
+++ b/Merge Sort/README.markdown	
@@ -6,7 +6,7 @@ Goal: Sort an array from low to high (or high to low)
 
 Invented in 1945 by John von Neumann, merge-sort is an efficient algorithm with a best, worst, and average time complexity of **O(n log n)**.
 
-The merge-sort algorithm uses the **divide and conquer** approach which is to divide a big problem into smaller problems and solve them. I think of the merge-sort algorithm as **split first** and **merge after**. 
+The merge-sort algorithm uses the **divide and conquer** approach which is to divide a big problem into smaller problems and solve them. I think of the merge-sort algorithm as **split first** and **merge after**.
 
 Assume you need to sort an array of *n* numbers in the right order. The merge-sort algorithm works as follows:
 
@@ -19,13 +19,13 @@ Assume you need to sort an array of *n* numbers in the right order. The merge-so
 
 ### Splitting
 
-Assume you are given an array of *n* numbers as`[2, 1, 5, 4, 9]`. This is an unsorted pile. The goal is to keep splitting the pile until you cannot split anymore. 
+Assume you are given an array of *n* numbers as`[2, 1, 5, 4, 9]`. This is an unsorted pile. The goal is to keep splitting the pile until you cannot split anymore.
 
 First, split the array into two halves: `[2, 1]` and `[5, 4, 9]`. Can you keep splitting them? Yes, you can!
 
 Focus on the left pile. Split`[2, 1]` into `[2]` and `[1]`. Can you keep splitting them? No. Time to check the other pile.
 
-Split `[5, 4, 9]` into `[5]` and `[4, 9]`. Unsurprisingly, `[5]` cannot be split anymore, but `[4, 9]` can be split into `[4]` and `[9]`. 
+Split `[5, 4, 9]` into `[5]` and `[4, 9]`. Unsurprisingly, `[5]` cannot be split anymore, but `[4, 9]` can be split into `[4]` and `[9]`.
 
 The splitting process ends with the following piles: `[2]` `[1]` `[5]` `[4]` `[9]`. Notice that each pile consists of just one element.
 
@@ -33,11 +33,11 @@ The splitting process ends with the following piles: `[2]` `[1]` `[5]` `[4]` `[9
 
 Now that you have split the array, you should **merge** the piles together **while sorting them**. Remember, the idea is to solve many small problems rather than a big one. For each merge iteration, you must be concerned at merging one pile with another.
 
-Given the piles `[2]` `[1]` `[5]` `[4]` `[9]`, the first pass will result in `[1, 2]` and `[4, 5]` and `[9]`. Since `[9]` is the odd one out, you cannot merge it with anything during this pass. 
+Given the piles `[2]` `[1]` `[5]` `[4]` `[9]`, the first pass will result in `[1, 2]` and `[4, 5]` and `[9]`. Since `[9]` is the odd one out, you cannot merge it with anything during this pass.
 
-The next pass will merge `[1, 2]` and `[4, 5]` together. This results in `[1, 2, 4, 5]`, with the `[9]` left out again because it is the odd one out. 
+The next pass will merge `[1, 2]` and `[4, 5]` together. This results in `[1, 2, 4, 5]`, with the `[9]` left out again because it is the odd one out.
 
-You are left with only two piles and `[9]`, finally gets its chance to merge, resulting in the sorted array as `[1, 2, 4, 5, 9]`. 
+You are left with only two piles `[1, 2, 4, 5]` and `[9]`, finally gets its chance to merge, resulting in the sorted array as `[1, 2, 4, 5, 9]`.
 
 ## Top-down implementation
 
@@ -61,7 +61,7 @@ A step-by-step explanation of how the code works:
 
 1. If the array is empty or contains a single element, there is no way to split it into smaller pieces. You must just return the array.
 
-2. Find the middle index. 
+2. Find the middle index.
 
 3. Using the middle index from the previous step, recursively split the left side of the array.
 
@@ -77,7 +77,7 @@ func merge(leftPile: [Int], rightPile: [Int]) -> [Int] {
   var leftIndex = 0
   var rightIndex = 0
 
-  // 2 
+  // 2
   var orderedPile = [Int]()
 
   // 3
@@ -144,16 +144,16 @@ This process repeats. At each step, we pick the smallest item from either the `l
 	leftPile       rightPile       orderedPile
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ 1, 3, 6 ]
          l              -->r
-	
+
 	leftPile       rightPile       orderedPile
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ 1, 3, 6, 7 ]
          -->l              r
-	
+
 	leftPile       rightPile       orderedPile
 	[ 1, 7, 8 ]    [ 3, 6, 9 ]     [ 1, 3, 6, 7, 8 ]
             -->l           r
 
-Now, there are no more items in the left pile. We simply add the remaining items from the right pile, and we are done. The merged pile is `[ 1, 3, 6, 7, 8, 9 ]`. 
+Now, there are no more items in the left pile. We simply add the remaining items from the right pile, and we are done. The merged pile is `[ 1, 3, 6, 7, 8, 9 ]`.
 
 Notice that, this algorithm is very simple: it moves from left-to-right through the two piles and at every step picks the smallest item. This works because we guarantee that each of the piles is already sorted.
 
@@ -169,20 +169,20 @@ func mergeSortBottomUp<T>(_ a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
   var z = [a, a]      // 1
   var d = 0
-    
+
   var width = 1
   while width < n {   // 2
-  
+
     var i = 0
     while i < n {     // 3
 
       var j = i
       var l = i
       var r = i + width
-      
+
       let lmax = min(l + width, n)
       let rmax = min(r + width, n)
-      
+
       while l < lmax && r < rmax {                // 4
         if isOrderedBefore(z[d][l], z[d][r]) {
           z[1 - d][j] = z[d][l]
@@ -206,7 +206,7 @@ func mergeSortBottomUp<T>(_ a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
       i += width*2
     }
-    
+
     width *= 2
     d = 1 - d      // 5
   }
@@ -239,11 +239,11 @@ mergeSortBottomUp(array, <)   // [1, 2, 4, 5, 9]
 
 ## Performance
 
-The speed of the merge-sort algorithm is dependent on the size of the array it needs to sort. The larger the array, the more work it needs to do. 
+The speed of the merge-sort algorithm is dependent on the size of the array it needs to sort. The larger the array, the more work it needs to do.
 
-Whether or not the initial array is sorted already doesnot affect the speed of the merge-sort algorithm since you will be doing the same amount splits and comparisons regardless of the initial order of the elements.
+Whether or not the initial array is sorted already does not affect the speed of the merge-sort algorithm since you will be doing the same amount splits and comparisons regardless of the initial order of the elements.
 
-Therefore, the time complexity for the best, worst, and average case will always be **O(n log n)**. 
+Therefore, the time complexity for the best, worst, and average case will always be **O(n log n)**.
 
 A disadvantage of the merge-sort algorithm is that it needs a temporary "working" array equal in size to the array being sorted. It is not an **in-place** sort, unlike for example [quicksort](../Quicksort/).
 

From bdedbff97fd610e27ae41c0137e7bdb057e3611f Mon Sep 17 00:00:00 2001
From: Artem Kirillov <artemkirillov@gmail.com>
Date: Fri, 10 Nov 2017 16:26:17 +0400
Subject: [PATCH 293/643] Fix a typo in Selection Sort article

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

diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index daebc64f4..cbcf5d352 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -19,7 +19,7 @@ It works as follows:
 - Find the lowest number in the rest of the array, starting from index 2, and swap it with the one at index 2. Now, the array is sorted from index 0 to 2; this range contains the three lowest numbers in the array.
 - And continue until no numbers remain to be sorted.
 
-It nis called a "selection" sort because at every step you search through the rest of the array to select the next lowest number.
+It is called a "selection" sort because at every step you search through the rest of the array to select the next lowest number.
 
 ## An example
 
@@ -108,7 +108,7 @@ The source file [SelectionSort.swift](SelectionSort.swift) has a version of this
 
 ## Performance
 
-The selection sort is easy to understand but it performs slow as **O(n^2)**. It is worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble%20Sort/). Finding the lowest element in the rest of the array is slow, especially since the inner loop will be performed repeatedly .
+The selection sort is easy to understand but it performs slow as **O(n^2)**. It is worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble%20Sort/). Finding the lowest element in the rest of the array is slow, especially since the inner loop will be performed repeatedly.
 
 The [Heap sort](../Heap%20Sort/) uses the same principle as selection sort but has a fast method for finding the minimum value in the rest of the array. The heap sort' performance is **O(n log n)**.
 

From 5a6e1a70151e0770f20db9412595795cc3a8eec1 Mon Sep 17 00:00:00 2001
From: Jacek Lampart <jlampa@gmail.com>
Date: Sat, 11 Nov 2017 19:25:42 +0000
Subject: [PATCH 294/643] Update README.markdown

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

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 49031dcc3..4344d9e7c 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -27,7 +27,7 @@ As a result of this heap property, a max-heap always stores its largest item at
 
 > **Note:** The root of the heap has the maximum or minimum element, but the sort order of other elements are not predictable. For example, the maximum element is always at index 0 in a max-heap, but the minimum element isn’t necessarily the last one. -- the only guarantee you have is that it is one of the leaf nodes, but not which one.
 
-## How does a heap can be compared to regular trees?
+## How does a heap compare to regular trees?
 
 A heap is not a replacement for a binary search tree, and there are similarities and differnces between them. Here are some main differences:
 

From 02d583e8be5267707a8d37a8e2b3cc68d6bae1c5 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 29 Jul 2017 08:58:05 -0700
Subject: [PATCH 295/643] Improvement of Red Black Tree

* Add count(), allElements(), isEmpty() functions
* Make the config right for RBTree in workspace
* Create a separate class for RBTree
---
 .../Sources/RedBlackTree.swift                | 1347 +++++++++--------
 Red-Black Tree/RedBlackTree.swift             |  795 ++++++++++
 2 files changed, 1491 insertions(+), 651 deletions(-)
 create mode 100644 Red-Black Tree/RedBlackTree.swift

diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index 59633031d..fc0411b42 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -21,730 +21,775 @@
 import Foundation
 
 private enum RBTreeColor {
-  case red
-  case black
+    case red
+    case black
 }
 
 private enum RotationDirection {
-  case left
-  case right
+    case left
+    case right
 }
 
 // MARK: - RBNode
 
 public class RBTreeNode<T: Comparable>: Equatable {
-  public typealias RBNode = RBTreeNode<T>
-  
-  fileprivate var color: RBTreeColor = .black
-  fileprivate var key: T?
-  var leftChild: RBNode?
-  var rightChild: RBNode?
-  fileprivate weak var parent: RBNode?
-  
-  public init(key: T?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
-    self.key = key
-    self.leftChild = leftChild
-    self.rightChild = rightChild
-    self.parent = parent
-    
-    self.leftChild?.parent = self
-    self.rightChild?.parent = self
-  }
-  
-  public convenience init(key: T?) {
-    self.init(key: key, leftChild: RBNode(), rightChild: RBNode(), parent: RBNode())
-  }
-  
-  // For initialising the nullLeaf
-  public convenience init() {
-    self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
-    self.color = .black
-  }
-  
-  var isRoot: Bool {
-    return parent == nil
-  }
-  
-  var isLeaf: Bool {
-    return rightChild == nil && leftChild == nil
-  }
-  
-  var isNullLeaf: Bool {
-    return key == nil && isLeaf && color == .black
-  }
-  
-  var isLeftChild: Bool {
-    return parent?.leftChild === self
-  }
-  
-  var isRightChild: Bool {
-    return parent?.rightChild === self
-  }
-  
-  var grandparent: RBNode? {
-    return parent?.parent
-  }
-  
-  var sibling: RBNode? {
-    if isLeftChild {
-      return parent?.rightChild
-    } else {
-      return parent?.leftChild
-    }
-  }
-  
-  var uncle: RBNode? {
-    return parent?.sibling
-  }
+    public typealias RBNode = RBTreeNode<T>
+    
+    fileprivate var color: RBTreeColor = .black
+    fileprivate var key: T?
+    var leftChild: RBNode?
+    var rightChild: RBNode?
+    fileprivate weak var parent: RBNode?
+    
+    public init(key: T?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
+        self.key = key
+        self.leftChild = leftChild
+        self.rightChild = rightChild
+        self.parent = parent
+        
+        self.leftChild?.parent = self
+        self.rightChild?.parent = self
+    }
+    
+    public convenience init(key: T?) {
+        self.init(key: key, leftChild: RBNode(), rightChild: RBNode(), parent: RBNode())
+    }
+    
+    // For initialising the nullLeaf
+    public convenience init() {
+        self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
+        self.color = .black
+    }
+    
+    var isRoot: Bool {
+        return parent == nil
+    }
+    
+    var isLeaf: Bool {
+        return rightChild == nil && leftChild == nil
+    }
+    
+    var isNullLeaf: Bool {
+        return key == nil && isLeaf && color == .black
+    }
+    
+    var isLeftChild: Bool {
+        return parent?.leftChild === self
+    }
+    
+    var isRightChild: Bool {
+        return parent?.rightChild === self
+    }
+    
+    var grandparent: RBNode? {
+        return parent?.parent
+    }
+    
+    var sibling: RBNode? {
+        if isLeftChild {
+            return parent?.rightChild
+        } else {
+            return parent?.leftChild
+        }
+    }
+    
+    var uncle: RBNode? {
+        return parent?.sibling
+    }
 }
 
 // MARK: - RedBlackTree
 
 public class RedBlackTree<T: Comparable> {
-  public typealias RBNode = RBTreeNode<T>
-  
-  fileprivate(set) var root: RBNode
-  fileprivate(set) var size = 0
-  fileprivate let nullLeaf = RBNode()
-  
-  public init() {
-    root = nullLeaf
-  }
+    public typealias RBNode = RBTreeNode<T>
+    
+    fileprivate(set) var root: RBNode
+    fileprivate(set) var size = 0
+    fileprivate let nullLeaf = RBNode()
+    fileprivate let allowDuplicateNode: Bool
+    
+    public init(_ allowDuplicateNode: Bool = false) {
+        root = nullLeaf
+        self.allowDuplicateNode = allowDuplicateNode
+    }
+}
+
+// MARK: - Size
+
+extension RedBlackTree {
+    public func count() -> Int {
+        return size
+    }
+    
+    public func isEmpty() -> Bool {
+        return size == 0
+    }
+    
+    public func allElements() -> [T] {
+        var nodes: [T] = []
+        
+        getAllElements(node: root, nodes: &nodes)
+        
+        return nodes
+    }
+    
+    private func getAllElements(node: RBTreeNode<T>, nodes: inout [T]) {
+        guard !node.isNullLeaf else {
+            return
+        }
+        
+        if let left = node.leftChild {
+            getAllElements(node: left, nodes: &nodes)
+        }
+        
+        if let key = node.key {
+            nodes.append(key)
+        }
+        
+        if let right = node.rightChild {
+            getAllElements(node: right, nodes: &nodes)
+        }
+    }
 }
 
 // MARK: - Equatable protocol
 
 extension RBTreeNode {
-  static public func == <T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
-    return lhs.key == rhs.key
-  }
+    static public func == <T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
+        return lhs.key == rhs.key
+    }
 }
 
 // MARK: - Finding a nodes successor
 
 extension RBTreeNode {
-  /*
-   * Returns the inorder successor node of a node
-   * The successor is a node with the next larger key value of the current node
-   */
-  public func getSuccessor() -> RBNode? {
-    // If node has right child: successor min of this right tree
-    if let rightChild = self.rightChild {
-      if !rightChild.isNullLeaf {
-        return rightChild.minimum()
-      }
-    }
-    // Else go upward until node left child
-    var currentNode = self
-    var parent = currentNode.parent
-    while currentNode.isRightChild {
-      if let parent = parent {
-        currentNode = parent
-      }
-      parent = currentNode.parent
-    }
-    return parent
-  }
+    /*
+     * Returns the inorder successor node of a node
+     * The successor is a node with the next larger key value of the current node
+     */
+    public func getSuccessor() -> RBNode? {
+        // If node has right child: successor min of this right tree
+        if let rightChild = self.rightChild {
+            if !rightChild.isNullLeaf {
+                return rightChild.minimum()
+            }
+        }
+        // Else go upward until node left child
+        var currentNode = self
+        var parent = currentNode.parent
+        while currentNode.isRightChild {
+            if let parent = parent {
+                currentNode = parent
+            }
+            parent = currentNode.parent
+        }
+        return parent
+    }
 }
 
 // MARK: - Searching
 
 extension RBTreeNode {
-  /*
-   * Returns the node with the minimum key of the current subtree
-   */
-  public func minimum() -> RBNode? {
-    if let leftChild = leftChild {
-      if !leftChild.isNullLeaf {
-        return leftChild.minimum()
-      }
-      return self
-    }
-    return self
-  }
-  
-  /*
-   * Returns the node with the maximum key of the current subtree
-   */
-  public func maximum() -> RBNode? {
-    if let rightChild = rightChild {
-      if !rightChild.isNullLeaf {
-        return rightChild.maximum()
-      }
-      return self
-    }
-    return self
-  }
+    /*
+     * Returns the node with the minimum key of the current subtree
+     */
+    public func minimum() -> RBNode? {
+        if let leftChild = leftChild {
+            if !leftChild.isNullLeaf {
+                return leftChild.minimum()
+            }
+            return self
+        }
+        return self
+    }
+    
+    /*
+     * Returns the node with the maximum key of the current subtree
+     */
+    public func maximum() -> RBNode? {
+        if let rightChild = rightChild {
+            if !rightChild.isNullLeaf {
+                return rightChild.maximum()
+            }
+            return self
+        }
+        return self
+    }
 }
 
 extension RedBlackTree {
-  /*
-   * Returns the node with the given key |input| if existing
-   */
-  public func search(input: T) -> RBNode? {
-    return search(key: input, node: root)
-  }
-  
-  /*
-   * Returns the node with given |key| in subtree of |node|
-   */
-  fileprivate func search(key: T, node: RBNode?) -> RBNode? {
-    // If node nil -> key not found
-    guard let node = node else {
-      return nil
-    }
-    // If node is nullLeaf == semantically same as if nil
-    if !node.isNullLeaf {
-      if let nodeKey = node.key {
-        // Node found
-        if key == nodeKey {
-          return node
-        } else if key < nodeKey {
-          return search(key: key, node: node.leftChild)
-        } else {
-          return search(key: key, node: node.rightChild)
+    /*
+     * Returns the node with the given key |input| if existing
+     */
+    public func search(input: T) -> RBNode? {
+        return search(key: input, node: root)
+    }
+    
+    /*
+     * Returns the node with given |key| in subtree of |node|
+     */
+    fileprivate func search(key: T, node: RBNode?) -> RBNode? {
+        // If node nil -> key not found
+        guard let node = node else {
+            return nil
+        }
+        // If node is nullLeaf == semantically same as if nil
+        if !node.isNullLeaf {
+            if let nodeKey = node.key {
+                // Node found
+                if key == nodeKey {
+                    return node
+                } else if key < nodeKey {
+                    return search(key: key, node: node.leftChild)
+                } else {
+                    return search(key: key, node: node.rightChild)
+                }
+            }
         }
-      }
+        return nil
     }
-    return nil
-  }
 }
 
 // MARK: - Finding maximum and minimum value
 
 extension RedBlackTree {
-  /*
-   * Returns the minimum key value of the whole tree
-   */
-  public func minValue() -> T? {
-    guard let minNode = root.minimum() else {
-      return nil
-    }
-    return minNode.key
-  }
-  
-  /*
-   * Returns the maximum key value of the whole tree
-   */
-  public func maxValue() -> T? {
-    guard let maxNode = root.maximum() else {
-      return nil
-    }
-    return maxNode.key
-  }
+    /*
+     * Returns the minimum key value of the whole tree
+     */
+    public func minValue() -> T? {
+        guard let minNode = root.minimum() else {
+            return nil
+        }
+        return minNode.key
+    }
+    
+    /*
+     * Returns the maximum key value of the whole tree
+     */
+    public func maxValue() -> T? {
+        guard let maxNode = root.maximum() else {
+            return nil
+        }
+        return maxNode.key
+    }
 }
 
 // MARK: - Inserting new nodes
 
 extension RedBlackTree {
-  /*
-   * Insert a node with key |key| into the tree
-   * 1. Perform normal insert operation as in a binary search tree
-   * 2. Fix red-black properties
-   * Runntime: O(log n)
-   */
-  public func insert(key: T) {
-    if root.isNullLeaf {
-      root = RBNode(key: key)
-    } else {
-      insert(input: RBNode(key: key), node: root)
-    }
-    
-    size += 1
-  }
-  
-  /*
-   * Nearly identical insert operation as in a binary search tree
-   * Differences: All nil pointers are replaced by the nullLeaf, we color the inserted node red,
-   * after inserting we call insertFixup to maintain the red-black properties
-   */
-  private func insert(input: RBNode, node: RBNode) {
-    guard let inputKey = input.key, let nodeKey = node.key else {
-        return
-    }
-    if inputKey < nodeKey {
-      guard let child = node.leftChild else {
-        addAsLeftChild(child: input, parent: node)
-        return
-      }
-      if child.isNullLeaf {
-        addAsLeftChild(child: input, parent: node)
-      } else {
-        insert(input: input, node: child)
-      }
-    } else {
-      guard let child = node.rightChild else {
-        addAsRightChild(child: input, parent: node)
-        return
-      }
-      if child.isNullLeaf {
-        addAsRightChild(child: input, parent: node)
-      } else {
-        insert(input: input, node: child)
-      }
-    }
-  }
-  
-  private func addAsLeftChild(child: RBNode, parent: RBNode) {
-    parent.leftChild = child
-    child.parent = parent
-    child.color = .red
-    insertFixup(node: child)
-  }
-  
-  private func addAsRightChild(child: RBNode, parent: RBNode) {
-    parent.rightChild = child
-    child.parent = parent
-    child.color = .red
-    insertFixup(node: child)
-  }
-  
-  /*
-   * Fixes possible violations of the red-black property after insertion
-   * Only violation of red-black properties occurs at inserted node |z| and z.parent
-   * We have 3 distinct cases: case 1, 2a and 2b
-   * - case 1: may repeat, but only h/2 steps, where h is the height of the tree
-   * - case 2a -> case 2b -> red-black tree
-   * - case 2b -> red-black tree
-   */
-  private func insertFixup(node z: RBNode) {
-    if !z.isNullLeaf {
-      guard let parentZ = z.parent else {
-        return
-      }
-      // If both |z| and his parent are red -> violation of red-black property -> need to fix it
-      if parentZ.color == .red {
-        guard let uncle = z.uncle else {
-          return
-        }
-        // Case 1: Uncle red -> recolor + move z
-        if uncle.color == .red {
-          parentZ.color = .black
-          uncle.color = .black
-          if let grandparentZ = parentZ.parent {
-            grandparentZ.color = .red
-            // Move z to grandparent and check again
-            insertFixup(node: grandparentZ)
-          }
-        }
-        // Case 2: Uncle black
-        else {
-          var zNew = z
-          // Case 2.a: z right child -> rotate
-          if parentZ.isLeftChild && z.isRightChild {
-            zNew = parentZ
-            leftRotate(node: zNew)
-          } else if parentZ.isRightChild && z.isLeftChild {
-            zNew = parentZ
-            rightRotate(node: zNew)
-          }
-          // Case 2.b: z left child -> recolor + rotate
-          zNew.parent?.color = .black
-          if let grandparentZnew = zNew.grandparent {
-            grandparentZnew.color = .red
-            if z.isLeftChild {
-              rightRotate(node: grandparentZnew)
+    /*
+     * Insert a node with key |key| into the tree
+     * 1. Perform normal insert operation as in a binary search tree
+     * 2. Fix red-black properties
+     * Runntime: O(log n)
+     */
+    public func insert(key: T) {
+        // If key must be unique and find the key already existed, quit
+        if search(input: key) != nil && !allowDuplicateNode {
+            return
+        }
+        
+        if root.isNullLeaf {
+            root = RBNode(key: key)
+        } else {
+            insert(input: RBNode(key: key), node: root)
+        }
+        
+        size += 1
+    }
+    
+    /*
+     * Nearly identical insert operation as in a binary search tree
+     * Differences: All nil pointers are replaced by the nullLeaf, we color the inserted node red,
+     * after inserting we call insertFixup to maintain the red-black properties
+     */
+    private func insert(input: RBNode, node: RBNode) {
+        guard let inputKey = input.key, let nodeKey = node.key else {
+            return
+        }
+        if inputKey < nodeKey {
+            guard let child = node.leftChild else {
+                addAsLeftChild(child: input, parent: node)
+                return
+            }
+            if child.isNullLeaf {
+                addAsLeftChild(child: input, parent: node)
+            } else {
+                insert(input: input, node: child)
+            }
+        } else {
+            guard let child = node.rightChild else {
+                addAsRightChild(child: input, parent: node)
+                return
+            }
+            if child.isNullLeaf {
+                addAsRightChild(child: input, parent: node)
             } else {
-              leftRotate(node: grandparentZnew)
+                insert(input: input, node: child)
             }
-            // We have a valid red-black-tree
-          }
         }
-      }
     }
-    root.color = .black
-  }
+    
+    private func addAsLeftChild(child: RBNode, parent: RBNode) {
+        parent.leftChild = child
+        child.parent = parent
+        child.color = .red
+        insertFixup(node: child)
+    }
+    
+    private func addAsRightChild(child: RBNode, parent: RBNode) {
+        parent.rightChild = child
+        child.parent = parent
+        child.color = .red
+        insertFixup(node: child)
+    }
+    
+    /*
+     * Fixes possible violations of the red-black property after insertion
+     * Only violation of red-black properties occurs at inserted node |z| and z.parent
+     * We have 3 distinct cases: case 1, 2a and 2b
+     * - case 1: may repeat, but only h/2 steps, where h is the height of the tree
+     * - case 2a -> case 2b -> red-black tree
+     * - case 2b -> red-black tree
+     */
+    private func insertFixup(node z: RBNode) {
+        if !z.isNullLeaf {
+            guard let parentZ = z.parent else {
+                return
+            }
+            // If both |z| and his parent are red -> violation of red-black property -> need to fix it
+            if parentZ.color == .red {
+                guard let uncle = z.uncle else {
+                    return
+                }
+                // Case 1: Uncle red -> recolor + move z
+                if uncle.color == .red {
+                    parentZ.color = .black
+                    uncle.color = .black
+                    if let grandparentZ = parentZ.parent {
+                        grandparentZ.color = .red
+                        // Move z to grandparent and check again
+                        insertFixup(node: grandparentZ)
+                    }
+                }
+                    // Case 2: Uncle black
+                else {
+                    var zNew = z
+                    // Case 2.a: z right child -> rotate
+                    if parentZ.isLeftChild && z.isRightChild {
+                        zNew = parentZ
+                        leftRotate(node: zNew)
+                    } else if parentZ.isRightChild && z.isLeftChild {
+                        zNew = parentZ
+                        rightRotate(node: zNew)
+                    }
+                    // Case 2.b: z left child -> recolor + rotate
+                    zNew.parent?.color = .black
+                    if let grandparentZnew = zNew.grandparent {
+                        grandparentZnew.color = .red
+                        if z.isLeftChild {
+                            rightRotate(node: grandparentZnew)
+                        } else {
+                            leftRotate(node: grandparentZnew)
+                        }
+                        // We have a valid red-black-tree
+                    }
+                }
+            }
+        }
+        root.color = .black
+    }
 }
 
 // MARK: - Deleting a node
 extension RedBlackTree {
-  /*
-   * Delete a node with key |key| from the tree
-   * 1. Perform standard delete operation as in a binary search tree
-   * 2. Fix red-black properties
-   * Runntime: O(log n)
-   */
-  public func delete(key: T) {
-    if size == 1 {
-      root = nullLeaf
-      size -= 1
-    } else if let node = search(key: key, node: root) {
-      if !node.isNullLeaf {
-        delete(node: node)
-        size -= 1
-      }
-    }
-  }
-  
-  /*
-   * Nearly identical delete operation as in a binary search tree
-   * Differences: All nil pointers are replaced by the nullLeaf,
-   * after deleting we call insertFixup to maintain the red-black properties if the delted node was
-   * black (as if it was red -> no violation of red-black properties)
-   */
-  private func delete(node z: RBNode) {
-    var nodeY = RBNode()
-    var nodeX = RBNode()
-    if let leftChild = z.leftChild, let rightChild = z.rightChild {
-      if leftChild.isNullLeaf || rightChild.isNullLeaf {
-        nodeY = z
-      } else {
-        if let successor = z.getSuccessor() {
-          nodeY = successor
-        }
-      }
-    }
-    if let leftChild = nodeY.leftChild {
-      if !leftChild.isNullLeaf {
-        nodeX = leftChild
-      } else if let rightChild = nodeY.rightChild {
-        nodeX = rightChild
-      }
-    }
-    nodeX.parent = nodeY.parent
-    if let parentY = nodeY.parent {
-      // Should never be the case, as parent of root = nil
-      if parentY.isNullLeaf {
-        root = nodeX
-      } else {
-        if nodeY.isLeftChild {
-          parentY.leftChild = nodeX
+    /*
+     * Delete a node with key |key| from the tree
+     * 1. Perform standard delete operation as in a binary search tree
+     * 2. Fix red-black properties
+     * Runntime: O(log n)
+     */
+    public func delete(key: T) {
+        if size == 1 {
+            root = nullLeaf
+            size -= 1
+        } else if let node = search(key: key, node: root) {
+            if !node.isNullLeaf {
+                delete(node: node)
+                size -= 1
+            }
+        }
+    }
+    
+    /*
+     * Nearly identical delete operation as in a binary search tree
+     * Differences: All nil pointers are replaced by the nullLeaf,
+     * after deleting we call insertFixup to maintain the red-black properties if the delted node was
+     * black (as if it was red -> no violation of red-black properties)
+     */
+    private func delete(node z: RBNode) {
+        var nodeY = RBNode()
+        var nodeX = RBNode()
+        if let leftChild = z.leftChild, let rightChild = z.rightChild {
+            if leftChild.isNullLeaf || rightChild.isNullLeaf {
+                nodeY = z
+            } else {
+                if let successor = z.getSuccessor() {
+                    nodeY = successor
+                }
+            }
+        }
+        if let leftChild = nodeY.leftChild {
+            if !leftChild.isNullLeaf {
+                nodeX = leftChild
+            } else if let rightChild = nodeY.rightChild {
+                nodeX = rightChild
+            }
+        }
+        nodeX.parent = nodeY.parent
+        if let parentY = nodeY.parent {
+            // Should never be the case, as parent of root = nil
+            if parentY.isNullLeaf {
+                root = nodeX
+            } else {
+                if nodeY.isLeftChild {
+                    parentY.leftChild = nodeX
+                } else {
+                    parentY.rightChild = nodeX
+                }
+            }
         } else {
-          parentY.rightChild = nodeX
-        }
-      }
-    } else {
-      root = nodeX
-    }
-    if nodeY != z {
-      z.key = nodeY.key
-    }
-    // If sliced out node was red -> nothing to do as red-black-property holds
-    // If it was black -> fix red-black-property
-    if nodeY.color == .black {
-      deleteFixup(node: nodeX)
-    }
-  }
-  
-  /*
-   * Fixes possible violations of the red-black property after deletion
-   * We have w distinct cases: only case 2 may repeat, but only h many steps, where h is the height 
-   * of the tree
-   * - case 1 -> case 2 -> red-black tree
-   *   case 1 -> case 3 -> case 4 -> red-black tree
-   *   case 1 -> case 4 -> red-black tree
-   * - case 3 -> case 4 -> red-black tree
-   * - case 4 -> red-black tree
-   */
-  private func deleteFixup(node x: RBNode) {
-    var xTmp = x
-    if !x.isRoot && x.color == .black {
-      guard var sibling = x.sibling else {
-        return
-      }
-      // Case 1: Sibling of x is red
-      if sibling.color == .red {
-        // Recolor
-        sibling.color = .black
-        if let parentX = x.parent {
-          parentX.color = .red
-          // Rotation
-          if x.isLeftChild {
-            leftRotate(node: parentX)
-          } else {
-            rightRotate(node: parentX)
-          }
-          // Update sibling
-          if let sibl = x.sibling {
-            sibling = sibl
-          }
-        }
-      }
-      // Case 2: Sibling is black with two black children
-      if sibling.leftChild?.color == .black && sibling.rightChild?.color == .black {
-        // Recolor
-        sibling.color = .red
-        // Move fake black unit upwards
-        if let parentX = x.parent {
-          deleteFixup(node: parentX)
-        }
-        // We have a valid red-black-tree
-      } else {
-        // Case 3: a. Sibling black with one black child to the right
-        if x.isLeftChild && sibling.rightChild?.color == .black {
-          // Recolor
-          sibling.leftChild?.color = .black
-          sibling.color = .red
-          // Rotate
-          rightRotate(node: sibling)
-          // Update sibling of x
-          if let sibl = x.sibling {
-            sibling = sibl
-          }
-        }
-        // Still case 3: b. One black child to the left
-        else if x.isRightChild && sibling.leftChild?.color == .black {
-          // Recolor
-          sibling.rightChild?.color = .black
-          sibling.color = .red
-          // Rotate
-          leftRotate(node: sibling)
-          // Update sibling of x
-          if let sibl = x.sibling {
-            sibling = sibl
-          }
-        }
-        // Case 4: Sibling is black with red right child
-        // Recolor
-        if let parentX = x.parent {
-          sibling.color = parentX.color
-          parentX.color = .black
-          // a. x left and sibling with red right child
-          if x.isLeftChild {
-            sibling.rightChild?.color = .black
-            // Rotate
-            leftRotate(node: parentX)
-          }
-          // b. x right and sibling with red left child
-          else {
-            sibling.leftChild?.color = .black
-            //Rotate
-            rightRotate(node: parentX)
-          }
-          // We have a valid red-black-tree
-          xTmp = root
-        }
-      }
-    }
-    xTmp.color = .black
-  }
+            root = nodeX
+        }
+        if nodeY != z {
+            z.key = nodeY.key
+        }
+        // If sliced out node was red -> nothing to do as red-black-property holds
+        // If it was black -> fix red-black-property
+        if nodeY.color == .black {
+            deleteFixup(node: nodeX)
+        }
+    }
+    
+    /*
+     * Fixes possible violations of the red-black property after deletion
+     * We have w distinct cases: only case 2 may repeat, but only h many steps, where h is the height
+     * of the tree
+     * - case 1 -> case 2 -> red-black tree
+     *   case 1 -> case 3 -> case 4 -> red-black tree
+     *   case 1 -> case 4 -> red-black tree
+     * - case 3 -> case 4 -> red-black tree
+     * - case 4 -> red-black tree
+     */
+    private func deleteFixup(node x: RBNode) {
+        var xTmp = x
+        if !x.isRoot && x.color == .black {
+            guard var sibling = x.sibling else {
+                return
+            }
+            // Case 1: Sibling of x is red
+            if sibling.color == .red {
+                // Recolor
+                sibling.color = .black
+                if let parentX = x.parent {
+                    parentX.color = .red
+                    // Rotation
+                    if x.isLeftChild {
+                        leftRotate(node: parentX)
+                    } else {
+                        rightRotate(node: parentX)
+                    }
+                    // Update sibling
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+            }
+            // Case 2: Sibling is black with two black children
+            if sibling.leftChild?.color == .black && sibling.rightChild?.color == .black {
+                // Recolor
+                sibling.color = .red
+                // Move fake black unit upwards
+                if let parentX = x.parent {
+                    deleteFixup(node: parentX)
+                }
+                // We have a valid red-black-tree
+            } else {
+                // Case 3: a. Sibling black with one black child to the right
+                if x.isLeftChild && sibling.rightChild?.color == .black {
+                    // Recolor
+                    sibling.leftChild?.color = .black
+                    sibling.color = .red
+                    // Rotate
+                    rightRotate(node: sibling)
+                    // Update sibling of x
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+                    // Still case 3: b. One black child to the left
+                else if x.isRightChild && sibling.leftChild?.color == .black {
+                    // Recolor
+                    sibling.rightChild?.color = .black
+                    sibling.color = .red
+                    // Rotate
+                    leftRotate(node: sibling)
+                    // Update sibling of x
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+                // Case 4: Sibling is black with red right child
+                // Recolor
+                if let parentX = x.parent {
+                    sibling.color = parentX.color
+                    parentX.color = .black
+                    // a. x left and sibling with red right child
+                    if x.isLeftChild {
+                        sibling.rightChild?.color = .black
+                        // Rotate
+                        leftRotate(node: parentX)
+                    }
+                        // b. x right and sibling with red left child
+                    else {
+                        sibling.leftChild?.color = .black
+                        //Rotate
+                        rightRotate(node: parentX)
+                    }
+                    // We have a valid red-black-tree
+                    xTmp = root
+                }
+            }
+        }
+        xTmp.color = .black
+    }
 }
 
 // MARK: - Rotation
 extension RedBlackTree {
-  /*
-   * Left rotation around node x
-   * Assumes that x.rightChild y is not a nullLeaf, rotates around the link from x to y,
-   * makes y the new root of the subtree with x as y's left child and y's left child as x's right 
-   * child, where n = a node, [n] = a subtree
-   *     |                |
-   *     x                y
-   *   /   \     ~>     /   \
-   * [A]    y          x    [C]
-   *       / \        / \
-   *     [B] [C]    [A] [B]
-   */
-  fileprivate func leftRotate(node x: RBNode) {
-    rotate(node: x, direction: .left)
-  }
-  
-  /*
-   * Right rotation around node y
-   * Assumes that y.leftChild x is not a nullLeaf, rotates around the link from y to x,
-   * makes x the new root of the subtree with y as x's right child and x's right child as y's left
-   * child, where n = a node, [n] = a subtree
-   *     |                |
-   *     x                y
-   *   /   \     <~     /   \
-   * [A]    y          x    [C]
-   *       / \        / \
-   *     [B] [C]    [A] [B]
-   */
-  fileprivate func rightRotate(node x: RBNode) {
-    rotate(node: x, direction: .right)
-  }
-  
-  /*
-   * Rotation around a node x
-   * Is a local operation preserving the binary-search-tree property that only exchanges pointers.
-   * Runntime: O(1)
-   */
-  private func rotate(node x: RBNode, direction: RotationDirection) {
-    var nodeY: RBNode? = RBNode()
-    
-    // Set |nodeY| and turn |nodeY|'s left/right subtree into |x|'s right/left subtree
-    switch direction {
-    case .left:
-      nodeY = x.rightChild
-      x.rightChild = nodeY?.leftChild
-      x.rightChild?.parent = x
-    case .right:
-      nodeY = x.leftChild
-      x.leftChild = nodeY?.rightChild
-      x.leftChild?.parent = x
-    }
-    
-    // Link |x|'s parent to nodeY
-    nodeY?.parent = x.parent
-    if x.isRoot {
-      if let node = nodeY {
-        root = node
-      }
-    } else if x.isLeftChild {
-      x.parent?.leftChild = nodeY
-    } else if x.isRightChild {
-      x.parent?.rightChild = nodeY
-    }
-    
-    // Put |x| on |nodeY|'s left
-    switch direction {
-    case .left:
-      nodeY?.leftChild = x
-    case .right:
-      nodeY?.rightChild = x
-    }
-    x.parent = nodeY
-  }
+    /*
+     * Left rotation around node x
+     * Assumes that x.rightChild y is not a nullLeaf, rotates around the link from x to y,
+     * makes y the new root of the subtree with x as y's left child and y's left child as x's right
+     * child, where n = a node, [n] = a subtree
+     *     |                |
+     *     x                y
+     *   /   \     ~>     /   \
+     * [A]    y          x    [C]
+     *       / \        / \
+     *     [B] [C]    [A] [B]
+     */
+    fileprivate func leftRotate(node x: RBNode) {
+        rotate(node: x, direction: .left)
+    }
+    
+    /*
+     * Right rotation around node y
+     * Assumes that y.leftChild x is not a nullLeaf, rotates around the link from y to x,
+     * makes x the new root of the subtree with y as x's right child and x's right child as y's left
+     * child, where n = a node, [n] = a subtree
+     *     |                |
+     *     x                y
+     *   /   \     <~     /   \
+     * [A]    y          x    [C]
+     *       / \        / \
+     *     [B] [C]    [A] [B]
+     */
+    fileprivate func rightRotate(node x: RBNode) {
+        rotate(node: x, direction: .right)
+    }
+    
+    /*
+     * Rotation around a node x
+     * Is a local operation preserving the binary-search-tree property that only exchanges pointers.
+     * Runntime: O(1)
+     */
+    private func rotate(node x: RBNode, direction: RotationDirection) {
+        var nodeY: RBNode? = RBNode()
+        
+        // Set |nodeY| and turn |nodeY|'s left/right subtree into |x|'s right/left subtree
+        switch direction {
+        case .left:
+            nodeY = x.rightChild
+            x.rightChild = nodeY?.leftChild
+            x.rightChild?.parent = x
+        case .right:
+            nodeY = x.leftChild
+            x.leftChild = nodeY?.rightChild
+            x.leftChild?.parent = x
+        }
+        
+        // Link |x|'s parent to nodeY
+        nodeY?.parent = x.parent
+        if x.isRoot {
+            if let node = nodeY {
+                root = node
+            }
+        } else if x.isLeftChild {
+            x.parent?.leftChild = nodeY
+        } else if x.isRightChild {
+            x.parent?.rightChild = nodeY
+        }
+        
+        // Put |x| on |nodeY|'s left
+        switch direction {
+        case .left:
+            nodeY?.leftChild = x
+        case .right:
+            nodeY?.rightChild = x
+        }
+        x.parent = nodeY
+    }
 }
 
 // MARK: - Verify
 extension RedBlackTree {
-  /*
-   * Verifies that the existing tree fulfills all red-black properties
-   * Returns true if the tree is a valid red-black tree, false otherwise
-   */
-  public func verify() -> Bool {
-    if root.isNullLeaf {
-      print("The tree is empty")
-      return true
-    }
-    return property2() && property4() && property5()
-  }
-  
-  // Property 1: Every node is either red or black -> fullfilled through setting node.color of type
-  // RBTreeColor
-  
-  // Property 2: The root is black
-  private func property2() -> Bool {
-    if root.color == .red {
-      print("Property-Error: Root is red")
-      return false
-    }
-    return true
-  }
-  
-  // Property 3: Every nullLeaf is black -> fullfilled through initialising nullLeafs with color = black
-  
-  // Property 4: If a node is red, then both its children are black
-  private func property4() -> Bool {
-    return property4(node: root)
-  }
-  
-  private func property4(node: RBNode) -> Bool {
-    if node.isNullLeaf {
-      return true
-    }
-    if let leftChild = node.leftChild, let rightChild = node.rightChild {
-      if node.color == .red {
-        if !leftChild.isNullLeaf && leftChild.color == .red {
-            print("Property-Error: Red node with key \(String(describing: node.key)) has red left child")
-          return false
-        }
-        if !rightChild.isNullLeaf && rightChild.color == .red {
-          print("Property-Error: Red node with key \(String(describing: node.key)) has red right child")
-          return false
-        }
-      }
-      return property4(node: leftChild) && property4(node: rightChild)
-    }
-    return false
-  }
-  
-  // Property 5: For each node, all paths from the node to descendant leaves contain the same number
-  // of black nodes (same blackheight)
-  private func property5() -> Bool {
-    if property5(node: root) == -1 {
-      return false
-    } else {
-      return true
-    }
-  }
-  
-  private func property5(node: RBNode) -> Int {
-    if node.isNullLeaf {
-      return 0
-    }
-    guard let leftChild = node.leftChild, let rightChild = node.rightChild else {
-      return -1
-    }
-    let left = property5(node: leftChild)
-    let right = property5(node: rightChild)
-    
-    if left == -1 || right == -1 {
-      return -1
-    } else if left == right {
-      let addedHeight = node.color == .black ? 1 : 0
-      return left + addedHeight
-    } else {
-      print("Property-Error: Black height violated at node with key \(String(describing: node.key))")
-      return -1
-    }
-  }
+    /*
+     * Verifies that the existing tree fulfills all red-black properties
+     * Returns true if the tree is a valid red-black tree, false otherwise
+     */
+    public func verify() -> Bool {
+        if root.isNullLeaf {
+            print("The tree is empty")
+            return true
+        }
+        return property2() && property4() && property5()
+    }
+    
+    // Property 1: Every node is either red or black -> fullfilled through setting node.color of type
+    // RBTreeColor
+    
+    // Property 2: The root is black
+    private func property2() -> Bool {
+        if root.color == .red {
+            print("Property-Error: Root is red")
+            return false
+        }
+        return true
+    }
+    
+    // Property 3: Every nullLeaf is black -> fullfilled through initialising nullLeafs with color = black
+    
+    // Property 4: If a node is red, then both its children are black
+    private func property4() -> Bool {
+        return property4(node: root)
+    }
+    
+    private func property4(node: RBNode) -> Bool {
+        if node.isNullLeaf {
+            return true
+        }
+        if let leftChild = node.leftChild, let rightChild = node.rightChild {
+            if node.color == .red {
+                if !leftChild.isNullLeaf && leftChild.color == .red {
+                    print("Property-Error: Red node with key \(String(describing: node.key)) has red left child")
+                    return false
+                }
+                if !rightChild.isNullLeaf && rightChild.color == .red {
+                    print("Property-Error: Red node with key \(String(describing: node.key)) has red right child")
+                    return false
+                }
+            }
+            return property4(node: leftChild) && property4(node: rightChild)
+        }
+        return false
+    }
+    
+    // Property 5: For each node, all paths from the node to descendant leaves contain the same number
+    // of black nodes (same blackheight)
+    private func property5() -> Bool {
+        if property5(node: root) == -1 {
+            return false
+        } else {
+            return true
+        }
+    }
+    
+    private func property5(node: RBNode) -> Int {
+        if node.isNullLeaf {
+            return 0
+        }
+        guard let leftChild = node.leftChild, let rightChild = node.rightChild else {
+            return -1
+        }
+        let left = property5(node: leftChild)
+        let right = property5(node: rightChild)
+        
+        if left == -1 || right == -1 {
+            return -1
+        } else if left == right {
+            let addedHeight = node.color == .black ? 1 : 0
+            return left + addedHeight
+        } else {
+            print("Property-Error: Black height violated at node with key \(String(describing: node.key))")
+            return -1
+        }
+    }
 }
 
 // MARK: - Debugging
 
 extension RBTreeNode: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    var s = ""
-    if isNullLeaf {
-      s = "nullLeaf"
-    } else {
-      if let key = key {
-        s = "key: \(key)"
-      } else {
-        s = "key: nil"
-      }
-      if let parent = parent {
-        s += ", parent: \(String(describing: parent.key))"
-      }
-      if let left = leftChild {
-        s += ", left = [" + left.debugDescription + "]"
-      }
-      if let right = rightChild {
-        s += ", right = [" + right.debugDescription + "]"
-      }
-      s += ", color = \(color)"
-    }
-    return s
-  }
+    public var debugDescription: String {
+        var s = ""
+        if isNullLeaf {
+            s = "nullLeaf"
+        } else {
+            if let key = key {
+                s = "key: \(key)"
+            } else {
+                s = "key: nil"
+            }
+            if let parent = parent {
+                s += ", parent: \(String(describing: parent.key))"
+            }
+            if let left = leftChild {
+                s += ", left = [" + left.debugDescription + "]"
+            }
+            if let right = rightChild {
+                s += ", right = [" + right.debugDescription + "]"
+            }
+            s += ", color = \(color)"
+        }
+        return s
+    }
 }
 
 extension RedBlackTree: CustomDebugStringConvertible {
-  public var debugDescription: String {
-    return root.debugDescription
-  }
+    public var debugDescription: String {
+        return root.debugDescription
+    }
 }
 
 extension RBTreeNode: CustomStringConvertible {
-  public var description: String {
-    var s = ""
-    if isNullLeaf {
-      s += "nullLeaf"
-    } else {
-      if let left = leftChild {
-        s += "(\(left.description)) <- "
-      }
-      if let key = key {
-        s += "\(key)"
-      } else {
-        s += "nil"
-      }
-      s += ", \(color)"
-      if let right = rightChild {
-        s += " -> (\(right.description))"
-      }
-    }
-    return s
-  }
+    public var description: String {
+        var s = ""
+        if isNullLeaf {
+            s += "nullLeaf"
+        } else {
+            if let left = leftChild {
+                s += "(\(left.description)) <- "
+            }
+            if let key = key {
+                s += "\(key)"
+            } else {
+                s += "nil"
+            }
+            s += ", \(color)"
+            if let right = rightChild {
+                s += " -> (\(right.description))"
+            }
+        }
+        return s
+    }
 }
 
 extension RedBlackTree: CustomStringConvertible {
-  public var description: String {
-    if root.isNullLeaf {
-      return "[]"
-    } else {
-      return root.description
+    public var description: String {
+        if root.isNullLeaf {
+            return "[]"
+        } else {
+            return root.description
+        }
     }
-  }
 }
diff --git a/Red-Black Tree/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.swift
new file mode 100644
index 000000000..fc0411b42
--- /dev/null
+++ b/Red-Black Tree/RedBlackTree.swift	
@@ -0,0 +1,795 @@
+//Copyright (c) 2016 Matthijs Hollemans and contributors
+//
+//Permission is hereby granted, free of charge, to any person obtaining a copy
+//of this software and associated documentation files (the "Software"), to deal
+//in the Software without restriction, including without limitation the rights
+//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//copies of the Software, and to permit persons to whom the Software is
+//furnished to do so, subject to the following conditions:
+//
+//The above copyright notice and this permission notice shall be included in
+//all copies or substantial portions of the Software.
+//
+//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+//THE SOFTWARE.
+
+import Foundation
+
+private enum RBTreeColor {
+    case red
+    case black
+}
+
+private enum RotationDirection {
+    case left
+    case right
+}
+
+// MARK: - RBNode
+
+public class RBTreeNode<T: Comparable>: Equatable {
+    public typealias RBNode = RBTreeNode<T>
+    
+    fileprivate var color: RBTreeColor = .black
+    fileprivate var key: T?
+    var leftChild: RBNode?
+    var rightChild: RBNode?
+    fileprivate weak var parent: RBNode?
+    
+    public init(key: T?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
+        self.key = key
+        self.leftChild = leftChild
+        self.rightChild = rightChild
+        self.parent = parent
+        
+        self.leftChild?.parent = self
+        self.rightChild?.parent = self
+    }
+    
+    public convenience init(key: T?) {
+        self.init(key: key, leftChild: RBNode(), rightChild: RBNode(), parent: RBNode())
+    }
+    
+    // For initialising the nullLeaf
+    public convenience init() {
+        self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
+        self.color = .black
+    }
+    
+    var isRoot: Bool {
+        return parent == nil
+    }
+    
+    var isLeaf: Bool {
+        return rightChild == nil && leftChild == nil
+    }
+    
+    var isNullLeaf: Bool {
+        return key == nil && isLeaf && color == .black
+    }
+    
+    var isLeftChild: Bool {
+        return parent?.leftChild === self
+    }
+    
+    var isRightChild: Bool {
+        return parent?.rightChild === self
+    }
+    
+    var grandparent: RBNode? {
+        return parent?.parent
+    }
+    
+    var sibling: RBNode? {
+        if isLeftChild {
+            return parent?.rightChild
+        } else {
+            return parent?.leftChild
+        }
+    }
+    
+    var uncle: RBNode? {
+        return parent?.sibling
+    }
+}
+
+// MARK: - RedBlackTree
+
+public class RedBlackTree<T: Comparable> {
+    public typealias RBNode = RBTreeNode<T>
+    
+    fileprivate(set) var root: RBNode
+    fileprivate(set) var size = 0
+    fileprivate let nullLeaf = RBNode()
+    fileprivate let allowDuplicateNode: Bool
+    
+    public init(_ allowDuplicateNode: Bool = false) {
+        root = nullLeaf
+        self.allowDuplicateNode = allowDuplicateNode
+    }
+}
+
+// MARK: - Size
+
+extension RedBlackTree {
+    public func count() -> Int {
+        return size
+    }
+    
+    public func isEmpty() -> Bool {
+        return size == 0
+    }
+    
+    public func allElements() -> [T] {
+        var nodes: [T] = []
+        
+        getAllElements(node: root, nodes: &nodes)
+        
+        return nodes
+    }
+    
+    private func getAllElements(node: RBTreeNode<T>, nodes: inout [T]) {
+        guard !node.isNullLeaf else {
+            return
+        }
+        
+        if let left = node.leftChild {
+            getAllElements(node: left, nodes: &nodes)
+        }
+        
+        if let key = node.key {
+            nodes.append(key)
+        }
+        
+        if let right = node.rightChild {
+            getAllElements(node: right, nodes: &nodes)
+        }
+    }
+}
+
+// MARK: - Equatable protocol
+
+extension RBTreeNode {
+    static public func == <T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
+        return lhs.key == rhs.key
+    }
+}
+
+// MARK: - Finding a nodes successor
+
+extension RBTreeNode {
+    /*
+     * Returns the inorder successor node of a node
+     * The successor is a node with the next larger key value of the current node
+     */
+    public func getSuccessor() -> RBNode? {
+        // If node has right child: successor min of this right tree
+        if let rightChild = self.rightChild {
+            if !rightChild.isNullLeaf {
+                return rightChild.minimum()
+            }
+        }
+        // Else go upward until node left child
+        var currentNode = self
+        var parent = currentNode.parent
+        while currentNode.isRightChild {
+            if let parent = parent {
+                currentNode = parent
+            }
+            parent = currentNode.parent
+        }
+        return parent
+    }
+}
+
+// MARK: - Searching
+
+extension RBTreeNode {
+    /*
+     * Returns the node with the minimum key of the current subtree
+     */
+    public func minimum() -> RBNode? {
+        if let leftChild = leftChild {
+            if !leftChild.isNullLeaf {
+                return leftChild.minimum()
+            }
+            return self
+        }
+        return self
+    }
+    
+    /*
+     * Returns the node with the maximum key of the current subtree
+     */
+    public func maximum() -> RBNode? {
+        if let rightChild = rightChild {
+            if !rightChild.isNullLeaf {
+                return rightChild.maximum()
+            }
+            return self
+        }
+        return self
+    }
+}
+
+extension RedBlackTree {
+    /*
+     * Returns the node with the given key |input| if existing
+     */
+    public func search(input: T) -> RBNode? {
+        return search(key: input, node: root)
+    }
+    
+    /*
+     * Returns the node with given |key| in subtree of |node|
+     */
+    fileprivate func search(key: T, node: RBNode?) -> RBNode? {
+        // If node nil -> key not found
+        guard let node = node else {
+            return nil
+        }
+        // If node is nullLeaf == semantically same as if nil
+        if !node.isNullLeaf {
+            if let nodeKey = node.key {
+                // Node found
+                if key == nodeKey {
+                    return node
+                } else if key < nodeKey {
+                    return search(key: key, node: node.leftChild)
+                } else {
+                    return search(key: key, node: node.rightChild)
+                }
+            }
+        }
+        return nil
+    }
+}
+
+// MARK: - Finding maximum and minimum value
+
+extension RedBlackTree {
+    /*
+     * Returns the minimum key value of the whole tree
+     */
+    public func minValue() -> T? {
+        guard let minNode = root.minimum() else {
+            return nil
+        }
+        return minNode.key
+    }
+    
+    /*
+     * Returns the maximum key value of the whole tree
+     */
+    public func maxValue() -> T? {
+        guard let maxNode = root.maximum() else {
+            return nil
+        }
+        return maxNode.key
+    }
+}
+
+// MARK: - Inserting new nodes
+
+extension RedBlackTree {
+    /*
+     * Insert a node with key |key| into the tree
+     * 1. Perform normal insert operation as in a binary search tree
+     * 2. Fix red-black properties
+     * Runntime: O(log n)
+     */
+    public func insert(key: T) {
+        // If key must be unique and find the key already existed, quit
+        if search(input: key) != nil && !allowDuplicateNode {
+            return
+        }
+        
+        if root.isNullLeaf {
+            root = RBNode(key: key)
+        } else {
+            insert(input: RBNode(key: key), node: root)
+        }
+        
+        size += 1
+    }
+    
+    /*
+     * Nearly identical insert operation as in a binary search tree
+     * Differences: All nil pointers are replaced by the nullLeaf, we color the inserted node red,
+     * after inserting we call insertFixup to maintain the red-black properties
+     */
+    private func insert(input: RBNode, node: RBNode) {
+        guard let inputKey = input.key, let nodeKey = node.key else {
+            return
+        }
+        if inputKey < nodeKey {
+            guard let child = node.leftChild else {
+                addAsLeftChild(child: input, parent: node)
+                return
+            }
+            if child.isNullLeaf {
+                addAsLeftChild(child: input, parent: node)
+            } else {
+                insert(input: input, node: child)
+            }
+        } else {
+            guard let child = node.rightChild else {
+                addAsRightChild(child: input, parent: node)
+                return
+            }
+            if child.isNullLeaf {
+                addAsRightChild(child: input, parent: node)
+            } else {
+                insert(input: input, node: child)
+            }
+        }
+    }
+    
+    private func addAsLeftChild(child: RBNode, parent: RBNode) {
+        parent.leftChild = child
+        child.parent = parent
+        child.color = .red
+        insertFixup(node: child)
+    }
+    
+    private func addAsRightChild(child: RBNode, parent: RBNode) {
+        parent.rightChild = child
+        child.parent = parent
+        child.color = .red
+        insertFixup(node: child)
+    }
+    
+    /*
+     * Fixes possible violations of the red-black property after insertion
+     * Only violation of red-black properties occurs at inserted node |z| and z.parent
+     * We have 3 distinct cases: case 1, 2a and 2b
+     * - case 1: may repeat, but only h/2 steps, where h is the height of the tree
+     * - case 2a -> case 2b -> red-black tree
+     * - case 2b -> red-black tree
+     */
+    private func insertFixup(node z: RBNode) {
+        if !z.isNullLeaf {
+            guard let parentZ = z.parent else {
+                return
+            }
+            // If both |z| and his parent are red -> violation of red-black property -> need to fix it
+            if parentZ.color == .red {
+                guard let uncle = z.uncle else {
+                    return
+                }
+                // Case 1: Uncle red -> recolor + move z
+                if uncle.color == .red {
+                    parentZ.color = .black
+                    uncle.color = .black
+                    if let grandparentZ = parentZ.parent {
+                        grandparentZ.color = .red
+                        // Move z to grandparent and check again
+                        insertFixup(node: grandparentZ)
+                    }
+                }
+                    // Case 2: Uncle black
+                else {
+                    var zNew = z
+                    // Case 2.a: z right child -> rotate
+                    if parentZ.isLeftChild && z.isRightChild {
+                        zNew = parentZ
+                        leftRotate(node: zNew)
+                    } else if parentZ.isRightChild && z.isLeftChild {
+                        zNew = parentZ
+                        rightRotate(node: zNew)
+                    }
+                    // Case 2.b: z left child -> recolor + rotate
+                    zNew.parent?.color = .black
+                    if let grandparentZnew = zNew.grandparent {
+                        grandparentZnew.color = .red
+                        if z.isLeftChild {
+                            rightRotate(node: grandparentZnew)
+                        } else {
+                            leftRotate(node: grandparentZnew)
+                        }
+                        // We have a valid red-black-tree
+                    }
+                }
+            }
+        }
+        root.color = .black
+    }
+}
+
+// MARK: - Deleting a node
+extension RedBlackTree {
+    /*
+     * Delete a node with key |key| from the tree
+     * 1. Perform standard delete operation as in a binary search tree
+     * 2. Fix red-black properties
+     * Runntime: O(log n)
+     */
+    public func delete(key: T) {
+        if size == 1 {
+            root = nullLeaf
+            size -= 1
+        } else if let node = search(key: key, node: root) {
+            if !node.isNullLeaf {
+                delete(node: node)
+                size -= 1
+            }
+        }
+    }
+    
+    /*
+     * Nearly identical delete operation as in a binary search tree
+     * Differences: All nil pointers are replaced by the nullLeaf,
+     * after deleting we call insertFixup to maintain the red-black properties if the delted node was
+     * black (as if it was red -> no violation of red-black properties)
+     */
+    private func delete(node z: RBNode) {
+        var nodeY = RBNode()
+        var nodeX = RBNode()
+        if let leftChild = z.leftChild, let rightChild = z.rightChild {
+            if leftChild.isNullLeaf || rightChild.isNullLeaf {
+                nodeY = z
+            } else {
+                if let successor = z.getSuccessor() {
+                    nodeY = successor
+                }
+            }
+        }
+        if let leftChild = nodeY.leftChild {
+            if !leftChild.isNullLeaf {
+                nodeX = leftChild
+            } else if let rightChild = nodeY.rightChild {
+                nodeX = rightChild
+            }
+        }
+        nodeX.parent = nodeY.parent
+        if let parentY = nodeY.parent {
+            // Should never be the case, as parent of root = nil
+            if parentY.isNullLeaf {
+                root = nodeX
+            } else {
+                if nodeY.isLeftChild {
+                    parentY.leftChild = nodeX
+                } else {
+                    parentY.rightChild = nodeX
+                }
+            }
+        } else {
+            root = nodeX
+        }
+        if nodeY != z {
+            z.key = nodeY.key
+        }
+        // If sliced out node was red -> nothing to do as red-black-property holds
+        // If it was black -> fix red-black-property
+        if nodeY.color == .black {
+            deleteFixup(node: nodeX)
+        }
+    }
+    
+    /*
+     * Fixes possible violations of the red-black property after deletion
+     * We have w distinct cases: only case 2 may repeat, but only h many steps, where h is the height
+     * of the tree
+     * - case 1 -> case 2 -> red-black tree
+     *   case 1 -> case 3 -> case 4 -> red-black tree
+     *   case 1 -> case 4 -> red-black tree
+     * - case 3 -> case 4 -> red-black tree
+     * - case 4 -> red-black tree
+     */
+    private func deleteFixup(node x: RBNode) {
+        var xTmp = x
+        if !x.isRoot && x.color == .black {
+            guard var sibling = x.sibling else {
+                return
+            }
+            // Case 1: Sibling of x is red
+            if sibling.color == .red {
+                // Recolor
+                sibling.color = .black
+                if let parentX = x.parent {
+                    parentX.color = .red
+                    // Rotation
+                    if x.isLeftChild {
+                        leftRotate(node: parentX)
+                    } else {
+                        rightRotate(node: parentX)
+                    }
+                    // Update sibling
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+            }
+            // Case 2: Sibling is black with two black children
+            if sibling.leftChild?.color == .black && sibling.rightChild?.color == .black {
+                // Recolor
+                sibling.color = .red
+                // Move fake black unit upwards
+                if let parentX = x.parent {
+                    deleteFixup(node: parentX)
+                }
+                // We have a valid red-black-tree
+            } else {
+                // Case 3: a. Sibling black with one black child to the right
+                if x.isLeftChild && sibling.rightChild?.color == .black {
+                    // Recolor
+                    sibling.leftChild?.color = .black
+                    sibling.color = .red
+                    // Rotate
+                    rightRotate(node: sibling)
+                    // Update sibling of x
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+                    // Still case 3: b. One black child to the left
+                else if x.isRightChild && sibling.leftChild?.color == .black {
+                    // Recolor
+                    sibling.rightChild?.color = .black
+                    sibling.color = .red
+                    // Rotate
+                    leftRotate(node: sibling)
+                    // Update sibling of x
+                    if let sibl = x.sibling {
+                        sibling = sibl
+                    }
+                }
+                // Case 4: Sibling is black with red right child
+                // Recolor
+                if let parentX = x.parent {
+                    sibling.color = parentX.color
+                    parentX.color = .black
+                    // a. x left and sibling with red right child
+                    if x.isLeftChild {
+                        sibling.rightChild?.color = .black
+                        // Rotate
+                        leftRotate(node: parentX)
+                    }
+                        // b. x right and sibling with red left child
+                    else {
+                        sibling.leftChild?.color = .black
+                        //Rotate
+                        rightRotate(node: parentX)
+                    }
+                    // We have a valid red-black-tree
+                    xTmp = root
+                }
+            }
+        }
+        xTmp.color = .black
+    }
+}
+
+// MARK: - Rotation
+extension RedBlackTree {
+    /*
+     * Left rotation around node x
+     * Assumes that x.rightChild y is not a nullLeaf, rotates around the link from x to y,
+     * makes y the new root of the subtree with x as y's left child and y's left child as x's right
+     * child, where n = a node, [n] = a subtree
+     *     |                |
+     *     x                y
+     *   /   \     ~>     /   \
+     * [A]    y          x    [C]
+     *       / \        / \
+     *     [B] [C]    [A] [B]
+     */
+    fileprivate func leftRotate(node x: RBNode) {
+        rotate(node: x, direction: .left)
+    }
+    
+    /*
+     * Right rotation around node y
+     * Assumes that y.leftChild x is not a nullLeaf, rotates around the link from y to x,
+     * makes x the new root of the subtree with y as x's right child and x's right child as y's left
+     * child, where n = a node, [n] = a subtree
+     *     |                |
+     *     x                y
+     *   /   \     <~     /   \
+     * [A]    y          x    [C]
+     *       / \        / \
+     *     [B] [C]    [A] [B]
+     */
+    fileprivate func rightRotate(node x: RBNode) {
+        rotate(node: x, direction: .right)
+    }
+    
+    /*
+     * Rotation around a node x
+     * Is a local operation preserving the binary-search-tree property that only exchanges pointers.
+     * Runntime: O(1)
+     */
+    private func rotate(node x: RBNode, direction: RotationDirection) {
+        var nodeY: RBNode? = RBNode()
+        
+        // Set |nodeY| and turn |nodeY|'s left/right subtree into |x|'s right/left subtree
+        switch direction {
+        case .left:
+            nodeY = x.rightChild
+            x.rightChild = nodeY?.leftChild
+            x.rightChild?.parent = x
+        case .right:
+            nodeY = x.leftChild
+            x.leftChild = nodeY?.rightChild
+            x.leftChild?.parent = x
+        }
+        
+        // Link |x|'s parent to nodeY
+        nodeY?.parent = x.parent
+        if x.isRoot {
+            if let node = nodeY {
+                root = node
+            }
+        } else if x.isLeftChild {
+            x.parent?.leftChild = nodeY
+        } else if x.isRightChild {
+            x.parent?.rightChild = nodeY
+        }
+        
+        // Put |x| on |nodeY|'s left
+        switch direction {
+        case .left:
+            nodeY?.leftChild = x
+        case .right:
+            nodeY?.rightChild = x
+        }
+        x.parent = nodeY
+    }
+}
+
+// MARK: - Verify
+extension RedBlackTree {
+    /*
+     * Verifies that the existing tree fulfills all red-black properties
+     * Returns true if the tree is a valid red-black tree, false otherwise
+     */
+    public func verify() -> Bool {
+        if root.isNullLeaf {
+            print("The tree is empty")
+            return true
+        }
+        return property2() && property4() && property5()
+    }
+    
+    // Property 1: Every node is either red or black -> fullfilled through setting node.color of type
+    // RBTreeColor
+    
+    // Property 2: The root is black
+    private func property2() -> Bool {
+        if root.color == .red {
+            print("Property-Error: Root is red")
+            return false
+        }
+        return true
+    }
+    
+    // Property 3: Every nullLeaf is black -> fullfilled through initialising nullLeafs with color = black
+    
+    // Property 4: If a node is red, then both its children are black
+    private func property4() -> Bool {
+        return property4(node: root)
+    }
+    
+    private func property4(node: RBNode) -> Bool {
+        if node.isNullLeaf {
+            return true
+        }
+        if let leftChild = node.leftChild, let rightChild = node.rightChild {
+            if node.color == .red {
+                if !leftChild.isNullLeaf && leftChild.color == .red {
+                    print("Property-Error: Red node with key \(String(describing: node.key)) has red left child")
+                    return false
+                }
+                if !rightChild.isNullLeaf && rightChild.color == .red {
+                    print("Property-Error: Red node with key \(String(describing: node.key)) has red right child")
+                    return false
+                }
+            }
+            return property4(node: leftChild) && property4(node: rightChild)
+        }
+        return false
+    }
+    
+    // Property 5: For each node, all paths from the node to descendant leaves contain the same number
+    // of black nodes (same blackheight)
+    private func property5() -> Bool {
+        if property5(node: root) == -1 {
+            return false
+        } else {
+            return true
+        }
+    }
+    
+    private func property5(node: RBNode) -> Int {
+        if node.isNullLeaf {
+            return 0
+        }
+        guard let leftChild = node.leftChild, let rightChild = node.rightChild else {
+            return -1
+        }
+        let left = property5(node: leftChild)
+        let right = property5(node: rightChild)
+        
+        if left == -1 || right == -1 {
+            return -1
+        } else if left == right {
+            let addedHeight = node.color == .black ? 1 : 0
+            return left + addedHeight
+        } else {
+            print("Property-Error: Black height violated at node with key \(String(describing: node.key))")
+            return -1
+        }
+    }
+}
+
+// MARK: - Debugging
+
+extension RBTreeNode: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        var s = ""
+        if isNullLeaf {
+            s = "nullLeaf"
+        } else {
+            if let key = key {
+                s = "key: \(key)"
+            } else {
+                s = "key: nil"
+            }
+            if let parent = parent {
+                s += ", parent: \(String(describing: parent.key))"
+            }
+            if let left = leftChild {
+                s += ", left = [" + left.debugDescription + "]"
+            }
+            if let right = rightChild {
+                s += ", right = [" + right.debugDescription + "]"
+            }
+            s += ", color = \(color)"
+        }
+        return s
+    }
+}
+
+extension RedBlackTree: CustomDebugStringConvertible {
+    public var debugDescription: String {
+        return root.debugDescription
+    }
+}
+
+extension RBTreeNode: CustomStringConvertible {
+    public var description: String {
+        var s = ""
+        if isNullLeaf {
+            s += "nullLeaf"
+        } else {
+            if let left = leftChild {
+                s += "(\(left.description)) <- "
+            }
+            if let key = key {
+                s += "\(key)"
+            } else {
+                s += "nil"
+            }
+            s += ", \(color)"
+            if let right = rightChild {
+                s += " -> (\(right.description))"
+            }
+        }
+        return s
+    }
+}
+
+extension RedBlackTree: CustomStringConvertible {
+    public var description: String {
+        if root.isNullLeaf {
+            return "[]"
+        } else {
+            return root.description
+        }
+    }
+}

From a642a929ae4ce72ba0f00fc037c292a02db0fc9a Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Thu, 16 Nov 2017 22:37:27 -0500
Subject: [PATCH 296/643] Add username as test

---
 gfm-render.sh | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/gfm-render.sh b/gfm-render.sh
index 09c026d55..88970dd15 100755
--- a/gfm-render.sh
+++ b/gfm-render.sh
@@ -1,5 +1,7 @@
 #!/usr/bin/env bash
 
+USERNAME="raywenderlich"
+
 # $1 - readme
 function render_markdown_to_html {
   # escape escaping characters

From 7cb8185679cdc3acf38e9123ef7503fba5b4d116 Mon Sep 17 00:00:00 2001
From: Alejandro Isaza <al@isaza.ca>
Date: Sat, 7 Oct 2017 15:50:19 -0700
Subject: [PATCH 297/643] Add A* algorithm

---
 A-Star/AStar.swift                            | 153 +++++++++
 A-Star/README.md                              |   7 +
 A-Star/Tests/AStarTests.swift                 |  57 ++++
 .../AStarTests.xcodeproj/project.pbxproj      | 291 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 A-Star/Tests/Info.plist                       |  24 ++
 Hashed Heap/HashedHeap.swift                  |  13 +-
 .../contents.xcworkspacedata                  |  23 ++
 8 files changed, 574 insertions(+), 1 deletion(-)
 create mode 100644 A-Star/AStar.swift
 create mode 100644 A-Star/README.md
 create mode 100755 A-Star/Tests/AStarTests.swift
 create mode 100644 A-Star/Tests/AStarTests.xcodeproj/project.pbxproj
 create mode 100644 A-Star/Tests/AStarTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 A-Star/Tests/Info.plist

diff --git a/A-Star/AStar.swift b/A-Star/AStar.swift
new file mode 100644
index 000000000..41a9fac6c
--- /dev/null
+++ b/A-Star/AStar.swift
@@ -0,0 +1,153 @@
+// Written by Alejandro Isaza.
+
+import Foundation
+
+public protocol Graph {
+    associatedtype Vertex: Hashable
+    associatedtype Edge: WeightedEdge where Edge.Vertex == Vertex
+
+    /// Lists all edges going out from a vertex.
+    func edgesOutgoing(from vertex: Vertex) -> [Edge]
+}
+
+public protocol WeightedEdge {
+    associatedtype Vertex
+
+    /// The edge's cost.
+    var cost: Double { get }
+
+    /// The target vertex.
+    var target: Vertex { get }
+}
+
+public final class AStar<G: Graph> {
+    /// The graph to search on.
+    public let graph: G
+
+    /// The heuristic cost function that estimates the cost between two vertices.
+    ///
+    /// - Note: The heuristic function needs to always return a value that is lower-than or equal to the actual
+    ///         cost for the resulting path of the A* search to be optimal.
+    public let heuristic: (G.Vertex, G.Vertex) -> Double
+
+    /// Open list of nodes to expand.
+    private var open: HashedHeap<Node<G.Vertex>>
+
+    /// Closed list of vertices already expanded.
+    private var closed = Set<G.Vertex>()
+
+    /// Actual vertex cost for vertices we already encountered (refered to as `g` on the literature).
+    private var costs = Dictionary<G.Vertex, Double>()
+
+    /// Store the previous node for each expanded node to recreate the path.
+    private var parents = Dictionary<G.Vertex, G.Vertex>()
+
+    /// Initializes `AStar` with a graph and a heuristic cost function.
+    public init(graph: G, heuristic: @escaping (G.Vertex, G.Vertex) -> Double) {
+        self.graph = graph
+        self.heuristic = heuristic
+        open = HashedHeap(sort: <)
+    }
+
+    /// Finds an optimal path between `source` and `target`.
+    ///
+    /// - Precondition: both `source` and `target` belong to `graph`.
+    public func path(start: G.Vertex, target: G.Vertex) -> [G.Vertex] {
+        open.insert(Node<G.Vertex>(vertex: start, cost: 0, estimate: heuristic(start, target)))
+        while !open.isEmpty {
+            guard let node = open.remove() else {
+                break
+            }
+            costs[node.vertex] = node.cost
+
+            if (node.vertex == target) {
+                let path = buildPath(start: start, target: target)
+                cleanup()
+                return path
+            }
+
+            if !closed.contains(node.vertex) {
+                expand(node: node, target: target)
+                closed.insert(node.vertex)
+            }
+        }
+
+        // No path found
+        return []
+    }
+
+    private func expand(node: Node<G.Vertex>, target: G.Vertex) {
+        let edges = graph.edgesOutgoing(from: node.vertex)
+        for edge in edges {
+            let g = cost(node.vertex) + edge.cost
+            if g < cost(edge.target) {
+                open.insert(Node<G.Vertex>(vertex: edge.target, cost: g, estimate: heuristic(edge.target, target)))
+                parents[edge.target] = node.vertex
+            }
+        }
+    }
+
+    private func cost(_ vertex: G.Edge.Vertex) -> Double {
+        if let c = costs[vertex] {
+            return c
+        }
+
+        let node = Node(vertex: vertex, cost: Double.greatestFiniteMagnitude, estimate: 0)
+        if let index = open.index(of: node) {
+            return open[index].cost
+        }
+
+        return Double.greatestFiniteMagnitude
+    }
+
+    private func buildPath(start: G.Vertex, target: G.Vertex) -> [G.Vertex] {
+        var path = Array<G.Vertex>()
+        path.append(target)
+
+        var current = target
+        while current != start {
+            guard let parent = parents[current] else {
+                return [] // no path found
+            }
+            current = parent
+            path.append(current)
+        }
+
+        return path.reversed()
+    }
+
+    private func cleanup() {
+        open.removeAll()
+        closed.removeAll()
+        parents.removeAll()
+    }
+}
+
+private struct Node<V: Hashable>: Hashable, Comparable {
+    /// The graph vertex.
+    var vertex: V
+
+    /// The actual cost between the start vertex and this vertex.
+    var cost: Double
+
+    /// Estimated (heuristic) cost betweent this vertex and the target vertex.
+    var estimate: Double
+
+    public init(vertex: V, cost: Double, estimate: Double) {
+        self.vertex = vertex
+        self.cost = cost
+        self.estimate = estimate
+    }
+
+    static func < (lhs: Node<V>, rhs: Node<V>) -> Bool {
+        return lhs.cost + lhs.estimate < rhs.cost + rhs.estimate
+    }
+
+    static func == (lhs: Node<V>, rhs: Node<V>) -> Bool {
+        return lhs.vertex == rhs.vertex
+    }
+
+    var hashValue: Int {
+        return vertex.hashValue
+    }
+}
diff --git a/A-Star/README.md b/A-Star/README.md
new file mode 100644
index 000000000..cafd5027a
--- /dev/null
+++ b/A-Star/README.md
@@ -0,0 +1,7 @@
+# A*
+
+A* (pronounced "ay star") is a heuristic best-first search algorithm. A* minimizes node expansions, therefore minimizing the search time, by using a heuristic function. The heuristic function gives an estimate of the distance between two vertices. For instance if you are searching for a path between two points in a city, you can estimate the actual street distance with the straight-line distance.
+
+A* works by expanding the most promising nodes first, according to the heuristic function. In the city example it would choose streets which go in the general direction of the target first and, only if those are dead ends, backtrack and try other streets. This speeds up search in most sitations.
+
+A* is optimal (it always find the shortest path) if the heuristic function is admissible. A heuristic function is admissible if it never overestimates the cost of reaching the goal. In the extreme case of the heuristic function always retuning `0` A* acts exactly the same as [Dijkstra's Algorithm](../Dijkstra). The closer the heuristic function is the the actual distance the faster the search.
diff --git a/A-Star/Tests/AStarTests.swift b/A-Star/Tests/AStarTests.swift
new file mode 100755
index 000000000..87f674cd5
--- /dev/null
+++ b/A-Star/Tests/AStarTests.swift
@@ -0,0 +1,57 @@
+import Foundation
+import XCTest
+
+struct GridGraph: Graph {
+    struct Vertex: Hashable {
+        var x: Int
+        var y: Int
+
+        static func == (lhs: Vertex, rhs: Vertex) -> Bool {
+            return lhs.x == rhs.x && lhs.y == rhs.y
+        }
+
+        public var hashValue: Int {
+            return x.hashValue ^ y.hashValue
+        }
+    }
+
+    struct Edge: WeightedEdge {
+        var cost: Double
+        var target: Vertex
+    }
+
+    func edgesOutgoing(from vertex: Vertex) -> [Edge] {
+        return [
+            Edge(cost: 1, target: Vertex(x: vertex.x - 1, y: vertex.y)),
+            Edge(cost: 1, target: Vertex(x: vertex.x + 1, y: vertex.y)),
+            Edge(cost: 1, target: Vertex(x: vertex.x, y: vertex.y - 1)),
+            Edge(cost: 1, target: Vertex(x: vertex.x, y: vertex.y + 1)),
+        ]
+    }
+}
+
+class AStarTests: XCTestCase {
+    func testSameStartAndEnd() {
+        let graph = GridGraph()
+        let astar = AStar(graph: graph, heuristic: manhattanDistance)
+        let path = astar.path(start: GridGraph.Vertex(x: 0, y: 0), target: GridGraph.Vertex(x: 0, y: 0))
+        XCTAssertEqual(path.count, 1)
+        XCTAssertEqual(path[0].x, 0)
+        XCTAssertEqual(path[0].y, 0)
+    }
+
+    func testDiagonal() {
+        let graph = GridGraph()
+        let astar = AStar(graph: graph, heuristic: manhattanDistance)
+        let path = astar.path(start: GridGraph.Vertex(x: 0, y: 0), target: GridGraph.Vertex(x: 10, y: 10))
+        XCTAssertEqual(path.count, 21)
+        XCTAssertEqual(path[0].x, 0)
+        XCTAssertEqual(path[0].y, 0)
+        XCTAssertEqual(path[20].x, 10)
+        XCTAssertEqual(path[20].y, 10)
+    }
+
+    func manhattanDistance(_ s: GridGraph.Vertex, _ t: GridGraph.Vertex) -> Double {
+        return Double(abs(s.x - t.x) + abs(s.y - t.y))
+    }
+}
diff --git a/A-Star/Tests/AStarTests.xcodeproj/project.pbxproj b/A-Star/Tests/AStarTests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..cacd1e5ae
--- /dev/null
+++ b/A-Star/Tests/AStarTests.xcodeproj/project.pbxproj
@@ -0,0 +1,291 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		611D099C1F8978AB00C7092B /* AStarTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 611D099B1F8978AB00C7092B /* AStarTests.swift */; };
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+			isa = PBXGroup;
+			children = (
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+				7B2BBC721C779D710067B71D /* Products */,
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+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "AStarTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "AStarTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC8D1C779D720067B71D /* Debug */,
+				7B2BBC8E1C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 7B2BBC691C779D710067B71D /* Project object */;
+}
diff --git a/A-Star/Tests/AStarTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/A-Star/Tests/AStarTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..6c0ea8493
--- /dev/null
+++ b/A-Star/Tests/AStarTests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Tests.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/A-Star/Tests/Info.plist b/A-Star/Tests/Info.plist
new file mode 100644
index 000000000..ba72822e8
--- /dev/null
+++ b/A-Star/Tests/Info.plist
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>en</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/Hashed Heap/HashedHeap.swift b/Hashed Heap/HashedHeap.swift
index be7d9ab78..106cdacb0 100644
--- a/Hashed Heap/HashedHeap.swift	
+++ b/Hashed Heap/HashedHeap.swift	
@@ -57,7 +57,12 @@ public struct HashedHeap<T: Hashable> {
   public var count: Int {
     return elements.count
   }
-  
+
+  /// Accesses an element by its index.
+  public subscript(index: Int) -> T {
+    return elements[index]
+  }
+
   /// Returns the index of the given element.
   ///
   /// This is the operation that a hashed heap optimizes in compassion with a normal heap. In a normal heap this
@@ -141,6 +146,12 @@ public struct HashedHeap<T: Hashable> {
     }
     return removeLast()
   }
+
+  /// Removes all elements from the heap.
+  public mutating func removeAll() {
+    elements.removeAll()
+    indices.removeAll()
+  }
   
   /// Removes the last element from the heap.
   ///
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 4cab8e2d4..28fb4f1a7 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -38,6 +38,29 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "container:A-Star"
+      name = "A-Star">
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <FileRef
+         location = "group:AStar.swift">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:AStarTests.xcodeproj">
+         </FileRef>
+         <FileRef
+            location = "group:AStarTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "container:"
       name = "3Sum and 4Sum">

From cb26964f1ea032be9fbe7b64f1f6e849d1fda5d5 Mon Sep 17 00:00:00 2001
From: Alejandro Isaza <al@isaza.ca>
Date: Sat, 7 Oct 2017 15:53:59 -0700
Subject: [PATCH 298/643] Add to .travis.yml

---
 .travis.yml                                   |  1 +
 .../xcschemes/AStarTests.xcscheme             | 67 +++++++++++++++++++
 2 files changed, 68 insertions(+)
 create mode 100644 A-Star/Tests/AStarTests.xcodeproj/xcshareddata/xcschemes/AStarTests.xcscheme

diff --git a/.travis.yml b/.travis.yml
index 7cd02c9bc..30b54f140 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -9,6 +9,7 @@ install:
 
 script:
 
+- xcodebuild test -project ./A-Star/Tests/AStarTests.xcodeproj -scheme AStarTests | xcpretty -f `xcpretty-travis-formatter`
 - xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
 - xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests | xcpretty -f `xcpretty-travis-formatter`
 - xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
diff --git a/A-Star/Tests/AStarTests.xcodeproj/xcshareddata/xcschemes/AStarTests.xcscheme b/A-Star/Tests/AStarTests.xcodeproj/xcshareddata/xcschemes/AStarTests.xcscheme
new file mode 100644
index 000000000..5473b4c0c
--- /dev/null
+++ b/A-Star/Tests/AStarTests.xcodeproj/xcshareddata/xcschemes/AStarTests.xcscheme
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "0900"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+               BuildableName = "AStarTests.xctest"
+               BlueprintName = "AStarTests"
+               ReferencedContainer = "container:AStarTests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "7B2BBC7F1C779D720067B71D"
+            BuildableName = "Tests.xctest"
+            BlueprintName = "Tests"
+            ReferencedContainer = "container:Tests.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      language = ""
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

From 2c2ec49e225861e9aa0da42b54e35c90f81ddbed Mon Sep 17 00:00:00 2001
From: Alejandro Isaza <al@isaza.ca>
Date: Thu, 16 Nov 2017 22:17:19 -0800
Subject: [PATCH 299/643] Add example to README

---
 A-Star/Images/graph.dot |  12 ++++++++++++
 A-Star/Images/graph.png | Bin 0 -> 20882 bytes
 A-Star/Images/step1.dot |  12 ++++++++++++
 A-Star/Images/step1.png | Bin 0 -> 28753 bytes
 A-Star/Images/step2.dot |  12 ++++++++++++
 A-Star/Images/step2.png | Bin 0 -> 29088 bytes
 A-Star/Images/step3.dot |  12 ++++++++++++
 A-Star/Images/step3.png | Bin 0 -> 30158 bytes
 A-Star/Images/step4.dot |  12 ++++++++++++
 A-Star/Images/step4.png | Bin 0 -> 30130 bytes
 A-Star/Images/step5.dot |  12 ++++++++++++
 A-Star/Images/step5.png | Bin 0 -> 29802 bytes
 A-Star/Images/step6.dot |  12 ++++++++++++
 A-Star/Images/step6.png | Bin 0 -> 29596 bytes
 A-Star/Images/step7.dot |  12 ++++++++++++
 A-Star/Images/step7.png | Bin 0 -> 30012 bytes
 A-Star/README.md        |  38 +++++++++++++++++++++++++++++++++++++-
 17 files changed, 133 insertions(+), 1 deletion(-)
 create mode 100644 A-Star/Images/graph.dot
 create mode 100644 A-Star/Images/graph.png
 create mode 100644 A-Star/Images/step1.dot
 create mode 100644 A-Star/Images/step1.png
 create mode 100644 A-Star/Images/step2.dot
 create mode 100644 A-Star/Images/step2.png
 create mode 100644 A-Star/Images/step3.dot
 create mode 100644 A-Star/Images/step3.png
 create mode 100644 A-Star/Images/step4.dot
 create mode 100644 A-Star/Images/step4.png
 create mode 100644 A-Star/Images/step5.dot
 create mode 100644 A-Star/Images/step5.png
 create mode 100644 A-Star/Images/step6.dot
 create mode 100644 A-Star/Images/step6.png
 create mode 100644 A-Star/Images/step7.dot
 create mode 100644 A-Star/Images/step7.png

diff --git a/A-Star/Images/graph.dot b/A-Star/Images/graph.dot
new file mode 100644
index 000000000..941d66232
--- /dev/null
+++ b/A-Star/Images/graph.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "h = 3" ] }
+    { rank = same; B [ label = "h = 2" ]; C [ label = "h = 2" ]; D [ label = "h = 2" ] }
+    { rank = same; E [ label = "h = 1" ]; F [ label = "h = 1" ]; G [ label = "h = 1" ] }
+    { H  [ label = "h = 0", style = filled, color = green ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/graph.png b/A-Star/Images/graph.png
new file mode 100644
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diff --git a/A-Star/Images/step1.dot b/A-Star/Images/step1.dot
new file mode 100644
index 000000000..5785aea4c
--- /dev/null
+++ b/A-Star/Images/step1.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = deepskyblue1 ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightgrey ]; C [ label = "g = 1\nh = 2", style = filled, color = lightgrey ]; D [ label = "g = 1\nh = 2", style = filled, color = lightgrey ] }
+    { rank = same; E [ label = "g = \?\nh = 1" ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = \?\nh = 1" ] }
+    { H  [ label = "g = \?\nh = 0" ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step1.png b/A-Star/Images/step1.png
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diff --git a/A-Star/Images/step2.dot b/A-Star/Images/step2.dot
new file mode 100644
index 000000000..0c8a9d53d
--- /dev/null
+++ b/A-Star/Images/step2.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = deepskyblue1 ]; C [ label = "g = 1\nh = 2", style = filled, color = lightgrey ]; D [ label = "g = 1\nh = 2", style = filled, color = lightgrey ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightgrey ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = \?\nh = 1" ] }
+    { H  [ label = "g = \?\nh = 0" ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step2.png b/A-Star/Images/step2.png
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diff --git a/A-Star/Images/step3.dot b/A-Star/Images/step3.dot
new file mode 100644
index 000000000..32a75891d
--- /dev/null
+++ b/A-Star/Images/step3.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = deepskyblue1 ]; D [ label = "g = 1\nh = 2", style = filled, color = lightgrey ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightgrey ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = \?\nh = 1" ] }
+    { H  [ label = "g = \?\nh = 0" ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step3.png b/A-Star/Images/step3.png
new file mode 100644
index 0000000000000000000000000000000000000000..e195e7e8e11651f774405e1ca5be8bff514399dc
GIT binary patch
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diff --git a/A-Star/Images/step4.dot b/A-Star/Images/step4.dot
new file mode 100644
index 000000000..16db76796
--- /dev/null
+++ b/A-Star/Images/step4.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = deepskyblue1 ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightgrey ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = 2\nh = 1", style = filled, color = lightgrey ] }
+    { H  [ label = "g = \?\nh = 0" ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step4.png b/A-Star/Images/step4.png
new file mode 100644
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diff --git a/A-Star/Images/step5.dot b/A-Star/Images/step5.dot
new file mode 100644
index 000000000..2986b6a90
--- /dev/null
+++ b/A-Star/Images/step5.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = lightblue ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = deepskyblue1 ]; F [ label = "g = 3\nh = 1", style = filled, color = lightgrey ]; G [ label = "g = 2\nh = 1", style = filled, color = lightgrey ] }
+    { H  [ label = "g = \?\nh = 0" ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step5.png b/A-Star/Images/step5.png
new file mode 100644
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diff --git a/A-Star/Images/step6.dot b/A-Star/Images/step6.dot
new file mode 100644
index 000000000..b5e3179b6
--- /dev/null
+++ b/A-Star/Images/step6.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = lightblue ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightblue ]; F [ label = "g = 3\nh = 1", style = filled, color = lightgrey ]; G [ label = "g = 2\nh = 1", style = filled, color = deepskyblue1 ] }
+    { H  [ label = "g = 3\nh = 0", style = filled, color = lightgrey ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step6.png b/A-Star/Images/step6.png
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diff --git a/A-Star/Images/step7.dot b/A-Star/Images/step7.dot
new file mode 100644
index 000000000..c5b26b6b3
--- /dev/null
+++ b/A-Star/Images/step7.dot
@@ -0,0 +1,12 @@
+digraph G {
+    rankdir=LR;
+    { A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
+    { rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = lightblue ] }
+    { rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightblue ]; F [ label = "g = 3\nh = 1", style = filled, color = lightgrey ]; G [ label = "g = 2\nh = 1", style = filled, color = lightblue ] }
+    { H  [ label = "g = 3\nh = 0", style = filled, color = deepskyblue1 ] }
+    A -> { B C D }
+    B -> E
+    E -> F
+    D -> G
+    G -> H
+}
diff --git a/A-Star/Images/step7.png b/A-Star/Images/step7.png
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diff --git a/A-Star/README.md b/A-Star/README.md
index cafd5027a..f362bb61e 100644
--- a/A-Star/README.md
+++ b/A-Star/README.md
@@ -4,4 +4,40 @@ A* (pronounced "ay star") is a heuristic best-first search algorithm. A* minimiz
 
 A* works by expanding the most promising nodes first, according to the heuristic function. In the city example it would choose streets which go in the general direction of the target first and, only if those are dead ends, backtrack and try other streets. This speeds up search in most sitations.
 
-A* is optimal (it always find the shortest path) if the heuristic function is admissible. A heuristic function is admissible if it never overestimates the cost of reaching the goal. In the extreme case of the heuristic function always retuning `0` A* acts exactly the same as [Dijkstra's Algorithm](../Dijkstra). The closer the heuristic function is the the actual distance the faster the search.
+A* is optimal (it always find the shortest path) if the heuristic function is admissible. A heuristic function is admissible if it never overestimates the cost of reaching the goal. In the extreme case of the heuristic function always retuning `0` A* acts exactly the same as [Dijkstra's Algorithm](../Dijkstra). The closer the heuristic function is to the actual distance the faster the search.
+
+## Example
+
+Let's run through an example on this simple directed graph. We are going to assume that all edges have a cost of 1 and the heuristic function is going to be the column starting at goal and going back:
+
+![Graph](Images/graph.png)
+
+On the first step we expand the root node on the left (blue). We set the cost `g` to zero and add all neighbors to the open list (grey). 
+
+![Step 1](Images/step1.png)
+
+We put the first not in the closed list (light blue) so that we don't try expanding it again if there were to be loops in the graph. Next we take the node on the open list with the smallest value of `g + h` where `g` is the current cost (0) plus the edge cost (1). Since all nodes in the open list have the same value we choose the top one.
+
+![Step 2](Images/step2.png)
+
+We repeat the process and pick the next node from the open list. In this case there are no new nodes to add to the open list.
+
+![Step 3](Images/step3.png)
+
+We expand the next node. One more node on the open list, but nothing exciting yet.
+
+![Step 4](Images/step4.png)
+
+Sicne the top and the bottom nodes have the same value we choose the top one. This is not a great choice but we could do better if we had a better heuristic function.
+
+![Step 5](Images/step5.png)
+
+Now we expand the bottom node because it has a smaller value than the middle node (2 + 1 < 3 + 1).
+
+![Step 6](Images/step6.png)
+
+And we finally reach the goal! We never even expanded that middle node. We didn't have to because its value is 4, which is equal to the total lenght of our solution and therefore guaranteed to not be part of the optimal solution.
+
+![Step 7](Images/step7.png)
+
+The final step is to backtrack from the goal node to buld the optimal path.

From 58245be3842c9c5f428fc63f35e637da6a551f63 Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Fri, 17 Nov 2017 16:51:17 -0500
Subject: [PATCH 300/643] Add Token for gfm render

---
 gfm-render.sh | 1 +
 1 file changed, 1 insertion(+)

diff --git a/gfm-render.sh b/gfm-render.sh
index 88970dd15..7a3df636c 100755
--- a/gfm-render.sh
+++ b/gfm-render.sh
@@ -1,6 +1,7 @@
 #!/usr/bin/env bash
 
 USERNAME="raywenderlich"
+TOKEN="e64530973ec12f12c94ac26cce8c93caf466fc89"
 
 # $1 - readme
 function render_markdown_to_html {

From 0c2aa34b5a93e4e5ecf18b451ecae932f480d8ad Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Fri, 17 Nov 2017 17:45:19 -0500
Subject: [PATCH 301/643] revoke token

---
 gfm-render.sh | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/gfm-render.sh b/gfm-render.sh
index 7a3df636c..09c026d55 100755
--- a/gfm-render.sh
+++ b/gfm-render.sh
@@ -1,8 +1,5 @@
 #!/usr/bin/env bash
 
-USERNAME="raywenderlich"
-TOKEN="e64530973ec12f12c94ac26cce8c93caf466fc89"
-
 # $1 - readme
 function render_markdown_to_html {
   # escape escaping characters

From d7f172a8db597a7c699679b9b9977bede7469487 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sun, 23 Jul 2017 13:13:39 -0700
Subject: [PATCH 302/643] Improvement of Apple Ordered Set

Add explaination for apple ordered set
---
 .../AppleOrderedSet.playground/Contents.swift |  13 +-
 .../Sources/AppleOrderedSet.swift             |   4 +
 Ordered Set/AppleOrderedSet.swift             |   4 +
 Ordered Set/README.markdown                   | 126 +++++++++++++++++-
 .../contents.xcworkspacedata                  |   8 +-
 5 files changed, 144 insertions(+), 11 deletions(-)

diff --git a/Ordered Set/AppleOrderedSet.playground/Contents.swift b/Ordered Set/AppleOrderedSet.playground/Contents.swift
index 4388c664b..c5548c2c2 100644
--- a/Ordered Set/AppleOrderedSet.playground/Contents.swift	
+++ b/Ordered Set/AppleOrderedSet.playground/Contents.swift	
@@ -6,8 +6,17 @@ s.add(-1)
 s.add(0)
 s.insert(4, at: 3)
 
-s.set(-1, at: 0)
+print(s.all()) // [1, 2, -1, 4, 0]
+
+s.set(-1, at: 0) // We already have -1 in index: 2, so we will do nothing here
+
+print(s.all()) // [1, 2, -1, 4, 0]
+
 s.remove(-1)
 
-print(s.object(at: 1))
+print(s.all()) // [1, 2, 4, 0]
+
+print(s.object(at: 1)) // 2
+
+print(s.object(at: 2)) // 4
 
diff --git a/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift
index 3ff19cb8d..6bd8f94a0 100644
--- a/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift	
+++ b/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift	
@@ -69,4 +69,8 @@ public class AppleOrderedSet<T: Hashable> {
             indexOfKey[objects[i]] = i
         }
     }
+    
+    public func all() -> [T] {
+        return objects
+    }
 }
diff --git a/Ordered Set/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.swift
index 3ff19cb8d..6bd8f94a0 100644
--- a/Ordered Set/AppleOrderedSet.swift	
+++ b/Ordered Set/AppleOrderedSet.swift	
@@ -69,4 +69,8 @@ public class AppleOrderedSet<T: Hashable> {
             indexOfKey[objects[i]] = i
         }
     }
+    
+    public func all() -> [T] {
+        return objects
+    }
 }
diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
index bc5003a61..11096d5bb 100644
--- a/Ordered Set/README.markdown	
+++ b/Ordered Set/README.markdown	
@@ -1,5 +1,7 @@
 # Ordered Set
 
+## Sorted Array Version
+
 An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest.
 
 The Ordered Set data type is a hybrid of:
@@ -323,15 +325,129 @@ The right side did not contain the item, so we look at the left side:
 
 	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
 	                              *        mid        
-
+	
 	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
 	                    *                  mid        
 
 Finally, we've found `Player 2`, and return index 3.
 
-## See Also
+## Apple's Ordered Set
+Below the ordered set is based on sorted array. But [Apple's version](https://developer.apple.com/documentation/foundation/nsorderedset), it's pretty different. Now, let's look into how to implement apple's ordered set.
+
+Here is the example about how it works
+
+```swift
+let s = AppleOrderedSet<Int>()
+
+s.add(1)
+s.add(2)
+s.add(-1)
+s.add(0)
+s.insert(4, at: 3)
+
+print(s.all()) // [1, 2, -1, 4, 0]
+
+s.set(-1, at: 0) // We already have -1 in index: 2, so we will do nothing here
+
+print(s.all()) // [1, 2, -1, 4, 0]
+
+s.remove(-1)
+
+print(s.all()) // [1, 2, 4, 0]
+
+print(s.object(at: 1)) // 2
+
+print(s.object(at: 2)) // 4
+```
+
+The significant difference is the the array is not sorted. The elements in the array are the same when insert them. Image the array without duplicates and with `O(logn)` or `O(1)` search time.
+
+The idea here is using a data structure to provide `O(1)` or `O(logn)` time complexity, so it's easy to think about hash table.
+
+```swift
+var indexOfKey: [T: Int]
+var objects: [T]
+```
+
+`indexOfKey` is used to track the index of the element. `objects` is array holding elements.
+
+We will go through some key functions details here.
+
+### Add
 
-[Apple Ordered Set](AppleOrderedSet.playground)
-@remlostime added an Apple version of `OrderedSet`
+Update `indexOfKey` and insert element in the end of `objects`
+
+```swift
+// O(1)
+public func add(_ object: T) {
+	guard indexOfKey[object] == nil else {
+		return
+	}
+
+	objects.append(object)
+	indexOfKey[object] = objects.count - 1
+}
+```
+
+### Insert
+
+Insert in a random place of the array will cost `O(n)` time.
+
+```swift
+// O(n)
+public func insert(_ object: T, at index: Int) {
+	assert(index < objects.count, "Index should be smaller than object count")
+	assert(index >= 0, "Index should be bigger than 0")
+
+	guard indexOfKey[object] == nil else {
+		return
+	}
+
+	objects.insert(object, at: index)
+	indexOfKey[object] = index
+	for i in index+1..<objects.count {
+		indexOfKey[objects[i]] = i
+	}
+}
+```
+
+###  Set
+
+If the `object` already existed in the `OrderedSet`, do nothing. Otherwise, we need to update the `indexOfkey` and `objects`.
+
+```swift
+// O(1)
+public func set(_ object: T, at index: Int) {
+	assert(index < objects.count, "Index should be smaller than object count")
+	assert(index >= 0, "Index should be bigger than 0")
+
+	guard indexOfKey[object] == nil else {
+		return
+	}
+
+	indexOfKey.removeValue(forKey: objects[index])
+	indexOfKey[object] = index
+	objects[index] = object
+}
+```
+
+### Remove
+
+Remove element in the array will cost `O(n)`. At the same time, we need to update all elements's index after the removed element.
+
+```swift
+// O(n)
+public func remove(_ object: T) {
+	guard let index = indexOfKey[object] else {
+		return 
+	}
+
+	indexOfKey.removeValue(forKey: object)
+	objects.remove(at: index)
+	for i in index..<objects.count {
+		indexOfKey[objects[i]] = i
+	}
+}
+```
 
-*Written By Zain Humayun*
+*Ordered Set is Written By Zain Humayun, Apple Ordered Set is Written By Kai Chen*
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 4cab8e2d4..fbaa4cd54 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1808,16 +1808,16 @@
       location = "group:Ordered Set"
       name = "Ordered Set">
       <FileRef
-         location = "group:OrderedSet.playground">
+         location = "group:AppleOrderedSet.playground">
       </FileRef>
       <FileRef
-         location = "group:OrderedSet.swift">
+         location = "group:AppleOrderedSet.swift">
       </FileRef>
       <FileRef
-         location = "group:AppleOrderedSet.swift">
+         location = "group:OrderedSet.playground">
       </FileRef>
       <FileRef
-         location = "group:AppleOrderedSet.playground">
+         location = "group:OrderedSet.swift">
       </FileRef>
       <FileRef
          location = "group:README.markdown">

From 95b45f038bfaba63fac2621c24dd3bd0bd9d59be Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 18 Nov 2017 20:08:36 -0800
Subject: [PATCH 303/643] Split sorted set and ordered set

---
 .../Sources/AppleOrderedSet.swift             |  76 ----
 .../contents.xcplayground                     |   4 -
 Ordered Set/AppleOrderedSet.swift             |  76 ----
 .../Contents.swift                            |   2 +-
 .../timeline.xctimeline                       |   6 -
 .../Sources/OrderedSet.swift                  | 171 ++++-----
 .../contents.xcplayground                     |   8 +-
 Ordered Set/OrderedSet.swift                  | 172 ++++-----
 Ordered Set/README.markdown                   | 336 +-----------------
 Sorted Set/README.markdown                    | 334 +++++++++++++++++
 .../Example 1.xcplaygroundpage/Contents.swift |   2 +-
 .../timeline.xctimeline                       |   6 +-
 .../Example 2.xcplaygroundpage/Contents.swift |   2 +-
 .../Example 3.xcplaygroundpage/Contents.swift |   2 +-
 .../Sources/Player.swift                      |   6 +-
 .../Sources/Random.swift                      |   4 +-
 .../Sources/SortedSet.swift                   | 118 ++++++
 .../contents.xcplayground                     |   8 +
 .../contents.xcworkspacedata                  |   0
 Sorted Set/SortedSet.swift                    | 118 ++++++
 .../contents.xcworkspacedata                  |  19 +-
 21 files changed, 738 insertions(+), 732 deletions(-)
 delete mode 100644 Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift
 delete mode 100644 Ordered Set/AppleOrderedSet.playground/contents.xcplayground
 delete mode 100644 Ordered Set/AppleOrderedSet.swift
 rename Ordered Set/{AppleOrderedSet.playground => OrderedSet.playground}/Contents.swift (91%)
 delete mode 100644 Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline
 create mode 100644 Sorted Set/README.markdown
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Pages/Example 1.xcplaygroundpage/Contents.swift (94%)
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Pages/Example 1.xcplaygroundpage/timeline.xctimeline (50%)
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Pages/Example 2.xcplaygroundpage/Contents.swift (95%)
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Pages/Example 3.xcplaygroundpage/Contents.swift (95%)
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Sources/Player.swift (95%)
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/Sources/Random.swift (88%)
 create mode 100644 Sorted Set/SortedSet.playground/Sources/SortedSet.swift
 create mode 100644 Sorted Set/SortedSet.playground/contents.xcplayground
 rename {Ordered Set/OrderedSet.playground => Sorted Set/SortedSet.playground}/playground.xcworkspace/contents.xcworkspacedata (100%)
 create mode 100644 Sorted Set/SortedSet.swift

diff --git a/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift
deleted file mode 100644
index 6bd8f94a0..000000000
--- a/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift	
+++ /dev/null
@@ -1,76 +0,0 @@
-public class AppleOrderedSet<T: Hashable> {
-    private var objects: [T] = []
-    private var indexOfKey: [T: Int] = [:]
-    
-    public init() {}
-    
-    // O(1)
-    public func add(_ object: T) {
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        objects.append(object)
-        indexOfKey[object] = objects.count - 1
-    }
-    
-    // O(n)
-    public func insert(_ object: T, at index: Int) {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        objects.insert(object, at: index)
-        indexOfKey[object] = index
-        for i in index+1..<objects.count {
-            indexOfKey[objects[i]] = i
-        }
-    }
-    
-    // O(1)
-    public func object(at index: Int) -> T {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        return objects[index]
-    }
-    
-    // O(1)
-    public func set(_ object: T, at index: Int) {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        indexOfKey.removeValue(forKey: objects[index])
-        indexOfKey[object] = index
-        objects[index] = object
-    }
-    
-    // O(1)
-    public func indexOf(_ object: T) -> Int {
-        return indexOfKey[object] ?? -1
-    }
-    
-    // O(n)
-    public func remove(_ object: T) {
-        guard let index = indexOfKey[object] else {
-            return
-        }
-        
-        indexOfKey.removeValue(forKey: object)
-        objects.remove(at: index)
-        for i in index..<objects.count {
-            indexOfKey[objects[i]] = i
-        }
-    }
-    
-    public func all() -> [T] {
-        return objects
-    }
-}
diff --git a/Ordered Set/AppleOrderedSet.playground/contents.xcplayground b/Ordered Set/AppleOrderedSet.playground/contents.xcplayground
deleted file mode 100644
index 5da2641c9..000000000
--- a/Ordered Set/AppleOrderedSet.playground/contents.xcplayground	
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file
diff --git a/Ordered Set/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.swift
deleted file mode 100644
index 6bd8f94a0..000000000
--- a/Ordered Set/AppleOrderedSet.swift	
+++ /dev/null
@@ -1,76 +0,0 @@
-public class AppleOrderedSet<T: Hashable> {
-    private var objects: [T] = []
-    private var indexOfKey: [T: Int] = [:]
-    
-    public init() {}
-    
-    // O(1)
-    public func add(_ object: T) {
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        objects.append(object)
-        indexOfKey[object] = objects.count - 1
-    }
-    
-    // O(n)
-    public func insert(_ object: T, at index: Int) {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        objects.insert(object, at: index)
-        indexOfKey[object] = index
-        for i in index+1..<objects.count {
-            indexOfKey[objects[i]] = i
-        }
-    }
-    
-    // O(1)
-    public func object(at index: Int) -> T {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        return objects[index]
-    }
-    
-    // O(1)
-    public func set(_ object: T, at index: Int) {
-        assert(index < objects.count, "Index should be smaller than object count")
-        assert(index >= 0, "Index should be bigger than 0")
-        
-        guard indexOfKey[object] == nil else {
-            return
-        }
-        
-        indexOfKey.removeValue(forKey: objects[index])
-        indexOfKey[object] = index
-        objects[index] = object
-    }
-    
-    // O(1)
-    public func indexOf(_ object: T) -> Int {
-        return indexOfKey[object] ?? -1
-    }
-    
-    // O(n)
-    public func remove(_ object: T) {
-        guard let index = indexOfKey[object] else {
-            return
-        }
-        
-        indexOfKey.removeValue(forKey: object)
-        objects.remove(at: index)
-        for i in index..<objects.count {
-            indexOfKey[objects[i]] = i
-        }
-    }
-    
-    public func all() -> [T] {
-        return objects
-    }
-}
diff --git a/Ordered Set/AppleOrderedSet.playground/Contents.swift b/Ordered Set/OrderedSet.playground/Contents.swift
similarity index 91%
rename from Ordered Set/AppleOrderedSet.playground/Contents.swift
rename to Ordered Set/OrderedSet.playground/Contents.swift
index c5548c2c2..6a2415231 100644
--- a/Ordered Set/AppleOrderedSet.playground/Contents.swift	
+++ b/Ordered Set/OrderedSet.playground/Contents.swift	
@@ -1,4 +1,4 @@
-let s = AppleOrderedSet<Int>()
+let s = OrderedSet<Int>()
 
 s.add(1)
 s.add(2)
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline b/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift
index 8490a3320..5508c3637 100644
--- a/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.playground/Sources/OrderedSet.swift	
@@ -1,117 +1,76 @@
-/*
-  An Ordered Set is a collection where all items in the set follow an ordering,
-  usually ordered from 'least' to 'most'. The way you value and compare items
-  can be user-defined.
-*/
-public struct OrderedSet<T: Comparable> {
-  private var internalSet = [T]()
-
-  public init() { }
-
-  // Returns the number of elements in the OrderedSet.
-  public var count: Int {
-    return internalSet.count
-  }
-
-  // Inserts an item. Performance: O(n)
-  public mutating func insert(_ item: T) {
-    if exists(item) {
-      return  // don't add an item if it already exists
-    }
-
-    // Insert new the item just before the one that is larger.
-    for i in 0..<count {
-      if internalSet[i] > item {
-        internalSet.insert(item, at: i)
-        return
-      }
+public class OrderedSet<T: Hashable> {
+  private var objects: [T] = []
+  private var indexOfKey: [T: Int] = [:]
+  
+  public init() {}
+  
+  // O(1)
+  public func add(_ object: T) {
+    guard indexOfKey[object] == nil else {
+      return
     }
-
-    // Append to the back if the new item is greater than any other in the set.
-    internalSet.append(item)
+    
+    objects.append(object)
+    indexOfKey[object] = objects.count - 1
   }
-
-  // Removes an item if it exists. Performance: O(n)
-  public mutating func remove(_ item: T) {
-    if let index = index(of: item) {
-      internalSet.remove(at: index)
+  
+  // O(n)
+  public func insert(_ object: T, at index: Int) {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    guard indexOfKey[object] == nil else {
+      return
     }
-  }
-
-  // Returns true if and only if the item exists somewhere in the set.
-  public func exists(_ item: T) -> Bool {
-    return index(of: item) != nil
-  }
-
-  // Returns the index of an item if it exists, or -1 otherwise.
-  public func index(of item: T) -> Int? {
-    var leftBound = 0
-    var rightBound = count - 1
-
-    while leftBound <= rightBound {
-      let mid = leftBound + ((rightBound - leftBound) / 2)
-
-      if internalSet[mid] > item {
-        rightBound = mid - 1
-      } else if internalSet[mid] < item {
-        leftBound = mid + 1
-      } else if internalSet[mid] == item {
-        return mid
-      } else {
-        // When we get here, we've landed on an item whose value is equal to the
-        // value of the item we're looking for, but the items themselves are not
-        // equal. We need to check the items with the same value to the right
-        // and to the left in order to find an exact match.
-
-        // Check to the right.
-        for j in stride(from: mid, to: count - 1, by: 1) {
-          if internalSet[j + 1] == item {
-            return j + 1
-          } else if internalSet[j] < internalSet[j + 1] {
-            break
-          }
-        }
-
-        // Check to the left.
-        for j in stride(from: mid, to: 0, by: -1) {
-          if internalSet[j - 1] == item {
-            return j - 1
-          } else if internalSet[j] > internalSet[j - 1] {
-            break
-          }
-        }
-        return nil
-      }
+    
+    objects.insert(object, at: index)
+    indexOfKey[object] = index
+    for i in index+1..<objects.count {
+      indexOfKey[objects[i]] = i
     }
-    return nil
   }
-
-  // Returns the item at the given index.
-  // Assertion fails if the index is out of the range of [0, count).
-  public subscript(index: Int) -> T {
-    assert(index >= 0 && index < count)
-    return internalSet[index]
+  
+  // O(1)
+  public func object(at index: Int) -> T {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    return objects[index]
   }
-
-  // Returns the 'maximum' or 'largest' value in the set.
-  public func max() -> T? {
-    return count == 0 ? nil : internalSet[count - 1]
+  
+  // O(1)
+  public func set(_ object: T, at index: Int) {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    guard indexOfKey[object] == nil else {
+      return
+    }
+    
+    indexOfKey.removeValue(forKey: objects[index])
+    indexOfKey[object] = index
+    objects[index] = object
   }
-
-  // Returns the 'minimum' or 'smallest' value in the set.
-  public func min() -> T? {
-    return count == 0 ? nil : internalSet[0]
+  
+  // O(1)
+  public func indexOf(_ object: T) -> Int {
+    return indexOfKey[object] ?? -1
   }
-
-  // Returns the k-th largest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kLargest(_ k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[count - k]
+  
+  // O(n)
+  public func remove(_ object: T) {
+    guard let index = indexOfKey[object] else {
+      return
+    }
+    
+    indexOfKey.removeValue(forKey: object)
+    objects.remove(at: index)
+    for i in index..<objects.count {
+      indexOfKey[objects[i]] = i
+    }
   }
-
-  // Returns the k-th smallest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kSmallest(_ k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  
+  public func all() -> [T] {
+    return objects
   }
 }
diff --git a/Ordered Set/OrderedSet.playground/contents.xcplayground b/Ordered Set/OrderedSet.playground/contents.xcplayground
index 18c02c912..5da2641c9 100644
--- a/Ordered Set/OrderedSet.playground/contents.xcplayground	
+++ b/Ordered Set/OrderedSet.playground/contents.xcplayground	
@@ -1,8 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='6.0' target-platform='ios' display-mode='raw' executeOnSourceChanges='false'>
-    <pages>
-        <page name='Example 1'/>
-        <page name='Example 2'/>
-        <page name='Example 3'/>
-    </pages>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Ordered Set/OrderedSet.swift b/Ordered Set/OrderedSet.swift
index a8b3b0966..8b6df7d3e 100644
--- a/Ordered Set/OrderedSet.swift	
+++ b/Ordered Set/OrderedSet.swift	
@@ -1,117 +1,77 @@
-/*
-  An Ordered Set is a collection where all items in the set follow an ordering,
-  usually ordered from 'least' to 'most'. The way you value and compare items
-  can be user-defined.
-*/
-public struct OrderedSet<T: Comparable> {
-  private var internalSet = [T]()
-
-  public init() { }
-
-  // Returns the number of elements in the OrderedSet.
-  public var count: Int {
-    return internalSet.count
-  }
-
-  // Inserts an item. Performance: O(n)
-  public mutating func insert(item: T) {
-    if exists(item) {
-      return  // don't add an item if it already exists
+public class OrderedSet<T: Hashable> {
+  private var objects: [T] = []
+  private var indexOfKey: [T: Int] = [:]
+  
+  public init() {}
+  
+  // O(1)
+  public func add(_ object: T) {
+    guard indexOfKey[object] == nil else {
+      return
     }
-
-    // Insert new the item just before the one that is larger.
-    for i in 0..<count {
-      if internalSet[i] > item {
-        internalSet.insert(item, atIndex: i)
-        return
-      }
-    }
-
-    // Append to the back if the new item is greater than any other in the set.
-    internalSet.append(item)
+    
+    objects.append(object)
+    indexOfKey[object] = objects.count - 1
   }
-
-  // Removes an item if it exists. Performance: O(n)
-  public mutating func remove(item: T) {
-    if let index = indexOf(item) {
-      internalSet.removeAtIndex(index)
+  
+  // O(n)
+  public func insert(_ object: T, at index: Int) {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    guard indexOfKey[object] == nil else {
+      return
     }
-  }
-
-  // Returns true if and only if the item exists somewhere in the set.
-  public func exists(item: T) -> Bool {
-    return indexOf(item) != nil
-  }
-
-  // Returns the index of an item if it exists, or -1 otherwise.
-  public func indexOf(item: T) -> Int? {
-    var leftBound = 0
-    var rightBound = count - 1
-
-    while leftBound <= rightBound {
-      let mid = leftBound + ((rightBound - leftBound) / 2)
-
-      if internalSet[mid] > item {
-        rightBound = mid - 1
-      } else if internalSet[mid] < item {
-        leftBound = mid + 1
-      } else if internalSet[mid] == item {
-        return mid
-      } else {
-        // When we get here, we've landed on an item whose value is equal to the
-        // value of the item we're looking for, but the items themselves are not
-        // equal. We need to check the items with the same value to the right
-        // and to the left in order to find an exact match.
-
-        // Check to the right.
-        for j in mid.stride(to: count - 1, by: 1) {
-          if internalSet[j + 1] == item {
-            return j + 1
-          } else if internalSet[j] < internalSet[j + 1] {
-            break
-          }
-        }
-
-        // Check to the left.
-        for j in mid.stride(to: 0, by: -1) {
-          if internalSet[j - 1] == item {
-            return j - 1
-          } else if internalSet[j] > internalSet[j - 1] {
-            break
-          }
-        }
-        return nil
-      }
+    
+    objects.insert(object, at: index)
+    indexOfKey[object] = index
+    for i in index+1..<objects.count {
+      indexOfKey[objects[i]] = i
     }
-    return nil
   }
-
-  // Returns the item at the given index.
-  // Assertion fails if the index is out of the range of [0, count).
-  public subscript(index: Int) -> T {
-    assert(index >= 0 && index < count)
-    return internalSet[index]
+  
+  // O(1)
+  public func object(at index: Int) -> T {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    return objects[index]
   }
-
-  // Returns the 'maximum' or 'largest' value in the set.
-  public func max() -> T? {
-    return count == 0 ? nil : internalSet[count - 1]
+  
+  // O(1)
+  public func set(_ object: T, at index: Int) {
+    assert(index < objects.count, "Index should be smaller than object count")
+    assert(index >= 0, "Index should be bigger than 0")
+    
+    guard indexOfKey[object] == nil else {
+      return
+    }
+    
+    indexOfKey.removeValue(forKey: objects[index])
+    indexOfKey[object] = index
+    objects[index] = object
   }
-
-  // Returns the 'minimum' or 'smallest' value in the set.
-  public func min() -> T? {
-    return count == 0 ? nil : internalSet[0]
+  
+  // O(1)
+  public func indexOf(_ object: T) -> Int {
+    return indexOfKey[object] ?? -1
   }
-
-  // Returns the k-th largest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kLargest(k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[count - k]
+  
+  // O(n)
+  public func remove(_ object: T) {
+    guard let index = indexOfKey[object] else {
+      return
+    }
+    
+    indexOfKey.removeValue(forKey: object)
+    objects.remove(at: index)
+    for i in index..<objects.count {
+      indexOfKey[objects[i]] = i
+    }
   }
-
-  // Returns the k-th smallest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kSmallest(k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  
+  public func all() -> [T] {
+    return objects
   }
 }
+
diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
index 11096d5bb..82d736731 100644
--- a/Ordered Set/README.markdown	
+++ b/Ordered Set/README.markdown	
@@ -1,338 +1,6 @@
 # Ordered Set
 
-## Sorted Array Version
-
-An Ordered Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest.
-
-The Ordered Set data type is a hybrid of:
-
-- a [Set](https://en.wikipedia.org/wiki/Set_%28mathematics%29), a collection of unique items where the order does not matter, and
-- a [Sequence](https://en.wikipedia.org/wiki/Sequence), an ordered list of items where each item may appear more than once.
-
-It's important to keep in mind that two items can have the same *value* but still may not be equal. For example, we could define "a" and "z" to have the same value (their lengths), but clearly "a" != "z".
-
-## Why use an ordered set?
-
-Ordered Sets should be considered when you need to keep your collection sorted at all times, and you do lookups on the collection much more frequently than inserting or deleting items. Many of the lookup operations for an Ordered Set are **O(1)**.
-
-A good example would be keeping track of the rankings of players in a scoreboard (see example 2 below).
-
-#### These are ordered sets
-
-A set of integers:
-
-	[1, 2, 3, 6, 8, 10, 1000]
-
-A set of strings:
-
-	["a", "is", "set", "this"]
-
-The "value" of these strings could be their text content, but also for example their length.
-
-#### These are not ordered sets
-
-This set violates the property of uniqueness:
-
-	[1, 1, 2, 3, 5, 8]
-
-This set violates the sorted property:
-
-	[1, 11, 2, 3]
-
-## The code
-
-We'll start by creating our internal representation for the Ordered Set. Since the idea of a set is similar to that of an array, we will use an array to represent our set. Furthermore, since we'll need to keep the set sorted, we need to be able to compare the individual elements. Thus, any type must conform to the [Comparable Protocol](https://developer.apple.com/library/watchos/documentation/Swift/Reference/Swift_Comparable_Protocol/index.html).
-
-```swift
-public struct OrderedSet<T: Comparable> {
-  private var internalSet = [T]()
-
-  // Returns the number of elements in the OrderedSet.
-  public var count: Int {
-    return internalSet.count
-  }
-  ...
-```
-
-Lets take a look at the `insert()` function first. This first checks if the item already exists in the collection. If so, it returns and does not insert the item.  Otherwise, it will insert the item through straightforward iteration.
-
-```swift
-  public mutating func insert(_ item: T){
-    if exists(item) {
-      return  // don't add an item if it already exists
-    }
-
-    // Insert new the item just before the one that is larger.
-    for i in 0..<count {
-      if internalSet[i] > item {
-        internalSet.insert(item, at: i)
-        return
-      }
-    }
-
-    // Append to the back if the new item is greater than any other in the set.
-    internalSet.append(item)
-  }
-```
-
-As we'll see later on, checking if the item is already in the set has an efficiency of **O(log(n) + k)** where **k** is the number of items with the same value as the item we are inserting.
-
-To insert the new item, the `for` loop starts from the beginning of the array, and checks to see if each item is larger than the item we want to insert. Once we find such an item, we insert the new one into its place. This shifts the rest of the array over to the right by 1 position. This loop is at worst **O(n)**.
-
-The total performance of the `insert()` function is therefore **O(n)**.
-
-Next up is the `remove()` function:
-
-```swift
-  public mutating func remove(_ item: T) {
-    if let index = index(of: item) {
-      internalSet.remove(at: index)
-    }
-  }
-```
-
-First this checks if the item exists and then removes it from the array. Because of the `removeAtIndex()` function, the efficiency for remove is **O(n)**.
-
-The next function is `indexOf()`, which takes in an object of type `T` and returns the index of the corresponding item if it is in the set, or `nil` if it is not. Since our set is sorted, we can use a binary search to quickly search for the item.
-
-```swift
-  public func index(of item: T) -> Int? {
-    var leftBound = 0
-    var rightBound = count - 1
-
-    while leftBound <= rightBound {
-      let mid = leftBound + ((rightBound - leftBound) / 2)
-
-      if internalSet[mid] > item {
-        rightBound = mid - 1
-      } else if internalSet[mid] < item {
-        leftBound = mid + 1
-      } else if internalSet[mid] == item {
-        return mid
-      } else {
-      	// see below
-      }
-    }
-    return nil
-  }
-```
-
-> **Note:** If you are not familiar with the concept of binary search, we have an [article that explains all about it](../Binary%20Search).
-
-However, there is an important issue to deal with here. Recall that two objects can be unequal yet still have the same "value" for the purposes of comparing them. Since a set can contain multiple items with the same value, it is important to check that the binary search has landed on the correct item.
-
-For example, consider this ordered set of `Player` objects. Each `Player` has a name and a number of points:
-
-	[ ("Bill", 50), ("Ada", 50), ("Jony", 50), ("Steve", 200), ("Jean-Louis", 500), ("Woz", 1000) ]
-
-We want the set to be ordered by points, from low to high. Multiple players can have the same number of points. The name of the player is not important for this ordering. However, the name *is* important for retrieving the correct item.
-
-Let's say we do `indexOf(bill)` where `bill` is player object `("Bill", 50)`. If we did a traditional binary search we'd land on index 2, which is the object `("Jony", 50)`. The value 50 matches, but it's not the object we're looking for!
-
-Therefore, we also need to check the items with the same value to the right and left of the midpoint. The code to check the left and right side looks like this:
-
-```swift
-        // Check to the right.
-        for j in mid.stride(to: count - 1, by: 1) {
-          if internalSet[j + 1] == item {
-            return j + 1
-          } else if internalSet[j] < internalSet[j + 1] {
-            break
-          }
-        }
-
-        // Check to the left.
-        for j in mid.stride(to: 0, by: -1) {
-          if internalSet[j - 1] == item {
-            return j - 1
-          } else if internalSet[j] > internalSet[j - 1] {
-            break
-          }
-        }
-
-        return nil
-```
-
-These loops start at the current `mid` value and then look at the neighboring values until we've found the correct object.
-
-The combined runtime for `indexOf()` is **O(log(n) + k)** where **n** is the length of the set, and **k** is the number of items with the same *value* as the one that is being searched for.
-
-Since the set is sorted, the following operations are all **O(1)**:
-
-```swift
-  // Returns the 'maximum' or 'largest' value in the set.
-  public func max() -> T? {
-    return count == 0 ? nil : internalSet[count - 1]
-  }
-
-  // Returns the 'minimum' or 'smallest' value in the set.
-  public func min() -> T? {
-    return count == 0 ? nil : internalSet[0]
-  }
-
-  // Returns the k-th largest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kLargest(_ k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[count - k]
-  }
-
-  // Returns the k-th smallest element in the set, if k is in the range
-  // [1, count]. Returns nil otherwise.
-  public func kSmallest(_ k: Int) -> T? {
-    return k > count || k <= 0 ? nil : internalSet[k - 1]
-  }
-```
-
-## Examples
-
-Below are a few examples that can be found in the playground file.
-
-### Example 1
-
-Here we create a set with random Integers. Printing the largest/smallest 5 numbers in the set is fairly easy.
-
-```swift
-// Example 1 with type Int
-var mySet = OrderedSet<Int>()
-
-// Insert random numbers into the set
-for _ in 0..<50 {
-  mySet.insert(randomNum(50, max: 500))
-}
-
-print(mySet)
-
-print(mySet.max())
-print(mySet.min())
-
-// Print the 5 largest values
-for k in 1...5 {
-  print(mySet.kLargest(k))
-}
-
-// Print the 5 lowest values
-for k in 1...5 {
-  print(mySet.kSmallest(k))
-}
-```
-
-### Example 2
-
-In this example we take a look at something a bit more interesting. We define a `Player` struct as follows:
-
-```swift
-public struct Player: Comparable {
-  public var name: String
-  public var points: Int
-}
-```
-
-The `Player` also gets its own `==` and `<` operators. The `<` operator is used to determine the sort order of the set, while `==` determines whether two objects are really equal.
-
-Note that `==` compares both the name and the points:  
-
-```swifr
-func ==(x: Player, y: Player) -> Bool {
-  return x.name == y.name && x.points == y.points
-}
-```
-
-But `<` only compares the points:
-
-```swift
-func <(x: Player, y: Player) -> Bool {
-  return x.points < y.points
-}
-```
-
-Therefore, two `Player`s can each have the same value (the number of points), but are not guaranteed to be equal (they can have different names).
-
-We create a new set and insert 20 random players. The `Player()` constructor gives each player a random name and score:
-
-```swift
-var playerSet = OrderedSet<Player>()
-
-// Populate the set with random players.
-for _ in 0..<20 {
-  playerSet.insert(Player())
-}
-```
-
-Insert another player:
-
-```swift
-var anotherPlayer = Player()
-playerSet.insert(anotherPlayer)
-```
-
-Now we use the `indexOf()` function to find out what rank `anotherPlayer` is.
-
-```swift
-let level = playerSet.count - playerSet.indexOf(anotherPlayer)!
-print("\(anotherPlayer.name) is ranked at level \(level) with \(anotherPlayer.points) points")
-```
-
-### Example 3
-
-The final example demonstrates the need to look for the right item even after the binary search has completed.
-
-We insert 9 players into the set:
-
-```swift
-var repeatedSet = OrderedSet<Player>()
-
-repeatedSet.insert(Player(name: "Player 1", points: 100))
-repeatedSet.insert(Player(name: "Player 2", points: 100))
-repeatedSet.insert(Player(name: "Player 3", points: 100))
-repeatedSet.insert(Player(name: "Player 4", points: 100))
-repeatedSet.insert(Player(name: "Player 5", points: 100))
-repeatedSet.insert(Player(name: "Player 6", points: 50))
-repeatedSet.insert(Player(name: "Player 7", points: 200))
-repeatedSet.insert(Player(name: "Player 8", points: 250))
-repeatedSet.insert(Player(name: "Player 9", points: 25))
-```
-
-Notice how several of these players have the same value of 100 points.
-
-The set looks something like this:
-
-	[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
-
-The next line looks for `Player 2`:
-
-```swift
-print(repeatedSet.index(of: Player(name: "Player 2", points: 100)))
-```
-
-After the binary search finishes, the value of `mid` is at index 5:
-
-	[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
-	                                                      mid
-
-However, this is not `Player 2`. Both `Player 4` and `Player 2` have the same points, but a different name. The binary search only looked at the points, not the name.
-
-But we do know that `Player 2` must be either to the immediate left or the right of `Player 4`, so we check both sides of `mid`. We only need to look at the objects with the same value as `Player 4`. The others are replaced by `X`:
-
-	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-	                                       mid
-
-The code then first checks on the right of `mid` (where the `*` is):
-
-	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-	                                       mid        *
-
-The right side did not contain the item, so we look at the left side:
-
-	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-	                              *        mid        
-	
-	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
-	                    *                  mid        
-
-Finally, we've found `Player 2`, and return index 3.
-
-## Apple's Ordered Set
-Below the ordered set is based on sorted array. But [Apple's version](https://developer.apple.com/documentation/foundation/nsorderedset), it's pretty different. Now, let's look into how to implement apple's ordered set.
+Let's look into how to implement [Ordered Set](https://developer.apple.com/documentation/foundation/nsorderedset).
 
 Here is the example about how it works
 
@@ -450,4 +118,4 @@ public func remove(_ object: T) {
 }
 ```
 
-*Ordered Set is Written By Zain Humayun, Apple Ordered Set is Written By Kai Chen*
+*Written By Kai Chen*
diff --git a/Sorted Set/README.markdown b/Sorted Set/README.markdown
new file mode 100644
index 000000000..a8b5ad1ea
--- /dev/null
+++ b/Sorted Set/README.markdown	
@@ -0,0 +1,334 @@
+# Sorted Set
+
+## Sorted Array Version
+
+An Sorted Set is a collection of unique items in sorted order. Items are usually sorted from least to greatest.
+
+The Sorted Set data type is a hybrid of:
+
+- a [Set](https://en.wikipedia.org/wiki/Set_%28mathematics%29), a collection of unique items where the order does not matter, and
+- a [Sequence](https://en.wikipedia.org/wiki/Sequence), an sorted list of items where each item may appear more than once.
+
+It's important to keep in mind that two items can have the same *value* but still may not be equal. For example, we could define "a" and "z" to have the same value (their lengths), but clearly "a" != "z".
+
+## Why use an sorted set?
+
+Sorted Sets should be considered when you need to keep your collection sorted at all times, and you do lookups on the collection much more frequently than inserting or deleting items. Many of the lookup operations for an Sorted Set are **O(1)**.
+
+A good example would be keeping track of the rankings of players in a scoreboard (see example 2 below).
+
+#### These are sorted sets
+
+A set of integers:
+
+	[1, 2, 3, 6, 8, 10, 1000]
+
+A set of strings:
+
+	["a", "is", "set", "this"]
+
+The "value" of these strings could be their text content, but also for example their length.
+
+#### These are not sorted sets
+
+This set violates the property of uniqueness:
+
+	[1, 1, 2, 3, 5, 8]
+
+This set violates the sorted property:
+
+	[1, 11, 2, 3]
+
+## The code
+
+We'll start by creating our internal representation for the Sorted Set. Since the idea of a set is similar to that of an array, we will use an array to represent our set. Furthermore, since we'll need to keep the set sorted, we need to be able to compare the individual elements. Thus, any type must conform to the [Comparable Protocol](https://developer.apple.com/library/watchos/documentation/Swift/Reference/Swift_Comparable_Protocol/index.html).
+
+```swift
+public struct SortedSet<T: Comparable> {
+  private var internalSet = [T]()
+
+  // Returns the number of elements in the SortedSet.
+  public var count: Int {
+    return internalSet.count
+  }
+  ...
+```
+
+Lets take a look at the `insert()` function first. This first checks if the item already exists in the collection. If so, it returns and does not insert the item.  Otherwise, it will insert the item through straightforward iteration.
+
+```swift
+  public mutating func insert(_ item: T){
+    if exists(item) {
+      return  // don't add an item if it already exists
+    }
+
+    // Insert new the item just before the one that is larger.
+    for i in 0..<count {
+      if internalSet[i] > item {
+        internalSet.insert(item, at: i)
+        return
+      }
+    }
+
+    // Append to the back if the new item is greater than any other in the set.
+    internalSet.append(item)
+  }
+```
+
+As we'll see later on, checking if the item is already in the set has an efficiency of **O(log(n) + k)** where **k** is the number of items with the same value as the item we are inserting.
+
+To insert the new item, the `for` loop starts from the beginning of the array, and checks to see if each item is larger than the item we want to insert. Once we find such an item, we insert the new one into its place. This shifts the rest of the array over to the right by 1 position. This loop is at worst **O(n)**.
+
+The total performance of the `insert()` function is therefore **O(n)**.
+
+Next up is the `remove()` function:
+
+```swift
+  public mutating func remove(_ item: T) {
+    if let index = index(of: item) {
+      internalSet.remove(at: index)
+    }
+  }
+```
+
+First this checks if the item exists and then removes it from the array. Because of the `removeAtIndex()` function, the efficiency for remove is **O(n)**.
+
+The next function is `indexOf()`, which takes in an object of type `T` and returns the index of the corresponding item if it is in the set, or `nil` if it is not. Since our set is sorted, we can use a binary search to quickly search for the item.
+
+```swift
+  public func index(of item: T) -> Int? {
+    var leftBound = 0
+    var rightBound = count - 1
+
+    while leftBound <= rightBound {
+      let mid = leftBound + ((rightBound - leftBound) / 2)
+
+      if internalSet[mid] > item {
+        rightBound = mid - 1
+      } else if internalSet[mid] < item {
+        leftBound = mid + 1
+      } else if internalSet[mid] == item {
+        return mid
+      } else {
+      	// see below
+      }
+    }
+    return nil
+  }
+```
+
+> **Note:** If you are not familiar with the concept of binary search, we have an [article that explains all about it](../Binary%20Search).
+
+However, there is an important issue to deal with here. Recall that two objects can be unequal yet still have the same "value" for the purposes of comparing them. Since a set can contain multiple items with the same value, it is important to check that the binary search has landed on the correct item.
+
+For example, consider this sorted set of `Player` objects. Each `Player` has a name and a number of points:
+
+	[ ("Bill", 50), ("Ada", 50), ("Jony", 50), ("Steve", 200), ("Jean-Louis", 500), ("Woz", 1000) ]
+
+We want the set to be sorted by points, from low to high. Multiple players can have the same number of points. The name of the player is not important for this ordering. However, the name *is* important for retrieving the correct item.
+
+Let's say we do `indexOf(bill)` where `bill` is player object `("Bill", 50)`. If we did a traditional binary search we'd land on index 2, which is the object `("Jony", 50)`. The value 50 matches, but it's not the object we're looking for!
+
+Therefore, we also need to check the items with the same value to the right and left of the midpoint. The code to check the left and right side looks like this:
+
+```swift
+        // Check to the right.
+        for j in mid.stride(to: count - 1, by: 1) {
+          if internalSet[j + 1] == item {
+            return j + 1
+          } else if internalSet[j] < internalSet[j + 1] {
+            break
+          }
+        }
+
+        // Check to the left.
+        for j in mid.stride(to: 0, by: -1) {
+          if internalSet[j - 1] == item {
+            return j - 1
+          } else if internalSet[j] > internalSet[j - 1] {
+            break
+          }
+        }
+
+        return nil
+```
+
+These loops start at the current `mid` value and then look at the neighboring values until we've found the correct object.
+
+The combined runtime for `indexOf()` is **O(log(n) + k)** where **n** is the length of the set, and **k** is the number of items with the same *value* as the one that is being searched for.
+
+Since the set is sorted, the following operations are all **O(1)**:
+
+```swift
+  // Returns the 'maximum' or 'largest' value in the set.
+  public func max() -> T? {
+    return count == 0 ? nil : internalSet[count - 1]
+  }
+
+  // Returns the 'minimum' or 'smallest' value in the set.
+  public func min() -> T? {
+    return count == 0 ? nil : internalSet[0]
+  }
+
+  // Returns the k-th largest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kLargest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[count - k]
+  }
+
+  // Returns the k-th smallest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kSmallest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  }
+```
+
+## Examples
+
+Below are a few examples that can be found in the playground file.
+
+### Example 1
+
+Here we create a set with random Integers. Printing the largest/smallest 5 numbers in the set is fairly easy.
+
+```swift
+// Example 1 with type Int
+var mySet = SortedSet<Int>()
+
+// Insert random numbers into the set
+for _ in 0..<50 {
+  mySet.insert(randomNum(50, max: 500))
+}
+
+print(mySet)
+
+print(mySet.max())
+print(mySet.min())
+
+// Print the 5 largest values
+for k in 1...5 {
+  print(mySet.kLargest(k))
+}
+
+// Print the 5 lowest values
+for k in 1...5 {
+  print(mySet.kSmallest(k))
+}
+```
+
+### Example 2
+
+In this example we take a look at something a bit more interesting. We define a `Player` struct as follows:
+
+```swift
+public struct Player: Comparable {
+  public var name: String
+  public var points: Int
+}
+```
+
+The `Player` also gets its own `==` and `<` operators. The `<` operator is used to determine the sort order of the set, while `==` determines whether two objects are really equal.
+
+Note that `==` compares both the name and the points:  
+
+```swifr
+func ==(x: Player, y: Player) -> Bool {
+  return x.name == y.name && x.points == y.points
+}
+```
+
+But `<` only compares the points:
+
+```swift
+func <(x: Player, y: Player) -> Bool {
+  return x.points < y.points
+}
+```
+
+Therefore, two `Player`s can each have the same value (the number of points), but are not guaranteed to be equal (they can have different names).
+
+We create a new set and insert 20 random players. The `Player()` constructor gives each player a random name and score:
+
+```swift
+var playerSet = SortedSet<Player>()
+
+// Populate the set with random players.
+for _ in 0..<20 {
+  playerSet.insert(Player())
+}
+```
+
+Insert another player:
+
+```swift
+var anotherPlayer = Player()
+playerSet.insert(anotherPlayer)
+```
+
+Now we use the `indexOf()` function to find out what rank `anotherPlayer` is.
+
+```swift
+let level = playerSet.count - playerSet.indexOf(anotherPlayer)!
+print("\(anotherPlayer.name) is ranked at level \(level) with \(anotherPlayer.points) points")
+```
+
+### Example 3
+
+The final example demonstrates the need to look for the right item even after the binary search has completed.
+
+We insert 9 players into the set:
+
+```swift
+var repeatedSet = SortedSet<Player>()
+
+repeatedSet.insert(Player(name: "Player 1", points: 100))
+repeatedSet.insert(Player(name: "Player 2", points: 100))
+repeatedSet.insert(Player(name: "Player 3", points: 100))
+repeatedSet.insert(Player(name: "Player 4", points: 100))
+repeatedSet.insert(Player(name: "Player 5", points: 100))
+repeatedSet.insert(Player(name: "Player 6", points: 50))
+repeatedSet.insert(Player(name: "Player 7", points: 200))
+repeatedSet.insert(Player(name: "Player 8", points: 250))
+repeatedSet.insert(Player(name: "Player 9", points: 25))
+```
+
+Notice how several of these players have the same value of 100 points.
+
+The set looks something like this:
+
+	[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
+
+The next line looks for `Player 2`:
+
+```swift
+print(repeatedSet.index(of: Player(name: "Player 2", points: 100)))
+```
+
+After the binary search finishes, the value of `mid` is at index 5:
+
+	[Player 9, Player 6, Player 1, Player 2, Player 3, Player 4, Player 5, Player 7, Player 8]
+	                                                      mid
+
+However, this is not `Player 2`. Both `Player 4` and `Player 2` have the same points, but a different name. The binary search only looked at the points, not the name.
+
+But we do know that `Player 2` must be either to the immediate left or the right of `Player 4`, so we check both sides of `mid`. We only need to look at the objects with the same value as `Player 4`. The others are replaced by `X`:
+
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                                       mid
+
+The code then first checks on the right of `mid` (where the `*` is):
+
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                                       mid        *
+
+The right side did not contain the item, so we look at the left side:
+
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                              *        mid        
+	
+	[X, X, Player 1, Player 2, Player 3, Player 4, Player 5, X, X]
+	                    *                  mid        
+
+Finally, we've found `Player 2`, and return index 3.
+
+*Written By Zain Humayun*
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
similarity index 94%
rename from Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
rename to Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
index c12dadf0f..45af5f99d 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
+++ b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
@@ -5,7 +5,7 @@ print("Hello, Swift 4!")
 
 //: # Example 1 with type Int
 
-var mySet = OrderedSet<Int>()
+var mySet = SortedSet<Int>()
 
 // Insert random numbers into the set
 for _ in 0..<50 {
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline
similarity index 50%
rename from Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline
rename to Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline
index 53114d22e..dffc42643 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline	
+++ b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/timeline.xctimeline	
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=21&amp;CharacterRangeLoc=371&amp;EndingColumnNumber=0&amp;EndingLineNumber=24&amp;StartingColumnNumber=1&amp;StartingLineNumber=23&amp;Timestamp=525333424.593074"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Sorted%20Set/SortedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=21&amp;CharacterRangeLoc=370&amp;EndingColumnNumber=0&amp;EndingLineNumber=24&amp;StartingColumnNumber=1&amp;StartingLineNumber=23&amp;Timestamp=532757103.131521"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=24&amp;CharacterRangeLoc=412&amp;EndingColumnNumber=0&amp;EndingLineNumber=26&amp;StartingColumnNumber=3&amp;StartingLineNumber=25&amp;Timestamp=525333424.593234"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Sorted%20Set/SortedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=24&amp;CharacterRangeLoc=411&amp;EndingColumnNumber=0&amp;EndingLineNumber=26&amp;StartingColumnNumber=3&amp;StartingLineNumber=25&amp;Timestamp=532757103.131695"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Ordered%20Set/OrderedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=25&amp;CharacterRangeLoc=511&amp;EndingColumnNumber=0&amp;EndingLineNumber=32&amp;StartingColumnNumber=3&amp;StartingLineNumber=31&amp;Timestamp=525333424.593352"
+         documentLocation = "file:///Users/kaichen/src/swift-algorithm-club/Sorted%20Set/SortedSet.playground/Pages/Example%201.xcplaygroundpage#CharacterRangeLen=25&amp;CharacterRangeLoc=510&amp;EndingColumnNumber=0&amp;EndingLineNumber=32&amp;StartingColumnNumber=3&amp;StartingLineNumber=31&amp;Timestamp=532757103.131826"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift b/Sorted Set/SortedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift
similarity index 95%
rename from Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift
rename to Sorted Set/SortedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift
index c30260fff..2408d35d2 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift	
+++ b/Sorted Set/SortedSet.playground/Pages/Example 2.xcplaygroundpage/Contents.swift	
@@ -2,7 +2,7 @@
 
 //: # Example 2 with Player objects
 
-var playerSet = OrderedSet<Player>()
+var playerSet = SortedSet<Player>()
 
 // Populate the set with random players.
 for _ in 0..<20 {
diff --git a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift b/Sorted Set/SortedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift
similarity index 95%
rename from Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift
rename to Sorted Set/SortedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift
index 52f154c05..63edd11d2 100644
--- a/Ordered Set/OrderedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift	
+++ b/Sorted Set/SortedSet.playground/Pages/Example 3.xcplaygroundpage/Contents.swift	
@@ -2,7 +2,7 @@
 
 //: # Example 3: multiple entries with the same value
 
-var repeatedSet = OrderedSet<Player>()
+var repeatedSet = SortedSet<Player>()
 
 repeatedSet.insert(Player(name: "Player 1", points: 100))
 repeatedSet.insert(Player(name: "Player 2", points: 100))
diff --git a/Ordered Set/OrderedSet.playground/Sources/Player.swift b/Sorted Set/SortedSet.playground/Sources/Player.swift
similarity index 95%
rename from Ordered Set/OrderedSet.playground/Sources/Player.swift
rename to Sorted Set/SortedSet.playground/Sources/Player.swift
index 26835b0a8..0960b2400 100644
--- a/Ordered Set/OrderedSet.playground/Sources/Player.swift	
+++ b/Sorted Set/SortedSet.playground/Sources/Player.swift	
@@ -3,12 +3,12 @@
 public struct Player: Comparable {
   public var name: String
   public var points: Int
-
+  
   public init() {
     self.name = String.random()
     self.points = random(min: 0, max: 5000)
   }
-
+  
   public init(name: String, points: Int) {
     self.name = name
     self.points = points
@@ -31,7 +31,7 @@ public func print(player: Player) {
   print("Player: \(player.name) | Points: \(player.points)")
 }
 
-public func print(set: OrderedSet<Player>) {
+public func print(set: SortedSet<Player>) {
   for i in 0..<set.count {
     print(set[set.count - i - 1])
   }
diff --git a/Ordered Set/OrderedSet.playground/Sources/Random.swift b/Sorted Set/SortedSet.playground/Sources/Random.swift
similarity index 88%
rename from Ordered Set/OrderedSet.playground/Sources/Random.swift
rename to Sorted Set/SortedSet.playground/Sources/Random.swift
index eccd65df6..3f6c7536d 100644
--- a/Ordered Set/OrderedSet.playground/Sources/Random.swift	
+++ b/Sorted Set/SortedSet.playground/Sources/Random.swift	
@@ -10,9 +10,9 @@ extension String {
   public static func random(length: Int = 8) -> String {
     let base = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
     var randomString: String = ""
-
+    
     for _ in 0..<length {
-      let randomValue = arc4random_uniform(UInt32(base.characters.count))
+      let randomValue = arc4random_uniform(UInt32(base.count))
       randomString += "\(base[base.index(base.startIndex, offsetBy: Int(randomValue))])"
     }
     return randomString
diff --git a/Sorted Set/SortedSet.playground/Sources/SortedSet.swift b/Sorted Set/SortedSet.playground/Sources/SortedSet.swift
new file mode 100644
index 000000000..69546da0d
--- /dev/null
+++ b/Sorted Set/SortedSet.playground/Sources/SortedSet.swift	
@@ -0,0 +1,118 @@
+/*
+ An Sorted Set is a collection where all items in the set follow an ordering,
+ usually sorted from 'least' to 'most'. The way you value and compare items
+ can be user-defined.
+ */
+public struct SortedSet<T: Comparable> {
+  private var internalSet = [T]()
+  
+  public init() { }
+  
+  // Returns the number of elements in the SortedSet.
+  public var count: Int {
+    return internalSet.count
+  }
+  
+  // Inserts an item. Performance: O(n)
+  public mutating func insert(_ item: T) {
+    if exists(item) {
+      return  // don't add an item if it already exists
+    }
+    
+    // Insert new the item just before the one that is larger.
+    for i in 0..<count {
+      if internalSet[i] > item {
+        internalSet.insert(item, at: i)
+        return
+      }
+    }
+    
+    // Append to the back if the new item is greater than any other in the set.
+    internalSet.append(item)
+  }
+  
+  // Removes an item if it exists. Performance: O(n)
+  public mutating func remove(_ item: T) {
+    if let index = index(of: item) {
+      internalSet.remove(at: index)
+    }
+  }
+  
+  // Returns true if and only if the item exists somewhere in the set.
+  public func exists(_ item: T) -> Bool {
+    return index(of: item) != nil
+  }
+  
+  // Returns the index of an item if it exists, or -1 otherwise.
+  public func index(of item: T) -> Int? {
+    var leftBound = 0
+    var rightBound = count - 1
+    
+    while leftBound <= rightBound {
+      let mid = leftBound + ((rightBound - leftBound) / 2)
+      
+      if internalSet[mid] > item {
+        rightBound = mid - 1
+      } else if internalSet[mid] < item {
+        leftBound = mid + 1
+      } else if internalSet[mid] == item {
+        return mid
+      } else {
+        // When we get here, we've landed on an item whose value is equal to the
+        // value of the item we're looking for, but the items themselves are not
+        // equal. We need to check the items with the same value to the right
+        // and to the left in order to find an exact match.
+        
+        // Check to the right.
+        for j in stride(from: mid, to: count - 1, by: 1) {
+          if internalSet[j + 1] == item {
+            return j + 1
+          } else if internalSet[j] < internalSet[j + 1] {
+            break
+          }
+        }
+        
+        // Check to the left.
+        for j in stride(from: mid, to: 0, by: -1) {
+          if internalSet[j - 1] == item {
+            return j - 1
+          } else if internalSet[j] > internalSet[j - 1] {
+            break
+          }
+        }
+        return nil
+      }
+    }
+    return nil
+  }
+  
+  // Returns the item at the given index.
+  // Assertion fails if the index is out of the range of [0, count).
+  public subscript(index: Int) -> T {
+    assert(index >= 0 && index < count)
+    return internalSet[index]
+  }
+  
+  // Returns the 'maximum' or 'largest' value in the set.
+  public func max() -> T? {
+    return count == 0 ? nil : internalSet[count - 1]
+  }
+  
+  // Returns the 'minimum' or 'smallest' value in the set.
+  public func min() -> T? {
+    return count == 0 ? nil : internalSet[0]
+  }
+  
+  // Returns the k-th largest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kLargest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[count - k]
+  }
+  
+  // Returns the k-th smallest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kSmallest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  }
+}
+
diff --git a/Sorted Set/SortedSet.playground/contents.xcplayground b/Sorted Set/SortedSet.playground/contents.xcplayground
new file mode 100644
index 000000000..18c02c912
--- /dev/null
+++ b/Sorted Set/SortedSet.playground/contents.xcplayground	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='6.0' target-platform='ios' display-mode='raw' executeOnSourceChanges='false'>
+    <pages>
+        <page name='Example 1'/>
+        <page name='Example 2'/>
+        <page name='Example 3'/>
+    </pages>
+</playground>
\ No newline at end of file
diff --git a/Ordered Set/OrderedSet.playground/playground.xcworkspace/contents.xcworkspacedata b/Sorted Set/SortedSet.playground/playground.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Ordered Set/OrderedSet.playground/playground.xcworkspace/contents.xcworkspacedata
rename to Sorted Set/SortedSet.playground/playground.xcworkspace/contents.xcworkspacedata
diff --git a/Sorted Set/SortedSet.swift b/Sorted Set/SortedSet.swift
new file mode 100644
index 000000000..69546da0d
--- /dev/null
+++ b/Sorted Set/SortedSet.swift	
@@ -0,0 +1,118 @@
+/*
+ An Sorted Set is a collection where all items in the set follow an ordering,
+ usually sorted from 'least' to 'most'. The way you value and compare items
+ can be user-defined.
+ */
+public struct SortedSet<T: Comparable> {
+  private var internalSet = [T]()
+  
+  public init() { }
+  
+  // Returns the number of elements in the SortedSet.
+  public var count: Int {
+    return internalSet.count
+  }
+  
+  // Inserts an item. Performance: O(n)
+  public mutating func insert(_ item: T) {
+    if exists(item) {
+      return  // don't add an item if it already exists
+    }
+    
+    // Insert new the item just before the one that is larger.
+    for i in 0..<count {
+      if internalSet[i] > item {
+        internalSet.insert(item, at: i)
+        return
+      }
+    }
+    
+    // Append to the back if the new item is greater than any other in the set.
+    internalSet.append(item)
+  }
+  
+  // Removes an item if it exists. Performance: O(n)
+  public mutating func remove(_ item: T) {
+    if let index = index(of: item) {
+      internalSet.remove(at: index)
+    }
+  }
+  
+  // Returns true if and only if the item exists somewhere in the set.
+  public func exists(_ item: T) -> Bool {
+    return index(of: item) != nil
+  }
+  
+  // Returns the index of an item if it exists, or -1 otherwise.
+  public func index(of item: T) -> Int? {
+    var leftBound = 0
+    var rightBound = count - 1
+    
+    while leftBound <= rightBound {
+      let mid = leftBound + ((rightBound - leftBound) / 2)
+      
+      if internalSet[mid] > item {
+        rightBound = mid - 1
+      } else if internalSet[mid] < item {
+        leftBound = mid + 1
+      } else if internalSet[mid] == item {
+        return mid
+      } else {
+        // When we get here, we've landed on an item whose value is equal to the
+        // value of the item we're looking for, but the items themselves are not
+        // equal. We need to check the items with the same value to the right
+        // and to the left in order to find an exact match.
+        
+        // Check to the right.
+        for j in stride(from: mid, to: count - 1, by: 1) {
+          if internalSet[j + 1] == item {
+            return j + 1
+          } else if internalSet[j] < internalSet[j + 1] {
+            break
+          }
+        }
+        
+        // Check to the left.
+        for j in stride(from: mid, to: 0, by: -1) {
+          if internalSet[j - 1] == item {
+            return j - 1
+          } else if internalSet[j] > internalSet[j - 1] {
+            break
+          }
+        }
+        return nil
+      }
+    }
+    return nil
+  }
+  
+  // Returns the item at the given index.
+  // Assertion fails if the index is out of the range of [0, count).
+  public subscript(index: Int) -> T {
+    assert(index >= 0 && index < count)
+    return internalSet[index]
+  }
+  
+  // Returns the 'maximum' or 'largest' value in the set.
+  public func max() -> T? {
+    return count == 0 ? nil : internalSet[count - 1]
+  }
+  
+  // Returns the 'minimum' or 'smallest' value in the set.
+  public func min() -> T? {
+    return count == 0 ? nil : internalSet[0]
+  }
+  
+  // Returns the k-th largest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kLargest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[count - k]
+  }
+  
+  // Returns the k-th smallest element in the set, if k is in the range
+  // [1, count]. Returns nil otherwise.
+  public func kSmallest(_ k: Int) -> T? {
+    return k > count || k <= 0 ? nil : internalSet[k - 1]
+  }
+}
+
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index fbaa4cd54..3c7134d72 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1,6 +1,19 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Workspace
    version = "1.0">
+   <Group
+      location = "container:"
+      name = "Sorted Set">
+      <FileRef
+         location = "group:Sorted Set/README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:Sorted Set/SortedSet.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Sorted Set/SortedSet.swift">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Egg Drop Problem"
       name = "Egg Drop Problem">
@@ -1807,12 +1820,6 @@
    <Group
       location = "group:Ordered Set"
       name = "Ordered Set">
-      <FileRef
-         location = "group:AppleOrderedSet.playground">
-      </FileRef>
-      <FileRef
-         location = "group:AppleOrderedSet.swift">
-      </FileRef>
       <FileRef
          location = "group:OrderedSet.playground">
       </FileRef>

From c284df5882a11ad0c882ef32f32ac1e0759ff184 Mon Sep 17 00:00:00 2001
From: Emmanuoel Haroutunian <emmanuoel.h@gmail.com>
Date: Wed, 22 Nov 2017 23:55:30 -0800
Subject: [PATCH 304/643] Update README code to Swift 4

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

diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index cbcf5d352..b958da927 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -74,7 +74,7 @@ func selectionSort(_ array: [Int]) -> [Int] {
     }
 
     if x != lowest {               // 5
-      swap(&a[x], &a[lowest])
+      a.swapAt(x, lowest)
     }
   }
   return a

From ec6d34dd662eb42857d3d82197f358d4b7e64fb3 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Sun, 26 Nov 2017 00:33:57 +0900
Subject: [PATCH 305/643] Fixed LinkedList as follows: * Modified
 node(atIndex:) method not to return nil, and code refactoring. * Deleted
 nodesBeforeAndAfter(index:) method, and modified insert methods.

---
 .../LinkedList.playground/Contents.swift      | 169 +++++++++---------
 Linked List/LinkedList.swift                  | 118 ++++++------
 Linked List/Tests/LinkedListTests.swift       |  59 +++---
 3 files changed, 166 insertions(+), 180 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index b78ee4809..559e652bb 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -42,45 +42,50 @@ public final class LinkedList<T> {
 
   /// Computed property to iterate through the linked list and return the last node in the list (if any)
   public var last: Node? {
-    if var node = head {
-      while case let next? = node.next {
-        node = next
-      }
-      return node
-    } else {
+    guard let head = head else {
       return nil
     }
+    var node = head
+    while let next = node.next {
+      node = next
+    }
+    return node
   }
 
   /// Computed property to iterate through the linked list and return the total number of nodes
   public var count: Int {
-    if var node = head {
-      var c = 1
-      while case let next? = node.next {
-        node = next
-        c += 1
-      }
-      return c
-    } else {
+    guard let head = head else {
       return 0
     }
+    var node = head
+    var count = 1
+    while let next = node.next {
+      node = next
+      count += 1
+    }
+    return count
   }
 
   /// Function to return the node at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameter index: Integer value of the node's index to be returned
   /// - Returns: Optional LinkedListNode
-  public func node(atIndex index: Int) -> Node? {
-    if index >= 0 {
-      var node = head
-      var i = index
-      while node != nil {
-        if i == 0 { return node }
-        i -= 1
-        node = node!.next
-      }
+  public func node(atIndex index: Int) -> Node {
+    assert(head != nil, "List is empty")
+    if index == 0 {
+        return head!
+    } else {
+        var node = head!.next
+        for _ in 1..<index {
+            node = node?.next
+            if node == nil {
+                break
+            }
+        }
+        
+        assert(node != nil, "index is out of bounds.")
+        return node!
     }
-    return nil
   }
 
   /// Subscript function to return the node at a specific index
@@ -88,8 +93,7 @@ public final class LinkedList<T> {
   /// - Parameter index: Integer value of the requested value's index
   public subscript(index: Int) -> T {
     let node = self.node(atIndex: index)
-    assert(node != nil)
-    return node!.value
+    return node.value
   }
 
   /// Append a value to the end of the list
@@ -104,7 +108,7 @@ public final class LinkedList<T> {
   ///
   /// - Parameter node: The node containing the value to be appended
   public func append(_ node: Node) {
-    let newNode = LinkedListNode(value: node.value)
+    let newNode = node
     if let lastNode = last {
       newNode.previous = lastNode
       lastNode.next = newNode
@@ -124,27 +128,6 @@ public final class LinkedList<T> {
     }
   }
 
-  /// A private helper funciton to find the nodes before and after a specified index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameter index: Integer value of the index between the nodes.
-  /// - Returns: A tuple of 2 nodes before & after the specified index respectively.
-  private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
-    assert(index >= 0)
-
-    var i = index
-    var next = head
-    var prev: Node?
-
-    while next != nil && i > 0 {
-      i -= 1
-      prev = next
-      next = next!.next
-    }
-    assert(i == 0)  // if > 0, then specified index was too large
-
-    return (prev, next)
-  }
-
   /// Insert a value at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameters:
@@ -161,18 +144,20 @@ public final class LinkedList<T> {
   ///   - node: The node containing the value to be inserted
   ///   - index: Integer value of the index to be inserted at
   public func insert(_ node: Node, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index: index)
     let newNode = LinkedListNode(value: node.value)
-    newNode.previous = prev
-    newNode.next = next
-    prev?.next = newNode
-    next?.previous = newNode
-
-    if prev == nil {
+    if index == 0 {
+      newNode.next = head
+      head?.previous = newNode
       head = newNode
+    } else {
+      let separator = self.node(atIndex: index-1)
+      newNode.previous = separator
+      newNode.next = separator.next
+      separator.next?.previous = newNode
+      separator.next = newNode
     }
   }
-
+    
   /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameters:
@@ -180,22 +165,21 @@ public final class LinkedList<T> {
   ///   - index: Integer value of the index to be inserted at
   public func insert(_ list: LinkedList, atIndex index: Int) {
     if list.isEmpty { return }
-    var (prev, next) = nodesBeforeAndAfter(index: index)
-    var nodeToCopy = list.head
-    var newNode: Node?
-    while let node = nodeToCopy {
-      newNode = Node(value: node.value)
-      newNode?.previous = prev
-      if let previous = prev {
-        previous.next = newNode
-      } else {
-        self.head = newNode
-      }
-      nodeToCopy = nodeToCopy?.next
-      prev = newNode
+    
+    if index == 0 {
+      let temp = head
+      head = list.head
+      list.last?.next = temp
+    } else {
+      let separate = self.node(atIndex: index-1)
+      let temp = separate.next
+
+      separate.next = list.head
+      list.head?.previous = separate
+
+      list.last?.next = temp
+      temp?.previous = list.last?.next
     }
-    prev?.next = next
-    next?.previous = prev
   }
 
   /// Function to remove all nodes/value from the list
@@ -237,8 +221,7 @@ public final class LinkedList<T> {
   /// - Returns: The data value contained in the deleted node
   @discardableResult public func remove(atIndex index: Int) -> T {
     let node = self.node(atIndex: index)
-    assert(node != nil)
-    return remove(node: node!)
+    return remove(node: node)
   }
 }
 
@@ -324,7 +307,7 @@ list.first                    // nil
 list.last                     // nil
 
 list.append("Hello")
-list.isEmpty
+list.isEmpty                  // false
 list.first!.value             // "Hello"
 list.last!.value              // "Hello"
 list.count                    // 1
@@ -339,9 +322,9 @@ list.first!.next!.value       // "World"
 list.last!.previous!.value    // "Hello"
 list.last!.next               // nil
 
-list.node(atIndex: 0)!.value    // "Hello"
-list.node(atIndex: 1)!.value    // "World"
-list.node(atIndex: 2)           // nil
+list.node(atIndex: 0).value    // "Hello"
+list.node(atIndex: 1).value    // "World"
+//list.node(atIndex: 2)           // crash!
 
 list[0]     // "Hello"
 list[1]     // "World"
@@ -364,11 +347,11 @@ print(list)
 
 list.reverse()   // [World, Swift, Hello]
 
-list.node(atIndex: 0)!.value = "Universe"
-list.node(atIndex: 1)!.value = "Swifty"
-let m = list.map { s in s.characters.count }
+list.node(atIndex: 0).value = "Universe"
+list.node(atIndex: 1).value = "Swifty"
+let m = list.map { s in s.count }
 m    // [8, 6, 5]
-let f = list.filter { s in s.characters.count > 5 }
+let f = list.filter { s in s.count > 5 }
 f    // [Universe, Swifty]
 
 list.remove(node: list.first!) // "Universe"
@@ -376,13 +359,37 @@ list.count                     // 2
 list[0]                        // "Swifty"
 list[1]                        // "Hello"
 
+list.count                     // 2
 list.removeLast()              // "Hello"
+list.head?.value
 list.count                     // 1
 list[0]                        // "Swifty"
 
 list.remove(atIndex: 0)        // "Swifty"
 list.count                     // 0
 
+let list3 = LinkedList<String>()
+list3.insert("2", atIndex: 0) // [2]
+list3.count                   // 1
+list3.insert("4", atIndex: 1) // [2,4]
+list3.count                   // 2
+list3.insert("5", atIndex: 2) // [2,4,5]
+list3.count                   // 3
+list3.insert("3", atIndex: 1) // [2,3,4,5]
+list3.insert("1", atIndex: 0) // [1,2,3,4,5]
+
+let list4 = LinkedList<String>()
+list4.insert(list3, atIndex: 0) // [1,2,3,4,5]
+list4.count                     // 5
+
+let list5 = LinkedList<String>()
+list5.append("0")                // [0]
+list5.insert("End", atIndex:1)   // [0,End]
+list5.count                      // 2
+list5.insert(list4, atIndex: 1)  // [0,1,2,3,4,5,End]
+list5.count                      // 7
+
+
 let linkedList: LinkedList<Int> = [1, 2, 3, 4] // [1, 2, 3, 4]
 linkedList.count               // 4
 linkedList[0]                  // 1
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index a5594eb31..cef6670de 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -36,35 +36,40 @@ public final class LinkedList<T> {
     }
 
     public var count: Int {
-        if var node = head {
-            var c = 1
-            while let next = node.next {
-                node = next
-                c += 1
-            }
-            return c
-        } else {
+        guard let head = head else {
             return 0
         }
-    }
-
-    public func node(atIndex index: Int) -> Node? {
-        if index >= 0 {
-            var node = head
-            var i = index
-            while node != nil {
-                if i == 0 { return node }
-                i -= 1
-                node = node!.next
+        var node = head
+        var count = 1
+        while let next = node.next {
+            node = next
+            count += 1
+        }
+        return count
+    }
+    
+    public func node(atIndex index: Int) -> Node {
+        assert(head != nil, "List is empty")
+        assert(index >= 0, "index must be greater than 0")
+        if index == 0 {
+            return head!
+        } else {
+            var node = head!.next
+            for _ in 1..<index {
+                node = node?.next
+                if node == nil {
+                    break
+                }
             }
+            
+            assert(node != nil, "index is out of bounds.")
+            return node!
         }
-        return nil
     }
 
     public subscript(index: Int) -> T {
         let node = self.node(atIndex: index)
-        assert(node != nil)
-        return node!.value
+        return node.value
     }
 
     public func append(_ value: T) {
@@ -73,7 +78,7 @@ public final class LinkedList<T> {
     }
 
     public func append(_ node: Node) {
-        let newNode = LinkedListNode(value: node.value)
+        let newNode = node
         if let lastNode = last {
             newNode.previous = lastNode
             lastNode.next = newNode
@@ -90,61 +95,45 @@ public final class LinkedList<T> {
         }
     }
 
-    private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
-        assert(index >= 0)
-
-        var i = index
-        var next = head
-        var prev: Node?
-
-        while next != nil && i > 0 {
-            i -= 1
-            prev = next
-            next = next!.next
-        }
-        assert(i == 0)  // if > 0, then specified index was too large
-
-        return (prev, next)
-    }
-
     public func insert(_ value: T, atIndex index: Int) {
         let newNode = Node(value: value)
         self.insert(newNode, atIndex: index)
     }
 
     public func insert(_ node: Node, atIndex index: Int) {
-        let (prev, next) = nodesBeforeAndAfter(index: index)
         let newNode = LinkedListNode(value: node.value)
-        newNode.previous = prev
-        newNode.next = next
-        prev?.next = newNode
-        next?.previous = newNode
-
-        if prev == nil {
+        if index == 0 {
+            newNode.next = head
+            head?.previous = newNode
             head = newNode
+        } else {
+            let separator = self.node(atIndex: index-1)
+            newNode.previous = separator
+            newNode.next = separator.next
+            separator.next?.previous = newNode
+            separator.next = newNode
         }
     }
-
+    
     public func insert(_ list: LinkedList, atIndex index: Int) {
         if list.isEmpty { return }
-        var (prev, next) = nodesBeforeAndAfter(index: index)
-        var nodeToCopy = list.head
-        var newNode: Node?
-        while let node = nodeToCopy {
-            newNode = Node(value: node.value)
-            newNode?.previous = prev
-            if let previous = prev {
-                previous.next = newNode
-            } else {
-                self.head = newNode
-            }
-            nodeToCopy = nodeToCopy?.next
-            prev = newNode
+        
+        if index == 0 {
+            let temp = head
+            head = list.head
+            list.last?.next = temp
+        } else {
+            let separate = self.node(atIndex: index-1)
+            let temp = separate.next
+            
+            separate.next = list.head
+            list.head?.previous = separate
+            
+            list.last?.next = temp
+            temp?.previous = list.last?.next
         }
-        prev?.next = next
-        next?.previous = prev
     }
-
+    
     public func removeAll() {
         head = nil
     }
@@ -172,8 +161,7 @@ public final class LinkedList<T> {
 
     @discardableResult public func remove(atIndex index: Int) -> T {
         let node = self.node(atIndex: index)
-        assert(node != nil)
-        return remove(node: node!)
+        return remove(node: node)
     }
 }
 
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 0b2b116df..5bc27b23d 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -93,19 +93,13 @@ class LinkedListTest: XCTestCase {
     XCTAssertNil(list.last!.next)
   }
 
-  func testNodeAtIndexInEmptyList() {
-    let list = LinkedList<Int>()
-    let node = list.node(atIndex: 0)
-    XCTAssertNil(node)
-  }
-
   func testNodeAtIndexInListWithOneElement() {
     let list = LinkedList<Int>()
     list.append(123)
 
     let node = list.node(atIndex: 0)
     XCTAssertNotNil(node)
-    XCTAssertEqual(node!.value, 123)
+    XCTAssertEqual(node.value, 123)
     XCTAssertTrue(node === list.first)
   }
 
@@ -115,23 +109,20 @@ class LinkedListTest: XCTestCase {
     let nodeCount = list.count
     XCTAssertEqual(nodeCount, numbers.count)
 
-    XCTAssertNil(list.node(atIndex: -1))
-    XCTAssertNil(list.node(atIndex: nodeCount))
-
     let first = list.node(atIndex: 0)
     XCTAssertNotNil(first)
     XCTAssertTrue(first === list.first)
-    XCTAssertEqual(first!.value, numbers[0])
+    XCTAssertEqual(first.value, numbers[0])
 
     let last = list.node(atIndex: nodeCount - 1)
     XCTAssertNotNil(last)
     XCTAssertTrue(last === list.last)
-    XCTAssertEqual(last!.value, numbers[nodeCount - 1])
+    XCTAssertEqual(last.value, numbers[nodeCount - 1])
 
     for i in 0..<nodeCount {
       let node = list.node(atIndex: i)
       XCTAssertNotNil(node)
-      XCTAssertEqual(node!.value, numbers[i])
+      XCTAssertEqual(node.value, numbers[i])
     }
   }
 
@@ -151,7 +142,7 @@ class LinkedListTest: XCTestCase {
 
     let node = list.node(atIndex: 0)
     XCTAssertNotNil(node)
-    XCTAssertEqual(node!.value, 123)
+    XCTAssertEqual(node.value, 123)
   }
 
   func testInsertAtIndex() {
@@ -164,13 +155,13 @@ class LinkedListTest: XCTestCase {
 
     let node = list.node(atIndex: 3)
     XCTAssertNotNil(node)
-    XCTAssertEqual(node!.value, 444)
+    XCTAssertEqual(node.value, 444)
     XCTAssertEqual(nodeCount + 1, list.count)
 
     XCTAssertFalse(prev === node)
     XCTAssertFalse(next === node)
-    XCTAssertTrue(prev!.next === node)
-    XCTAssertTrue(next!.previous === node)
+    XCTAssertTrue(prev.next === node)
+    XCTAssertTrue(next.previous === node)
   }
 
   func testInsertListAtIndex() {
@@ -180,10 +171,10 @@ class LinkedListTest: XCTestCase {
     list2.append(102)
     list.insert(list2, atIndex: 2)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 1)?.value, 2)
-    XCTAssertEqual(list.node(atIndex: 2)?.value, 99)
-    XCTAssertEqual(list.node(atIndex: 3)?.value, 102)
-    XCTAssertEqual(list.node(atIndex: 4)?.value, 10)
+    XCTAssertEqual(list.node(atIndex: 1).value, 2)
+    XCTAssertEqual(list.node(atIndex: 2).value, 99)
+    XCTAssertEqual(list.node(atIndex: 3).value, 102)
+    XCTAssertEqual(list.node(atIndex: 4).value, 10)
   }
 
   func testInsertListAtFirstIndex() {
@@ -193,9 +184,9 @@ class LinkedListTest: XCTestCase {
     list2.append(102)
     list.insert(list2, atIndex: 0)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 0)?.value, 99)
-    XCTAssertEqual(list.node(atIndex: 1)?.value, 102)
-    XCTAssertEqual(list.node(atIndex: 2)?.value, 8)
+    XCTAssertEqual(list.node(atIndex: 0).value, 99)
+    XCTAssertEqual(list.node(atIndex: 1).value, 102)
+    XCTAssertEqual(list.node(atIndex: 2).value, 8)
   }
 
   func testInsertListAtLastIndex() {
@@ -205,9 +196,9 @@ class LinkedListTest: XCTestCase {
     list2.append(102)
     list.insert(list2, atIndex: list.count)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 5)?.value, 5)
-    XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
-    XCTAssertEqual(list.node(atIndex: 7)?.value, 102)
+    XCTAssertEqual(list.node(atIndex: 5).value, 5)
+    XCTAssertEqual(list.node(atIndex: 6).value, 99)
+    XCTAssertEqual(list.node(atIndex: 7).value, 102)
   }
 
   func testAppendList() {
@@ -217,9 +208,9 @@ class LinkedListTest: XCTestCase {
     list2.append(102)
     list.append(list2)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 5)?.value, 5)
-    XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
-    XCTAssertEqual(list.node(atIndex: 7)?.value, 102)
+    XCTAssertEqual(list.node(atIndex: 5).value, 5)
+    XCTAssertEqual(list.node(atIndex: 6).value, 99)
+    XCTAssertEqual(list.node(atIndex: 7).value, 102)
   }
 
   func testAppendListToEmptyList() {
@@ -229,8 +220,8 @@ class LinkedListTest: XCTestCase {
     list2.append(10)
     list.append(list2)
     XCTAssertTrue(list.count == 2)
-    XCTAssertEqual(list.node(atIndex: 0)?.value, 5)
-    XCTAssertEqual(list.node(atIndex: 1)?.value, 10)
+    XCTAssertEqual(list.node(atIndex: 0).value, 5)
+    XCTAssertEqual(list.node(atIndex: 1).value, 10)
   }
 
   func testRemoveAtIndexOnListWithOneElement() {
@@ -259,8 +250,8 @@ class LinkedListTest: XCTestCase {
 
     let node = list.node(atIndex: 3)
     XCTAssertTrue(next === node)
-    XCTAssertTrue(prev!.next === node)
-    XCTAssertTrue(node!.previous === prev)
+    XCTAssertTrue(prev.next === node)
+    XCTAssertTrue(node.previous === prev)
     XCTAssertEqual(nodeCount, list.count)
   }
 

From dc810d2a08c7f2d619a43626b1e9883e897f6f16 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Sun, 26 Nov 2017 11:39:40 +0900
Subject: [PATCH 306/643] Modified last and count method after review.

---
 Linked List/LinkedList.playground/Contents.swift |  8 ++++----
 Linked List/LinkedList.swift                     | 16 ++++++++--------
 2 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 559e652bb..167e55b56 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -42,10 +42,10 @@ public final class LinkedList<T> {
 
   /// Computed property to iterate through the linked list and return the last node in the list (if any)
   public var last: Node? {
-    guard let head = head else {
+    guard var node = head else {
       return nil
     }
-    var node = head
+    
     while let next = node.next {
       node = next
     }
@@ -54,10 +54,10 @@ public final class LinkedList<T> {
 
   /// Computed property to iterate through the linked list and return the total number of nodes
   public var count: Int {
-    guard let head = head else {
+    guard var node = head else {
       return 0
     }
-    var node = head
+    
     var count = 1
     while let next = node.next {
       node = next
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index cef6670de..e29bee86b 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -25,21 +25,21 @@ public final class LinkedList<T> {
     }
 
     public var last: Node? {
-        if var node = head {
-            while let next = node.next {
-                node = next
-            }
-            return node
-        } else {
+        guard var node = head else {
             return nil
         }
+        
+        while let next = node.next {
+            node = next
+        }
+        return node
     }
 
     public var count: Int {
-        guard let head = head else {
+        guard var node = head else {
             return 0
         }
-        var node = head
+        
         var count = 1
         while let next = node.next {
             node = next

From 71ae5a3bfb18cba13314593cad2a5da8d0906873 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Sun, 26 Nov 2017 11:57:13 +0900
Subject: [PATCH 307/643] Renamed variables in insert methods and code
 refactoring.

---
 .../LinkedList.playground/Contents.swift      | 20 +++++++++----------
 Linked List/LinkedList.swift                  | 20 +++++++++----------
 2 files changed, 20 insertions(+), 20 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 167e55b56..f8216fc6f 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -144,17 +144,17 @@ public final class LinkedList<T> {
   ///   - node: The node containing the value to be inserted
   ///   - index: Integer value of the index to be inserted at
   public func insert(_ node: Node, atIndex index: Int) {
-    let newNode = LinkedListNode(value: node.value)
+    let newNode = node
     if index == 0 {
       newNode.next = head
       head?.previous = newNode
       head = newNode
     } else {
-      let separator = self.node(atIndex: index-1)
-      newNode.previous = separator
-      newNode.next = separator.next
-      separator.next?.previous = newNode
-      separator.next = newNode
+      let prev = self.node(atIndex: index-1)
+      newNode.previous = prev
+      newNode.next = prev.next
+      prev.next?.previous = newNode
+      prev.next = newNode
     }
   }
     
@@ -171,11 +171,11 @@ public final class LinkedList<T> {
       head = list.head
       list.last?.next = temp
     } else {
-      let separate = self.node(atIndex: index-1)
-      let temp = separate.next
+      let prev = self.node(atIndex: index-1)
+      let temp = prev.next
 
-      separate.next = list.head
-      list.head?.previous = separate
+      prev.next = list.head
+      list.head?.previous = prev
 
       list.last?.next = temp
       temp?.previous = list.last?.next
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index e29bee86b..c0331bc0e 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -101,17 +101,17 @@ public final class LinkedList<T> {
     }
 
     public func insert(_ node: Node, atIndex index: Int) {
-        let newNode = LinkedListNode(value: node.value)
+        let newNode = node
         if index == 0 {
             newNode.next = head
             head?.previous = newNode
             head = newNode
         } else {
-            let separator = self.node(atIndex: index-1)
-            newNode.previous = separator
-            newNode.next = separator.next
-            separator.next?.previous = newNode
-            separator.next = newNode
+            let prev = self.node(atIndex: index-1)
+            newNode.previous = prev
+            newNode.next = prev.next
+            prev.next?.previous = newNode
+            prev.next = newNode
         }
     }
     
@@ -123,11 +123,11 @@ public final class LinkedList<T> {
             head = list.head
             list.last?.next = temp
         } else {
-            let separate = self.node(atIndex: index-1)
-            let temp = separate.next
+            let prev = self.node(atIndex: index-1)
+            let temp = prev.next
             
-            separate.next = list.head
-            list.head?.previous = separate
+            prev.next = list.head
+            list.head?.previous = prev
             
             list.last?.next = temp
             temp?.previous = list.last?.next

From bd7e4b1ef7a3d0c787aa74e06bc54750cf140805 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Sun, 26 Nov 2017 12:09:43 +0900
Subject: [PATCH 308/643] Fixed node(atIndex:) method to be the same in
 LinkedList.swift file.

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

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index f8216fc6f..af27f63a0 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -72,6 +72,8 @@ public final class LinkedList<T> {
   /// - Returns: Optional LinkedListNode
   public func node(atIndex index: Int) -> Node {
     assert(head != nil, "List is empty")
+    assert(index >= 0, "index must be greater than 0")
+    
     if index == 0 {
         return head!
     } else {

From b68e1fd411e8698c5de39bccb240fd6649acd3f7 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Sun, 26 Nov 2017 12:12:52 +0500
Subject: [PATCH 309/643] Fix a few typos in QuadTree/README.md

Quadrees -> Quadtrees
containts -> contains
Wiki -> Wikipedia

Also my editor automatically removed trailing spaces from empty lines
---
 QuadTree/README.md | 33 ++++++++++++++++-----------------
 1 file changed, 16 insertions(+), 17 deletions(-)

diff --git a/QuadTree/README.md b/QuadTree/README.md
index ff71a66f0..ff660f852 100644
--- a/QuadTree/README.md
+++ b/QuadTree/README.md
@@ -6,11 +6,11 @@ A quadtree is a [tree](https://github.com/raywenderlich/swift-algorithm-club/tre
 
 ### Problem
 
-Consider the following problem: your need to store a number of points (each point is a pair of `X` and `Y` coordinates) and then you need to answer which points lie in a certain rectangular region. A naive solution would be to store the points inside an array and then iterate over the points and check each one individually. This solution runs in O(n) though. 
+Consider the following problem: your need to store a number of points (each point is a pair of `X` and `Y` coordinates) and then you need to answer which points lie in a certain rectangular region. A naive solution would be to store the points inside an array and then iterate over the points and check each one individually. This solution runs in O(n) though.
 
 ### A Better Approach
 
-Quadrees are most commonly used to partition a two-dimensional space by recursively subdividing it into four regions(quadrants). Let's see how we can use a Quadtree to store the points.
+Quadtrees are most commonly used to partition a two-dimensional space by recursively subdividing it into four regions(quadrants). Let's see how we can use a Quadtree to store the points.
 
 Each node in the tree represents a rectangular region and stores a limited number(`maxPointCapacity`) of points that all lie in its region.
 
@@ -40,7 +40,7 @@ class QuadTreeNode {
   init(rect: Rect) {
     self.rect = rect
   }
-  
+
   ...
 }
 
@@ -52,11 +52,11 @@ extension QuadTreeNode {
 
   @discardableResult
   func add(point: Point) -> Bool {
-    
-    if !rect.containts(point: point) {
+
+    if !rect.contains(point: point) {
       return false
     }
-    
+
     switch type {
     case .internal(let children):
       // pass the point to one of the children
@@ -75,7 +75,7 @@ extension QuadTreeNode {
     }
     return true
   }
-  
+
   private func subdivide() {
     switch type {
     case .leaf:
@@ -105,9 +105,9 @@ To find the points that lie in a given region we can now traverse the tree from
 class QuadTree {
 
   ...
-  
+
   let root: QuadTreeNode
-  
+
    public func points(inRect rect: Rect) -> [Point] {
     return root.points(inRect: rect)
   }
@@ -115,23 +115,23 @@ class QuadTree {
 
 extension QuadTreeNode {
   func points(inRect rect: Rect) -> [Point] {
-    
+
     // if the node's rect and the given rect don't intersect, return an empty array,
     // because there can't be any points that lie the node's (or its children's) rect and
     // in the given rect
     if !self.rect.intersects(rect: rect) {
       return []
     }
-    
+
     var result: [Point] = []
-    
+
     // collect the node's points that lie in the rect
     for point in points {
-      if rect.containts(point: point) {
+      if rect.contains(point: point) {
         result.append(point)
       }
     }
-    
+
     switch type {
     case .leaf:
       break
@@ -141,7 +141,7 @@ extension QuadTreeNode {
         result.append(contentsOf: childNode.points(inRect: rect))
       }
     }
-    
+
     return result
   }
 }
@@ -154,7 +154,6 @@ Both adding a point and searching can still take up to O(n) in the worst case, s
 
 Displaying a large amount of objects in a MapView - a great use case for a Quadtree ([Thoughtbot Article](https://robots.thoughtbot.com/how-to-handle-large-amounts-of-data-on-maps))
 
-More info on [Wiki](https://en.wikipedia.org/wiki/Quadtree)
+More info on [Wikipedia](https://en.wikipedia.org/wiki/Quadtree)
 
 *Written for Swift Algorithm Club by Timur Galimov*
-

From fcf235ce42ae0bc281e78b48a79fa6e5174b2109 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Sun, 26 Nov 2017 12:27:27 +0500
Subject: [PATCH 310/643] Fix typos

alogrithm -> algorithm
collison -> collison

Also added a "to" to improved grammar and added newline to the file
---
 Rabin-Karp/README.markdown | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Rabin-Karp/README.markdown b/Rabin-Karp/README.markdown
index 79699caa8..4470c7f75 100644
--- a/Rabin-Karp/README.markdown
+++ b/Rabin-Karp/README.markdown
@@ -1,6 +1,6 @@
 # Rabin-Karp string search algorithm
 
-The Rabin-Karp string search alogrithm is used to search text for a pattern.
+The Rabin-Karp string search algorithm is used to search text for a pattern.
 
 A practical application of the algorithm is detecting plagiarism. Given source material, the algorithm can rapidly search through a paper for instances of sentences from the source material, ignoring details such as case and punctuation. Because of the abundance of the sought strings, single-string searching algorithms are impractical.
 
@@ -12,10 +12,10 @@ at a time (e.g. "he ") and subtracts out the previous hash from the "T".
 
 ## Algorithm
 
-The Rabin-Karp alogrithm uses a sliding window the size of the search pattern.  It starts by hashing the search pattern, then
+The Rabin-Karp algorithm uses a sliding window the size of the search pattern.  It starts by hashing the search pattern, then
 hashing the first x characters of the text string where x is the length of the search pattern.  It then slides the window one character over and uses
 the previous hash value to calculate the new hash faster.  Only when it finds a hash that matches the hash of the search pattern will it compare
-the two strings it see if they are the same (prevent a hash collision from producing a false positive)
+the two strings it see if they are the same (to prevent a hash collision from producing a false positive).
 
 ## The code
 
@@ -37,7 +37,7 @@ public func search(text: String , pattern: String) -> Int {
     let firstHash = hash(array: firstChars)
 
     if (patternHash == firstHash) {
-        // Verify this was not a hash collison
+        // Verify this was not a hash collision
         if firstChars == patternArray {
             return 0
         }
@@ -76,4 +76,4 @@ This will return 13 since ump is in the 13 position of the zero based string.
 [Rabin-Karp Wikipedia](https://en.wikipedia.org/wiki/Rabin%E2%80%93Karp_algorithm)
 
 
-*Written by [Bill Barbour](https://github.com/brbatwork)*
\ No newline at end of file
+*Written by [Bill Barbour](https://github.com/brbatwork)*

From 7e75d1086ee7c0dbac5ee2096eb294ef14c30324 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Sun, 26 Nov 2017 12:27:47 +0500
Subject: [PATCH 311/643] Fix warning: 'characters' is deprecated: Please use
 String or Substring directly

---
 Rabin-Karp/README.markdown                      | 4 ++--
 Rabin-Karp/Rabin-Karp.playground/Contents.swift | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Rabin-Karp/README.markdown b/Rabin-Karp/README.markdown
index 4470c7f75..a618d3981 100644
--- a/Rabin-Karp/README.markdown
+++ b/Rabin-Karp/README.markdown
@@ -24,8 +24,8 @@ The major search method is next.  More implementation details are in rabin-karp.
 ```swift
 public func search(text: String , pattern: String) -> Int {
     // convert to array of ints
-    let patternArray = pattern.characters.flatMap { $0.asInt }
-    let textArray = text.characters.flatMap { $0.asInt }
+    let patternArray = pattern.flatMap { $0.asInt }
+    let textArray = text.flatMap { $0.asInt }
 
     if textArray.count < patternArray.count {
         return -1
diff --git a/Rabin-Karp/Rabin-Karp.playground/Contents.swift b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
index c0a99339a..739b74e2a 100644
--- a/Rabin-Karp/Rabin-Karp.playground/Contents.swift
+++ b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
@@ -30,8 +30,8 @@ extension Character {
 // Find first position of pattern in the text using Rabin Karp algorithm
 public func search(text: String, pattern: String) -> Int {
     // convert to array of ints
-    let patternArray = pattern.characters.flatMap { $0.asInt }
-    let textArray = text.characters.flatMap { $0.asInt }
+    let patternArray = pattern.flatMap { $0.asInt }
+    let textArray = text.flatMap { $0.asInt }
 
     if textArray.count < patternArray.count {
         return -1

From 885d9d3d650296e15fa8b12eba734c36afb9069a Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Sun, 26 Nov 2017 12:48:57 +0500
Subject: [PATCH 312/643] Fix warning: Result of call to 'addNode' is unused

---
 .../DepthFirstSearch.playground/Sources/Graph.swift              | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift
index 34ee2fa3a..48b8feed5 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift	
@@ -5,6 +5,7 @@ public class Graph: CustomStringConvertible, Equatable {
     self.nodes = []
   }
   
+  @discardableResult
   public func addNode(_ label: String) -> Node {
     let node = Node(label)
     nodes.append(node)

From 0b129e8894ec9699f5ebee60c2bcddddc256b770 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Tue, 28 Nov 2017 00:56:30 +0900
Subject: [PATCH 313/643] Modified readme file in LinkedList.

---
 Linked List/README.markdown | 227 ++++++++++++++++++++----------------
 1 file changed, 124 insertions(+), 103 deletions(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 2e1f03ece..55b61e910 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -110,14 +110,14 @@ Let's also add a property that gives you the last node in the list. This is wher
 
 ```swift
   public var last: Node? {
-    if var node = head {
-      while let next = node.next {
-        node = next
-      }
-      return node
-    } else {
+    guard var node = head else {
       return nil
     }
+  
+    while let next = node.next {
+      node = next
+    }
+    return node
   }
 ```
 
@@ -198,16 +198,16 @@ Let's add a method to count how many nodes are in the list. This will look very
 
 ```swift
   public var count: Int {
-    if var node = head {
-      var c = 1
-      while let next = node.next {
-        node = next
-        c += 1
-      }
-      return c
-    } else {
+    guard var node = head else {
       return 0
     }
+  
+    var count = 1
+    while let next = node.next {
+      node = next
+      count += 1
+    }
+    return count
   }
 ```
 
@@ -218,37 +218,43 @@ It loops through the list in the same manner but this time increments a counter
 What if we wanted to find the node at a specific index in the list? With an array we can just write `array[index]` and it's an **O(1)** operation. It's a bit more involved with linked lists, but again the code follows a similar pattern:
 
 ```swift
-  public func nodeAt(_ index: Int) -> Node? {
-    if index >= 0 {
-      var node = head
-      var i = index
-      while node != nil {
-        if i == 0 { return node }
-        i -= 1
-        node = node!.next
+  public func node(atIndex index: Int) -> Node {
+    if index == 0 {
+      return head!
+    } else {
+      var node = head!.next
+      for _ in 1..<index {
+        node = node?.next
+        if node == nil { //(*1)
+          break
+        }
       }
+      return node!
     }
-    return nil
   }
 ```
 
-The loop looks a little different but it does the same thing: it starts at `head` and then keeps following the `node.next` pointers to step through the list. We're done when we've seen `index` nodes, i.e. when the counter has reached 0.
+First we check whether the given index is 0 or not. Because if it is 0, it returns the head as it is.
+However, when the given index is greater than 0, it starts at head then keeps following the node.next pointers to step through the list.
+The difference from count method at this time is that there are two termination conditions.
+One is when the for-loop statement reaches index, and we were able to acquire the node of the given index.
+The second is when `node.next` in for-loop statement returns nil and cause break. (*1)
+This means that the given index is out of bounds and it causes a crash.
 
 Try it out:
 
 ```swift
 list.nodeAt(0)!.value    // "Hello"
 list.nodeAt(1)!.value    // "World"
-list.nodeAt(2)           // nil
+// list.nodeAt(2)           // crash
 ```
 
 For fun we can implement a `subscript` method too:
 
 ```swift
   public subscript(index: Int) -> T {
-    let node = nodeAt(index)
-    assert(node != nil)
-    return node!.value
+    let node = node(atIndex: index)
+    return node.value
   }
 ```
 
@@ -264,84 +270,100 @@ It crashes on `list[2]` because there is no node at that index.
 
 So far we've written code to add new nodes to the end of the list, but that's slow because you need to find the end of the list first. (It would be fast if we used a tail pointer.) For this reason, if the order of the items in the list doesn't matter, you should insert at the front of the list instead. That's always an **O(1)** operation.
 
-Let's write a method that lets you insert a new node at any index in the list. First, we'll define a helper function:
-
-```swift
-  private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
-    assert(index >= 0)
-
-    var i = index
-    var next = head
-    var prev: Node?
-
-    while next != nil && i > 0 {
-      i -= 1
-      prev = next
-      next = next!.next
-    }
-    assert(i == 0)
-
-    return (prev, next)
-  }
-```
-
-This returns a tuple containing the node currently at the specified index and the node that immediately precedes it, if any. The loop is very similar to `nodeAtIndex()`, except that here we also keep track of what the previous node is as we iterate through the list.
-
-Let's look at an example. Suppose we have the following list:
 
-	head --> A --> B --> C --> D --> E --> nil
-
-We want to find the nodes before and after index 3. As we start the loop, `i = 3`, `next` points at `"A"`, and `prev` is nil.
-
-	head --> A --> B --> C --> D --> E --> nil
-	        next
-
-We decrement `i`, make `prev` point to `"A"`, and move `next` to the next node, `"B"`:
-
-	head --> A --> B --> C --> D --> E --> F --> nil
-	        prev  next
-
-Again, we decrement `i` and update the pointers. Now `prev` points to `"B"`, and `next` points to `"C"`:
-
-	head --> A --> B --> C --> D --> E --> F --> nil
-	              prev  next
-
-As you can see, `prev` always follows one behind `next`. We do this one more time and then `i` equals 0 and we exit the loop:
-
-	head --> A --> B --> C --> D --> E --> F --> nil
-	                    prev  next
-
-The `assert()` after the loop checks whether there really were enough nodes in the list. If `i > 0` at this point, then the specified index was too large.
-
-> **Note:** If any of the loops in this article don't make much sense to you, then draw a linked list on a piece of paper and step through the loop by hand, just like what we did here.
-
-For this example, the function returns `("C", "D")` because `"D"` is the node at index 3 and `"C"` is the one right before that.
-
-Now that we have this helper function, we can write the method for inserting nodes:
+Let's write a method that lets you insert a new node at any index in the list.
 
 ```swift
-  public func insert(value: T, atIndex index: Int) {
-    let (prev, next) = nodesBeforeAndAfter(index)     // 1
-
-    let newNode = Node(value: value)    // 2
-    newNode.previous = prev
-    newNode.next = next
-    prev?.next = newNode
-    next?.previous = newNode
-
-    if prev == nil {                    // 3
-      head = newNode
-    }
-  }
+  public func insert(_ node: Node, atIndex index: Int) {
+   let newNode = node
+   if index == 0 {
+     newNode.next = head                      
+     head?.previous = newNode
+     head = newNode
+   } else {
+     let prev = self.node(atIndex: index-1)
+     let next = prev.next
+
+     newNode.previous = prev
+     newNode.next = prev.next
+     prev.next = newNode
+     next?.previous = newNode
+   }
+}
 ```
 
-Some remarks about this method:
-
-1. First, we need to find where to insert this node. After calling the helper method, `prev` points to the previous node and `next` is the node currently at the given index. We'll insert the new node in between these two. Note that `prev` can be nil (index is 0), `next` can be nil (index equals size of the list), or both can be nil if the list is empty.
+As with node(atIndex :) method, insert(_: at:) method also branches depending on whether the given index is 0 or not.
+First let's look at the former case. Suppose we have the following list and the new node(C).
+
+             +---------+     +---------+
+    head --->|         |---->|         |-----//----->
+             |    A    |     |    B    |
+     nil <---|         |<----|         |<----//------
+             +---------+     +---------+ 
+                 [0]             [1]
+                  
+                  
+             +---------+ 
+     new --->|         |----> nil
+             |    C    |
+             |         |
+             +---------+
+    
+Now put the new node before the first node. In this way: 
+
+    new.next = head
+    head.previous = new
+    
+             +---------+            +---------+     +---------+
+     new --->|         |--> head -->|         |---->|         |-----//----->
+             |    C    |            |    A    |     |    B    |
+             |         |<-----------|         |<----|         |<----//------
+             +---------+            +---------+     +---------+ 
+
+
+Finally, replace the head with the new node.
+
+    head = new
+    
+             +---------+    +---------+     +---------+
+    head --->|         |--->|         |---->|         |-----//----->
+             |    C    |    |    A    |     |    B    |
+     nil <---|         |<---|         |<----|         |<----//------
+             +---------+    +---------+     +---------+ 
+                 [0]            [1]
+
+
+However, when the given index is greater than 0, it is necessary to get the node previous and next index and insert between them.
+You can also obtain the previous and next node using node(atIndex:) as follows:
+
+             +---------+         +---------+     +---------+    
+    head --->|         |---//--->|         |---->|         |----
+             |    0    |         |    A    |     |    B    |    
+     nil <---|         |---//<---|         |<----|         |<---
+             +---------+         +---------+     +---------+    
+                                  [index-1]        [index]      
+                                      ^               ^ 
+                                      |               | 
+                                     prev            next
+    
+    prev = node(at: index-1)
+    next = prev.next
+
+Now insert new node between the prev and the next.
+
+    new.prev = prev; prev.next = new  // connect prev and new.
+    new.next = next; next.prev = new  // connect new and next.
+
+             +---------+         +---------+     +---------+     +---------+
+    head --->|         |---//--->|         |---->|         |---->|         |
+             |    0    |         |    A    |     |    C    |     |    B    |
+     nil <---|         |---//<---|         |<----|         |<----|         |
+             +---------+         +---------+     +---------+     +---------+
+                                  [index-1]        [index]        [index+1]
+                                      ^               ^               ^
+                                      |               |               |
+                                     prev            new             next
 
-2. Create the new node and connect the `previous` and `next` pointers. Because the local `prev` and `next` variables are optionals and may be nil, so we use optional chaining here.
-
-3. If the new node is being inserted at the front of the list, we need to update the `head` pointer. (Note: If the list had a tail pointer, you'd also need to update that pointer here if `next == nil`, because that means the last element has changed.)
 
 Try it out:
 
@@ -353,8 +375,7 @@ list[2]     // "World"
 ```
 
 Also try adding new nodes to the front and back of the list, to verify that this works properly.
-
-> **Note:** The `nodesBeforeAndAfter()` and `insert(atIndex)` functions can also be used with a singly linked list because we don't depend on the node's `previous` pointer to find the previous element.
+> **Note:** The `node(atIndex:)` and `insert(_: atIndex:)` functions can also be used with a singly linked list because we don't depend on the node's `previous` pointer to find the previous element.
 
 What else do we need? Removing nodes, of course! First we'll do `removeAll()`, which is really simple:
 
@@ -515,7 +536,7 @@ And here's filter:
 And a silly example:
 
 ```swift
-let f = list.filter { s in s.characters.count > 5 }
+let f = list.filter { s in s.count > 5 }
 f    // [Universe, Swifty]
 ```
 

From 3de5a1bfc49f9019badd6ba32fa23b0452e30d71 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Wed, 29 Nov 2017 13:12:47 +0900
Subject: [PATCH 314/643] Fixed insert method and some related files.

---
 .../LinkedList.playground/Contents.swift      | 21 +++++++++----------
 Linked List/LinkedList.swift                  | 19 ++++++++---------
 Linked List/README.markdown                   | 10 ++++-----
 3 files changed, 24 insertions(+), 26 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index af27f63a0..2b7d2873b 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -145,17 +145,17 @@ public final class LinkedList<T> {
   /// - Parameters:
   ///   - node: The node containing the value to be inserted
   ///   - index: Integer value of the index to be inserted at
-  public func insert(_ node: Node, atIndex index: Int) {
-    let newNode = node
+  public func insert(_ newNode: Node, atIndex index: Int) {
     if index == 0 {
       newNode.next = head
       head?.previous = newNode
       head = newNode
     } else {
-      let prev = self.node(atIndex: index-1)
+      let prev = node(atIndex: index-1)
+      let next = prev.next
       newNode.previous = prev
-      newNode.next = prev.next
-      prev.next?.previous = newNode
+      newNode.next = next
+      next?.previous = newNode
       prev.next = newNode
     }
   }
@@ -169,18 +169,17 @@ public final class LinkedList<T> {
     if list.isEmpty { return }
     
     if index == 0 {
-      let temp = head
+      list.last?.next = head
       head = list.head
-      list.last?.next = temp
     } else {
-      let prev = self.node(atIndex: index-1)
-      let temp = prev.next
+      let prev = node(atIndex: index-1)
+      let next = prev.next
 
       prev.next = list.head
       list.head?.previous = prev
 
-      list.last?.next = temp
-      temp?.previous = list.last?.next
+      list.last?.next = next
+      next?.previous = list.last?.next
     }
   }
 
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index c0331bc0e..a9848328d 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -100,17 +100,17 @@ public final class LinkedList<T> {
         self.insert(newNode, atIndex: index)
     }
 
-    public func insert(_ node: Node, atIndex index: Int) {
-        let newNode = node
+    public func insert(_ newNode: Node, atIndex index: Int) {
         if index == 0 {
             newNode.next = head
             head?.previous = newNode
             head = newNode
         } else {
-            let prev = self.node(atIndex: index-1)
+            let prev = node(atIndex: index-1)
+            let next = prev.next
             newNode.previous = prev
-            newNode.next = prev.next
-            prev.next?.previous = newNode
+            newNode.next = next
+            next?.previous = newNode
             prev.next = newNode
         }
     }
@@ -119,18 +119,17 @@ public final class LinkedList<T> {
         if list.isEmpty { return }
         
         if index == 0 {
-            let temp = head
+            list.last?.next = head
             head = list.head
-            list.last?.next = temp
         } else {
             let prev = self.node(atIndex: index-1)
-            let temp = prev.next
+            let next = prev.next
             
             prev.next = list.head
             list.head?.previous = prev
             
-            list.last?.next = temp
-            temp?.previous = list.last?.next
+            list.last?.next = next
+            next?.previous = list.last?.next
         }
     }
     
diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 55b61e910..52e30261a 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -330,7 +330,7 @@ Finally, replace the head with the new node.
              |    C    |    |    A    |     |    B    |
      nil <---|         |<---|         |<----|         |<----//------
              +---------+    +---------+     +---------+ 
-                 [0]            [1]
+                 [0]            [1]             [2]
 
 
 However, when the given index is greater than 0, it is necessary to get the node previous and next index and insert between them.
@@ -338,10 +338,10 @@ You can also obtain the previous and next node using node(atIndex:) as follows:
 
              +---------+         +---------+     +---------+    
     head --->|         |---//--->|         |---->|         |----
-             |    0    |         |    A    |     |    B    |    
+             |         |         |    A    |     |    B    |    
      nil <---|         |---//<---|         |<----|         |<---
              +---------+         +---------+     +---------+    
-                                  [index-1]        [index]      
+                 [0]              [index-1]        [index]      
                                       ^               ^ 
                                       |               | 
                                      prev            next
@@ -356,10 +356,10 @@ Now insert new node between the prev and the next.
 
              +---------+         +---------+     +---------+     +---------+
     head --->|         |---//--->|         |---->|         |---->|         |
-             |    0    |         |    A    |     |    C    |     |    B    |
+             |         |         |    A    |     |    C    |     |    B    |
      nil <---|         |---//<---|         |<----|         |<----|         |
              +---------+         +---------+     +---------+     +---------+
-                                  [index-1]        [index]        [index+1]
+                 [0]              [index-1]        [index]        [index+1]
                                       ^               ^               ^
                                       |               |               |
                                      prev            new             next

From bb21f61b53dc08af0e5d5081951c683d0f57a979 Mon Sep 17 00:00:00 2001
From: yoshi-kou <kosuke.yoshimoto@gmail.com>
Date: Thu, 30 Nov 2017 15:40:48 +0900
Subject: [PATCH 315/643] [Code refactoring] Renamed `atIndex` label in method
 to `at`.

---
 .../LinkedList.playground/Contents.swift      | 52 +++++++-------
 Linked List/LinkedList.swift                  | 20 +++---
 Linked List/Tests/LinkedListTests.swift       | 68 +++++++++----------
 3 files changed, 70 insertions(+), 70 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 2b7d2873b..b215bb3c7 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -70,7 +70,7 @@ public final class LinkedList<T> {
   ///
   /// - Parameter index: Integer value of the node's index to be returned
   /// - Returns: Optional LinkedListNode
-  public func node(atIndex index: Int) -> Node {
+  public func node(at index: Int) -> Node {
     assert(head != nil, "List is empty")
     assert(index >= 0, "index must be greater than 0")
     
@@ -94,7 +94,7 @@ public final class LinkedList<T> {
   ///
   /// - Parameter index: Integer value of the requested value's index
   public subscript(index: Int) -> T {
-    let node = self.node(atIndex: index)
+    let node = self.node(at: index)
     return node.value
   }
 
@@ -135,9 +135,9 @@ public final class LinkedList<T> {
   /// - Parameters:
   ///   - value: The data value to be inserted
   ///   - index: Integer value of the index to be insterted at
-  public func insert(_ value: T, atIndex index: Int) {
+  public func insert(_ value: T, at index: Int) {
     let newNode = Node(value: value)
-    self.insert(newNode, atIndex: index)
+    self.insert(newNode, at: index)
   }
 
   /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
@@ -145,13 +145,13 @@ public final class LinkedList<T> {
   /// - Parameters:
   ///   - node: The node containing the value to be inserted
   ///   - index: Integer value of the index to be inserted at
-  public func insert(_ newNode: Node, atIndex index: Int) {
+  public func insert(_ newNode: Node, at index: Int) {
     if index == 0 {
       newNode.next = head
       head?.previous = newNode
       head = newNode
     } else {
-      let prev = node(atIndex: index-1)
+      let prev = node(at: index-1)
       let next = prev.next
       newNode.previous = prev
       newNode.next = next
@@ -165,14 +165,14 @@ public final class LinkedList<T> {
   /// - Parameters:
   ///   - list: The LinkedList to be copied and inserted
   ///   - index: Integer value of the index to be inserted at
-  public func insert(_ list: LinkedList, atIndex index: Int) {
+  public func insert(_ list: LinkedList, at index: Int) {
     if list.isEmpty { return }
     
     if index == 0 {
       list.last?.next = head
       head = list.head
     } else {
-      let prev = node(atIndex: index-1)
+      let prev = node(at: index-1)
       let next = prev.next
 
       prev.next = list.head
@@ -220,8 +220,8 @@ public final class LinkedList<T> {
   ///
   /// - Parameter index: Integer value of the index of the node to be removed
   /// - Returns: The data value contained in the deleted node
-  @discardableResult public func remove(atIndex index: Int) -> T {
-    let node = self.node(atIndex: index)
+  @discardableResult public func remove(at index: Int) -> T {
+    let node = self.node(at: index)
     return remove(node: node)
   }
 }
@@ -323,9 +323,9 @@ list.first!.next!.value       // "World"
 list.last!.previous!.value    // "Hello"
 list.last!.next               // nil
 
-list.node(atIndex: 0).value    // "Hello"
-list.node(atIndex: 1).value    // "World"
-//list.node(atIndex: 2)           // crash!
+list.node(at: 0).value    // "Hello"
+list.node(at: 1).value    // "World"
+//list.node(at: 2)           // crash!
 
 list[0]     // "Hello"
 list[1]     // "World"
@@ -338,9 +338,9 @@ list.append(list2)            // [Hello, World, Goodbye, World]
 list2.removeAll()             // [ ]
 list2.isEmpty                 // true
 list.removeLast()             // "World"
-list.remove(atIndex: 2)       // "Goodbye"
+list.remove(at: 2)       // "Goodbye"
 
-list.insert("Swift", atIndex: 1)
+list.insert("Swift", at: 1)
 list[0]     // "Hello"
 list[1]     // "Swift"
 list[2]     // "World"
@@ -348,8 +348,8 @@ print(list)
 
 list.reverse()   // [World, Swift, Hello]
 
-list.node(atIndex: 0).value = "Universe"
-list.node(atIndex: 1).value = "Swifty"
+list.node(at: 0).value = "Universe"
+list.node(at: 1).value = "Swifty"
 let m = list.map { s in s.count }
 m    // [8, 6, 5]
 let f = list.filter { s in s.count > 5 }
@@ -366,28 +366,28 @@ list.head?.value
 list.count                     // 1
 list[0]                        // "Swifty"
 
-list.remove(atIndex: 0)        // "Swifty"
+list.remove(at: 0)        // "Swifty"
 list.count                     // 0
 
 let list3 = LinkedList<String>()
-list3.insert("2", atIndex: 0) // [2]
+list3.insert("2", at: 0) // [2]
 list3.count                   // 1
-list3.insert("4", atIndex: 1) // [2,4]
+list3.insert("4", at: 1) // [2,4]
 list3.count                   // 2
-list3.insert("5", atIndex: 2) // [2,4,5]
+list3.insert("5", at: 2) // [2,4,5]
 list3.count                   // 3
-list3.insert("3", atIndex: 1) // [2,3,4,5]
-list3.insert("1", atIndex: 0) // [1,2,3,4,5]
+list3.insert("3", at: 1) // [2,3,4,5]
+list3.insert("1", at: 0) // [1,2,3,4,5]
 
 let list4 = LinkedList<String>()
-list4.insert(list3, atIndex: 0) // [1,2,3,4,5]
+list4.insert(list3, at: 0) // [1,2,3,4,5]
 list4.count                     // 5
 
 let list5 = LinkedList<String>()
 list5.append("0")                // [0]
-list5.insert("End", atIndex:1)   // [0,End]
+list5.insert("End", at:1)   // [0,End]
 list5.count                      // 2
-list5.insert(list4, atIndex: 1)  // [0,1,2,3,4,5,End]
+list5.insert(list4, at: 1)  // [0,1,2,3,4,5,End]
 list5.count                      // 7
 
 
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index a9848328d..14f2ffe29 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -48,7 +48,7 @@ public final class LinkedList<T> {
         return count
     }
     
-    public func node(atIndex index: Int) -> Node {
+    public func node(at index: Int) -> Node {
         assert(head != nil, "List is empty")
         assert(index >= 0, "index must be greater than 0")
         if index == 0 {
@@ -68,7 +68,7 @@ public final class LinkedList<T> {
     }
 
     public subscript(index: Int) -> T {
-        let node = self.node(atIndex: index)
+        let node = self.node(at: index)
         return node.value
     }
 
@@ -95,18 +95,18 @@ public final class LinkedList<T> {
         }
     }
 
-    public func insert(_ value: T, atIndex index: Int) {
+    public func insert(_ value: T, at index: Int) {
         let newNode = Node(value: value)
-        self.insert(newNode, atIndex: index)
+        self.insert(newNode, at: index)
     }
 
-    public func insert(_ newNode: Node, atIndex index: Int) {
+    public func insert(_ newNode: Node, at index: Int) {
         if index == 0 {
             newNode.next = head
             head?.previous = newNode
             head = newNode
         } else {
-            let prev = node(atIndex: index-1)
+            let prev = node(at: index-1)
             let next = prev.next
             newNode.previous = prev
             newNode.next = next
@@ -115,14 +115,14 @@ public final class LinkedList<T> {
         }
     }
     
-    public func insert(_ list: LinkedList, atIndex index: Int) {
+    public func insert(_ list: LinkedList, at index: Int) {
         if list.isEmpty { return }
         
         if index == 0 {
             list.last?.next = head
             head = list.head
         } else {
-            let prev = self.node(atIndex: index-1)
+            let prev = self.node(at: index-1)
             let next = prev.next
             
             prev.next = list.head
@@ -158,8 +158,8 @@ public final class LinkedList<T> {
         return remove(node: last!)
     }
 
-    @discardableResult public func remove(atIndex index: Int) -> T {
-        let node = self.node(atIndex: index)
+    @discardableResult public func remove(at index: Int) -> T {
+        let node = self.node(at: index)
         return remove(node: node)
     }
 }
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 5bc27b23d..969ee5e08 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -97,7 +97,7 @@ class LinkedListTest: XCTestCase {
     let list = LinkedList<Int>()
     list.append(123)
 
-    let node = list.node(atIndex: 0)
+    let node = list.node(at: 0)
     XCTAssertNotNil(node)
     XCTAssertEqual(node.value, 123)
     XCTAssertTrue(node === list.first)
@@ -109,18 +109,18 @@ class LinkedListTest: XCTestCase {
     let nodeCount = list.count
     XCTAssertEqual(nodeCount, numbers.count)
 
-    let first = list.node(atIndex: 0)
+    let first = list.node(at: 0)
     XCTAssertNotNil(first)
     XCTAssertTrue(first === list.first)
     XCTAssertEqual(first.value, numbers[0])
 
-    let last = list.node(atIndex: nodeCount - 1)
+    let last = list.node(at: nodeCount - 1)
     XCTAssertNotNil(last)
     XCTAssertTrue(last === list.last)
     XCTAssertEqual(last.value, numbers[nodeCount - 1])
 
     for i in 0..<nodeCount {
-      let node = list.node(atIndex: i)
+      let node = list.node(at: i)
       XCTAssertNotNil(node)
       XCTAssertEqual(node.value, numbers[i])
     }
@@ -135,25 +135,25 @@ class LinkedListTest: XCTestCase {
 
   func testInsertAtIndexInEmptyList() {
     let list = LinkedList<Int>()
-    list.insert(123, atIndex: 0)
+    list.insert(123, at: 0)
 
     XCTAssertFalse(list.isEmpty)
     XCTAssertEqual(list.count, 1)
 
-    let node = list.node(atIndex: 0)
+    let node = list.node(at: 0)
     XCTAssertNotNil(node)
     XCTAssertEqual(node.value, 123)
   }
 
   func testInsertAtIndex() {
     let list = buildList()
-    let prev = list.node(atIndex: 2)
-    let next = list.node(atIndex: 3)
+    let prev = list.node(at: 2)
+    let next = list.node(at: 3)
     let nodeCount = list.count
 
-    list.insert(444, atIndex: 3)
+    list.insert(444, at: 3)
 
-    let node = list.node(atIndex: 3)
+    let node = list.node(at: 3)
     XCTAssertNotNil(node)
     XCTAssertEqual(node.value, 444)
     XCTAssertEqual(nodeCount + 1, list.count)
@@ -169,12 +169,12 @@ class LinkedListTest: XCTestCase {
     let list2 = LinkedList<Int>()
     list2.append(99)
     list2.append(102)
-    list.insert(list2, atIndex: 2)
+    list.insert(list2, at: 2)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 1).value, 2)
-    XCTAssertEqual(list.node(atIndex: 2).value, 99)
-    XCTAssertEqual(list.node(atIndex: 3).value, 102)
-    XCTAssertEqual(list.node(atIndex: 4).value, 10)
+    XCTAssertEqual(list.node(at: 1).value, 2)
+    XCTAssertEqual(list.node(at: 2).value, 99)
+    XCTAssertEqual(list.node(at: 3).value, 102)
+    XCTAssertEqual(list.node(at: 4).value, 10)
   }
 
   func testInsertListAtFirstIndex() {
@@ -182,11 +182,11 @@ class LinkedListTest: XCTestCase {
     let list2 = LinkedList<Int>()
     list2.append(99)
     list2.append(102)
-    list.insert(list2, atIndex: 0)
+    list.insert(list2, at: 0)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 0).value, 99)
-    XCTAssertEqual(list.node(atIndex: 1).value, 102)
-    XCTAssertEqual(list.node(atIndex: 2).value, 8)
+    XCTAssertEqual(list.node(at: 0).value, 99)
+    XCTAssertEqual(list.node(at: 1).value, 102)
+    XCTAssertEqual(list.node(at: 2).value, 8)
   }
 
   func testInsertListAtLastIndex() {
@@ -194,11 +194,11 @@ class LinkedListTest: XCTestCase {
     let list2 = LinkedList<Int>()
     list2.append(99)
     list2.append(102)
-    list.insert(list2, atIndex: list.count)
+    list.insert(list2, at: list.count)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 5).value, 5)
-    XCTAssertEqual(list.node(atIndex: 6).value, 99)
-    XCTAssertEqual(list.node(atIndex: 7).value, 102)
+    XCTAssertEqual(list.node(at: 5).value, 5)
+    XCTAssertEqual(list.node(at: 6).value, 99)
+    XCTAssertEqual(list.node(at: 7).value, 102)
   }
 
   func testAppendList() {
@@ -208,9 +208,9 @@ class LinkedListTest: XCTestCase {
     list2.append(102)
     list.append(list2)
     XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(atIndex: 5).value, 5)
-    XCTAssertEqual(list.node(atIndex: 6).value, 99)
-    XCTAssertEqual(list.node(atIndex: 7).value, 102)
+    XCTAssertEqual(list.node(at: 5).value, 5)
+    XCTAssertEqual(list.node(at: 6).value, 99)
+    XCTAssertEqual(list.node(at: 7).value, 102)
   }
 
   func testAppendListToEmptyList() {
@@ -220,15 +220,15 @@ class LinkedListTest: XCTestCase {
     list2.append(10)
     list.append(list2)
     XCTAssertTrue(list.count == 2)
-    XCTAssertEqual(list.node(atIndex: 0).value, 5)
-    XCTAssertEqual(list.node(atIndex: 1).value, 10)
+    XCTAssertEqual(list.node(at: 0).value, 5)
+    XCTAssertEqual(list.node(at: 1).value, 10)
   }
 
   func testRemoveAtIndexOnListWithOneElement() {
     let list = LinkedList<Int>()
     list.append(123)
 
-    let value = list.remove(atIndex: 0)
+    let value = list.remove(at: 0)
     XCTAssertEqual(value, 123)
 
     XCTAssertTrue(list.isEmpty)
@@ -239,16 +239,16 @@ class LinkedListTest: XCTestCase {
 
   func testRemoveAtIndex() {
     let list = buildList()
-    let prev = list.node(atIndex: 2)
-    let next = list.node(atIndex: 3)
+    let prev = list.node(at: 2)
+    let next = list.node(at: 3)
     let nodeCount = list.count
 
-    list.insert(444, atIndex: 3)
+    list.insert(444, at: 3)
 
-    let value = list.remove(atIndex: 3)
+    let value = list.remove(at: 3)
     XCTAssertEqual(value, 444)
 
-    let node = list.node(atIndex: 3)
+    let node = list.node(at: 3)
     XCTAssertTrue(next === node)
     XCTAssertTrue(prev.next === node)
     XCTAssertTrue(node.previous === prev)

From aa6e2bf750322666722c8fdea77b2dae4476cc5b Mon Sep 17 00:00:00 2001
From: Hai Nguyen <aquarchitecture@gmail.com>
Date: Sat, 2 Dec 2017 14:43:05 -0800
Subject: [PATCH 316/643] GitHub Pages Script Updates (#670)

* Move inline css to the main stylesheet - github-light.css & parse the repo README to
html instead of generating one.

* Minor clean up

* Fix image link

* Parse other markdown files
---
 .travis.yml     |   1 +
 README.markdown |   8 +--
 gfm-render.sh   | 175 +++++++++++++++++++++++++++++-------------------
 3 files changed, 110 insertions(+), 74 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index 7cd02c9bc..edf1cf89f 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -50,4 +50,5 @@ script:
 - xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
 
 after_success:
+
 - if [[ "$TRAVIS_BRANCH" == "master" ]]; then ./gfm-render.sh; fi
diff --git a/README.markdown b/README.markdown
index b15bd1527..46544682e 100644
--- a/README.markdown
+++ b/README.markdown
@@ -1,4 +1,4 @@
-![Swift Algorithm Club](/Images/SwiftAlgorithm-410-transp.png)
+![Swift Algorithm Club](Images/SwiftAlgorithm-410-transp.png)
 
 # Welcome to the Swift Algorithm Club!
 
@@ -156,14 +156,14 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Splay Tree](Splay%20Tree/). A self balancing binary search tree that enables fast retrieval of recently updated elements.
 - [Threaded Binary Tree](Threaded%20Binary%20Tree/). A binary tree that maintains a few extra variables for cheap and fast in-order traversals.
 - [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
-  - [Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation) 
+  - [Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
 - [Trie](Trie/). A special type of tree used to store associative data structures.
 - [B-Tree](B-Tree/). A self-balancing search tree, in which nodes can have more than two children.
 - [QuadTree](QuadTree/). A tree with 4 children.
-- [Octree](Octree/). A tree with 8 children. 
+- [Octree](Octree/). A tree with 8 children.
 
 ### Hashing
 
@@ -208,7 +208,7 @@ For more information, check out these great books:
 - [The Algorithm Design Manual](http://www.algorist.com) by Skiena
 - [Elements of Programming Interviews](http://elementsofprogramminginterviews.com) by Aziz, Lee, Prakash
 - [Algorithms](http://www.cs.princeton.edu/~rs/) by Sedgewick
-- [Grokking Algorithms](https://www.manning.com/books/grokking-algorithms) by Aditya Bhargava 
+- [Grokking Algorithms](https://www.manning.com/books/grokking-algorithms) by Aditya Bhargava
 
 The following books are available for free online:
 
diff --git a/gfm-render.sh b/gfm-render.sh
index 09c026d55..4e18c8560 100755
--- a/gfm-render.sh
+++ b/gfm-render.sh
@@ -1,50 +1,108 @@
 #!/usr/bin/env bash
 
-# $1 - readme
+set -e
+
+# $1 - readme file name
 function render_markdown_to_html {
-  # escape escaping characters
-  if [[ $(uname) == "Darwin" ]]; then
-    content=$(
-      cat "$1"                                          \
-        | sed 's/\\/\\\\/g'                             \
-        | sed 's/"/\\"/g'                               \
-        | sed $'s/\t/\\\\t/g'                           \
-        | sed -e ':a' -e 'N' -e '$!ba' -e 's/\n/\\\n/g' \
-    )
-  else
-    content=$(
-      cat "$1"                          \
-        | sed 's/\\/\\\\/g'             \
-        | sed 's/"/\\"/g'               \
-        | sed 's/\t/\\t/g'              \
-        | sed ':a;N;$!ba;s/\n/\\n/g'    \
-    )
-  fi
+  # escape escaping characters on Darwin only
+  content=$(
+    cat "$1"                                          \
+      | sed 's/\\/\\\\/g'                             \
+      | sed 's/"/\\"/g'                               \
+      | sed $'s/\t/\\\\t/g'                           \
+      | sed -e ':a' -e 'N' -e '$!ba' -e 's/\n/\\\n/g' \
+  )
 
   # network call to GitHub API
   json="{\"text\":\"$content\",\"mode\":\"gfm\",\"context\":\"$USERNAME/swift-algorithm-club\"}"
   echo -e "$(curl -s --data "$json" -u $USERNAME:$TOKEN https://api.github.com/markdown)"
 }
 
-# $1 - comment
-function push_to_gh_pages {
-  git checkout -b gh-pages
-  git add .
-  git commit -m "$1"
-  git push -f https://$TOKEN@github.com/$USERNAME/swift-algorithm-club.git gh-pages
-}
-
 # download github systax highlight stylesheet
 echo "> Downloading github-light.css..."
 curl -s -O https://raw.githubusercontent.com/primer/github-syntax-light/master/lib/github-light.css
 
+# slightly modify the main stylesheet
+echo "> Modifying github-light.css..."
+cat >> github-light.css << EOF
+#container {
+  margin: 0 auto;
+  width: 75%;
+  min-width: 768px;
+  max-width: 896px;
+  position: relative;
+}
+
+body {
+  font-size: 18px;
+}
+
+code {
+    padding: 0.2em;
+    margin: 0;
+    font-size: 85%;
+    background-color: #f6f8fa;
+    line-height: 1.45;
+    border-radius: 3px
+}
+
+pre code {
+    padding: 0px;
+    background-color: transparent;
+}
+
+.highlight {
+  margin: 0px;
+  padding: 0px 16px;
+  font-size: 85%;
+  line-height: 1.45;
+  overflow: auto;
+  background-color: #f6f8fa;
+  border-radius: 3px;
+}
+
+@media (max-width: 768px) {
+  #container {
+    position: absolute;
+    margin: 0;
+    width: 100%;
+    height: 100%;
+    min-width: 100%;
+  }
+}
+EOF
+
+# other markdown articles
+for title in "What are Algorithms" "Big-O Notation" "Algorithm Design" "Why Algorithms"; do
+  echo "> Generating $title.html..."
+
+  cat > "$title.html" << EOF
+<!DOCTYPE html>
+<head>
+  <title>$title</title>
+  <link rel="stylesheet" type="text/css" href="github-light.css">
+</head>
+<body>
+  <div id="container">$(render_markdown_to_html "$title.markdown")</div>
+</body>
+</html>
+EOF
+done
+
 # if index.html does not exist, create one;
 # otherwise, empty its content.
-if [[ -z index.html ]]; then
-  touch index.html
-else
-  > index.html
-fi
+echo "> Generating index.html..."
+cat > index.html << EOF
+<!DOCTYPE html>
+<head>
+  <title>Swift Algorithm Club</title>
+  <link rel="stylesheet" type="text/css" href="github-light.css">
+</head>
+<body>
+  <div id="container">$(render_markdown_to_html README.markdown | sed 's/.markdown/.html/g')</div>
+</body>
+</html>
+EOF
 
 # iterate immediate directories
 find . -maxdepth 1 -type d | while read folder; do
@@ -54,53 +112,30 @@ find . -maxdepth 1 -type d | while read folder; do
   if [[ -f $folder/README.md ]]; then readme="$folder/README.md"; fi
   if [[ -f $folder/README.markdown ]]; then readme="$folder/README.markdown"; fi
 
-  # exclude the repository's README
-  if [[ !(-z $readme) && ($readme != "./README.markdown") ]]; then
-    name=$(basename "$folder")
-    echo "> Generating $name/index.html..."
+  # skip if there is no README or it it the README of the repository
+  if [[ (-z $readme) || $readme == "./README.markdown" ]]; then continue; fi
+
+  # render README to HTML
+  name=$(basename "$folder")
+  echo "> Generating $name/index.html..."
 
-    cat > "$folder/index.html" << EOF
+  cat > "$folder/index.html" << EOF
 <!DOCTYPE html>
 <head>
+  <title>$name</title>
   <link rel="stylesheet" type="text/css" href="../github-light.css">
-  <style>
-    body {
-      font-size: 18px;
-    }
-    code {
-        padding: 0.2em;
-        margin: 0;
-        font-size: 85%;
-        background-color: #f6f8fa;
-        line-height: 1.45;
-        border-radius: 3px
-    }
-    pre code {
-        padding: 0px;
-        background-color: transparent;
-    }
-    .highlight {
-      margin: 0px;
-      padding: 0px 16px;
-      font-size: 85%;
-      line-height: 1.45;
-      overflow: auto;
-      background-color: #f6f8fa;
-      border-radius: 3px;
-    }
-  </style>
 </head>
 <body>
-    $(render_markdown_to_html "$readme")
+  <div id="container">$(render_markdown_to_html "$readme")</div>
 </body>
 </html>
 EOF
-    # temporarily write the list of HTML filenames to the main index.html
-    echo "$lists<li><a href=\"$name/index.html\">$name</a></li>" >> index.html
-  fi
 done
 
-echo "<!DOCTYPE html><body><h1>Swift Algorithm</h1><ul>$(echo -n $(cat index.html))</ul></body></html>" > index.html
-
 # push to gh-pages
-if [[ $CI = true ]]; then push_to_gh_pages "Generated by TravisCI on $(date +%D)"; fi
+if [[ $CI = true ]]; then
+  git checkout -b gh-pages
+  git add .
+  git commit -m "$Generated by TravisCI on $(date +%D)"
+  git push -f https://$TOKEN@github.com/$USERNAME/swift-algorithm-club.git gh-pages
+fi

From aa1c3f799020bc854a934b3b107ff97a8412ae5f Mon Sep 17 00:00:00 2001
From: n0an <nantog@gmail.com>
Date: Wed, 20 Dec 2017 13:49:51 +0300
Subject: [PATCH 317/643] RadixTree syntax updated to Swift 4

Characters removed (deprecated in Swift 4). Substring removed (deprecated in Swift 4). String slicing subscript used for substrings creation.
---
 .../Sources/RadixTree.swift                   | 46 +++++++++----------
 Radix Tree/RadixTree.swift                    | 46 +++++++++----------
 2 files changed, 46 insertions(+), 46 deletions(-)

diff --git a/Radix Tree/RadixTree.playground/Sources/RadixTree.swift b/Radix Tree/RadixTree.playground/Sources/RadixTree.swift
index 1914f57bc..77e289f7d 100644
--- a/Radix Tree/RadixTree.playground/Sources/RadixTree.swift	
+++ b/Radix Tree/RadixTree.playground/Sources/RadixTree.swift	
@@ -181,10 +181,10 @@ public class RadixTree {
 				else if shared == e.label {
 					currEdge = e
 					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = searchStr.characters.index(after: tempIndex)
+					for _ in 1...shared.count {
+						tempIndex = searchStr.index(after: tempIndex)
 					}
-                    searchStr = searchStr.substring(from: tempIndex)
+                    searchStr = String(searchStr[tempIndex...])
 					found = true
 					break
 				}
@@ -192,18 +192,18 @@ public class RadixTree {
 				// If the child's label and the search string share a partial prefix,
 				// then both the label and the search string need to be substringed
 				// and a new branch needs to be created
-				else if shared.characters.count > 0 {
-					var labelIndex = e.label.characters.startIndex
+				else if shared.count > 0 {
+					var labelIndex = e.label.startIndex
 
 					// Create index objects and move them to after the shared prefix
-					for _ in 1...shared.characters.count {
-                        index = searchStr.characters.index(after: index)
-						labelIndex = e.label.characters.index(after: labelIndex)
+					for _ in 1...shared.count {
+                        index = searchStr.index(after: index)
+						labelIndex = e.label.index(after: labelIndex)
 					}
 
 					// Substring both the search string and the label from the shared prefix
-                    searchStr = searchStr.substring(from: index)
-                    e.label = e.label.substring(from: labelIndex)
+                    searchStr = String(searchStr[index...])
+                    e.label = String(e.label[labelIndex...])
 
 					// Create 2 new edges and update parent/children values
 					let newEdge = Edge(e.label)
@@ -266,16 +266,16 @@ public class RadixTree {
 				if shared == c.label {
 					currEdge = c
 					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = searchStr.characters.index(after: tempIndex)
+					for _ in 1...shared.count {
+						tempIndex = searchStr.index(after: tempIndex)
 					}
-					searchStr = searchStr.substring(from: tempIndex)
+					searchStr = String(searchStr[tempIndex...])
 					found = true
 					break
 				}
 
 				// If the shared string is empty, go to the next child
-				else if shared.characters.count == 0 {
+				else if shared.count == 0 {
 					continue
 				}
 
@@ -287,7 +287,7 @@ public class RadixTree {
 				// If the search string and the child's label only share some characters,
 				// the string is not in the tree, return false
 				else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
-				  shared.characters.count < c.label.characters.count {
+				  shared.count < c.label.count {
 				  	return false
 				}
 			}
@@ -340,10 +340,10 @@ public class RadixTree {
 				if shared == currEdge.children[c].label {
 					currEdge = currEdge.children[c]
 					var tempIndex = searchStr.startIndex
-					for _ in 1...shared.characters.count {
-						tempIndex = searchStr.characters.index(after: tempIndex)
+					for _ in 1...shared.count {
+						tempIndex = searchStr.index(after: tempIndex)
 					}
-					searchStr = searchStr.substring(from: tempIndex)
+					searchStr = String(searchStr[tempIndex...])
 					found = true
 					break
 				}
@@ -366,13 +366,13 @@ public class RadixTree {
 // i.e. sharedPrefix("court", "coral") -> "co"
 public func sharedPrefix(_ str1: String, _ str2: String) -> String {
 	var temp = ""
-	var c1 = str1.characters.startIndex
-	var c2 = str2.characters.startIndex
-	for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
+	var c1 = str1.startIndex
+	var c2 = str2.startIndex
+	for _ in 0...min(str1.count-1, str2.count-1) {
 		if str1[c1] == str2[c2] {
 			temp.append( str1[c1] )
-            c1 = str1.characters.index(after:c1)
-            c2 = str2.characters.index(after:c2)
+            c1 = str1.index(after:c1)
+            c2 = str2.index(after:c2)
 		} else {
 			return temp
 		}
diff --git a/Radix Tree/RadixTree.swift b/Radix Tree/RadixTree.swift
index 958ffb4e6..943000dd3 100644
--- a/Radix Tree/RadixTree.swift	
+++ b/Radix Tree/RadixTree.swift	
@@ -181,10 +181,10 @@ public class RadixTree {
         else if shared == e.label {
           currEdge = e
           var tempIndex = searchStr.startIndex
-          for _ in 1...shared.characters.count {
-            tempIndex = searchStr.characters.index(after: tempIndex)
+          for _ in 1...shared.count {
+            tempIndex = searchStr.index(after: tempIndex)
           }
-          searchStr = searchStr.substring(from: tempIndex)
+          searchStr = String(searchStr[tempIndex...])
           found = true
           break
         }
@@ -192,18 +192,18 @@ public class RadixTree {
           // If the child's label and the search string share a partial prefix,
           // then both the label and the search string need to be substringed
           // and a new branch needs to be created
-        else if shared.characters.count > 0 {
-          var labelIndex = e.label.characters.startIndex
+        else if shared.count > 0 {
+          var labelIndex = e.label.startIndex
 
           // Create index objects and move them to after the shared prefix
-          for _ in 1...shared.characters.count {
-            index = searchStr.characters.index(after: index)
-            labelIndex = e.label.characters.index(after: labelIndex)
+          for _ in 1...shared.count {
+            index = searchStr.index(after: index)
+            labelIndex = e.label.index(after: labelIndex)
           }
 
           // Substring both the search string and the label from the shared prefix
-          searchStr = searchStr.substring(from: index)
-          e.label = e.label.substring(from: labelIndex)
+          searchStr = String(searchStr[index...])
+          e.label = String(e.label[labelIndex...])
 
           // Create 2 new edges and update parent/children values
           let newEdge = Edge(e.label)
@@ -266,16 +266,16 @@ public class RadixTree {
         if shared == c.label {
           currEdge = c
           var tempIndex = searchStr.startIndex
-          for _ in 1...shared.characters.count {
-            tempIndex = searchStr.characters.index(after: tempIndex)
+          for _ in 1...shared.count {
+            tempIndex = searchStr.index(after: tempIndex)
           }
-          searchStr = searchStr.substring(from: tempIndex)
+          searchStr = String(searchStr[tempIndex...])
           found = true
           break
         }
 
           // If the shared string is empty, go to the next child
-        else if shared.characters.count == 0 {
+        else if shared.count == 0 {
           continue
         }
 
@@ -287,7 +287,7 @@ public class RadixTree {
           // If the search string and the child's label only share some characters,
           // the string is not in the tree, return false
         else if shared[shared.startIndex] == c.label[c.label.startIndex] &&
-          shared.characters.count < c.label.characters.count {
+          shared.count < c.label.count {
           return false
         }
       }
@@ -340,10 +340,10 @@ public class RadixTree {
         if shared == currEdge.children[c].label {
           currEdge = currEdge.children[c]
           var tempIndex = searchStr.startIndex
-          for _ in 1...shared.characters.count {
-            tempIndex = searchStr.characters.index(after: tempIndex)
+          for _ in 1...shared.count {
+            tempIndex = searchStr.index(after: tempIndex)
           }
-          searchStr = searchStr.substring(from: tempIndex)
+          searchStr = String(searchStr[tempIndex...])
           found = true
           break
         }
@@ -366,13 +366,13 @@ public class RadixTree {
 // i.e. sharedPrefix("court", "coral") -> "co"
 public func sharedPrefix(_ str1: String, _ str2: String) -> String {
   var temp = ""
-  var c1 = str1.characters.startIndex
-  var c2 = str2.characters.startIndex
-  for _ in 0...min(str1.characters.count-1, str2.characters.count-1) {
+  var c1 = str1.startIndex
+  var c2 = str2.startIndex
+  for _ in 0...min(str1.count-1, str2.count-1) {
     if str1[c1] == str2[c2] {
       temp.append( str1[c1] )
-      c1 = str1.characters.index(after:c1)
-      c2 = str2.characters.index(after:c2)
+      c1 = str1.index(after:c1)
+      c2 = str2.index(after:c2)
     } else {
       return temp
     }

From f035a25111c9d87335a187afcedda77afd4d7ee4 Mon Sep 17 00:00:00 2001
From: Aamir Anwar <aamir.anwar021193@gmail.com>
Date: Fri, 22 Dec 2017 16:02:39 +0530
Subject: [PATCH 318/643] Fixed typo in the README for the word 'example'

---
 Splay Tree/readme.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index 2c5e87ed7..f3b852f22 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -159,7 +159,7 @@ Now suppose a *insert(7)* operation was performed and we're in a *ZigZag* case.
 
 ## Advantages 
 
-Splay trees provide an efficient way to quickly access elements that are frequently requested. This characteristic makes then a good choice to implement, for exmaple, caches or garbage collection algorithms, or in any other problem involving frequent access to a certain numbers of elements from a data set.
+Splay trees provide an efficient way to quickly access elements that are frequently requested. This characteristic makes then a good choice to implement, for example, caches or garbage collection algorithms, or in any other problem involving frequent access to a certain numbers of elements from a data set.
 
 ## Disadvantages
 

From bcd0896b446c91c76a2e758bd8add3b882fa5126 Mon Sep 17 00:00:00 2001
From: Hemang <hemangshah.in@gmail.com>
Date: Wed, 3 Jan 2018 12:06:27 +0530
Subject: [PATCH 319/643] Update README.markdown

Corrected the Written by (Author) URL for Palindrome algorithm.
---
 Palindromes/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 18518adbe..69520a132 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -104,4 +104,4 @@ racecar -> left index == right index -> return true
 [Palindrome Wikipedia](https://en.wikipedia.org/wiki/Palindrome)
 
 
-*Written by [Joshua Alvarado](https://github.com/https://github.com/lostatseajoshua)*
+*Written by [Joshua Alvarado](https://github.com/lostatseajoshua)*

From a51f98aa0737063e5dc882c19df22b9de388bccf Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Thu, 4 Jan 2018 16:29:14 +0800
Subject: [PATCH 320/643] Fix a spelling mistake

change the `probablistic` to `probabilistic`
---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 46544682e..7c9482d0c 100644
--- a/README.markdown
+++ b/README.markdown
@@ -145,7 +145,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 ### Lists
 
 - [Linked List](Linked%20List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
-- [Skip-List](Skip-List/). Skip List is a probablistic data-structure with same logarithmic time bound and efficiency as AVL/ or Red-Black tree and provides a clever compromise to efficiently support search and update operations.
+- [Skip-List](Skip-List/). Skip List is a probabilistic data-structure with same logarithmic time bound and efficiency as AVL/ or Red-Black tree and provides a clever compromise to efficiently support search and update operations.
 
 ### Trees
 

From 677e3cefa18c9a815d7d2509e1198553c7a63468 Mon Sep 17 00:00:00 2001
From: Giuseppe Lanza <giuseppe@getdrop.com>
Date: Thu, 4 Jan 2018 14:48:07 +0000
Subject: [PATCH 321/643] IntroSort playground implementation

---
 Introsort/Introsort.playground/Contents.swift | 41 +++++++++++++++
 .../Sources/HeapSort.swift                    | 50 +++++++++++++++++++
 .../Sources/InsertionSort.swift               | 28 +++++++++++
 .../Sources/Partition.swift                   | 43 ++++++++++++++++
 .../Sources/Randomize.swift                   |  9 ++++
 .../Introsort.playground/Sources/Sort3.swift  | 21 ++++++++
 .../contents.xcplayground                     |  4 ++
 7 files changed, 196 insertions(+)
 create mode 100644 Introsort/Introsort.playground/Contents.swift
 create mode 100644 Introsort/Introsort.playground/Sources/HeapSort.swift
 create mode 100644 Introsort/Introsort.playground/Sources/InsertionSort.swift
 create mode 100644 Introsort/Introsort.playground/Sources/Partition.swift
 create mode 100644 Introsort/Introsort.playground/Sources/Randomize.swift
 create mode 100644 Introsort/Introsort.playground/Sources/Sort3.swift
 create mode 100644 Introsort/Introsort.playground/contents.xcplayground

diff --git a/Introsort/Introsort.playground/Contents.swift b/Introsort/Introsort.playground/Contents.swift
new file mode 100644
index 000000000..43ee02e3f
--- /dev/null
+++ b/Introsort/Introsort.playground/Contents.swift
@@ -0,0 +1,41 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+func introsort<T>(_ array: inout [T],  by areInIncreasingOrder: (T, T) -> Bool) {
+    //The depth limit is as best practice 2 * log( n )
+    let depthLimit = 2 * floor(log2(Double(array.count)))
+    
+    introSortImplementation(for: &array, range: 0..<array.count, depthLimit: Int(depthLimit), by: areInIncreasingOrder)
+}
+
+///This method is recursively executed for each partition result of the quicksort part of the algorithm
+private func introSortImplementation<T>(for array: inout [T], range: Range<Int>, depthLimit: Int, by areInIncreasingOrder: (T, T) -> Bool) {
+    if array.distance(from: range.lowerBound, to: range.upperBound) < 20 {
+        //if the partition count is less than 20 we can sort it using insertion sort. This algorithm in fact performs well on collections
+        //of this size, plus, at this point is quite probable that the quisksort part of the algorithm produced a partition which is
+        //nearly sorted. As we knoe insertion sort tends to O( n ) if this is the case.
+        insertionSort(for: &array, range: range, by: areInIncreasingOrder)
+    } else if depthLimit == 0 {
+        //If we reached the depth limit for this recursion branch, it's possible that we are hitting quick sort's worst case.
+        //Since quicksort degrades to O( n^2 ) in its worst case we stop using quicksort for this recursion branch and we switch to heapsort.
+        //Our preference remains quicksort, and we hope to be rare to see this condition to be true
+        heapsort(for: &array, range: range, by: areInIncreasingOrder)
+    } else {
+        //By default we use quicksort to sort our collection. The partition index method chose a pivot, and puts all the
+        //elements less than pivot on the left, and the ones bigger than pivot on the right. At the end of the operation the
+        //position of the pivot in the array is returned so that we can form the two partitions.
+        let partIdx = partitionIndex(for: &array, subRange: range, by: areInIncreasingOrder)
+        
+        //We can recursively call introsort implementation, decreasing the depthLimit for the left partition and the right partition.
+        introSortImplementation(for: &array, range: range.lowerBound..<partIdx, depthLimit: depthLimit &- 1, by: areInIncreasingOrder)
+        introSortImplementation(for: &array, range: partIdx..<range.upperBound, depthLimit: depthLimit &- 1, by: areInIncreasingOrder)
+    }
+}
+
+var unsorted = randomize(n: 1000)
+
+let swiftSorted = unsorted.sorted()
+introsort(&unsorted, by: <)
+
+print("does it work? \(unsorted == swiftSorted)")
diff --git a/Introsort/Introsort.playground/Sources/HeapSort.swift b/Introsort/Introsort.playground/Sources/HeapSort.swift
new file mode 100644
index 000000000..f5bc466da
--- /dev/null
+++ b/Introsort/Introsort.playground/Sources/HeapSort.swift
@@ -0,0 +1,50 @@
+import Foundation
+
+private func shiftDown<T>(_ elements: inout [T], _ index: Int, _ range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    let countToIndex = elements.distance(from: range.lowerBound, to: index)
+    let countFromIndex = elements.distance(from: index, to: range.upperBound)
+    
+    guard countToIndex + 1 < countFromIndex else { return }
+    
+    let left = elements.index(index, offsetBy: countToIndex + 1)
+    var largest = index
+    if areInIncreasingOrder(elements[largest], elements[left]) {
+        largest = left
+    }
+    
+    if countToIndex + 2 < countFromIndex {
+        let right = elements.index(after: left)
+        if areInIncreasingOrder(elements[largest], elements[right]) {
+            largest = right
+        }
+    }
+
+    if largest != index {
+        elements.swapAt(index, largest)
+        shiftDown(&elements, largest, range, by: areInIncreasingOrder)
+    }
+    
+}
+
+private func heapify<T>(_ list: inout [T], _ range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    let root = range.lowerBound
+    var node = list.index(root, offsetBy: list.distance(from: range.lowerBound, to: range.upperBound)/2)
+    
+    while node != root {
+        list.formIndex(before: &node)
+        shiftDown(&list, node, range, by: areInIncreasingOrder)
+    }
+}
+
+public func heapsort<T>(for array: inout [T], range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    var hi = range.upperBound
+    let lo = range.lowerBound
+    heapify(&array, range, by: areInIncreasingOrder)
+    array.formIndex(before: &hi)
+    
+    while hi != lo {
+        array.swapAt(lo, hi)
+        shiftDown(&array, lo, lo..<hi, by: areInIncreasingOrder)
+        array.formIndex(before: &hi)
+    }
+}
diff --git a/Introsort/Introsort.playground/Sources/InsertionSort.swift b/Introsort/Introsort.playground/Sources/InsertionSort.swift
new file mode 100644
index 000000000..36887ea06
--- /dev/null
+++ b/Introsort/Introsort.playground/Sources/InsertionSort.swift
@@ -0,0 +1,28 @@
+import Foundation
+
+public func insertionSort<T>(for array: inout [T], range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    guard !range.isEmpty else { return }
+    
+    let start = range.lowerBound
+    var sortedEnd = start
+    
+    array.formIndex(after: &sortedEnd)
+    while sortedEnd != range.upperBound {
+        let x = array[sortedEnd]
+        
+        var i = sortedEnd
+        repeat {
+            let predecessor = array[array.index(before: i)]
+            
+            guard areInIncreasingOrder(x, predecessor) else { break }
+            array[i] = predecessor
+            array.formIndex(before: &i)
+        } while i != start
+        
+        if i != sortedEnd {
+            array[i] = x
+        }
+        array.formIndex(after: &sortedEnd)
+    }
+    
+}
diff --git a/Introsort/Introsort.playground/Sources/Partition.swift b/Introsort/Introsort.playground/Sources/Partition.swift
new file mode 100644
index 000000000..e24636da7
--- /dev/null
+++ b/Introsort/Introsort.playground/Sources/Partition.swift
@@ -0,0 +1,43 @@
+import Foundation
+
+public func partitionIndex<T>(for elements: inout [T], subRange range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) -> Int {
+    var lo = range.lowerBound
+    var hi = elements.index(before: range.upperBound)
+    
+    // Sort the first, middle, and last elements, then use the middle value
+    // as the pivot for the partition.
+    let half = elements.distance(from: lo, to: hi) / 2
+    let mid = elements.index(lo, offsetBy: half)
+    
+    sort3(in: &elements, a: lo, b: mid, c: hi, by: areInIncreasingOrder)
+    let pivot = elements[mid]
+    
+    while true {
+        elements.formIndex(after: &lo)
+        guard findLo(in: elements, pivot: pivot, from: &lo, to: hi, by: areInIncreasingOrder) else { break }
+        elements.formIndex(before: &hi)
+        guard findHi(in: elements, pivot: pivot, from: lo, to: &hi, by: areInIncreasingOrder) else { break }
+        elements.swapAt(lo, hi)
+    }
+
+    
+    return lo
+}
+
+private func findLo<T>(in array: [T], pivot: T, from lo: inout Int, to hi: Int, by areInIncreasingOrder: (T, T)->Bool) -> Bool {
+    while lo != hi {
+        if !areInIncreasingOrder(array[lo], pivot) {
+            return true
+        }
+        array.formIndex(after: &lo)
+    }
+    return false
+}
+
+private func findHi<T>(in array: [T], pivot: T, from lo: Int, to hi: inout Int, by areInIncreasingOrder: (T, T)->Bool) -> Bool {
+    while hi != lo {
+        if areInIncreasingOrder(array[hi], pivot) { return true }
+        array.formIndex(before: &hi)
+    }
+    return false
+}
diff --git a/Introsort/Introsort.playground/Sources/Randomize.swift b/Introsort/Introsort.playground/Sources/Randomize.swift
new file mode 100644
index 000000000..6d1d57132
--- /dev/null
+++ b/Introsort/Introsort.playground/Sources/Randomize.swift
@@ -0,0 +1,9 @@
+import Foundation
+
+public func randomize(n: Int) -> [Int] {
+    var unsorted = [Int]()
+    for _ in 0..<n {
+        unsorted.append(Int(arc4random()))
+    }
+    return unsorted
+}
diff --git a/Introsort/Introsort.playground/Sources/Sort3.swift b/Introsort/Introsort.playground/Sources/Sort3.swift
new file mode 100644
index 000000000..04d20a6a6
--- /dev/null
+++ b/Introsort/Introsort.playground/Sources/Sort3.swift
@@ -0,0 +1,21 @@
+import Foundation
+
+public func sort3<T>(in array: inout [T], a: Int, b: Int, c: Int, by areInIncreasingOrder: (T, T) -> Bool) {
+    switch (areInIncreasingOrder(array[b], array[a]),
+            areInIncreasingOrder(array[c], array[b])) {
+    case (false, false): break
+    case (true, true): array.swapAt(a, c)
+    case (true, false):
+        array.swapAt(a, b)
+        
+        if areInIncreasingOrder(array[c], array[b]) {
+            array.swapAt(b, c)
+        }
+    case (false, true):
+        array.swapAt(b, c)
+        
+        if areInIncreasingOrder(array[b], array[a]) {
+            array.swapAt(a, b)
+        }
+    }
+}
diff --git a/Introsort/Introsort.playground/contents.xcplayground b/Introsort/Introsort.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Introsort/Introsort.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file

From 717ba94933686ea00068b5fc4ea0bc223c93cf38 Mon Sep 17 00:00:00 2001
From: Giuseppe Lanza <giuseppe@getdrop.com>
Date: Thu, 4 Jan 2018 15:49:29 +0000
Subject: [PATCH 322/643] Added readme file

---
 Introsort/HeapSort.swift      |  50 ++++++++++++++++
 Introsort/InsertionSort.swift |  28 +++++++++
 Introsort/IntroSort.swift     |  32 ++++++++++
 Introsort/Partition.swift     |  43 +++++++++++++
 Introsort/README.markdown     | 110 ++++++++++++++++++++++++++++++++++
 Introsort/Randomize.swift     |   9 +++
 Introsort/Sort3.swift         |  21 +++++++
 README.markdown               |   4 ++
 8 files changed, 297 insertions(+)
 create mode 100644 Introsort/HeapSort.swift
 create mode 100644 Introsort/InsertionSort.swift
 create mode 100644 Introsort/IntroSort.swift
 create mode 100644 Introsort/Partition.swift
 create mode 100644 Introsort/README.markdown
 create mode 100644 Introsort/Randomize.swift
 create mode 100644 Introsort/Sort3.swift

diff --git a/Introsort/HeapSort.swift b/Introsort/HeapSort.swift
new file mode 100644
index 000000000..f5bc466da
--- /dev/null
+++ b/Introsort/HeapSort.swift
@@ -0,0 +1,50 @@
+import Foundation
+
+private func shiftDown<T>(_ elements: inout [T], _ index: Int, _ range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    let countToIndex = elements.distance(from: range.lowerBound, to: index)
+    let countFromIndex = elements.distance(from: index, to: range.upperBound)
+    
+    guard countToIndex + 1 < countFromIndex else { return }
+    
+    let left = elements.index(index, offsetBy: countToIndex + 1)
+    var largest = index
+    if areInIncreasingOrder(elements[largest], elements[left]) {
+        largest = left
+    }
+    
+    if countToIndex + 2 < countFromIndex {
+        let right = elements.index(after: left)
+        if areInIncreasingOrder(elements[largest], elements[right]) {
+            largest = right
+        }
+    }
+
+    if largest != index {
+        elements.swapAt(index, largest)
+        shiftDown(&elements, largest, range, by: areInIncreasingOrder)
+    }
+    
+}
+
+private func heapify<T>(_ list: inout [T], _ range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    let root = range.lowerBound
+    var node = list.index(root, offsetBy: list.distance(from: range.lowerBound, to: range.upperBound)/2)
+    
+    while node != root {
+        list.formIndex(before: &node)
+        shiftDown(&list, node, range, by: areInIncreasingOrder)
+    }
+}
+
+public func heapsort<T>(for array: inout [T], range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    var hi = range.upperBound
+    let lo = range.lowerBound
+    heapify(&array, range, by: areInIncreasingOrder)
+    array.formIndex(before: &hi)
+    
+    while hi != lo {
+        array.swapAt(lo, hi)
+        shiftDown(&array, lo, lo..<hi, by: areInIncreasingOrder)
+        array.formIndex(before: &hi)
+    }
+}
diff --git a/Introsort/InsertionSort.swift b/Introsort/InsertionSort.swift
new file mode 100644
index 000000000..36887ea06
--- /dev/null
+++ b/Introsort/InsertionSort.swift
@@ -0,0 +1,28 @@
+import Foundation
+
+public func insertionSort<T>(for array: inout [T], range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) {
+    guard !range.isEmpty else { return }
+    
+    let start = range.lowerBound
+    var sortedEnd = start
+    
+    array.formIndex(after: &sortedEnd)
+    while sortedEnd != range.upperBound {
+        let x = array[sortedEnd]
+        
+        var i = sortedEnd
+        repeat {
+            let predecessor = array[array.index(before: i)]
+            
+            guard areInIncreasingOrder(x, predecessor) else { break }
+            array[i] = predecessor
+            array.formIndex(before: &i)
+        } while i != start
+        
+        if i != sortedEnd {
+            array[i] = x
+        }
+        array.formIndex(after: &sortedEnd)
+    }
+    
+}
diff --git a/Introsort/IntroSort.swift b/Introsort/IntroSort.swift
new file mode 100644
index 000000000..866b2603f
--- /dev/null
+++ b/Introsort/IntroSort.swift
@@ -0,0 +1,32 @@
+import Foundation
+
+public func introsort<T>(_ array: inout [T],  by areInIncreasingOrder: (T, T) -> Bool) {
+    //The depth limit is as best practice 2 * log( n )
+    let depthLimit = 2 * floor(log2(Double(array.count)))
+    
+    introSortImplementation(for: &array, range: 0..<array.count, depthLimit: Int(depthLimit), by: areInIncreasingOrder)
+}
+
+///This method is recursively executed for each partition result of the quicksort part of the algorithm
+private func introSortImplementation<T>(for array: inout [T], range: Range<Int>, depthLimit: Int, by areInIncreasingOrder: (T, T) -> Bool) {
+    if array.distance(from: range.lowerBound, to: range.upperBound) < 20 {
+        //if the partition count is less than 20 we can sort it using insertion sort. This algorithm in fact performs well on collections
+        //of this size, plus, at this point is quite probable that the quisksort part of the algorithm produced a partition which is
+        //nearly sorted. As we knoe insertion sort tends to O( n ) if this is the case.
+        insertionSort(for: &array, range: range, by: areInIncreasingOrder)
+    } else if depthLimit == 0 {
+        //If we reached the depth limit for this recursion branch, it's possible that we are hitting quick sort's worst case.
+        //Since quicksort degrades to O( n^2 ) in its worst case we stop using quicksort for this recursion branch and we switch to heapsort.
+        //Our preference remains quicksort, and we hope to be rare to see this condition to be true
+        heapsort(for: &array, range: range, by: areInIncreasingOrder)
+    } else {
+        //By default we use quicksort to sort our collection. The partition index method chose a pivot, and puts all the
+        //elements less than pivot on the left, and the ones bigger than pivot on the right. At the end of the operation the
+        //position of the pivot in the array is returned so that we can form the two partitions.
+        let partIdx = partitionIndex(for: &array, subRange: range, by: areInIncreasingOrder)
+        
+        //We can recursively call introsort implementation, decreasing the depthLimit for the left partition and the right partition.
+        introSortImplementation(for: &array, range: range.lowerBound..<partIdx, depthLimit: depthLimit &- 1, by: areInIncreasingOrder)
+        introSortImplementation(for: &array, range: partIdx..<range.upperBound, depthLimit: depthLimit &- 1, by: areInIncreasingOrder)
+    }
+}
diff --git a/Introsort/Partition.swift b/Introsort/Partition.swift
new file mode 100644
index 000000000..e24636da7
--- /dev/null
+++ b/Introsort/Partition.swift
@@ -0,0 +1,43 @@
+import Foundation
+
+public func partitionIndex<T>(for elements: inout [T], subRange range: Range<Int>, by areInIncreasingOrder: (T, T) -> Bool) -> Int {
+    var lo = range.lowerBound
+    var hi = elements.index(before: range.upperBound)
+    
+    // Sort the first, middle, and last elements, then use the middle value
+    // as the pivot for the partition.
+    let half = elements.distance(from: lo, to: hi) / 2
+    let mid = elements.index(lo, offsetBy: half)
+    
+    sort3(in: &elements, a: lo, b: mid, c: hi, by: areInIncreasingOrder)
+    let pivot = elements[mid]
+    
+    while true {
+        elements.formIndex(after: &lo)
+        guard findLo(in: elements, pivot: pivot, from: &lo, to: hi, by: areInIncreasingOrder) else { break }
+        elements.formIndex(before: &hi)
+        guard findHi(in: elements, pivot: pivot, from: lo, to: &hi, by: areInIncreasingOrder) else { break }
+        elements.swapAt(lo, hi)
+    }
+
+    
+    return lo
+}
+
+private func findLo<T>(in array: [T], pivot: T, from lo: inout Int, to hi: Int, by areInIncreasingOrder: (T, T)->Bool) -> Bool {
+    while lo != hi {
+        if !areInIncreasingOrder(array[lo], pivot) {
+            return true
+        }
+        array.formIndex(after: &lo)
+    }
+    return false
+}
+
+private func findHi<T>(in array: [T], pivot: T, from lo: Int, to hi: inout Int, by areInIncreasingOrder: (T, T)->Bool) -> Bool {
+    while hi != lo {
+        if areInIncreasingOrder(array[hi], pivot) { return true }
+        array.formIndex(before: &hi)
+    }
+    return false
+}
diff --git a/Introsort/README.markdown b/Introsort/README.markdown
new file mode 100644
index 000000000..c4ee6f804
--- /dev/null
+++ b/Introsort/README.markdown
@@ -0,0 +1,110 @@
+# IntroSort
+
+Goal: Sort an array from low to high (or high to low).
+
+IntroSort is the algorithm used by swift to sort a collection. Introsort is an hybrid algorithm invented by David Musser  in 1993 with the purpose of giving a generic sorting algorithm for the C++ standard library. The classic implementation of introsort expect a recursive Quicksort with fallback to Heapsort in case the recursion depth level reached a certain max. The maximum depends on the number of elements in the collection and it is usually 2 * log(n). The reason behind this “fallback” is that if Quicksort was not able to get the solution after 2 * log(n) recursions for a branch, probably it hit its worst case and it is degrading to complexity O( n^2 ). To optimise even further this algorithm, the swift implementation introduce an extra step in each recursion where the partition is sorted using InsertionSort if the count of the partition is less than 20.
+
+The number 20 is an empiric number obtained observing the behaviour of InsertionSort with lists of this size.
+
+Here's an implementation in Pseudocode:
+
+```
+procedure sort(A : array):
+    let maxdepth = ⌊log(length(A))⌋ × 2
+    introSort(A, maxdepth)
+
+procedure introsort(A, maxdepth):
+    n ← length(A)
+    if n < 20:
+        insertionsort(A)
+    else if maxdepth = 0:
+        heapsort(A)
+    else:
+        p ← partition(A)  // the pivot is selected using median of 3
+        introsort(A[0:p], maxdepth - 1)
+        introsort(A[p+1:n], maxdepth - 1)
+```
+
+## An example
+
+Let's walk through the example. The array is initially:
+
+	[ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
+
+
+for this example let's assume that `maxDepth` is **2** and that the size of the partition for the insertionSort to kick in is **5**
+
+At the first iteration we run introSort on the full collection that counts 13 elements. the maxDepth is 2, therefore we fall in the else case where quicksort acts.
+
+The `partition`  method picks the first element, the median and the last, it sorts them and uses the new median as pivot.
+
+    [ 10, 8, 26 ] -> [ 8, 10, 26 ]
+    
+Our array is now
+
+    [ 8, 0, 3, 9, 2, 14, 10, 27, 1, 5, 8, -1, 26 ]
+
+**10** is the pivot. After the choice of the pivot, the `partition` method swaps elements to get all the elements less than pivot on the left, and all the elements more or equal than pivot on the right.
+
+    [ 8, 0, 3, 9, 2, 1, 5, 8, -1, 10, 27, 14, 26 ]
+    
+Because of the swaps, the index of of pivot is now changed and returned. The next step of introsort is to call recursively itself for the two sub arrays:
+
+    less: [ 8, 0, 3, 9, 2, 1, 5, 8, -1, 10 ]
+    greater: [ 27, 14, 26 ]
+
+## maxDepth: 1, branch: less
+
+    [ 8, 0, 3, 9, 2, 1, 5, 8, -1, 10 ]
+
+The count of the array is still more than 5 so we don't meet yet the conditions for insertion sort to kick in. At this iteration maxDepth is decreased by one but it is still more than zero, so heapsort will not act.
+
+Just like in the previous iteration quicksort wins and the `partition` method choses a pivot and sorts the elemets less than pivot on the left and the elements more or equeal than pivot on the right.
+
+    array: [ 8, 0, 3, 9, 2, 1, 5, 8, -1, 10 ]
+    pivot candidates: [ 8, 1, 10] -> [ 1, 8, 10]
+    pivot: 8
+    before partition: [ 1, 0, 3, 9, 2, 8, 5, 8, -1, 10 ]
+    after partition: [ 1, 0, 3, -1, 2, 5, 8, 8, 9, 10 ]
+    
+    less: [ 1, 0, 3, -1, 2, 5, 8 ]
+    greater: [ 8, 9, 10 ]
+    
+## maxDepth: 0, branch: less
+
+    [ 1, 0, 3, -1, 2, 5, 8 ]
+    
+Just like before, introsort is recursively executed for `less` and greater. This time `less`has a count more than **5** so it will not be sorted with insertion sort, but the maxDepth decreased again by 1 is now 0 and heapsort takes over sorting the array.
+
+    heapsort -> [ -1, 0, 1, 2, 3, 5, 8 ]
+    
+## maxDepth: 0, branch: greater
+
+    [ 8, 9, 10 ]
+
+following greater in this recursion, the count of elements is 3, which is less than 5, so this partition is sorted using insertionSort.
+
+    insertionSort -> [ 8, 9 , 10]
+    
+
+## back to maxDepth = 1, branch: greater
+
+    [ 27, 14, 26 ]
+
+At this point the original array has mutated to be
+
+    [ -1, 0, 1, 2, 3, 5, 8, 8, 9, 10, 27, 14, 26 ]
+    
+now the `less` partition is sorted  and since the count of the `greater` partition is 3 it will be sorted with insertion sort  `[ 14, 26, 27 ]`
+
+The array is now successfully sorted
+
+    [ -1, 0, 1, 2, 3, 5, 8, 8, 9, 10, 14, 26, 27 ]
+
+
+## See also
+
+[Introsort on Wikipedia](https://en.wikipedia.org/wiki/Introsort)
+[Introsort comparison with other sorting algorithms](http://agostini.tech/2017/12/18/swift-sorting-algorithm/)
+
+*Written for Swift Algorithm Club by Giuseppe Lanza*
diff --git a/Introsort/Randomize.swift b/Introsort/Randomize.swift
new file mode 100644
index 000000000..6d1d57132
--- /dev/null
+++ b/Introsort/Randomize.swift
@@ -0,0 +1,9 @@
+import Foundation
+
+public func randomize(n: Int) -> [Int] {
+    var unsorted = [Int]()
+    for _ in 0..<n {
+        unsorted.append(Int(arc4random()))
+    }
+    return unsorted
+}
diff --git a/Introsort/Sort3.swift b/Introsort/Sort3.swift
new file mode 100644
index 000000000..04d20a6a6
--- /dev/null
+++ b/Introsort/Sort3.swift
@@ -0,0 +1,21 @@
+import Foundation
+
+public func sort3<T>(in array: inout [T], a: Int, b: Int, c: Int, by areInIncreasingOrder: (T, T) -> Bool) {
+    switch (areInIncreasingOrder(array[b], array[a]),
+            areInIncreasingOrder(array[c], array[b])) {
+    case (false, false): break
+    case (true, true): array.swapAt(a, c)
+    case (true, false):
+        array.swapAt(a, b)
+        
+        if areInIncreasingOrder(array[c], array[b]) {
+            array.swapAt(b, c)
+        }
+    case (false, true):
+        array.swapAt(b, c)
+        
+        if areInIncreasingOrder(array[b], array[a]) {
+            array.swapAt(a, b)
+        }
+    }
+}
diff --git a/README.markdown b/README.markdown
index 46544682e..beac173d6 100644
--- a/README.markdown
+++ b/README.markdown
@@ -73,6 +73,10 @@ Fast sorts:
 - [Merge Sort](Merge%20Sort/)
 - [Heap Sort](Heap%20Sort/)
 
+Hybrid sorts:
+
+- [Introsort](Introsort/)
+
 Special-purpose sorts:
 
 - [Counting Sort](Counting%20Sort/)

From e30467bcc9a9681780cee9d7206f4e2bda776ac6 Mon Sep 17 00:00:00 2001
From: Davis Riedel <mail@davis-riedel.de>
Date: Sat, 6 Jan 2018 22:47:22 +0100
Subject: [PATCH 323/643] Improvements to Heap

- renamed "elements" to "nodes" to clarify the difference between array and heap. This also unifies code and comments, which were sometimes referring to the array as "nodes".
- made nodes publicly readable but only settable within the heap itself. To change the nodes/operate on the heap, the provided functions should be used, to guarantee the heaps structure.
- renamed isOrderedBefore to orderCriteria. The variable name isOrderedBefore did not clearly explain what the variable is for/what the closure stored within does
- added method to get node at a specific index
- replace method should not force the replaced value to be higher/lower than its parent. Instead replace should remove the node to be replaced and insert the given value as a new one in order to preserve the heap's structure. Asserting crashes the whole program.
- added @discardableResult to removeAt. If remove is @discardableResult removeAt should be as well in for consistency.
- replaced while true in shiftDown with a recursive call. while true is bad programming style.
- simplified indexOf method
- added a removeNode method for heaps with equatable data type
- improved, adjusted and added descriptions
- made functions private where fileprivate was not needed
- added tests for new functions and tested everything
- updated README where necessary (to conform to new code, only a few changes)
---
 Heap/Heap.swift                               | 187 +++++++++---------
 Heap/README.markdown                          |  12 +-
 Heap/Tests/HeapTests.swift                    |  97 +++++----
 Heap/Tests/Tests.xcodeproj/project.pbxproj    |  14 +-
 .../contents.xcworkspacedata                  |   0
 .../xcshareddata/xcschemes/Tests.xcscheme     |   2 +-
 6 files changed, 172 insertions(+), 140 deletions(-)
 mode change 100644 => 100755 Heap/Heap.swift
 mode change 100644 => 100755 Heap/README.markdown
 mode change 100644 => 100755 Heap/Tests/HeapTests.swift
 mode change 100644 => 100755 Heap/Tests/Tests.xcodeproj/project.pbxproj
 mode change 100644 => 100755 Heap/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 mode change 100644 => 100755 Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
old mode 100644
new mode 100755
index b0355da5d..a33fc0b94
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -4,58 +4,55 @@
 //
 
 public struct Heap<T> {
+  
   /** The array that stores the heap's nodes. */
-  var elements = [T]()
+  private(set) var nodes = [T]()
   
-  /** Determines whether this is a max-heap (>) or min-heap (<). */
-  fileprivate var isOrderedBefore: (T, T) -> Bool
+  /**
+   * Determines how to compare two nodes in the heap.
+   * Use '>' for a max-heap or '<' for a min-heap,
+   * or provide a comparing method if the heap is made
+   * of custom elements, for example tuples.
+   */
+  private var orderCriteria: (T, T) -> Bool
   
   /**
    * Creates an empty heap.
    * The sort function determines whether this is a min-heap or max-heap.
-   * For integers, > makes a max-heap, < makes a min-heap.
+   * For comparable data types, > makes a max-heap, < makes a min-heap.
    */
   public init(sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
+    self.orderCriteria = sort
   }
   
   /**
    * Creates a heap from an array. The order of the array does not matter;
    * the elements are inserted into the heap in the order determined by the
-   * sort function.
+   * sort function. For comparable data types, '>' makes a max-heap,
+   * '<' makes a min-heap.
    */
   public init(array: [T], sort: @escaping (T, T) -> Bool) {
-    self.isOrderedBefore = sort
+    self.orderCriteria = sort
     buildHeap(fromArray: array)
   }
   
-  /*
-   // This version has O(n log n) performance.
-   private mutating func buildHeap(array: [T]) {
-   elements.reserveCapacity(array.count)
-   for value in array {
-   insert(value)
-   }
-   }
-   */
-  
   /**
-   * Converts an array to a max-heap or min-heap in a bottom-up manner.
+   * Creates the max-heap or min-heap from an array, in a bottom-up manner.
    * Performance: This runs pretty much in O(n).
    */
-  fileprivate mutating func buildHeap(fromArray array: [T]) {
-    elements = array
-    for i in stride(from: (elements.count/2 - 1), through: 0, by: -1) {
-      shiftDown(i, heapSize: elements.count)
+  private mutating func buildHeap(fromArray array: [T]) {
+    nodes = array
+    for i in stride(from: (nodes.count/2-1), through: 0, by: -1) {
+      shiftDown(i)
     }
   }
   
   public var isEmpty: Bool {
-    return elements.isEmpty
+    return nodes.isEmpty
   }
   
   public var count: Int {
-    return elements.count
+    return nodes.count
   }
   
   /**
@@ -89,7 +86,13 @@ public struct Heap<T> {
    * value (for a min-heap).
    */
   public func peek() -> T? {
-    return elements.first
+    return nodes.first
+  }
+  
+  /** Returns the node at given index */
+  public func node(at i: Int) -> T? {
+    guard i < nodes.count else { return nil }
+    return nodes[i]
   }
   
   /**
@@ -97,10 +100,14 @@ public struct Heap<T> {
    * or min-heap property still holds. Performance: O(log n).
    */
   public mutating func insert(_ value: T) {
-    elements.append(value)
-    shiftUp(elements.count - 1)
+    nodes.append(value)
+    shiftUp(nodes.count - 1)
   }
   
+  /**
+   * Adds a sequence of values to the heap. This reorders the heap so that
+   * the max-heap or min-heap property still holds. Performance: O(log n).
+   */
   public mutating func insert<S: Sequence>(_ sequence: S) where S.Iterator.Element == T {
     for value in sequence {
       insert(value)
@@ -108,15 +115,14 @@ public struct Heap<T> {
   }
   
   /**
-   * Allows you to change an element. In a max-heap, the new element should be
-   * larger than the old one; in a min-heap it should be smaller.
+   * Allows you to change an element. This reorders the heap so that
+   * the max-heap or min-heap property still holds.
    */
   public mutating func replace(index i: Int, value: T) {
-    guard i < elements.count else { return }
+    guard i < nodes.count else { return }
     
-    assert(isOrderedBefore(value, elements[i]))
-    elements[i] = value
-    shiftUp(i)
+    removeAt(i)
+    insert(value)
   }
   
   /**
@@ -124,34 +130,35 @@ public struct Heap<T> {
    * value; for a min-heap it is the minimum value. Performance: O(log n).
    */
   @discardableResult public mutating func remove() -> T? {
-    if elements.isEmpty {
-      return nil
-    } else if elements.count == 1 {
-      return elements.removeLast()
-    } else {
-      // Use the last node to replace the first one, then fix the heap by
-      // shifting this new first node into its proper position.
-      let value = elements[0]
-      elements[0] = elements.removeLast()
-      shiftDown()
-      return value
+    if !nodes.isEmpty {
+      if nodes.count == 1 {
+        return nodes.removeLast()
+      } else {
+        // Use the last node to replace the first one, then fix the heap by
+        // shifting this new first node into its proper position.
+        let value = nodes[0]
+        nodes[0] = nodes.removeLast()
+        shiftDown(0)
+        return value
+      }
     }
+    return nil
   }
   
   /**
-   * Removes an arbitrary node from the heap. Performance: O(log n). You need
-   * to know the node's index, which may actually take O(n) steps to find.
+   * Removes an arbitrary node from the heap. Performance: O(log n).
+   * Note that you need to know the node's index.
    */
-  public mutating func removeAt(_ index: Int) -> T? {
-    guard index < elements.count else { return nil }
+  @discardableResult public mutating func removeAt(_ index: Int) -> T? {
+    guard index < nodes.count else { return nil }
     
-    let size = elements.count - 1
+    let size = nodes.count - 1
     if index != size {
-      elements.swapAt(index, size)
-      shiftDown(index, heapSize: size)
+      nodes.swapAt(index, size)
+      shiftDown(from: index, until: size)
       shiftUp(index)
     }
-    return elements.removeLast()
+    return nodes.removeLast()
   }
   
   /**
@@ -160,68 +167,64 @@ public struct Heap<T> {
    */
   mutating func shiftUp(_ index: Int) {
     var childIndex = index
-    let child = elements[childIndex]
+    let child = nodes[childIndex]
     var parentIndex = self.parentIndex(ofIndex: childIndex)
     
-    while childIndex > 0 && isOrderedBefore(child, elements[parentIndex]) {
-      elements[childIndex] = elements[parentIndex]
+    while childIndex > 0 && orderCriteria(child, nodes[parentIndex]) {
+      nodes[childIndex] = nodes[parentIndex]
       childIndex = parentIndex
       parentIndex = self.parentIndex(ofIndex: childIndex)
     }
     
-    elements[childIndex] = child
-  }
-  
-  mutating func shiftDown() {
-    shiftDown(0, heapSize: elements.count)
+    nodes[childIndex] = child
   }
   
   /**
    * Looks at a parent node and makes sure it is still larger (max-heap) or
    * smaller (min-heap) than its childeren.
    */
-  mutating func shiftDown(_ index: Int, heapSize: Int) {
-    var parentIndex = index
+  private mutating func shiftDown(from index: Int, until endIndex: Int) {
+    let leftChildIndex = self.leftChildIndex(ofIndex: index)
+    let rightChildIndex = leftChildIndex + 1
     
-    while true {
-      let leftChildIndex = self.leftChildIndex(ofIndex: parentIndex)
-      let rightChildIndex = leftChildIndex + 1
-      
-      // Figure out which comes first if we order them by the sort function:
-      // the parent, the left child, or the right child. If the parent comes
-      // first, we're done. If not, that element is out-of-place and we make
-      // it "float down" the tree until the heap property is restored.
-      var first = parentIndex
-      if leftChildIndex < heapSize && isOrderedBefore(elements[leftChildIndex], elements[first]) {
-        first = leftChildIndex
-      }
-      if rightChildIndex < heapSize && isOrderedBefore(elements[rightChildIndex], elements[first]) {
-        first = rightChildIndex
-      }
-      if first == parentIndex { return }
-      
-      elements.swapAt(parentIndex, first)
-      parentIndex = first
+    // Figure out which comes first if we order them by the sort function:
+    // the parent, the left child, or the right child. If the parent comes
+    // first, we're done. If not, that element is out-of-place and we make
+    // it "float down" the tree until the heap property is restored.
+    var first = index
+    if leftChildIndex < endIndex && orderCriteria(nodes[leftChildIndex], nodes[first]) {
+      first = leftChildIndex
+    }
+    if rightChildIndex < endIndex && orderCriteria(nodes[rightChildIndex], nodes[first]) {
+      first = rightChildIndex
     }
+    if first == index { return }
+    
+    nodes.swapAt(index, first)
+    shiftDown(from: first, until: endIndex)
+  }
+  
+  private mutating func shiftDown(_ index: Int) {
+    shiftDown(from: index, until: nodes.count)
   }
+  
 }
 
 // MARK: - Searching
 
 extension Heap where T: Equatable {
-  /**
-   * Searches the heap for the given element. Performance: O(n).
-   */
-  public func index(of element: T) -> Int? {
-    return index(of: element, 0)
+  
+  /** Get the index of a node in the heap. Performance: O(n). */
+  public func index(of node: T) -> Int? {
+    return nodes.index(where: { $0 == node })
   }
   
-  fileprivate func index(of element: T, _ i: Int) -> Int? {
-    if i >= count { return nil }
-    if isOrderedBefore(element, elements[i]) { return nil }
-    if element == elements[i] { return i }
-    if let j = index(of: element, self.leftChildIndex(ofIndex: i)) { return j }
-    if let j = index(of: element, self.rightChildIndex(ofIndex: i)) { return j }
+  /** Removes the first occurrence of a node from the heap. Performance: O(n log n). */
+  @discardableResult public mutating func remove(node: T) -> T? {
+    if let index = index(of: node) {
+      return removeAt(index)
+    }
     return nil
   }
+  
 }
diff --git a/Heap/README.markdown b/Heap/README.markdown
old mode 100644
new mode 100755
index 4344d9e7c..76d2bee39
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -38,7 +38,7 @@ A heap is not a replacement for a binary search tree, and there are similarities
 
 **Balancing.** A binary search tree must be "balanced" so that most operations have **O(log n)** performance. You can either insert and delete your data in a random order or use something like an [AVL tree](../AVL%20Tree/) or [red-black tree](../Red-Black%20Tree/), but with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
 
-**Searching.** Whereas searching is fast in a binary tree, it is slow in a heap. Searching isn't a top priority in a heap since the purpose of a heap is to put the largest (or smallest) node at the front and to allow relatively fast inserts and deletes. 
+**Searching.** Whereas searching is fast in a binary tree, it is slow in a heap. Searching isn't a top priority in a heap since the purpose of a heap is to put the largest (or smallest) node at the front and to allow relatively fast inserts and deletes.
 
 ## The tree inside an array
 
@@ -148,7 +148,7 @@ There are two primitive operations necessary to make sure the heap is a valid ma
 
 Shifting up or down is a recursive procedure that takes **O(log n)** time.
 
-Here are other operations that are built on primitive operations: 
+Here are other operations that are built on primitive operations:
 
 - `insert(value)`: Adds the new element to the end of the heap and then uses `shiftUp()` to fix the heap.
 
@@ -190,7 +190,7 @@ The `(16)` was added to the first available space on the last row.
 
 Unfortunately, the heap property is no longer satisfied because `(2)` is above `(16)`, and we want higher numbers above lower numbers. (This is a max-heap.)
 
-To restore the heap property, we swap `(16)` and `(2)`. 
+To restore the heap property, we swap `(16)` and `(2)`.
 
 ![The heap before insertion](Images/Insert2.png)
 
@@ -214,7 +214,7 @@ What happens to the empty spot at the top?
 
 ![The root is gone](Images/Remove1.png)
 
-When inserting, we put the new value at the end of the array. Here, we do the opposite: we take the last object we have, stick it up on top of the tree, and restore the heap property. 
+When inserting, we put the new value at the end of the array. Here, we do the opposite: we take the last object we have, stick it up on top of the tree, and restore the heap property.
 
 ![The last node goes to the root](Images/Remove2.png)
 
@@ -226,7 +226,7 @@ Keep shifting down until the node does not have any children or it is larger tha
 
 ![The last node goes to the root](Images/Remove4.png)
 
-The time required for shifting all the way down is proportional to the height of the tree which takes **O(log n)** time. 
+The time required for shifting all the way down is proportional to the height of the tree which takes **O(log n)** time.
 
 > **Note:** `shiftUp()` and `shiftDown()` can only fix one out-of-place element at a time. If there are multiple elements in the wrong place, you need to call these functions once for each of those elements.
 
@@ -279,7 +279,7 @@ In code:
 ```swift
   private mutating func buildHeap(fromArray array: [T]) {
     elements = array
-    for i in (elements.count/2 - 1).stride(through: 0, by: -1) {
+    for i in stride(from: (nodes.count/2-1), through: 0, by: -1) {
       shiftDown(index: i, heapSize: elements.count)
     }
   }
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
old mode 100644
new mode 100755
index 66be0931c..36035fe93
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -19,9 +19,9 @@ class HeapTests: XCTestCase {
       let left = h.leftChildIndex(ofIndex: i)
       let right = h.rightChildIndex(ofIndex: i)
       let parent = h.parentIndex(ofIndex: i)
-      if left < h.count && h.elements[i] < h.elements[left] { return false }
-      if right < h.count && h.elements[i] < h.elements[right] { return false }
-      if i > 0 && h.elements[parent] < h.elements[i] { return false }
+      if left < h.count && h.nodes[i] < h.nodes[left] { return false }
+      if right < h.count && h.nodes[i] < h.nodes[right] { return false }
+      if i > 0 && h.nodes[parent] < h.nodes[i] { return false }
     }
     return true
   }
@@ -31,9 +31,9 @@ class HeapTests: XCTestCase {
       let left = h.leftChildIndex(ofIndex: i)
       let right = h.rightChildIndex(ofIndex: i)
       let parent = h.parentIndex(ofIndex: i)
-      if left < h.count && h.elements[i] > h.elements[left] { return false }
-      if right < h.count && h.elements[i] > h.elements[right] { return false }
-      if i > 0 && h.elements[parent] > h.elements[i] { return false }
+      if left < h.count && h.nodes[i] > h.nodes[left] { return false }
+      if right < h.count && h.nodes[i] > h.nodes[right] { return false }
+      if i > 0 && h.nodes[parent] > h.nodes[i] { return false }
     }
     return true
   }
@@ -90,7 +90,7 @@ class HeapTests: XCTestCase {
     let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: >)
     XCTAssertTrue(verifyMaxHeap(h1))
     XCTAssertFalse(verifyMinHeap(h1))
-    XCTAssertEqual(h1.elements, [7, 5, 6, 4, 2, 1, 3])
+    XCTAssertEqual(h1.nodes, [7, 5, 6, 4, 2, 1, 3])
     XCTAssertFalse(h1.isEmpty)
     XCTAssertEqual(h1.count, 7)
     XCTAssertEqual(h1.peek()!, 7)
@@ -98,7 +98,7 @@ class HeapTests: XCTestCase {
     let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(h2))
     XCTAssertFalse(verifyMinHeap(h2))
-    XCTAssertEqual(h2.elements, [7, 6, 5, 4, 3, 2, 1])
+    XCTAssertEqual(h2.nodes, [7, 6, 5, 4, 3, 2, 1])
     XCTAssertFalse(h2.isEmpty)
     XCTAssertEqual(h2.count, 7)
     XCTAssertEqual(h2.peek()!, 7)
@@ -106,7 +106,7 @@ class HeapTests: XCTestCase {
     let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: >)
     XCTAssertTrue(verifyMaxHeap(h3))
     XCTAssertFalse(verifyMinHeap(h3))
-    XCTAssertEqual(h3.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
+    XCTAssertEqual(h3.nodes, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
     XCTAssertFalse(h3.isEmpty)
     XCTAssertEqual(h3.count, 10)
     XCTAssertEqual(h3.peek()!, 16)
@@ -114,7 +114,7 @@ class HeapTests: XCTestCase {
     let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: >)
     XCTAssertTrue(verifyMaxHeap(h4))
     XCTAssertFalse(verifyMinHeap(h4))
-    XCTAssertEqual(h4.elements, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
+    XCTAssertEqual(h4.nodes, [27, 17, 10, 16, 13, 9, 1, 5, 7, 12, 4, 8, 3, 0])
     XCTAssertFalse(h4.isEmpty)
     XCTAssertEqual(h4.count, 14)
     XCTAssertEqual(h4.peek()!, 27)
@@ -124,7 +124,7 @@ class HeapTests: XCTestCase {
     let h1 = Heap(array: [1, 2, 3, 4, 5, 6, 7], sort: <)
     XCTAssertTrue(verifyMinHeap(h1))
     XCTAssertFalse(verifyMaxHeap(h1))
-    XCTAssertEqual(h1.elements, [1, 2, 3, 4, 5, 6, 7])
+    XCTAssertEqual(h1.nodes, [1, 2, 3, 4, 5, 6, 7])
     XCTAssertFalse(h1.isEmpty)
     XCTAssertEqual(h1.count, 7)
     XCTAssertEqual(h1.peek()!, 1)
@@ -132,7 +132,7 @@ class HeapTests: XCTestCase {
     let h2 = Heap(array: [7, 6, 5, 4, 3, 2, 1], sort: <)
     XCTAssertTrue(verifyMinHeap(h2))
     XCTAssertFalse(verifyMaxHeap(h2))
-    XCTAssertEqual(h2.elements, [1, 3, 2, 4, 6, 7, 5])
+    XCTAssertEqual(h2.nodes, [1, 3, 2, 4, 6, 7, 5])
     XCTAssertFalse(h2.isEmpty)
     XCTAssertEqual(h2.count, 7)
     XCTAssertEqual(h2.peek()!, 1)
@@ -140,7 +140,7 @@ class HeapTests: XCTestCase {
     let h3 = Heap(array: [4, 1, 3, 2, 16, 9, 10, 14, 8, 7], sort: <)
     XCTAssertTrue(verifyMinHeap(h3))
     XCTAssertFalse(verifyMaxHeap(h3))
-    XCTAssertEqual(h3.elements, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
+    XCTAssertEqual(h3.nodes, [1, 2, 3, 4, 7, 9, 10, 14, 8, 16])
     XCTAssertFalse(h3.isEmpty)
     XCTAssertEqual(h3.count, 10)
     XCTAssertEqual(h3.peek()!, 1)
@@ -148,7 +148,7 @@ class HeapTests: XCTestCase {
     let h4 = Heap(array: [27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0], sort: <)
     XCTAssertTrue(verifyMinHeap(h4))
     XCTAssertFalse(verifyMaxHeap(h4))
-    XCTAssertEqual(h4.elements, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
+    XCTAssertEqual(h4.nodes, [0, 4, 1, 5, 12, 8, 3, 16, 7, 17, 13, 10, 9, 27])
     XCTAssertFalse(h4.isEmpty)
     XCTAssertEqual(h4.count, 14)
     XCTAssertEqual(h4.peek()!, 0)
@@ -158,14 +158,14 @@ class HeapTests: XCTestCase {
     let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(heap))
     XCTAssertTrue(verifyMinHeap(heap))
-    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+    XCTAssertEqual(heap.nodes, [1, 1, 1, 1, 1])
   }
   
   func testCreateMinHeapEqualElements() {
     let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
     XCTAssertTrue(verifyMinHeap(heap))
     XCTAssertTrue(verifyMaxHeap(heap))
-    XCTAssertEqual(heap.elements, [1, 1, 1, 1, 1])
+    XCTAssertEqual(heap.nodes, [1, 1, 1, 1, 1])
   }
   
   fileprivate func randomArray(_ n: Int) -> [Int] {
@@ -183,7 +183,7 @@ class HeapTests: XCTestCase {
       XCTAssertTrue(verifyMaxHeap(h))
       XCTAssertFalse(h.isEmpty)
       XCTAssertEqual(h.count, n)
-      XCTAssertTrue(isPermutation(a, h.elements))
+      XCTAssertTrue(isPermutation(a, h.nodes))
     }
   }
   
@@ -194,58 +194,58 @@ class HeapTests: XCTestCase {
       XCTAssertTrue(verifyMinHeap(h))
       XCTAssertFalse(h.isEmpty)
       XCTAssertEqual(h.count, n)
-      XCTAssertTrue(isPermutation(a, h.elements))
+      XCTAssertTrue(isPermutation(a, h.nodes))
     }
   }
   
-  func testRemoving() {
+  func testRemovingAtIndex() {
     var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+    XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 60, 65])
     
     //test index out of bounds
     let v = h.removeAt(10)
     XCTAssertEqual(v, nil)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 60, 65])
+    XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 60, 65])
     
     let v1 = h.removeAt(5)
     XCTAssertEqual(v1, 60)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 50, 70, 10, 20, 65])
+    XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 65])
     
     let v2 = h.removeAt(4)
     XCTAssertEqual(v2, 20)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 65, 70, 10, 50])
+    XCTAssertEqual(h.nodes, [100, 65, 70, 10, 50])
     
     let v3 = h.removeAt(4)
     XCTAssertEqual(v3, 50)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [100, 65, 70, 10])
+    XCTAssertEqual(h.nodes, [100, 65, 70, 10])
     
     let v4 = h.removeAt(0)
     XCTAssertEqual(v4, 100)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [70, 65, 10])
+    XCTAssertEqual(h.nodes, [70, 65, 10])
     
     XCTAssertEqual(h.peek()!, 70)
     let v5 = h.remove()
     XCTAssertEqual(v5, 70)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [65, 10])
+    XCTAssertEqual(h.nodes, [65, 10])
     
     XCTAssertEqual(h.peek()!, 65)
     let v6 = h.remove()
     XCTAssertEqual(v6, 65)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [10])
+    XCTAssertEqual(h.nodes, [10])
     
     XCTAssertEqual(h.peek()!, 10)
     let v7 = h.remove()
     XCTAssertEqual(v7, 10)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [])
+    XCTAssertEqual(h.nodes, [])
     
     XCTAssertNil(h.peek())
   }
@@ -259,12 +259,23 @@ class HeapTests: XCTestCase {
   func testRemoveRoot() {
     var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+    XCTAssertEqual(h.nodes, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
     XCTAssertEqual(h.peek()!, 15)
     let v = h.remove()
     XCTAssertEqual(v, 15)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
+    XCTAssertEqual(h.nodes, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
+  }
+  
+  func testRemoveNode() {
+    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertEqual(h.nodes, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+    XCTAssertEqual(h.node(at: 3)!, 5)
+    let v = h.remove(node: 5)
+    XCTAssertEqual(v, 5)
+    XCTAssertTrue(verifyMaxHeap(h))
+    XCTAssertFalse(h.nodes.contains(5))
   }
   
   func testRemoveRandomItems() {
@@ -272,19 +283,27 @@ class HeapTests: XCTestCase {
       var a = randomArray(n)
       var h = Heap(array: a, sort: >)
       XCTAssertTrue(verifyMaxHeap(h))
-      XCTAssertTrue(isPermutation(a, h.elements))
+      XCTAssertTrue(isPermutation(a, h.nodes))
       
       let m = (n + 1)/2
       for k in 1...m {
         let i = Int(arc4random_uniform(UInt32(n - k + 1)))
-        let v = h.removeAt(i)!
-        let j = a.index(of: v)!
+        
+        var v: Int? = nil
+        if k == 2 || k == m {
+          v = h.remove(node: h.node(at: i)!)
+        } else {
+          v = h.removeAt(i)
+        }
+        XCTAssertNotNil(v)
+        
+        let j = a.index(of: v!)!
         a.remove(at: j)
         
         XCTAssertTrue(verifyMaxHeap(h))
         XCTAssertEqual(h.count, a.count)
         XCTAssertEqual(h.count, n - k)
-        XCTAssertTrue(isPermutation(a, h.elements))
+        XCTAssertTrue(isPermutation(a, h.nodes))
       }
     }
   }
@@ -292,17 +311,17 @@ class HeapTests: XCTestCase {
   func testInsert() {
     var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
+    XCTAssertEqual(h.nodes, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
     
     h.insert(10)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
+    XCTAssertEqual(h.nodes, [15, 13, 10, 5, 12, 9, 7, 4, 0, 6, 2, 1, 8])
   }
   
   func testInsertArrayAndRemove() {
     var heap = Heap<Int>(sort: >)
     heap.insert([1, 3, 2, 7, 5, 9])
-    XCTAssertEqual(heap.elements, [9, 5, 7, 1, 3, 2])
+    XCTAssertEqual(heap.nodes, [9, 5, 7, 1, 3, 2])
     
     XCTAssertEqual(9, heap.remove())
     XCTAssertEqual(7, heap.remove())
@@ -316,15 +335,13 @@ class HeapTests: XCTestCase {
   func testReplace() {
     var h = Heap(array: [16, 14, 10, 8, 7, 9, 3, 2, 4, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 10, 8, 7, 9, 3, 2, 4, 1])
     
     h.replace(index: 5, value: 13)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
     
     //test index out of bounds
     h.replace(index: 20, value: 2)
     XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.elements, [16, 14, 13, 8, 7, 10, 3, 2, 4, 1])
   }
+  
 }
diff --git a/Heap/Tests/Tests.xcodeproj/project.pbxproj b/Heap/Tests/Tests.xcodeproj/project.pbxproj
old mode 100644
new mode 100755
index 617e29f27..51433ee64
--- a/Heap/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Heap/Tests/Tests.xcodeproj/project.pbxproj
@@ -83,7 +83,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 0920;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -141,14 +141,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -187,14 +193,20 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
diff --git a/Heap/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Heap/Tests/Tests.xcodeproj/project.xcworkspace/contents.xcworkspacedata
old mode 100644
new mode 100755
diff --git a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
old mode 100644
new mode 100755
index 80ed35600..77d01bebc
--- a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "0920"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 92f67b5136fb4623cb9c0cfb9826b72562455534 Mon Sep 17 00:00:00 2001
From: Davis Riedel <mail@davis-riedel.de>
Date: Mon, 8 Jan 2018 10:47:59 +0100
Subject: [PATCH 324/643] - Adopted discussed improvements - Made nodes and
 some other methods internal, so that extensions like HeapSort can use them.
 This fixes the HeapSort algorithm as well as the tests for both.

---
 Heap Sort/HeapSort.swift   |  8 +++---
 Heap/Heap.swift            | 55 +++++++++++++++++---------------------
 Heap/Tests/HeapTests.swift | 39 +++++++--------------------
 3 files changed, 38 insertions(+), 64 deletions(-)

diff --git a/Heap Sort/HeapSort.swift b/Heap Sort/HeapSort.swift
index 6b5e91dc5..0354817a6 100644
--- a/Heap Sort/HeapSort.swift	
+++ b/Heap Sort/HeapSort.swift	
@@ -1,10 +1,10 @@
 extension Heap {
   public mutating func sort() -> [T] {
-    for i in stride(from: (elements.count - 1), through: 1, by: -1) {
-      elements.swapAt(0, i)
-      shiftDown(0, heapSize: i)
+    for i in stride(from: (nodes.count - 1), through: 1, by: -1) {
+      nodes.swapAt(0, i)
+      shiftDown(from: 0, until: i)
     }
-    return elements
+    return nodes
   }
 }
 
diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index a33fc0b94..ae392d448 100755
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -6,7 +6,7 @@
 public struct Heap<T> {
   
   /** The array that stores the heap's nodes. */
-  private(set) var nodes = [T]()
+  internal var nodes = [T]()
   
   /**
    * Determines how to compare two nodes in the heap.
@@ -33,14 +33,14 @@ public struct Heap<T> {
    */
   public init(array: [T], sort: @escaping (T, T) -> Bool) {
     self.orderCriteria = sort
-    buildHeap(fromArray: array)
+    configureHeap(from: array)
   }
   
   /**
-   * Creates the max-heap or min-heap from an array, in a bottom-up manner.
+   * Configures the max-heap or min-heap from an array, in a bottom-up manner.
    * Performance: This runs pretty much in O(n).
    */
-  private mutating func buildHeap(fromArray array: [T]) {
+  private mutating func configureHeap(from array: [T]) {
     nodes = array
     for i in stride(from: (nodes.count/2-1), through: 0, by: -1) {
       shiftDown(i)
@@ -59,7 +59,7 @@ public struct Heap<T> {
    * Returns the index of the parent of the element at index i.
    * The element at index 0 is the root of the tree and has no parent.
    */
-  @inline(__always) func parentIndex(ofIndex i: Int) -> Int {
+  @inline(__always) internal func parentIndex(ofIndex i: Int) -> Int {
     return (i - 1) / 2
   }
   
@@ -68,7 +68,7 @@ public struct Heap<T> {
    * Note that this index can be greater than the heap size, in which case
    * there is no left child.
    */
-  @inline(__always) func leftChildIndex(ofIndex i: Int) -> Int {
+  @inline(__always) internal func leftChildIndex(ofIndex i: Int) -> Int {
     return 2*i + 1
   }
   
@@ -77,7 +77,7 @@ public struct Heap<T> {
    * Note that this index can be greater than the heap size, in which case
    * there is no right child.
    */
-  @inline(__always) func rightChildIndex(ofIndex i: Int) -> Int {
+  @inline(__always) internal func rightChildIndex(ofIndex i: Int) -> Int {
     return 2*i + 2
   }
   
@@ -89,12 +89,6 @@ public struct Heap<T> {
     return nodes.first
   }
   
-  /** Returns the node at given index */
-  public func node(at i: Int) -> T? {
-    guard i < nodes.count else { return nil }
-    return nodes[i]
-  }
-  
   /**
    * Adds a new value to the heap. This reorders the heap so that the max-heap
    * or min-heap property still holds. Performance: O(log n).
@@ -121,7 +115,7 @@ public struct Heap<T> {
   public mutating func replace(index i: Int, value: T) {
     guard i < nodes.count else { return }
     
-    removeAt(i)
+    remove(at: i)
     insert(value)
   }
   
@@ -130,26 +124,25 @@ public struct Heap<T> {
    * value; for a min-heap it is the minimum value. Performance: O(log n).
    */
   @discardableResult public mutating func remove() -> T? {
-    if !nodes.isEmpty {
-      if nodes.count == 1 {
-        return nodes.removeLast()
-      } else {
-        // Use the last node to replace the first one, then fix the heap by
-        // shifting this new first node into its proper position.
-        let value = nodes[0]
-        nodes[0] = nodes.removeLast()
-        shiftDown(0)
-        return value
-      }
+    guard !nodes.isEmpty else { return nil }
+    
+    if nodes.count == 1 {
+      return nodes.removeLast()
+    } else {
+      // Use the last node to replace the first one, then fix the heap by
+      // shifting this new first node into its proper position.
+      let value = nodes[0]
+      nodes[0] = nodes.removeLast()
+      shiftDown(0)
+      return value
     }
-    return nil
   }
   
   /**
    * Removes an arbitrary node from the heap. Performance: O(log n).
    * Note that you need to know the node's index.
    */
-  @discardableResult public mutating func removeAt(_ index: Int) -> T? {
+  @discardableResult public mutating func remove(at index: Int) -> T? {
     guard index < nodes.count else { return nil }
     
     let size = nodes.count - 1
@@ -165,7 +158,7 @@ public struct Heap<T> {
    * Takes a child node and looks at its parents; if a parent is not larger
    * (max-heap) or not smaller (min-heap) than the child, we exchange them.
    */
-  mutating func shiftUp(_ index: Int) {
+  internal mutating func shiftUp(_ index: Int) {
     var childIndex = index
     let child = nodes[childIndex]
     var parentIndex = self.parentIndex(ofIndex: childIndex)
@@ -183,7 +176,7 @@ public struct Heap<T> {
    * Looks at a parent node and makes sure it is still larger (max-heap) or
    * smaller (min-heap) than its childeren.
    */
-  private mutating func shiftDown(from index: Int, until endIndex: Int) {
+  internal mutating func shiftDown(from index: Int, until endIndex: Int) {
     let leftChildIndex = self.leftChildIndex(ofIndex: index)
     let rightChildIndex = leftChildIndex + 1
     
@@ -204,7 +197,7 @@ public struct Heap<T> {
     shiftDown(from: first, until: endIndex)
   }
   
-  private mutating func shiftDown(_ index: Int) {
+  internal mutating func shiftDown(_ index: Int) {
     shiftDown(from: index, until: nodes.count)
   }
   
@@ -222,7 +215,7 @@ extension Heap where T: Equatable {
   /** Removes the first occurrence of a node from the heap. Performance: O(n log n). */
   @discardableResult public mutating func remove(node: T) -> T? {
     if let index = index(of: node) {
-      return removeAt(index)
+      return remove(at: index)
     }
     return nil
   }
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index 36035fe93..1ed15c726 100755
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -154,14 +154,14 @@ class HeapTests: XCTestCase {
     XCTAssertEqual(h4.peek()!, 0)
   }
   
-  func testCreateMaxHeapEqualElements() {
+  func testCreateMaxHeapEqualnodes() {
     let heap = Heap(array: [1, 1, 1, 1, 1], sort: >)
     XCTAssertTrue(verifyMaxHeap(heap))
     XCTAssertTrue(verifyMinHeap(heap))
     XCTAssertEqual(heap.nodes, [1, 1, 1, 1, 1])
   }
   
-  func testCreateMinHeapEqualElements() {
+  func testCreateMinHeapEqualnodes() {
     let heap = Heap(array: [1, 1, 1, 1, 1], sort: <)
     XCTAssertTrue(verifyMinHeap(heap))
     XCTAssertTrue(verifyMaxHeap(heap))
@@ -198,33 +198,33 @@ class HeapTests: XCTestCase {
     }
   }
   
-  func testRemovingAtIndex() {
+  func testRemoving() {
     var h = Heap(array: [100, 50, 70, 10, 20, 60, 65], sort: >)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 60, 65])
     
     //test index out of bounds
-    let v = h.removeAt(10)
+    let v = h.remove(at: 10)
     XCTAssertEqual(v, nil)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 60, 65])
     
-    let v1 = h.removeAt(5)
+    let v1 = h.remove(at: 5)
     XCTAssertEqual(v1, 60)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [100, 50, 70, 10, 20, 65])
     
-    let v2 = h.removeAt(4)
+    let v2 = h.remove(at: 4)
     XCTAssertEqual(v2, 20)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [100, 65, 70, 10, 50])
     
-    let v3 = h.removeAt(4)
+    let v3 = h.remove(at: 4)
     XCTAssertEqual(v3, 50)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [100, 65, 70, 10])
     
-    let v4 = h.removeAt(0)
+    let v4 = h.remove(at: 0)
     XCTAssertEqual(v4, 100)
     XCTAssertTrue(verifyMaxHeap(h))
     XCTAssertEqual(h.nodes, [70, 65, 10])
@@ -267,17 +267,6 @@ class HeapTests: XCTestCase {
     XCTAssertEqual(h.nodes, [13, 12, 9, 5, 6, 8, 7, 4, 0, 1, 2])
   }
   
-  func testRemoveNode() {
-    var h = Heap(array: [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1], sort: >)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertEqual(h.nodes, [15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1])
-    XCTAssertEqual(h.node(at: 3)!, 5)
-    let v = h.remove(node: 5)
-    XCTAssertEqual(v, 5)
-    XCTAssertTrue(verifyMaxHeap(h))
-    XCTAssertFalse(h.nodes.contains(5))
-  }
-  
   func testRemoveRandomItems() {
     for n in 1...40 {
       var a = randomArray(n)
@@ -288,16 +277,8 @@ class HeapTests: XCTestCase {
       let m = (n + 1)/2
       for k in 1...m {
         let i = Int(arc4random_uniform(UInt32(n - k + 1)))
-        
-        var v: Int? = nil
-        if k == 2 || k == m {
-          v = h.remove(node: h.node(at: i)!)
-        } else {
-          v = h.removeAt(i)
-        }
-        XCTAssertNotNil(v)
-        
-        let j = a.index(of: v!)!
+        let v = h.remove(at: i)!
+        let j = a.index(of: v)!
         a.remove(at: j)
         
         XCTAssertTrue(verifyMaxHeap(h))

From 39b7311ec6fe68af0fb83b6322d7121a6d9c8f62 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 8 Jan 2018 17:47:10 -0800
Subject: [PATCH 325/643] Removes redundant `internal` modifier.

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

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index ae392d448..cf39fb8a5 100755
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -6,7 +6,7 @@
 public struct Heap<T> {
   
   /** The array that stores the heap's nodes. */
-  internal var nodes = [T]()
+  var nodes = [T]()
   
   /**
    * Determines how to compare two nodes in the heap.

From d4d471ba02dfcca3c58221a35159f650d15eb570 Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Wed, 10 Jan 2018 11:28:05 +0800
Subject: [PATCH 326/643] Update README.markdown

fix Code syntax error
---
 Binary Search Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 1d9321591..84e278f5c 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -268,7 +268,7 @@ If there are no more nodes to look at -- when `left` or `right` is nil -- then w
 Searching is a recursive process, but you can also implement it with a simple loop instead:
 
 ```swift
-  public func search(value: T) -> BinarySearchTree? {
+  public func search(_ value: T) -> BinarySearchTree? {
     var node: BinarySearchTree? = self
     while let n = node {
       if value < n.value {

From b36304c7ae0ae92dacf59f9d8c96f7fe7f4b5315 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Wed, 10 Jan 2018 22:18:14 -0800
Subject: [PATCH 327/643] add update to readme

---
 Red-Black Tree/README.markdown | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Red-Black Tree/README.markdown b/Red-Black Tree/README.markdown
index 74fffa415..6db827ea6 100644
--- a/Red-Black Tree/README.markdown	
+++ b/Red-Black Tree/README.markdown	
@@ -39,6 +39,9 @@ Tree:
 * `insert(key:)` Inserts the key value into the tree
 * `delete(key:)` Delete the node with the respective key value from the tree
 * `verify()` Verifies that the given tree fulfills the red-black tree properties
+* `count()` Returns how many nodes in the tree
+* `isEmpty()` Returns if the tree has no nodes
+* `allElements()` Returns an array containing all nodes (in-order traversal) in the tree.
 
 The rotation, insertion and deletion algorithms are implemented based on the pseudo-code provided in [CLRS]
 

From adf606599050c8eaf4b63a0c8e18a5b52a4892b7 Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Wed, 19 Jul 2017 15:47:40 -0700
Subject: [PATCH 328/643] Encode and Decode A Binary Tree

Encode and Decode A Binary Tree
---
 .../Contents.swift                            |  49 +++++++++
 .../Sources/EncodeAndDecodeTree.swift         | 104 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../EncodeAndDecodeTree.swift                 | 104 ++++++++++++++++++
 Encode and Decode Tree/readme.md              |  27 +++++
 .../contents.xcworkspacedata                  |  10 ++
 6 files changed, 298 insertions(+)
 create mode 100644 Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift
 create mode 100644 Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift
 create mode 100644 Encode and Decode Tree/EncodeAndDecodeTree.playground/contents.xcplayground
 create mode 100644 Encode and Decode Tree/EncodeAndDecodeTree.swift
 create mode 100644 Encode and Decode Tree/readme.md

diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift
new file mode 100644
index 000000000..dbd2fd180
--- /dev/null
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift	
@@ -0,0 +1,49 @@
+//: Playground - noun: a place where people can play
+
+
+func printTree(_ root: TreeNode?) {
+    guard let root = root else {
+        return
+    }
+
+    var pointer = root
+
+    let leftVal = root.left == nil ? "nil" : root.left!.val
+    let rightVal = root.right == nil ? "nil" : root.right!.val
+
+    print("val: \(root.val) left: \(leftVal) right: \(rightVal)")
+
+    printTree(root.left)
+    printTree(root.right)
+}
+
+let s = EncodeAndDecodeTree()
+
+let node1 = TreeNode("a")
+let node2 = TreeNode("b")
+let node3 = TreeNode("c")
+let node4 = TreeNode("d")
+let node5 = TreeNode("e")
+
+node1.left = node2
+node1.right = node3
+node3.left = node4
+node3.right = node5
+
+let encodeStr = s.encode(node1)
+print(encodeStr)
+// "a b # # c d # # e # #"
+
+
+let root = s.decode(encodeStr)
+print("Tree:")
+printTree(root)
+/*
+ Tree:
+ val: a left: b right: c
+ val: b left: nil right: nil
+ val: c left: d right: e
+ val: d left: nil right: nil
+ val: e left: nil right: nil
+ */
+
diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift
new file mode 100644
index 000000000..e9d22f8a9
--- /dev/null
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift	
@@ -0,0 +1,104 @@
+//
+//  EncodeAndDecodeTree.swift
+//  
+//
+//  Created by Kai Chen on 19/07/2017.
+//
+//
+
+import Foundation
+
+public class TreeNode {
+    public var val: String
+    public var left: TreeNode?
+    public var right: TreeNode?
+
+    public init(_ val: String, left: TreeNode? = nil, right: TreeNode? = nil) {
+        self.val = val
+        self.left = left
+        self.right = right
+    }
+}
+
+public class EncodeAndDecodeTree {
+    private var encodeStr = ""
+    private var ret: [String] = []
+
+    public init() {}
+
+    public func encode(_ root: TreeNode?) -> String {
+        encodeIt(root)
+
+        return encodeStr
+    }
+
+    public func decode(_ data: String) -> TreeNode? {
+        var s = data
+        while (s.contains(" ")) {
+            let index = s.index(of: " ")
+            let endIndex = s.index(before: index)
+            let element = s[s.startIndex...endIndex]
+            ret.append(element)
+            let range = ClosedRange(uncheckedBounds: (lower: s.startIndex, upper: index))
+            s.removeSubrange(range)
+        }
+
+        if ret.count == 0 {
+            return nil
+        }
+
+        var dep = 0
+        let root = decodeIt(&dep)
+
+        return root
+    }
+
+    private func getNode(_ element: String) -> TreeNode? {
+        if element == "#" {
+            return nil
+        }
+
+        return TreeNode(element)
+    }
+
+    private func decodeIt(_ dep: inout Int) -> TreeNode? {
+        guard let currentNode = getNode(ret[dep]) else {
+            return nil
+        }
+
+        dep += 1
+        let left = decodeIt(&dep)
+        dep += 1
+        let right = decodeIt(&dep)
+
+        currentNode.left = left
+        currentNode.right = right
+
+        return currentNode
+    }
+
+    private func encodeIt(_ root: TreeNode?) {
+        guard let root = root else {
+            encodeStr += "# "
+            return
+        }
+
+        encodeStr += root.val + " "
+        encodeIt(root.left)
+        encodeIt(root.right)
+    }
+}
+
+extension String {
+    func index(of target: Character) -> String.Index {
+        var i = 0
+        for c in self.characters {
+            if c == target {
+                return self.index(self.startIndex, offsetBy: i)
+            }
+            i += 1
+        }
+
+        return self.endIndex
+    }
+}
diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.playground/contents.xcplayground b/Encode and Decode Tree/EncodeAndDecodeTree.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.swift b/Encode and Decode Tree/EncodeAndDecodeTree.swift
new file mode 100644
index 000000000..daa3c3ea2
--- /dev/null
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.swift	
@@ -0,0 +1,104 @@
+//
+//  EncodeAndDecodeTree.swift
+//
+//
+//  Created by Kai Chen on 19/07/2017.
+//
+//
+
+import Foundation
+
+public class TreeNode {
+    public var val: String
+    public var left: TreeNode?
+    public var right: TreeNode?
+
+    public init(_ val: String, left: TreeNode? = nil, right: TreeNode? = nil) {
+        self.val = val
+        self.left = left
+        self.right = right
+    }
+}
+
+public class EncodeAndDecodeTree {
+    private var encodeStr = ""
+    private var ret: [String] = []
+
+    public init() {}
+
+    public func encode(_ root: TreeNode?) -> String {
+        encodeIt(root)
+
+        return encodeStr
+    }
+
+    public func decode(_ data: String) -> TreeNode? {
+        var s = data
+        while (s.contains(" ")) {
+            let index = s.index(of: " ")
+            let endIndex = s.index(before: index)
+            let element = s[s.startIndex...endIndex]
+            ret.append(element)
+            let range = ClosedRange(uncheckedBounds: (lower: s.startIndex, upper: index))
+            s.removeSubrange(range)
+        }
+
+        if ret.count == 0 {
+            return nil
+        }
+
+        var dep = 0
+        let root = decodeIt(&dep)
+
+        return root
+    }
+
+    private func getNode(_ element: String) -> TreeNode? {
+        if element == "#" {
+            return nil
+        }
+
+        return TreeNode(element)
+    }
+
+    private func decodeIt(_ dep: inout Int) -> TreeNode? {
+        guard let currentNode = getNode(ret[dep]) else {
+            return nil
+        }
+
+        dep += 1
+        let left = decodeIt(&dep)
+        dep += 1
+        let right = decodeIt(&dep)
+
+        currentNode.left = left
+        currentNode.right = right
+
+        return currentNode
+    }
+
+    private func encodeIt(_ root: TreeNode?) {
+        guard let root = root else {
+            encodeStr += "# "
+            return
+        }
+
+        encodeStr += root.val + " "
+        encodeIt(root.left)
+        encodeIt(root.right)
+    }
+}
+
+extension String {
+    func index(of target: Character) -> String.Index {
+        var i = 0
+        for c in self.characters {
+            if c == target {
+                return self.index(self.startIndex, offsetBy: i)
+            }
+            i += 1
+        }
+        
+        return self.endIndex
+    }
+}
diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
new file mode 100644
index 000000000..c986d9147
--- /dev/null
+++ b/Encode and Decode Tree/readme.md	
@@ -0,0 +1,27 @@
+# Encode and Decode Binary Tree
+
+We need to design an algorithm to encode and decode a binary tree. 
+* **Encode**: Convert a tree into a string that can be stored in the disk.
+* **Decode**: Given the encoded string, you need to convert it into a Tree.
+
+For example, you may serialize the following tree
+
+
+as "[1,2,3,null,null,4,5]", just the same as how LeetCode OJ serializes a binary tree. You do not necessarily need to follow this format, so please be creative and come up with different approaches yourself.
+Note: Do not use class member/global/static variables to store states. Your serialize and deserialize algorithms should be stateless.
+
+## Solution
+For example, given a tree like this
+>       a
+>      /  \\
+>
+>    b     c
+>
+>    ​      /  \\
+>    ​    d    e
+
+We can use inorder traversal to convert the tree into the string like this `a b # # c d # # e # #`
+
+So, the idea is for the empty node, we use `#` to represent.
+
+For the decode process, we can still use inorder to convert the string back to a tree.
\ No newline at end of file
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 4cab8e2d4..77f124fc3 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -117,6 +117,16 @@
          location = "group:LRU Cache/Readme.md">
       </FileRef>
    </Group>
+   <Group
+      location = "container:"
+      name = "Encode and Decode Tree">
+      <FileRef
+         location = "group:Encode and Decode Tree/EncodeAndDecodeTree.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Encode and Decode Tree/EncodeAndDecodeTree.swift">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Miller-Rabin Primality Test"
       name = "Miller-Rabin Primality Test">

From f5c74b9aa9f34e7e57fc16059ee3076642abcdc9 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 16 Nov 2017 09:13:20 -0800
Subject: [PATCH 329/643] Refactor in progress

---
 Encode and Decode Tree/readme.md | 58 ++++++++++++++++++++++----------
 1 file changed, 40 insertions(+), 18 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index c986d9147..7f3e5538d 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -1,27 +1,49 @@
 # Encode and Decode Binary Tree
 
-We need to design an algorithm to encode and decode a binary tree. 
-* **Encode**: Convert a tree into a string that can be stored in the disk.
-* **Decode**: Given the encoded string, you need to convert it into a Tree.
+> **Note**: The prerequisite for this article is an understanding of how [binary trees](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Binary%20Tree) work.
 
-For example, you may serialize the following tree
+Trees are complex structures. Unlike linear collections such as arrays or linked lists, trees are *non-linear* and each element in a tree has positional information such as the *parent-child* relationship between nodes. When you want to send a tree structure to your backend, you need to send the data of each node, and a way to represent the parent-child relationship for each node.
 
+Your strategy in how you choose to represent this information is called your **encoding** strategy. The opposite of that - changing your encoded data back to its original form - is your **decoding** strategy. 
 
-as "[1,2,3,null,null,4,5]", just the same as how LeetCode OJ serializes a binary tree. You do not necessarily need to follow this format, so please be creative and come up with different approaches yourself.
-Note: Do not use class member/global/static variables to store states. Your serialize and deserialize algorithms should be stateless.
+There are many ways to encode a tree and decode a tree. The important thing to keep in mind is that encoding and decoding strategies are closely related. The way you choose to encode a tree directly affects how you might decode a tree. 
 
-## Solution
-For example, given a tree like this
->       a
->      /  \\
->
->    b     c
->
->    ​      /  \\
->    ​    d    e
+Encoding and decoding are synonyms to *serializing* and *deserializing* trees. 
 
-We can use inorder traversal to convert the tree into the string like this `a b # # c d # # e # #`
+As a reference, the following code represents the typical `Node` type of a binary tree:
 
-So, the idea is for the empty node, we use `#` to represent.
+```swift
+class BinaryNode<Element: Comparable> {
+  var data: Element
+  var leftChild: BinaryNode?
+  var rightChild: BinaryNode?
+
+  // ... (rest of the implementation)
+}
+```
+
+## Encoding
+
+As mentioned before, there are different ways to do encoding. For no particular reason, you'll opt for the following rules:
+
+1. The result of the encoding will be a `String` object.
+2. You'll encode using *pre-order* traversal.
+
+Here's an example of this operation in code:
+
+```swift
+extension BinaryNode {
+  var encodedString: String {
+    var str = ""
+    preOrderTraversal { str.append($0) }
+    return str
+  }
+  
+  func preOrderTraversal(visit: (T) -> ()) {
+    visit(data)
+    leftChild?.preOrderTraversal(visit: visit)
+    rightChild?.preOrderTraversal(visit: visit)
+  }
+}
+```
 
-For the decode process, we can still use inorder to convert the string back to a tree.
\ No newline at end of file

From b772141951fe32729c6976d9a082b5c2f3eef203 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 16 Nov 2017 10:06:14 -0800
Subject: [PATCH 330/643] More progress

---
 Encode and Decode Tree/readme.md | 77 ++++++++++++++++++++++++++++++--
 1 file changed, 73 insertions(+), 4 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index 7f3e5538d..3b2281224 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -33,17 +33,86 @@ Here's an example of this operation in code:
 
 ```swift
 extension BinaryNode {
+  // 1
+  private var splitter: String { return "," }
+  private var nilNode: String { return "nil" }
+  
+  // 2
   var encodedString: String {
     var str = ""
-    preOrderTraversal { str.append($0) }
+    preOrderTraversal { data in
+      if let data = data {
+        let string = String(describing: data)
+        str.append(string)
+      } else {
+        str.append(nilNode)
+      }
+      str.append(splitter)
+    }
     return str
   }
   
-  func preOrderTraversal(visit: (T) -> ()) {
+  // 3
+  func preOrderTraversal(visit: (T?) -> ()) {
     visit(data)
-    leftChild?.preOrderTraversal(visit: visit)
-    rightChild?.preOrderTraversal(visit: visit)
+    
+    if let leftChild = leftChild {
+      leftChild.preOrderTraversal(visit: visit)
+    } else {
+      visit(nil)
+    }
+    
+    if let rightChild = rightChild {
+      rightChild.preOrderTraversal(visit: visit)
+    } else {
+      visit(nil)
+    }
   }
 }
 ```
 
+Here's a high level overview of the above code:
+
+1. `splitter` is a way to distinguish the nodes in a string. To illustrate its importance, consider the following encoded string "banana". How did the tree structure look like before encoding? Without the `splitter`, you can't tell.
+
+2. `encodedString` is the result of the encoding process. Returns a string representation of the tree. For example: "ba,nana,nil" represents a tree with two nodes - "ba" and "nana" - in pre-order format.
+
+3. It is interesting to note that this pre-order traversal implementation also emits `nil` values in place of absent children.
+
+## Decoding
+
+Your decoding strategy is the exact opposite of your encoding strategy. You'll take an encoded string, and turn it back into your binary tree.
+
+Your encoding strategy followed the following rules:
+
+1. The result of the encoding will be a `String` object.
+2. You'll encode using *pre-order* traversal.
+
+The implementation also added a few important details:
+
+* node values are separated by `,` 
+* `nil` children are denoted by the `nil` string
+
+These details will shape your `decode` operation. Here's a possible implementation:
+
+```swift
+extension BinaryTree {
+  
+  static func decode<Element>(from string: String) -> BinaryNode<Element>? {
+    let array = string.split(separator: ",")
+    let deque: Deque<String> = array
+    return decode(from: deque)
+  }
+  
+  static func decode<Elements: RangeReplaceableCollection>(from deque: RangeReplaceableCollection) 
+    -> BinaryNode<Elements.Element>? {
+    
+  }
+}
+```
+
+
+
+
+
+

From 959aaafe2d16b9e82f830381c6856c396590c51f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 16 Nov 2017 10:22:28 -0800
Subject: [PATCH 331/643] More progress.

---
 Encode and Decode Tree/readme.md | 23 ++++++++++++++++++-----
 1 file changed, 18 insertions(+), 5 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index 3b2281224..506bfbe05 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -34,8 +34,8 @@ Here's an example of this operation in code:
 ```swift
 extension BinaryNode {
   // 1
-  private var splitter: String { return "," }
-  private var nilNode: String { return "nil" }
+  fileprivate var splitter: String { return "," }
+  fileprivate var nilNode: String { return "nil" }
   
   // 2
   var encodedString: String {
@@ -98,19 +98,32 @@ These details will shape your `decode` operation. Here's a possible implementati
 ```swift
 extension BinaryTree {
   
+  // 1
   static func decode<Element>(from string: String) -> BinaryNode<Element>? {
     let array = string.split(separator: ",")
-    let deque: Deque<String> = array
-    return decode(from: deque)
+    return decode(from: array)
   }
   
-  static func decode<Elements: RangeReplaceableCollection>(from deque: RangeReplaceableCollection) 
+  // 2
+  static func decode<Elements: Sequence>(from sequence: Sequence) 
     -> BinaryNode<Elements.Element>? {
     
+    guard let value = sequence.first else { return nil }
+    if value == nilNode {
+      return nil
+    } else {
+      let node = BinaryNode<Elements.Element>(value: value)
+      node.leftChild = decode(from: AnySequence<Elements.Element>(sequence.dropFirst()))
+      node.rightChild = decode(from: AnySequence<Elements.Element>(sequence.dropFirst()))
+    }    
   }
 }
 ```
 
+Here's a high level overview of the above code:
+
+1. Takes a `String`, and uses `split` to partition the contents of `string` into an array based on the `","` character. 
+2. Takes any `Sequence` type and recursively creates a binary tree based on the rules declared in the encoding operation.
 
 
 

From e1599029f885de746bb8b7626246d57f7bdbd664 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 18 Nov 2017 01:45:12 -0800
Subject: [PATCH 332/643] More progress

---
 Encode and Decode Tree/readme.md | 60 +++++++++++++++++---------------
 1 file changed, 31 insertions(+), 29 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index 506bfbe05..e0c38531c 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -34,8 +34,8 @@ Here's an example of this operation in code:
 ```swift
 extension BinaryNode {
   // 1
-  fileprivate var splitter: String { return "," }
-  fileprivate var nilNode: String { return "nil" }
+  fileprivate var separator: String { return "," }
+  fileprivate var nilNode: String { return "X" }
   
   // 2
   var encodedString: String {
@@ -47,25 +47,25 @@ extension BinaryNode {
       } else {
         str.append(nilNode)
       }
-      str.append(splitter)
+      str.append(separator)
     }
     return str
   }
   
   // 3
-  func preOrderTraversal(visit: (T?) -> ()) {
-    visit(data)
+  func preOrderTraversal(visit: (Element?) throws -> ()) rethrows {
+    try visit(data)
     
     if let leftChild = leftChild {
-      leftChild.preOrderTraversal(visit: visit)
+      try leftChild.preOrderTraversal(visit: visit)
     } else {
-      visit(nil)
+      try visit(nil)
     }
     
     if let rightChild = rightChild {
-      rightChild.preOrderTraversal(visit: visit)
+      try rightChild.preOrderTraversal(visit: visit)
     } else {
-      visit(nil)
+      try visit(nil)
     }
   }
 }
@@ -73,7 +73,7 @@ extension BinaryNode {
 
 Here's a high level overview of the above code:
 
-1. `splitter` is a way to distinguish the nodes in a string. To illustrate its importance, consider the following encoded string "banana". How did the tree structure look like before encoding? Without the `splitter`, you can't tell.
+1. `separator` is a way to distinguish the nodes in a string. To illustrate its importance, consider the following encoded string "banana". How did the tree structure look like before encoding? Without the `separator`, you can't tell.
 
 2. `encodedString` is the result of the encoding process. Returns a string representation of the tree. For example: "ba,nana,nil" represents a tree with two nodes - "ba" and "nana" - in pre-order format.
 
@@ -96,34 +96,36 @@ The implementation also added a few important details:
 These details will shape your `decode` operation. Here's a possible implementation:
 
 ```swift
-extension BinaryTree {
-  
+extension BinaryNode {
+
   // 1
-  static func decode<Element>(from string: String) -> BinaryNode<Element>? {
-    let array = string.split(separator: ",")
-    return decode(from: array)
+  public static func decode(from str: String) -> AVLNode<String>? {
+    let components = encoded.lazy.split(separator: separator).reversed().map(String.init)
+    return decode(from: components)
   }
-  
-  // 2
-  static func decode<Elements: Sequence>(from sequence: Sequence) 
-    -> BinaryNode<Elements.Element>? {
+
+  public static func decode(from array: inout [String])
+    -> AVLNode<String>? {
     
-    guard let value = sequence.first else { return nil }
-    if value == nilNode {
-      return nil
-    } else {
-      let node = BinaryNode<Elements.Element>(value: value)
-      node.leftChild = decode(from: AnySequence<Elements.Element>(sequence.dropFirst()))
-      node.rightChild = decode(from: AnySequence<Elements.Element>(sequence.dropFirst()))
-    }    
+      guard !array.isEmpty else { return nil }
+      let value = array.removeLast()
+      guard value != "\(nilNode)" else { return nil }
+      
+      let node = AVLNode<String>(value: value)
+      node.leftChild = decode(from: &array)
+      node.rightChild = decode(from: &array)
+      return node
   }
 }
 ```
 
 Here's a high level overview of the above code:
 
-1. Takes a `String`, and uses `split` to partition the contents of `string` into an array based on the `","` character. 
-2. Takes any `Sequence` type and recursively creates a binary tree based on the rules declared in the encoding operation.
+1. Takes a `String`, and uses `split` to partition the contents of `string` into an array based on the `separator` defined in the encoding step. The result is first `reversed`, and then mapped to a `String`. The `reverse` step is an optimization for the next function, allowing us to use `array.removeLast()` instead of `array.removeFirst()`.
+
+2. Using an array as a stack, you recursively decode each node. The array keeps track of sequence of nodes and progress.
+
+
 
 
 

From 8bc6ab70c45d36d55466046d613509f64ca8ee59 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 18 Nov 2017 01:51:20 -0800
Subject: [PATCH 333/643] Added example case.

---
 Encode and Decode Tree/readme.md | 42 ++++++++++++++++++++++++++++++--
 1 file changed, 40 insertions(+), 2 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index e0c38531c..d7dd89424 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -125,9 +125,47 @@ Here's a high level overview of the above code:
 
 2. Using an array as a stack, you recursively decode each node. The array keeps track of sequence of nodes and progress.
 
+Here's an example output of a tree undergoing the encoding and decoding process:
 
-
-
+```
+Original Tree
+
+  ┌──8423
+ ┌──8391
+ │ └──nil
+┌──7838
+│ │ ┌──4936
+│ └──3924
+│  └──2506
+830
+│ ┌──701
+└──202
+ └──169
+
+Encoded tree: 830,202,169,X,X,701,X,X,7838,3924,2506,X,X,4936,X,X,8391,X,8423,X,X,
+
+Decoded tree
+
+  ┌──8423
+ ┌──8391
+ │ └──nil
+┌──7838
+│ │ ┌──4936
+│ └──3924
+│  └──2506
+830
+│ ┌──701
+└──202
+ └──169
+ ```
+
+Notice the original tree and decoded tree are identical. 
+
+## Further Reading & References
+
+- [LeetCode](https://leetcode.com/problems/serialize-and-deserialize-binary-tree/description/)
+
+*Written for the Swift Algorithm Club by Kai Chen & Kelvin Lau*
 
 
 

From eeea2027fe024dcf7a553f6c3c3479e39942045f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 21 Nov 2017 22:32:03 -0800
Subject: [PATCH 334/643] Updates readme to reference new class to handle
 encoding and decoding operations

---
 Encode and Decode Tree/readme.md | 103 +++++++++++++++++++------------
 1 file changed, 65 insertions(+), 38 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index d7dd89424..d60075e63 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -13,7 +13,7 @@ Encoding and decoding are synonyms to *serializing* and *deserializing* trees.
 As a reference, the following code represents the typical `Node` type of a binary tree:
 
 ```swift
-class BinaryNode<Element: Comparable> {
+class BinaryNode<Element: Comparable & Encodable> {
   var data: Element
   var leftChild: BinaryNode?
   var rightChild: BinaryNode?
@@ -22,6 +22,24 @@ class BinaryNode<Element: Comparable> {
 }
 ```
 
+Your encoding and decoding methods will reside in the `BinaryNodeEncoder` and `BinaryNodeDecoder` classes:
+
+```swift
+class BinaryNodeCoder {
+ 
+  // transforms nodes into string representation
+  func encode<T>(_ node: BinaryNode<T>) throws -> String where T: Encodable {
+    
+  }
+  
+  // transforms string into `BinaryNode` representation
+  func decode<T>(_ node: BinaryNode<T>Type, from string: String) 
+    throws -> BinaryNode<T> where T: Decodable {
+  
+  }
+}
+```
+
 ## Encoding
 
 As mentioned before, there are different ways to do encoding. For no particular reason, you'll opt for the following rules:
@@ -32,27 +50,9 @@ As mentioned before, there are different ways to do encoding. For no particular
 Here's an example of this operation in code:
 
 ```swift
-extension BinaryNode {
-  // 1
-  fileprivate var separator: String { return "," }
-  fileprivate var nilNode: String { return "X" }
-  
-  // 2
-  var encodedString: String {
-    var str = ""
-    preOrderTraversal { data in
-      if let data = data {
-        let string = String(describing: data)
-        str.append(string)
-      } else {
-        str.append(nilNode)
-      }
-      str.append(separator)
-    }
-    return str
-  }
+fileprivate extension BinaryNode {
   
-  // 3
+  // 1
   func preOrderTraversal(visit: (Element?) throws -> ()) rethrows {
     try visit(data)
     
@@ -69,15 +69,41 @@ extension BinaryNode {
     }
   }
 }
+
+class BinaryNodeCoder {
+
+  // 2
+  private var separator: String { return "," }
+  
+  // 3
+  private var nilNode: String { return "X" }
+  
+  // 4
+  func encode<T: Encodable>(_ node: BinaryNode<T>) -> String {
+    var str = ""
+    node.preOrderTraversal { data in
+      if let data = data {
+        let string = String(describing: data)
+        str.append(string)
+      } else {
+        str.append(nilNode)
+      }
+      str.append(separator)
+    }
+    return str
+  }
+  
+  // ...
+}
 ```
 
 Here's a high level overview of the above code:
 
-1. `separator` is a way to distinguish the nodes in a string. To illustrate its importance, consider the following encoded string "banana". How did the tree structure look like before encoding? Without the `separator`, you can't tell.
+2. `separator` is a way to distinguish the nodes in a string. To illustrate its importance, consider the following encoded string "banana". How did the tree structure look like before encoding? Without the `separator`, you can't tell.
 
-2. `encodedString` is the result of the encoding process. Returns a string representation of the tree. For example: "ba,nana,nil" represents a tree with two nodes - "ba" and "nana" - in pre-order format.
+3. `nilNode` is used to identify empty children. This a necesssary piece of information to retain in order to rebuild the tree later.
 
-3. It is interesting to note that this pre-order traversal implementation also emits `nil` values in place of absent children.
+4. `encode` returns a `String` representation of the `BinaryNode`. For example: "ba,nana,nil" represents a tree with two nodes - "ba" and "nana" - in pre-order format.
 
 ## Decoding
 
@@ -96,28 +122,29 @@ The implementation also added a few important details:
 These details will shape your `decode` operation. Here's a possible implementation:
 
 ```swift
-extension BinaryNode {
 
+class BinaryNodeCoder {
+
+  // ...
+  
   // 1
-  public static func decode(from str: String) -> AVLNode<String>? {
+  func decode<T: Decodable>(_ string: String) -> BinaryNode<T>? {
     let components = encoded.lazy.split(separator: separator).reversed().map(String.init)
     return decode(from: components)
   }
-
-  public static func decode(from array: inout [String])
-    -> AVLNode<String>? {
+  
+  // 2
+  private func decode(from array: inout [String]) -> AVLNode<String>? {
+    guard !array.isEmpty else { return nil }
+    let value = array.removeLast()
+    guard value != "\(nilNode)" else { return nil }
     
-      guard !array.isEmpty else { return nil }
-      let value = array.removeLast()
-      guard value != "\(nilNode)" else { return nil }
-      
-      let node = AVLNode<String>(value: value)
-      node.leftChild = decode(from: &array)
-      node.rightChild = decode(from: &array)
-      return node
+    let node = AVLNode<String>(value: value)
+    node.leftChild = decode(from: &array)
+    node.rightChild = decode(from: &array)
+    return node
   }
 }
-```
 
 Here's a high level overview of the above code:
 

From 4187a9af9f6b316479562589fd78c7685b633f22 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 23 Nov 2017 01:54:56 -0800
Subject: [PATCH 335/643] Fixed some formatting.

---
 Encode and Decode Tree/readme.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index d60075e63..ce5b45aaf 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -33,7 +33,7 @@ class BinaryNodeCoder {
   }
   
   // transforms string into `BinaryNode` representation
-  func decode<T>(_ node: BinaryNode<T>Type, from string: String) 
+  func decode<T>(from string: String) 
     throws -> BinaryNode<T> where T: Decodable {
   
   }
@@ -145,6 +145,7 @@ class BinaryNodeCoder {
     return node
   }
 }
+```
 
 Here's a high level overview of the above code:
 

From 25e6a190af8d13ee4e72bd41087fe593d49eba0f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 23 Nov 2017 23:34:24 -0800
Subject: [PATCH 336/643] Removed mentions of Encodable and Decodable protocol.
 Fixed a typo.

---
 Encode and Decode Tree/readme.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Encode and Decode Tree/readme.md b/Encode and Decode Tree/readme.md
index ce5b45aaf..b60e0a504 100644
--- a/Encode and Decode Tree/readme.md	
+++ b/Encode and Decode Tree/readme.md	
@@ -13,7 +13,7 @@ Encoding and decoding are synonyms to *serializing* and *deserializing* trees.
 As a reference, the following code represents the typical `Node` type of a binary tree:
 
 ```swift
-class BinaryNode<Element: Comparable & Encodable> {
+class BinaryNode<Element: Comparable> {
   var data: Element
   var leftChild: BinaryNode?
   var rightChild: BinaryNode?
@@ -79,7 +79,7 @@ class BinaryNodeCoder {
   private var nilNode: String { return "X" }
   
   // 4
-  func encode<T: Encodable>(_ node: BinaryNode<T>) -> String {
+  func encode<T>(_ node: BinaryNode<T>) -> String {
     var str = ""
     node.preOrderTraversal { data in
       if let data = data {
@@ -128,13 +128,13 @@ class BinaryNodeCoder {
   // ...
   
   // 1
-  func decode<T: Decodable>(_ string: String) -> BinaryNode<T>? {
+  func decode<T>(_ string: String) -> BinaryNode<T>? {
     let components = encoded.lazy.split(separator: separator).reversed().map(String.init)
     return decode(from: components)
   }
   
   // 2
-  private func decode(from array: inout [String]) -> AVLNode<String>? {
+  private func decode(from array: inout [String]) -> BinaryNode<String>? {
     guard !array.isEmpty else { return nil }
     let value = array.removeLast()
     guard value != "\(nilNode)" else { return nil }

From 074dac29084d235f93edb68e58d2deb92ffc0bbf Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Sun, 14 Jan 2018 18:16:35 -0800
Subject: [PATCH 337/643] Address comments and update the code to sync up with
 readme

---
 .../Contents.swift                            |  21 ++-
 .../Sources/EncodeAndDecodeTree.swift         | 137 ++++++++----------
 .../EncodeAndDecodeTree.swift                 | 137 ++++++++----------
 3 files changed, 137 insertions(+), 158 deletions(-)

diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift
index dbd2fd180..44c2440d5 100644
--- a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift	
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Contents.swift	
@@ -1,13 +1,10 @@
 //: Playground - noun: a place where people can play
 
-
-func printTree(_ root: TreeNode?) {
+func printTree(_ root: BinaryNode<String>?) {
     guard let root = root else {
         return
     }
 
-    var pointer = root
-
     let leftVal = root.left == nil ? "nil" : root.left!.val
     let rightVal = root.right == nil ? "nil" : root.right!.val
 
@@ -17,25 +14,25 @@ func printTree(_ root: TreeNode?) {
     printTree(root.right)
 }
 
-let s = EncodeAndDecodeTree()
+let coder = BinaryNodeCoder<String>()
 
-let node1 = TreeNode("a")
-let node2 = TreeNode("b")
-let node3 = TreeNode("c")
-let node4 = TreeNode("d")
-let node5 = TreeNode("e")
+let node1 = BinaryNode("a")
+let node2 = BinaryNode("b")
+let node3 = BinaryNode("c")
+let node4 = BinaryNode("d")
+let node5 = BinaryNode("e")
 
 node1.left = node2
 node1.right = node3
 node3.left = node4
 node3.right = node5
 
-let encodeStr = s.encode(node1)
+let encodeStr = try coder.encode(node1)
 print(encodeStr)
 // "a b # # c d # # e # #"
 
 
-let root = s.decode(encodeStr)
+let root: BinaryNode<String> = coder.decode(from: encodeStr)!
 print("Tree:")
 printTree(root)
 /*
diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift
index e9d22f8a9..10bb277f5 100644
--- a/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift	
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.playground/Sources/EncodeAndDecodeTree.swift	
@@ -8,97 +8,88 @@
 
 import Foundation
 
-public class TreeNode {
-    public var val: String
-    public var left: TreeNode?
-    public var right: TreeNode?
-
-    public init(_ val: String, left: TreeNode? = nil, right: TreeNode? = nil) {
-        self.val = val
-        self.left = left
-        self.right = right
-    }
+protocol BinaryNodeEncoder {
+  func encode<T>(_ node: BinaryNode<T>?) throws -> String
 }
 
-public class EncodeAndDecodeTree {
-    private var encodeStr = ""
-    private var ret: [String] = []
+protocol BinaryNodeDecoder {
+  func decode<T>(from string: String) -> BinaryNode<T>?
+}
 
-    public init() {}
+public class BinaryNodeCoder<T: Comparable>: BinaryNodeEncoder, BinaryNodeDecoder {
 
-    public func encode(_ root: TreeNode?) -> String {
-        encodeIt(root)
+  // MARK: Private
 
-        return encodeStr
-    }
+  private let separator: Character = ","
+  private let nilNode = "X"
 
-    public func decode(_ data: String) -> TreeNode? {
-        var s = data
-        while (s.contains(" ")) {
-            let index = s.index(of: " ")
-            let endIndex = s.index(before: index)
-            let element = s[s.startIndex...endIndex]
-            ret.append(element)
-            let range = ClosedRange(uncheckedBounds: (lower: s.startIndex, upper: index))
-            s.removeSubrange(range)
-        }
-
-        if ret.count == 0 {
-            return nil
-        }
-
-        var dep = 0
-        let root = decodeIt(&dep)
-
-        return root
+  private func decode<T>(from array: inout [String]) -> BinaryNode<T>? {
+    guard !array.isEmpty else {
+      return nil
     }
 
-    private func getNode(_ element: String) -> TreeNode? {
-        if element == "#" {
-            return nil
-        }
+    let value = array.removeLast()
 
-        return TreeNode(element)
+    guard value != nilNode, let val = value as? T else {
+      return nil
     }
 
-    private func decodeIt(_ dep: inout Int) -> TreeNode? {
-        guard let currentNode = getNode(ret[dep]) else {
-            return nil
-        }
+    let node = BinaryNode<T>(val)
+    node.left = decode(from: &array)
+    node.right = decode(from: &array)
 
-        dep += 1
-        let left = decodeIt(&dep)
-        dep += 1
-        let right = decodeIt(&dep)
+    return node
+  }
 
-        currentNode.left = left
-        currentNode.right = right
+  // MARK: Public
 
-        return currentNode
+  public init() {}
+
+  public func encode<T>(_ node: BinaryNode<T>?) throws -> String {
+    var str = ""
+    node?.preOrderTraversal { data in
+      if let data = data {
+        let string = String(describing: data)
+        str.append(string)
+      } else {
+        str.append(nilNode)
+      }
+      str.append(separator)
     }
 
-    private func encodeIt(_ root: TreeNode?) {
-        guard let root = root else {
-            encodeStr += "# "
-            return
-        }
+    return str
+  }
 
-        encodeStr += root.val + " "
-        encodeIt(root.left)
-        encodeIt(root.right)
-    }
+  public func decode<T>(from string: String) -> BinaryNode<T>? {
+    var components = string.split(separator: separator).reversed().map(String.init)
+    return decode(from: &components)
+  }
 }
 
-extension String {
-    func index(of target: Character) -> String.Index {
-        var i = 0
-        for c in self.characters {
-            if c == target {
-                return self.index(self.startIndex, offsetBy: i)
-            }
-            i += 1
-        }
-
-        return self.endIndex
+public class BinaryNode<Element: Comparable> {
+  public var val: Element
+  public var left: BinaryNode?
+  public var right: BinaryNode?
+
+  public init(_ val: Element, left: BinaryNode? = nil, right: BinaryNode? = nil) {
+    self.val = val
+    self.left = left
+    self.right = right
+  }
+
+  public func preOrderTraversal(visit: (Element?) throws -> ()) rethrows {
+    try visit(val)
+
+    if let left = left {
+      try left.preOrderTraversal(visit: visit)
+    } else {
+      try visit(nil)
+    }
+
+    if let right = right {
+      try right.preOrderTraversal(visit: visit)
+    } else {
+      try visit(nil)
     }
+  }
 }
diff --git a/Encode and Decode Tree/EncodeAndDecodeTree.swift b/Encode and Decode Tree/EncodeAndDecodeTree.swift
index daa3c3ea2..6ec8a3046 100644
--- a/Encode and Decode Tree/EncodeAndDecodeTree.swift	
+++ b/Encode and Decode Tree/EncodeAndDecodeTree.swift	
@@ -8,97 +8,88 @@
 
 import Foundation
 
-public class TreeNode {
-    public var val: String
-    public var left: TreeNode?
-    public var right: TreeNode?
-
-    public init(_ val: String, left: TreeNode? = nil, right: TreeNode? = nil) {
-        self.val = val
-        self.left = left
-        self.right = right
-    }
+protocol BinaryNodeEncoder {
+  func encode<T>(_ node: BinaryNode<T>?) throws -> String
 }
 
-public class EncodeAndDecodeTree {
-    private var encodeStr = ""
-    private var ret: [String] = []
+protocol BinaryNodeDecoder {
+  func decode<T>(from string: String) -> BinaryNode<T>?
+}
 
-    public init() {}
+public class BinaryNodeCoder<T: Comparable>: BinaryNodeEncoder, BinaryNodeDecoder {
 
-    public func encode(_ root: TreeNode?) -> String {
-        encodeIt(root)
+  // MARK: Private
 
-        return encodeStr
-    }
+  private let separator: Character = ","
+  private let nilNode = "X"
 
-    public func decode(_ data: String) -> TreeNode? {
-        var s = data
-        while (s.contains(" ")) {
-            let index = s.index(of: " ")
-            let endIndex = s.index(before: index)
-            let element = s[s.startIndex...endIndex]
-            ret.append(element)
-            let range = ClosedRange(uncheckedBounds: (lower: s.startIndex, upper: index))
-            s.removeSubrange(range)
-        }
-
-        if ret.count == 0 {
-            return nil
-        }
-
-        var dep = 0
-        let root = decodeIt(&dep)
-
-        return root
+  private func decode<T>(from array: inout [String]) -> BinaryNode<T>? {
+    guard !array.isEmpty else {
+      return nil
     }
 
-    private func getNode(_ element: String) -> TreeNode? {
-        if element == "#" {
-            return nil
-        }
+    let value = array.removeLast()
 
-        return TreeNode(element)
+    guard value != nilNode, let val = value as? T else {
+      return nil
     }
 
-    private func decodeIt(_ dep: inout Int) -> TreeNode? {
-        guard let currentNode = getNode(ret[dep]) else {
-            return nil
-        }
+    let node = BinaryNode<T>(val)
+    node.left = decode(from: &array)
+    node.right = decode(from: &array)
 
-        dep += 1
-        let left = decodeIt(&dep)
-        dep += 1
-        let right = decodeIt(&dep)
+    return node
+  }
 
-        currentNode.left = left
-        currentNode.right = right
+  // MARK: Public
 
-        return currentNode
+  public init() {}
+
+  public func encode<T>(_ node: BinaryNode<T>?) throws -> String {
+    var str = ""
+    node?.preOrderTraversal { data in
+      if let data = data {
+        let string = String(describing: data)
+        str.append(string)
+      } else {
+        str.append(nilNode)
+      }
+      str.append(separator)
     }
 
-    private func encodeIt(_ root: TreeNode?) {
-        guard let root = root else {
-            encodeStr += "# "
-            return
-        }
+    return str
+  }
 
-        encodeStr += root.val + " "
-        encodeIt(root.left)
-        encodeIt(root.right)
-    }
+  public func decode<T>(from string: String) -> BinaryNode<T>? {
+    var components = string.split(separator: separator).reversed().map(String.init)
+    return decode(from: &components)
+  }
 }
 
-extension String {
-    func index(of target: Character) -> String.Index {
-        var i = 0
-        for c in self.characters {
-            if c == target {
-                return self.index(self.startIndex, offsetBy: i)
-            }
-            i += 1
-        }
-        
-        return self.endIndex
+public class BinaryNode<Element: Comparable> {
+  public var val: Element
+  public var left: BinaryNode?
+  public var right: BinaryNode?
+
+  public init(_ val: Element, left: BinaryNode? = nil, right: BinaryNode? = nil) {
+    self.val = val
+    self.left = left
+    self.right = right
+  }
+
+  public func preOrderTraversal(visit: (Element?) throws -> ()) rethrows {
+    try visit(val)
+
+    if let left = left {
+      try left.preOrderTraversal(visit: visit)
+    } else {
+      try visit(nil)
+    }
+
+    if let right = right {
+      try right.preOrderTraversal(visit: visit)
+    } else {
+      try visit(nil)
     }
+  }
 }

From 90ac6b3b8cc3b341bc3e691998dc02a2cfd9de18 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 22 Jan 2018 08:09:08 -0800
Subject: [PATCH 338/643] Updates link to new contribution

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

diff --git a/README.markdown b/README.markdown
index 7c9482d0c..6169b07b1 100644
--- a/README.markdown
+++ b/README.markdown
@@ -200,6 +200,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 - [Finding Palindromes](Palindromes/)
 - [Dining Philosophers](DiningPhilosophers/)
 - [Egg Drop Problem](Egg%20Drop%20Problem/)
+- [Encoding and Decoding Binary Tree](Encode%20and%20Decode%20Tree/)
 ## Learn more!
 
 For more information, check out these great books:

From 5ff583027979d8826d2a9328f84534a1e5712323 Mon Sep 17 00:00:00 2001
From: Chris <cconover@gmail.com>
Date: Fri, 26 Jan 2018 10:54:10 -0800
Subject: [PATCH 339/643] Fix typo: bottom-left -> bottom-right

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

diff --git a/Longest Common Subsequence/README.markdown b/Longest Common Subsequence/README.markdown
index 4cd2c2fcb..a62c562a6 100644
--- a/Longest Common Subsequence/README.markdown	
+++ b/Longest Common Subsequence/README.markdown	
@@ -99,7 +99,7 @@ And so on... this is how `lcsLength(_:)` fills in the entire matrix.
 
 ## Backtracking to find the actual subsequence
 
-So far we've calculated the length of every possible subsequence. The length of the longest subsequence is found in the bottom-left corner of matrix, at `matrix[n+1][m+1]`. In the above example it is 4, so the LCS consists of 4 characters.
+So far we've calculated the length of every possible subsequence. The length of the longest subsequence is found in the bottom-right corner of matrix, at `matrix[n+1][m+1]`. In the above example it is 4, so the LCS consists of 4 characters.
 
 Having the length of every combination of substrings makes it possible to determine *which* characters are part of the LCS itself by using a backtracking strategy.
 

From 157431e2a6f5615a70495c045d6f21a1f86d4f14 Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Sun, 28 Jan 2018 07:06:45 +0800
Subject: [PATCH 340/643] Update README.markdown

Find a kth smallest element should use a[k-1]
---
 Kth Largest Element/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Kth Largest Element/README.markdown b/Kth Largest Element/README.markdown
index aba2d9c29..f1721df96 100644
--- a/Kth Largest Element/README.markdown	
+++ b/Kth Largest Element/README.markdown	
@@ -40,7 +40,7 @@ Now, all we must do is take the value at index `a.count - k`:
 a[a.count - k] = a[8 - 4] = a[4] = 9
 ```
 
-Of course, if you were looking for the k-th *smallest* element, you'd use `a[k]`.
+Of course, if you were looking for the k-th *smallest* element, you'd use `a[k-1]`.
 
 ## A faster solution
 

From e14a46f35964c4d1c0d41a90fd7b1ddbda5ad0bd Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Mon, 29 Jan 2018 09:04:10 +0800
Subject: [PATCH 341/643] Update README.markdown

update the code in the article same as source code
---
 Kth Largest Element/README.markdown | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Kth Largest Element/README.markdown b/Kth Largest Element/README.markdown
index f1721df96..b23d22b74 100644
--- a/Kth Largest Element/README.markdown	
+++ b/Kth Largest Element/README.markdown	
@@ -84,29 +84,29 @@ The index of pivot `9` is 4, and that's exactly the *k* we're looking for. We're
 The following function implements these ideas:
 
 ```swift
-public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
+public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
   var a = array
 
-  func randomPivot<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> T {
+  func randomPivot<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int) -> T {
     let pivotIndex = random(min: low, max: high)
-    swap(&a, pivotIndex, high)
+    a.swapAt(pivotIndex, high)
     return a[high]
   }
 
-  func randomizedPartition<T: Comparable>(inout a: [T], _ low: Int, _ high: Int) -> Int {
+  func randomizedPartition<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int) -> Int {
     let pivot = randomPivot(&a, low, high)
     var i = low
     for j in low..<high {
       if a[j] <= pivot {
-        swap(&a, i, j)
+        a.swapAt(i, j)
         i += 1
       }
     }
-    swap(&a, i, high)
+    a.swapAt(i, high)
     return i
   }
 
-  func randomizedSelect<T: Comparable>(inout a: [T], _ low: Int, _ high: Int, _ k: Int) -> T {
+  func randomizedSelect<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int, _ k: Int) -> T {
     if low < high {
       let p = randomizedPartition(&a, low, high)
       if k == p {

From 2924b2dced521f2ccf3a0f276f3f58f57822f914 Mon Sep 17 00:00:00 2001
From: i303071 <adam.borbas@sap.com>
Date: Mon, 29 Jan 2018 11:04:29 +0100
Subject: [PATCH 342/643] HashTable CustomStringConvertible conformance in
 protocol

---
 .../Sources/HashTable.swift                   | 38 ++++++++++---------
 1 file changed, 20 insertions(+), 18 deletions(-)

diff --git a/Hash Table/HashTable.playground/Sources/HashTable.swift b/Hash Table/HashTable.playground/Sources/HashTable.swift
index 2383b8192..476a51174 100644
--- a/Hash Table/HashTable.playground/Sources/HashTable.swift	
+++ b/Hash Table/HashTable.playground/Sources/HashTable.swift	
@@ -30,7 +30,7 @@
  Insert:  O(1)     O(n)
  Delete:  O(1)     O(n)
  */
-public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
+public struct HashTable<Key: Hashable, Value> {
     private typealias Element = (key: Key, value: Value)
     private typealias Bucket = [Element]
     private var buckets: [Bucket]
@@ -41,23 +41,6 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
     /// A Boolean value that indicates whether the hash table is empty.
     public var isEmpty: Bool { return count == 0 }
 
-    /// A string that represents the contents of the hash table.
-    public var description: String {
-        let pairs = buckets.flatMap { b in b.map { e in "\(e.key) = \(e.value)" } }
-        return pairs.joined(separator: ", ")
-    }
-
-    /// A string that represents the contents of
-    /// the hash table, suitable for debugging.
-    public var debugDescription: String {
-        var str = ""
-        for (i, bucket) in buckets.enumerated() {
-            let pairs = bucket.map { e in "\(e.key) = \(e.value)" }
-            str += "bucket \(i): " + pairs.joined(separator: ", ") + "\n"
-        }
-        return str
-    }
-
     /**
      Create a hash table with the given capacity.
      */
@@ -151,3 +134,22 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         return abs(key.hashValue) % buckets.count
     }
 }
+
+extension HashTable: CustomStringConvertible {
+    /// A string that represents the contents of the hash table.
+    public var description: String {
+        let pairs = buckets.flatMap { b in b.map { e in "\(e.key) = \(e.value)" } }
+        return pairs.joined(separator: ", ")
+    }
+    
+    /// A string that represents the contents of
+    /// the hash table, suitable for debugging.
+    public var debugDescription: String {
+        var str = ""
+        for (i, bucket) in buckets.enumerated() {
+            let pairs = bucket.map { e in "\(e.key) = \(e.value)" }
+            str += "bucket \(i): " + pairs.joined(separator: ", ") + "\n"
+        }
+        return str
+    }
+}

From 5beb84acec563fefef04ce87683484e4359f5350 Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Wed, 31 Jan 2018 23:40:15 +0800
Subject: [PATCH 343/643] Update README.markdown

when k > n/2 ,  we just need random select a.count - k elements and remove them from the original array
---
 Selection Sampling/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Selection Sampling/README.markdown b/Selection Sampling/README.markdown
index ff80791e1..741f592f4 100644
--- a/Selection Sampling/README.markdown	
+++ b/Selection Sampling/README.markdown	
@@ -193,7 +193,7 @@ print(output.count)
 
 The performance of this second algorithm is **O(n)** as it may require a pass through the entire input array.
 
-> **Note:** If `k > n/2`, then it's more efficient to do it the other way around and choose `k` items to remove.
+> **Note:** If `k > n/2`, then it's more efficient to do it the other way around and choose `a.count - k` items to remove.
 
 Based on code from Algorithm Alley, Dr. Dobb's Magazine, October 1993.
 

From f34ccf2f6fb873bbf1b21fa39841534dbb5a04c4 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Wed, 7 Feb 2018 02:11:29 -0800
Subject: [PATCH 344/643] English Edit

---
 Introsort/README.markdown | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/Introsort/README.markdown b/Introsort/README.markdown
index c4ee6f804..376703cf7 100644
--- a/Introsort/README.markdown
+++ b/Introsort/README.markdown
@@ -6,7 +6,7 @@ IntroSort is the algorithm used by swift to sort a collection. Introsort is an h
 
 The number 20 is an empiric number obtained observing the behaviour of InsertionSort with lists of this size.
 
-Here's an implementation in Pseudocode:
+Here's an implementation in pseudocode:
 
 ```
 procedure sort(A : array):
@@ -32,9 +32,9 @@ Let's walk through the example. The array is initially:
 	[ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
 
 
-for this example let's assume that `maxDepth` is **2** and that the size of the partition for the insertionSort to kick in is **5**
+For this example let's assume that `maxDepth` is **2** and that the size of the partition for the insertionSort to kick in is **5**
 
-At the first iteration we run introSort on the full collection that counts 13 elements. the maxDepth is 2, therefore we fall in the else case where quicksort acts.
+The first iteration of introsort begins by attempting to use insertionSort. The collection has 13 elements, so it tries to do heapsort instead. The condition for heapsort to occur is if `maxdepth == 0` evaluates true. Since `maxdepth` is currently **2** for the first iteration, introsort will default to quicksort.
 
 The `partition`  method picks the first element, the median and the last, it sorts them and uses the new median as pivot.
 
@@ -106,5 +106,6 @@ The array is now successfully sorted
 
 [Introsort on Wikipedia](https://en.wikipedia.org/wiki/Introsort)
 [Introsort comparison with other sorting algorithms](http://agostini.tech/2017/12/18/swift-sorting-algorithm/)
+[Introsort implementation from the Swift standard library](https://github.com/apple/swift/blob/09f77ff58d250f5d62855ea359fc304f40b531df/stdlib/public/core/Sort.swift.gyb)
 
 *Written for Swift Algorithm Club by Giuseppe Lanza*

From b59cd5f6b28130146cd03384e926ac5c4ff2622d Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 23 Feb 2018 15:30:42 -0600
Subject: [PATCH 345/643] working on readme.. finally finishing this PR

---
 Genetic/README.markdown                      | 169 ++++++++++++++++++-
 Genetic/gen.playground/Contents.swift        |  91 ++++++++++
 Genetic/gen.playground/contents.xcplayground |   4 +
 Genetic/gen.swift                            |  38 +++--
 4 files changed, 282 insertions(+), 20 deletions(-)
 create mode 100644 Genetic/gen.playground/Contents.swift
 create mode 100644 Genetic/gen.playground/contents.xcplayground

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index 7cad649cb..fd208a19d 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -1,2 +1,167 @@
-# todo
-refactoring https://gist.github.com/blainerothrock/efda6e12fe10792c99c990f8ff3daeba for swift 4. Creating a tutorial and writing in more playground friendly format
+# Genetic Algorthim
+
+## What is it?
+
+A genetic algorithm (GA) is process inspired by natural selection to find high quality solutions. Most commonly used for optimization. GAs rely on the bio-inspired processes of natural selection, more specifically the process of selection (fitness), mutation and crossover. To understand more, let's walk through these process in terms of biology:
+
+### Selection
+>**Selection**, in biology, the preferential survival and reproduction or preferential elimination of individuals with certain genotypes (genetic compositions), by means of natural or artificial controlling factors. [Britannica](britannica)
+
+In other words, survival of the fittest. Organism that survive in their environment tend to reproduce more. With GAs we generate a fitness model that will rank offspring and give them a better chance for reproduction.
+
+### Mutation
+>**Mutation**, an alteration in the genetic material (the genome) of a cell of a living organism or of a virus that is more or less permanent and that can be transmitted to the cell’s or the virus’s descendants. [Britannica](https://www.britannica.com/science/mutation-genetics)
+
+The randomization that allows for organisms to change over time. In GAs we build a randomization process that will mutate offspring in a populate in order to randomly introduce fitness variance.
+
+### Crossover
+>**Chromosomal crossover** (or crossing over) is the exchange of genetic material between homologous chromosomes that results in recombinant chromosomes during sexual reproduction [Wikipedia](https://en.wikipedia.org/wiki/Chromosomal_crossover)
+
+Simply reproduction. A generation will a mixed representation of the previous generation, with offspring taking data (DNA) from both parents. GAs do this by randomly, but weightily, mating offspring to create new generations.
+
+### Resources:
+* [Wikipedia]()
+
+
+## The Code
+
+### Problem
+For this quick and dirty example, we are going to obtain a optimize string using a simple genetic algorithm. More specifically we are trying to take a randomly generated origin string of a fixed length and evolve it into the most optimized string of our choosing.
+
+We will be creating a bio-inspired world where the absolute existence is string `Hello, World!`. Nothing in this universe is better and it's our goal to get as close to it as possible.  
+
+### Define the Universe
+
+Before we dive into the core processes we need to set up our "universe". First let's define a lexicon, a set of everything that exists in our universe.
+
+```swift
+let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+```
+
+To make things easier, we are actually going to work in ASCII values, so let's define a String extension to help with that.
+
+```swift
+extension String {
+  var asciiArray: [UInt8] {
+    return [UInt8](self.utf8)
+  }
+}
+```
+
+ Now, let's define a few global variables for the universe:
+
+ ```swift
+// This is the end goal and what we will be using to rate fitness. In the real world this will not exist
+let OPTIMAL:[UInt8] = "Hello, World".asciiArray
+
+// The length of the string in our population. Organisms need to be similar
+let DNA_SIZE = OPTIMAL.count
+
+// size of each generation
+let POP_SIZE = 50
+
+// max number of generations, script will stop when it reach 5000 if the optimal value is not found
+let GENERATIONS = 5000
+
+// The chance in which a random nucleotide can mutate (1/n)
+let MUTATION_CHANCE = 100
+ ```
+
+ The last piece we need for set up is a function to give us a random ASCII value from our lexicon:
+
+ ```swift
+ func randomChar(from lexicon: [UInt8]) -> UInt8 {
+     let len = UInt32(lexicon.count-1)
+     let rand = Int(arc4random_uniform(len))
+     return lexicon[rand]
+ }
+ ```
+
+ ### Population Zero
+
+ Before selecting, mutating and reproduction, we need population to start with. Now that we have the universe defined we can write that function:
+
+ ```swift
+ func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
+
+    let len = UInt32(lexicon.count)
+
+    var pop = [[UInt8]]()
+
+    for _ in 0..<populationSize {
+        var dna = [UInt8]()
+        for _ in 0..<dnaSize {
+            let char = randomChar(from: lexicon)
+            dna.append(char)
+        }
+        pop.append(dna)
+    }
+    return pop
+}
+ ```
+
+### Selection
+
+There are two parts to the selection process, the first is calculating the fitness, which will assign a rating to a individual. We do this by simply calculating how close the individual is to the optimal string using ASCII values:
+
+```swift
+func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
+    var fitness = 0
+    for c in 0...dna.count-1 {
+        fitness += abs(Int(dna[c]) - Int(optimal[c]))
+    }
+    return fitness
+}
+```
+
+The above is a very simple fitness calculation, but it'll work for our example. In a real world problem, the optimal solution is unknown or impossible. [Here](https://iccl.inf.tu-dresden.de/w/images/b/b7/GA_for_TSP.pdf) is a paper about optimizing a solution for the famous [traveling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) using GA. In this example the problem is unsolvable by modern computers, but you can rate a individual solution by distance traveled. The optimal fitness here is an impossible 0. The closer the solution is to 0, the better chance for survival.
+
+The second part to selection is weighted choice, also called roulette wheel selection. This defines how individuals are selected for the reproduction process out of the current population. Just because you are the best choice for natural selection doesn't mean the environment will select you. The individual could fall off a cliff, get dysentery or not be able to reproduce.
+
+Let's take a second and ask why on this one. Why would you not always want to select the most fit from a population? It's hard to see from this simple example, but let's think about dog breeding, because breeders remove this process and hand select dogs for the next generation. As a result you get improved desired characteristics, but the individuals will also continue to carry genetic disorders that come along with those traits. This is essentially leading the evolution down a linear path. A certain "branch" of evolution may beat out the current fittest solution at a later time.
+
+ok, back to code. Here is our weighted choice function:
+
+```swift
+func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+
+    let total = items.reduce(0.0) { return $0 + $1.weight}
+
+    var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
+
+    for itemTuple in items {
+        if n < itemTuple.weight {
+            return itemTuple
+        }
+        n = n - itemTuple.weight
+    }
+    return items[1]
+}
+```
+
+The above function takes a list of individuals with their calculated fitness. Then selects one at random offset by their fitness value.
+
+## Mutation
+
+The all powerful mutation. The great randomization that turns bacteria into humans, just add time. So powerful yet so simple:
+
+```swift
+func mutate(dna:[UInt8], mutationChance:Int) -> [UInt8] {
+    var outputDna = dna
+
+    for i in 0..<dna.count {
+        let rand = Int(arc4random_uniform(UInt32(mutationChance)))
+        if rand == 1 {
+            outputDna[i] = randomChar()
+        }
+    }
+
+    return outputDna
+}
+```
+
+Takes a mutation chance and a individual and returns that individual with mutations, if any.
+
+This allows for a population to explore all the possibilities of it's building blocks and randomly stumble on a better solution. If there is too much mutation, the evolution process will get nowhere. If there is too little the populations will become too similar and never be able to branch out of a defect to meet their changing environment.
+
+## Crossover
diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
new file mode 100644
index 000000000..b84fd13e3
--- /dev/null
+++ b/Genetic/gen.playground/Contents.swift
@@ -0,0 +1,91 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+extension String {
+    var asciiArray: [UInt8] {
+        return [UInt8](self.utf8)
+    }
+}
+
+
+let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+
+// This is the end goal and what we will be using to rate fitness. In the real world this will not exist
+let OPTIMAL:[UInt8] = "Hello, World".asciiArray
+
+// The length of the string in our population. Organisms need to be similar
+let DNA_SIZE = OPTIMAL.count
+
+// size of each generation
+let POP_SIZE = 50
+
+// max number of generations, script will stop when it reach 5000 if the optimal value is not found
+let GENERATIONS = 5000
+
+// The chance in which a random nucleotide can mutate (1/n)
+let MUTATION_CHANCE = 100
+
+func randomChar(from lexicon: [UInt8]) -> UInt8 {
+    let len = UInt32(lexicon.count-1)
+    let rand = Int(arc4random_uniform(len))
+    return lexicon[rand]
+}
+
+func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
+    
+    let len = UInt32(lexicon.count)
+    
+    var pop = [[UInt8]]()
+    
+    for _ in 0..<populationSize {
+        var dna = [UInt8]()
+        for _ in 0..<dnaSize {
+            let char = randomChar(from: lexicon)
+            dna.append(char)
+        }
+        pop.append(dna)
+    }
+    return pop
+}
+
+randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+
+func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
+    
+    var fitness = 0
+    for c in 0...dna.count-1 {
+        fitness += abs(Int(dna[c]) - Int(optimal[c]))
+    }
+    return fitness
+}
+
+calculateFitness(dna: "Hillo, World".asciiArray, optimal: "Hello, World".asciiArray)
+
+func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+
+    let total = items.reduce(0.0) { return $0 + $1.weight}
+    
+    var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
+    
+    for itemTuple in items {
+        if n < itemTuple.weight {
+            return itemTuple
+        }
+        n = n - itemTuple.weight
+    }
+    return items[1]
+}
+
+func mutate(dna:[UInt8], mutationChance:Int) -> [UInt8] {
+    var outputDna = dna
+    
+    for i in 0..<dna.count {
+        let rand = Int(arc4random_uniform(UInt32(mutationChance)))
+        if rand == 1 {
+            outputDna[i] = randomChar()
+        }
+    }
+    
+    return outputDna
+}
diff --git a/Genetic/gen.playground/contents.xcplayground b/Genetic/gen.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Genetic/gen.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Genetic/gen.swift b/Genetic/gen.swift
index 72830b8a7..17df6d002 100644
--- a/Genetic/gen.swift
+++ b/Genetic/gen.swift
@@ -14,14 +14,16 @@ extension String {
     }
 }
 
+let lex = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".map {  }
+
 /*
     helper function to return a random character string
 */
 func randomChar() -> UInt8 {
-    
+
     let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
     let len = UInt32(letters.count-1)
-    
+
     let rand = Int(arc4random_uniform(len))
     return letters[rand]
 }
@@ -40,7 +42,7 @@ let MUTATION_CHANCE = 100
     optimal string comparsion = 0
 */
 func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
-    
+
     var fitness = 0
     for c in 0...dna.count-1 {
         fitness += abs(Int(dna[c]) - Int(optimal[c]))
@@ -53,7 +55,7 @@ func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
 */
 func mutate(dna:[UInt8], mutationChance:Int, dnaSize:Int) -> [UInt8] {
     var outputDna = dna
-    
+
     for i in 0..<dnaSize {
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
@@ -70,10 +72,10 @@ func mutate(dna:[UInt8], mutationChance:Int, dnaSize:Int) -> [UInt8] {
 */
 func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
     let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
-    
+
     let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
     let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
-    
+
     return (
         [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
         [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
@@ -85,12 +87,12 @@ func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[
 returns a random population, used to start the evolution
 */
 func randomPopulation(populationSize: Int, dnaSize: Int) -> [[UInt8]] {
-    
+
     let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
     let len = UInt32(letters.count)
 
     var pop = [[UInt8]]()
-    
+
     for _ in 0..<populationSize {
         var dna = [UInt8]()
         for _ in 0..<dnaSize {
@@ -112,7 +114,7 @@ func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], wei
     for itemTuple in items {
         weightTotal += itemTuple.weight;
     }
-    
+
     var n = Double(arc4random_uniform(UInt32(weightTotal * 1000000.0))) / 1000000.0
 
     for itemTuple in items {
@@ -133,36 +135,36 @@ func main() {
 
     for generation in 0...GENERATIONS {
         print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
-        
+
         var weightedPopulation = [(item:[UInt8], weight:Double)]()
-        
+
         // calulcated the fitness of each individual in the population
         // and add it to the weight population (weighted = 1.0/fitness)
         for individual in population {
             let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
-            
+
             let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
-            
+
             weightedPopulation.append(pair)
         }
-        
+
         population = []
-        
+
         // create a new generation using the individuals in the origional population
         for _ in 0...POP_SIZE/2 {
             let ind1 = weightedChoice(items: weightedPopulation)
             let ind2 = weightedChoice(items: weightedPopulation)
-            
+
             let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
 
             // append to the population and mutate
             population.append(mutate(dna: offspring.dna1, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
             population.append(mutate(dna: offspring.dna2, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
         }
-        
+
         fittest = population[0]
         var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
-        
+
         // parse the population for the fittest string
         for indv in population {
             let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)

From c6381646601bb162f650106c2e8ddcd4c9cb86f6 Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 23 Feb 2018 16:05:01 -0600
Subject: [PATCH 346/643] readme updates

---
 Genetic/README.markdown                       | 30 +++++++++++++++++--
 Genetic/gen.playground/Contents.swift         | 19 ++++++++++--
 .../contents.xcworkspacedata                  |  7 +++++
 3 files changed, 50 insertions(+), 6 deletions(-)
 create mode 100644 Genetic/gen.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index fd208a19d..6ebbf2cf7 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -114,7 +114,9 @@ func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
 }
 ```
 
-The above is a very simple fitness calculation, but it'll work for our example. In a real world problem, the optimal solution is unknown or impossible. [Here](https://iccl.inf.tu-dresden.de/w/images/b/b7/GA_for_TSP.pdf) is a paper about optimizing a solution for the famous [traveling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) using GA. In this example the problem is unsolvable by modern computers, but you can rate a individual solution by distance traveled. The optimal fitness here is an impossible 0. The closer the solution is to 0, the better chance for survival.
+The above will produce a fitness value to an individual. The perfect solution, "Hello, World" will have a fitness of 0. "Gello, World" will have a fitness of 1 since it is one ASCII value off from the optimal.
+
+This example is very, but it'll work for our example. In a real world problem, the optimal solution is unknown or impossible. [Here](https://iccl.inf.tu-dresden.de/w/images/b/b7/GA_for_TSP.pdf) is a paper about optimizing a solution for the famous [traveling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) using GA. In this example the problem is unsolvable by modern computers, but you can rate a individual solution by distance traveled. The optimal fitness here is an impossible 0. The closer the solution is to 0, the better chance for survival.
 
 The second part to selection is weighted choice, also called roulette wheel selection. This defines how individuals are selected for the reproduction process out of the current population. Just because you are the best choice for natural selection doesn't mean the environment will select you. The individual could fall off a cliff, get dysentery or not be able to reproduce.
 
@@ -146,13 +148,13 @@ The above function takes a list of individuals with their calculated fitness. Th
 The all powerful mutation. The great randomization that turns bacteria into humans, just add time. So powerful yet so simple:
 
 ```swift
-func mutate(dna:[UInt8], mutationChance:Int) -> [UInt8] {
+func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
 
     for i in 0..<dna.count {
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
-            outputDna[i] = randomChar()
+            outputDna[i] = randomChar(from: lexicon)
         }
     }
 
@@ -165,3 +167,25 @@ Takes a mutation chance and a individual and returns that individual with mutati
 This allows for a population to explore all the possibilities of it's building blocks and randomly stumble on a better solution. If there is too much mutation, the evolution process will get nowhere. If there is too little the populations will become too similar and never be able to branch out of a defect to meet their changing environment.
 
 ## Crossover
+
+Crossover, the sexy part of a GA, is how offspring are created from 2 selected individuals in the current population. This is done by splitting the parents into 2 parts, then combining 1 part from each parent to create the offspring. To promote diversity, we randomly select a index to split the parents:
+
+```swift
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+    let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
+
+    let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
+    let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
+
+    return (
+        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
+        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
+    )
+}
+```
+
+The above is used to generate a completely new generation based on the current generation.
+
+## Putting it all together -- Running the Genetic Algorithm
+
+We now have all the methods we need to kick off the process. What is missing a `main()` function that loops though each generation of the GA.
diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
index b84fd13e3..50d4c4fc8 100644
--- a/Genetic/gen.playground/Contents.swift
+++ b/Genetic/gen.playground/Contents.swift
@@ -60,7 +60,7 @@ func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
     return fitness
 }
 
-calculateFitness(dna: "Hillo, World".asciiArray, optimal: "Hello, World".asciiArray)
+calculateFitness(dna: "Gello, World".asciiArray, optimal: "Hello, World".asciiArray)
 
 func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
 
@@ -77,15 +77,28 @@ func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], wei
     return items[1]
 }
 
-func mutate(dna:[UInt8], mutationChance:Int) -> [UInt8] {
+func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
     
     for i in 0..<dna.count {
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
-            outputDna[i] = randomChar()
+            outputDna[i] = randomChar(from: lexicon)
         }
     }
     
     return outputDna
 }
+
+
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+    let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
+    
+    let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
+    let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
+    
+    return (
+        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
+        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
+    )
+}
diff --git a/Genetic/gen.playground/playground.xcworkspace/contents.xcworkspacedata b/Genetic/gen.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Genetic/gen.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

From 247c308a0ae5c4c18a89f5b58be5e770a673be22 Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Tue, 27 Feb 2018 20:51:41 +0900
Subject: [PATCH 347/643] :tada: Add Myers Difference Algorithm directory and
 playground

---
 .../MyersDifferenceAlgorithm.playground/Contents.swift     | 5 +++++
 .../contents.xcplayground                                  | 4 ++++
 .../timeline.xctimeline                                    | 6 ++++++
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata  | 7 +++++++
 4 files changed, 22 insertions(+)
 create mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift
 create mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/contents.xcplayground
 create mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline

diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift
new file mode 100644
index 000000000..c9a67424b
--- /dev/null
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift	
@@ -0,0 +1,5 @@
+//: Playground - noun: a place where people can play
+
+import UIKit
+
+var str = "Hello, playground"
diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/contents.xcplayground b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 142713e62..5d5bf1906 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -51,6 +51,13 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "group:Myers Difference Algorithm"
+      name = "Myers Difference Algorithm">
+      <FileRef
+         location = "group:MyersDifferenceAlgorithm.playground">
+      </FileRef>
+   </Group>
    <Group
       location = "container:"
       name = "3Sum and 4Sum">

From 574a19e22890585752b505f9905e2c2dbcd185b4 Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Tue, 27 Feb 2018 21:54:29 +0900
Subject: [PATCH 348/643] :sparkles: Add Myers Algorithm source code

---
 .../Contents.swift                            | 21 +++++-
 .../Sources/MyersDifferenceAlgorithm.swift    | 67 +++++++++++++++++++
 .../timeline.xctimeline                       |  6 --
 .../MyersDifferenceAlgorithm.swift            | 67 +++++++++++++++++++
 Myers Difference Algorithm/README.md          |  2 +
 .../contents.xcworkspacedata                  |  6 ++
 6 files changed, 161 insertions(+), 8 deletions(-)
 create mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Sources/MyersDifferenceAlgorithm.swift
 delete mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline
 create mode 100644 Myers Difference Algorithm/MyersDifferenceAlgorithm.swift
 create mode 100644 Myers Difference Algorithm/README.md

diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift
index c9a67424b..113487acc 100644
--- a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift	
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Contents.swift	
@@ -1,5 +1,22 @@
 //: Playground - noun: a place where people can play
+import Foundation
 
-import UIKit
+let shortestEditDistance: ([String], [String]) -> Int = MyersDifferenceAlgorithm.calculateShortestEditDistance(from:to:)
 
-var str = "Hello, playground"
+/***
+ All elements are same, so any scripts do not need.
+ So, the edit distance is 0
+ ***/
+shortestEditDistance(["1", "2", "3"], ["1", "2", "3"])
+
+/***
+ Last element "3" should be inserted.
+ So, the edit distance is 1
+ ***/
+shortestEditDistance(["1", "2"], ["1", "2", "3"])
+
+/***
+ First, remove "1", then insert "1" after "2".
+ So, the edit distance is 2
+***/
+shortestEditDistance(["1", "2", "3"], ["2", "1", "3"])
diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Sources/MyersDifferenceAlgorithm.swift b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Sources/MyersDifferenceAlgorithm.swift
new file mode 100644
index 000000000..aedbf3e71
--- /dev/null
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/Sources/MyersDifferenceAlgorithm.swift	
@@ -0,0 +1,67 @@
+//
+//  MyersDifferenceAlgorithm.swift
+//
+//  Created by Yuya Horita on 2018/02/27.
+//  Copyright © 2018年 hy. All rights reserved.
+//
+
+import Foundation
+
+public struct MyersDifferenceAlgorithm<E: Equatable> {
+    public static func calculateShortestEditDistance(from fromArray: Array<E>, to toArray: Array<E>) -> Int {
+        let fromCount = fromArray.count
+        let toCount = toArray.count
+        let totalCount = toCount + fromCount
+        var furthestReaching = Array(repeating: 0, count: 2 * totalCount + 1)
+        
+        let isReachedAtSink: (Int, Int) -> Bool = { x, y in
+            return x == fromCount && y == toCount
+        }
+        
+        let snake: (Int, Int, Int) -> Int = { x, D, k in
+            var _x = x
+            while _x < fromCount && _x - k < toCount && fromArray[_x] == toArray[_x - k] {
+                _x += 1
+            }
+            return _x
+        }
+        
+        for D in 0...totalCount {
+            for k in stride(from: -D, through: D, by: 2) {
+                let index = k + totalCount
+                
+                // (x, D, k) => the x position on the k_line where the number of scripts is D
+                // scripts means insertion or deletion
+                var x = 0
+                if D == 0 { }
+                    // k == -D, D will be the boundary k_line
+                    // when k == -D, moving right on the Edit Graph(is delete script) from k - 1_line where D - 1 is unavailable.
+                    // when k == D, moving bottom on the Edit Graph(is insert script) from k + 1_line where D - 1 is unavailable.
+                    // furthestReaching x position has higher calculating priority. (x, D - 1, k - 1), (x, D - 1, k + 1)
+                else if k == -D || k != D && furthestReaching[index - 1] < furthestReaching[index + 1] {
+                    // Getting initial x position
+                    // ,using the furthestReaching X position on the k + 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k + 1) + moving bottom + snake
+                    // this moving bottom on the edit graph is compatible with insert script
+                    x = furthestReaching[index + 1]
+                } else {
+                    // Getting initial x position
+                    // ,using the futrhest X position on the k - 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k - 1) + moving right + snake
+                    // this moving right on the edit graph is compatible with delete script
+                    x = furthestReaching[index - 1] + 1
+                }
+                
+                // snake
+                // diagonal moving can be performed with 0 cost.
+                // `same` script is needed ?
+                let _x = snake(x, D, k)
+                
+                if isReachedAtSink(_x, _x - k) { return D }
+                furthestReaching[index] = _x
+            }
+        }
+        
+        fatalError("Never comes here")
+    }
+}
diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline b/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Myers Difference Algorithm/MyersDifferenceAlgorithm.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift b/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift
new file mode 100644
index 000000000..aedbf3e71
--- /dev/null
+++ b/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift	
@@ -0,0 +1,67 @@
+//
+//  MyersDifferenceAlgorithm.swift
+//
+//  Created by Yuya Horita on 2018/02/27.
+//  Copyright © 2018年 hy. All rights reserved.
+//
+
+import Foundation
+
+public struct MyersDifferenceAlgorithm<E: Equatable> {
+    public static func calculateShortestEditDistance(from fromArray: Array<E>, to toArray: Array<E>) -> Int {
+        let fromCount = fromArray.count
+        let toCount = toArray.count
+        let totalCount = toCount + fromCount
+        var furthestReaching = Array(repeating: 0, count: 2 * totalCount + 1)
+        
+        let isReachedAtSink: (Int, Int) -> Bool = { x, y in
+            return x == fromCount && y == toCount
+        }
+        
+        let snake: (Int, Int, Int) -> Int = { x, D, k in
+            var _x = x
+            while _x < fromCount && _x - k < toCount && fromArray[_x] == toArray[_x - k] {
+                _x += 1
+            }
+            return _x
+        }
+        
+        for D in 0...totalCount {
+            for k in stride(from: -D, through: D, by: 2) {
+                let index = k + totalCount
+                
+                // (x, D, k) => the x position on the k_line where the number of scripts is D
+                // scripts means insertion or deletion
+                var x = 0
+                if D == 0 { }
+                    // k == -D, D will be the boundary k_line
+                    // when k == -D, moving right on the Edit Graph(is delete script) from k - 1_line where D - 1 is unavailable.
+                    // when k == D, moving bottom on the Edit Graph(is insert script) from k + 1_line where D - 1 is unavailable.
+                    // furthestReaching x position has higher calculating priority. (x, D - 1, k - 1), (x, D - 1, k + 1)
+                else if k == -D || k != D && furthestReaching[index - 1] < furthestReaching[index + 1] {
+                    // Getting initial x position
+                    // ,using the furthestReaching X position on the k + 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k + 1) + moving bottom + snake
+                    // this moving bottom on the edit graph is compatible with insert script
+                    x = furthestReaching[index + 1]
+                } else {
+                    // Getting initial x position
+                    // ,using the futrhest X position on the k - 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k - 1) + moving right + snake
+                    // this moving right on the edit graph is compatible with delete script
+                    x = furthestReaching[index - 1] + 1
+                }
+                
+                // snake
+                // diagonal moving can be performed with 0 cost.
+                // `same` script is needed ?
+                let _x = snake(x, D, k)
+                
+                if isReachedAtSink(_x, _x - k) { return D }
+                furthestReaching[index] = _x
+            }
+        }
+        
+        fatalError("Never comes here")
+    }
+}
diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
new file mode 100644
index 000000000..def447593
--- /dev/null
+++ b/Myers Difference Algorithm/README.md	
@@ -0,0 +1,2 @@
+#  Myers Difference Algorithm
+
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 5d5bf1906..5b8dd996f 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -54,9 +54,15 @@
    <Group
       location = "group:Myers Difference Algorithm"
       name = "Myers Difference Algorithm">
+      <FileRef
+         location = "group:/Users/a14757/Documents/Commiter/swift-algorithm-club/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift">
+      </FileRef>
       <FileRef
          location = "group:MyersDifferenceAlgorithm.playground">
       </FileRef>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
    </Group>
    <Group
       location = "container:"

From 4e61fa1287d9a1caf1adcc4eb9fa71c4d65ce505 Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Tue, 27 Feb 2018 22:11:02 +0900
Subject: [PATCH 349/643] :sparkles: EditGraph Images were added

---
 .../Images/EditGraph.png                       | Bin 0 -> 193070 bytes
 .../Images/EditGraph_k_move.png                | Bin 0 -> 206377 bytes
 .../contents.xcworkspacedata                   |   7 +++++++
 3 files changed, 7 insertions(+)
 create mode 100644 Myers Difference Algorithm/Images/EditGraph.png
 create mode 100644 Myers Difference Algorithm/Images/EditGraph_k_move.png

diff --git a/Myers Difference Algorithm/Images/EditGraph.png b/Myers Difference Algorithm/Images/EditGraph.png
new file mode 100644
index 0000000000000000000000000000000000000000..f31bb50a3e8614ed7a6da5eb363f21691ba469e4
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diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 5b8dd996f..ea6bdfa32 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -54,6 +54,13 @@
    <Group
       location = "group:Myers Difference Algorithm"
       name = "Myers Difference Algorithm">
+      <Group
+         location = "container:"
+         name = "Images">
+         <FileRef
+            location = "group:Myers Difference Algorithm/Images/EditGraph_k_move.png">
+         </FileRef>
+      </Group>
       <FileRef
          location = "group:/Users/a14757/Documents/Commiter/swift-algorithm-club/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift">
       </FileRef>

From be679572a9403d8c4c6fb8219b9f08dbda4f0f8c Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Wed, 28 Feb 2018 01:14:33 +0900
Subject: [PATCH 350/643] :pencil: README

---
 Myers Difference Algorithm/README.md          | 145 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   3 +
 2 files changed, 148 insertions(+)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index def447593..4e48a704f 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -1,2 +1,147 @@
 #  Myers Difference Algorithm
 
+Myers Difference Algorithm is the algorithm to find a longest common subsequence or shortest edit scripts (LCS/SES dual probrem) of two sequences by a simple O(ND) time, where N is the sum of the lengths of the two sequences. Common subsequence is the sequence of elements that appear in the same order in both sequences. Edit script will be discussed below.
+
+For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2", "3", "4"]`, `["2"], ["2", "3"]` are common sequences. Furthermore, the latter `["2", "3"]` is the longest common subsequence.  But `["1", "2"], ["3", "2"]` are not. Because, `["1", "2"]` contains `"1"` that is not included in `B`, `["3", 2]` has elements are included in both, but the appearing order is not correct.
+
+## Finding the length of the Longest Common Subsequence with Myers Algorithm on Edit Graph
+
+### Edit Graph
+
+Myers Algorithm uses Edit Graph for solving LCS/SES problem. Edit Graph is the graph like below.
+
+<img src='Images/EditGraph.png' height="250">
+
+Here, we think about the length of the LCS of sequences `X = [A, B, C, A, B, B, A]`, `Y = [C, B, A, B, A, C]`.
+
+In Myers Algorithm, edit graph are prepared by
+
+1. Line the element of sequence `X` on the x axis. And do for `Y` on the y axis.
+2. Make grid and vertex at each point in the grid (x, y), `x in [0, N] and y in [0, M]`. `N` is the length of sequence `X`, `M` is of `Y`
+3. Line for `x - y = k`, this line called k-line. Pink line is this.
+3. Check the points `(i, j)`, where `X[i] = Y[j]`, called match point.
+4. Connect vertex `(i - 1, j - 1)` and vertex `(i, j)`, then diagonal edge appears.
+
+> **Note:** Here, the sequences' start index is 1 not 0, so `X[1] = A`, `Y[1] = C`
+
+We discuss about which path is the shortest from `source` to `sink`. Can move on the edges on the graph. I mean we can move on  the grid, horizontal and vertical edges, and the diagonal edges.
+
+The movements are compatible with the `Edit Scripts`, insert or delete. The word `Edit Scripts` appeared here, as referred at Introduction SES is Shortest Edit Scripts.
+
+Let's get back on track. On this edit graph, the horizontal movement to vertex `(i, j)` is compatible with the script  `delete at index i from X`, the vertical movement to vertex `(i, j)` is compatible with the script `insert the element of Y at index j to immediately after the element of X at index i`. How about for the diagonal movement?. This movement to vertex `(i, j)` means `X[i] = Y[j]`, so no script needs.
+
+- horizontal movement -> delete
+- vertical movement -> insert
+- diagonal movement -> no script because both are same.
+
+Next, add cost 1 for non-diagonal movement, because they can be compatible with script. And 0 for diagonal movement, same means no script.
+
+The total cost for the minimum path, exploring from `source` to `sink`, is the same as the length of the Longest Common Subsequence or Shortest Edit Script.
+
+So, LSC/SES problem can be solved by finding the shortest path from `source` to `sink`.
+
+### Myers Algorithm
+
+As mentioned above, the problem of finding a shortest edit script can be reduced to finding a path from `source (0, 0)` to `sink (N, M)` with the fewest number of horizontal and vertical edges. Let `D-path` be a path starting at `source` that has exactly `D` non-diagonal edges, or must move non-diagonally D-times.
+
+For example, A 0-path consists solely of diagonal edges. This means both sequences are completely same.
+
+By a simple induction, D-path must consist of a (D-1)-path followed by a non-diagonal edge and then diagonal edges, which called `snake`. The minimum value of D is 0, both sequences being same. To the contrary, the maximum value of D is N + M because delete all elements from X and insert all elements from Y to X is the worst case edit scripts. For getting D, or the length of SES, running loop from 0 to N + M is enough.
+
+```swift
+for D in 0...N + M
+```
+
+Next, thinking about, where is the furthest reaching point for D-path on k-line. Like below, moving horizontally from k-line reaches (k+1)-line, moving vertically from k-line reaches (k-1)-line.
+
+<img src='Images/EditGraph_k_move.png' height="250">
+
+So, threre are several end points of D-path, or D-path can end on several k-line. We need the information to get the next path ((D+1)-path) as mentioned above. In fact, D-path must end on
+k-line, where k in { -D, -D + 2, ....., D - 2, D }. This is so simple, starting point, `source` is `(0, 0)` on (k=0)-line. D is the number of non-diagonal edges and non-diagonal movement changes current k-line to (kpm1)-line. Because 0 is even number, if D is even number D-path will end on (even_k)-line, if D is odd number D-path will end on (odd_k)-line.
+
+Searching loop outline will be below.
+
+```swift
+for D in 0...N + M {
+    for k in stride(from: -D, through: D, by: 2) {
+        //Find the end point of the furthest reaching D-path in k-line.
+        if furthestReachingX == N && furthestReachingY == M {
+            // The D-path is the shortest path
+            // D is the length of Shortest Edit Script
+            return
+        }
+    }
+}
+```
+
+The D-path on k-line can be decomposed into
+- a furthest reaching (D-1)-path on (k-1)-line, followed by a horizontal edge, followed by `snake`.
+- a furthest reaching (D-1)-path on (k+1)-line, followed by a vertical edge, followed by `snake`.
+as discussed above.
+
+The Myers Algorithm key point are these.
+- D-path must end on k-line, where k in { -D, -D + 2, ....., D - 2, D }
+- The D-path on k-line can be decomposed into two patterns
+
+thanks for these, the number of calculation become less.
+
+```swift
+public struct MyersDifferenceAlgorithm<E: Equatable> {
+    public static func calculateShortestEditDistance(from fromArray: Array<E>, to toArray: Array<E>) -> Int {
+        let fromCount = fromArray.count
+        let toCount = toArray.count
+        let totalCount = toCount + fromCount
+        var furthestReaching = Array(repeating: 0, count: 2 * totalCount + 1)
+
+        let isReachedAtSink: (Int, Int) -> Bool = { x, y in
+            return x == fromCount && y == toCount
+        }
+
+        let snake: (Int, Int, Int) -> Int = { x, D, k in
+            var _x = x
+            while _x < fromCount && _x - k < toCount && fromArray[_x] == toArray[_x - k] {
+                _x += 1
+            }
+            return _x
+        }
+
+        for D in 0...totalCount {
+            for k in stride(from: -D, through: D, by: 2) {
+                let index = k + totalCount
+            
+                // (x, D, k) => the x position on the k_line where the number of scripts is D
+                // scripts means insertion or deletion
+                var x = 0
+                if D == 0 { }
+                    // k == -D, D will be the boundary k_line
+                    // when k == -D, moving right on the Edit Graph(is delete script) from k - 1_line where D - 1 is unavailable.
+                    // when k == D, moving bottom on the Edit Graph(is insert script) from k + 1_line where D - 1 is unavailable.
+                    // furthestReaching x position has higher calculating priority. (x, D - 1, k - 1), (x, D - 1, k + 1)
+                else if k == -D || k != D && furthestReaching[index - 1] < furthestReaching[index + 1] {
+                    // Getting initial x position
+                    // ,using the furthestReaching X position on the k + 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k + 1) + moving bottom + snake
+                    // this moving bottom on the edit graph is compatible with insert script
+                    x = furthestReaching[index + 1]
+                } else {
+                    // Getting initial x position
+                    // ,using the futrhest X position on the k - 1_line where D - 1
+                    // ,meaning get (x, D, k) by (x, D - 1, k - 1) + moving right + snake
+                    // this moving right on the edit graph is compatible with delete script
+                    x = furthestReaching[index - 1] + 1
+                }
+                
+                // snake
+                // diagonal moving can be performed with 0 cost.
+                // `same` script is needed ?
+                let _x = snake(x, D, k)
+                
+                if isReachedAtSink(_x, _x - k) { return D }
+                furthestReaching[index] = _x
+            }
+        }
+
+        fatalError("Never comes here")
+    }
+}
+```
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index ea6bdfa32..724755669 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -60,6 +60,9 @@
          <FileRef
             location = "group:Myers Difference Algorithm/Images/EditGraph_k_move.png">
          </FileRef>
+         <FileRef
+            location = "group:Myers Difference Algorithm/Images/EditGraph.png">
+         </FileRef>
       </Group>
       <FileRef
          location = "group:/Users/a14757/Documents/Commiter/swift-algorithm-club/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift">

From b22d54af4185f54947cf143e2bf03359eb2263b8 Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Wed, 28 Feb 2018 01:36:54 +0900
Subject: [PATCH 351/643] :hammer: fix typo and description

---
 Myers Difference Algorithm/README.md | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index 4e48a704f..2f6c3c579 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -2,7 +2,7 @@
 
 Myers Difference Algorithm is the algorithm to find a longest common subsequence or shortest edit scripts (LCS/SES dual probrem) of two sequences by a simple O(ND) time, where N is the sum of the lengths of the two sequences. Common subsequence is the sequence of elements that appear in the same order in both sequences. Edit script will be discussed below.
 
-For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2", "3", "4"]`, `["2"], ["2", "3"]` are common sequences. Furthermore, the latter `["2", "3"]` is the longest common subsequence.  But `["1", "2"], ["3", "2"]` are not. Because, `["1", "2"]` contains `"1"` that is not included in `B`, `["3", 2]` has elements are included in both, but the appearing order is not correct.
+For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2", "3", "4"]`, `["2"], ["2", "3"]` are common sequences. Furthermore, the latter `["2", "3"]` is the longest common subsequence.  But `["1", "2"], ["3", "2"]` are not. Because, `["1", "2"]` contains `"1"` that is not included in `B`, `["3", "2"]` has elements are included in both, but the appearing order is not correct.
 
 ## Finding the length of the Longest Common Subsequence with Myers Algorithm on Edit Graph
 
@@ -10,7 +10,7 @@ For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2"
 
 Myers Algorithm uses Edit Graph for solving LCS/SES problem. Edit Graph is the graph like below.
 
-<img src='Images/EditGraph.png' height="250">
+<img src='Images/EditGraph.png' height="400">
 
 Here, we think about the length of the LCS of sequences `X = [A, B, C, A, B, B, A]`, `Y = [C, B, A, B, A, C]`.
 
@@ -18,15 +18,15 @@ In Myers Algorithm, edit graph are prepared by
 
 1. Line the element of sequence `X` on the x axis. And do for `Y` on the y axis.
 2. Make grid and vertex at each point in the grid (x, y), `x in [0, N] and y in [0, M]`. `N` is the length of sequence `X`, `M` is of `Y`
-3. Line for `x - y = k`, this line called k-line. Pink line is this.
-3. Check the points `(i, j)`, where `X[i] = Y[j]`, called match point.
-4. Connect vertex `(i - 1, j - 1)` and vertex `(i, j)`, then diagonal edge appears.
+3. Line for `x - y = k`, this line called k-line. Black dot line is this and pink number is the value of k.
+3. Check the points `(i, j)`, where `X[i] = Y[j]`, called match point, light green one.
+4. Connect vertex `(i - 1, j - 1)` and vertex `(i, j)`, where `(i, j)` is match point, then diagonal edge appears.
 
 > **Note:** Here, the sequences' start index is 1 not 0, so `X[1] = A`, `Y[1] = C`
 
 We discuss about which path is the shortest from `source` to `sink`. Can move on the edges on the graph. I mean we can move on  the grid, horizontal and vertical edges, and the diagonal edges.
 
-The movements are compatible with the `Edit Scripts`, insert or delete. The word `Edit Scripts` appeared here, as referred at Introduction SES is Shortest Edit Scripts.
+The movements are compatible with the `Edit Scripts`, insert or delete. The word `Edit Scripts` appeared here, as referred at Introduction, SES is Shortest Edit Scripts.
 
 Let's get back on track. On this edit graph, the horizontal movement to vertex `(i, j)` is compatible with the script  `delete at index i from X`, the vertical movement to vertex `(i, j)` is compatible with the script `insert the element of Y at index j to immediately after the element of X at index i`. How about for the diagonal movement?. This movement to vertex `(i, j)` means `X[i] = Y[j]`, so no script needs.
 
@@ -38,7 +38,7 @@ Next, add cost 1 for non-diagonal movement, because they can be compatible with
 
 The total cost for the minimum path, exploring from `source` to `sink`, is the same as the length of the Longest Common Subsequence or Shortest Edit Script.
 
-So, LSC/SES problem can be solved by finding the shortest path from `source` to `sink`.
+So, LCS/SES problem can be solved by finding the shortest path from `source` to `sink`.
 
 ### Myers Algorithm
 
@@ -52,9 +52,9 @@ By a simple induction, D-path must consist of a (D-1)-path followed by a non-dia
 for D in 0...N + M
 ```
 
-Next, thinking about, where is the furthest reaching point for D-path on k-line. Like below, moving horizontally from k-line reaches (k+1)-line, moving vertically from k-line reaches (k-1)-line.
+Next, thinking about, where is the furthest reaching point for D-path on k-line. Like below, moving horizontally from k-line reaches (k+1)-line, moving vertically from k-line reaches (k-1)-line. Red chalky line shows that.
 
-<img src='Images/EditGraph_k_move.png' height="250">
+<img src='Images/EditGraph_k_move.png' height="400">
 
 So, threre are several end points of D-path, or D-path can end on several k-line. We need the information to get the next path ((D+1)-path) as mentioned above. In fact, D-path must end on
 k-line, where k in { -D, -D + 2, ....., D - 2, D }. This is so simple, starting point, `source` is `(0, 0)` on (k=0)-line. D is the number of non-diagonal edges and non-diagonal movement changes current k-line to (kpm1)-line. Because 0 is even number, if D is even number D-path will end on (even_k)-line, if D is odd number D-path will end on (odd_k)-line.

From 81befa64507475361183cd52d29b14ce65da2e03 Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Mon, 5 Mar 2018 09:22:32 -0600
Subject: [PATCH 352/643] tutorial; weighted choice

---
 Genetic/README.markdown               |  49 +++++++-
 Genetic/gen.playground/Contents.swift |  52 +++++++++
 Genetic/gen.swift                     | 154 +++++++++++---------------
 3 files changed, 167 insertions(+), 88 deletions(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index 6ebbf2cf7..fdc6d5d92 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -188,4 +188,51 @@ The above is used to generate a completely new generation based on the current g
 
 ## Putting it all together -- Running the Genetic Algorithm
 
-We now have all the methods we need to kick off the process. What is missing a `main()` function that loops though each generation of the GA.
+We now have all the functions we need to kick off the algorthim. Let's start from the beginning, first we need a random population to serve as a starting point. We will also initialize a fittest variable to hold the fittest individual, we will initialize it with the first individual of our random population.
+
+```swift
+var population:[[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+var fittest = population[0]
+```
+
+Now for the meat, the remainder of the code will take place in the generation loop, running once for every generation:
+
+```swift
+for generation in 0...GENERATIONS {
+  // run
+}
+```
+
+Now, for each individual in the population, we need to calculate its fitness and weighted value. For weighted choice we store the fitness as a percent `1 / fitness`.
+
+```swift
+var weightedPopulation = [(item:[UInt8], weight:Double)]()
+
+for individual in population {
+  let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
+  let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
+  weightedPopulation.append(pair)
+}
+```
+
+To understand weighted choice, let walk though a smaller example, let's say we have the following population, where 0 is the best fitness:
+
+```txt
+1: 10
+2: 5
+3: 4
+4: 7
+5: 11
+```
+
+Now here is the weight of each:
+
+```txt
+1:
+2:
+3:
+4:
+5:
+
+total =
+```
diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
index 50d4c4fc8..4c67f8bd1 100644
--- a/Genetic/gen.playground/Contents.swift
+++ b/Genetic/gen.playground/Contents.swift
@@ -102,3 +102,55 @@ func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[
         [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
     )
 }
+
+func main() {
+    
+    // generate the starting random population
+    var population:[[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+    // print("population: \(population), dnaSize: \(DNA_SIZE) ")
+    var fittest = [UInt8]()
+    
+    for generation in 0...GENERATIONS {
+        print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
+        
+        var weightedPopulation = [(item:[UInt8], weight:Double)]()
+        
+        // calulcated the fitness of each individual in the population
+        // and add it to the weight population (weighted = 1.0/fitness)
+        for individual in population {
+            let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
+            
+            let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
+            
+            weightedPopulation.append(pair)
+        }
+        
+        population = []
+        
+        // create a new generation using the individuals in the origional population
+        for _ in 0...POP_SIZE/2 {
+            let ind1 = weightedChoice(items: weightedPopulation)
+            let ind2 = weightedChoice(items: weightedPopulation)
+            
+            let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+            
+            // append to the population and mutate
+            population.append(mutate(lexicon: lex, dna: offspring.dna1, mutationChance: MUTATION_CHANCE))
+            population.append(mutate(lexicon: lex, dna: offspring.dna2, mutationChance: MUTATION_CHANCE))
+        }
+        
+        fittest = population[0]
+        var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
+        
+        // parse the population for the fittest string
+        for indv in population {lex
+            let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
+            if indvFitness < minFitness {
+                fittest = indv
+                minFitness = indvFitness
+            }
+        }
+        if minFitness == 0 { break; }
+    }
+    print("fittest string: \(String(bytes: fittest, encoding: .ascii)!)")
+}
diff --git a/Genetic/gen.swift b/Genetic/gen.swift
index 17df6d002..f664fd5f7 100644
--- a/Genetic/gen.swift
+++ b/Genetic/gen.swift
@@ -1,46 +1,56 @@
-/*
-  base .. to be refactored
-*/
+//: Playground - noun: a place where people can play
 
 import Foundation
 
-// HELPERS
-/*
-    String extension to convert a string to ascii value
-*/
 extension String {
     var asciiArray: [UInt8] {
-        return unicodeScalars.filter{$0.isASCII}.map{UInt8($0.value)}
+        return [UInt8](self.utf8)
     }
 }
 
-let lex = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".map {  }
 
-/*
-    helper function to return a random character string
-*/
-func randomChar() -> UInt8 {
+let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
 
-    let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
-    let len = UInt32(letters.count-1)
+// This is the end goal and what we will be using to rate fitness. In the real world this will not exist
+let OPTIMAL:[UInt8] = "Hello, World".asciiArray
 
-    let rand = Int(arc4random_uniform(len))
-    return letters[rand]
-}
+// The length of the string in our population. Organisms need to be similar
+let DNA_SIZE = OPTIMAL.count
 
-// END HELPERS
+// size of each generation
+let POP_SIZE = 200
 
-let OPTIMAL:[UInt8] = "Hello, World".asciiArray
-let DNA_SIZE = OPTIMAL.count
-let POP_SIZE = 50
+// max number of generations, script will stop when it reach 5000 if the optimal value is not found
 let GENERATIONS = 5000
+
+// The chance in which a random nucleotide can mutate (1/n)
 let MUTATION_CHANCE = 100
 
-/*
-    calculated the fitness based on approximate string matching
-    compares each character ascii value difference and adds that to a total fitness
-    optimal string comparsion = 0
-*/
+func randomChar(from lexicon: [UInt8]) -> UInt8 {
+    let len = UInt32(lexicon.count-1)
+    let rand = Int(arc4random_uniform(len))
+    return lexicon[rand]
+}
+
+func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
+
+    let len = UInt32(lexicon.count)
+
+    var pop = [[UInt8]]()
+
+    for _ in 0..<populationSize {
+        var dna = [UInt8]()
+        for _ in 0..<dnaSize {
+            let char = randomChar(from: lexicon)
+            dna.append(char)
+        }
+        pop.append(dna)
+    }
+    return pop
+}
+
+randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+
 func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
 
     var fitness = 0
@@ -50,26 +60,37 @@ func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
     return fitness
 }
 
-/*
-    randomly mutate the string
-*/
-func mutate(dna:[UInt8], mutationChance:Int, dnaSize:Int) -> [UInt8] {
+calculateFitness(dna: "Gello, World".asciiArray, optimal: "Hello, World".asciiArray)
+
+func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+
+    let total = items.reduce(0.0) { return $0 + $1.weight}
+
+    var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
+
+    for itemTuple in items {
+        if n < itemTuple.weight {
+            return itemTuple
+        }
+        n = n - itemTuple.weight
+    }
+    return items[1]
+}
+
+func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
 
-    for i in 0..<dnaSize {
+    for i in 0..<dna.count {
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
-            outputDna[i] = randomChar()
+            outputDna[i] = randomChar(from: lexicon)
         }
     }
 
     return outputDna
 }
 
-/*
-    combine two parents to create an offspring
-    parent = xy & yx, offspring = xx, yy
-*/
+
 func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
     let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
 
@@ -82,59 +103,15 @@ func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[
     )
 }
 
-
-/*
-returns a random population, used to start the evolution
-*/
-func randomPopulation(populationSize: Int, dnaSize: Int) -> [[UInt8]] {
-
-    let letters : [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
-    let len = UInt32(letters.count)
-
-    var pop = [[UInt8]]()
-
-    for _ in 0..<populationSize {
-        var dna = [UInt8]()
-        for _ in 0..<dnaSize {
-            let rand = arc4random_uniform(len)
-            let nextChar = letters[Int(rand)]
-            dna.append(nextChar)
-        }
-        pop.append(dna)
-    }
-    return pop
-}
-
-
-/*
-function to return random canidate of a population randomally, but weight on fitness.
-*/
-func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
-    var weightTotal = 0.0
-    for itemTuple in items {
-        weightTotal += itemTuple.weight;
-    }
-
-    var n = Double(arc4random_uniform(UInt32(weightTotal * 1000000.0))) / 1000000.0
-
-    for itemTuple in items {
-        if n < itemTuple.weight {
-            return itemTuple
-        }
-        n = n - itemTuple.weight
-    }
-    return items[1]
-}
-
 func main() {
 
     // generate the starting random population
-    var population:[[UInt8]] = randomPopulation(populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+    var population:[[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
     // print("population: \(population), dnaSize: \(DNA_SIZE) ")
     var fittest = [UInt8]()
 
     for generation in 0...GENERATIONS {
-        print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
+        // print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
 
         var weightedPopulation = [(item:[UInt8], weight:Double)]()
 
@@ -143,7 +120,7 @@ func main() {
         for individual in population {
             let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
 
-            let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
+            let pair = ( individual, fitnessValue == 0 ? 1.0 : Double(100/POP_SIZE)/Double( fitnessValue ) )
 
             weightedPopulation.append(pair)
         }
@@ -158,15 +135,15 @@ func main() {
             let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
 
             // append to the population and mutate
-            population.append(mutate(dna: offspring.dna1, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
-            population.append(mutate(dna: offspring.dna2, mutationChance: MUTATION_CHANCE, dnaSize: DNA_SIZE))
+            population.append(mutate(lexicon: lex, dna: offspring.dna1, mutationChance: MUTATION_CHANCE))
+            population.append(mutate(lexicon: lex, dna: offspring.dna2, mutationChance: MUTATION_CHANCE))
         }
 
         fittest = population[0]
         var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
 
         // parse the population for the fittest string
-        for indv in population {
+        for indv in population {lex
             let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
             if indvFitness < minFitness {
                 fittest = indv
@@ -174,6 +151,9 @@ func main() {
             }
         }
         if minFitness == 0 { break; }
+        if generation % 1000 == 0 {
+          print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
+        }
     }
     print("fittest string: \(String(bytes: fittest, encoding: .ascii)!)")
 }

From 66f75d2c51b97f51259e8e6706433773e4a6e1af Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 9 Mar 2018 14:50:30 -0600
Subject: [PATCH 353/643] tutotial complete

---
 Genetic/README.markdown               | 143 +++++++++++++++++++++-----
 Genetic/gen.playground/Contents.swift |  25 ++---
 Genetic/gen.swift                     |  21 ++--
 3 files changed, 139 insertions(+), 50 deletions(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index fdc6d5d92..92f121daa 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -1,4 +1,4 @@
-# Genetic Algorthim
+individual# Genetic Algorthim
 
 ## What is it?
 
@@ -20,7 +20,9 @@ The randomization that allows for organisms to change over time. In GAs we build
 Simply reproduction. A generation will a mixed representation of the previous generation, with offspring taking data (DNA) from both parents. GAs do this by randomly, but weightily, mating offspring to create new generations.
 
 ### Resources:
-* [Wikipedia]()
+* [Genetic Algorithms in Search Optimization, and Machine Learning](https://www.amazon.com/Genetic-Algorithms-Optimization-Machine-Learning/dp/0201157675/ref=sr_1_sc_1?ie=UTF8&qid=1520628364&sr=8-1-spell&keywords=Genetic+Algortithms+in+search)
+* [Wikipedia](https://en.wikipedia.org/wiki/Genetic_algorithm)
+* [My Original Gist](https://gist.github.com/blainerothrock/efda6e12fe10792c99c990f8ff3daeba)
 
 
 ## The Code
@@ -141,7 +143,7 @@ func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], wei
 }
 ```
 
-The above function takes a list of individuals with their calculated fitness. Then selects one at random offset by their fitness value.
+The above function takes a list of individuals with their calculated fitness. Then selects one at random offset by their fitness value. The horrible 1,000,000 multiplication and division is to insure precision by calculating decimals. `arc4random` only uses integers so this is required to convert to a precise Double, it's not perfect, but enough for our example.
 
 ## Mutation
 
@@ -168,19 +170,16 @@ This allows for a population to explore all the possibilities of it's building b
 
 ## Crossover
 
-Crossover, the sexy part of a GA, is how offspring are created from 2 selected individuals in the current population. This is done by splitting the parents into 2 parts, then combining 1 part from each parent to create the offspring. To promote diversity, we randomly select a index to split the parents:
+Crossover, the sexy part of a GA, is how offspring are created from 2 selected individuals in the current population. This is done by splitting the parents into 2 parts, then combining 1 part from each parent to create the offspring. To promote diversity, we randomly select a index to split the parents.
 
 ```swift
-func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> [UInt8] {
     let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
 
     let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
     let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
 
-    return (
-        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
-        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
-    )
+    return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
 }
 ```
 
@@ -203,7 +202,7 @@ for generation in 0...GENERATIONS {
 }
 ```
 
-Now, for each individual in the population, we need to calculate its fitness and weighted value. For weighted choice we store the fitness as a percent `1 / fitness`.
+Now, for each individual in the population, we need to calculate its fitness and weighted value. Since 0 is the best value we will use `1/fitness` to represent the weighted value. Note this is not a percent, but just how much more likely the value is to be selected over others. If the highest number was the most fit, the weight calculation would be `fitness/totalFitness`, which would be a percent.
 
 ```swift
 var weightedPopulation = [(item:[UInt8], weight:Double)]()
@@ -215,24 +214,118 @@ for individual in population {
 }
 ```
 
-To understand weighted choice, let walk though a smaller example, let's say we have the following population, where 0 is the best fitness:
+From here we can start to build the next generation.
 
-```txt
-1: 10
-2: 5
-3: 4
-4: 7
-5: 11
+```swift
+var nextGeneration = []
+```
+
+The below loop is where we pull everything together. We loop for `POP_SIZE`, selecting 2 individuals by weighted choice, crossover their values to produce a offspring, then finial subject the new individual to mutation. Once completed we have a completely new generation based on the last generation.
+
+```swift
+0...POP_SIZE).forEach { _ in
+    let ind1 = weightedChoice(items: weightedPopulation)
+    let ind2 = weightedChoice(items: weightedPopulation)
+
+    let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+
+    // append to the population and mutate
+    nextGeneration.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
+}
+```
+
+The final piece to the main loop is to select the fittest individual of a population:
+
+```swift
+fittest = population[0]
+var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
+
+for indv in population {lex
+    let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
+    if indvFitness < minFitness {
+        fittest = indv
+        minFitness = indvFitness
+    }
+}
+if minFitness == 0 { break; }
+print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
 ```
 
-Now here is the weight of each:
+Since we know the fittest string, I've added a `break` to kill the program if we find it. At the end of a loop at a print statement for the fittest string:
 
-```txt
-1:
-2:
-3:
-4:
-5:
+```swift
+print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
+```
 
-total =
+Now we can run the program! Playgrounds are a nice place to develop, but are going to run this program **very slow**. I highly suggest running in Terminal: `swift gen.swift`. When running you should see something like this and it should not take too long to get `Hello, World`:
+
+```text
+0: RXclh F HDko
+1: DkyssjgElk];
+2: TiM4u) DrKvZ
+3: Dkysu) DrKvZ
+4: -kysu) DrKvZ
+5: Tlwsu) DrKvZ
+6: Tlwsu) Drd}k
+7: Tlwsu) Drd}k
+8: Tlwsu) Drd}k
+9: Tlwsu) Drd}k
+10: G^csu) |zd}k
+11: G^csu) |zdko
+12: G^csu) |zdko
+13: Dkysu) Drd}k
+14: G^wsu) `rd}k
+15: Dkysu) `rdko
+16: Dkysu) `rdko
+17: Glwsu) `rdko
+18: TXysu) `rdkc
+19: U^wsu) `rdko
+20: G^wsu) `rdko
+21: Glysu) `rdko
+22: G^ysu) `rdko
+23: G^ysu) `ryko
+24: G^wsu) `rdko
+25: G^wsu) `rdko
+26: G^wsu) `rdko
+...
+1408: Hello, Wormd
+1409: Hello, Wormd
+1410: Hello, Wormd
+1411: Hello, Wormd
+1412: Hello, Wormd
+1413: Hello, Wormd
+1414: Hello, Wormd
+1415: Hello, Wormd
+1416: Hello, Wormd
+1417: Hello, Wormd
+1418: Hello, Wormd
+1419: Hello, Wormd
+1420: Hello, Wormd
+1421: Hello, Wormd
+1422: Hello, Wormd
+1423: Hello, Wormd
+1424: Hello, Wormd
+1425: Hello, Wormd
+1426: Hello, Wormd
+1427: Hello, Wormd
+1428: Hello, Wormd
+1429: Hello, Wormd
+1430: Hello, Wormd
+1431: Hello, Wormd
+1432: Hello, Wormd
+1433: Hello, Wormd
+1434: Hello, Wormd
+1435: Hello, Wormd
+fittest string: Hello, World
 ```
+
+How long it takes will vary since this is based on randomization, but it should almost always finish in under 5000 generations. Woo!
+
+
+## Now What?
+
+We did it, we have a running simple genetic algorithm. Take some time a play around with the global variables, `POP_SIZE`, `OPTIMAL`, `MUTATION_CHANCE`, `GENERATIONS`. Just make sure to only add characters that are in the lexicon, but go ahead and update too!
+
+For an example let's try something much longer: `Ray Wenderlich's Swift Algorithm Club Rocks`. Plug that string into `OPTIMAL` and change `GENERATIONS` to `10000`. You'll be able to see that the we are getting somewhere, but you most likely will not reach the optimal string in 10,000 generations. Since we have a larger string let's raise our mutation chance to `200` (1/2 as likely to mutate). You may not get there, but you should get a lot closer than before. With a longer string, too much mutate can make it hard for fit strings to survive. Now try either upping `POP_SIZE` or increase `GENERATIONS`. Either way you should eventually get the value, but there will be a "sweet spot" for an individual of a certain size.
+
+Please submit any kind of update to this tutorial or add more examples!
diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
index 4c67f8bd1..8e1976ca6 100644
--- a/Genetic/gen.playground/Contents.swift
+++ b/Genetic/gen.playground/Contents.swift
@@ -63,7 +63,7 @@ func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
 calculateFitness(dna: "Gello, World".asciiArray, optimal: "Hello, World".asciiArray)
 
 func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
-
+    
     let total = items.reduce(0.0) { return $0 + $1.weight}
     
     var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
@@ -91,16 +91,13 @@ func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
 }
 
 
-func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> [UInt8] {
     let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
     
     let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
     let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
     
-    return (
-        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
-        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
-    )
+    return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
 }
 
 func main() {
@@ -111,7 +108,7 @@ func main() {
     var fittest = [UInt8]()
     
     for generation in 0...GENERATIONS {
-        print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
+        // print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
         
         var weightedPopulation = [(item:[UInt8], weight:Double)]()
         
@@ -120,7 +117,7 @@ func main() {
         for individual in population {
             let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
             
-            let pair = ( individual, fitnessValue == 0 ? 1.0 : 1.0/Double( fitnessValue ) )
+            let pair = ( individual, fitnessValue == 0 ? 1.0 : Double(100/POP_SIZE)/Double( fitnessValue ) )
             
             weightedPopulation.append(pair)
         }
@@ -128,15 +125,14 @@ func main() {
         population = []
         
         // create a new generation using the individuals in the origional population
-        for _ in 0...POP_SIZE/2 {
+        (0...POP_SIZE).forEach { _ in
             let ind1 = weightedChoice(items: weightedPopulation)
             let ind2 = weightedChoice(items: weightedPopulation)
             
             let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
             
             // append to the population and mutate
-            population.append(mutate(lexicon: lex, dna: offspring.dna1, mutationChance: MUTATION_CHANCE))
-            population.append(mutate(lexicon: lex, dna: offspring.dna2, mutationChance: MUTATION_CHANCE))
+            population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
         }
         
         fittest = population[0]
@@ -151,6 +147,11 @@ func main() {
             }
         }
         if minFitness == 0 { break; }
+        print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
+        
     }
-    print("fittest string: \(String(bytes: fittest, encoding: .ascii)!)")
+    print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
 }
+
+main()
+
diff --git a/Genetic/gen.swift b/Genetic/gen.swift
index f664fd5f7..a2a1b1410 100644
--- a/Genetic/gen.swift
+++ b/Genetic/gen.swift
@@ -18,7 +18,7 @@ let OPTIMAL:[UInt8] = "Hello, World".asciiArray
 let DNA_SIZE = OPTIMAL.count
 
 // size of each generation
-let POP_SIZE = 200
+let POP_SIZE = 50
 
 // max number of generations, script will stop when it reach 5000 if the optimal value is not found
 let GENERATIONS = 5000
@@ -91,16 +91,13 @@ func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
 }
 
 
-func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> (dna1:[UInt8], dna2:[UInt8]) {
+func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> [UInt8] {
     let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
 
     let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
     let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
 
-    return (
-        [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1)),
-        [UInt8](dna2.prefix(upTo: dna2Index1) + dna1.suffix(from: dna1Index1))
-    )
+    return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
 }
 
 func main() {
@@ -128,15 +125,14 @@ func main() {
         population = []
 
         // create a new generation using the individuals in the origional population
-        for _ in 0...POP_SIZE/2 {
+        (0...POP_SIZE).forEach { _ in
             let ind1 = weightedChoice(items: weightedPopulation)
             let ind2 = weightedChoice(items: weightedPopulation)
 
             let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
 
             // append to the population and mutate
-            population.append(mutate(lexicon: lex, dna: offspring.dna1, mutationChance: MUTATION_CHANCE))
-            population.append(mutate(lexicon: lex, dna: offspring.dna2, mutationChance: MUTATION_CHANCE))
+            population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
         }
 
         fittest = population[0]
@@ -151,11 +147,10 @@ func main() {
             }
         }
         if minFitness == 0 { break; }
-        if generation % 1000 == 0 {
-          print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
-        }
+        print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
+
     }
-    print("fittest string: \(String(bytes: fittest, encoding: .ascii)!)")
+    print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
 }
 
 main()

From ca6f0f0c71773a9117db63546b7c94b0c8de3a0e Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 9 Mar 2018 15:32:58 -0600
Subject: [PATCH 354/643] readme updates

---
 Genetic/README.markdown | 79 ++++++++++++++++++++---------------------
 1 file changed, 38 insertions(+), 41 deletions(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index 92f121daa..d6a474a10 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -2,35 +2,34 @@ individual# Genetic Algorthim
 
 ## What is it?
 
-A genetic algorithm (GA) is process inspired by natural selection to find high quality solutions. Most commonly used for optimization. GAs rely on the bio-inspired processes of natural selection, more specifically the process of selection (fitness), mutation and crossover. To understand more, let's walk through these process in terms of biology:
+A genetic algorithm (GA) is process inspired by natural selection to find high quality solutions. Most commonly used for optimization. GAs rely on the bio-inspired processes of natural selection, more specifically the process of selection (fitness), crossover and mutation. To understand more, let's walk through these processes in terms of biology:
 
 ### Selection
 >**Selection**, in biology, the preferential survival and reproduction or preferential elimination of individuals with certain genotypes (genetic compositions), by means of natural or artificial controlling factors. [Britannica](britannica)
 
-In other words, survival of the fittest. Organism that survive in their environment tend to reproduce more. With GAs we generate a fitness model that will rank offspring and give them a better chance for reproduction.
-
-### Mutation
->**Mutation**, an alteration in the genetic material (the genome) of a cell of a living organism or of a virus that is more or less permanent and that can be transmitted to the cell’s or the virus’s descendants. [Britannica](https://www.britannica.com/science/mutation-genetics)
-
-The randomization that allows for organisms to change over time. In GAs we build a randomization process that will mutate offspring in a populate in order to randomly introduce fitness variance.
+In other words, survival of the fittest. Organisms that survive in their environment tend to reproduce more. With GAs we generate a fitness model that will rank individuals and give them a better chance for reproduction.
 
 ### Crossover
 >**Chromosomal crossover** (or crossing over) is the exchange of genetic material between homologous chromosomes that results in recombinant chromosomes during sexual reproduction [Wikipedia](https://en.wikipedia.org/wiki/Chromosomal_crossover)
 
-Simply reproduction. A generation will a mixed representation of the previous generation, with offspring taking data (DNA) from both parents. GAs do this by randomly, but weightily, mating offspring to create new generations.
+Simply reproduction. A generation will be a mixed representation of the previous generation, with offspring taking DNA from both parents. GAs do this by randomly, but weightily, mating offspring to create new generations.
+
+### Mutation
+>**Mutation**, an alteration in the genetic material (the genome) of a cell of a living organism or of a virus that is more or less permanent and that can be transmitted to the cell’s or the virus’s descendants. [Britannica](https://www.britannica.com/science/mutation-genetics)
+
+The randomization that allows for organisms to change over time. In GAs we build a randomization process that will mutate offspring in a population in order to introduce fitness variance.
 
 ### Resources:
 * [Genetic Algorithms in Search Optimization, and Machine Learning](https://www.amazon.com/Genetic-Algorithms-Optimization-Machine-Learning/dp/0201157675/ref=sr_1_sc_1?ie=UTF8&qid=1520628364&sr=8-1-spell&keywords=Genetic+Algortithms+in+search)
 * [Wikipedia](https://en.wikipedia.org/wiki/Genetic_algorithm)
 * [My Original Gist](https://gist.github.com/blainerothrock/efda6e12fe10792c99c990f8ff3daeba)
 
-
 ## The Code
 
 ### Problem
-For this quick and dirty example, we are going to obtain a optimize string using a simple genetic algorithm. More specifically we are trying to take a randomly generated origin string of a fixed length and evolve it into the most optimized string of our choosing.
+For this quick and dirty example, we are going to produce an optimized string using a simple genetic algorithm. More specifically we are trying to take a randomly generated origin string of a fixed length and evolve it into the most optimized string of our choosing.
 
-We will be creating a bio-inspired world where the absolute existence is string `Hello, World!`. Nothing in this universe is better and it's our goal to get as close to it as possible.  
+We will be creating a bio-inspired world where the absolute existence is the string `Hello, World!`. Nothing in this universe is better and it's our goal to get as close to it as possible to ensure survival. 
 
 ### Define the Universe
 
@@ -40,36 +39,32 @@ Before we dive into the core processes we need to set up our "universe". First l
 let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
 ```
 
-To make things easier, we are actually going to work in ASCII values, so let's define a String extension to help with that.
+To make things easier, we are actually going to work in [Unicode values](https://en.wikipedia.org/wiki/List_of_Unicode_characters), so let's define a String extension to help with that.
 
 ```swift
 extension String {
-  var asciiArray: [UInt8] {
+  var unicodeArray: [UInt8] {
     return [UInt8](self.utf8)
   }
 }
 ```
 
  Now, let's define a few global variables for the universe:
+ * `OPTIMAL`: This is the end goal and what we will be using to rate fitness. In the real world this will not exist
+ * `DNA_SIZE`: The length of the string in our population. Organisms need to be similar
+ * `POP_SIZE`: Size of each generation
+ * `MAX_GENERATIONS`: Max number of generations, script will stop when it reach 5000 if the optimal value is not found
+ * `MUTATION_CHANCE`: The chance in which a random nucleotide can mutate (`1/MUTATION_CHANCE`)
 
  ```swift
-// This is the end goal and what we will be using to rate fitness. In the real world this will not exist
-let OPTIMAL:[UInt8] = "Hello, World".asciiArray
-
-// The length of the string in our population. Organisms need to be similar
+let OPTIMAL:[UInt8] = "Hello, World".unicodeArray
 let DNA_SIZE = OPTIMAL.count
-
-// size of each generation
 let POP_SIZE = 50
-
-// max number of generations, script will stop when it reach 5000 if the optimal value is not found
-let GENERATIONS = 5000
-
-// The chance in which a random nucleotide can mutate (1/n)
+let MAX_GENERATIONS = 5000
 let MUTATION_CHANCE = 100
  ```
 
- The last piece we need for set up is a function to give us a random ASCII value from our lexicon:
+ The last piece we need for set up is a function to give us a random unicode value from our lexicon:
 
  ```swift
  func randomChar(from lexicon: [UInt8]) -> UInt8 {
@@ -78,10 +73,12 @@ let MUTATION_CHANCE = 100
      return lexicon[rand]
  }
  ```
+ 
+ **Note**: `arc4random_uniform` is strickly used in this example. It would be fun to play around with some of the [randomization in GameKit](https://developer.apple.com/library/content/documentation/General/Conceptual/GameplayKit_Guide/RandomSources.html)
 
  ### Population Zero
 
- Before selecting, mutating and reproduction, we need population to start with. Now that we have the universe defined we can write that function:
+Before selecting, crossover and mutation, we need a population to start with. Now that we have the universe defined we can write that function:
 
  ```swift
  func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
@@ -90,9 +87,9 @@ let MUTATION_CHANCE = 100
 
     var pop = [[UInt8]]()
 
-    for _ in 0..<populationSize {
+    (0..<populationSize).forEach { _ in
         var dna = [UInt8]()
-        for _ in 0..<dnaSize {
+        (0..<dnaSize).forEach { _ in
             let char = randomChar(from: lexicon)
             dna.append(char)
         }
@@ -104,27 +101,27 @@ let MUTATION_CHANCE = 100
 
 ### Selection
 
-There are two parts to the selection process, the first is calculating the fitness, which will assign a rating to a individual. We do this by simply calculating how close the individual is to the optimal string using ASCII values:
+There are two parts to the selection process, the first is calculating the fitness, which will assign a rating to a individual. We do this by simply calculating how close the individual is to the optimal string using unicode values:
 
 ```swift
 func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
     var fitness = 0
-    for c in 0...dna.count-1 {
+    (0...dna.count-1).forEach { c in
         fitness += abs(Int(dna[c]) - Int(optimal[c]))
     }
     return fitness
 }
 ```
 
-The above will produce a fitness value to an individual. The perfect solution, "Hello, World" will have a fitness of 0. "Gello, World" will have a fitness of 1 since it is one ASCII value off from the optimal.
+The above will produce a fitness value to an individual. The perfect solution, "Hello, World" will have a fitness of 0. "Gello, World" will have a fitness of 1 since it is one unicode value off from the optimal (`H->G`).
 
-This example is very, but it'll work for our example. In a real world problem, the optimal solution is unknown or impossible. [Here](https://iccl.inf.tu-dresden.de/w/images/b/b7/GA_for_TSP.pdf) is a paper about optimizing a solution for the famous [traveling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) using GA. In this example the problem is unsolvable by modern computers, but you can rate a individual solution by distance traveled. The optimal fitness here is an impossible 0. The closer the solution is to 0, the better chance for survival.
+This example is very simple, but it'll work for our example. In a real world problem, the optimal solution is unknown or impossible. [Here](https://iccl.inf.tu-dresden.de/w/images/b/b7/GA_for_TSP.pdf) is a paper about optimizing a solution for the famous [traveling salesman problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) using a GA. In this example the problem is unsolvable by modern computers, but you can rate a individual solution by distance traveled. The optimal fitness here is an impossible 0. The closer the solution is to 0, the better chance for survival. In our example we will reach our goal, a fitness of 0.
 
-The second part to selection is weighted choice, also called roulette wheel selection. This defines how individuals are selected for the reproduction process out of the current population. Just because you are the best choice for natural selection doesn't mean the environment will select you. The individual could fall off a cliff, get dysentery or not be able to reproduce.
+The second part to selection is weighted choice, also called roulette wheel selection. This defines how individuals are selected for the reproduction process out of the current population. Just because you are the best choice for natural selection doesn't mean the environment will select you. The individual could fall off a cliff, get dysentery or be unable to reproduce.
 
-Let's take a second and ask why on this one. Why would you not always want to select the most fit from a population? It's hard to see from this simple example, but let's think about dog breeding, because breeders remove this process and hand select dogs for the next generation. As a result you get improved desired characteristics, but the individuals will also continue to carry genetic disorders that come along with those traits. This is essentially leading the evolution down a linear path. A certain "branch" of evolution may beat out the current fittest solution at a later time.
+Let's take a second and ask why on this one. Why would you not always want to select the most fit from a population? It's hard to see from this simple example, but let's think about dog breeding, because breeders remove this process and hand select dogs for the next generation. As a result you get improved desired characteristics, but the individuals will also continue to carry genetic disorders that come along with those traits. A certain "branch" of evolution may beat out the current fittest solution at a later time. This may be ok depending on the problem, but to keep this educational we will go with the bio-inspired way.
 
-ok, back to code. Here is our weighted choice function:
+With all that, here is our weight choice function:
 
 ```swift
 func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
@@ -147,13 +144,13 @@ The above function takes a list of individuals with their calculated fitness. Th
 
 ## Mutation
 
-The all powerful mutation. The great randomization that turns bacteria into humans, just add time. So powerful yet so simple:
+The all powerful mutation, the thing that introduces otherwise non exisitant fitness variance. It can either hurt of improve a individuals fitness but over time it will cause evolution towards more fit populations. Imagine if our initial random population was missing the charachter `H`, in that case we need to rely on mutation to introduce that character into the population in order to achive the optimal solution.
 
 ```swift
 func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
 
-    for i in 0..<dna.count {
+    (0..<dna.count).forEach { i in
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
             outputDna[i] = randomChar(from: lexicon)
@@ -202,7 +199,7 @@ for generation in 0...GENERATIONS {
 }
 ```
 
-Now, for each individual in the population, we need to calculate its fitness and weighted value. Since 0 is the best value we will use `1/fitness` to represent the weighted value. Note this is not a percent, but just how much more likely the value is to be selected over others. If the highest number was the most fit, the weight calculation would be `fitness/totalFitness`, which would be a percent.
+Now, for each individual in the population, we need to calculate its fitness and weighted value. Since 0 is the best value we will use `1/fitness` to represent the weight. Note this is not a percent, but just how much more likely the value is to be selected over others. If the highest number was the most fit, the weight calculation would be `fitness/totalFitness`, which would be a percent.
 
 ```swift
 var weightedPopulation = [(item:[UInt8], weight:Double)]()
@@ -251,7 +248,7 @@ if minFitness == 0 { break; }
 print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
 ```
 
-Since we know the fittest string, I've added a `break` to kill the program if we find it. At the end of a loop at a print statement for the fittest string:
+Since we know the fittest string, I've added a `break` to kill the program if we find it. At the end of a loop add a print statement for the fittest string:
 
 ```swift
 print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
@@ -324,8 +321,8 @@ How long it takes will vary since this is based on randomization, but it should
 
 ## Now What?
 
-We did it, we have a running simple genetic algorithm. Take some time a play around with the global variables, `POP_SIZE`, `OPTIMAL`, `MUTATION_CHANCE`, `GENERATIONS`. Just make sure to only add characters that are in the lexicon, but go ahead and update too!
+We did it, we have a running simple genetic algorithm. Take some time a play around with the global variables, `POP_SIZE`, `OPTIMAL`, `MUTATION_CHANCE`, `GENERATIONS`. Just make sure to only add characters that are in the lexicon or update the lexicon.
 
-For an example let's try something much longer: `Ray Wenderlich's Swift Algorithm Club Rocks`. Plug that string into `OPTIMAL` and change `GENERATIONS` to `10000`. You'll be able to see that the we are getting somewhere, but you most likely will not reach the optimal string in 10,000 generations. Since we have a larger string let's raise our mutation chance to `200` (1/2 as likely to mutate). You may not get there, but you should get a lot closer than before. With a longer string, too much mutate can make it hard for fit strings to survive. Now try either upping `POP_SIZE` or increase `GENERATIONS`. Either way you should eventually get the value, but there will be a "sweet spot" for an individual of a certain size.
+For an example let's try something much longer: `Ray Wenderlich's Swift Algorithm Club Rocks`. Plug that string into `OPTIMAL` and change `GENERATIONS` to `10000`. You'll be able to see that the we are getting somewhere, but you most likely will not reach the optimal string in 10,000 generations. Since we have a larger string let's raise our mutation chance to `200` (1/2 as likely to mutate). You may not get there, but you should get a lot closer than before. With a longer string, too much mutation can make it hard for fit strings to survive. Now try either upping `POP_SIZE` or increase `GENERATIONS`. Either way you should eventually get the value, but there will be a "sweet spot" for an string of a certain size.
 
 Please submit any kind of update to this tutorial or add more examples!

From 6c6b46b330d68698f1d7826276895ddcae82ed98 Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 9 Mar 2018 15:43:15 -0600
Subject: [PATCH 355/643] typos

---
 Genetic/README.markdown               | 30 +++++++-------
 Genetic/gen.playground/Contents.swift | 39 +++++++------------
 Genetic/gen.swift                     | 56 ++++++++++++---------------
 3 files changed, 53 insertions(+), 72 deletions(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index d6a474a10..07547c4b4 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -29,7 +29,7 @@ The randomization that allows for organisms to change over time. In GAs we build
 ### Problem
 For this quick and dirty example, we are going to produce an optimized string using a simple genetic algorithm. More specifically we are trying to take a randomly generated origin string of a fixed length and evolve it into the most optimized string of our choosing.
 
-We will be creating a bio-inspired world where the absolute existence is the string `Hello, World!`. Nothing in this universe is better and it's our goal to get as close to it as possible to ensure survival. 
+We will be creating a bio-inspired world where the absolute existence is the string `Hello, World!`. Nothing in this universe is better and it's our goal to get as close to it as possible to ensure survival.
 
 ### Define the Universe
 
@@ -73,8 +73,8 @@ let MUTATION_CHANCE = 100
      return lexicon[rand]
  }
  ```
- 
- **Note**: `arc4random_uniform` is strickly used in this example. It would be fun to play around with some of the [randomization in GameKit](https://developer.apple.com/library/content/documentation/General/Conceptual/GameplayKit_Guide/RandomSources.html)
+
+ **Note**: `arc4random_uniform` is strictly used in this example. It would be fun to play around with some of the [randomization in GameKit](https://developer.apple.com/library/content/documentation/General/Conceptual/GameplayKit_Guide/RandomSources.html)
 
  ### Population Zero
 
@@ -83,8 +83,6 @@ Before selecting, crossover and mutation, we need a population to start with. No
  ```swift
  func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
 
-    let len = UInt32(lexicon.count)
-
     var pop = [[UInt8]]()
 
     (0..<populationSize).forEach { _ in
@@ -96,7 +94,7 @@ Before selecting, crossover and mutation, we need a population to start with. No
         pop.append(dna)
     }
     return pop
-}
+ }
  ```
 
 ### Selection
@@ -124,17 +122,17 @@ Let's take a second and ask why on this one. Why would you not always want to se
 With all that, here is our weight choice function:
 
 ```swift
-func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weight:Double) {
 
     let total = items.reduce(0.0) { return $0 + $1.weight}
 
     var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
 
-    for itemTuple in items {
-        if n < itemTuple.weight {
-            return itemTuple
+    for item in items {
+        if n < item.weight {
+            return item
         }
-        n = n - itemTuple.weight
+        n = n - item.weight
     }
     return items[1]
 }
@@ -144,7 +142,7 @@ The above function takes a list of individuals with their calculated fitness. Th
 
 ## Mutation
 
-The all powerful mutation, the thing that introduces otherwise non exisitant fitness variance. It can either hurt of improve a individuals fitness but over time it will cause evolution towards more fit populations. Imagine if our initial random population was missing the charachter `H`, in that case we need to rely on mutation to introduce that character into the population in order to achive the optimal solution.
+The all powerful mutation, the thing that introduces otherwise non existent fitness variance. It can either hurt of improve a individuals fitness but over time it will cause evolution towards more fit populations. Imagine if our initial random population was missing the charachter `H`, in that case we need to rely on mutation to introduce that character into the population in order to achieve the optimal solution.
 
 ```swift
 func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
@@ -184,7 +182,7 @@ The above is used to generate a completely new generation based on the current g
 
 ## Putting it all together -- Running the Genetic Algorithm
 
-We now have all the functions we need to kick off the algorthim. Let's start from the beginning, first we need a random population to serve as a starting point. We will also initialize a fittest variable to hold the fittest individual, we will initialize it with the first individual of our random population.
+We now have all the functions we need to kick off the algorithm. Let's start from the beginning, first we need a random population to serve as a starting point. We will also initialize a fittest variable to hold the fittest individual, we will initialize it with the first individual of our random population.
 
 ```swift
 var population:[[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
@@ -202,7 +200,7 @@ for generation in 0...GENERATIONS {
 Now, for each individual in the population, we need to calculate its fitness and weighted value. Since 0 is the best value we will use `1/fitness` to represent the weight. Note this is not a percent, but just how much more likely the value is to be selected over others. If the highest number was the most fit, the weight calculation would be `fitness/totalFitness`, which would be a percent.
 
 ```swift
-var weightedPopulation = [(item:[UInt8], weight:Double)]()
+var weightedPopulation = [(dna:[UInt8], weight:Double)]()
 
 for individual in population {
   let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
@@ -224,7 +222,7 @@ The below loop is where we pull everything together. We loop for `POP_SIZE`, sel
     let ind1 = weightedChoice(items: weightedPopulation)
     let ind2 = weightedChoice(items: weightedPopulation)
 
-    let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+    let offspring = crossover(dna1: ind1.dna, dna2: ind2.dna, dnaSize: DNA_SIZE)
 
     // append to the population and mutate
     nextGeneration.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
@@ -237,7 +235,7 @@ The final piece to the main loop is to select the fittest individual of a popula
 fittest = population[0]
 var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
 
-for indv in population {lex
+population.forEach { indv in
     let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
     if indvFitness < minFitness {
         fittest = indv
diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
index 8e1976ca6..79a398ceb 100644
--- a/Genetic/gen.playground/Contents.swift
+++ b/Genetic/gen.playground/Contents.swift
@@ -3,16 +3,16 @@
 import Foundation
 
 extension String {
-    var asciiArray: [UInt8] {
+    var unicodeArray: [UInt8] {
         return [UInt8](self.utf8)
     }
 }
 
 
-let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".unicodeArray
 
 // This is the end goal and what we will be using to rate fitness. In the real world this will not exist
-let OPTIMAL:[UInt8] = "Hello, World".asciiArray
+let OPTIMAL:[UInt8] = "Hello, World".unicodeArray
 
 // The length of the string in our population. Organisms need to be similar
 let DNA_SIZE = OPTIMAL.count
@@ -34,13 +34,11 @@ func randomChar(from lexicon: [UInt8]) -> UInt8 {
 
 func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
     
-    let len = UInt32(lexicon.count)
-    
     var pop = [[UInt8]]()
     
-    for _ in 0..<populationSize {
+    (0..<populationSize).forEach { _ in
         var dna = [UInt8]()
-        for _ in 0..<dnaSize {
+        (0..<dnaSize).forEach { _ in
             let char = randomChar(from: lexicon)
             dna.append(char)
         }
@@ -49,30 +47,25 @@ func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int)
     return pop
 }
 
-randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
-
 func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
-    
     var fitness = 0
-    for c in 0...dna.count-1 {
+    (0...dna.count-1).forEach { c in
         fitness += abs(Int(dna[c]) - Int(optimal[c]))
     }
     return fitness
 }
 
-calculateFitness(dna: "Gello, World".asciiArray, optimal: "Hello, World".asciiArray)
-
-func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weight:Double) {
     
     let total = items.reduce(0.0) { return $0 + $1.weight}
     
     var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
     
-    for itemTuple in items {
-        if n < itemTuple.weight {
-            return itemTuple
+    for item in items {
+        if n < item.weight {
+            return item
         }
-        n = n - itemTuple.weight
+        n = n - item.weight
     }
     return items[1]
 }
@@ -80,7 +73,7 @@ func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], wei
 func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
     
-    for i in 0..<dna.count {
+    (0..<dna.count).forEach { i in
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
             outputDna[i] = randomChar(from: lexicon)
@@ -108,9 +101,8 @@ func main() {
     var fittest = [UInt8]()
     
     for generation in 0...GENERATIONS {
-        // print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
         
-        var weightedPopulation = [(item:[UInt8], weight:Double)]()
+        var weightedPopulation = [(dna:[UInt8], weight:Double)]()
         
         // calulcated the fitness of each individual in the population
         // and add it to the weight population (weighted = 1.0/fitness)
@@ -129,7 +121,7 @@ func main() {
             let ind1 = weightedChoice(items: weightedPopulation)
             let ind2 = weightedChoice(items: weightedPopulation)
             
-            let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+            let offspring = crossover(dna1: ind1.dna, dna2: ind2.dna, dnaSize: DNA_SIZE)
             
             // append to the population and mutate
             population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
@@ -139,7 +131,7 @@ func main() {
         var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
         
         // parse the population for the fittest string
-        for indv in population {lex
+        population.forEach { indv in
             let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
             if indvFitness < minFitness {
                 fittest = indv
@@ -154,4 +146,3 @@ func main() {
 }
 
 main()
-
diff --git a/Genetic/gen.swift b/Genetic/gen.swift
index a2a1b1410..aad499d04 100644
--- a/Genetic/gen.swift
+++ b/Genetic/gen.swift
@@ -3,16 +3,16 @@
 import Foundation
 
 extension String {
-    var asciiArray: [UInt8] {
+    var unicodeArray: [UInt8] {
         return [UInt8](self.utf8)
     }
 }
 
 
-let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".asciiArray
+let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".unicodeArray
 
 // This is the end goal and what we will be using to rate fitness. In the real world this will not exist
-let OPTIMAL:[UInt8] = "Hello, World".asciiArray
+let OPTIMAL:[UInt8] = "Hello, World".unicodeArray
 
 // The length of the string in our population. Organisms need to be similar
 let DNA_SIZE = OPTIMAL.count
@@ -34,45 +34,38 @@ func randomChar(from lexicon: [UInt8]) -> UInt8 {
 
 func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
 
-    let len = UInt32(lexicon.count)
-
-    var pop = [[UInt8]]()
-
-    for _ in 0..<populationSize {
-        var dna = [UInt8]()
-        for _ in 0..<dnaSize {
-            let char = randomChar(from: lexicon)
-            dna.append(char)
-        }
-        pop.append(dna)
-    }
-    return pop
+   var pop = [[UInt8]]()
+
+   (0..<populationSize).forEach { _ in
+       var dna = [UInt8]()
+       (0..<dnaSize).forEach { _ in
+           let char = randomChar(from: lexicon)
+           dna.append(char)
+       }
+       pop.append(dna)
+   }
+   return pop
 }
 
-randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
-
 func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
-
     var fitness = 0
-    for c in 0...dna.count-1 {
+    (0...dna.count-1).forEach { c in
         fitness += abs(Int(dna[c]) - Int(optimal[c]))
     }
     return fitness
 }
 
-calculateFitness(dna: "Gello, World".asciiArray, optimal: "Hello, World".asciiArray)
-
-func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], weight:Double) {
+func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weight:Double) {
 
     let total = items.reduce(0.0) { return $0 + $1.weight}
 
     var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
 
-    for itemTuple in items {
-        if n < itemTuple.weight {
-            return itemTuple
+    for item in items {
+        if n < item.weight {
+            return item
         }
-        n = n - itemTuple.weight
+        n = n - item.weight
     }
     return items[1]
 }
@@ -80,7 +73,7 @@ func weightedChoice(items:[(item:[UInt8], weight:Double)]) -> (item:[UInt8], wei
 func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
     var outputDna = dna
 
-    for i in 0..<dna.count {
+    (0..<dna.count).forEach { i in
         let rand = Int(arc4random_uniform(UInt32(mutationChance)))
         if rand == 1 {
             outputDna[i] = randomChar(from: lexicon)
@@ -108,9 +101,8 @@ func main() {
     var fittest = [UInt8]()
 
     for generation in 0...GENERATIONS {
-        // print("Generation \(generation) with random sample: \(String(bytes: population[0], encoding:.ascii)!)")
 
-        var weightedPopulation = [(item:[UInt8], weight:Double)]()
+        var weightedPopulation = [(dna:[UInt8], weight:Double)]()
 
         // calulcated the fitness of each individual in the population
         // and add it to the weight population (weighted = 1.0/fitness)
@@ -129,7 +121,7 @@ func main() {
             let ind1 = weightedChoice(items: weightedPopulation)
             let ind2 = weightedChoice(items: weightedPopulation)
 
-            let offspring = crossover(dna1: ind1.item, dna2: ind2.item, dnaSize: DNA_SIZE)
+            let offspring = crossover(dna1: ind1.dna, dna2: ind2.dna, dnaSize: DNA_SIZE)
 
             // append to the population and mutate
             population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
@@ -139,7 +131,7 @@ func main() {
         var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
 
         // parse the population for the fittest string
-        for indv in population {lex
+        population.forEach { indv in
             let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
             if indvFitness < minFitness {
                 fittest = indv

From e1074a1aa7ac3fab3e809b8563dec3cf1d9454bb Mon Sep 17 00:00:00 2001
From: Blaine Rothrock <blaine.rothrock@trunkclub.com>
Date: Fri, 9 Mar 2018 16:05:03 -0600
Subject: [PATCH 356/643] MAX_GENERATIONS

---
 Genetic/gen.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Genetic/gen.swift b/Genetic/gen.swift
index aad499d04..a61e61785 100644
--- a/Genetic/gen.swift
+++ b/Genetic/gen.swift
@@ -21,7 +21,7 @@ let DNA_SIZE = OPTIMAL.count
 let POP_SIZE = 50
 
 // max number of generations, script will stop when it reach 5000 if the optimal value is not found
-let GENERATIONS = 5000
+let MAX_GENERATIONS = 5000
 
 // The chance in which a random nucleotide can mutate (1/n)
 let MUTATION_CHANCE = 100
@@ -100,7 +100,7 @@ func main() {
     // print("population: \(population), dnaSize: \(DNA_SIZE) ")
     var fittest = [UInt8]()
 
-    for generation in 0...GENERATIONS {
+    for generation in 0...MAX_GENERATIONS {
 
         var weightedPopulation = [(dna:[UInt8], weight:Double)]()
 

From 1bc39d21853c4fe869a6861354c54d213cd624bf Mon Sep 17 00:00:00 2001
From: Philip Ridgeway <philip.ridgeway@gmail.com>
Date: Sat, 10 Mar 2018 10:57:39 -0800
Subject: [PATCH 357/643] Replaces references to indexOf(_:) with index(of:).

The global function `indexOf(_:)` was replaced with
`Collection.index(of:)` in Swift 2.
---
 Binary Search/README.markdown | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Binary Search/README.markdown b/Binary Search/README.markdown
index 09b141e04..0cecce6cf 100644
--- a/Binary Search/README.markdown	
+++ b/Binary Search/README.markdown	
@@ -4,15 +4,15 @@ Goal: Quickly find an element in an array.
 
 Let's say you have an array of numbers and you want to determine whether a specific number is in that array, and if so, at which index.
 
-In most cases, Swift's `indexOf()` function is good enough for that:
+In most cases, Swift's `Collection.index(of:)` function is good enough for that:
 
 ```swift
 let numbers = [11, 59, 3, 2, 53, 17, 31, 7, 19, 67, 47, 13, 37, 61, 29, 43, 5, 41, 23]
 
-numbers.indexOf(43)  // returns 15
+numbers.index(of: 43)  // returns 15
 ```
 
-The built-in `indexOf()` function performs a [linear search](../Linear%20Search/). In code that looks something like this:
+The built-in `Collection.index(of:)` function performs a [linear search](../Linear%20Search/). In code that looks something like this:
 
 ```swift
 func linearSearch<T: Equatable>(_ a: [T], _ key: T) -> Int? {

From 0bcbd08988c5ab000a9901c6a6c03ab1a29aed6a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 11 Mar 2018 12:59:19 -0700
Subject: [PATCH 358/643] Grammar fixes for first bit.

---
 Myers Difference Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index 2f6c3c579..a9d92a227 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -1,6 +1,6 @@
 #  Myers Difference Algorithm
 
-Myers Difference Algorithm is the algorithm to find a longest common subsequence or shortest edit scripts (LCS/SES dual probrem) of two sequences by a simple O(ND) time, where N is the sum of the lengths of the two sequences. Common subsequence is the sequence of elements that appear in the same order in both sequences. Edit script will be discussed below.
+Myers Difference Algorithm is an algorithm that finds a longest common subsequence or shortest edit scripts (LCS/SES dual probrem) of two sequences. MDA can accomplish this in O(ND) time, where N is the sum of the lengths of the two sequences. The common subsequence of two sequences is the sequence of elements that appear in the same order in both sequences. The edit scripts will be discussed below.
 
 For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2", "3", "4"]`, `["2"], ["2", "3"]` are common sequences. Furthermore, the latter `["2", "3"]` is the longest common subsequence.  But `["1", "2"], ["3", "2"]` are not. Because, `["1", "2"]` contains `"1"` that is not included in `B`, `["3", "2"]` has elements are included in both, but the appearing order is not correct.
 

From 90afdf77d5fe66f20f1d68f38c9cf24d8070f363 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 11 Mar 2018 13:07:53 -0700
Subject: [PATCH 359/643] Couple more edits.

---
 Myers Difference Algorithm/README.md | 22 +++++++++++++++++-----
 1 file changed, 17 insertions(+), 5 deletions(-)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index a9d92a227..c1aa2da3a 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -1,20 +1,32 @@
 #  Myers Difference Algorithm
 
-Myers Difference Algorithm is an algorithm that finds a longest common subsequence or shortest edit scripts (LCS/SES dual probrem) of two sequences. MDA can accomplish this in O(ND) time, where N is the sum of the lengths of the two sequences. The common subsequence of two sequences is the sequence of elements that appear in the same order in both sequences. The edit scripts will be discussed below.
+Myers Difference Algorithm is an algorithm that finds a longest common subsequence(LCS) or shortest edit scripts(SES) of two sequences. MDA can accomplish this in O(ND) time, where N is the sum of the lengths of the two sequences. The common subsequence of two sequences is the sequence of elements that appear in the same order in both sequences. 
 
-For example, assuming that sequence `A = ["1", "2", "3"]` and sequence `B = ["2", "3", "4"]`, `["2"], ["2", "3"]` are common sequences. Furthermore, the latter `["2", "3"]` is the longest common subsequence.  But `["1", "2"], ["3", "2"]` are not. Because, `["1", "2"]` contains `"1"` that is not included in `B`, `["3", "2"]` has elements are included in both, but the appearing order is not correct.
+For example, let's assume you have two arrays:
+
+```
+A = [1, 2, 3]
+B = [2, 3, 4]
+```
+
+The common subsequences of these two arrays are `[2]`, and `[2,3]`. The longest common sequence in this case is `[2,3]`.
 
 ## Finding the length of the Longest Common Subsequence with Myers Algorithm on Edit Graph
 
 ### Edit Graph
 
-Myers Algorithm uses Edit Graph for solving LCS/SES problem. Edit Graph is the graph like below.
+MDA uses an **Edit Graph** to solve the LCS/SES problem. Below is a illustration depicting an edit graph:
 
 <img src='Images/EditGraph.png' height="400">
 
-Here, we think about the length of the LCS of sequences `X = [A, B, C, A, B, B, A]`, `Y = [C, B, A, B, A, C]`.
+In this case, the arrays are:
+
+```
+X = [A, B, C, A, B, B, A]
+Y = [C, B, A, B, A, C]
+```
 
-In Myers Algorithm, edit graph are prepared by
+MDA generates the edit graph through the following steps:
 
 1. Line the element of sequence `X` on the x axis. And do for `Y` on the y axis.
 2. Make grid and vertex at each point in the grid (x, y), `x in [0, N] and y in [0, M]`. `N` is the length of sequence `X`, `M` is of `Y`

From 38966972f6a602cb1a855d674bae58197af14c77 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 11 Mar 2018 13:11:57 -0700
Subject: [PATCH 360/643] Few more updates to the edit graph.

---
 Myers Difference Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index c1aa2da3a..6c242de88 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -19,7 +19,7 @@ MDA uses an **Edit Graph** to solve the LCS/SES problem. Below is a illustration
 
 <img src='Images/EditGraph.png' height="400">
 
-In this case, the arrays are:
+The x-axis at the top of the graph represents one of the sequences, `X`. The y-axis at the left side of the graph represents the other sequence, `Y`. Hence, the two sequences in question is the following:
 
 ```
 X = [A, B, C, A, B, B, A]

From 81534d54a2f890ab1a5032941e77838b5e585d4b Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Wed, 14 Mar 2018 09:46:07 -0700
Subject: [PATCH 361/643] Update README.markdown

---
 Brute-Force String Search/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Brute-Force String Search/README.markdown b/Brute-Force String Search/README.markdown
index 4e967bcfb..599fe75ea 100644
--- a/Brute-Force String Search/README.markdown	
+++ b/Brute-Force String Search/README.markdown	
@@ -51,6 +51,6 @@ extension String {
 
 This looks at each character in the source string in turn. If the character equals the first character of the search pattern, then the inner loop checks whether the rest of the pattern matches. If no match is found, the outer loop continues where it left off. This repeats until a complete match is found or the end of the source string is reached.
 
-The brute-force approach works OK, but it's not very efficient (or pretty). It should work fine on small strings, though. For a smarter algorithm that works better with large chunks of text, check out [Boyer-Moore](../Boyer-Moore/) string search.
+The brute-force approach works OK, but it's not very efficient (or pretty). It should work fine on small strings, though. For a smarter algorithm that works better with large chunks of text, check out [Boyer-Moore](../Boyer-Moore-Horspool) string search.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 2d5d8d0f552044b54b61409a46bd5b007f2fd2a2 Mon Sep 17 00:00:00 2001
From: James Lawson <jameslawson@users.noreply.github.com>
Date: Sun, 18 Mar 2018 10:00:41 +0000
Subject: [PATCH 362/643] Add Sparse Table link to README

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

diff --git a/README.markdown b/README.markdown
index 5706fc8e5..dc0fc1f57 100644
--- a/README.markdown
+++ b/README.markdown
@@ -162,6 +162,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
   - [Lazy Propagation](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree/LazyPropagation)
 - kd-Tree
+- [Sparse Table](Sparse%20Table/). Another take on quickly computing a function over a portion of an array, but this time we'll make it even quicker!.
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
 - [Trie](Trie/). A special type of tree used to store associative data structures.

From 39da67cf7f5124fd3e5d270ea59361d86c512d78 Mon Sep 17 00:00:00 2001
From: Mike R <mike.rudoi@gmail.com>
Date: Sun, 25 Mar 2018 12:41:35 +0300
Subject: [PATCH 363/643] change function name for future code explanations

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

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 84e278f5c..30dc8d922 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -375,7 +375,7 @@ As an exercise, see if you can implement filter and reduce.
 We can make the code more readable by defining some helper functions.
 
 ```swift
-  private func reconnectParentToNode(node: BinarySearchTree?) {
+  private func reconnectParentTo(node: BinarySearchTree?) {
     if let parent = parent {
       if isLeftChild {
         parent.left = node

From 8baf3549e597edbef432218eb3b52469a75c9df9 Mon Sep 17 00:00:00 2001
From: Daniel Strobusch <1847260+dastrobu@users.noreply.github.com>
Date: Sun, 25 Mar 2018 18:23:11 +0200
Subject: [PATCH 364/643] fixed typo

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

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index ae84cb63b..cd9d86154 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -44,7 +44,7 @@ Based on the Chandy and Misra's analysis, a system of preference levels is deriv
 
 # Swift implementation
 
-This Swift 3.0 implementation of the Chandy/Misra solution is based on the GCD and Semaphore tecnique that can be built on both macOS and Linux.
+This Swift 3.0 implementation of the Chandy/Misra solution is based on the GCD and Semaphore technique that can be built on both macOS and Linux.
 
 The code is based on a ForkPair struct used for holding an array of DispatchSemaphore and a Philosopher struct for associate a couple of forks to each Philosopher.
 

From e4ce8d3f2894745ec4bd62d6fed82311bbe685ea Mon Sep 17 00:00:00 2001
From: James Lawson <jameslawson@users.noreply.github.com>
Date: Wed, 28 Mar 2018 19:21:44 +0100
Subject: [PATCH 365/643] Add Sparse Table

---
 Sparse Table/Images/idempotency.png           | Bin 0 -> 33715 bytes
 Sparse Table/Images/query.png                 | Bin 0 -> 25405 bytes
 Sparse Table/Images/query_example.png         | Bin 0 -> 29984 bytes
 Sparse Table/Images/recursion.png             | Bin 0 -> 78302 bytes
 Sparse Table/Images/recursion_examples.png    | Bin 0 -> 120693 bytes
 Sparse Table/Images/structure.png             | Bin 0 -> 100125 bytes
 Sparse Table/Images/structure_examples.png    | Bin 0 -> 157486 bytes
 Sparse Table/README.markdown                  | 310 ++++++++++++++++++
 .../Sparse Table.playground/Contents.swift    | 144 ++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 11 files changed, 465 insertions(+)
 create mode 100644 Sparse Table/Images/idempotency.png
 create mode 100644 Sparse Table/Images/query.png
 create mode 100644 Sparse Table/Images/query_example.png
 create mode 100644 Sparse Table/Images/recursion.png
 create mode 100644 Sparse Table/Images/recursion_examples.png
 create mode 100644 Sparse Table/Images/structure.png
 create mode 100644 Sparse Table/Images/structure_examples.png
 create mode 100644 Sparse Table/README.markdown
 create mode 100644 Sparse Table/Sparse Table.playground/Contents.swift
 create mode 100644 Sparse Table/Sparse Table.playground/contents.xcplayground
 create mode 100644 Sparse Table/Sparse Table.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Sparse Table/Images/idempotency.png b/Sparse Table/Images/idempotency.png
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diff --git a/Sparse Table/Images/query_example.png b/Sparse Table/Images/query_example.png
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+# Sparse Table
+
+I'm excited to present **Sparse Tables**. Despite being somewhat niche, Sparse Tables are simple to implement and extremely powerful.
+
+### The Problem
+
+Let's suppose:
+- we have an array **a** of some type
+- we have some associative binary function **f** <sup>[\*]</sup>. The function can be: min, max, [gcd](../GCD/), boolean AND, boolean OR ...
+
+*<sup>[\*]</sup> where **f** is also "idempotent". Don't worry, I'll explain this in a moment.*
+
+Our task is as follows:
+
+- Given two indices **l** and **r**, answer a **query** for the interval `[l, r)` by performing `f(a[l], a[l + 1], a[l + 2], ..., a[r - 1])`; taking all the elements in the range and applying **f** to them
+- There will be a *huge* number **Q** of these queries to answer ... so we should be able to answer each query *quickly*!  
+
+For example, if we have an array of numbers:
+
+```swift
+var a = [ 20, 3, -1, 101, 14, 29, 5, 61, 99 ]
+```
+and our function **f** is the *min* function.
+
+Then we may be given a query for interval `[3, 8)`. That means we look at the elements:
+
+```
+101, 14, 29, 5, 61
+```
+
+because these are the elements of **a** with indices 
+that lie in our range `[3, 8)` – elements from index 3 up to, but not including, index 8.
+We then we pass all of these numbers into the min function, 
+which takes the minimum. The answer to the query is `5`, because that's the result of `min(101, 14, 29, 5, 61)`.
+
+Imagine we have millions of these queries to process.
+> - *Query 1*: Find minimum of all elements between 2 and 5
+> - *Query 2*: Find minimum of all elements between 3 and 9
+> - ...
+> - *Query 1000000*: Find minimum of all elements between 1 and 4
+
+And our array is very large. Here, let's say **Q** = 1000000 and **N** = 500000. Both numbers are *huge*. We want to make sure that we can answer each query really quickly, or else the number of queries will overwhelm us! 
+
+*So that's the problem.* 
+
+The naive solution to this problem is to perform a `for` loop
+to compute the answer for each query. However, for very large **Q** and very large **N** this 
+will be too slow. We can speed up the time to compute the answer by using a data structure called
+a **Sparse Table**. You'll notice that so far, our problem is exactly the same as that of the [Segment Tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree) 
+(assuming you're familiar). However! ... there's one crucial difference between Segment Trees
+and Sparse Tables ... and it concerns our choice of **f**.
+
+
+### A small gotcha ... Idempotency
+
+Suppose we wanted to find the answer to **`[A, D)`**.
+And we already know the answer to two ranges  **`[A, B)`** and **`[C, D)`**.
+And importantly here, ... *these ranges overlap*!! We have **C** < **B**. 
+
+![Overlapping ranges](Images/idempotency.png)
+
+
+So what? Well, for **f** = minimum function, we can take our answers for **`[A, B)`** and **`[C, D)`** 
+and combine them!
+We can just take the minimum of the two answers: `result = min(x1, x2)` ... *voilà!*, we have the minimum for **`[A, D)`**.
+It didn't matter that the intervals overlap - we still found the correct minimum.
+But now suppose **f** is the addition operation `+`. Ok, so now we're taking sums over ranges.
+If we tried the same approach again, it wouldn't work. That is, 
+if we took our answers for **`[A, B)`** and **`[C, D)`** 
+and added them together we'd get a wrong answer for **`[A, D)`**.
+*Why?* Well, we'd have counted some elements twice because of the overlap.
+
+Later, we'll see that in order to answer queries, Sparse Tables use this very technique. 
+They combine answers in the same way as shown above. Unfortunately this means
+we have to exclude certain binary operators from being **f**, including `+`, `*`, XOR, ...
+because they don't work with this technique.
+In order to get the best speed of a Sparse Table, 
+we need to make sure that the **f** we're using is an **[idempotent](https://en.wikipedia.org/wiki/Idempotence)** binary operator.
+Mathematically, these are operators that satisfy `f(x, x) = x` for all possible **x** that could be in **a**. 
+Practically speaking, these are the only operators that work; allowing us to combine answers from overlapping ranges.
+Examples of idempotent **f**'s are min, max, gcd, boolean AND, boolean OR, bitwise AND and bitwise OR.
+Note that for Segment Trees, **f** does not have to be idempotent. That's the crucial difference between
+Segment Trees and Sparse Tables.
+
+*Phew!* Now that we've got that out of the way, let's dive in!
+
+## Structure of a Sparse Table
+
+Let's use **f** = min and use the array:
+
+```swift
+var a = [ 10, 6, 5, -7, 9, -8, 2, 4, 20 ]
+```
+
+In this case, the Sparse Table looks like this:
+
+![Sparse Table](Images/structure.png)
+
+What's going on here? There seems to be loads of intervals.
+*Correct!* Sparse tables are preloaded with the answers for lots of queries `[l, r)`.
+Here's the idea. Before we process our **Q** queries, we'll pre-populate our Sparse Table `table`
+with answers to loads of queries;
+making it act a bit like a *cache*. When we come to answer one of our queries, we can break the query
+down into smaller "sub-queries", each having an answer that's already in the cache. 
+We lookup the cached answers for the sub-queries in 
+`table` in constant time
+and combine the answers together 
+to give the overall answer to the original query in speedy time.
+
+The problem is, we can't store the answers for every single possible query that we could ever have ... 
+or else our table would be too big! After all, our Sparse Table needs to be *sparse*. So what do we do?
+We only pick the "best" intervals to store answers for. And as it turns out, the "best" intervals are those 
+that have a **width that is a power of two**!
+
+For example, the answer for the query `[10, 18)` is in our table 
+because the interval width: `18 - 10 = 8 = 2**3` is a power of two (`**` is the [exponentiation operator](https://en.wikipedia.org/wiki/Exponentiation)).
+Also, the answer for `[15, 31)` is in our table because its width: `31 - 15 = 16 = 2**4` is again a power of two.
+However, the answer for `[1, 6)` is *not* in there because the interval's width: `6 - 1 = 5` is *not* a power of two.
+Consequently, we don't store answers for *all* possible intervals that fit inside **a** –
+only the ones with a width that is a power of two. 
+This is true irrespective of where the interval starts within **a**.
+We'll gradually see that this approach works and that relatively speaking, it uses very little space.
+
+A **Sparse Table** is a table where `table[w][l]` contains the answer for `[l, l + 2**w)`.     
+It has entries `table[w][l]` where:
+- **w** tells us our **width** ... the number of elements or the *width* is `2**w`
+- **l** tells us the **lower bound** ... it's the starting point of our interval
+
+Some examples:
+- `table[3][0] = -8`: our width is `2**3`, we start at `l = 0` so our query is `[0, 0 + 2**3) = [0, 8)`.    
+   The answer for this query is `min(10, 6, 5, -7, 9, -8, 2, 4, 20) = -8`.
+- `table[2][1] = -7`: our width is `2**2`, we start at `l = 1` so our query is  `[1, 1 + 2**2) = [1, 5)`.    
+   The answer for this query is `min(6, 5, -7, 9) = -7`.
+- `table[1][7] = 4`: our width is `2**1`, we start at `l = 7` so our query is `[7, 7 + 2**1) = [7, 9)`.     
+   The answer for this query is `min(4, 20) = 4`.
+- `table[0][8] = 20`: our width is `2**0`, we start at `l = 8` so our query is`[8, 8 + 2**0) = [8, 9)`.    
+   The answer for this query is `min(20) = 20`.
+
+
+![Sparse Table](Images/structure_examples.png)
+
+
+A Sparse Table can be implemented using a [two-dimentional array](../2D%20Array).    
+
+```swift
+public class SparseTable<T> {
+  private var table: [[T]]
+
+  public init(array: [T], function: @escaping (T, T) -> T, defaultT: T) {
+      table = [[T]](repeating: [T](repeating: defaultT, count: N), count: W)
+  }
+  // ...    
+}
+```
+
+
+## Building a Sparse Table
+
+To build a Sparse Table, we compute each table entry starting from the bottom-left and moving up towards
+the top-right (in accordance with the diagram).
+First we'll compute all the intervals for  **w** = 0, then compute all the intervals
+and for **w**  = 1 and so on. We'll continue up until **w** is big enough such that our intervals are can cover at least half the array.
+For each **w**, we compute the interval for **l** = 0, 1, 2, 3, ... until we reach **N**.
+This is all achieved using a double `for`-`in` loop:
+
+```swift
+for w in 0..<W {
+  for l in 0..<N {
+    // compute table[w][l]
+  }
+}
+```
+
+To compute `table[w][l]`:
+
+- **Base Case (w = 0)**: Each interval has width `2**w = 1`. 
+    - We have *one* element intervals of the form: `[l, l + 1)`. 
+    - The answer is just `a[l]` (e.g. the minimum of over a list with one element 
+is just the element itself).
+      ```
+      table[w][l] = a[l]
+      ``` 
+- **Inductive Case (w > 0)**: We need to find out the answer to `[l, l + 2**w)` for some **l**. 
+This interval, like all of our intervals in our table has a width that
+is a power of two (e.g.  2, 4, 8, 16) ... so we can cut it into two equal halves.
+    - Our interval with width ``2**w`` is cut into two intervals, each of width ``2**(w - 1)``.
+    - Because each half has a width that is a power of two, we can look them up in our Sparse Table.
+    - We combine them together using **f**. 
+        ```
+        table[w][l] = f(table[w - 1][l], table[w - 1][l + 2 ** (w - 1)])
+        ```     
+
+
+![Sparse Table](Images/recursion.png)
+
+For example for `a = [ 10, 6, 5, -7, 9, -8, 2, 4, 20 ]` and **f** = *min*:
+
+- we compute `table[0][2] = 5`. We just had to look at `a[2]` because the range has a width of one.
+- we compute `table[1][7] = 4`. We looked at `table[0][7]` and `table[0][8]` and apply **f** to them.
+- we compute `table[3][1] = -8`. We looked at `table[2][1]` and `table[2][5]` and apply **f** to them.
+
+
+![Sparse Table](Images/recursion_examples.png)
+
+
+
+```swift
+public init(array: [T], function: @escaping (T, T) -> T, defaultT: T) {
+ let N = array.count
+ let W = Int(ceil(log2(Double(N))))
+ table = [[T]](repeating: [T](repeating: defaultT, count: N), count: W)
+ self.function = function
+ self.defaultT = defaultT
+
+ for w in 0..<W {
+   for l in 0..<N {
+     if w == 0 {
+       table[w][l] = array[l]
+     } else {
+       let first = self.table[w - 1][l]
+       let secondIndex = l + (1 << (w - 1))
+       let second = ((0..<N).contains(secondIndex)) ? table[w - 1][secondIndex] : defaultT
+       table[w][l] = function(first, second)
+     }
+   }
+ }
+}
+```
+
+Building a Sparse Table takes **O(NlogN)** time.    
+The table itself uses **O(NlgN)** additional space.
+
+## Getting Answers to Queries
+
+Suppose we've built our Sparse Table. And now we're going to process our **Q** queries.
+Here's where our work pays off.
+
+Let's suppose **f** = min and we have: 
+```swift
+var a = [ 10, 6, 5, -7, 9, -8, 2, 4, 20 ]
+```
+And we have a query `[3, 9)`.
+
+1. First let's find the largest power of two that fits inside `[3, 9)`. Our interval has width `9 - 3 = 6`. So the largest power of two    that fits inside is four. 
+2. We create two new queries of `[3, 7)` and `[5, 9)` that have a width of four.
+   And, we arrange them so that to that they span the whole interval without leaving any gaps.
+   ![Sparse Table](Images/query_example.png)
+
+3. Because these two intervals have a width that is exactly a power of two we can lookup their answers in the Sparse Table using the 
+   entries for **w** = 2. The answer to `[3, 7)` is given by `table[2][3]`, and the answer to `[5, 9)` is given by `table[2][5]`.
+   We compute and return `min(table[2][3], table[2][5])`. This is our final answer! :tada:. Although the two intervals overlap, it doesn't matter because the **f** = min we originally chose is idempotent.
+
+In general, for each query: `[l, r)` ...
+
+1. Find **W**, by looking for the largest width that fits inside the interval that's also a power of two. Let largest such width = `2**W`.
+2. Form two sub-queries of width `2**W` and arrange them to that they span the whole interval without leaving gaps.
+   To guarantee there are no gaps, we need to align one half to the left and the align other half to the right.
+   ![Sparse Table](Images/query.png)
+3. Compute and return `f(table[W][l], table[W][r - 2**W])`.
+
+      ```swift
+      public func query(from l: Int, until r: Int) -> T {
+        let width = r - l
+        let W = Int(floor(log2(Double(width))))
+        let lo = table[W][l]
+        let hi = table[W][r - (1 << W)]
+        return function(lo, hi)
+     }
+      ```
+
+Finding answers to queries takes **O(1)** time.
+
+## Analysing Sparse Tables
+
+- **Query Time** - Both table lookups take constant time. All other operations inside `query` take constant time. 
+So answering a single query also takes constant time: **O(1)**. But instead of one query we're actually answering **Q** queries, 
+and we'll need time to built the table before-hand.
+Overall time is: **O(NlgN + Q)** to build the table and answer all queries. 
+The naive approach is to do a for loop for each query. The overall time for the naive approach is: **O(NQ)**. 
+For very large **Q**, the naive approach will scale poorly. For example if `Q = O(N*N)`
+then the naive approach is `O(N*N*N)` where a Sparse Table takes time `O(N*N)`.
+- **Space**-  The number of possible **w** is **lgN** and the number of possible **i** our table is **N**. So the table
+has uses **O(NlgN)** additional space.
+
+### Comparison with Segment Trees
+
+- **Pre-processing** - Segment Trees take **O(N)** time to build and use **O(N)** space. Sparse Tables take **O(NlgN)** time to build and use **O(NlgN)** space.
+- **Queries** - Segment Tree queries are **O(lgN)** time for any **f** (idempotent or not idempotent). Sparse Table queries are **O(1)** time if **f** is idempotent and are not supported if **f** is not idempotent. <sup>[†]</sup>
+- **Replacing Items** - Segment Trees allow us to efficiently update an element in **a** and update the segment tree in **O(lgN)** time. Sparse Tables do not allow this to be done efficiently. If we were to update an element in **a**, we'd have to rebuild the Sparse Table all over again in **O(NlgN)** time.
+
+
+<sup>[†]</sup> *Although technically, it's possible to rewrite the `query` method 
+to add support for non-idempotent functions. But in doing so, we'd bump up the time up from O(1) to O(lgn), 
+completely defeating the original purpose of Sparse Tables - supporting lightening quick queries. 
+In such a case, we'd be better off using a Segment Tree (or a Fenwick Tree)*
+
+## Summary
+
+That's it! See the playground for more examples involving Sparse Tables.
+You'll see examples for: min, max, gcd, boolean operators and logical operators. 
+
+### See also
+
+- [Segment Trees (Swift Algorithm Club)](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Segment%20Tree)
+- [How to write O(lgn) time query function to support non-idempontent functions (GeeksForGeeks)](https://www.geeksforgeeks.org/range-sum-query-using-sparse-table/) 
+- [Fenwick Trees / Binary Indexed Trees (TopCoder)](https://www.topcoder.com/community/data-science/data-science-tutorials/binary-indexed-trees/) 
+- [Semilattice (Wikipedia)](https://en.wikipedia.org/wiki/Semilattice)
+
+*Written for Swift Algorithm Club by [James Lawson](https://github.com/jameslawson)*
+
diff --git a/Sparse Table/Sparse Table.playground/Contents.swift b/Sparse Table/Sparse Table.playground/Contents.swift
new file mode 100644
index 000000000..4eae8a6c2
--- /dev/null
+++ b/Sparse Table/Sparse Table.playground/Contents.swift	
@@ -0,0 +1,144 @@
+//
+//  Swift Algorithm Club - Sparse Table
+//  Author: James Lawson (github.com/jameslawson)
+//
+
+import Foundation
+
+// Last checked with Xcode Version 9.2 (9C40b)
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
+public class SparseTable<T> {
+  private var defaultT: T
+  private var table: [[T]]
+  private var function: (T, T) -> T
+  
+  public init(array: [T], function: @escaping (T, T) -> T, defaultT: T) {
+    let N = array.count
+    let W = Int(ceil(log2(Double(N))))
+    table = [[T]](repeating: [T](repeating: defaultT, count: N), count: W)
+    self.function = function
+    self.defaultT = defaultT
+    
+    for w in 0..<W {
+      for l in 0..<N {
+        if w == 0 {
+          table[w][l] = array[l]
+        } else {
+          let first = self.table[w - 1][l]
+          let secondIndex = l + (1 << (w - 1))
+          let second = ((0..<N).contains(secondIndex)) ? table[w - 1][secondIndex] : defaultT
+          table[w][l] = function(first, second)
+        }
+      }
+    }
+  }
+  
+  public func query(from l: Int, until r: Int) -> T {
+    let width = r - l
+    let N = table[0].count
+    if width <= 0 || l >= N {
+      return defaultT
+    }
+    let r = min(N, r)
+    let W = Int(floor(log2(Double(width))))
+    let lo = table[W][l]
+    let hi = table[W][r - (1 << W)]
+    return function(lo, hi)
+  }
+}
+
+print("---------------------------- EXAMPLE 1 -------------------------------------")
+// Here we have an array of integers and we're repeatedly
+// finding the minimum over various ranges
+
+let intArray = [1, -11, -7, 3, 2, 4]
+let minIntTable = SparseTable<Int>(array: intArray, function: min, defaultT: Int.max)
+print(minIntTable.query(from: 0, until: 6)) // min(1, 3, -11, 3, 2, 4) = -11
+print(minIntTable.query(from: 3, until: 5)) // min(3, 2) = 2
+print(minIntTable.query(from: 2, until: 6)) // min(-7, 3, 2, 4) = -7
+print(minIntTable.query(from: 0, until: 1)) // min(1) = 1
+print(minIntTable.query(from: 0, until: 0)) // min(<empty range>) = Int.max
+print("----------------------------------------------------------------------------\n\n")
+
+
+print("---------------------------- EXAMPLE 2 -------------------------------------")
+// Now we have an array of doubles and we're repeatedly
+// finding the maximum over various ranges
+
+let doubleArray = [1.5, 20.0, 3.5, 15.0, 18.0, -10.0, 5.5]
+let maxDoubleTable = SparseTable<Double>(array: doubleArray, function: max, defaultT: -.infinity)
+print(maxDoubleTable.query(from: 0, until: 4)) // max(1.5, 20.0, 3.5, 15.0) = 20.0
+print(maxDoubleTable.query(from: 3, until: 4)) // max(3.5, 15.0) = 15.0
+print(maxDoubleTable.query(from: 4, until: 6)) // max(18.0, -10.0, 5.5) = 18.0
+print(maxDoubleTable.query(from: 1, until: 2)) // max(20.0) = 20.0
+print(maxDoubleTable.query(from: 0, until: 0)) // max(<empty range>) = -inf
+print("----------------------------------------------------------------------------\n\n")
+
+
+print("---------------------------- EXAMPLE 3 -------------------------------------")
+// An array of booleans and we're repeatedly
+// finding the boolean AND over various ranges
+
+let boolArray = [true, false, true, true, true, false, false]
+func and(_ x: Bool, _ y: Bool) -> Bool { return x && y }
+
+let maxBoolTable = SparseTable<Bool>(array: boolArray, function: and, defaultT: false)
+print(maxBoolTable.query(from: 0, until: 4)) // and(T, F, T, T) = F
+print(maxBoolTable.query(from: 2, until: 5)) // and(T, T, T) = T
+print(maxBoolTable.query(from: 2, until: 6)) // and(T, T, T, F) = F
+print(maxBoolTable.query(from: 0, until: 1)) // and(T) = T
+print(maxBoolTable.query(from: 1, until: 2)) // and(F) = F
+print(maxBoolTable.query(from: 0, until: 0)) // and(<empty range>) = F
+print("----------------------------------------------------------------------------\n\n")
+
+print("---------------------------- EXAMPLE 4 -------------------------------------")
+// An array of positive integers and we're repeatedly finding
+// the gcd (greatest common divisor) over various ranges. The gcd operator is
+// associative and idempontent so we can use it with sparse tables
+
+let posIntArray = [7, 2, 3, 4, 6, 5, 25, 75, 100]
+func gcd(_ m: Int, _ n: Int) -> Int {
+  var a = 0
+  var b = max(m, n)
+  var r = min(m, n)
+  
+  while r != 0 {
+    a = b
+    b = r
+    r = a % b
+  }
+  return b
+}
+
+let gcdTable = SparseTable<Int>(array: posIntArray, function: gcd, defaultT: 1)
+print(gcdTable.query(from: 0, until: 4)) // gcd(7, 2, 3) = 1
+print(gcdTable.query(from: 3, until: 5)) // gcd(4, 6) = 2
+print(gcdTable.query(from: 5, until: 7)) // gcd(5, 25, 75) = 5
+print(gcdTable.query(from: 6, until: 9)) // gcd(25, 75, 100) = 25
+print(gcdTable.query(from: 3, until: 4)) // gcd(4) = 4
+print(gcdTable.query(from: 0, until: 0)) // gcd(<empty range>) = 1
+print("------------------------------------------------------------------------\n\n")
+
+
+
+print("---------------------------- EXAMPLE 5 -------------------------------------")
+// An array of nonnegative integers where for each integer we consider its binary representation.
+// We're repeatedly finding the binary OR (|) over various ranges. The binary operator is
+// associative and idempontent so we can use it with sparse tables
+
+let binArray = [0b1001, 0b1100, 0b0000, 0b0001, 0b0010, 0b0100, 0b0000, 0b1111]
+
+
+let orTable = SparseTable<Int>(array: binArray, function: |, defaultT: 0b0000)
+print(String(orTable.query(from: 0, until: 2), radix: 2)) // binary_or(1001, 1100) = 1101
+print(String(orTable.query(from: 3, until: 5), radix: 2)) // binary_or(0001, 0010) = 0011
+
+print(String(orTable.query(from: 3, until: 6), radix: 2)) // binary_or(0001, 0010, 0100) = 0111
+print(String(orTable.query(from: 6, until: 8), radix: 2)) // binary_or(0000, 1111) = 1111
+print(String(orTable.query(from: 1, until: 5), radix: 2)) // binary_or(1100, 0000, 0001, 0010) = 1111
+print(String(orTable.query(from: 0, until: 1), radix: 2)) // binary_or(1001) = 1001
+print(String(orTable.query(from: 0, until: 0), radix: 2)) // binary_or(<empty range>) = 0000
+print("----------------------------------------------------------------------------\n\n")
diff --git a/Sparse Table/Sparse Table.playground/contents.xcplayground b/Sparse Table/Sparse Table.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Sparse Table/Sparse Table.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Sparse Table/Sparse Table.playground/playground.xcworkspace/contents.xcworkspacedata b/Sparse Table/Sparse Table.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Sparse Table/Sparse Table.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

From 7d759ee1a1b2983fb887e514341509842a26a60d Mon Sep 17 00:00:00 2001
From: James Lawson <jameslawson@users.noreply.github.com>
Date: Wed, 28 Mar 2018 19:29:45 +0100
Subject: [PATCH 366/643] Fix typo. Rename varaible from i to l

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

diff --git a/Sparse Table/README.markdown b/Sparse Table/README.markdown
index 701a33f21..31bd5a781 100644
--- a/Sparse Table/README.markdown	
+++ b/Sparse Table/README.markdown	
@@ -279,7 +279,7 @@ Overall time is: **O(NlgN + Q)** to build the table and answer all queries.
 The naive approach is to do a for loop for each query. The overall time for the naive approach is: **O(NQ)**. 
 For very large **Q**, the naive approach will scale poorly. For example if `Q = O(N*N)`
 then the naive approach is `O(N*N*N)` where a Sparse Table takes time `O(N*N)`.
-- **Space**-  The number of possible **w** is **lgN** and the number of possible **i** our table is **N**. So the table
+- **Space**-  The number of possible **w** is **lgN** and the number of possible **l** our table is **N**. So the table
 has uses **O(NlgN)** additional space.
 
 ### Comparison with Segment Trees

From 11a5e7cb24279b86da99c8ffcd791c2bbfbe6b58 Mon Sep 17 00:00:00 2001
From: James Lawson <jameslawson@users.noreply.github.com>
Date: Wed, 28 Mar 2018 19:33:16 +0100
Subject: [PATCH 367/643] Fix typo "Idempotent"

---
 Sparse Table/Sparse Table.playground/Contents.swift | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Sparse Table/Sparse Table.playground/Contents.swift b/Sparse Table/Sparse Table.playground/Contents.swift
index 4eae8a6c2..ef83263b0 100644
--- a/Sparse Table/Sparse Table.playground/Contents.swift	
+++ b/Sparse Table/Sparse Table.playground/Contents.swift	
@@ -14,14 +14,14 @@ public class SparseTable<T> {
   private var defaultT: T
   private var table: [[T]]
   private var function: (T, T) -> T
-  
+
   public init(array: [T], function: @escaping (T, T) -> T, defaultT: T) {
     let N = array.count
     let W = Int(ceil(log2(Double(N))))
     table = [[T]](repeating: [T](repeating: defaultT, count: N), count: W)
     self.function = function
     self.defaultT = defaultT
-    
+
     for w in 0..<W {
       for l in 0..<N {
         if w == 0 {
@@ -35,7 +35,7 @@ public class SparseTable<T> {
       }
     }
   }
-  
+
   public func query(from l: Int, until r: Int) -> T {
     let width = r - l
     let N = table[0].count
@@ -97,14 +97,14 @@ print("-------------------------------------------------------------------------
 print("---------------------------- EXAMPLE 4 -------------------------------------")
 // An array of positive integers and we're repeatedly finding
 // the gcd (greatest common divisor) over various ranges. The gcd operator is
-// associative and idempontent so we can use it with sparse tables
+// associative and idempotent so we can use it with sparse tables
 
 let posIntArray = [7, 2, 3, 4, 6, 5, 25, 75, 100]
 func gcd(_ m: Int, _ n: Int) -> Int {
   var a = 0
   var b = max(m, n)
   var r = min(m, n)
-  
+
   while r != 0 {
     a = b
     b = r
@@ -127,7 +127,7 @@ print("------------------------------------------------------------------------\
 print("---------------------------- EXAMPLE 5 -------------------------------------")
 // An array of nonnegative integers where for each integer we consider its binary representation.
 // We're repeatedly finding the binary OR (|) over various ranges. The binary operator is
-// associative and idempontent so we can use it with sparse tables
+// associative and idempotent so we can use it with sparse tables
 
 let binArray = [0b1001, 0b1100, 0b0000, 0b0001, 0b0010, 0b0100, 0b0000, 0b1111]
 

From eda68c40eba5aef49b3f23b8fccf9bab62eb6e9d Mon Sep 17 00:00:00 2001
From: Stephen Clark <contact.stephenclark@gmail.com>
Date: Fri, 30 Mar 2018 16:15:25 +0100
Subject: [PATCH 368/643] Convex Hull: Clarified Readme, and small code clarity
 changes.

Began to clarify Convex Hull readme, and code. (Needs more work!!)
---
 .../Convex Hull.xcodeproj/project.pbxproj      |  6 +++---
 .../xcshareddata/IDEWorkspaceChecks.plist      |  8 ++++++++
 Convex Hull/Convex Hull/View.swift             | 12 ++----------
 Convex Hull/README.md                          | 18 ++++++++++++++----
 4 files changed, 27 insertions(+), 17 deletions(-)
 create mode 100644 Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
index 651a5bed3..c11cbf4d6 100644
--- a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -149,7 +149,7 @@
 					};
 					8E6D68B51E59989400161780 = {
 						CreatedOnToolsVersion = 8.2.1;
-						DevelopmentTeam = 7C4LVS3ZVC;
+						DevelopmentTeam = 4SQG5NJNPF;
 						ProvisioningStyle = Automatic;
 					};
 				};
@@ -384,7 +384,7 @@
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				DEVELOPMENT_TEAM = 4SQG5NJNPF;
 				INFOPLIST_FILE = "Convex Hull/Info.plist";
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
@@ -397,7 +397,7 @@
 			isa = XCBuildConfiguration;
 			buildSettings = {
 				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
-				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				DEVELOPMENT_TEAM = 4SQG5NJNPF;
 				INFOPLIST_FILE = "Convex Hull/Info.plist";
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
diff --git a/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index a50cc247a..33d1426c3 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -11,20 +11,12 @@ import UIKit
 class View: UIView {
 
   let MAX_POINTS = 100
-
   var points = [CGPoint]()
-
   var convexHull = [CGPoint]()
 
   override init(frame: CGRect) {
     super.init(frame: frame)
-
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-    
-    generatePoints()
+    generateRandomPoints()
     quickHull(points: points)
   }
 
@@ -32,7 +24,7 @@ class View: UIView {
     fatalError("init(coder:) has not been implemented")
   }
 
-  func generatePoints() {
+  func generateRandomPoints() {
     for _ in 0..<MAX_POINTS {
       let offset: CGFloat = 50
       let xrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.width - offset) + 0.5 * offset
diff --git a/Convex Hull/README.md b/Convex Hull/README.md
index 2e1fbe6a3..d27027a45 100644
--- a/Convex Hull/README.md	
+++ b/Convex Hull/README.md	
@@ -1,14 +1,23 @@
 # Convex Hull
 
-There are multiple Convex Hull algorithms. This particular implementation uses the Quickhull algorithm.
+Given a group of points on a plane. The Convex Hull algorithm calculates the shape (made up from the points itself) containing all these points. It can also be used on a collection of points of different dimensions. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points. In comparing different solutions to this problem we can describe each algorithm in terms of it's big-O time complexity.
 
-Given a group of points on a plane. The Convex Hull algorithm calculates the shape (made up from the points itself) containing all these points. It can also be used on a collection of points of different dimensions. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points.
+There are multiple Convex Hull algorithms but this solution is called Quickhull, is comes from the work of both W. Eddy in 1977 and also separately A. Bykat in 1978, this algorithm has an expected time complexity of O(n log n), but it's worst-case time-complexity can be O(n^2) . With average conditions the algorithm has ok efficiency, but it's time-complexity can start to head become more exponential in cases of high symmetry or where there are points lying on the circumference of a circle for example.
 
 ## Quickhull
 
 The quickhull algorithm works as follows:
-The algorithm takes an input of a collection of points. These points should be ordered on their x-coordinate value. We pick the two points A and B with the smallest(A) and the largest(B) x-coordinate. These of course have to be part of the hull. Imagine a line from point A to point B. All points to the right of this line are grouped in an array S1. Imagine now a line from point B to point A. (this is of course the same line as before just with opposite direction) Again all points to the right of this line are grouped in an array, S2 this time.
-We now define the following recursive function:
+
+- The algorithm takes an input of a collection of points. These points should be ordered on their x-coordinate value. 
+- We first find the two points A and B with the minimum(A) and the maximum(B) x-coordinates (as these will obviously be part of the hull). 
+- Use the line formed by the two points to divide the set in two subsets of points, which will be processed recursively.
+- Determine the point, on one side of the line, with the maximum distance from the line. The two points found before along with this one form a triangle.
+- The points lying inside of that triangle cannot be part of the convex hull and can therefore be ignored in the next steps.
+- Repeat the previous two steps on the two lines formed by the triangle (not the initial line).
+- Keep on doing so on until no more points are left, the recursion has come to an end and the points selected constitute the convex hull.
+
+
+Our functioni will have the following defininition:
 
 `findHull(points: [CGPoint], p1: CGPoint, p2: CGPoint)`
 
@@ -18,6 +27,7 @@ findHull(S2, B, A)
 ```
 
 What this function does is the following:
+
 1. If `points` is empty we return as there are no points to the right of our line to add to our hull.
 2. Draw a line from `p1` to `p2`.
 3. Find the point in `points` that is furthest away from this line. (`maxPoint`)

From 2ce84e9dc6c7cba09192d621c0fb76e0d6cfb729 Mon Sep 17 00:00:00 2001
From: Aamir Anwar <aamir.anwar021193@gmail.com>
Date: Sat, 31 Mar 2018 14:12:06 +0530
Subject: [PATCH 369/643] Fixed broken youtube link in splay tree readme

---
 Splay Tree/readme.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index f3b852f22..75c3c0389 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -263,7 +263,7 @@ If the rotations would had been taking first the parent and not the grandparent
 
 [Splay Tree on Wikipedia](https://en.wikipedia.org/wiki/Splay_tree)
 
-[Splay Tree by University of California in Berkeley - CS 61B Lecture 34](https://www.youtube.com/watch?v=G5QIXywcJlY)
+[Splay Tree by University of California in Berkeley - CS 61B Lecture 34](https://www.youtube.com/watch?v=8Zs1lj_bUV0)
 
 
 ----------------

From 3bf65574bf04db1e0540494ece247f2beba79a5c Mon Sep 17 00:00:00 2001
From: horita-yuya <horita_yuya@cyberagent.co.jp>
Date: Sat, 7 Apr 2018 03:30:09 +0900
Subject: [PATCH 370/643] add explanation

---
 Myers Difference Algorithm/README.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index 6c242de88..e6137e8ce 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -34,6 +34,11 @@ MDA generates the edit graph through the following steps:
 3. Check the points `(i, j)`, where `X[i] = Y[j]`, called match point, light green one.
 4. Connect vertex `(i - 1, j - 1)` and vertex `(i, j)`, where `(i, j)` is match point, then diagonal edge appears.
 
+Each elements on the figure shows that,
+- `Red number and dotted lines`: The red number is the value of k and dotted lines are k-line.
+- `Green dots: The match points`, which is the point `(i, j)` where `X[i] == Y[j]`
+- `Blue line`: The shortest path from source to sink, which is the path we are going to find finally.
+
 > **Note:** Here, the sequences' start index is 1 not 0, so `X[1] = A`, `Y[1] = C`
 
 We discuss about which path is the shortest from `source` to `sink`. Can move on the edges on the graph. I mean we can move on  the grid, horizontal and vertical edges, and the diagonal edges.

From 6bf3a160912dd4b7bf91379175549321fd45cecc Mon Sep 17 00:00:00 2001
From: Jorge <minuscorp@gmail.com>
Date: Wed, 11 Apr 2018 19:17:12 +0200
Subject: [PATCH 371/643] Update Combinatorics to match Swift 4 API

---
 Combinatorics/README.markdown | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Combinatorics/README.markdown b/Combinatorics/README.markdown
index b365b389b..a2432a680 100644
--- a/Combinatorics/README.markdown
+++ b/Combinatorics/README.markdown
@@ -99,17 +99,17 @@ Here's a recursive algorithm by Niklaus Wirth:
 
 ```swift
 func permuteWirth<T>(_ a: [T], _ n: Int) {
-  if n == 0 {
-    print(a)   // display the current permutation
-  } else {
-    var a = a
-    permuteWirth(a, n - 1)
-    for i in 0..<n {
-      swap(&a[i], &a[n])
-      permuteWirth(a, n - 1)
-      swap(&a[i], &a[n])
+    if n == 0 {
+        print(a)   // display the current permutation
+    } else {
+        var a = a
+        permuteWirth(a, n - 1)
+        for i in 0..<n {
+            a.swapAt(i, n)
+            permuteWirth(a, n - 1)
+            a.swapAt(i, n)
+        }
     }
-  }
 }
 ```
 

From 7e1c2891d309fb0c2a875d6d3f3a872d8e3ee470 Mon Sep 17 00:00:00 2001
From: Ray Wenderlich <ray.wenderlich@gmail.com>
Date: Tue, 17 Apr 2018 08:46:31 -0400
Subject: [PATCH 372/643] Added link to Swift Alg Club book

---
 ...DataStructuresAndAlgorithmsInSwiftBook.png | Bin 0 -> 136406 bytes
 README.markdown                               |  26 ++++--------------
 2 files changed, 6 insertions(+), 20 deletions(-)
 create mode 100644 Images/DataStructuresAndAlgorithmsInSwiftBook.png

diff --git a/Images/DataStructuresAndAlgorithmsInSwiftBook.png b/Images/DataStructuresAndAlgorithmsInSwiftBook.png
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diff --git a/README.markdown b/README.markdown
index dc0fc1f57..481e25f62 100644
--- a/README.markdown
+++ b/README.markdown
@@ -206,32 +206,18 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 - [Dining Philosophers](DiningPhilosophers/)
 - [Egg Drop Problem](Egg%20Drop%20Problem/)
 - [Encoding and Decoding Binary Tree](Encode%20and%20Decode%20Tree/)
-## Learn more!
 
-For more information, check out these great books:
+## Learn more!
 
-- [Introduction to Algorithms](https://mitpress.mit.edu/books/introduction-algorithms) by Cormen, Leiserson, Rivest, Stein
-- [The Algorithm Design Manual](http://www.algorist.com) by Skiena
-- [Elements of Programming Interviews](http://elementsofprogramminginterviews.com) by Aziz, Lee, Prakash
-- [Algorithms](http://www.cs.princeton.edu/~rs/) by Sedgewick
-- [Grokking Algorithms](https://www.manning.com/books/grokking-algorithms) by Aditya Bhargava
+Like what you see? Check out [Data Structures & Algorithms in Swift](https://store.raywenderlich.com/products/data-structures-and-algorithms-in-swift), the official book by the Swift Algorithm Club team!
 
-The following books are available for free online:
+![Data Structures & Algorithms in Swift Book](Images/DataStructuresAndAlgorithmsInSwift.png)
 
-- [Algorithms](http://www.beust.com/algorithms.pdf) by Dasgupta, Papadimitriou, Vazirani
-- [Algorithms, Etc.](http://jeffe.cs.illinois.edu/teaching/algorithms/) by Erickson
-- [Algorithms + Data Structures = Programs](http://www.ethoberon.ethz.ch/WirthPubl/AD.pdf) by Wirth
-- Algorithms and Data Structures: The Basic Toolbox by Mehlhorn and Sanders
-- [Open Data Structures](http://opendatastructures.org) by Pat Morin
-- [Wikibooks: Algorithms and Implementations](https://en.wikibooks.org/wiki/Algorithm_Implementation)
+You’ll start with the fundamental structures of linked lists, queues and stacks, and see how to implement them in a highly Swift-like way. Move on to working with various types of trees, including general purpose trees, binary trees, AVL trees, binary search trees, and tries. 
 
-Other algorithm repositories:
+Go beyond bubble and insertion sort with better-performing algorithms, including mergesort, radix sort, heap sort, and quicksort. Learn how to construct directed, non-directed and weighted graphs to represent many real-world models, and traverse graphs and trees efficiently with breadth-first, depth-first, Dijkstra’s and Prim’s algorithms to solve problems such as finding the shortest path or lowest cost in a network.
 
-- [EKAlgorithms](https://github.com/EvgenyKarkan/EKAlgorithms). A great collection of algorithms in Objective-C.
-- [@lorentey](https://github.com/lorentey/). Production-quality Swift implementations of common algorithms and data structures.
-- [Rosetta Code](http://rosettacode.org). Implementations in pretty much any language you can think of.
-- [AlgorithmVisualizer](http://jasonpark.me/AlgorithmVisualizer/). Visualize algorithms on your browser.
-- [Swift Structures](https://github.com/waynewbishop/SwiftStructures) Data Structures with directions on how to use them [here](http://waynewbishop.com/swift)
+By the end of this book, you’ll have hands-on experience solving common issues with data structures and algorithms — and you’ll be well on your way to developing your own efficient and useful implementations!
 
 ## Credits
 

From 8010ec629e93228bd960da271b406420d6cb9cb0 Mon Sep 17 00:00:00 2001
From: Ray Wenderlich <ray.wenderlich@gmail.com>
Date: Tue, 17 Apr 2018 08:47:31 -0400
Subject: [PATCH 373/643] Fixed typo in link

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

diff --git a/README.markdown b/README.markdown
index 481e25f62..783750fbc 100644
--- a/README.markdown
+++ b/README.markdown
@@ -211,7 +211,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 
 Like what you see? Check out [Data Structures & Algorithms in Swift](https://store.raywenderlich.com/products/data-structures-and-algorithms-in-swift), the official book by the Swift Algorithm Club team!
 
-![Data Structures & Algorithms in Swift Book](Images/DataStructuresAndAlgorithmsInSwift.png)
+![Data Structures & Algorithms in Swift Book](Images/DataStructuresAndAlgorithmsInSwiftBook.png)
 
 You’ll start with the fundamental structures of linked lists, queues and stacks, and see how to implement them in a highly Swift-like way. Move on to working with various types of trees, including general purpose trees, binary trees, AVL trees, binary search trees, and tries. 
 

From 12471a2f8ed0586269c8cb693efc5a33e31c45c0 Mon Sep 17 00:00:00 2001
From: Ray Wenderlich <ray.wenderlich@gmail.com>
Date: Tue, 17 Apr 2018 08:48:25 -0400
Subject: [PATCH 374/643] Added final link to book

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

diff --git a/README.markdown b/README.markdown
index 783750fbc..919f1b67f 100644
--- a/README.markdown
+++ b/README.markdown
@@ -219,6 +219,8 @@ Go beyond bubble and insertion sort with better-performing algorithms, including
 
 By the end of this book, you’ll have hands-on experience solving common issues with data structures and algorithms — and you’ll be well on your way to developing your own efficient and useful implementations!
 
+You can find the book on the [raywenderlich.com store](https://store.raywenderlich.com/products/data-structures-and-algorithms-in-swift).
+
 ## Credits
 
 The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://github.com/hollance).

From 730059ec7ba7dd16115f09d5d58a01b068df9beb Mon Sep 17 00:00:00 2001
From: APKaramyshev <38246803+APKaramyshev@users.noreply.github.com>
Date: Sat, 21 Apr 2018 21:54:58 +0300
Subject: [PATCH 375/643] Fixed two misspellings in O(n!) example

---
 Big-O Notation.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 19a1ddbde..257f80462 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -132,9 +132,9 @@ Below are some examples for each category of performance:
   The most trivial example of function that takes O(n!) time is given below.
 
   ```swift
-  func nFacFunc(n: Int) {
+  func nFactFunc(n: Int) {
     for i in stride(from: 0, to: n, by: 1) {
-      nFactFunc(n - 1)
+      nFactFunc(n: n - 1)
     }
   }
   ```

From a0cfcee54c015e1110ca7ab102d9ba84bda0ae85 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 22 Apr 2018 18:29:44 -0700
Subject: [PATCH 376/643] Update README.markdown

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

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index 07547c4b4..18afb9639 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -1,4 +1,4 @@
-individual# Genetic Algorthim
+# Genetic Algorthim
 
 ## What is it?
 

From 83b08626a172030777db1924513599ad55c32f34 Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Mon, 23 Apr 2018 15:31:04 +0800
Subject: [PATCH 377/643] Update README.markdown

Here should be right.  Bottom-left corner of the matrix is `matrix[0][m+1]`
---
 Longest Common Subsequence/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Longest Common Subsequence/README.markdown b/Longest Common Subsequence/README.markdown
index 4cd2c2fcb..a62c562a6 100644
--- a/Longest Common Subsequence/README.markdown	
+++ b/Longest Common Subsequence/README.markdown	
@@ -99,7 +99,7 @@ And so on... this is how `lcsLength(_:)` fills in the entire matrix.
 
 ## Backtracking to find the actual subsequence
 
-So far we've calculated the length of every possible subsequence. The length of the longest subsequence is found in the bottom-left corner of matrix, at `matrix[n+1][m+1]`. In the above example it is 4, so the LCS consists of 4 characters.
+So far we've calculated the length of every possible subsequence. The length of the longest subsequence is found in the bottom-right corner of matrix, at `matrix[n+1][m+1]`. In the above example it is 4, so the LCS consists of 4 characters.
 
 Having the length of every combination of substrings makes it possible to determine *which* characters are part of the LCS itself by using a backtracking strategy.
 

From e0c0200ba34960f7b48dc742a33fd2a966843a83 Mon Sep 17 00:00:00 2001
From: Keith <ustbfxx@163.com>
Date: Mon, 23 Apr 2018 16:18:23 +0800
Subject: [PATCH 378/643] Update README.markdown

Fix typo: top-right -> top-left
---
 Longest Common Subsequence/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Longest Common Subsequence/README.markdown b/Longest Common Subsequence/README.markdown
index a62c562a6..8a4a763c6 100644
--- a/Longest Common Subsequence/README.markdown	
+++ b/Longest Common Subsequence/README.markdown	
@@ -156,7 +156,7 @@ func backtrack(_ matrix: [[Int]]) -> String {
 }
 ```  
 
-This backtracks from `matrix[n+1][m+1]` (bottom-right corner) to `matrix[1][1]` (top-right corner), looking for characters that are common to both strings. It adds those characters to a new string, `lcs`.
+This backtracks from `matrix[n+1][m+1]` (bottom-right corner) to `matrix[1][1]` (top-left corner), looking for characters that are common to both strings. It adds those characters to a new string, `lcs`.
 
 The `charInSequence` variable is an index into the string given by `self`. Initially this points to the last character of the string. Each time we decrement `i`, we also move back `charInSequence`. When the two characters are found to be equal, we add the character at `self[charInSequence]` to the new `lcs` string. (We can't just write `self[i]` because `i` may not map to the current position inside the Swift string.)
 

From 898db6fd3f266812be8387a2b2478d5f072cf872 Mon Sep 17 00:00:00 2001
From: Sergey Pugach <sergei.pygach@gmail.com>
Date: Mon, 30 Apr 2018 04:37:26 +0300
Subject: [PATCH 379/643] Refactors LinkedList implementation to be more
 Swifty. (#705)

* fix versions merge

* replace if to guard check
---
 .../LinkedList.playground/Contents.swift      | 585 ++++++++--------
 Linked List/LinkedList.swift                  | 263 ++++---
 Linked List/Tests/LinkedListTests.swift       | 662 +++++++++---------
 3 files changed, 779 insertions(+), 731 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 2ce3b4d66..4b58bb65e 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -9,371 +9,364 @@ print("Hello, Swift 4!")
 #endif
 
 public final class LinkedList<T> {
-
-  /// Linked List's Node Class Declaration
-  public class LinkedListNode<T> {
-    var value: T
-    var next: LinkedListNode?
-    weak var previous: LinkedListNode?
-
-    public init(value: T) {
-      self.value = value
+    
+    /// Linked List's Node Class Declaration
+    public class LinkedListNode<T> {
+        var value: T
+        var next: LinkedListNode?
+        weak var previous: LinkedListNode?
+        
+        public init(value: T) {
+            self.value = value
+        }
     }
-  }
-
-  /// Typealiasing the node class to increase readability of code
-  public typealias Node = LinkedListNode<T>
-
-  /// The head of the Linked List
-  fileprivate var head: Node?
-
-  /// Default initializer
-  public init() {}
-
-  /// Computed property to check if the linked list is empty
-  public var isEmpty: Bool {
-    return head == nil
-  }
-
-  /// Computed property to get the first node in the linked list (if any)
-  public var first: Node? {
-    return head
-  }
-
-  /// Computed property to iterate through the linked list and return the last node in the list (if any)
-  public var last: Node? {
-    guard var node = head else {
-      return nil
+    
+    /// Typealiasing the node class to increase readability of code
+    public typealias Node = LinkedListNode<T>
+    
+    
+    /// The head of the Linked List
+    private(set) var head: Node?
+    
+    /// Computed property to iterate through the linked list and return the last node in the list (if any)
+    public var last: Node? {
+        guard var node = head else {
+            return nil
+        }
+        
+        while let next = node.next {
+            node = next
+        }
+        return node
     }
     
-    while let next = node.next {
-      node = next
+    /// Computed property to check if the linked list is empty
+    public var isEmpty: Bool {
+        return head == nil
     }
-    return node
-  }
-
-  /// Computed property to iterate through the linked list and return the total number of nodes
-  public var count: Int {
-    guard var node = head else {
-      return 0
+    
+    /// Computed property to iterate through the linked list and return the total number of nodes
+    public var count: Int {
+        guard var node = head else {
+            return 0
+        }
+        
+        var count = 1
+        while let next = node.next {
+            node = next
+            count += 1
+        }
+        return count
     }
     
-    var count = 1
-    while let next = node.next {
-      node = next
-      count += 1
+    /// Default initializer
+    public init() {}
+    
+    
+    /// Subscript function to return the node at a specific index
+    ///
+    /// - Parameter index: Integer value of the requested value's index
+    public subscript(index: Int) -> T {
+        let node = self.node(at: index)
+        return node.value
     }
-    return count
-  }
-
-  /// Function to return the node at a specific index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameter index: Integer value of the node's index to be returned
-  /// - Returns: Optional LinkedListNode
-  public func node(at index: Int) -> Node {
-    assert(head != nil, "List is empty")
-    assert(index >= 0, "index must be greater than 0")
     
-    if index == 0 {
-        return head!
-    } else {
-        var node = head!.next
-        for _ in 1..<index {
-            node = node?.next
-            if node == nil {
-                break
+    /// Function to return the node at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameter index: Integer value of the node's index to be returned
+    /// - Returns: LinkedListNode
+    public func node(at index: Int) -> Node {
+        assert(head != nil, "List is empty")
+        assert(index >= 0, "index must be greater than 0")
+        
+        if index == 0 {
+            return head!
+        } else {
+            var node = head!.next
+            for _ in 1..<index {
+                node = node?.next
+                if node == nil {
+                    break
+                }
             }
+            
+            assert(node != nil, "index is out of bounds.")
+            return node!
         }
-        
-        assert(node != nil, "index is out of bounds.")
-        return node!
     }
-  }
-
-  /// Subscript function to return the node at a specific index
-  ///
-  /// - Parameter index: Integer value of the requested value's index
-  public subscript(index: Int) -> T {
-    let node = self.node(at: index)
-    return node.value
-  }
-
-  /// Append a value to the end of the list
-  ///
-  /// - Parameter value: The data value to be appended
-  public func append(_ value: T) {
-    let newNode = Node(value: value)
-    self.append(newNode)
-  }
-
-  /// Append a copy of a LinkedListNode to the end of the list.
-  ///
-  /// - Parameter node: The node containing the value to be appended
-  public func append(_ node: Node) {
-    let newNode = node
-    if let lastNode = last {
-      newNode.previous = lastNode
-      lastNode.next = newNode
-    } else {
-      head = newNode
+    
+    /// Append a value to the end of the list
+    ///
+    /// - Parameter value: The data value to be appended
+    public func append(_ value: T) {
+        let newNode = Node(value: value)
+        append(newNode)
+    }
+    
+    /// Append a copy of a LinkedListNode to the end of the list.
+    ///
+    /// - Parameter node: The node containing the value to be appended
+    public func append(_ node: Node) {
+        let newNode = node
+        if let lastNode = last {
+            newNode.previous = lastNode
+            lastNode.next = newNode
+        } else {
+            head = newNode
+        }
+    }
+    
+    /// Append a copy of a LinkedList to the end of the list.
+    ///
+    /// - Parameter list: The list to be copied and appended.
+    public func append(_ list: LinkedList) {
+        var nodeToCopy = list.head
+        while let node = nodeToCopy {
+            append(node.value)
+            nodeToCopy = node.next
+        }
+    }
+    
+    /// Insert a value at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - value: The data value to be inserted
+    ///   - index: Integer value of the index to be insterted at
+    public func insert(_ value: T, at index: Int) {
+        let newNode = Node(value: value)
+        insert(newNode, at: index)
+    }
+    
+    /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - node: The node containing the value to be inserted
+    ///   - index: Integer value of the index to be inserted at
+    public func insert(_ newNode: Node, at index: Int) {
+        if index == 0 {
+            newNode.next = head
+            head?.previous = newNode
+            head = newNode
+        } else {
+            let prev = node(at: index - 1)
+            let next = prev.next
+            newNode.previous = prev
+            newNode.next = next
+            next?.previous = newNode
+            prev.next = newNode
+        }
     }
-  }
-
-  /// Append a copy of a LinkedList to the end of the list.
-  ///
-  /// - Parameter list: The list to be copied and appended.
-  public func append(_ list: LinkedList) {
-    var nodeToCopy = list.head
-    while let node = nodeToCopy {
-      self.append(node.value)
-      nodeToCopy = node.next
+    
+    /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - list: The LinkedList to be copied and inserted
+    ///   - index: Integer value of the index to be inserted at
+    public func insert(_ list: LinkedList, at index: Int) {
+        if list.isEmpty { return }
+        
+        if index == 0 {
+            list.last?.next = head
+            head = list.head
+        } else {
+            let prev = node(at: index - 1)
+            let next = prev.next
+            
+            prev.next = list.head
+            list.head?.previous = prev
+            
+            list.last?.next = next
+            next?.previous = list.last?.next
+        }
     }
-  }
-
-  /// Insert a value at a specific index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameters:
-  ///   - value: The data value to be inserted
-  ///   - index: Integer value of the index to be insterted at
-  public func insert(_ value: T, at index: Int) {
-    let newNode = Node(value: value)
-    self.insert(newNode, at: index)
-  }
-
-  /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameters:
-  ///   - node: The node containing the value to be inserted
-  ///   - index: Integer value of the index to be inserted at
-  public func insert(_ newNode: Node, at index: Int) {
-    if index == 0 {
-      newNode.next = head
-      head?.previous = newNode
-      head = newNode
-    } else {
-      let prev = node(at: index-1)
-      let next = prev.next
-      newNode.previous = prev
-      newNode.next = next
-      next?.previous = newNode
-      prev.next = newNode
+    
+    /// Function to remove all nodes/value from the list
+    public func removeAll() {
+        head = nil
     }
-  }
     
-  /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameters:
-  ///   - list: The LinkedList to be copied and inserted
-  ///   - index: Integer value of the index to be inserted at
-  public func insert(_ list: LinkedList, at index: Int) {
-    if list.isEmpty { return }
+    /// Function to remove a specific node.
+    ///
+    /// - Parameter node: The node to be deleted
+    /// - Returns: The data value contained in the deleted node.
+    @discardableResult public func remove(node: Node) -> T {
+        let prev = node.previous
+        let next = node.next
+        
+        if let prev = prev {
+            prev.next = next
+        } else {
+            head = next
+        }
+        next?.previous = prev
+        
+        node.previous = nil
+        node.next = nil
+        return node.value
+    }
     
-    if index == 0 {
-      list.last?.next = head
-      head = list.head
-    } else {
-      let prev = node(at: index-1)
-      let next = prev.next
-
-      prev.next = list.head
-      list.head?.previous = prev
-
-      list.last?.next = next
-      next?.previous = list.last?.next
+    /// Function to remove the last node/value in the list. Crashes if the list is empty
+    ///
+    /// - Returns: The data value contained in the deleted node.
+    @discardableResult public func removeLast() -> T {
+        assert(!isEmpty)
+        return remove(node: last!)
     }
-  }
-
-  /// Function to remove all nodes/value from the list
-  public func removeAll() {
-    head = nil
-  }
-
-  /// Function to remove a specific node.
-  ///
-  /// - Parameter node: The node to be deleted
-  /// - Returns: The data value contained in the deleted node.
-  @discardableResult public func remove(node: Node) -> T {
-    let prev = node.previous
-    let next = node.next
-
-    if let prev = prev {
-      prev.next = next
-    } else {
-      head = next
+    
+    /// Function to remove a node/value at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameter index: Integer value of the index of the node to be removed
+    /// - Returns: The data value contained in the deleted node
+    @discardableResult public func remove(at index: Int) -> T {
+        let node = self.node(at: index)
+        return remove(node: node)
     }
-    next?.previous = prev
-
-    node.previous = nil
-    node.next = nil
-    return node.value
-  }
-
-  /// Function to remove the last node/value in the list. Crashes if the list is empty
-  ///
-  /// - Returns: The data value contained in the deleted node.
-  @discardableResult public func removeLast() -> T {
-    assert(!isEmpty)
-    return remove(node: last!)
-  }
-
-  /// Function to remove a node/value at a specific index. Crashes if index is out of bounds (0...self.count)
-  ///
-  /// - Parameter index: Integer value of the index of the node to be removed
-  /// - Returns: The data value contained in the deleted node
-  @discardableResult public func remove(at index: Int) -> T {
-    let node = self.node(at: index)
-    return remove(node: node)
-  }
 }
 
 //: End of the base class declarations & beginning of extensions' declarations:
 
 // MARK: - Extension to enable the standard conversion of a list to String 
 extension LinkedList: CustomStringConvertible {
-  public var description: String {
-    var s = "["
-    var node = head
-    while node != nil {
-      s += "\(node!.value)"
-      node = node!.next
-      if node != nil { s += ", " }
+    public var description: String {
+        var s = "["
+        var node = head
+        while let nd = node {
+            s += "\(nd.value)"
+            node = nd.next
+            if node != nil { s += ", " }
+        }
+        return s + "]"
     }
-    return s + "]"
-  }
 }
 
 // MARK: - Extension to add a 'reverse' function to the list
 extension LinkedList {
-  public func reverse() {
-    var node = head
-    while let currentNode = node {
-      node = currentNode.next
-      swap(&currentNode.next, &currentNode.previous)
-      head = currentNode
+    public func reverse() {
+        var node = head
+        while let currentNode = node {
+            node = currentNode.next
+            swap(&currentNode.next, &currentNode.previous)
+            head = currentNode
+        }
     }
-  }
 }
 
 // MARK: - An extension with an implementation of 'map' & 'filter' functions
 extension LinkedList {
-  public func map<U>(transform: (T) -> U) -> LinkedList<U> {
-    let result = LinkedList<U>()
-    var node = head
-    while node != nil {
-      result.append(transform(node!.value))
-      node = node!.next
+    public func map<U>(transform: (T) -> U) -> LinkedList<U> {
+        let result = LinkedList<U>()
+        var node = head
+        while let nd = node {
+            result.append(transform(nd.value))
+            node = nd.next
+        }
+        return result
     }
-    return result
-  }
-
-  public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
-    let result = LinkedList<T>()
-    var node = head
-    while node != nil {
-      if predicate(node!.value) {
-        result.append(node!.value)
-      }
-      node = node!.next
+    
+    public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
+        let result = LinkedList<T>()
+        var node = head
+        while let nd = node {
+            if predicate(nd.value) {
+                result.append(nd.value)
+            }
+            node = nd.next
+        }
+        return result
     }
-    return result
-  }
 }
 
 // MARK: - Extension to enable initialization from an Array
 extension LinkedList {
-  convenience init(array: Array<T>) {
-    self.init()
-
-    for element in array {
-      self.append(element)
+    convenience init(array: Array<T>) {
+        self.init()
+        
+        array.forEach { append($0) }
     }
-  }
 }
 
 // MARK: - Extension to enable initialization from an Array Literal
 extension LinkedList: ExpressibleByArrayLiteral {
-  public convenience init(arrayLiteral elements: T...) {
-    self.init()
-
-    for element in elements {
-      self.append(element)
+    public convenience init(arrayLiteral elements: T...) {
+        self.init()
+        
+        elements.forEach { append($0) }
     }
-  }
 }
 
 // MARK: - Collection
-extension LinkedList : Collection {
-  
-  public typealias Index = LinkedListIndex<T>
-  
-  /// The position of the first element in a nonempty collection.
-  ///
-  /// If the collection is empty, `startIndex` is equal to `endIndex`.
-  /// - Complexity: O(1)
-  public var startIndex: Index {
-    get {
-      return LinkedListIndex<T>(node: head, tag: 0)
+extension LinkedList: Collection {
+    
+    public typealias Index = LinkedListIndex<T>
+    
+    /// The position of the first element in a nonempty collection.
+    ///
+    /// If the collection is empty, `startIndex` is equal to `endIndex`.
+    /// - Complexity: O(1)
+    public var startIndex: Index {
+        get {
+            return LinkedListIndex<T>(node: head, tag: 0)
+        }
+    }
+    
+    /// The collection's "past the end" position---that is, the position one
+    /// greater than the last valid subscript argument.
+    /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
+    ///   to the last node in the collection.
+    public var endIndex: Index {
+        get {
+            if let h = self.head {
+                return LinkedListIndex<T>(node: h, tag: count)
+            } else {
+                return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
+            }
+        }
     }
-  }
-  
-  /// The collection's "past the end" position---that is, the position one
-  /// greater than the last valid subscript argument.
-  /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
-  ///   to the last node in the collection.
-  public var endIndex: Index {
-    get {
-      if let h = self.head {
-        return LinkedListIndex<T>(node: h, tag: count)
-      } else {
-        return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
-      }
+    
+    public subscript(position: Index) -> T {
+        get {
+            return position.node!.value
+        }
     }
-  }
-  
-  public subscript(position: Index) -> T {
-    get {
-      return position.node!.value
+    
+    public func index(after idx: Index) -> Index {
+        return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag + 1)
     }
-  }
-  
-  public func index(after idx: Index) -> Index {
-    return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
-  }
 }
 
 // MARK: - Collection Index
 /// Custom index type that contains a reference to the node at index 'tag'
-public struct LinkedListIndex<T> : Comparable {
-  fileprivate let node: LinkedList<T>.LinkedListNode<T>?
-  fileprivate let tag: Int
-  
-  public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
-    return (lhs.tag == rhs.tag)
-  }
-  
-  public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
-    return (lhs.tag < rhs.tag)
-  }
+public struct LinkedListIndex<T>: Comparable {
+    fileprivate let node: LinkedList<T>.LinkedListNode<T>?
+    fileprivate let tag: Int
+    
+    public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+        return (lhs.tag == rhs.tag)
+    }
+    
+    public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+        return (lhs.tag < rhs.tag)
+    }
 }
 //: Ok, now that the declarations are done, let's see our Linked List in action:
 let list = LinkedList<String>()
 list.isEmpty                  // true
-list.first                    // nil
+list.head                    // nil
 list.last                     // nil
 
 list.append("Hello")
 list.isEmpty                  // false
-list.first!.value             // "Hello"
+list.head!.value             // "Hello"
 list.last!.value              // "Hello"
 list.count                    // 1
 
 list.append("World")
-list.first!.value             // "Hello"
+list.head!.value             // "Hello"
 list.last!.value              // "World"
 list.count                    // 2
 
-list.first!.previous          // nil
-list.first!.next!.value       // "World"
+list.head!.previous          // nil
+list.head!.next!.value       // "World"
 list.last!.previous!.value    // "Hello"
 list.last!.next               // nil
 
@@ -409,7 +402,7 @@ m    // [8, 6, 5]
 let f = list.filter { s in s.count > 5 }
 f    // [Universe, Swifty]
 
-list.remove(node: list.first!) // "Universe"
+list.remove(node: list.head!) // "Universe"
 list.count                     // 2
 list[0]                        // "Swifty"
 list[1]                        // "Hello"
@@ -464,7 +457,7 @@ let value = collection[index2] // 3
 // Iterating in a for loop, since the Sequence protocol allows this.
 var sum = 0
 for element in collection {
-  sum += element
+    sum += element
 }
 // sum is 15
 
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 569cea82b..285c85588 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -1,29 +1,24 @@
 public final class LinkedList<T> {
-
+    
+    /// Linked List's Node Class Declaration
     public class LinkedListNode<T> {
         var value: T
         var next: LinkedListNode?
         weak var previous: LinkedListNode?
-
+        
         public init(value: T) {
             self.value = value
         }
     }
-
+    
+    /// Typealiasing the node class to increase readability of code
     public typealias Node = LinkedListNode<T>
-
-    fileprivate var head: Node?
-
-    public init() {}
-
-    public var isEmpty: Bool {
-        return head == nil
-    }
-
-    public var first: Node? {
-        return head
-    }
-
+    
+    
+    /// The head of the Linked List
+    private(set) var head: Node?
+    
+    /// Computed property to iterate through the linked list and return the last node in the list (if any)
     public var last: Node? {
         guard var node = head else {
             return nil
@@ -34,7 +29,13 @@ public final class LinkedList<T> {
         }
         return node
     }
-
+    
+    /// Computed property to check if the linked list is empty
+    public var isEmpty: Bool {
+        return head == nil
+    }
+    
+    /// Computed property to iterate through the linked list and return the total number of nodes
     public var count: Int {
         guard var node = head else {
             return 0
@@ -48,9 +49,26 @@ public final class LinkedList<T> {
         return count
     }
     
+    /// Default initializer
+    public init() {}
+    
+    
+    /// Subscript function to return the node at a specific index
+    ///
+    /// - Parameter index: Integer value of the requested value's index
+    public subscript(index: Int) -> T {
+        let node = self.node(at: index)
+        return node.value
+    }
+    
+    /// Function to return the node at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameter index: Integer value of the node's index to be returned
+    /// - Returns: LinkedListNode
     public func node(at index: Int) -> Node {
         assert(head != nil, "List is empty")
         assert(index >= 0, "index must be greater than 0")
+        
         if index == 0 {
             return head!
         } else {
@@ -66,17 +84,18 @@ public final class LinkedList<T> {
             return node!
         }
     }
-
-    public subscript(index: Int) -> T {
-        let node = self.node(at: index)
-        return node.value
-    }
-
+    
+    /// Append a value to the end of the list
+    ///
+    /// - Parameter value: The data value to be appended
     public func append(_ value: T) {
         let newNode = Node(value: value)
-        self.append(newNode)
+        append(newNode)
     }
-
+    
+    /// Append a copy of a LinkedListNode to the end of the list.
+    ///
+    /// - Parameter node: The node containing the value to be appended
     public func append(_ node: Node) {
         let newNode = node
         if let lastNode = last {
@@ -86,27 +105,40 @@ public final class LinkedList<T> {
             head = newNode
         }
     }
-
+    
+    /// Append a copy of a LinkedList to the end of the list.
+    ///
+    /// - Parameter list: The list to be copied and appended.
     public func append(_ list: LinkedList) {
         var nodeToCopy = list.head
         while let node = nodeToCopy {
-            self.append(node.value)
+            append(node.value)
             nodeToCopy = node.next
         }
     }
-
+    
+    /// Insert a value at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - value: The data value to be inserted
+    ///   - index: Integer value of the index to be insterted at
     public func insert(_ value: T, at index: Int) {
         let newNode = Node(value: value)
-        self.insert(newNode, at: index)
+        insert(newNode, at: index)
     }
-
+    
+    /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - node: The node containing the value to be inserted
+    ///   - index: Integer value of the index to be inserted at
     public func insert(_ newNode: Node, at index: Int) {
         if index == 0 {
             newNode.next = head
             head?.previous = newNode
             head = newNode
         } else {
-            let prev = node(at: index-1)
+            let prev = node(at: index - 1)
             let next = prev.next
             newNode.previous = prev
             newNode.next = next
@@ -115,14 +147,19 @@ public final class LinkedList<T> {
         }
     }
     
+    /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameters:
+    ///   - list: The LinkedList to be copied and inserted
+    ///   - index: Integer value of the index to be inserted at
     public func insert(_ list: LinkedList, at index: Int) {
-        if list.isEmpty { return }
+        guard !list.isEmpty else { return }
         
         if index == 0 {
             list.last?.next = head
             head = list.head
         } else {
-            let prev = self.node(at: index-1)
+            let prev = node(at: index - 1)
             let next = prev.next
             
             prev.next = list.head
@@ -133,50 +170,66 @@ public final class LinkedList<T> {
         }
     }
     
+    /// Function to remove all nodes/value from the list
     public func removeAll() {
         head = nil
     }
-
+    
+    /// Function to remove a specific node.
+    ///
+    /// - Parameter node: The node to be deleted
+    /// - Returns: The data value contained in the deleted node.
     @discardableResult public func remove(node: Node) -> T {
         let prev = node.previous
         let next = node.next
-
+        
         if let prev = prev {
             prev.next = next
         } else {
             head = next
         }
         next?.previous = prev
-
+        
         node.previous = nil
         node.next = nil
         return node.value
     }
-
+    
+    /// Function to remove the last node/value in the list. Crashes if the list is empty
+    ///
+    /// - Returns: The data value contained in the deleted node.
     @discardableResult public func removeLast() -> T {
         assert(!isEmpty)
         return remove(node: last!)
     }
-
+    
+    /// Function to remove a node/value at a specific index. Crashes if index is out of bounds (0...self.count)
+    ///
+    /// - Parameter index: Integer value of the index of the node to be removed
+    /// - Returns: The data value contained in the deleted node
     @discardableResult public func remove(at index: Int) -> T {
         let node = self.node(at: index)
         return remove(node: node)
     }
 }
 
+//: End of the base class declarations & beginning of extensions' declarations:
+
+// MARK: - Extension to enable the standard conversion of a list to String
 extension LinkedList: CustomStringConvertible {
     public var description: String {
         var s = "["
         var node = head
-        while node != nil {
-            s += "\(node!.value)"
-            node = node!.next
+        while let nd = node {
+            s += "\(nd.value)"
+            node = nd.next
             if node != nil { s += ", " }
         }
         return s + "]"
     }
 }
 
+// MARK: - Extension to add a 'reverse' function to the list
 extension LinkedList {
     public func reverse() {
         var node = head
@@ -188,99 +241,101 @@ extension LinkedList {
     }
 }
 
+// MARK: - An extension with an implementation of 'map' & 'filter' functions
 extension LinkedList {
     public func map<U>(transform: (T) -> U) -> LinkedList<U> {
         let result = LinkedList<U>()
         var node = head
-        while node != nil {
-            result.append(transform(node!.value))
-            node = node!.next
+        while let nd = node {
+            result.append(transform(nd.value))
+            node = nd.next
         }
         return result
     }
-
+    
     public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
         let result = LinkedList<T>()
         var node = head
-        while node != nil {
-            if predicate(node!.value) {
-                result.append(node!.value)
+        while let nd = node {
+            if predicate(nd.value) {
+                result.append(nd.value)
             }
-            node = node!.next
+            node = nd.next
         }
         return result
     }
 }
 
+// MARK: - Extension to enable initialization from an Array
 extension LinkedList {
     convenience init(array: Array<T>) {
         self.init()
-
-        for element in array {
-            self.append(element)
-        }
+        
+        array.forEach { append($0) }
     }
 }
 
+// MARK: - Extension to enable initialization from an Array Literal
 extension LinkedList: ExpressibleByArrayLiteral {
-  public convenience init(arrayLiteral elements: T...) {
-    self.init()
-
-    for element in elements {
-      self.append(element)
+    public convenience init(arrayLiteral elements: T...) {
+        self.init()
+        
+        elements.forEach { append($0) }
     }
-  }
 }
 
-extension LinkedList : Collection {
-  
-  public typealias Index = LinkedListIndex<T>
-  
-  /// The position of the first element in a nonempty collection.
-  ///
-  /// If the collection is empty, `startIndex` is equal to `endIndex`.
-  /// - Complexity: O(1)
-  public var startIndex: Index {
-    get {
-      return LinkedListIndex<T>(node: head, tag: 0)
+// MARK: - Collection
+extension LinkedList: Collection {
+    
+    public typealias Index = LinkedListIndex<T>
+    
+    /// The position of the first element in a nonempty collection.
+    ///
+    /// If the collection is empty, `startIndex` is equal to `endIndex`.
+    /// - Complexity: O(1)
+    public var startIndex: Index {
+        get {
+            return LinkedListIndex<T>(node: head, tag: 0)
+        }
+    }
+    
+    /// The collection's "past the end" position---that is, the position one
+    /// greater than the last valid subscript argument.
+    /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
+    ///   to the last node in the collection.
+    public var endIndex: Index {
+        get {
+            if let h = self.head {
+                return LinkedListIndex<T>(node: h, tag: count)
+            } else {
+                return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
+            }
+        }
     }
-  }
-  
-  /// The collection's "past the end" position---that is, the position one
-  /// greater than the last valid subscript argument.
-  /// - Complexity: O(n), where n is the number of elements in the list. This can be improved by keeping a reference
-  ///   to the last node in the collection.
-  public var endIndex: Index {
-    get {
-      if let h = self.head {
-        return LinkedListIndex<T>(node: h, tag: count)
-      } else {
-        return LinkedListIndex<T>(node: nil, tag: startIndex.tag)
-      }
+    
+    public subscript(position: Index) -> T {
+        get {
+            return position.node!.value
+        }
     }
-  }
-  
-  public subscript(position: Index) -> T {
-    get {
-      return position.node!.value
+    
+    public func index(after idx: Index) -> Index {
+        return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag + 1)
     }
-  }
-  
-  public func index(after idx: Index) -> Index {
-    return LinkedListIndex<T>(node: idx.node?.next, tag: idx.tag+1)
-  }
 }
 
+// MARK: - Collection Index
 /// Custom index type that contains a reference to the node at index 'tag'
-public struct LinkedListIndex<T> : Comparable {
-  fileprivate let node: LinkedList<T>.LinkedListNode<T>?
-  fileprivate let tag: Int
-  
-  public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
-    return (lhs.tag == rhs.tag)
-  }
-  
-  public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
-    return (lhs.tag < rhs.tag)
-  }
+public struct LinkedListIndex<T>: Comparable {
+    fileprivate let node: LinkedList<T>.LinkedListNode<T>?
+    fileprivate let tag: Int
+    
+    public static func==<T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+        return (lhs.tag == rhs.tag)
+    }
+    
+    public static func< <T>(lhs: LinkedListIndex<T>, rhs: LinkedListIndex<T>) -> Bool {
+        return (lhs.tag < rhs.tag)
+    }
 }
+
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 9ed698849..b16af05ba 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -1,339 +1,339 @@
 import XCTest
 
 class LinkedListTest: XCTestCase {
-  let numbers = [8, 2, 10, 9, 7, 5]
-
-  fileprivate func buildList() -> LinkedList<Int> {
-    let list = LinkedList<Int>()
-    for number in numbers {
-      list.append(number)
+    let numbers = [8, 2, 10, 9, 7, 5]
+    
+    fileprivate func buildList() -> LinkedList<Int> {
+        let list = LinkedList<Int>()
+        for number in numbers {
+            list.append(number)
+        }
+        return list
     }
-    return list
-  }
-
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-
-  func testEmptyList() {
-    let list = LinkedList<Int>()
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    XCTAssertFalse(list.isEmpty)
-    XCTAssertEqual(list.count, 1)
-
-    XCTAssertNotNil(list.first)
-    XCTAssertNil(list.first!.previous)
-    XCTAssertNil(list.first!.next)
-    XCTAssertEqual(list.first!.value, 123)
-
-    XCTAssertNotNil(list.last)
-    XCTAssertNil(list.last!.previous)
-    XCTAssertNil(list.last!.next)
-    XCTAssertEqual(list.last!.value, 123)
-
-    XCTAssertTrue(list.first === list.last)
-  }
-
-  func testListWithTwoElements() {
-    let list = LinkedList<Int>()
-    list.append(123)
-    list.append(456)
-
-    XCTAssertEqual(list.count, 2)
-
-    XCTAssertNotNil(list.first)
-    XCTAssertEqual(list.first!.value, 123)
-
-    XCTAssertNotNil(list.last)
-    XCTAssertEqual(list.last!.value, 456)
-
-    XCTAssertTrue(list.first !== list.last)
-
-    XCTAssertNil(list.first!.previous)
-    XCTAssertTrue(list.first!.next === list.last)
-    XCTAssertTrue(list.last!.previous === list.first)
-    XCTAssertNil(list.last!.next)
-  }
-
-  func testListWithThreeElements() {
-    let list = LinkedList<Int>()
-    list.append(123)
-    list.append(456)
-    list.append(789)
-
-    XCTAssertEqual(list.count, 3)
-
-    XCTAssertNotNil(list.first)
-    XCTAssertEqual(list.first!.value, 123)
-
-    let second = list.first!.next
-    XCTAssertNotNil(second)
-    XCTAssertEqual(second!.value, 456)
-
-    XCTAssertNotNil(list.last)
-    XCTAssertEqual(list.last!.value, 789)
-
-    XCTAssertNil(list.first!.previous)
-    XCTAssertTrue(list.first!.next === second)
-    XCTAssertTrue(second!.previous === list.first)
-    XCTAssertTrue(second!.next === list.last)
-    XCTAssertTrue(list.last!.previous === second)
-    XCTAssertNil(list.last!.next)
-  }
-
-  func testNodeAtIndexInListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    let node = list.node(at: 0)
-    XCTAssertNotNil(node)
-    XCTAssertEqual(node.value, 123)
-    XCTAssertTrue(node === list.first)
-  }
-
-  func testNodeAtIndex() {
-    let list = buildList()
-
-    let nodeCount = list.count
-    XCTAssertEqual(nodeCount, numbers.count)
-
-    let first = list.node(at: 0)
-    XCTAssertNotNil(first)
-    XCTAssertTrue(first === list.first)
-    XCTAssertEqual(first.value, numbers[0])
-
-    let last = list.node(at: nodeCount - 1)
-    XCTAssertNotNil(last)
-    XCTAssertTrue(last === list.last)
-    XCTAssertEqual(last.value, numbers[nodeCount - 1])
-
-    for i in 0..<nodeCount {
-      let node = list.node(at: i)
-      XCTAssertNotNil(node)
-      XCTAssertEqual(node.value, numbers[i])
+    
+    func testSwift4() {
+        // last checked with Xcode 9.0b4
+        #if swift(>=4.0)
+            print("Hello, Swift 4!")
+        #endif
     }
-  }
-
-  func testSubscript() {
-    let list = buildList()
-    for i in 0 ..< list.count {
-      XCTAssertEqual(list[i], numbers[i])
+    
+    func testEmptyList() {
+        let list = LinkedList<Int>()
+        XCTAssertTrue(list.isEmpty)
+        XCTAssertEqual(list.count, 0)
+        XCTAssertNil(list.first)
+        XCTAssertNil(list.last)
+    }
+    
+    func testListWithOneElement() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        
+        XCTAssertFalse(list.isEmpty)
+        XCTAssertEqual(list.count, 1)
+        
+        XCTAssertNotNil(list.first)
+        XCTAssertNil(list.head!.previous)
+        XCTAssertNil(list.head!.next)
+        XCTAssertEqual(list.head!.value, 123)
+        
+        XCTAssertNotNil(list.last)
+        XCTAssertNil(list.last!.previous)
+        XCTAssertNil(list.last!.next)
+        XCTAssertEqual(list.last!.value, 123)
+        
+        XCTAssertTrue(list.head === list.last)
+    }
+    
+    func testListWithTwoElements() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        list.append(456)
+        
+        XCTAssertEqual(list.count, 2)
+        
+        XCTAssertNotNil(list.first)
+        XCTAssertEqual(list.head!.value, 123)
+        
+        XCTAssertNotNil(list.last)
+        XCTAssertEqual(list.last!.value, 456)
+        
+        XCTAssertTrue(list.head !== list.last)
+        
+        XCTAssertNil(list.head!.previous)
+        XCTAssertTrue(list.head!.next === list.last)
+        XCTAssertTrue(list.last!.previous === list.head)
+        XCTAssertNil(list.last!.next)
+    }
+    
+    func testListWithThreeElements() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        list.append(456)
+        list.append(789)
+        
+        XCTAssertEqual(list.count, 3)
+        
+        XCTAssertNotNil(list.first)
+        XCTAssertEqual(list.head!.value, 123)
+        
+        let second = list.head!.next
+        XCTAssertNotNil(second)
+        XCTAssertEqual(second!.value, 456)
+        
+        XCTAssertNotNil(list.last)
+        XCTAssertEqual(list.last!.value, 789)
+        
+        XCTAssertNil(list.head!.previous)
+        XCTAssertTrue(list.head!.next === second)
+        XCTAssertTrue(second!.previous === list.head)
+        XCTAssertTrue(second!.next === list.last)
+        XCTAssertTrue(list.last!.previous === second)
+        XCTAssertNil(list.last!.next)
+    }
+    
+    func testNodeAtIndexInListWithOneElement() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        
+        let node = list.node(at: 0)
+        XCTAssertNotNil(node)
+        XCTAssertEqual(node.value, 123)
+        XCTAssertTrue(node === list.head)
+    }
+    
+    func testNodeAtIndex() {
+        let list = buildList()
+        
+        let nodeCount = list.count
+        XCTAssertEqual(nodeCount, numbers.count)
+        
+        let first = list.node(at: 0)
+        XCTAssertNotNil(first)
+        XCTAssertTrue(first === list.head)
+        XCTAssertEqual(first.value, numbers[0])
+        
+        let last = list.node(at: nodeCount - 1)
+        XCTAssertNotNil(last)
+        XCTAssertTrue(last === list.last)
+        XCTAssertEqual(last.value, numbers[nodeCount - 1])
+        
+        for i in 0..<nodeCount {
+            let node = list.node(at: i)
+            XCTAssertNotNil(node)
+            XCTAssertEqual(node.value, numbers[i])
+        }
+    }
+    
+    func testSubscript() {
+        let list = buildList()
+        for i in 0 ..< list.count {
+            XCTAssertEqual(list[i], numbers[i])
+        }
+    }
+    
+    func testInsertAtIndexInEmptyList() {
+        let list = LinkedList<Int>()
+        list.insert(123, at: 0)
+        
+        XCTAssertFalse(list.isEmpty)
+        XCTAssertEqual(list.count, 1)
+        
+        let node = list.node(at: 0)
+        XCTAssertNotNil(node)
+        XCTAssertEqual(node.value, 123)
+    }
+    
+    func testInsertAtIndex() {
+        let list = buildList()
+        let prev = list.node(at: 2)
+        let next = list.node(at: 3)
+        let nodeCount = list.count
+        
+        list.insert(444, at: 3)
+        
+        let node = list.node(at: 3)
+        XCTAssertNotNil(node)
+        XCTAssertEqual(node.value, 444)
+        XCTAssertEqual(nodeCount + 1, list.count)
+        
+        XCTAssertFalse(prev === node)
+        XCTAssertFalse(next === node)
+        XCTAssertTrue(prev.next === node)
+        XCTAssertTrue(next.previous === node)
     }
-  }
-
-  func testInsertAtIndexInEmptyList() {
-    let list = LinkedList<Int>()
-    list.insert(123, at: 0)
-
-    XCTAssertFalse(list.isEmpty)
-    XCTAssertEqual(list.count, 1)
-
-    let node = list.node(at: 0)
-    XCTAssertNotNil(node)
-    XCTAssertEqual(node.value, 123)
-  }
-
-  func testInsertAtIndex() {
-    let list = buildList()
-    let prev = list.node(at: 2)
-    let next = list.node(at: 3)
-    let nodeCount = list.count
-
-    list.insert(444, at: 3)
-
-    let node = list.node(at: 3)
-    XCTAssertNotNil(node)
-    XCTAssertEqual(node.value, 444)
-    XCTAssertEqual(nodeCount + 1, list.count)
-
-    XCTAssertFalse(prev === node)
-    XCTAssertFalse(next === node)
-    XCTAssertTrue(prev.next === node)
-    XCTAssertTrue(next.previous === node)
-  }
-
-  func testInsertListAtIndex() {
-    let list = buildList()
-    let list2 = LinkedList<Int>()
-    list2.append(99)
-    list2.append(102)
-    list.insert(list2, at: 2)
-    XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(at: 1).value, 2)
-    XCTAssertEqual(list.node(at: 2).value, 99)
-    XCTAssertEqual(list.node(at: 3).value, 102)
-    XCTAssertEqual(list.node(at: 4).value, 10)
-  }
-
-  func testInsertListAtFirstIndex() {
-    let list = buildList()
-    let list2 = LinkedList<Int>()
-    list2.append(99)
-    list2.append(102)
-    list.insert(list2, at: 0)
-    XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(at: 0).value, 99)
-    XCTAssertEqual(list.node(at: 1).value, 102)
-    XCTAssertEqual(list.node(at: 2).value, 8)
-  }
-
-  func testInsertListAtLastIndex() {
-    let list = buildList()
-    let list2 = LinkedList<Int>()
-    list2.append(99)
-    list2.append(102)
-    list.insert(list2, at: list.count)
-    XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(at: 5).value, 5)
-    XCTAssertEqual(list.node(at: 6).value, 99)
-    XCTAssertEqual(list.node(at: 7).value, 102)
-  }
-
-  func testAppendList() {
-    let list = buildList()
-    let list2 = LinkedList<Int>()
-    list2.append(99)
-    list2.append(102)
-    list.append(list2)
-    XCTAssertTrue(list.count == 8)
-    XCTAssertEqual(list.node(at: 5).value, 5)
-    XCTAssertEqual(list.node(at: 6).value, 99)
-    XCTAssertEqual(list.node(at: 7).value, 102)
-  }
-
-  func testAppendListToEmptyList() {
-    let list = LinkedList<Int>()
-    let list2 = LinkedList<Int>()
-    list2.append(5)
-    list2.append(10)
-    list.append(list2)
-    XCTAssertTrue(list.count == 2)
-    XCTAssertEqual(list.node(at: 0).value, 5)
-    XCTAssertEqual(list.node(at: 1).value, 10)
-  }
-
-  func testRemoveAtIndexOnListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    let value = list.remove(at: 0)
-    XCTAssertEqual(value, 123)
-
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testRemoveAtIndex() {
-    let list = buildList()
-    let prev = list.node(at: 2)
-    let next = list.node(at: 3)
-    let nodeCount = list.count
-
-    list.insert(444, at: 3)
-
-    let value = list.remove(at: 3)
-    XCTAssertEqual(value, 444)
-
-    let node = list.node(at: 3)
-    XCTAssertTrue(next === node)
-    XCTAssertTrue(prev.next === node)
-    XCTAssertTrue(node.previous === prev)
-    XCTAssertEqual(nodeCount, list.count)
-  }
-
-  func testRemoveLastOnListWithOneElement() {
-    let list = LinkedList<Int>()
-    list.append(123)
-
-    let value = list.removeLast()
-    XCTAssertEqual(value, 123)
-
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testRemoveLast() {
-    let list = buildList()
-    let last = list.last
-    let prev = last!.previous
-    let nodeCount = list.count
-
-    let value = list.removeLast()
-    XCTAssertEqual(value, 5)
-
-    XCTAssertNil(last!.previous)
-    XCTAssertNil(last!.next)
-
-    XCTAssertNil(prev!.next)
-    XCTAssertTrue(list.last === prev)
-    XCTAssertEqual(nodeCount - 1, list.count)
-  }
-
-  func testRemoveAll() {
-    let list = buildList()
-    list.removeAll()
-    XCTAssertTrue(list.isEmpty)
-    XCTAssertEqual(list.count, 0)
-    XCTAssertNil(list.first)
-    XCTAssertNil(list.last)
-  }
-
-  func testReverseLinkedList() {
-    let list = buildList()
-    let first = list.first
-    let last = list.last
-    let nodeCount = list.count
-
-    list.reverse()
-
-    XCTAssertTrue(first === list.last)
-    XCTAssertTrue(last === list.first)
-    XCTAssertEqual(nodeCount, list.count)
-  }
-
-  func testArrayLiteralInitTypeInfer() {
-    let arrayLiteralInitInfer: LinkedList = [1.0, 2.0, 3.0]
-
-    XCTAssertEqual(arrayLiteralInitInfer.count, 3)
-    XCTAssertEqual(arrayLiteralInitInfer.first?.value, 1.0)
-    XCTAssertEqual(arrayLiteralInitInfer.last?.value, 3.0)
-    XCTAssertEqual(arrayLiteralInitInfer[1], 2.0)
-    XCTAssertEqual(arrayLiteralInitInfer.removeLast(), 3.0)
-    XCTAssertEqual(arrayLiteralInitInfer.count, 2)
-  }
-
-  func testArrayLiteralInitExplicit() {
-    let arrayLiteralInitExplicit: LinkedList<Int> = [1, 2, 3]
-
-    XCTAssertEqual(arrayLiteralInitExplicit.count, 3)
-    XCTAssertEqual(arrayLiteralInitExplicit.first?.value, 1)
-    XCTAssertEqual(arrayLiteralInitExplicit.last?.value, 3)
-    XCTAssertEqual(arrayLiteralInitExplicit[1], 2)
-    XCTAssertEqual(arrayLiteralInitExplicit.removeLast(), 3)
-    XCTAssertEqual(arrayLiteralInitExplicit.count, 2)
-  }
-  
-  func testConformanceToCollectionProtocol() {
-    let collection: LinkedList<Int> = [1, 2, 3, 4, 5]
-    let index2 = collection.index(collection.startIndex, offsetBy: 2)
-    let value = collection[index2]
     
-    XCTAssertTrue(value == 3)
-  }
+    func testInsertListAtIndex() {
+        let list = buildList()
+        let list2 = LinkedList<Int>()
+        list2.append(99)
+        list2.append(102)
+        list.insert(list2, at: 2)
+        XCTAssertTrue(list.count == 8)
+        XCTAssertEqual(list.node(at: 1).value, 2)
+        XCTAssertEqual(list.node(at: 2).value, 99)
+        XCTAssertEqual(list.node(at: 3).value, 102)
+        XCTAssertEqual(list.node(at: 4).value, 10)
+    }
+    
+    func testInsertListAtFirstIndex() {
+        let list = buildList()
+        let list2 = LinkedList<Int>()
+        list2.append(99)
+        list2.append(102)
+        list.insert(list2, at: 0)
+        XCTAssertTrue(list.count == 8)
+        XCTAssertEqual(list.node(at: 0).value, 99)
+        XCTAssertEqual(list.node(at: 1).value, 102)
+        XCTAssertEqual(list.node(at: 2).value, 8)
+    }
+    
+    func testInsertListAtLastIndex() {
+        let list = buildList()
+        let list2 = LinkedList<Int>()
+        list2.append(99)
+        list2.append(102)
+        list.insert(list2, at: list.count)
+        XCTAssertTrue(list.count == 8)
+        XCTAssertEqual(list.node(at: 5).value, 5)
+        XCTAssertEqual(list.node(at: 6).value, 99)
+        XCTAssertEqual(list.node(at: 7).value, 102)
+    }
+    
+    func testAppendList() {
+        let list = buildList()
+        let list2 = LinkedList<Int>()
+        list2.append(99)
+        list2.append(102)
+        list.append(list2)
+        XCTAssertTrue(list.count == 8)
+        XCTAssertEqual(list.node(at: 5).value, 5)
+        XCTAssertEqual(list.node(at: 6).value, 99)
+        XCTAssertEqual(list.node(at: 7).value, 102)
+    }
+    
+    func testAppendListToEmptyList() {
+        let list = LinkedList<Int>()
+        let list2 = LinkedList<Int>()
+        list2.append(5)
+        list2.append(10)
+        list.append(list2)
+        XCTAssertTrue(list.count == 2)
+        XCTAssertEqual(list.node(at: 0).value, 5)
+        XCTAssertEqual(list.node(at: 1).value, 10)
+    }
+    
+    func testRemoveAtIndexOnListWithOneElement() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        
+        let value = list.remove(at: 0)
+        XCTAssertEqual(value, 123)
+        
+        XCTAssertTrue(list.isEmpty)
+        XCTAssertEqual(list.count, 0)
+        XCTAssertNil(list.first)
+        XCTAssertNil(list.last)
+    }
+    
+    func testRemoveAtIndex() {
+        let list = buildList()
+        let prev = list.node(at: 2)
+        let next = list.node(at: 3)
+        let nodeCount = list.count
+        
+        list.insert(444, at: 3)
+        
+        let value = list.remove(at: 3)
+        XCTAssertEqual(value, 444)
+        
+        let node = list.node(at: 3)
+        XCTAssertTrue(next === node)
+        XCTAssertTrue(prev.next === node)
+        XCTAssertTrue(node.previous === prev)
+        XCTAssertEqual(nodeCount, list.count)
+    }
+    
+    func testRemoveLastOnListWithOneElement() {
+        let list = LinkedList<Int>()
+        list.append(123)
+        
+        let value = list.removeLast()
+        XCTAssertEqual(value, 123)
+        
+        XCTAssertTrue(list.isEmpty)
+        XCTAssertEqual(list.count, 0)
+        XCTAssertNil(list.first)
+        XCTAssertNil(list.last)
+    }
+    
+    func testRemoveLast() {
+        let list = buildList()
+        let last = list.last
+        let prev = last!.previous
+        let nodeCount = list.count
+        
+        let value = list.removeLast()
+        XCTAssertEqual(value, 5)
+        
+        XCTAssertNil(last!.previous)
+        XCTAssertNil(last!.next)
+        
+        XCTAssertNil(prev!.next)
+        XCTAssertTrue(list.last === prev)
+        XCTAssertEqual(nodeCount - 1, list.count)
+    }
+    
+    func testRemoveAll() {
+        let list = buildList()
+        list.removeAll()
+        XCTAssertTrue(list.isEmpty)
+        XCTAssertEqual(list.count, 0)
+        XCTAssertNil(list.first)
+        XCTAssertNil(list.last)
+    }
+    
+    func testReverseLinkedList() {
+        let list = buildList()
+        let first = list.head
+        let last = list.last
+        let nodeCount = list.count
+        
+        list.reverse()
+        
+        XCTAssertTrue(first === list.last)
+        XCTAssertTrue(last === list.head)
+        XCTAssertEqual(nodeCount, list.count)
+    }
+    
+    func testArrayLiteralInitTypeInfer() {
+        let arrayLiteralInitInfer: LinkedList = [1.0, 2.0, 3.0]
+        
+        XCTAssertEqual(arrayLiteralInitInfer.count, 3)
+        XCTAssertEqual(arrayLiteralInitInfer.head?.value, 1.0)
+        XCTAssertEqual(arrayLiteralInitInfer.last?.value, 3.0)
+        XCTAssertEqual(arrayLiteralInitInfer[1], 2.0)
+        XCTAssertEqual(arrayLiteralInitInfer.removeLast(), 3.0)
+        XCTAssertEqual(arrayLiteralInitInfer.count, 2)
+    }
+    
+    func testArrayLiteralInitExplicit() {
+        let arrayLiteralInitExplicit: LinkedList<Int> = [1, 2, 3]
+        
+        XCTAssertEqual(arrayLiteralInitExplicit.count, 3)
+        XCTAssertEqual(arrayLiteralInitExplicit.head?.value, 1)
+        XCTAssertEqual(arrayLiteralInitExplicit.last?.value, 3)
+        XCTAssertEqual(arrayLiteralInitExplicit[1], 2)
+        XCTAssertEqual(arrayLiteralInitExplicit.removeLast(), 3)
+        XCTAssertEqual(arrayLiteralInitExplicit.count, 2)
+    }
+    
+    func testConformanceToCollectionProtocol() {
+        let collection: LinkedList<Int> = [1, 2, 3, 4, 5]
+        let index2 = collection.index(collection.startIndex, offsetBy: 2)
+        let value = collection[index2]
+        
+        XCTAssertTrue(value == 3)
+    }
 }

From 444b993d571d955b36aa0aa64cd03dd1a31761b3 Mon Sep 17 00:00:00 2001
From: Bill Barbour <bill.barbour@oracle.com>
Date: Tue, 8 May 2018 15:24:10 -0400
Subject: [PATCH 380/643] Updated number to be prime; and Swift 4 update

---
 Rabin-Karp/Rabin-Karp.playground/Contents.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Rabin-Karp/Rabin-Karp.playground/Contents.swift b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
index 739b74e2a..40cd176a6 100644
--- a/Rabin-Karp/Rabin-Karp.playground/Contents.swift
+++ b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
@@ -8,7 +8,7 @@ print("Hello, Swift 4!")
 import UIKit
 
 struct Constants {
-    static let hashMultiplier = 69069
+    static let hashMultiplier = 69061
 }
 
 precedencegroup PowerPrecedence { higherThan: MultiplicationPrecedence }
@@ -30,8 +30,8 @@ extension Character {
 // Find first position of pattern in the text using Rabin Karp algorithm
 public func search(text: String, pattern: String) -> Int {
     // convert to array of ints
-    let patternArray = pattern.flatMap { $0.asInt }
-    let textArray = text.flatMap { $0.asInt }
+    let patternArray = pattern.compactMap { $0.asInt }
+    let textArray = text.compactMap { $0.asInt }
 
     if textArray.count < patternArray.count {
         return -1

From 65e3d4d18485598b030068be0ab4b82c1c21b823 Mon Sep 17 00:00:00 2001
From: Ruslan Skorb <ruslan@rsk-lab.com>
Date: Mon, 30 Apr 2018 10:11:12 +0300
Subject: [PATCH 381/643] [Binary Search Tree] [enum] Fix `height`.

https://en.wikipedia.org/wiki/Tree_\(data_structure\)\#Terminology
---
 Binary Search Tree/README.markdown                   | 4 ++--
 Binary Search Tree/Solution 2/BinarySearchTree.swift | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 30dc8d922..0b382f204 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -615,8 +615,8 @@ This implementation is recursive, and each case of the enum will be treated diff
 
   public var height: Int {
     switch self {
-    case .Empty: return 0
-    case .Leaf: return 1
+    case .Empty: return -1
+    case .Leaf: return 0
     case let .Node(left, _, right): return 1 + max(left.height, right.height)
     }
   }
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.swift b/Binary Search Tree/Solution 2/BinarySearchTree.swift
index 272b86368..23b1c8aca 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.swift	
@@ -20,8 +20,8 @@ public enum BinarySearchTree<T: Comparable> {
   /* Distance of this node to its lowest leaf. Performance: O(n). */
   public var height: Int {
     switch self {
-    case .empty: return 0
-    case .leaf: return 1
+    case .empty: return -1
+    case .leaf: return 0
     case let .node(left, _, right): return 1 + max(left.height, right.height)
     }
   }

From 9b7ecd6a47e4522ae0b48ae4d938dc97a31f8a22 Mon Sep 17 00:00:00 2001
From: Ahmed Nader <ahmednader111@gmail.com>
Date: Fri, 11 May 2018 23:23:20 +0200
Subject: [PATCH 382/643] Closest Pair of points algorithm

---
 .../ClosestPair.playground/Contents.swift     | 224 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/IDEWorkspaceChecks.plist     |   8 +
 .../UserInterfaceState.xcuserstate            | Bin 0 -> 10014 bytes
 .../Images/1200px-Closest_pair_of_points.png  | Bin 0 -> 17683 bytes
 Closest Pair/Images/Case.png                  | Bin 0 -> 17660 bytes
 Closest Pair/Images/Strip.png                 | Bin 0 -> 18824 bytes
 Closest Pair/README.markdown                  |  88 +++++++
 9 files changed, 331 insertions(+)
 create mode 100644 Closest Pair/ClosestPair.playground/Contents.swift
 create mode 100644 Closest Pair/ClosestPair.playground/contents.xcplayground
 create mode 100644 Closest Pair/ClosestPair.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Closest Pair/ClosestPair.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Closest Pair/ClosestPair.playground/playground.xcworkspace/xcuserdata/admin.xcuserdatad/UserInterfaceState.xcuserstate
 create mode 100644 Closest Pair/Images/1200px-Closest_pair_of_points.png
 create mode 100644 Closest Pair/Images/Case.png
 create mode 100644 Closest Pair/Images/Strip.png
 create mode 100644 Closest Pair/README.markdown

diff --git a/Closest Pair/ClosestPair.playground/Contents.swift b/Closest Pair/ClosestPair.playground/Contents.swift
new file mode 100644
index 000000000..c11c1770b
--- /dev/null
+++ b/Closest Pair/ClosestPair.playground/Contents.swift	
@@ -0,0 +1,224 @@
+//Created by Ahmed Nader (github: AhmedNader42) on 4/4/18.
+
+func ClosestPairOf(points: [Point]) -> (minimum:Double, firstPoint:Point, secondPoint:Point) {
+    var innerPoints = mergeSort(points, sortAccording : true)
+    let result = ClosestPair(&innerPoints, innerPoints.count)
+    return (result.minValue, result.firstPoint, result.secondPoint)
+}
+
+func ClosestPair(_ p : inout [Point],_ n : Int) -> (minValue: Double,firstPoint: Point,secondPoint: Point)
+{
+    // Brute force if only 3 points (To end recursion)
+    if n <= 3
+    {
+        var i=0, j = i+1
+        var minDist = Double.infinity
+        var newFirst:Point? = nil
+        var newSecond:Point? = nil
+        while i<n
+        {
+            j = i+1
+            while j < n
+            {
+                if dist(p[i], p[j]) <= minDist
+                {
+                    minDist = dist(p[i], p[j])
+                    newFirst = p[i]
+                    newSecond = p[j]
+                }
+                j+=1
+            }
+            i+=1
+            
+        }
+        return (minDist, newFirst ?? Point(0,0), newSecond ?? Point(0,0))
+    }
+    
+    
+    
+    let mid:Int = n/2
+    let line:Double = (p[mid].x + p[mid+1].x)/2
+    
+    // Split the array.
+    var leftSide = [Point]()
+    var rightSide = [Point]()
+    for s in 0..<mid
+    {
+        leftSide.append(p[s])
+    }
+    for s in mid..<p.count
+    {
+        rightSide.append(p[s])
+    }
+    
+    
+    // Recurse on the left and right part of the array.
+    let valueFromLeft = ClosestPair(&leftSide, mid)
+    let minLeft:Double = valueFromLeft.minValue
+    let valueFromRight = ClosestPair(&rightSide, n-mid)
+    let minRight:Double = valueFromRight.minValue
+    
+    // Starting current min must be the largest possible to not affect the real calculations.
+    var min = Double.infinity
+    
+    var first:Point
+    var second:Point
+    
+    // Get the minimum between the left and the right.
+    if minLeft < minRight {
+        min = minLeft
+        first = valueFromLeft.firstPoint
+        second = valueFromLeft.secondPoint
+    }
+    else {
+        min = minRight
+        first = valueFromRight.firstPoint
+        second = valueFromRight.secondPoint
+    }
+    
+    // Sort the array according to Y.
+    p = mergeSort(p, sortAccording: false)
+    
+    
+    var strip = [Point]()
+    
+    // If the value is less than the min distance away in X from the line then take it into consideration.
+    var i=0, j = 0
+    while i<n
+    {
+        if abs(p[i].x - line) < min
+        {
+            strip.append(p[i])
+            j+=1
+        }
+        i+=1
+    }
+    
+    
+    i=0
+    var x = i+1
+    var temp = min
+    var tempFirst:Point = Point(0,0)
+    var tempSecond:Point = Point(0,0)
+    // Get the values between the points in the strip but only if it is less min dist in Y.
+    while i<j
+    {
+        x = i+1
+        while x < j
+        {
+            if (abs(strip[x].y - strip[i].y)) > min { break }
+            if dist(strip[i], strip[x]) < temp
+            {
+                temp = dist(strip[i], strip[x])
+                tempFirst = strip[i]
+                tempSecond = strip[x]
+            }
+            x+=1
+        }
+        i+=1
+    }
+    
+    if temp < min
+    {
+        min = temp;
+        first = tempFirst
+        second = tempSecond
+    }
+    return (min, first, second)
+}
+
+
+
+
+// MergeSort the array (Taken from Swift Algorithms Club with
+// minor addition)
+// sortAccodrding : true -> x, false -> y.
+func mergeSort(_ array: [Point], sortAccording : Bool) -> [Point] {
+    guard array.count > 1 else { return array }
+    let middleIndex = array.count / 2
+    let leftArray = mergeSort(Array(array[0..<middleIndex]), sortAccording: sortAccording)
+    let rightArray = mergeSort(Array(array[middleIndex..<array.count]), sortAccording: sortAccording)
+    return merge(leftPile: leftArray, rightPile: rightArray, sortAccording: sortAccording)
+}
+
+
+private func merge(leftPile: [Point], rightPile: [Point], sortAccording: Bool) -> [Point] {
+    
+    var compare : (Point, Point) -> Bool
+    
+    // Choose to compare with X or Y.
+    if sortAccording
+    {
+        compare = { p1,p2 in
+            return p1.x < p2.x
+        }
+    }
+    else
+    {
+        compare = { p1, p2 in
+            return p1.y < p2.y
+        }
+    }
+    
+    var leftIndex = 0
+    var rightIndex = 0
+    var orderedPile = [Point]()
+    if orderedPile.capacity < leftPile.count + rightPile.count {
+        orderedPile.reserveCapacity(leftPile.count + rightPile.count)
+    }
+    
+    while true {
+        guard leftIndex < leftPile.endIndex else {
+            orderedPile.append(contentsOf: rightPile[rightIndex..<rightPile.endIndex])
+            break
+        }
+        guard rightIndex < rightPile.endIndex else {
+            orderedPile.append(contentsOf: leftPile[leftIndex..<leftPile.endIndex])
+            break
+        }
+        
+        if compare(leftPile[leftIndex], rightPile[rightIndex]) {
+            orderedPile.append(leftPile[leftIndex])
+            leftIndex += 1
+        } else {
+            orderedPile.append(rightPile[rightIndex])
+            rightIndex += 1
+        }
+    }
+    return orderedPile
+}
+
+
+// Structure to represent a point.
+struct Point
+{
+    var x: Double
+    var y: Double
+    
+    init(_ x:Double,_ y:Double) {
+        self.x = x
+        self.y = y
+    }
+}
+// Get the distance between two points a, b.
+func dist(_ a: Point,_ b: Point) -> Double
+{
+    let equation:Double = (((a.x-b.x)*(a.x-b.x))) + (((a.y-b.y)*(a.y-b.y)))
+    return equation.squareRoot()
+}
+
+
+var a = Point(0,2)
+var b = Point(6,67)
+var c = Point(43,71)
+var d = Point(1000,1000)
+var e = Point(39,107)
+var f = Point(2000,2000)
+var g = Point(3000,3000)
+var h = Point(4000,4000)
+
+
+var points = [a,b,c,d,e,f,g,h]
+let endResult = ClosestPairOf(points: points)
+print("Minimum Distance : \(endResult.minimum), The two points : (\(endResult.firstPoint.x ),\(endResult.firstPoint.y)), (\(endResult.secondPoint.x),\(endResult.secondPoint.y))")
+
diff --git a/Closest Pair/ClosestPair.playground/contents.xcplayground b/Closest Pair/ClosestPair.playground/contents.xcplayground
new file mode 100644
index 000000000..a93d4844a
--- /dev/null
+++ b/Closest Pair/ClosestPair.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='macos' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Closest Pair/ClosestPair.playground/playground.xcworkspace/contents.xcworkspacedata b/Closest Pair/ClosestPair.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Closest Pair/ClosestPair.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Closest Pair/ClosestPair.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Closest Pair/ClosestPair.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Closest Pair/ClosestPair.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Closest Pair/ClosestPair.playground/playground.xcworkspace/xcuserdata/admin.xcuserdatad/UserInterfaceState.xcuserstate b/Closest Pair/ClosestPair.playground/playground.xcworkspace/xcuserdata/admin.xcuserdatad/UserInterfaceState.xcuserstate
new file mode 100644
index 0000000000000000000000000000000000000000..82b1303405d67c83db2a30dbba741c883e40fdff
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diff --git a/Closest Pair/README.markdown b/Closest Pair/README.markdown
new file mode 100644
index 000000000..57786c7ff
--- /dev/null
+++ b/Closest Pair/README.markdown	
@@ -0,0 +1,88 @@
+# ClosestPair
+
+Closest Pair is an algorithm that finds the closest pair of a given array of points By utilizing the Divide and Conquer methodology of solving problems so that it reaches the correct solution with O(nlogn) complexity.
+
+![Given points and we're required to find the two red ones](../Closest Pair/Images/1200px-Closest_pair_of_points.png)
+
+As we see in the above image there are an array of points and we need to find the closest two, But how do we do that without having to compare each two points which results in a whopping O(n^2) complexity?
+
+Here is the main algorithm (Steps) we'll follow.
+
+- Sort the array according to their position on the X-axis so that they are sorted in the array as they are naturally in math.
+
+```swift
+var innerPoints = mergeSort(points, sortAccording : true)
+```
+
+- Divide the points into two arrays Left, Right and keep dividing until you reach to only having 3 points in your array.
+
+- The base case is you have less than 3 points compare those against each other (Brute force) then return the minimum distance you found and the two points.
+
+- Now we get the first observation in the below image, There could be 2 points both very close to each other and indeed those two are the closest pair but since our algorithm so far divides from the middle
+ 
+```swift
+let line:Double = (p[mid].x + p[mid+1].x)/2
+```
+
+and just recursively calls itself until it reaches the base case we don't detect those points.
+
+![ Points lying near the division line](../Closest Pair/Images/Case.png)
+
+- To solve this we start by sorting the array on the Y-axis to get the points in their natural order and then we start getting the difference between the X position of the point and the line we drew to divide and if it is less than the min we got so far from the recursion we add it to the strip 
+
+```swift
+var strip = [Point]()   
+var i=0, j = 0
+while i<n
+{
+	if abs(p[i].x - line) < min
+	{
+		strip.append(p[i])
+		j+=1
+	}
+	i+=1
+}
+```
+
+- After you insert the points that could possibly give you a better min distance we get to another observation in the image below.
+
+![The strip with 4 points shown](..//Closest Pair/Images/Strip.png)
+
+- Searching the strip is a brute force loop (But doesn't that just destroy everything we did? You ask) but it has an advantage it could never iterate on more than 8 points (worst case).
+
+- The reason is that the strip is constructed as a rectangle with sides of length = min that we got from the recursion and we ignore any points that have a Y difference bigger than min distance so to be able to place them ALL inside the rectangle with these conditions they'll have to be in the shape above with each one of them EXACTLY min distance away from the other which gives us 4 possible points for each one and 8 in total.
+
+```swift
+while i<j
+    {
+        x = i+1
+        while x < j
+        {
+            if (abs(strip[x].y - strip[i].y)) > min { break }
+            if dist(strip[i], strip[x]) < temp
+            {
+                temp = dist(strip[i], strip[x])
+                tempFirst = strip[i]
+                tempSecond = strip[x]
+            }
+            x+=1
+        }
+        i+=1
+    }
+```
+
+- Of course not every time you end up with the same shape but this is the worst case and it's rare to happen so in reality you end up with far less points valid for comparison and this is why the algorithm gets performance in addition to the sorting tricks we did.
+
+- Compare the points in the strip and if you find a smaller distance replace the current one with it.
+
+
+So this is the rundown of how the algorithm works and you could see the fun little math tricks used to optimize this and we end up with O(nlogn) complexity mainly because of the sorting.
+
+
+## See also
+
+See the playground to play around with the implementation of the algorithm
+
+[Wikipedia](https://en.wikipedia.org/wiki/Closest_pair_of_points_problem)
+
+*Written for Swift Algorithm Club by [Ahmed Nader](https://github.com/ahmednader42)*

From 9b0a3c517d1e26ced6bd506b42af25bf2b99d287 Mon Sep 17 00:00:00 2001
From: Ahmed Nader <ahmednader111@gmail.com>
Date: Fri, 11 May 2018 23:24:32 +0200
Subject: [PATCH 383/643] Images

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

diff --git a/Closest Pair/README.markdown b/Closest Pair/README.markdown
index 57786c7ff..35ea15653 100644
--- a/Closest Pair/README.markdown	
+++ b/Closest Pair/README.markdown	
@@ -2,7 +2,7 @@
 
 Closest Pair is an algorithm that finds the closest pair of a given array of points By utilizing the Divide and Conquer methodology of solving problems so that it reaches the correct solution with O(nlogn) complexity.
 
-![Given points and we're required to find the two red ones](../Closest Pair/Images/1200px-Closest_pair_of_points.png)
+![Given points and we're required to find the two red ones](Closest Pair/Images/1200px-Closest_pair_of_points.png)
 
 As we see in the above image there are an array of points and we need to find the closest two, But how do we do that without having to compare each two points which results in a whopping O(n^2) complexity?
 
@@ -26,7 +26,7 @@ let line:Double = (p[mid].x + p[mid+1].x)/2
 
 and just recursively calls itself until it reaches the base case we don't detect those points.
 
-![ Points lying near the division line](../Closest Pair/Images/Case.png)
+![ Points lying near the division line](Closest Pair/Images/Case.png)
 
 - To solve this we start by sorting the array on the Y-axis to get the points in their natural order and then we start getting the difference between the X position of the point and the line we drew to divide and if it is less than the min we got so far from the recursion we add it to the strip 
 
@@ -46,7 +46,7 @@ while i<n
 
 - After you insert the points that could possibly give you a better min distance we get to another observation in the image below.
 
-![The strip with 4 points shown](..//Closest Pair/Images/Strip.png)
+![The strip with 4 points shown](Closest Pair/Images/Strip.png)
 
 - Searching the strip is a brute force loop (But doesn't that just destroy everything we did? You ask) but it has an advantage it could never iterate on more than 8 points (worst case).
 

From 4de991b7a6d0984eadd77341a6ea83ca4dafe2f7 Mon Sep 17 00:00:00 2001
From: Ahmed Nader <ahmednader111@gmail.com>
Date: Fri, 11 May 2018 23:26:43 +0200
Subject: [PATCH 384/643] Update README.markdown

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

diff --git a/Closest Pair/README.markdown b/Closest Pair/README.markdown
index 35ea15653..3ce08dd49 100644
--- a/Closest Pair/README.markdown	
+++ b/Closest Pair/README.markdown	
@@ -2,7 +2,7 @@
 
 Closest Pair is an algorithm that finds the closest pair of a given array of points By utilizing the Divide and Conquer methodology of solving problems so that it reaches the correct solution with O(nlogn) complexity.
 
-![Given points and we're required to find the two red ones](Closest Pair/Images/1200px-Closest_pair_of_points.png)
+![Given points and we're required to find the two red ones](../Closest\ Pair/Images/1200px-Closest_pair_of_points.png)
 
 As we see in the above image there are an array of points and we need to find the closest two, But how do we do that without having to compare each two points which results in a whopping O(n^2) complexity?
 

From a018f72d59fd33a3990f343725dfd823f84a0340 Mon Sep 17 00:00:00 2001
From: Ahmed Nader <ahmednader111@gmail.com>
Date: Fri, 11 May 2018 23:30:35 +0200
Subject: [PATCH 385/643] Update README.markdown

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

diff --git a/Closest Pair/README.markdown b/Closest Pair/README.markdown
index 3ce08dd49..5224bcef4 100644
--- a/Closest Pair/README.markdown	
+++ b/Closest Pair/README.markdown	
@@ -2,7 +2,7 @@
 
 Closest Pair is an algorithm that finds the closest pair of a given array of points By utilizing the Divide and Conquer methodology of solving problems so that it reaches the correct solution with O(nlogn) complexity.
 
-![Given points and we're required to find the two red ones](../Closest\ Pair/Images/1200px-Closest_pair_of_points.png)
+![Given points and we're required to find the two red ones](../Images/1200px-Closest_pair_of_points.png)
 
 As we see in the above image there are an array of points and we need to find the closest two, But how do we do that without having to compare each two points which results in a whopping O(n^2) complexity?
 

From 4174a840c332ee07f875306b098f710c0e3601bb Mon Sep 17 00:00:00 2001
From: Ahmed Nader <ahmednader111@gmail.com>
Date: Fri, 11 May 2018 23:31:20 +0200
Subject: [PATCH 386/643] Update README.markdown

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

diff --git a/Closest Pair/README.markdown b/Closest Pair/README.markdown
index 5224bcef4..a4de4a28b 100644
--- a/Closest Pair/README.markdown	
+++ b/Closest Pair/README.markdown	
@@ -2,7 +2,7 @@
 
 Closest Pair is an algorithm that finds the closest pair of a given array of points By utilizing the Divide and Conquer methodology of solving problems so that it reaches the correct solution with O(nlogn) complexity.
 
-![Given points and we're required to find the two red ones](../Images/1200px-Closest_pair_of_points.png)
+![Given points and we're required to find the two red ones](Images/1200px-Closest_pair_of_points.png)
 
 As we see in the above image there are an array of points and we need to find the closest two, But how do we do that without having to compare each two points which results in a whopping O(n^2) complexity?
 
@@ -26,7 +26,7 @@ let line:Double = (p[mid].x + p[mid+1].x)/2
 
 and just recursively calls itself until it reaches the base case we don't detect those points.
 
-![ Points lying near the division line](Closest Pair/Images/Case.png)
+![ Points lying near the division line](Images/Case.png)
 
 - To solve this we start by sorting the array on the Y-axis to get the points in their natural order and then we start getting the difference between the X position of the point and the line we drew to divide and if it is less than the min we got so far from the recursion we add it to the strip 
 
@@ -46,7 +46,7 @@ while i<n
 
 - After you insert the points that could possibly give you a better min distance we get to another observation in the image below.
 
-![The strip with 4 points shown](Closest Pair/Images/Strip.png)
+![The strip with 4 points shown](Images/Strip.png)
 
 - Searching the strip is a brute force loop (But doesn't that just destroy everything we did? You ask) but it has an advantage it could never iterate on more than 8 points (worst case).
 

From bcb037d505afcc80a245db5ea43041b63a1d7c3f Mon Sep 17 00:00:00 2001
From: Abbey Jackson <abbey@abbeyjackson.ca>
Date: Tue, 22 May 2018 11:43:26 -0700
Subject: [PATCH 387/643] Fixed broken link

Link to shortest path example was broken
---
 Breadth-First Search/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index b2298822f..097f4278d 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -151,7 +151,7 @@ This will output: `["a", "b", "c", "d", "e", "f", "g", "h"]`
 
 Breadth-first search can be used to solve many problems. A small selection:
 
-* Computing the [shortest path](../Shortest%20Path/) between a source node and each of the other nodes (only for unweighted graphs).
+* Computing the [shortest path](../Shortest%20Path%20(Unweighted)/) between a source node and each of the other nodes (only for unweighted graphs).
 * Calculating the [minimum spanning tree](../Minimum%20Spanning%20Tree%20(Unweighted)/) on an unweighted graph.
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*

From bcdd28236d981f8763fdda9ebe41b699ea624579 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 4 Jun 2018 21:01:09 -0700
Subject: [PATCH 388/643] Updates maintainer list.

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

diff --git a/README.markdown b/README.markdown
index 919f1b67f..f5fc4247a 100644
--- a/README.markdown
+++ b/README.markdown
@@ -225,7 +225,7 @@ You can find the book on the [raywenderlich.com store](https://store.raywenderli
 
 The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://github.com/hollance).
 
-It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), [Kelvin Lau](https://github.com/kelvinlauKL) and [Ross O'brien](https://www.raywenderlich.com/u/narrativium).
+It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), and [Kelvin Lau](https://github.com/kelvinlauKL).
 
 The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](.github/CONTRIBUTING.md)? :]
 

From f4afbabffe020f8c81dc84a74e90e49f5ef90061 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Fri, 8 Jun 2018 01:47:25 -0700
Subject: [PATCH 389/643] Refactors first blurb.

---
 Myers Difference Algorithm/README.md | 10 ++++------
 1 file changed, 4 insertions(+), 6 deletions(-)

diff --git a/Myers Difference Algorithm/README.md b/Myers Difference Algorithm/README.md
index e6137e8ce..6be30ecda 100644
--- a/Myers Difference Algorithm/README.md	
+++ b/Myers Difference Algorithm/README.md	
@@ -1,15 +1,13 @@
 #  Myers Difference Algorithm
 
-Myers Difference Algorithm is an algorithm that finds a longest common subsequence(LCS) or shortest edit scripts(SES) of two sequences. MDA can accomplish this in O(ND) time, where N is the sum of the lengths of the two sequences. The common subsequence of two sequences is the sequence of elements that appear in the same order in both sequences. 
-
-For example, let's assume you have two arrays:
+Myers Difference Algorithm(MDA) is an algorithm that finds a longest common subsequence(LCS) or shortest edit scripts(SES) of two sequences. The common subsequence of two sequences is the sequence of elements that appear in the same order in both sequences. For example, let's assume you have two arrays:
 
 ```
-A = [1, 2, 3]
-B = [2, 3, 4]
+let firstArray = [1, 2, 3]
+let secondArray = [2, 3, 4]
 ```
 
-The common subsequences of these two arrays are `[2]`, and `[2,3]`. The longest common sequence in this case is `[2,3]`.
+The common subsequences of these two arrays are `[2]`, and `[2, 3]`. The longest common sequence in this case is `[2, 3]`. MDA can accomplish this in O(ND) time, where N is the sum of the lengths of the two sequences. 
 
 ## Finding the length of the Longest Common Subsequence with Myers Algorithm on Edit Graph
 

From 66db524690e73646b183eb28d3bb4ae77490b80b Mon Sep 17 00:00:00 2001
From: Ta-Cuong Nguyen <cuongnt04230@gmail.com>
Date: Sat, 9 Jun 2018 11:19:49 +0700
Subject: [PATCH 390/643] Update README.markdown

Update document for Hoare's partitioning scheme
---
 Quicksort/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index b8a908985..a9356f921 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -288,7 +288,7 @@ func partitionHoare<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
     repeat { i += 1 } while a[i] < pivot
     
     if i < j {
-      swap(&a[i], &a[j])
+      a.swapAt(i, j)
     } else {
       return j
     }

From 22e44960a9e5f8ec0010c8ed3a3cb0d3c23c724e Mon Sep 17 00:00:00 2001
From: augustoavelino <augusto_avelino@icloud.com>
Date: Mon, 11 Jun 2018 16:29:05 -0300
Subject: [PATCH 391/643] Fixed issue in LinkedList insert(_:, at:) method
 where next?.previous was referencing next itself.

---
 Linked List/LinkedList.playground/Contents.swift | 2 +-
 Linked List/LinkedList.swift                     | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 4b58bb65e..cfa3a8b45 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -176,7 +176,7 @@ public final class LinkedList<T> {
             list.head?.previous = prev
             
             list.last?.next = next
-            next?.previous = list.last?.next
+            next?.previous = list.last
         }
     }
     
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 285c85588..7c2cbb3b1 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -166,7 +166,7 @@ public final class LinkedList<T> {
             list.head?.previous = prev
             
             list.last?.next = next
-            next?.previous = list.last?.next
+            next?.previous = list.last
         }
     }
     

From 4528471976af69ce2e98dada083bd32b3fe9fd7f Mon Sep 17 00:00:00 2001
From: Denis Litvin <den.litvinn@gmail.com>
Date: Thu, 14 Jun 2018 14:23:11 +0300
Subject: [PATCH 392/643] Fix

---
 Rabin-Karp/Rabin-Karp.playground/Contents.swift           | 6 +++---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 11 insertions(+), 3 deletions(-)
 create mode 100644 Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Rabin-Karp/Rabin-Karp.playground/Contents.swift b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
index 739b74e2a..f5d4137c4 100644
--- a/Rabin-Karp/Rabin-Karp.playground/Contents.swift
+++ b/Rabin-Karp/Rabin-Karp.playground/Contents.swift
@@ -1,6 +1,6 @@
 //: Taking our rabin-karp algorithm for a walk
 
-// last checked with Xcode 9.0b4
+// last checked with Xcode 9.4
 #if swift(>=4.0)
 print("Hello, Swift 4!")
 #endif
@@ -30,8 +30,8 @@ extension Character {
 // Find first position of pattern in the text using Rabin Karp algorithm
 public func search(text: String, pattern: String) -> Int {
     // convert to array of ints
-    let patternArray = pattern.flatMap { $0.asInt }
-    let textArray = text.flatMap { $0.asInt }
+    let patternArray = pattern.compactMap { $0.asInt }
+    let textArray = text.compactMap { $0.asInt }
 
     if textArray.count < patternArray.count {
         return -1
diff --git a/Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Rabin-Karp/Rabin-Karp.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From bf51c93414900e44baffbb2c7bd57aca76b22909 Mon Sep 17 00:00:00 2001
From: Milad Taghavi <mitghi@me.com>
Date: Wed, 20 Jun 2018 12:34:14 +0200
Subject: [PATCH 393/643] Add Simulated annealing to README

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

diff --git a/README.markdown b/README.markdown
index f5fc4247a..90b310752 100644
--- a/README.markdown
+++ b/README.markdown
@@ -119,6 +119,7 @@ Bad sorting algorithms (don't use these!):
 - Neural Networks
 - PageRank
 - [Naive Bayes Classifier](Naive%20Bayes%20Classifier/)
+- [Simulated annealing](Simulated%20annealing/). Probabilistic technique for approximating the global maxima in a (often discrete) large search space.
 
 ## Data structures
 

From 88f75eb2d05ff4a0e9ba18d4824158f7e9b1e84e Mon Sep 17 00:00:00 2001
From: Weslie <iwesliechen@gmail.com>
Date: Mon, 30 Jul 2018 11:22:18 +0800
Subject: [PATCH 394/643] [Swift 4 Update]add parentheses

Single argument function types require parentheses
---
 Binary Tree/BinaryTree.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Binary Tree/BinaryTree.swift b/Binary Tree/BinaryTree.swift
index 102f23e06..6146880b4 100644
--- a/Binary Tree/BinaryTree.swift	
+++ b/Binary Tree/BinaryTree.swift	
@@ -29,7 +29,7 @@ extension BinaryTree: CustomStringConvertible {
 }
 
 extension BinaryTree {
-  public func traverseInOrder(process: T -> Void) {
+  public func traverseInOrder(process: (T) -> Void) {
     if case let .node(left, value, right) = self {
       left.traverseInOrder(process: process)
       process(value)
@@ -37,7 +37,7 @@ extension BinaryTree {
     }
   }
 
-  public func traversePreOrder(process: T -> Void) {
+  public func traversePreOrder(process: (T) -> Void) {
     if case let .node(left, value, right) = self {
       process(value)
       left.traversePreOrder(process: process)
@@ -45,7 +45,7 @@ extension BinaryTree {
     }
   }
 
-  public func traversePostOrder(process: T -> Void) {
+  public func traversePostOrder(process: (T) -> Void) {
     if case let .node(left, value, right) = self {
       left.traversePostOrder(process: process)
       right.traversePostOrder(process: process)

From 2b932ac83689f2e29e387a763f104e47aa6ae1c2 Mon Sep 17 00:00:00 2001
From: Jen <Jchangho@grubhub.com>
Date: Fri, 3 Aug 2018 13:57:38 -0400
Subject: [PATCH 395/643] Fixes Issue#371: Simulated Annealing demo crashes

---
 Simulated annealing/simann.swift         | 16 ++---------
 Simulated annealing/simann_example.swift | 36 +++++++-----------------
 2 files changed, 13 insertions(+), 39 deletions(-)

diff --git a/Simulated annealing/simann.swift b/Simulated annealing/simann.swift
index 8adfbf817..5dc624d04 100644
--- a/Simulated annealing/simann.swift	
+++ b/Simulated annealing/simann.swift	
@@ -22,16 +22,6 @@
   import Glibc
 #endif
 
-public extension Double {  
-  public static func random(_ lower: Double, _ upper: Double) -> Double {
-    #if os(OSX)
-      return (Double(arc4random()) / 0xFFFFFFFF) * (upper - lower) + lower
-    #elseif os(Linux)
-      return (Double(random()) / 0xFFFFFFFF) * (upper - lower) + lower
-    #endif
-  }
-}
-
 protocol Clonable {
   init(current: Self)
 }
@@ -85,13 +75,13 @@ func SimulatedAnnealing<T: SAObject>(initial: T, temperature: Double, coolingRat
   
   while temp > 1 {    
     let newSolution: T = currentSolution.clone()
-    let pos1: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
-    let pos2: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    let pos1: Int = Int.random(in: 0 ..< newSolution.count)
+    let pos2: Int = Int.random(in: 0 ..< newSolution.count)
     newSolution.randSwap(a: pos1, b: pos2)
     let currentEnergy: Double  = currentSolution.currentEnergy()
     let newEnergy: Double = newSolution.currentEnergy()
     
-    if acceptance(currentEnergy, newEnergy, temp) > Double.random(0, 1) {
+    if acceptance(currentEnergy, newEnergy, temp) > Double.random(in: 0 ..< 1) {
       currentSolution = newSolution.clone()
     }
     if currentSolution.currentEnergy() < bestSolution.currentEnergy() {
diff --git a/Simulated annealing/simann_example.swift b/Simulated annealing/simann_example.swift
index a0dfaa19a..0e07e0024 100644
--- a/Simulated annealing/simann_example.swift	
+++ b/Simulated annealing/simann_example.swift	
@@ -18,21 +18,11 @@
 
 #if os(OSX)
   import Foundation
+  import Cocoa
 #elseif os(Linux)
   import Glibc
 #endif
 
-public extension Double {
-  
-  public static func random(_ lower: Double, _ upper: Double) -> Double {
-    #if os(OSX)
-      return (Double(arc4random()) / 0xFFFFFFFF) * (upper - lower) + lower
-    #elseif os(Linux)
-      return (Double(random()) / 0xFFFFFFFF) * (upper - lower) + lower
-    #endif
-  }
-}
-
 protocol Clonable {
   init(current: Self)
 }
@@ -96,8 +86,8 @@ extension Point {
   static func <-> (left: Point, right: Point) -> Double {
     let xDistance = (left.x - right.x)
     let yDistance = (left.y - right.y)
-    
-    return Double(sqrt(Double((xDistance * xDistance) + (yDistance * yDistance))))
+
+    return Double((xDistance * xDistance) + (yDistance * yDistance)).squareRoot()
   }
 }
 
@@ -128,15 +118,6 @@ extension Tour {
     self[a] = cpos2
     self[b] = cpos1
   }
-  
-  func shuffle() {
-    for i in stride(from:  self.count - 1, through: 1, by: -1) {
-      let j = Int(arc4random()) % (i + 1)
-      if i != j {
-        swap(&self.tour[i], &self.tour[j])
-      }
-    }
-  }
 
   func currentEnergy() -> Double {
     if self.energy == 0 {
@@ -155,7 +136,10 @@ extension Tour {
     }
     return self.energy
   }
-  
+
+  func shuffle() {
+    self.shuffle()
+  }
 }
 
 // MARK: - subscript to manipulate elements of Tour.
@@ -180,13 +164,13 @@ func SimulatedAnnealing<T: SAObject>(initial: T, temperature: Double, coolingRat
   
   while temp > 1 {
     let newSolution: T = currentSolution.clone()
-    let pos1: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
-    let pos2: Int = Int(arc4random_uniform(UInt32(newSolution.count)))
+    let pos1: Int = Int.random(in: 0 ..< newSolution.count)
+    let pos2: Int = Int.random(in: 0 ..< newSolution.count)
     newSolution.randSwap(a: pos1, b: pos2)
     let currentEnergy: Double  = currentSolution.currentEnergy()
     let newEnergy: Double = newSolution.currentEnergy()
     
-    if acceptance(currentEnergy, newEnergy, temp) > Double.random(0, 1) {
+    if acceptance(currentEnergy, newEnergy, temp) > Double.random(in: 0 ..< 1) {
       currentSolution = newSolution.clone()
     }
     if currentSolution.currentEnergy() < bestSolution.currentEnergy() {

From 8e207266be665e4a7426db2a7c30bc79bda93274 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Mon, 10 Sep 2018 20:51:35 -0700
Subject: [PATCH 396/643] Update maintainers list.

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

diff --git a/README.markdown b/README.markdown
index 90b310752..7d3156ae7 100644
--- a/README.markdown
+++ b/README.markdown
@@ -226,7 +226,7 @@ You can find the book on the [raywenderlich.com store](https://store.raywenderli
 
 The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://github.com/hollance).
 
-It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), and [Kelvin Lau](https://github.com/kelvinlauKL).
+It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), [Kelvin Lau](https://github.com/kelvinlauKL), and [Richard Ash](https://github.com/richard-ash).
 
 The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](.github/CONTRIBUTING.md)? :]
 

From 380bfc27b505ab14abd336465cade9d6ede57c57 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Wed, 26 Sep 2018 00:10:14 -0700
Subject: [PATCH 397/643] Update README.markdown

Fix contributors link to point to the raywenderlich repo instead of the rwenderlich fork
---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 7d3156ae7..ff8bfe778 100644
--- a/README.markdown
+++ b/README.markdown
@@ -228,7 +228,7 @@ The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://
 
 It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka), [Kelvin Lau](https://github.com/kelvinlauKL), and [Richard Ash](https://github.com/richard-ash).
 
-The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/rwenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](.github/CONTRIBUTING.md)? :]
+The Swift Algorithm Club is a collaborative effort from the [most algorithmic members](https://github.com/raywenderlich/swift-algorithm-club/graphs/contributors) of the [raywenderlich.com](https://www.raywenderlich.com) community. We're always looking for help - why not [join the club](.github/CONTRIBUTING.md)? :]
 
 ## License
 

From b3ba0467b88ff48eaf6221482b05ca8908ab5bb0 Mon Sep 17 00:00:00 2001
From: Andy Ron <randy.njfu@gmail.com>
Date: Thu, 27 Sep 2018 17:34:40 +0800
Subject: [PATCH 398/643] Update README.md

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

diff --git a/B-Tree/README.md b/B-Tree/README.md
index f6924aadc..10a06853e 100644
--- a/B-Tree/README.md
+++ b/B-Tree/README.md
@@ -133,7 +133,7 @@ Else:
 
 ![Moving Key](Images/MovingKey.png)
 
-####Merging two nodes
+#### Merging two nodes
 
 Let's say we want to merge the child `c1` at index `i` in its parent's children array.
 

From 106b65ede0191fe7c6ba78fcd519334b7ea56e6a Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 15:33:23 -0300
Subject: [PATCH 399/643] addition of Bubble sort algorithm

---
 .../MyPlayground.playground/Contents.swift    | 27 ++++++++++++
 .../Sources/BubbleSort.swift                  | 42 +++++++++++++++++++
 .../contents.xcplayground                     |  4 ++
 .../contents.xcworkspacedata                  |  7 ++++
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++
 6 files changed, 96 insertions(+)
 create mode 100644 Bubble Sort/MyPlayground.playground/Contents.swift
 create mode 100644 Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift
 create mode 100644 Bubble Sort/MyPlayground.playground/contents.xcplayground
 create mode 100644 Bubble Sort/MyPlayground.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Bubble Sort/MyPlayground.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bubble Sort/MyPlayground.playground/Contents.swift b/Bubble Sort/MyPlayground.playground/Contents.swift
new file mode 100644
index 000000000..d0cf07ab3
--- /dev/null
+++ b/Bubble Sort/MyPlayground.playground/Contents.swift	
@@ -0,0 +1,27 @@
+import Foundation
+
+public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
+    var array = elements
+    
+    for i in 0..<array.count {
+        for j in i+1..<array.count {
+            if array[j] < array[i] {
+                let tmp = array[i]
+                array[i] = array[j]
+                array[j] = tmp
+            }
+        }
+    }
+    
+    return array
+}
+
+
+var array = [Int]()
+
+for _ in 0...10 {
+    array.append(Int.random(in: 0...500))
+}
+
+print("before:",array)
+print("after:",BubbleSort(array))
diff --git a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift
new file mode 100644
index 000000000..8f1ec80f8
--- /dev/null
+++ b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
@@ -0,0 +1,42 @@
+//
+//  BubbleSort.swift
+//
+//  Created by Julio Brazil on 1/10/18.
+//
+//  Permission is hereby granted, free of charge, to any person obtaining a copy of this software and
+//  associated documentation files (the "Software"), to deal in the Software without restriction, including
+//  without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//  copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the
+//  following conditions:
+//
+//  The above copyright notice and this permission notice shall be included in all copies or substantial
+//  portions of the Software.
+//
+//  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
+//  LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO
+//  EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
+//  AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
+//  OR OTHER DEALINGS IN THE SOFTWARE.
+//
+
+import Foundation
+
+/// Performs the bubble sort algorithm in the array
+///
+/// - Parameter elements: the array to be sorted
+/// - Returns: an array with the same elements but in order
+public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
+    var array = elements
+    
+    for i in 0..<array.count {
+        for j in i+1..<array.count {
+            if array[j] < array[i] {
+                let tmp = array[i]
+                array[i] = array[j]
+                array[j] = tmp
+            }
+        }
+    }
+    
+    return array
+}
diff --git a/Bubble Sort/MyPlayground.playground/contents.xcplayground b/Bubble Sort/MyPlayground.playground/contents.xcplayground
new file mode 100644
index 000000000..9f5f2f40c
--- /dev/null
+++ b/Bubble Sort/MyPlayground.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Bubble Sort/MyPlayground.playground/playground.xcworkspace/contents.xcworkspacedata b/Bubble Sort/MyPlayground.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Bubble Sort/MyPlayground.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Bubble Sort/MyPlayground.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bubble Sort/MyPlayground.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bubble Sort/MyPlayground.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 44711ad86d5fafc1f6db40bfebb5e94e277377b1 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 15:57:40 -0300
Subject: [PATCH 400/643] addition of convenience method

---
 .../SelectionSort.playground/Contents.swift   |  1 +
 .../Sources/SelectionSort.swift               | 26 +++++++++++++++++--
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++++
 3 files changed, 33 insertions(+), 2 deletions(-)
 create mode 100644 Selection Sort/SelectionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Selection Sort/SelectionSort.playground/Contents.swift b/Selection Sort/SelectionSort.playground/Contents.swift
index e0bfdf259..b16dadb8d 100644
--- a/Selection Sort/SelectionSort.playground/Contents.swift	
+++ b/Selection Sort/SelectionSort.playground/Contents.swift	
@@ -6,5 +6,6 @@ print("Hello, Swift 4!")
 #endif
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
+selectionSort(list)
 selectionSort(list, <)
 selectionSort(list, >)
diff --git a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
index 3015fde9b..b0bdfab55 100644
--- a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
@@ -1,4 +1,4 @@
-public func selectionSort<T: Comparable>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+public func selectionSort<T: Comparable>(_ array: [T]) -> [T] {
   guard array.count > 1 else { return array }
 
   var a = array
@@ -7,7 +7,7 @@ public func selectionSort<T: Comparable>(_ array: [T], _ isOrderedBefore: (T, T)
     // Find the lowest value in the rest of the array.
     var lowest = x
     for y in x + 1 ..< a.count {
-      if isOrderedBefore(a[y], a[lowest]) {
+      if a[y] < a[lowest] {
         lowest = y
       }
     }
@@ -19,3 +19,25 @@ public func selectionSort<T: Comparable>(_ array: [T], _ isOrderedBefore: (T, T)
   }
   return a
 }
+
+public func selectionSort<T>(_ array: [T], _ isLowerThan: (T, T) -> Bool) -> [T] {
+    guard array.count > 1 else { return array }
+    
+    var a = array
+    for x in 0 ..< a.count - 1 {
+        
+        // Find the lowest value in the rest of the array.
+        var lowest = x
+        for y in x + 1 ..< a.count {
+            if isLowerThan(a[y], a[lowest]) {
+                lowest = y
+            }
+        }
+        
+        // Swap the lowest value with the current array index.
+        if x != lowest {
+            a.swapAt(x, lowest)
+        }
+    }
+    return a
+}
diff --git a/Selection Sort/SelectionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Selection Sort/SelectionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Selection Sort/SelectionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From d078c50bc281d92f0369fe3b6bac5508988e175a Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 16:02:04 -0300
Subject: [PATCH 401/643] addition of function description

---
 .../Sources/SelectionSort.swift                        | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
index b0bdfab55..3a27ef9dd 100644
--- a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
@@ -1,3 +1,7 @@
+/// Performs the Selection sort algorithm on a array
+///
+/// - Parameter array: array of elements that conform to the Comparable protocol
+/// - Returns: an array in ascending order
 public func selectionSort<T: Comparable>(_ array: [T]) -> [T] {
   guard array.count > 1 else { return array }
 
@@ -20,6 +24,12 @@ public func selectionSort<T: Comparable>(_ array: [T]) -> [T] {
   return a
 }
 
+/// Performs the Selection sort algorithm on a array using the provided comparisson method
+///
+/// - Parameters:
+///   - array: array of elements that conform to the Comparable protocol
+///   - isLowerThan: returns true if the two provided elements are in the correct order
+/// - Returns: a sorted array
 public func selectionSort<T>(_ array: [T], _ isLowerThan: (T, T) -> Bool) -> [T] {
     guard array.count > 1 else { return array }
     

From d82954fc2c7533181c72cd800cd892a4bf7ab987 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 19:22:36 -0300
Subject: [PATCH 402/643] added convenience method

---
 .../InsertionSort.playground/Contents.swift   | 35 +++++++++++++------
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 Insertion Sort/InsertionSort.swift            | 14 ++++++++
 3 files changed, 47 insertions(+), 10 deletions(-)
 create mode 100644 Insertion Sort/InsertionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index 91e18640f..6c84a4a3e 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -6,19 +6,34 @@ print("Hello, Swift 4!")
 #endif
 
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
-  var a = array
-  for x in 1..<a.count {
-    var y = x
-    let temp = a[y]
-    while y > 0 && isOrderedBefore(temp, a[y - 1]) {
-      a[y] = a[y - 1]
-      y -= 1
+    var a = array
+    for x in 1..<a.count {
+        var y = x
+        let temp = a[y]
+        while y > 0 && isOrderedBefore(temp, a[y - 1]) {
+            a[y] = a[y - 1]
+            y -= 1
+        }
+        a[y] = temp
     }
-    a[y] = temp
-  }
-  return a
+    return a
+}
+
+func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
+    var a = array
+    for x in 1..<a.count {
+        var y = x
+        let temp = a[y]
+        while y > 0 && temp < a[y - 1] {
+            a[y] = a[y - 1]
+            y -= 1
+        }
+        a[y] = temp
+    }
+    return a
 }
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
+insertionSort(list)
 insertionSort(list, <)
 insertionSort(list, >)
diff --git a/Insertion Sort/InsertionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Insertion Sort/InsertionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Insertion Sort/InsertionSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 5d8a9565b..362c8565a 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -13,3 +13,17 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   }
   return a
 }
+
+func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
+    var a = array
+    for x in 1..<a.count {
+        var y = x
+        let temp = a[y]
+        while y > 0 && temp < a[y - 1] {
+            a[y] = a[y - 1]
+            y -= 1
+        }
+        a[y] = temp
+    }
+    return a
+}

From 06e894bf80c8940fa20db172c291fa9be713350a Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 19:26:55 -0300
Subject: [PATCH 403/643] added primitive documentation

---
 Insertion Sort/InsertionSort.swift                     | 10 ++++++++++
 .../xcshareddata/IDEWorkspaceChecks.plist              |  8 ++++++++
 2 files changed, 18 insertions(+)
 create mode 100644 Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 362c8565a..2d623adc9 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -1,3 +1,9 @@
+/// Performs the Insertion sort algorithm to a given array
+///
+/// - Parameters:
+///   - array: the array of elements to be sorted
+///   - isOrderedBefore: returns true if the elements provided are in the corect order
+/// - Returns: a sorted array containing the same elements
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   guard array.count > 1 else { return array }
 
@@ -14,6 +20,10 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
   return a
 }
 
+/// Performs the Insertion sort algorithm to a given array
+///
+/// - Parameter array: the array to be sorted, conatining elements that conform to the Comparable protocol
+/// - Returns: a sorted array containing the same elements
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
     var a = array
     for x in 1..<a.count {
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Insertion Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 46742c7998828cf4e4ed8a49925bee046c3ae268 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 1 Oct 2018 22:05:20 -0300
Subject: [PATCH 404/643] fixing dumb mistake

---
 .../InsertionSort.playground/Contents.swift    | 18 +++++++++++++++---
 .../contents.xcplayground                      |  2 +-
 Insertion Sort/InsertionSort.swift             |  2 ++
 3 files changed, 18 insertions(+), 4 deletions(-)

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index 6c84a4a3e..9a10ec04a 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -5,7 +5,15 @@
 print("Hello, Swift 4!")
 #endif
 
+/// Performs the Insertion sort algorithm to a given array
+///
+/// - Parameters:
+///   - array: the array of elements to be sorted
+///   - isOrderedBefore: returns true if the elements provided are in the corect order
+/// - Returns: a sorted array containing the same elements
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
+    guard array.count > 1 else { return array }
+    
     var a = array
     for x in 1..<a.count {
         var y = x
@@ -19,6 +27,10 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
     return a
 }
 
+/// Performs the Insertion sort algorithm to a given array
+///
+/// - Parameter array: the array to be sorted, conatining elements that conform to the Comparable protocol
+/// - Returns: a sorted array containing the same elements
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
     var a = array
     for x in 1..<a.count {
@@ -34,6 +46,6 @@ func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
 }
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
-insertionSort(list)
-insertionSort(list, <)
-insertionSort(list, >)
+print(insertionSort(list))
+print(insertionSort(list, <))
+print(insertionSort(list, >))
diff --git a/Insertion Sort/InsertionSort.playground/contents.xcplayground b/Insertion Sort/InsertionSort.playground/contents.xcplayground
index 06828af92..9f9eecc96 100644
--- a/Insertion Sort/InsertionSort.playground/contents.xcplayground	
+++ b/Insertion Sort/InsertionSort.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' executeOnSourceChanges='false'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 2d623adc9..9faf9dc42 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -25,6 +25,8 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 /// - Parameter array: the array to be sorted, conatining elements that conform to the Comparable protocol
 /// - Returns: a sorted array containing the same elements
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
+    guard array.count > 1 else { return array }
+
     var a = array
     for x in 1..<a.count {
         var y = x

From a9b6c5f68e9d7ac0989e6f42c0bd98265740bc36 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Tue, 2 Oct 2018 11:49:32 -0300
Subject: [PATCH 405/643] correction in the algorithm

---
 .../MyPlayground.playground/Contents.swift       | 16 ++++++----------
 .../Sources/BubbleSort.swift                     |  8 ++++----
 2 files changed, 10 insertions(+), 14 deletions(-)

diff --git a/Bubble Sort/MyPlayground.playground/Contents.swift b/Bubble Sort/MyPlayground.playground/Contents.swift
index d0cf07ab3..16466e0bc 100644
--- a/Bubble Sort/MyPlayground.playground/Contents.swift	
+++ b/Bubble Sort/MyPlayground.playground/Contents.swift	
@@ -4,10 +4,11 @@ public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
     var array = elements
     
     for i in 0..<array.count {
-        for j in i+1..<array.count {
-            if array[j] < array[i] {
-                let tmp = array[i]
-                array[i] = array[j]
+        for j in 1..<array.count-i {
+            print(array,"comparing [\(j-1)] with [\(j)]")
+            if array[j] < array[j-1] {
+                let tmp = array[j-1]
+                array[j-1] = array[j]
                 array[j] = tmp
             }
         }
@@ -16,12 +17,7 @@ public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
     return array
 }
 
-
-var array = [Int]()
-
-for _ in 0...10 {
-    array.append(Int.random(in: 0...500))
-}
+var array = [4,2,1,3]
 
 print("before:",array)
 print("after:",BubbleSort(array))
diff --git a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift
index 8f1ec80f8..5ce18ef9b 100644
--- a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
+++ b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
@@ -29,10 +29,10 @@ public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
     var array = elements
     
     for i in 0..<array.count {
-        for j in i+1..<array.count {
-            if array[j] < array[i] {
-                let tmp = array[i]
-                array[i] = array[j]
+        for j in 1..<array.count-i {
+            if array[j] < array[j-1] {
+                let tmp = array[j-1]
+                array[j-1] = array[j]
                 array[j] = tmp
             }
         }

From b90632c00634d276312c23ea4bb462060cd5225a Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Tue, 2 Oct 2018 13:36:20 -0300
Subject: [PATCH 406/643] added imlementation information on readme

---
 Bubble Sort/README.markdown | 72 ++++++++++++++++++++++++++++++++++++-
 1 file changed, 71 insertions(+), 1 deletion(-)

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index 93d370827..80161ce56 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -1,6 +1,6 @@
 # Bubble Sort
 
-Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.
+Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.Sometimes this algorithm is refered as Sinking sort, due to the larger, or heavier elements sinking to the end of the array.
 
 ##### Runtime:
 - Average: O(N^2)
@@ -12,3 +12,73 @@ Bubble sort is a sorting algorithm that is implemented by starting in the beginn
 ### Implementation:
 
 The implementation will not be shown as the average and worst runtimes show that this is a very inefficient algorithm. However, having a grasp of the concept will help you understand the basics of simple sorting algorithms.
+
+Bubble sort is a very simple sorting algorithm, it consists in comparing pairs of adjacent elements in the array, if the first element is larger, swap them, otherwise, you do nothing and go for the next comparison.
+This is accomplished by looking through the array `n` times, `n` being the amount of elements in the array.
+
+#### Example
+Let us take the array `[5, 1, 4, 2, 8]`, and sort the array from lowest number to greatest number using bubble sort. In each step, elements written in bold are being compared. Three passes will be required.
+
+##### First Pass
+[ **5 1** 4 2 8 ] -> [ **1 5** 4 2 8 ], Here, algorithm compares the first two elements, and swaps since 5 > 1.
+
+[ 1 **5 4** 2 8 ] -> [ 1 **4 5** 2 8 ], Swap since 5 > 4 
+
+[ 1 4 **5 2** 8 ] -> [ 1 4 **2 5** 8 ], Swap since 5 > 2 
+
+[ 1 4 2 **5 8** ] -> [ 1 4 2 **5 8** ], Now, since these elements are already in order (8 > 5), algorithm does not swap them.
+
+##### Second Pass
+[ **1 4** 2 5 8 ] -> [ **1 4** 2 5 8 ]
+
+[ 1 **4 2** 5 8 ] -> [ 1 **2 4** 5 8 ], Swap since 4 > 2 
+
+[ 1 2 **4 5** 8 ] -> [ 1 2 **4 5** 8 ]
+
+[ 1 2 4 **5 8** ] -> [ 1 2 4 **5 8** ]
+Now, the array is already sorted, but the algorithm does not know if it is completed. The algorithm needs one whole pass without any swap to know it is sorted.
+
+##### Third Pass
+[ **1 2** 4 5 8 ] -> [ **1 2** 4 5 8 ]
+
+[ 1 **2 4** 5 8 ] -> [ 1 **2 4** 5 8 ]
+
+[ 1 2 **4 5** 8 ] -> [ 1 2 **4 5** 8 ]
+
+[ 1 2 4 **5 8** ] -> [ 1 2 4 **5 8** ]
+
+This is the same for the forth and fifth passes.
+
+#### Code
+```swift
+for i in 0..<array.count {
+for j in 1..<array.count {
+if array[j] < array[i] {
+let tmp = array[i]
+array[i] = array[j]
+array[j] = tmp
+}
+}
+}
+return array
+```
+
+#### Optimization
+The bubble sort algorithm can be easily optimized by observing that the `n-th` pass finds the `n-th` largest element and puts it into its final place. So, the inner loop can avoid looking at the last `n-1` items when running for the `n-th` time:
+
+```swift
+for i in 0..<array.count {
+for j in 1..<array.count - i {
+if array[j] < array[i] {
+let tmp = array[i]
+array[i] = array[j]
+array[j] = tmp
+}
+}
+}
+return array
+```
+
+The only change made was on the second line, changing the interval from `1..<array.count` to `1..<array.count - i`, effectively cutting the number of comparisons by half.
+
+That said, this is still a terribly inefficient sorting algorithm.

From a2493d861d5fc09e3b73269e653b0c74f344b09b Mon Sep 17 00:00:00 2001
From: Daniil Subbotin <mail@subdan.ru>
Date: Wed, 3 Oct 2018 21:35:49 +0300
Subject: [PATCH 407/643] [Swift 4.2] Update Binary Search

---
 Binary Search/BinarySearch.playground/Contents.swift        | 5 -----
 Binary Search/BinarySearch.playground/contents.xcplayground | 2 +-
 2 files changed, 1 insertion(+), 6 deletions(-)

diff --git a/Binary Search/BinarySearch.playground/Contents.swift b/Binary Search/BinarySearch.playground/Contents.swift
index 715fb5dc2..f673f25c4 100644
--- a/Binary Search/BinarySearch.playground/Contents.swift	
+++ b/Binary Search/BinarySearch.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // An unsorted array of numbers
 let numbers = [11, 59, 3, 2, 53, 17, 31, 7, 19, 67, 47, 13, 37, 61, 29, 43, 5, 41, 23]
 
diff --git a/Binary Search/BinarySearch.playground/contents.xcplayground b/Binary Search/BinarySearch.playground/contents.xcplayground
index 06828af92..69d154d1e 100644
--- a/Binary Search/BinarySearch.playground/contents.xcplayground	
+++ b/Binary Search/BinarySearch.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 7457400c6df02091f0943296335933a4645e58e1 Mon Sep 17 00:00:00 2001
From: Daniil Subbotin <mail@subdan.ru>
Date: Wed, 3 Oct 2018 22:06:41 +0300
Subject: [PATCH 408/643] [Swift 4.2] Update Shuffle

---
 Shuffle/README.markdown                          | 8 ++------
 Shuffle/Shuffle.playground/Contents.swift        | 5 -----
 Shuffle/Shuffle.playground/Sources/Shuffle.swift | 9 ++-------
 3 files changed, 4 insertions(+), 18 deletions(-)

diff --git a/Shuffle/README.markdown b/Shuffle/README.markdown
index ced138572..63868767b 100644
--- a/Shuffle/README.markdown
+++ b/Shuffle/README.markdown
@@ -33,8 +33,6 @@ You should see three different arrangements -- or [permutations](../Combinatoric
 
 This shuffle works *in place*, it modifies the contents of the original array. The algorithm works by creating a new array, `temp`, that is initially empty. Then we randomly choose an element from the original array and append it to `temp`, until the original array is empty. Finally, the temporary array is copied back into the original one.
 
-> **Note:** `random()` is a helper function that returns a random integer between 0 and the given maximum.
-
 This code works just fine but it's not very efficient. Removing an element from an array is an **O(n)** operation and we perform this **n** times, making the total algorithm **O(n^2)**. We can do better!
 
 ## The Fisher-Yates / Knuth shuffle
@@ -45,7 +43,7 @@ Here is a much improved version of the shuffle algorithm:
 extension Array {
   public mutating func shuffle() {
     for i in stride(from: count - 1, through: 1, by: -1) {
-      let j = random(i + 1)
+      let j = Int.random(in: 0...i)
       if i != j {
         swap(&self[i], &self[j])
       }
@@ -56,8 +54,6 @@ extension Array {
 
 Again, this picks objects at random. In the naive version we placed those objects into a new temporary array so we could keep track of which objects were already shuffled and which still remained to be done. In this improved algorithm, however, we'll move the shuffled objects to the end of the original array. 
 
-> **Note**: When you write `random(x)`, the largest number it will return is `x - 1`. We want to have `j <= i`, not `j < i`, so the largest number from the random number generator needs to be `i`, not `i - 1`. That's why we do `random(i + 1)`. If we didn't add that 1 to compensate, it would make some shuffle orders more likely to occur than others.
-
 Let's walk through the example. We have the array:
 
 	[ "a", "b", "c", "d", "e", "f", "g" ]
@@ -99,7 +95,7 @@ Here is the code:
 public func shuffledArray(_ n: Int) -> [Int] {
   var a = [Int](repeating: 0, count: n)
   for i in 0..<n {
-    let j = random(i + 1)
+    let j = Int.random(in: 0...i)
     if i != j {
       a[i] = a[j]
     }
diff --git a/Shuffle/Shuffle.playground/Contents.swift b/Shuffle/Shuffle.playground/Contents.swift
index ac9181660..9c3cabd27 100644
--- a/Shuffle/Shuffle.playground/Contents.swift
+++ b/Shuffle/Shuffle.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 var list = [ "a", "b", "c", "d", "e", "f", "g" ]
diff --git a/Shuffle/Shuffle.playground/Sources/Shuffle.swift b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
index 553832d43..500d3c245 100644
--- a/Shuffle/Shuffle.playground/Sources/Shuffle.swift
+++ b/Shuffle/Shuffle.playground/Sources/Shuffle.swift
@@ -1,10 +1,5 @@
 import Foundation
 
-/* Returns a random integer between 0 and n-1. */
-public func random(_ n: Int) -> Int {
-  return Int(arc4random_uniform(UInt32(n)))
-}
-
 extension Array {
   /*
    Randomly shuffles the array in-place
@@ -13,7 +8,7 @@ extension Array {
    */
   public mutating func shuffle() {
     for i in (1...count-1).reversed() {
-      let j = random(i + 1)
+      let j = Int.random(in: 0...i)
       if i != j {
         let t = self[i]
         self[i] = self[j]
@@ -29,7 +24,7 @@ extension Array {
 public func shuffledArray(_ n: Int) -> [Int] {
   var a = Array(repeating: 0, count: n)
   for i in 0..<n {
-    let j = random(i + 1)
+    let j = Int.random(in: 0...i)
     if i != j {
       a[i] = a[j]
     }

From 04127deb3d50256856e9d41ebff580d662747dbb Mon Sep 17 00:00:00 2001
From: mmcbee1 <meghankmcbee@gmail.com>
Date: Wed, 3 Oct 2018 21:49:24 -0700
Subject: [PATCH 409/643] [Swift 4.2] Update Stack

---
 Stack/Stack.playground/Contents.swift        | 6 ------
 Stack/Stack.playground/contents.xcplayground | 2 +-
 2 files changed, 1 insertion(+), 7 deletions(-)

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index e9e3e9a57..1eb705f20 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -1,9 +1,3 @@
-
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 /*
   Stack
 
diff --git a/Stack/Stack.playground/contents.xcplayground b/Stack/Stack.playground/contents.xcplayground
index 5da2641c9..a40c0f554 100644
--- a/Stack/Stack.playground/contents.xcplayground
+++ b/Stack/Stack.playground/contents.xcplayground
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
+<playground version='5.0' target-platform='ios' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From c2d0169719cf1c76533c9402fcd96248e3e6978e Mon Sep 17 00:00:00 2001
From: Ashish Kakkad <ashishkakkad8@gmail.com>
Date: Thu, 4 Oct 2018 22:07:39 +0530
Subject: [PATCH 410/643] Swift 4.2 [Array2D]

---
 Array2D/Array2D.playground/Contents.swift     | 5 -----
 Array2D/Tests/Tests.xcodeproj/project.pbxproj | 4 ++--
 2 files changed, 2 insertions(+), 7 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 77c0b364c..d31d77540 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 /*
  Two-dimensional array with a fixed number of rows and columns.
  This is mostly handy for games that are played on a grid, such as chess.
diff --git a/Array2D/Tests/Tests.xcodeproj/project.pbxproj b/Array2D/Tests/Tests.xcodeproj/project.pbxproj
index a0fb1480b..af9b7c3b8 100644
--- a/Array2D/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Array2D/Tests/Tests.xcodeproj/project.pbxproj
@@ -226,7 +226,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -238,7 +238,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};

From c7d17128ccda1f80da11e85e5a381102e1fab8c6 Mon Sep 17 00:00:00 2001
From: Ashish Kakkad <ashishkakkad8@gmail.com>
Date: Thu, 4 Oct 2018 22:51:29 +0530
Subject: [PATCH 411/643] [Swift 4.2] Graph

---
 Graph/Graph.playground/Contents.swift              |  6 ------
 Graph/Graph.playground/timeline.xctimeline         |  2 +-
 Graph/Graph.xcodeproj/project.pbxproj              | 14 +++++++++-----
 .../xcshareddata/xcschemes/Graph.xcscheme          |  2 +-
 .../xcshareddata/xcschemes/GraphTests.xcscheme     |  2 +-
 Graph/GraphTests/GraphTests.swift                  |  7 -------
 6 files changed, 12 insertions(+), 21 deletions(-)

diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph.playground/Contents.swift
index 0410942f8..fde396e64 100644
--- a/Graph/Graph.playground/Contents.swift
+++ b/Graph/Graph.playground/Contents.swift
@@ -1,11 +1,5 @@
 import Graph
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
-
 for graph in [AdjacencyMatrixGraph<Int>(), AdjacencyListGraph<Int>()] {
 
   let v1 = graph.createVertex(1)
diff --git a/Graph/Graph.playground/timeline.xctimeline b/Graph/Graph.playground/timeline.xctimeline
index 6afe06b6f..59717856a 100644
--- a/Graph/Graph.playground/timeline.xctimeline
+++ b/Graph/Graph.playground/timeline.xctimeline
@@ -3,7 +3,7 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/kachen/src/swift-algorithm-club/Graph/Graph.playground#CharacterRangeLen=12&amp;CharacterRangeLoc=1322&amp;EndingColumnNumber=4&amp;EndingLineNumber=45&amp;StartingColumnNumber=7&amp;StartingLineNumber=44&amp;Timestamp=523289935.918656"
+         documentLocation = "file:///Users/ashishkakkad/Ashish/iOS/GitHub/swift-algorithm-club/Graph/Graph.playground#CharacterRangeLen=12&amp;CharacterRangeLoc=1238&amp;EndingColumnNumber=4&amp;EndingLineNumber=39&amp;StartingColumnNumber=7&amp;StartingLineNumber=38&amp;Timestamp=560365411.415967"
          selectedRepresentationIndex = "1"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Graph/Graph.xcodeproj/project.pbxproj b/Graph/Graph.xcodeproj/project.pbxproj
index 17a5a7d6b..790f6ac18 100644
--- a/Graph/Graph.xcodeproj/project.pbxproj
+++ b/Graph/Graph.xcodeproj/project.pbxproj
@@ -158,7 +158,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0900;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					49BFA2FC1CDF886B00522D66 = {
@@ -251,12 +251,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -289,7 +291,7 @@
 				ONLY_ACTIVE_ARCH = YES;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -308,12 +310,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -339,7 +343,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -364,7 +368,7 @@
 				SKIP_INSTALL = YES;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -386,7 +390,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
index a12d85dad..73524effc 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
index 28df1be50..873f1d7b4 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Graph/GraphTests/GraphTests.swift b/Graph/GraphTests/GraphTests.swift
index 92a4ce828..289d9aa64 100644
--- a/Graph/GraphTests/GraphTests.swift
+++ b/Graph/GraphTests/GraphTests.swift
@@ -10,13 +10,6 @@ import XCTest
 
 class GraphTests: XCTestCase {
 
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-
   func testAdjacencyMatrixGraphDescription() {
 
     let graph = AdjacencyMatrixGraph<String>()

From 7442c10f596fec191eacbec644fcf8d5fae7f30a Mon Sep 17 00:00:00 2001
From: Vyacheslav Khorkov <artfintch@ya.ru>
Date: Thu, 4 Oct 2018 22:34:48 +0500
Subject: [PATCH 412/643] Update Z-Algorithm up to Swift 4.2.

---
 Z-Algorithm/README.markdown                         |  5 ++---
 Z-Algorithm/ZAlgorithm.swift                        |  3 +--
 Z-Algorithm/ZetaAlgorithm.playground/Contents.swift | 10 ++--------
 Z-Algorithm/ZetaAlgorithm.swift                     |  2 +-
 4 files changed, 6 insertions(+), 14 deletions(-)

diff --git a/Z-Algorithm/README.markdown b/Z-Algorithm/README.markdown
index 8b84c28bf..a6423be03 100644
--- a/Z-Algorithm/README.markdown
+++ b/Z-Algorithm/README.markdown
@@ -28,8 +28,7 @@ This a simple description of the idea that is behind this algorithm. There are a
 Here is the code of the function that computes the Z-array:
 ```swift
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-
-    let pattern = Array(ptrn.characters)
+    let pattern = Array(ptrn)
     let patternLength: Int = pattern.count
 
     guard patternLength > 0 else {
@@ -131,7 +130,7 @@ The Z-Algorithm discussed above leads to the simplest linear-time string matchin
 extension String {
 
     func indexesOf(pattern: String) -> [Int]? {
-        let patternLength: Int = pattern.characters.count
+        let patternLength: Int = pattern.count
         /* Let's calculate the Z-Algorithm on the concatenation of pattern and text */
         let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
 
diff --git a/Z-Algorithm/ZAlgorithm.swift b/Z-Algorithm/ZAlgorithm.swift
index 969a3599b..65acaabd1 100644
--- a/Z-Algorithm/ZAlgorithm.swift
+++ b/Z-Algorithm/ZAlgorithm.swift
@@ -9,8 +9,7 @@
 import Foundation
 
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-
-  let pattern = Array(ptrn.characters)
+  let pattern = Array(ptrn)
   let patternLength = pattern.count
 
   guard patternLength > 0 else {
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
index d057080a1..56aa92170 100644
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -1,13 +1,7 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-
-  let pattern = Array(ptrn.characters)
+  let pattern = Array(ptrn)
   let patternLength = pattern.count
 
   guard patternLength > 0 else {
@@ -65,7 +59,7 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
 extension String {
 
   func indexesOf(pattern: String) -> [Int]? {
-    let patternLength = pattern.characters.count
+    let patternLength = pattern.count
     let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
 
     guard zeta != nil else {
diff --git a/Z-Algorithm/ZetaAlgorithm.swift b/Z-Algorithm/ZetaAlgorithm.swift
index e60c1617f..f2c453364 100644
--- a/Z-Algorithm/ZetaAlgorithm.swift
+++ b/Z-Algorithm/ZetaAlgorithm.swift
@@ -11,7 +11,7 @@ import Foundation
 extension String {
 
   func indexesOf(pattern: String) -> [Int]? {
-    let patternLength = pattern.characters.count
+    let patternLength = pattern.count
     let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
 
     guard zeta != nil else {

From 3c3168ea6e8d01972727d8db5ebea10f4aa794d3 Mon Sep 17 00:00:00 2001
From: Vyacheslav Khorkov <artfintch@ya.ru>
Date: Thu, 4 Oct 2018 23:13:45 +0500
Subject: [PATCH 413/643] Update Deque up to Swift 4.2.

---
 Deque/Deque-Simple.swift              | 2 +-
 Deque/Deque.playground/Contents.swift | 5 -----
 Deque/README.markdown                 | 2 +-
 3 files changed, 2 insertions(+), 7 deletions(-)

diff --git a/Deque/Deque-Simple.swift b/Deque/Deque-Simple.swift
index f4f5f0409..fc0fcb2b2 100644
--- a/Deque/Deque-Simple.swift
+++ b/Deque/Deque-Simple.swift
@@ -21,7 +21,7 @@ public struct Deque<T> {
   }
 
   public mutating func enqueueFront(_ element: T) {
-    array.insert(element, atIndex: 0)
+    array.insert(element, at: 0)
   }
 
   public mutating func dequeue() -> T? {
diff --git a/Deque/Deque.playground/Contents.swift b/Deque/Deque.playground/Contents.swift
index df9b57a5e..9e7b22c02 100644
--- a/Deque/Deque.playground/Contents.swift
+++ b/Deque/Deque.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 public struct Deque<T> {
   private var array = [T]()
 
diff --git a/Deque/README.markdown b/Deque/README.markdown
index fda1de5f8..f3172e16e 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -23,7 +23,7 @@ public struct Deque<T> {
   }
 
   public mutating func enqueueFront(_ element: T) {
-    array.insert(element, atIndex: 0)
+    array.insert(element, at: 0)
   }
 
   public mutating func dequeue() -> T? {

From ed155f211d5b98fc54e3de40b55680367b5e1e93 Mon Sep 17 00:00:00 2001
From: Vyacheslav Khorkov <artfintch@ya.ru>
Date: Thu, 4 Oct 2018 23:21:00 +0500
Subject: [PATCH 414/643] Remove notice from GCD playground.

---
 GCD/GCD.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index f0fceb0da..c44f28310 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Recursive version
 func gcd(_ a: Int, _ b: Int) -> Int {
   let r = a % b

From 945c7cbe8e6f79dd31f4e0f3468d22d0f5f024c2 Mon Sep 17 00:00:00 2001
From: Vyacheslav Khorkov <artfintch@ya.ru>
Date: Thu, 4 Oct 2018 23:28:36 +0500
Subject: [PATCH 415/643] Remove notice from FixedSizeArray playground.

---
 Fixed Size Array/FixedSizeArray.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
index 8b5bc1147..616f8443d 100644
--- a/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-  print("Hello, Swift 4!")
-#endif
-
 /*
  An unordered array with a maximum size.
  

From 8ea8a6590457b2ba931444ea75506e329850e788 Mon Sep 17 00:00:00 2001
From: Vyacheslav Khorkov <artfintch@ya.ru>
Date: Thu, 4 Oct 2018 23:34:40 +0500
Subject: [PATCH 416/643] Update Insertion Sort up to Swift 4.2.

---
 .../InsertionSort.playground/Contents.swift   |  5 ----
 .../Tests/Tests.xcodeproj/project.pbxproj     | 26 ++++++++++++++++---
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 3 files changed, 23 insertions(+), 10 deletions(-)

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index 9a10ec04a..184fc36e4 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 /// Performs the Insertion sort algorithm to a given array
 ///
 /// - Parameters:
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj b/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj
index ee3ca1cae..e9ea3bc53 100644
--- a/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Insertion Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,12 +86,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -145,14 +145,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -191,14 +199,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -230,7 +246,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -242,7 +259,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 14f27f777..afd69e6a7 100644
--- a/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Insertion Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 8943b0925cc937b7e87c5d5b7f39e9ca00e750d1 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 4 Oct 2018 20:49:35 +0200
Subject: [PATCH 417/643] Update project with Xcode 10.

---
 .../Tests/Tests.xcodeproj/project.pbxproj     | 24 +++++++++++++++----
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 3 files changed, 29 insertions(+), 5 deletions(-)
 create mode 100644 Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj
index 6493fd153..f0649ba26 100644
--- a/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bloom Filter/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,12 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -141,14 +141,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -188,14 +196,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -228,7 +244,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -240,7 +256,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bloom Filter/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 14f27f777..afd69e6a7 100644
--- a/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bloom Filter/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 06cdc9f9f779ca3c18fca97419060de0bde350ea Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 4 Oct 2018 20:50:05 +0200
Subject: [PATCH 418/643] Remove use of deprecated `characters` property.

---
 Bloom Filter/Tests/BloomFilterTests.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Bloom Filter/Tests/BloomFilterTests.swift b/Bloom Filter/Tests/BloomFilterTests.swift
index 30df702a7..d88ec0a31 100644
--- a/Bloom Filter/Tests/BloomFilterTests.swift	
+++ b/Bloom Filter/Tests/BloomFilterTests.swift	
@@ -6,7 +6,7 @@ import XCTest
 func djb2(_ x: String) -> Int {
   var hash = 5381
 
-  for char in x.characters {
+  for char in x {
     hash = ((hash << 5) &+ hash) &+ char.hashValue
   }
 
@@ -16,7 +16,7 @@ func djb2(_ x: String) -> Int {
 func sdbm(_ x: String) -> Int {
   var hash = 0
 
-  for char in x.characters {
+  for char in x {
     hash = char.hashValue &+ (hash << 6) &+ (hash << 16) &- hash
   }
 

From 6ef7a6e6ad07781320418d276a67eaa4e3d635d7 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 4 Oct 2018 20:57:46 +0200
Subject: [PATCH 419/643] Xcode 10 automated changes.

---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 Bloom Filter/BloomFilter.playground/timeline.xctimeline   | 6 ------
 2 files changed, 8 insertions(+), 6 deletions(-)
 create mode 100644 Bloom Filter/BloomFilter.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 Bloom Filter/BloomFilter.playground/timeline.xctimeline

diff --git a/Bloom Filter/BloomFilter.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bloom Filter/BloomFilter.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bloom Filter/BloomFilter.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Bloom Filter/BloomFilter.playground/timeline.xctimeline b/Bloom Filter/BloomFilter.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Bloom Filter/BloomFilter.playground/timeline.xctimeline	
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>

From 4201fb4fc8bfefe4ab9651f5c393c55ddfd5f294 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 4 Oct 2018 20:58:26 +0200
Subject: [PATCH 420/643] Update for Swift 4.2.

* Remove the top code snippet, as per instructions.
* Remove use of deprecated `characters` property.
---
 Bloom Filter/BloomFilter.playground/Contents.swift | 9 +++------
 1 file changed, 3 insertions(+), 6 deletions(-)

diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index 9e4a89351..7a3719d57 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -1,8 +1,5 @@
 //: Playground - noun: a place where people can play
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+
 public class BloomFilter<T> {
   fileprivate var array: [Bool]
   private var hashFunctions: [(T) -> Int]
@@ -54,7 +51,7 @@ public class BloomFilter<T> {
 
 func djb2(x: String) -> Int {
   var hash = 5381
-  for char in x.characters {
+  for char in x {
     hash = ((hash << 5) &+ hash) &+ char.hashValue
   }
   return Int(hash)
@@ -62,7 +59,7 @@ func djb2(x: String) -> Int {
 
 func sdbm(x: String) -> Int {
   var hash = 0
-  for char in x.characters {
+  for char in x {
     hash = char.hashValue &+ (hash << 6) &+ (hash << 16) &- hash
   }
   return Int(hash)

From 849309c5eb5d2ef29918940536cc1b011b665b3c Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 4 Oct 2018 21:45:50 +0200
Subject: [PATCH 421/643] Add note about Hasher in README.

* Adds a section about another Bloom filter approach, using only a single hashing function with Swift 4.2's `Hasher`.
* Adds links to some more documentation and a blog post implementing the Bloom filter in this way.
* Adds my name as updater.
---
 Bloom Filter/README.markdown | 27 ++++++++++++++++++++++++++-
 1 file changed, 26 insertions(+), 1 deletion(-)

diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
index 3fff0a379..4364db857 100644
--- a/Bloom Filter/README.markdown	
+++ b/Bloom Filter/README.markdown	
@@ -100,4 +100,29 @@ public func query(_ value: T) -> Bool {
 
 If you're coming from another imperative language, you might notice the unusual syntax in the `exists` assignment. Swift makes use of functional paradigms when it makes code more consise and readable, and in this case `reduce` is a much more consise way to check if all the required bits are `true` than a `for` loop.
 
-*Written for Swift Algorithm Club by Jamil Dhanani. Edited by Matthijs Hollemans.*
+## Another approach
+
+Another approach to create different hashes of an element for use in the Bloom filter, is to use the same hash function for every iteration, but combine it with different random numbers. This can help, because finding good hashing functions is hard, but combining them is equally non-trivial.
+
+```
+hash("Hello world!") >> hash(987654321) // would flip bit 8
+hash("Hello world!") >> hash(123456789) // would flip bit 2
+```
+
+Since Swift 4.2, `Hasher` is now included in the Standard library, which is designed to reduce multiple hashes to a single hash in an efficient manner. This makes combining the hashes trivial.
+
+```
+private func computeHashes(_ value: T) -> [Int] {
+  return randomSeeds.map() { seed in
+		let hasher = Hasher()
+		hasher.combine(seed)
+		hasher.combine(value)
+		let hashValue = hasher.finalize()
+		return abs(hashValue % array.count)
+	}
+}
+```
+
+If you want to learn more about this approach, you can read about the [Hasher documentation](https://developer.apple.com/documentation/swift/hasher) or Soroush Khanlou's [Swift 4.2 Bloom filter](http://khanlou.com/2018/09/bloom-filters/) implementation.
+
+*Written for Swift Algorithm Club by Jamil Dhanani. Edited by Matthijs Hollemans. Updated by Bruno Scheele.*

From a56b88370d49aaf0d5640ca59d955f61178108f8 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 21:33:32 -0400
Subject: [PATCH 422/643] [Swift 4.2] Update Binary Search Tree

---
 .../Contents.swift                            |  5 --
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 47 ++++++++++++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 .../Contents.swift                            |  5 --
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++
 .../Sources/BinarySearch.swift                | 52 -------------------
 .../contents.xcworkspacedata                  |  7 ---
 9 files changed, 64 insertions(+), 78 deletions(-)
 create mode 100644 Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 Binary Search/BinarySearch.playground/Sources/BinarySearch.swift
 delete mode 100644 Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index 8c06ae9e1..ec9902283 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let tree = BinarySearchTree<Int>(value: 7)
 tree.insert(value: 2)
 tree.insert(value: 5)
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj
index f4c3f65c7..ff594fff8 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
@@ -3,7 +3,7 @@
 	archiveVersion = 1;
 	classes = {
 	};
-	objectVersion = 46;
+	objectVersion = 51;
 	objects = {
 
 /* Begin PBXBuildFile section */
@@ -83,17 +83,17 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
 			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
-			compatibilityVersion = "Xcode 3.2";
+			compatibilityVersion = "Xcode 10.0";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
@@ -141,13 +141,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -185,13 +195,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -210,6 +230,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_COMPILATION_MODE = wholemodule;
 			};
 			name = Release;
 		};
@@ -218,10 +239,15 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -230,10 +256,15 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..afd69e6a7 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index afa4338a9..2b5dcc341 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Each time you insert something, you get back a completely new tree.
 var tree = BinarySearchTree.leaf(7)
 tree = tree.insert(newValue: 2)
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift b/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift
deleted file mode 100644
index d6623e355..000000000
--- a/Binary Search/BinarySearch.playground/Sources/BinarySearch.swift	
+++ /dev/null
@@ -1,52 +0,0 @@
-/**
- Binary Search
- 
- Recursively splits the array in half until the value is found.
- 
- If there is more than one occurrence of the search key in the array, then
- there is no guarantee which one it finds.
- 
- Note: The array must be sorted!
- **/
-
-import Foundation
-
-// The recursive version of binary search.
-
-public func binarySearch<T: Comparable>(_ a: [T], key: T, range: Range<Int>) -> Int? {
-    if range.lowerBound >= range.upperBound {
-        return nil
-    } else {
-        let midIndex = range.lowerBound + (range.upperBound - range.lowerBound) / 2
-        if a[midIndex] > key {
-            return binarySearch(a, key: key, range: range.lowerBound ..< midIndex)
-        } else if a[midIndex] < key {
-            return binarySearch(a, key: key, range: midIndex + 1 ..< range.upperBound)
-        } else {
-            return midIndex
-        }
-    }
-}
-
-/**
- The iterative version of binary search.
- 
- Notice how similar these functions are. The difference is that this one
- uses a while loop, while the other calls itself recursively.
- **/
-
-public func binarySearch<T: Comparable>(_ a: [T], key: T) -> Int? {
-    var lowerBound = 0
-    var upperBound = a.count
-    while lowerBound < upperBound {
-        let midIndex = lowerBound + (upperBound - lowerBound) / 2
-        if a[midIndex] == key {
-            return midIndex
-        } else if a[midIndex] < key {
-            lowerBound = midIndex + 1
-        } else {
-            upperBound = midIndex
-        }
-    }
-    return nil
-}
diff --git a/Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata b/Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata
deleted file mode 100644
index 919434a62..000000000
--- a/Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata	
+++ /dev/null
@@ -1,7 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Workspace
-   version = "1.0">
-   <FileRef
-      location = "self:">
-   </FileRef>
-</Workspace>

From 54ac83543efd7bb47d1a976fcf9016ac618c3793 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 21:38:01 -0400
Subject: [PATCH 423/643] [Swift 4.2] Update Binary Search Tree

---
 .../Contents.swift                            |  5 ++
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ----
 .../Tests/Tests.xcodeproj/project.pbxproj     | 47 ++++---------------
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ----
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 .../Contents.swift                            |  5 ++
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ----
 7 files changed, 19 insertions(+), 64 deletions(-)
 delete mode 100644 Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index ec9902283..8c06ae9e1 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 let tree = BinarySearchTree<Int>(value: 7)
 tree.insert(value: 2)
 tree.insert(value: 5)
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj
index ff594fff8..f4c3f65c7 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
@@ -3,7 +3,7 @@
 	archiveVersion = 1;
 	classes = {
 	};
-	objectVersion = 51;
+	objectVersion = 46;
 	objects = {
 
 /* Begin PBXBuildFile section */
@@ -83,17 +83,17 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 1000;
+				LastUpgradeCheck = 0720;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 1000;
+						LastSwiftMigration = 0820;
 					};
 				};
 			};
 			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
-			compatibilityVersion = "Xcode 10.0";
+			compatibilityVersion = "Xcode 3.2";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
@@ -141,23 +141,13 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
-				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
-				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
-				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
-				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
-				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
-				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
-				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
-				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
-				CLANG_WARN_STRICT_PROTOTYPES = YES;
-				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -195,23 +185,13 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
-				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
-				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
-				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
-				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
-				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
-				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
-				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
-				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
-				CLANG_WARN_STRICT_PROTOTYPES = YES;
-				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -230,7 +210,6 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
-				SWIFT_COMPILATION_MODE = wholemodule;
 			};
 			name = Release;
 		};
@@ -239,15 +218,10 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = (
-					"$(inherited)",
-					"@executable_path/../Frameworks",
-					"@loader_path/../Frameworks",
-				);
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
-				SWIFT_VERSION = 4.2;
+				SWIFT_VERSION = 3.0;
 			};
 			name = Debug;
 		};
@@ -256,15 +230,10 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = (
-					"$(inherited)",
-					"@executable_path/../Frameworks",
-					"@loader_path/../Frameworks",
-				);
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
-				SWIFT_VERSION = 4.2;
+				SWIFT_VERSION = 3.0;
 			};
 			name = Release;
 		};
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index afd69e6a7..8ef8d8581 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "1000"
+   LastUpgradeVersion = "0720"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index 2b5dcc341..afa4338a9 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -1,5 +1,10 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
+
 // Each time you insert something, you get back a completely new tree.
 var tree = BinarySearchTree.leaf(7)
 tree = tree.insert(newValue: 2)
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>

From d6099b34226cef00bc5e83fa503437c88fbd39b2 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 21:38:36 -0400
Subject: [PATCH 424/643] [Swift 4.2] Dijkstra Algorithm

---
 Dijkstra Algorithm/Dijkstra.playground/Contents.swift     | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../VisualizedDijkstra.playground/Contents.swift          | 5 -----
 .../VisualizedDijkstra.playground/Sources/Window.swift    | 2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 5 files changed, 17 insertions(+), 11 deletions(-)
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index 1cd1254b1..7c7f1a4b0 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -1,11 +1,6 @@
 //: Playground - noun: a place where people can play
 import Foundation
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 var vertices: Set<Vertex> = Set()
 
 func createNotConnectedVertices() {
diff --git a/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift
index 8e61ef49b..de6b49834 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift	
@@ -9,11 +9,6 @@
 import UIKit
 import PlaygroundSupport
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 /*:
  First of all, let's set up colors for our window and graph. The visited color will be applied to visited vertices. The checking color will be applied to an edge and an edge neighbor every time the algorithm is checking some vertex neighbors. And default colors are just initial colors for elements.
  */
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift
index 73c512e6b..9a169b8c7 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
@@ -134,7 +134,7 @@ public class Window: UIView, GraphDelegate {
         let origin = CGPoint(x: center.x - 25, y: 100)
         let activityIndicatorFrame = CGRect(origin: origin, size: size)
         activityIndicator = UIActivityIndicatorView(frame: activityIndicatorFrame)
-        activityIndicator.activityIndicatorViewStyle = .whiteLarge
+        activityIndicator.style = .whiteLarge
     }
 
     @objc private func createGraphButtonTap() {
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From e6a2aa77f23a515081d8bc806e46efc81d785321 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 21:43:56 -0400
Subject: [PATCH 425/643] [Swift 4.2] Update Binary Search Tree

---
 .../Contents.swift                            |  5 ---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 31 ++++++++++++++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 .../Contents.swift                            |  5 ---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 7 files changed, 52 insertions(+), 15 deletions(-)
 create mode 100644 Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift
index 8c06ae9e1..ec9902283 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let tree = BinarySearchTree<Int>(value: 7)
 tree.insert(value: 2)
 tree.insert(value: 5)
diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj
index f4c3f65c7..d7c687e0c 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,12 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -141,13 +141,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -185,13 +195,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -210,6 +230,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_COMPILATION_MODE = wholemodule;
 			};
 			name = Release;
 		};
@@ -221,7 +242,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -233,7 +255,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..afd69e6a7 100644
--- a/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Binary Search Tree/Solution 1/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift
index afa4338a9..2b5dcc341 100644
--- a/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Each time you insert something, you get back a completely new tree.
 var tree = BinarySearchTree.leaf(7)
 tree = tree.insert(newValue: 2)
diff --git a/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Search Tree/Solution 2/BinarySearchTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 1d452b31d82f06ad964ae5acd6d0bd7e8b2cadd8 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 22:01:22 -0400
Subject: [PATCH 426/643] [Swift 4.2] Queue

---
 Queue/Tests/Tests.xcodeproj/project.pbxproj   | 26 ++++++++++++++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 3 files changed, 31 insertions(+), 5 deletions(-)
 create mode 100644 Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Queue/Tests/Tests.xcodeproj/project.pbxproj b/Queue/Tests/Tests.xcodeproj/project.pbxproj
index a554fd16e..f7fc3e048 100644
--- a/Queue/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Queue/Tests/Tests.xcodeproj/project.pbxproj
@@ -83,12 +83,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -141,14 +141,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -187,14 +195,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -226,7 +242,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -238,7 +255,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 14f27f777..afd69e6a7 100644
--- a/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Queue/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 8eb0b26584b69603ca64ae634cfee1859a72be69 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 22:05:37 -0400
Subject: [PATCH 427/643] [Swift 4.2] Queue

---
 Queue/Queue.playground/Contents.swift                     | 6 ------
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 Queue/Tests/Tests.xcodeproj/project.pbxproj               | 4 ++--
 3 files changed, 10 insertions(+), 8 deletions(-)
 create mode 100644 Queue/Queue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index 22d2a84ca..08327783f 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -1,9 +1,3 @@
-
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 /*
   Queue
 
diff --git a/Queue/Queue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Queue/Queue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Queue/Queue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Queue/Tests/Tests.xcodeproj/project.pbxproj b/Queue/Tests/Tests.xcodeproj/project.pbxproj
index f7fc3e048..f927aba0d 100644
--- a/Queue/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Queue/Tests/Tests.xcodeproj/project.pbxproj
@@ -242,7 +242,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
@@ -255,7 +255,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.2;
 			};
 			name = Release;

From 01ba34cc5084c7f70beb3955d71918f75fb30bd0 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Thu, 4 Oct 2018 22:17:58 -0400
Subject: [PATCH 428/643] [Swift 4.2] Merge Sort

---
 Merge Sort/MergeSort.playground/Contents.swift            | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Merge Sort/MergeSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index b05332bfe..ca1347890 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -1,10 +1,5 @@
 /* Top-down recursive version */
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 func mergeSort<T: Comparable>(_ array: [T]) -> [T] {
   guard array.count > 1 else { return array }
   let middleIndex = array.count / 2
diff --git a/Merge Sort/MergeSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Merge Sort/MergeSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Merge Sort/MergeSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 3f0bdc6ec0009bf08251458a04b11631d13cb7c7 Mon Sep 17 00:00:00 2001
From: danielchick <daniel.chick@hotmail.com>
Date: Thu, 4 Oct 2018 22:44:53 -0500
Subject: [PATCH 429/643] [Swift 4.2] Update Tree

---
 Tree/Tree.playground/Contents.swift        | 4 ++--
 Tree/Tree.playground/contents.xcplayground | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index 49cf41054..06f992fa8 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -1,8 +1,8 @@
 //: Playground - noun: a place where people can play
 
 // last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
+#if swift(>=4.2)
+print("Hello, Swift 4.2!")
 #endif
 
 let tree = TreeNode<String>(value: "beverages")
diff --git a/Tree/Tree.playground/contents.xcplayground b/Tree/Tree.playground/contents.xcplayground
index 06828af92..69d154d1e 100644
--- a/Tree/Tree.playground/contents.xcplayground
+++ b/Tree/Tree.playground/contents.xcplayground
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From f24a004b0420dcd3dc3156b368852e30b9841e89 Mon Sep 17 00:00:00 2001
From: imvm <imvm@cin.ufpe.br>
Date: Fri, 5 Oct 2018 02:51:06 -0300
Subject: [PATCH 430/643] Remove notice from Strassen Multiplication Matrix
 playground

---
 .../StrassensMatrixMultiplication.playground/Contents.swift  | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index 409e28c52..6b9314557 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 var A = Matrix(rows: 2, columns: 4, initialValue: 0)

From 6ab163e4431ba09a6870b4b101dc536cffcf759d Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Fri, 5 Oct 2018 09:34:07 +0200
Subject: [PATCH 431/643] Update to Xcode 10.

---
 Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj         | 6 +++++-
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme | 4 +---
 3 files changed, 14 insertions(+), 4 deletions(-)
 create mode 100644 Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj
index 84a305784..6df507720 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -83,7 +83,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0900;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -145,12 +145,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -197,12 +199,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bucket Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 538a6f4fa..afd69e6a7 100644
--- a/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Bucket Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,7 +26,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -47,7 +46,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From bd0c74e0f4342d3a303779b6fb93beac96eed428 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Fri, 5 Oct 2018 09:49:56 +0200
Subject: [PATCH 432/643] Refactor to remove dependency on pre-Swift 4.

The code used to depend on pre-Swift 4's optional operators, which have since been replaced. Now, the one possible case for comparing a potential `nil` maximum value has been handled.
---
 Bucket Sort/BucketSort.swift | 31 +++++--------------------------
 1 file changed, 5 insertions(+), 26 deletions(-)

diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index 108073288..4c2abd372 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -20,31 +20,6 @@
 //
 //
 
-import Foundation
-// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
-// Consider refactoring the code to use the non-optional operators.
-fileprivate func < <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
-  switch (lhs, rhs) {
-  case let (l?, r?):
-    return l < r
-  case (nil, _?):
-    return true
-  default:
-    return false
-  }
-}
-
-// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
-// Consider refactoring the code to use the non-optional operators.
-fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
-  switch (lhs, rhs) {
-  case let (l?, r?):
-    return l >= r
-  default:
-    return !(lhs < rhs)
-  }
-}
-
 //////////////////////////////////////
 // MARK: Main algorithm
 //////////////////////////////////////
@@ -87,7 +62,11 @@ private func enoughSpaceInBuckets<T>(_ buckets: [Bucket<T>], elements: [T]) -> B
     let maximumValue = elements.max()?.toInt()
     let totalCapacity = buckets.count * (buckets.first?.capacity)!
 
-    return totalCapacity >= maximumValue
+    guard let max = maximumValue else {
+        return false
+    }
+    
+    return totalCapacity >= max
 }
 
 //////////////////////////////////////

From 8f2bf19304b379d60551359f913080e22b8d7ed3 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Fri, 5 Oct 2018 09:55:40 +0200
Subject: [PATCH 433/643] Change playground as well.

---
 .../Sources/BucketSort.swift                  | 31 +++----------------
 .../contents.xcplayground                     |  2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 3 files changed, 14 insertions(+), 27 deletions(-)
 create mode 100644 Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
index bafd216fa..64408eca4 100644
--- a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -20,31 +20,6 @@
 //
 //
 
-import Foundation
-// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
-// Consider refactoring the code to use the non-optional operators.
-fileprivate func < <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
-    switch (lhs, rhs) {
-    case let (l?, r?):
-        return l < r
-    case (nil, _?):
-        return true
-    default:
-        return false
-    }
-}
-
-// FIXME: comparison operators with optionals were removed from the Swift Standard Libary.
-// Consider refactoring the code to use the non-optional operators.
-fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
-    switch (lhs, rhs) {
-    case let (l?, r?):
-        return l >= r
-    default:
-        return !(lhs < rhs)
-    }
-}
-
 //////////////////////////////////////
 // MARK: Main algorithm
 //////////////////////////////////////
@@ -87,7 +62,11 @@ private func enoughSpaceInBuckets<T>(_ buckets: [Bucket<T>], elements: [T]) -> B
     let maximumValue = elements.max()?.toInt()
     let totalCapacity = buckets.count * (buckets.first?.capacity)!
     
-    return totalCapacity >= maximumValue
+    guard let max = maximumValue else {
+        return false
+    }
+    
+    return totalCapacity >= max
 }
 
 //////////////////////////////////////
diff --git a/Bucket Sort/BucketSort.playground/contents.xcplayground b/Bucket Sort/BucketSort.playground/contents.xcplayground
index 5da2641c9..9f5f2f40c 100644
--- a/Bucket Sort/BucketSort.playground/contents.xcplayground	
+++ b/Bucket Sort/BucketSort.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bucket Sort/BucketSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From f28973201916ac83c3b95f4115215a09715d22b7 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Fri, 5 Oct 2018 09:58:24 +0200
Subject: [PATCH 434/643] Add credit to README.

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

diff --git a/Bucket Sort/README.markdown b/Bucket Sort/README.markdown
index f572fc9a1..f2708d71e 100644
--- a/Bucket Sort/README.markdown	
+++ b/Bucket Sort/README.markdown	
@@ -256,4 +256,4 @@ The following are some of the variation to the general [Bucket Sort](https://en.
 - [Postman Sort](https://en.wikipedia.org/wiki/Bucket_sort#Postman.27s_sort)
 - [Shuffle Sort](https://en.wikipedia.org/wiki/Bucket_sort#Shuffle_sort)
 
-*Written for Swift Algorithm Club by Barbara Rodeker. Images from Wikipedia.*
+*Written for Swift Algorithm Club by Barbara Rodeker. Images from Wikipedia. Updated by Bruno Scheele.*

From 184786db68a17e40cfe2e4de6f7f212a84db42d4 Mon Sep 17 00:00:00 2001
From: KelCodesStuff <codesmithk@gmail.com>
Date: Fri, 5 Oct 2018 21:27:02 -0400
Subject: [PATCH 435/643] [Swift 4.2] Threaded Binary Tree

---
 .../ThreadedBinaryTree.playground/Contents.swift          | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift
index 4ce9d8157..ece1966e0 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Simple little debug function to make testing output pretty
 func check(_ tree: ThreadedBinaryTree<Int>?) {
   if let tree = tree {
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From cafba43a1c38bad9f62400e42ef46b9f51c60df3 Mon Sep 17 00:00:00 2001
From: Aleph Retamal <retamal.ph@gmail.com>
Date: Sat, 6 Oct 2018 18:11:50 +1000
Subject: [PATCH 436/643] [Swift 4.2] Update K-Means

---
 K-Means/KMeans.swift                          |  2 +-
 K-Means/Tests/KMeansTests.swift               |  7 ------
 K-Means/Tests/Tests.xcodeproj/project.pbxproj | 24 +++++++++++++++----
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 5 files changed, 30 insertions(+), 13 deletions(-)
 create mode 100644 K-Means/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/K-Means/KMeans.swift b/K-Means/KMeans.swift
index 4a89a3fae..bccc6efd3 100644
--- a/K-Means/KMeans.swift
+++ b/K-Means/KMeans.swift
@@ -12,7 +12,7 @@ class KMeans<Label: Hashable> {
   }
 
   private func indexOfNearestCenter(_ x: Vector, centers: [Vector]) -> Int {
-    var nearestDist = DBL_MAX
+    var nearestDist = Double.greatestFiniteMagnitude
     var minIndex = 0
 
     for (idx, center) in centers.enumerated() {
diff --git a/K-Means/Tests/KMeansTests.swift b/K-Means/Tests/KMeansTests.swift
index e6f4b08a1..7e0c93004 100644
--- a/K-Means/Tests/KMeansTests.swift
+++ b/K-Means/Tests/KMeansTests.swift
@@ -10,13 +10,6 @@ import Foundation
 import XCTest
 
 class KMeansTests: XCTestCase {
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-
   func genPoints(_ numPoints: Int, numDimensions: Int) -> [Vector] {
     var points = [Vector]()
     for _ in 0..<numPoints {
diff --git a/K-Means/Tests/Tests.xcodeproj/project.pbxproj b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
index 139f6baf5..1cbd139e5 100644
--- a/K-Means/Tests/Tests.xcodeproj/project.pbxproj
+++ b/K-Means/Tests/Tests.xcodeproj/project.pbxproj
@@ -85,11 +85,11 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				TargetAttributes = {
 					B80894DF1C852D100018730E = {
 						CreatedOnToolsVersion = 7.2.1;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -137,12 +137,20 @@
 		B80894D91C852CDC0018730E /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -162,12 +170,20 @@
 		B80894DA1C852CDC0018730E /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -229,7 +245,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -271,7 +287,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = com.alvahouse322.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/K-Means/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/K-Means/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/K-Means/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 2b401e86e..73ba8f37d 100644
--- a/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/K-Means/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 8ed7739498a2a3fa2c8974ab48eecfcec8863cbf Mon Sep 17 00:00:00 2001
From: Aleph Retamal <retamal.ph@gmail.com>
Date: Sat, 6 Oct 2018 19:28:22 +1000
Subject: [PATCH 437/643] [Swift 4.2] Update Egg Drop Problem

---
 Egg Drop Problem/EggDrop.playground/Contents.swift        | 4 ----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../xcshareddata/WorkspaceSettings.xcsettings             | 5 +++++
 3 files changed, 13 insertions(+), 4 deletions(-)
 create mode 100644 Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

diff --git a/Egg Drop Problem/EggDrop.playground/Contents.swift b/Egg Drop Problem/EggDrop.playground/Contents.swift
index 0b707da98..decaacdca 100644
--- a/Egg Drop Problem/EggDrop.playground/Contents.swift	
+++ b/Egg Drop Problem/EggDrop.playground/Contents.swift	
@@ -1,7 +1,3 @@
-#if swift(>=4.0)
-  print("Hello, Swift 4!")
-#endif
-
 drop(numberOfEggs: 2, numberOfFloors: 2) //expected answer: 2
 drop(numberOfEggs: 2, numberOfFloors: 4) //expected answer: 3
 drop(numberOfEggs: 2, numberOfFloors: 6) //expected answer: 3
diff --git a/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..0c67376eb
--- /dev/null
+++ b/Egg Drop Problem/EggDrop.playground/playground.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings	
@@ -0,0 +1,5 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict/>
+</plist>

From 2d60bb78c249085c47714474d27d97297a09fa2f Mon Sep 17 00:00:00 2001
From: askari01 <farrukh.askari01@gmail.com>
Date: Sat, 6 Oct 2018 23:02:19 +0500
Subject: [PATCH 438/643] 2 sum problem with swift 4.2

---
 Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift | 5 +----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift | 5 +----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 4 files changed, 18 insertions(+), 8 deletions(-)
 create mode 100644 Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift
index 26bfae449..00a39b04a 100644
--- a/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/Contents.swift	
@@ -1,8 +1,5 @@
 //: Two Sum
-// Last checked with: Version 9.0 (9A235)
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+// Last checked with: Version 10.0 (10A255)
 
 func twoSum(_ nums: [Int], target: Int) -> (Int, Int)? {
     var dict = [Int: Int]()
diff --git a/Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Two-Sum Problem/Solution 1/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift
index 4cb3d9283..469c15b5f 100644
--- a/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/Contents.swift	
@@ -1,8 +1,5 @@
 //: Playground - noun: a place where people can play
-// Last checked with: Version 9.0 beta 4 (9M189t)
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+// Last checked with: Version 10.0 (10A255)
 
 func twoSumProblem(_ a: [Int], k: Int) -> ((Int, Int))? {
   var i = 0
diff --git a/Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Two-Sum Problem/Solution 2/2Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From f0ce485316036d977470c7d38e9a1959e8a60f08 Mon Sep 17 00:00:00 2001
From: askari01 <farrukh.askari01@gmail.com>
Date: Sat, 6 Oct 2018 23:08:23 +0500
Subject: [PATCH 439/643] updated readme for 2 sum problem with swift 4.2

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

diff --git a/Two-Sum Problem/README.markdown b/Two-Sum Problem/README.markdown
index 4d8ffcd95..bbd033343 100644
--- a/Two-Sum Problem/README.markdown	
+++ b/Two-Sum Problem/README.markdown	
@@ -168,4 +168,4 @@ I'm quite enamored by this little algorithm. It shows that with some basic prepr
 
 * [3Sum / 4Sum](https://github.com/raywenderlich/swift-algorithm-club/tree/master/3Sum%20and%204Sum)
 
-*Written for Swift Algorithm Club by Matthijs Hollemans and Daniel Speiser*
+*Written for Swift Algorithm Club by Matthijs Hollemans and Daniel Speiser updated to swift 4.2 by Farrukh Askari*

From 86d6cd114d34a602f987ab0f7a7b21d1ff7580ee Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 8 Oct 2018 19:06:01 +1100
Subject: [PATCH 440/643] [Swift 4.2] Update Karatsuba multiplication

Changed the way the characters in a String were accessed since `characters` was deprecated on Swift 4.0.
Removed the code snippet at the beggining of the file.
---
 .../Contents.swift                              | 17 +++++++----------
 .../xcshareddata/IDEWorkspaceChecks.plist       |  8 ++++++++
 .../KaratsubaMultiplication.swift               | 12 ++++++------
 3 files changed, 21 insertions(+), 16 deletions(-)
 create mode 100644 Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 04aff1ec4..e0ce23b19 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -1,10 +1,7 @@
 //: Playground - noun: a place where people can play
 
 import Foundation
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4")
-#endif
+
 precedencegroup ExponentiativePrecedence {
   higherThan: MultiplicationPrecedence
   lowerThan: BitwiseShiftPrecedence
@@ -18,8 +15,8 @@ func ^^ (radix: Int, power: Int) -> Int {
 
 // Long Multiplication - O(n^2)
 func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
-  let num1Array = String(num1).characters.reversed().map { Int(String($0))! }
-  let num2Array = String(num2).characters.reversed().map { Int(String($0))! }
+  let num1Array = String(num1).reversed().map { Int(String($0))! }
+  let num2Array = String(num2).reversed().map { Int(String($0))! }
   
   var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
   
@@ -38,14 +35,14 @@ func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
 
 // Karatsuba Multiplication - O(n^log2(3))
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
-  let num1Array = String(num1).characters
-  let num2Array = String(num2).characters
+  let num1String = String(num1)
+  let num2String = String(num2)
   
-  guard num1Array.count > 1 && num2Array.count > 1 else {
+  guard num1String.count > 1 && num2String.count > 1 else {
     return multiply(num1, by: num2)
   }
   
-  let n = max(num1Array.count, num2Array.count)
+  let n = max(num1String.count, num2String.count)
   let nBy2 = n / 2
   
   let a = num1 / 10^^nBy2
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
index fb20a667d..a82e82658 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -20,14 +20,14 @@ func ^^ (radix: Int, power: Int) -> Int {
 }
 
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
-  let num1Array = String(num1).characters
-  let num2Array = String(num2).characters
+  let num1String = String(num1)
+  let num2String = String(num2)
   
-  guard num1Array.count > 1 && num2Array.count > 1 else {
-    return num1 * num2
+  guard num1String.count > 1 && num2String.count > 1 else {
+    return multiply(num1, by: num2)
   }
-  
-  let n = max(num1Array.count, num2Array.count)
+
+  let n = max(num1String.count, num2String.count)
   let nBy2 = n / 2
   
   let a = num1 / 10^^nBy2

From ab20d205384c4fc40908f99dcfb941d485cac3c6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 8 Oct 2018 19:22:09 +1100
Subject: [PATCH 441/643] [Swift 4.2] Update README.md for Karatsuba
 multiplication

---
 Karatsuba Multiplication/README.markdown | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Karatsuba Multiplication/README.markdown b/Karatsuba Multiplication/README.markdown
index c86f69831..3a48ed39d 100644
--- a/Karatsuba Multiplication/README.markdown	
+++ b/Karatsuba Multiplication/README.markdown	
@@ -71,15 +71,15 @@ Here's the full implementation. Note that the recursive algorithm is most effici
 
 ```swift
 // Karatsuba Multiplication
-func karatsuba(_ num1: Int, by num2: Int) -> Int {
-  let num1Array = String(num1).characters
-  let num2Array = String(num2).characters
+  func karatsuba(_ num1: Int, by num2: Int) -> Int {
+  let num1String = String(num1)
+  let num2String = String(num2)
   
-  guard num1Array.count > 1 && num2Array.count > 1 else {
-    return num1*num2
+  guard num1String.count > 1 && num2String.count > 1 else {
+  return multiply(num1, by: num2)
   }
   
-  let n = max(num1Array.count, num2Array.count)
+  let n = max(num1String.count, num2String.count)
   let nBy2 = n / 2
   
   let a = num1 / 10^^nBy2

From 2d1d22316401f52ac6a08325c781e812e40542c5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 8 Oct 2018 20:20:30 +1100
Subject: [PATCH 442/643] [Swift 4.2] added tests

---
 .travis.yml                                   |   1 +
 .../KaratsubaMultiplication.swift             |  31 +-
 .../Tests/KaratsubaMultiplicationTests.swift  |  17 +
 .../Tests/Tests.xcodeproj/project.pbxproj     | 305 ++++++++++++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  56 ++++
 .../Tests/Tests/Info.plist                    |  22 ++
 .../contents.xcworkspacedata                  |   7 +
 7 files changed, 434 insertions(+), 5 deletions(-)
 create mode 100644 Karatsuba Multiplication/Tests/KaratsubaMultiplicationTests.swift
 create mode 100644 Karatsuba Multiplication/Tests/Tests.xcodeproj/project.pbxproj
 create mode 100644 Karatsuba Multiplication/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
 create mode 100644 Karatsuba Multiplication/Tests/Tests/Info.plist

diff --git a/.travis.yml b/.travis.yml
index edf1cf89f..56e205656 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -48,6 +48,7 @@ script:
 - xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
 - xcodebuild test -project ./Palindromes/Test/Test.xcodeproj -scheme Test | xcpretty -f `xcpretty-travis-formatter`
 - xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
+- xcodebuild test -project ./Karatsuba\ Multiplication/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
 
 after_success:
 
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.swift b/Karatsuba Multiplication/KaratsubaMultiplication.swift
index a82e82658..3d14a243a 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.swift	
@@ -19,27 +19,48 @@ func ^^ (radix: Int, power: Int) -> Int {
   return Int(pow(Double(radix), Double(power)))
 }
 
+// Long Multiplication - O(n^2)
+func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
+  let num1Array = String(num1).reversed().map { Int(String($0))! }
+  let num2Array = String(num2).reversed().map { Int(String($0))! }
+
+  var product = Array(repeating: 0, count: num1Array.count + num2Array.count)
+
+  for i in num1Array.indices {
+    var carry = 0
+    for j in num2Array.indices {
+      product[i + j] += carry + num1Array[i] * num2Array[j]
+      carry = product[i + j] / base
+      product[i + j] %= base
+    }
+    product[i + num2Array.count] += carry
+  }
+
+  return Int(product.reversed().map { String($0) }.reduce("", +))!
+}
+
+// Karatsuba Multiplication - O(n^log2(3))
 func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1String = String(num1)
   let num2String = String(num2)
-  
+
   guard num1String.count > 1 && num2String.count > 1 else {
     return multiply(num1, by: num2)
   }
 
   let n = max(num1String.count, num2String.count)
   let nBy2 = n / 2
-  
+
   let a = num1 / 10^^nBy2
   let b = num1 % 10^^nBy2
   let c = num2 / 10^^nBy2
   let d = num2 % 10^^nBy2
-  
+
   let ac = karatsuba(a, by: c)
   let bd = karatsuba(b, by: d)
   let adPlusbc = karatsuba(a+b, by: c+d) - ac - bd
-  
+
   let product = ac * 10^^(2 * nBy2) + adPlusbc * 10^^nBy2 + bd
-  
+
   return product
 }
diff --git a/Karatsuba Multiplication/Tests/KaratsubaMultiplicationTests.swift b/Karatsuba Multiplication/Tests/KaratsubaMultiplicationTests.swift
new file mode 100644
index 000000000..379c9e812
--- /dev/null
+++ b/Karatsuba Multiplication/Tests/KaratsubaMultiplicationTests.swift	
@@ -0,0 +1,17 @@
+//
+//  KaratsubaMultiplicationTests.swift
+//  Tests
+//
+//  Created by Afonso Graça on 8/10/18.
+//
+
+import XCTest
+
+final class KaratsubaMultiplicationTests: XCTestCase {
+
+    func testReadmeExample() {
+        let subject = karatsuba(1234, by: 5678)
+
+        XCTAssertEqual(subject, 7006652)
+    }
+}
diff --git a/Karatsuba Multiplication/Tests/Tests.xcodeproj/project.pbxproj b/Karatsuba Multiplication/Tests/Tests.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..ef23067ee
--- /dev/null
+++ b/Karatsuba Multiplication/Tests/Tests.xcodeproj/project.pbxproj	
@@ -0,0 +1,305 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 50;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		6AF099AC216B54E200F69B16 /* KaratsubaMultiplication.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AF099AB216B54E200F69B16 /* KaratsubaMultiplication.swift */; };
+		6AF099AE216B55A100F69B16 /* KaratsubaMultiplicationTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AF099AD216B55A100F69B16 /* KaratsubaMultiplicationTests.swift */; };
+/* End PBXBuildFile section */
+
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+		6AF099A2216B54D500F69B16 /* Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Tests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
+		6AF099A7216B54D500F69B16 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; name = Info.plist; path = Tests/Info.plist; sourceTree = SOURCE_ROOT; };
+		6AF099AB216B54E200F69B16 /* KaratsubaMultiplication.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = KaratsubaMultiplication.swift; path = ../KaratsubaMultiplication.swift; sourceTree = "<group>"; };
+		6AF099AD216B55A100F69B16 /* KaratsubaMultiplicationTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = KaratsubaMultiplicationTests.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
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+		6AF0999F216B54D500F69B16 /* Frameworks */ = {
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+			buildActionMask = 2147483647;
+			files = (
+			);
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+/* End PBXFrameworksBuildPhase section */
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+		6AF09997216B545D00F69B16 = {
+			isa = PBXGroup;
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+				6AF099A7216B54D500F69B16 /* Info.plist */,
+			);
+			name = Tests;
+			sourceTree = SOURCE_ROOT;
+		};
+/* End PBXGroup section */
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+/* End PBXNativeTarget section */
+
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+			isa = PBXProject;
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+				LastSwiftUpdateCheck = 1000;
+				LastUpgradeCheck = 1000;
+				TargetAttributes = {
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+
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+			);
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+/* End PBXResourcesBuildPhase section */
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+			files = (
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+			buildSettings = {
+			};
+			name = Debug;
+		};
+		6AF0999D216B545D00F69B16 /* Release */ = {
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+			buildSettings = {
+			};
+			name = Release;
+		};
+		6AF099A9216B54D500F69B16 /* Debug */ = {
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+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
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+				CLANG_ENABLE_OBJC_WEAK = YES;
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+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
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+				CODE_SIGN_IDENTITY = "-";
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+				COMBINE_HIDPI_IMAGES = YES;
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+				ENABLE_TESTABILITY = YES;
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+				GCC_DYNAMIC_NO_PIC = NO;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_OPTIMIZATION_LEVEL = 0;
+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Tests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
+				MACOSX_DEPLOYMENT_TARGET = 10.14;
+				MTL_ENABLE_DEBUG_INFO = INCLUDE_SOURCE;
+				MTL_FAST_MATH = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 4.2;
+			};
+			name = Debug;
+		};
+		6AF099AA216B54D500F69B16 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_ANALYZER_NONNULL = YES;
+				CLANG_ANALYZER_NUMBER_OBJECT_CONVERSION = YES_AGGRESSIVE;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++14";
+				CLANG_CXX_LIBRARY = "libc++";
+				CLANG_ENABLE_MODULES = YES;
+				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_ENABLE_OBJC_WEAK = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
+				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
+				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
+				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNGUARDED_AVAILABILITY = YES_AGGRESSIVE;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				CODE_SIGN_IDENTITY = "-";
+				CODE_SIGN_STYLE = Automatic;
+				COMBINE_HIDPI_IMAGES = YES;
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu11;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Tests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
+				MACOSX_DEPLOYMENT_TARGET = 10.14;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				MTL_FAST_MATH = YES;
+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SDKROOT = macosx;
+				SWIFT_COMPILATION_MODE = wholemodule;
+				SWIFT_OPTIMIZATION_LEVEL = "-O";
+				SWIFT_VERSION = 4.2;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		6AF0999B216B545D00F69B16 /* Build configuration list for PBXProject "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				6AF0999C216B545D00F69B16 /* Debug */,
+				6AF0999D216B545D00F69B16 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		6AF099A8216B54D500F69B16 /* Build configuration list for PBXNativeTarget "Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				6AF099A9216B54D500F69B16 /* Debug */,
+				6AF099AA216B54D500F69B16 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 6AF09998216B545D00F69B16 /* Project object */;
+}
diff --git a/Karatsuba Multiplication/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Karatsuba Multiplication/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
new file mode 100644
index 000000000..1288fd9a8
--- /dev/null
+++ b/Karatsuba Multiplication/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -0,0 +1,56 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "1000"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <Testables>
+         <TestableReference
+            skipped = "NO">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "6AF099A1216B54D500F69B16"
+               BuildableName = "Tests.xctest"
+               BlueprintName = "Tests"
+               ReferencedContainer = "container:Tests.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      allowLocationSimulation = "YES">
+      <AdditionalOptions>
+      </AdditionalOptions>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Release"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>
diff --git a/Karatsuba Multiplication/Tests/Tests/Info.plist b/Karatsuba Multiplication/Tests/Tests/Info.plist
new file mode 100644
index 000000000..6c40a6cd0
--- /dev/null
+++ b/Karatsuba Multiplication/Tests/Tests/Info.plist	
@@ -0,0 +1,22 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>$(DEVELOPMENT_LANGUAGE)</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>BNDL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+</dict>
+</plist>
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 142713e62..9305ae37c 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1472,6 +1472,13 @@
       <FileRef
          location = "group:README.markdown">
       </FileRef>
+      <Group
+         location = "group:"
+         name = "Tests">
+         <FileRef
+            location = "group:Tests/Tests.xcodeproj">
+         </FileRef>
+      </Group>
    </Group>
    <Group
       location = "group:Knuth-Morris-Pratt"

From 34526e97eb792f62a942c8379968f0494ae084c1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 8 Oct 2018 20:31:20 +1100
Subject: [PATCH 443/643] [Swift 4.2] Update Fizz Buzz

There was no need to update the source code, simply removed the code snippet.
---
 Fizz Buzz/FizzBuzz.playground/Contents.swift              | 5 +----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 9 insertions(+), 4 deletions(-)
 create mode 100644 Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Fizz Buzz/FizzBuzz.playground/Contents.swift b/Fizz Buzz/FizzBuzz.playground/Contents.swift
index 37acdab61..ae966bbcc 100644
--- a/Fizz Buzz/FizzBuzz.playground/Contents.swift	
+++ b/Fizz Buzz/FizzBuzz.playground/Contents.swift	
@@ -1,7 +1,4 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+// last checked with Xcode 10.0 (10A255)
 
 func fizzBuzz(_ numberOfTurns: Int) {
   for i in 1...numberOfTurns {
diff --git a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 409e85fdc8968230758ef703804f51956dc524a7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=9F=D0=B0=D0=BD=D0=BA=D0=BE=D0=B2=D0=B0=20=D0=9C=D0=B0?=
 =?UTF-8?q?=D1=80=D0=B8=D1=8F=20=D0=92=D0=B8=D1=82=D0=B0=D0=BB=D1=8C=D0=B5?=
 =?UTF-8?q?=D0=B2=D0=BD=D0=B0?= <mv.pankova@2Gis.ru>
Date: Mon, 8 Oct 2018 21:49:03 +0700
Subject: [PATCH 444/643] [Swift 4.2] Update Convex Hull

---
 .../Convex Hull.xcodeproj/project.pbxproj     | 26 +++++++++++++++----
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 +--
 .../AppIcon.appiconset/Contents.json          |  5 ++++
 Convex Hull/Convex Hull/View.swift            |  4 +--
 4 files changed, 29 insertions(+), 10 deletions(-)

diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
index c11cbf4d6..27ca4eb25 100644
--- a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -139,7 +139,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0900;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = Workmoose;
 				TargetAttributes = {
 					1CB6142C1F89456C00A14493 = {
@@ -254,7 +254,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.mnespor.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				TARGETED_DEVICE_FAMILY = "1,2";
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Convex Hull.app/Convex Hull";
 			};
@@ -281,7 +281,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks @loader_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = com.mnespor.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				TARGETED_DEVICE_FAMILY = "1,2";
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Convex Hull.app/Convex Hull";
 			};
@@ -296,15 +296,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -346,15 +354,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -389,7 +405,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -402,7 +418,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 1f93a0c4f..8f04a0f51 100644
--- a/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Convex Hull/Convex Hull.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -10,7 +10,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -31,7 +30,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"
diff --git a/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json b/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json
index 1d060ed28..d8db8d65f 100644
--- a/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json	
+++ b/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json	
@@ -84,6 +84,11 @@
       "idiom" : "ipad",
       "size" : "83.5x83.5",
       "scale" : "2x"
+    },
+    {
+      "idiom" : "ios-marketing",
+      "size" : "1024x1024",
+      "scale" : "1x"
     }
   ],
   "info" : {
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index 33d1426c3..e75c73ed0 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -27,8 +27,8 @@ class View: UIView {
   func generateRandomPoints() {
     for _ in 0..<MAX_POINTS {
       let offset: CGFloat = 50
-      let xrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.width - offset) + 0.5 * offset
-      let yrand = CGFloat(arc4random()) / CGFloat(UINT32_MAX) * (self.frame.height - offset) + 0.5 * offset
+      let xrand = CGFloat(arc4random()) / CGFloat(UInt32.max) * (self.frame.width - offset) + 0.5 * offset
+      let yrand = CGFloat(arc4random()) / CGFloat(UInt32.max) * (self.frame.height - offset) + 0.5 * offset
       let point = CGPoint(x: xrand, y: yrand)
       points.append(point)
     }

From 0e83ef2e5d287d737153a4c14d15ff8ed2cf7fca Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 8 Oct 2018 19:30:25 -0300
Subject: [PATCH 445/643] removed duplicate implementation

---
 .../MyPlayground.playground/Contents.swift      | 17 -----------------
 1 file changed, 17 deletions(-)

diff --git a/Bubble Sort/MyPlayground.playground/Contents.swift b/Bubble Sort/MyPlayground.playground/Contents.swift
index 16466e0bc..8d27d801e 100644
--- a/Bubble Sort/MyPlayground.playground/Contents.swift	
+++ b/Bubble Sort/MyPlayground.playground/Contents.swift	
@@ -1,22 +1,5 @@
 import Foundation
 
-public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
-    var array = elements
-    
-    for i in 0..<array.count {
-        for j in 1..<array.count-i {
-            print(array,"comparing [\(j-1)] with [\(j)]")
-            if array[j] < array[j-1] {
-                let tmp = array[j-1]
-                array[j-1] = array[j]
-                array[j] = tmp
-            }
-        }
-    }
-    
-    return array
-}
-
 var array = [4,2,1,3]
 
 print("before:",array)

From da34da5b85a2f40869305e8c03d3e78e7b04a5e7 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 8 Oct 2018 19:30:58 -0300
Subject: [PATCH 446/643] changed tab width to 2 spaces instead of 4

---
 .../Sources/BubbleSort.swift                  | 24 +++++++++----------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift
index 5ce18ef9b..9c091b661 100644
--- a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
+++ b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
@@ -26,17 +26,17 @@ import Foundation
 /// - Parameter elements: the array to be sorted
 /// - Returns: an array with the same elements but in order
 public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
-    var array = elements
-    
-    for i in 0..<array.count {
-        for j in 1..<array.count-i {
-            if array[j] < array[j-1] {
-                let tmp = array[j-1]
-                array[j-1] = array[j]
-                array[j] = tmp
-            }
-        }
+  var array = elements
+  
+  for i in 0..<array.count {
+    for j in 1..<array.count-i {
+      if array[j] < array[j-1] {
+        let tmp = array[j-1]
+        array[j-1] = array[j]
+        array[j] = tmp
+      }
     }
-    
-    return array
+  }
+  
+  return array
 }

From ab3b6cdd61031bfd8a03803f6258f3369db0fa74 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 8 Oct 2018 20:16:55 -0300
Subject: [PATCH 447/643] updated readme to conform with changes requested

---
 Bubble Sort/README.markdown | 75 +++++++++++++++++++++++++++++--------
 1 file changed, 59 insertions(+), 16 deletions(-)

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index 80161ce56..e55129d93 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -1,6 +1,6 @@
 # Bubble Sort
 
-Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array.Sometimes this algorithm is refered as Sinking sort, due to the larger, or heavier elements sinking to the end of the array.
+Bubble sort is a sorting algorithm that is implemented by starting in the beginning of the array and swapping the first two elements only if the first element is greater than the second element. This comparison is then moved onto the next pair and so on and so forth. This is done until the array is completely sorted. The smaller items slowly “bubble” up to the beginning of the array. Sometimes this algorithm is refered as Sinking sort, due to the larger, or heavier elements sinking to the end of the array.
 
 ##### Runtime:
 - Average: O(N^2)
@@ -16,6 +16,10 @@ The implementation will not be shown as the average and worst runtimes show that
 Bubble sort is a very simple sorting algorithm, it consists in comparing pairs of adjacent elements in the array, if the first element is larger, swap them, otherwise, you do nothing and go for the next comparison.
 This is accomplished by looking through the array `n` times, `n` being the amount of elements in the array.
 
+![animated gif of the bubble sort algorithm](https://s3.amazonaws.com/codecademy-content/programs/tdd-js/articles/BubbleSort.gif)
+
+This GIF shows a inverted implementation than 
+
 #### Example
 Let us take the array `[5, 1, 4, 2, 8]`, and sort the array from lowest number to greatest number using bubble sort. In each step, elements written in bold are being compared. Three passes will be required.
 
@@ -52,13 +56,13 @@ This is the same for the forth and fifth passes.
 #### Code
 ```swift
 for i in 0..<array.count {
-for j in 1..<array.count {
-if array[j] < array[i] {
-let tmp = array[i]
-array[i] = array[j]
-array[j] = tmp
-}
-}
+  for j in 1..<array.count {
+    if array[j] < array[i] {
+      let tmp = array[i]
+      array[i] = array[j]
+      array[j] = tmp
+    }
+  }
 }
 return array
 ```
@@ -68,17 +72,56 @@ The bubble sort algorithm can be easily optimized by observing that the `n-th` p
 
 ```swift
 for i in 0..<array.count {
-for j in 1..<array.count - i {
-if array[j] < array[i] {
-let tmp = array[i]
-array[i] = array[j]
-array[j] = tmp
-}
-}
+  for j in 1..<array.count - i {
+    if array[j] < array[i] {
+      let tmp = array[i]
+      array[i] = array[j]
+      array[j] = tmp
+    }
+  }
 }
 return array
 ```
 
 The only change made was on the second line, changing the interval from `1..<array.count` to `1..<array.count - i`, effectively cutting the number of comparisons by half.
 
-That said, this is still a terribly inefficient sorting algorithm.
+The ordering with the optimized code would look something like this for the array  `[5, 1, 4, 2, 8]`:
+
+##### First Pass
+[ **5 1** 4 2 8 ] -> [ **1 5** 4 2 8 ], Swaps since 5 > 1
+
+[ 1 **5 4** 2 8 ] -> [ 1 **4 5** 2 8 ], Swap since 5 > 4 
+
+[ 1 4 **5 2** 8 ] -> [ 1 4 **2 5** 8 ], Swap since 5 > 2 
+
+[ 1 4 2 **5 8** ] -> [ 1 4 2 **5 8** ], Now, since these elements are already in order (8 > 5), algorithm does not swap them. 
+
+*by the end of the first pass, the last element is guaranteed to be the largest*
+
+##### Second Pass
+[ **1 4** 2 5 8 ] -> [ **1 4** 2 5 8 ]
+
+[ 1 **4 2** 5 8 ] -> [ 1 **2 4** 5 8 ], Swap since 4 > 2 
+
+[ 1 2 **4 5** 8 ] -> [ 1 2 **4 5** 8 ], As the first loop has occured once, the inner loop stops here, not comparing 5 with 8
+
+##### Third Pass
+[ **1 2** 4 5 8 ] -> [ **1 2** 4 5 8 ]
+
+[ 1 **2 4** 5 8 ] -> [ 1 **2 4** 5 8 ] again, stoping one comparison short
+
+##### Fourth Pass
+[ **1 2** 4 5 8 ] -> [ **1 2** 4 5 8 ]
+
+There is no Fifth pass
+
+#### Conclusion
+
+Even with the proposed optimizations, this is still a terribly inefficient sorting algorithm. A good alternative is [Merge Sort](), that not only is better performing, has a similar degree of dificulty to implement.
+
+*Updated for the Swift Algorithm Club by Julio Brazil*
+
+##### Supporting Links
+[Code Pumpkin](https://codepumpkin.com/bubble-sort/)
+[Wikipedia](https://en.wikipedia.org/wiki/Bubble_sort)
+[GeeksforGeeks](https://www.geeksforgeeks.org/bubble-sort/)

From 39971b49661a7179117511ddfc6c79e1bde12378 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=95=D0=BA=D0=B0=D1=82=D0=B5=D1=80=D0=B8=D0=BD=D0=B0=20?=
 =?UTF-8?q?=D0=91=D0=B0=D1=82=D0=B5=D0=B5=D0=B2=D0=B0?= <bateeva-k@mail.ru>
Date: Wed, 10 Oct 2018 22:39:38 +0300
Subject: [PATCH 448/643] [Swift 4.2] Update Boyer-Moore-Horspool

---
 .../BoyerMooreHorspool.playground/Contents.swift          | 6 +++---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../BoyerMooreHorspool.playground/timeline.xctimeline     | 6 +++---
 Boyer-Moore-Horspool/BoyerMooreHorspool.swift             | 6 +++---
 4 files changed, 17 insertions(+), 9 deletions(-)
 create mode 100644 Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
index e88a1b93d..5817cc41f 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
@@ -16,13 +16,13 @@ extension String {
     func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
index 89bc76f90..2688d72c1 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=37&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.616217"
+         documentLocation = "file:///Users/neifmetus/Documents/Projects/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=560891520.806637"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=26&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.61657"
+         documentLocation = "file:///Users/neifmetus/Documents/Projects/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=560891520.806855"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=25&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.616725"
+         documentLocation = "file:///Users/neifmetus/Documents/Projects/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=560891520.807023"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
index af8aea9d9..dbd738740 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
@@ -9,13 +9,13 @@ extension String {
     func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 

From 8e6c983cd0c5ae26a68531bb54521b85f3926120 Mon Sep 17 00:00:00 2001
From: Varun <varunkapoor989@gmail.com>
Date: Thu, 11 Oct 2018 13:41:40 +0530
Subject: [PATCH 449/643] updated LinkedList.playground to swift 4.2

---
 Linked List/LinkedList.playground/Contents.swift        | 4 ----
 Linked List/LinkedList.playground/contents.xcplayground | 2 +-
 2 files changed, 1 insertion(+), 5 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index cfa3a8b45..894b2d37f 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -3,10 +3,6 @@
 // For best results, don't forget to select "Show Rendered Markup" from XCode's "Editor" menu
 
 //: Linked List Class Declaration:
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 public final class LinkedList<T> {
     
diff --git a/Linked List/LinkedList.playground/contents.xcplayground b/Linked List/LinkedList.playground/contents.xcplayground
index 3de2b51ba..5e28f2dd0 100644
--- a/Linked List/LinkedList.playground/contents.xcplayground	
+++ b/Linked List/LinkedList.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx' display-mode='rendered'>
+<playground version='5.0' target-platform='osx' display-mode='rendered' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 3f0ee826265621d22205316a3f52f22d7e5ee39f Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 11 Oct 2018 14:17:34 +0200
Subject: [PATCH 450/643] Update to Swift 4.2.

Also removed unused Tests group from project.
---
 .../project.pbxproj                           | 22 ++++++++-----------
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++++
 2 files changed, 17 insertions(+), 13 deletions(-)
 create mode 100644 DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
index ecb060026..97f3c4847 100755
--- a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
@@ -27,13 +27,6 @@
 /* End PBXFrameworksBuildPhase section */
 
 /* Begin PBXGroup section */
-		OBJ_10 /* Tests */ = {
-			isa = PBXGroup;
-			children = (
-			);
-			path = Tests;
-			sourceTree = "<group>";
-		};
 		OBJ_11 /* Products */ = {
 			isa = PBXGroup;
 			children = (
@@ -42,15 +35,13 @@
 			name = Products;
 			sourceTree = BUILT_PRODUCTS_DIR;
 		};
-		OBJ_5 /*  */ = {
+		OBJ_5 = {
 			isa = PBXGroup;
 			children = (
 				OBJ_6 /* Package.swift */,
 				OBJ_7 /* Sources */,
-				OBJ_10 /* Tests */,
 				OBJ_11 /* Products */,
 			);
-			name = "";
 			sourceTree = "<group>";
 		};
 		OBJ_7 /* Sources */ = {
@@ -96,6 +87,11 @@
 			isa = PBXProject;
 			attributes = {
 				LastUpgradeCheck = 9999;
+				TargetAttributes = {
+					OBJ_13 = {
+						LastSwiftMigration = 1000;
+					};
+				};
 			};
 			buildConfigurationList = OBJ_2 /* Build configuration list for PBXProject "DiningPhilosophers" */;
 			compatibilityVersion = "Xcode 3.2";
@@ -104,7 +100,7 @@
 			knownRegions = (
 				en,
 			);
-			mainGroup = OBJ_5 /*  */;
+			mainGroup = OBJ_5;
 			productRefGroup = OBJ_11 /* Products */;
 			projectDirPath = "";
 			projectRoot = "";
@@ -139,7 +135,7 @@
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = SWIFT_PACKAGE;
 				SWIFT_FORCE_DYNAMIC_LINK_STDLIB = YES;
 				SWIFT_FORCE_STATIC_LINK_STDLIB = NO;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				TARGET_NAME = DiningPhilosophers;
 			};
 			name = Debug;
@@ -157,7 +153,7 @@
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = SWIFT_PACKAGE;
 				SWIFT_FORCE_DYNAMIC_LINK_STDLIB = YES;
 				SWIFT_FORCE_STATIC_LINK_STDLIB = NO;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 				TARGET_NAME = DiningPhilosophers;
 			};
 			name = Release;
diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 6c48b3d493b4e6f023b006871f58fbe485db96b1 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 11 Oct 2018 14:18:45 +0200
Subject: [PATCH 451/643] Add README.md to project.

This makes it easier to read along with the code.
---
 DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
index 97f3c4847..7699219de 100755
--- a/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
+++ b/DiningPhilosophers/DiningPhilosophers.xcodeproj/project.pbxproj
@@ -11,6 +11,7 @@
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
+		232D7939216F76F700831A74 /* README.md */ = {isa = PBXFileReference; lastKnownFileType = net.daringfireball.markdown; path = README.md; sourceTree = "<group>"; };
 		OBJ_12 /* DiningPhilosophers */ = {isa = PBXFileReference; explicitFileType = "compiled.mach-o.executable"; path = DiningPhilosophers; sourceTree = BUILT_PRODUCTS_DIR; };
 		OBJ_6 /* Package.swift */ = {isa = PBXFileReference; explicitFileType = sourcecode.swift; path = Package.swift; sourceTree = "<group>"; };
 		OBJ_9 /* main.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = main.swift; sourceTree = "<group>"; };
@@ -38,6 +39,7 @@
 		OBJ_5 = {
 			isa = PBXGroup;
 			children = (
+				232D7939216F76F700831A74 /* README.md */,
 				OBJ_6 /* Package.swift */,
 				OBJ_7 /* Sources */,
 				OBJ_11 /* Products */,

From f2c04f7ac0ed2634221eca58ed303e3a3b239cd9 Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 11 Oct 2018 14:18:54 +0200
Subject: [PATCH 452/643] Add credit to README.md.

---
 DiningPhilosophers/README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index cd9d86154..aed9dfe59 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -57,3 +57,4 @@ A background DispatchQueue is then used to let any Philosopher run asyncrounosly
 Dining Philosophers on Wikipedia https://en.wikipedia.org/wiki/Dining_philosophers_problem
 
 Written for Swift Algorithm Club by Jacopo Mangiavacchi
+Swift 4.2 check by Bruno Scheele

From eeb116e4073a0b1a0a9d13701bbe27d29e1ec6bb Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 11 Oct 2018 14:26:17 +0200
Subject: [PATCH 453/643] Update to Swift 4.2.

---
 Red-Black Tree/RedBlackTree.playground/Contents.swift     | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Red-Black Tree/RedBlackTree.playground/Contents.swift b/Red-Black Tree/RedBlackTree.playground/Contents.swift
index f14f18e58..d1133bc98 100644
--- a/Red-Black Tree/RedBlackTree.playground/Contents.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Contents.swift	
@@ -2,11 +2,6 @@
 // Test for  the RedBlackTree implementation provided in the Source folder of this Playground
 import Foundation
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let redBlackTree = RedBlackTree<Double>()
 
 let randomMax = Double(0x10000000)
diff --git a/Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From af9a6564f87da3390d9c0287995ba213f47c94ad Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 11 Oct 2018 14:26:34 +0200
Subject: [PATCH 454/643] Add credit to README.md.

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

diff --git a/Red-Black Tree/README.markdown b/Red-Black Tree/README.markdown
index 74fffa415..fd6c4db18 100644
--- a/Red-Black Tree/README.markdown	
+++ b/Red-Black Tree/README.markdown	
@@ -186,4 +186,4 @@ The overall runtime of delete is O(log n).
 ## Resources:
 [CLRS]  T. Cormen, C. Leiserson, R. Rivest, and C. Stein. "Introduction to Algorithms", Third Edition. 2009
 
-*Written for Swift Algorithm Club by Ute Schiehlen. Updated from Jaap Wijnen and Ashwin Raghuraman's contributions.*
+*Written for Swift Algorithm Club by Ute Schiehlen. Updated from Jaap Wijnen and Ashwin Raghuraman's contributions. Swift 4.2 check by Bruno Scheele.*

From d3d382f1d2f76c91a14a9b61b02375f7c6388265 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=95=D0=BA=D0=B0=D1=82=D0=B5=D1=80=D0=B8=D0=BD=D0=B0=20?=
 =?UTF-8?q?=D0=91=D0=B0=D1=82=D0=B5=D0=B5=D0=B2=D0=B0?= <bateeva-k@mail.ru>
Date: Fri, 12 Oct 2018 23:06:22 +0300
Subject: [PATCH 455/643] Fix HarversineDistance pi parameter in "Converts from
 degrees to radians"

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

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index 5b3f591d6..7aa686645 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -16,7 +16,7 @@ func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radi
     
     // Converts from degrees to radians
     let dToR = { (angle: Double) -> Double in
-        return (angle / 360) * 2 * M_PI
+        return (angle / 360) * 2 * .pi
     }
     
     let lat1 = dToR(la1)

From acb21c32df8cc6c2ba8c153497902c24a661fff4 Mon Sep 17 00:00:00 2001
From: Nick Thompson <dev@nickthompson.guru>
Date: Fri, 12 Oct 2018 17:18:55 -0400
Subject: [PATCH 456/643] Updated MST to Swift 4.2

---
 .../MinimumSpanningTree.playground/Contents.swift         | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift
index c4f0a811b..7e3532429 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
@@ -3,11 +3,6 @@
  Kruskal's and Prim's algorithms.
  */
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 func minimumSpanningTreeKruskal<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
     var cost: Int = 0
     var tree = Graph<T>()
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From e0c6676601b6de0b093d3a171bf7497c73947522 Mon Sep 17 00:00:00 2001
From: Nick Thompson <dev@nickthompson.guru>
Date: Fri, 12 Oct 2018 17:37:17 -0400
Subject: [PATCH 457/643] Updated MST (Unweighted) to Swift 4.2

---
 .../Contents.swift                                        | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift
index 65aa9fbc4..8ad04379c 100644
--- a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/Pages/Minimum spanning tree example.xcplaygroundpage/Contents.swift	
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 func breadthFirstSearchMinimumSpanningTree(_ graph: Graph, source: Node) -> Graph {
   let minimumSpanningTree = graph.duplicate()
 
diff --git a/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Minimum Spanning Tree (Unweighted)/MinimumSpanningTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 45cca894960b5aab35f8e675c1e2066025e7df91 Mon Sep 17 00:00:00 2001
From: Nick Thompson <dev@nickthompson.guru>
Date: Fri, 12 Oct 2018 17:40:24 -0400
Subject: [PATCH 458/643] Updated MST (Unweighted) tests to Swift 4.2

---
 .../Tests/Tests.xcodeproj/project.pbxproj     | 31 ++++++++++++++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 3 files changed, 36 insertions(+), 5 deletions(-)
 create mode 100644 Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj
index a066b7a71..afb3b8acb 100644
--- a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.pbxproj	
@@ -89,12 +89,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0720;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -149,13 +149,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,13 +203,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -218,6 +238,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_COMPILATION_MODE = wholemodule;
 			};
 			name = Release;
 		};
@@ -231,7 +252,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -244,7 +266,8 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 8ef8d8581..afd69e6a7 100644
--- a/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Minimum Spanning Tree (Unweighted)/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0720"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 685b315c166d9fa8ee8af81ffb7029d242b03921 Mon Sep 17 00:00:00 2001
From: Viktor Sokolov <bntrsokolov@gmail.com>
Date: Sat, 13 Oct 2018 10:59:37 +0300
Subject: [PATCH 459/643] update Huffman Coding to Swift 4.2

---
 Huffman Coding/Huffman.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Huffman Coding/Huffman.playground/Contents.swift b/Huffman Coding/Huffman.playground/Contents.swift
index 6242ad272..2d59908e9 100644
--- a/Huffman Coding/Huffman.playground/Contents.swift	
+++ b/Huffman Coding/Huffman.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 let s1 = "so much words wow many compression"

From 85738885f0ec2e2f6041eb8545a4cfa99233e783 Mon Sep 17 00:00:00 2001
From: Viktor Sokolov <bntrsokolov@gmail.com>
Date: Sat, 13 Oct 2018 11:21:15 +0300
Subject: [PATCH 460/643] Update Quad Tree to Swift 4.2

---
 QuadTree/QuadTree.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/QuadTree/QuadTree.playground/Contents.swift b/QuadTree/QuadTree.playground/Contents.swift
index f0d8cb2ef..ad8ee31f8 100644
--- a/QuadTree/QuadTree.playground/Contents.swift
+++ b/QuadTree/QuadTree.playground/Contents.swift
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b5
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 let tree = QuadTree(rect: Rect(origin: Point(0, 0), size: Size(xLength: 10, yLength: 10)))

From 61400ea88862429ea588cf07e396377ca485d9b0 Mon Sep 17 00:00:00 2001
From: Viktor Sokolov <bntrsokolov@gmail.com>
Date: Sat, 13 Oct 2018 11:31:57 +0300
Subject: [PATCH 461/643] Update Multiset to Swift 4.2

---
 Multiset/Multiset.playground/Contents.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/Multiset/Multiset.playground/Contents.swift b/Multiset/Multiset.playground/Contents.swift
index b4f64ee1f..64b729df1 100644
--- a/Multiset/Multiset.playground/Contents.swift
+++ b/Multiset/Multiset.playground/Contents.swift
@@ -1,9 +1,5 @@
 //: Playground - noun: a place where people can play
 
-#if swift(>=4.0)
-  print("Hello, Swift 4!")
-#endif
-
 import Cocoa
 
 var set = Multiset<String>()

From bb9ae3b6629da9b837c4cf33f9dfd977b13a635d Mon Sep 17 00:00:00 2001
From: Viktor Sokolov <bntrsokolov@gmail.com>
Date: Sat, 13 Oct 2018 11:39:24 +0300
Subject: [PATCH 462/643] Update Monty Hall to Swift 4.2

---
 Monty Hall Problem/MontyHall.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Monty Hall Problem/MontyHall.playground/Contents.swift b/Monty Hall Problem/MontyHall.playground/Contents.swift
index 4bfff2340..a809410c7 100644
--- a/Monty Hall Problem/MontyHall.playground/Contents.swift	
+++ b/Monty Hall Problem/MontyHall.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-  print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 func random(_ n: Int) -> Int {

From 33a50920ebefc92ce844d6f024e8c4a49f2eb3ef Mon Sep 17 00:00:00 2001
From: Viktor Sokolov <bntrsokolov@gmail.com>
Date: Sat, 13 Oct 2018 11:49:26 +0300
Subject: [PATCH 463/643] Update Ring Buffer to Swift 4.2

---
 Ring Buffer/RingBuffer.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Ring Buffer/RingBuffer.playground/Contents.swift b/Ring Buffer/RingBuffer.playground/Contents.swift
index f9ddb9c99..adcf146b4 100644
--- a/Ring Buffer/RingBuffer.playground/Contents.swift	
+++ b/Ring Buffer/RingBuffer.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 public struct RingBuffer<T> {
   fileprivate var array: [T?]
   fileprivate var readIndex = 0

From 2a2971800f986286b098928f0cce0199a749ba9e Mon Sep 17 00:00:00 2001
From: NORMANDY REAL <mandy@NORMANDYs-MacBook-Pro.local>
Date: Sat, 13 Oct 2018 22:25:30 +0800
Subject: [PATCH 464/643] Migrate to Swift 4.2

---
 Ordered Array/OrderedArray.playground/Contents.swift | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index 5b6be6420..e48af22e2 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -1,9 +1,6 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+
 
 public struct OrderedArray<T: Comparable> {
   fileprivate var array = [T]()

From 58af4187be04c17586a3bb37f30fd269bffd2692 Mon Sep 17 00:00:00 2001
From: Nick Thompson <dev@nickthompson.guru>
Date: Sat, 13 Oct 2018 10:32:59 -0400
Subject: [PATCH 465/643] Updated LRU Cache to Swift 4.2

---
 LRU Cache/LRUCache.playground/Contents.swift              | 5 -----
 .../playground.xcworkspace/contents.xcworkspacedata       | 7 +++++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 15 insertions(+), 5 deletions(-)
 create mode 100644 LRU Cache/LRUCache.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 LRU Cache/LRUCache.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/LRU Cache/LRUCache.playground/Contents.swift b/LRU Cache/LRUCache.playground/Contents.swift
index 2ebc03242..35dcc5d59 100644
--- a/LRU Cache/LRUCache.playground/Contents.swift	
+++ b/LRU Cache/LRUCache.playground/Contents.swift	
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let cache = LRUCache<String>(2)
 cache.set("a", val: 1)
 cache.set("b", val: 2)
diff --git a/LRU Cache/LRUCache.playground/playground.xcworkspace/contents.xcworkspacedata b/LRU Cache/LRUCache.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/LRU Cache/LRUCache.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/LRU Cache/LRUCache.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 4130f3502c344e0b43f09c0ba6cef0221ef1ff92 Mon Sep 17 00:00:00 2001
From: karolms <comksantana@gmail.com>
Date: Sun, 14 Oct 2018 01:37:22 -0300
Subject: [PATCH 466/643] Updated Bit Set to Swift 4.2

---
 Bit Set/BitSet.playground/Contents.swift                  | 4 ----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 4 deletions(-)
 create mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 95253ea27..568202a33 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -1,9 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 // Create a bit set that stores 140 bits
 var bits = BitSet(size: 140)
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From d4d5b473774e68a24d3320865749d3dfe257da88 Mon Sep 17 00:00:00 2001
From: karolms <comksantana@gmail.com>
Date: Sun, 14 Oct 2018 01:51:54 -0300
Subject: [PATCH 467/643] Updated Kth largest element to Swift 4.2

---
 Kth Largest Element/kthLargest.playground/Contents.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/Kth Largest Element/kthLargest.playground/Contents.swift b/Kth Largest Element/kthLargest.playground/Contents.swift
index e6fca2ceb..a27dfce7d 100644
--- a/Kth Largest Element/kthLargest.playground/Contents.swift	
+++ b/Kth Largest Element/kthLargest.playground/Contents.swift	
@@ -1,9 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 let a = [5, 1, 3, 2, 7, 6, 4]
 

From 75182345961675c51823a5d8ec514d85e91c7de8 Mon Sep 17 00:00:00 2001
From: karolms <comksantana@gmail.com>
Date: Sun, 14 Oct 2018 02:02:21 -0300
Subject: [PATCH 468/643] Revert "Updated Bit Set to Swift 4.2"

This reverts commit 4130f3502c344e0b43f09c0ba6cef0221ef1ff92.
---
 Bit Set/BitSet.playground/Contents.swift                  | 4 ++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 --------
 2 files changed, 4 insertions(+), 8 deletions(-)
 delete mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 568202a33..95253ea27 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -1,5 +1,9 @@
 //: Playground - noun: a place where people can play
 
+// last checked with Xcode 9.0b4
+#if swift(>=4.0)
+print("Hello, Swift 4!")
+#endif
 
 // Create a bit set that stores 140 bits
 var bits = BitSet(size: 140)
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>

From f7b3996dd301816a66618fc497edb546706e68d0 Mon Sep 17 00:00:00 2001
From: karolms <comksantana@gmail.com>
Date: Sun, 14 Oct 2018 02:09:18 -0300
Subject: [PATCH 469/643] Updated Knuth-Morris-Pratt to Swift 4.2

---
 .../KnuthMorrisPratt.playground/Contents.swift           | 9 ++-------
 1 file changed, 2 insertions(+), 7 deletions(-)

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
index 6609c9abe..9b4a50fa0 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -1,13 +1,8 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift4!")
-#endif
-
 func ZetaAlgorithm(ptnr: String) -> [Int]? {
   
-  let pattern = Array(ptnr.characters)
+  let pattern = Array(ptnr)
   let patternLength: Int = pattern.count
   
   guard patternLength > 0 else {
@@ -65,7 +60,7 @@ extension String {
   
   func indexesOf(ptnr: String) -> [Int]? {
     
-    let text = Array(self.characters)
+    let text = Array(self)
     let pattern = Array(ptnr.characters)
     
     let textLength: Int = text.count

From 6c2aa24b0674a97e755bf8c0acf480d6e107e756 Mon Sep 17 00:00:00 2001
From: karolms <comksantana@gmail.com>
Date: Sun, 14 Oct 2018 02:23:51 -0300
Subject: [PATCH 470/643] Updated AVL Tree to Swift 4.2

---
 AVL Tree/AVLTree.playground/Contents.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/AVL Tree/AVLTree.playground/Contents.swift b/AVL Tree/AVLTree.playground/Contents.swift
index 04ef78d07..34c1e6ddd 100644
--- a/AVL Tree/AVLTree.playground/Contents.swift	
+++ b/AVL Tree/AVLTree.playground/Contents.swift	
@@ -1,9 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 let tree = AVLTree<Int, String>()
 

From 6536cd7af049eec810033f9611e6e8e5767a8a54 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 15 Oct 2018 13:17:08 +1100
Subject: [PATCH 471/643] fix indentation typos in the README.md

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

diff --git a/Karatsuba Multiplication/README.markdown b/Karatsuba Multiplication/README.markdown
index 3a48ed39d..aef0d744a 100644
--- a/Karatsuba Multiplication/README.markdown	
+++ b/Karatsuba Multiplication/README.markdown	
@@ -71,12 +71,12 @@ Here's the full implementation. Note that the recursive algorithm is most effici
 
 ```swift
 // Karatsuba Multiplication
-  func karatsuba(_ num1: Int, by num2: Int) -> Int {
+func karatsuba(_ num1: Int, by num2: Int) -> Int {
   let num1String = String(num1)
   let num2String = String(num2)
   
   guard num1String.count > 1 && num2String.count > 1 else {
-  return multiply(num1, by: num2)
+    return multiply(num1, by: num2)
   }
   
   let n = max(num1String.count, num2String.count)

From 32fe7e84c0378daacf3e4048cf2f4d55bdb22c65 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Afonso=20Gra=C3=A7a?= <afonso.graca@me.com>
Date: Mon, 15 Oct 2018 13:25:42 +1100
Subject: [PATCH 472/643] [Swift 4.2] Update Miller-Rabin Primality Test

References #748
There were no necessary code changes for Swift 4.2.
Removed the  snippet requested
---
 .../MRPrimality.playground/Contents.swift                 | 5 -----
 .../playground.xcworkspace/contents.xcworkspacedata       | 4 ++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 12 insertions(+), 5 deletions(-)
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift
index d8fd7fad8..98032bd59 100644
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Real primes
 mrPrimalityTest(5)
 mrPrimalityTest(439)
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..94b2795e2
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+</Workspace>
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 027dc783bb15853c40f15bfd11daa9dcb7771120 Mon Sep 17 00:00:00 2001
From: Pragati <44121852+pragatiahuja@users.noreply.github.com>
Date: Mon, 15 Oct 2018 23:50:03 +0530
Subject: [PATCH 473/643] final README

Add recursive implementation for reversing a singly linked list.
---
 Linked List/README.markdown | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 0c8431157..0998349fc 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -471,6 +471,7 @@ This will print the list like so:
 
 How about reversing a list, so that the head becomes the tail and vice versa? There is a very fast algorithm for that:
 
+Iterative Approach:
 ```swift
   public func reverse() {
     var node = head
@@ -482,6 +483,18 @@ How about reversing a list, so that the head becomes the tail and vice versa? Th
     }
   }
 ```
+Recursive Approach:
+```swift
+  public func reverse(node: head) {
+    if (!head || !(head.next)) {
+      return head
+    }
+    let temp = reverse(head.next)
+    head.next.next = head;
+    head.next = NULL;
+    return temp;
+  }
+```
 
 This loops through the entire list and simply swaps the `next` and `previous` pointers of each node. It also moves the `head` pointer to the very last element. (If you had a tail pointer you'd also need to update it.) You end up with something like this:
 

From 75783274fd291f6f9e6e801734c1eefa3b77eb38 Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Tue, 16 Oct 2018 11:35:51 -0300
Subject: [PATCH 474/643] replaced repetitive implementation with call

---
 .../Sources/SelectionSort.swift               | 20 +------------------
 1 file changed, 1 insertion(+), 19 deletions(-)

diff --git a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
index 3a27ef9dd..e7c66481d 100644
--- a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
@@ -3,25 +3,7 @@
 /// - Parameter array: array of elements that conform to the Comparable protocol
 /// - Returns: an array in ascending order
 public func selectionSort<T: Comparable>(_ array: [T]) -> [T] {
-  guard array.count > 1 else { return array }
-
-  var a = array
-  for x in 0 ..< a.count - 1 {
-
-    // Find the lowest value in the rest of the array.
-    var lowest = x
-    for y in x + 1 ..< a.count {
-      if a[y] < a[lowest] {
-        lowest = y
-      }
-    }
-
-    // Swap the lowest value with the current array index.
-    if x != lowest {
-      a.swapAt(x, lowest)
-    }
-  }
-  return a
+  return insertionSort(array, <)
 }
 
 /// Performs the Selection sort algorithm on a array using the provided comparisson method

From 35ca62c82b39506203e551c8d05938113aec3e2f Mon Sep 17 00:00:00 2001
From: TaeJoongYoon <tryump225@gmail.com>
Date: Wed, 17 Oct 2018 04:05:46 +0900
Subject: [PATCH 475/643] Add CounterClockWise(CCW)

---
 .../Contents.swift                            |  76 +++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 ++
 .../xcshareddata/IDEWorkspaceChecks.plist     |   8 ++
 CounterClockWise/CounterClockWise.swift       |  50 ++++++++
 CounterClockWise/Images/Pentagon_img.png      | Bin 0 -> 20639 bytes
 CounterClockWise/Images/Quadrilateral_img.jpg | Bin 0 -> 9081 bytes
 CounterClockWise/Images/Shoelace.png          | Bin 0 -> 77353 bytes
 CounterClockWise/Images/Triangle_img.jpg      | Bin 0 -> 10346 bytes
 CounterClockWise/Images/pentagon.png          | Bin 0 -> 25285 bytes
 CounterClockWise/Images/quadrilateral.png     | Bin 0 -> 22372 bytes
 CounterClockWise/Images/triangle.png          | Bin 0 -> 19654 bytes
 CounterClockWise/README.md                    | 118 ++++++++++++++++++
 README.markdown                               |   1 +
 14 files changed, 264 insertions(+)
 create mode 100644 CounterClockWise/CounterClockWise.playground/Contents.swift
 create mode 100644 CounterClockWise/CounterClockWise.playground/contents.xcplayground
 create mode 100644 CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 CounterClockWise/CounterClockWise.swift
 create mode 100644 CounterClockWise/Images/Pentagon_img.png
 create mode 100644 CounterClockWise/Images/Quadrilateral_img.jpg
 create mode 100644 CounterClockWise/Images/Shoelace.png
 create mode 100644 CounterClockWise/Images/Triangle_img.jpg
 create mode 100644 CounterClockWise/Images/pentagon.png
 create mode 100644 CounterClockWise/Images/quadrilateral.png
 create mode 100644 CounterClockWise/Images/triangle.png
 create mode 100644 CounterClockWise/README.md

diff --git a/CounterClockWise/CounterClockWise.playground/Contents.swift b/CounterClockWise/CounterClockWise.playground/Contents.swift
new file mode 100644
index 000000000..ffa91ecbb
--- /dev/null
+++ b/CounterClockWise/CounterClockWise.playground/Contents.swift
@@ -0,0 +1,76 @@
+/*
+ CounterClockWise(CCW) Algorithm
+ The user cross-multiplies corresponding coordinates to find the area encompassing the polygon,
+ and subtracts it from the surrounding polygon to find the area of the polygon within.
+ This code is based on the "Shoelace formula" by Carl Friedrich Gauss
+ https://en.wikipedia.org/wiki/Shoelace_formula
+ */
+
+import Foundation
+
+// MARK : Point struct for defining 2-D coordinate(x,y)
+public struct Point{
+  // Coordinate(x,y)
+  var x: Int
+  var y: Int
+  
+  public init(x: Int ,y: Int){
+    self.x = x
+    self.y = y
+  }
+}
+
+// MARK : Function that determine the area of a simple polygon whose vertices are described
+//        by their Cartesian coordinates in the plane.
+func ccw(points: [Point]) -> Int{
+  let polygon = points.count
+  var orientation = 0
+  
+  // Take the first x-coordinate and multiply it by the second y-value,
+  // then take the second x-coordinate and multiply it by the third y-value,
+  // and repeat as many times until it is done for all wanted points.
+  for i in 0..<polygon{
+      orientation += (points[i%polygon].x*points[(i+1)%polygon].y
+                      - points[(i+1)%polygon].x*points[i%polygon].y)
+  }
+  
+  // If the points are labeled sequentially in the counterclockwise direction,
+  // then the sum of the above determinants is positive and the absolute value signs can be omitted
+  // if they are labeled in the clockwise direction, the sum of the determinants will be negative.
+  // This is because the formula can be viewed as a special case of Green's Theorem.
+  switch orientation {
+  case Int.min..<0:
+    return -1 // if operation < 0 : ClockWise
+  case 0:
+    return 0 // if operation == 0 : Parallel
+  default:
+    return 1 // if operation > 0 : CounterClockWise
+  }
+}
+
+// A few simple tests
+
+
+// Triangle
+var p1 = Point(x: 5, y: 8)
+var p2 = Point(x: 9, y: 1)
+var p3 = Point(x: 3, y: 6)
+
+print(ccw(points: [p1,p2,p3])) // -1 means ClockWise
+
+// Quadrilateral
+var p4 = Point(x: 5, y: 8)
+var p5 = Point(x: 2, y: 3)
+var p6 = Point(x: 6, y: 1)
+var p7 = Point(x: 9, y: 3)
+
+print(ccw(points: [p4,p5,p6,p7])) // 1 means CounterClockWise
+
+// Pentagon
+var p8 = Point(x: 5, y: 11)
+var p9 = Point(x: 3, y: 4)
+var p10 = Point(x: 5, y: 6)
+var p11 = Point(x: 9, y: 5)
+var p12 = Point(x: 12, y: 8)
+
+print(ccw(points: [p8,p9,p10,p11,p12])) // 1 means CounterClockWise
diff --git a/CounterClockWise/CounterClockWise.playground/contents.xcplayground b/CounterClockWise/CounterClockWise.playground/contents.xcplayground
new file mode 100644
index 000000000..9f5f2f40c
--- /dev/null
+++ b/CounterClockWise/CounterClockWise.playground/contents.xcplayground
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/contents.xcworkspacedata
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/CounterClockWise/CounterClockWise.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/CounterClockWise/CounterClockWise.swift b/CounterClockWise/CounterClockWise.swift
new file mode 100644
index 000000000..07c422ea5
--- /dev/null
+++ b/CounterClockWise/CounterClockWise.swift
@@ -0,0 +1,50 @@
+/*
+ CounterClockWise(CCW) Algorithm
+ The user cross-multiplies corresponding coordinates to find the area encompassing the polygon,
+ and subtracts it from the surrounding polygon to find the area of the polygon within.
+ This code is based on the "Shoelace formula" by Carl Friedrich Gauss
+ https://en.wikipedia.org/wiki/Shoelace_formula
+ */
+
+
+import Foundation
+
+// MARK : Point struct for defining 2-D coordinate(x,y)
+public struct Point{
+  // Coordinate(x,y)
+  var x: Int
+  var y: Int
+  
+  public init(x: Int ,y: Int){
+    self.x = x
+    self.y = y
+  }
+}
+
+// MARK : Function that determine the area of a simple polygon whose vertices are described
+//        by their Cartesian coordinates in the plane.
+func ccw(points: [Point]) -> Int{
+  let polygon = points.count
+  var orientation = 0
+  
+  // Take the first x-coordinate and multiply it by the second y-value,
+  // then take the second x-coordinate and multiply it by the third y-value,
+  // and repeat as many times until it is done for all wanted points.
+  for i in 0..<polygon{
+    orientation += (points[i%polygon].x*points[(i+1)%polygon].y
+      - points[(i+1)%polygon].x*points[i%polygon].y)
+  }
+  
+  // If the points are labeled sequentially in the counterclockwise direction,
+  // then the sum of the above determinants is positive and the absolute value signs can be omitted
+  // if they are labeled in the clockwise direction, the sum of the determinants will be negative.
+  // This is because the formula can be viewed as a special case of Green's Theorem.
+  switch orientation {
+  case Int.min..<0:
+    return -1 // if operation < 0 : ClockWise
+  case 0:
+    return 0 // if operation == 0 : Parallel
+  default:
+    return 1 // if operation > 0 : CounterClockWise
+  }
+}
diff --git a/CounterClockWise/Images/Pentagon_img.png b/CounterClockWise/Images/Pentagon_img.png
new file mode 100644
index 0000000000000000000000000000000000000000..44d8583036420e6a63fd0c339f65845632ebf28c
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diff --git a/CounterClockWise/README.md b/CounterClockWise/README.md
new file mode 100644
index 000000000..6b6c1a1da
--- /dev/null
+++ b/CounterClockWise/README.md
@@ -0,0 +1,118 @@
+# CounterClockWise
+
+Goal : Determine what direction to take when multiple points are given.
+
+CounterClockWise(CCW) is based on [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula#Examples) by Carl Friedrich Gauss.
+
+
+
+1. Take the first x-coordinate and multiply it by the second y-value, then take the second x-coordinate and multiply it by the third y-value, and repeat as many times until it is done for all wanted points.
+2. If the points are labeled sequentially in the counterclockwise direction, then the sum of the above determinants is positive and the absolute value signs can be omitted if they are labeled in the clockwise direction, the sum of the determinants will be negative. This is because the formula can be viewed as a special case of [Green's theorem](https://en.wikipedia.org/wiki/Green%27s_theorem).
+
+![Shoelace](./Images/Shoelace.png)
+
+
+
+Here's an implementation in Swift that should be easy to understand:
+
+```swift
+func ccw(points: [Point]) -> Int{
+  let polygon = points.count
+  var orientation = 0
+
+  for i in 0..<polygon{
+    orientation += (points[i%polygon].x*points[(i+1)%polygon].y
+      - points[(i+1)%polygon].x*points[i%polygon].y)
+  }
+    
+  switch orientation {
+  case Int.min..<0:
+    return -1 // if operation < 0 : ClockWise
+  case 0:
+    return 0 // if operation == 0 : Parallel
+  default:
+    return 1 // if operation > 0 : CounterClockWise
+  }
+}
+```
+
+Put this code in a playground and test it like so:
+
+```swift
+var p1 = Point(x: 5, y: 8)
+var p2 = Point(x: 9, y: 1)
+var p3 = Point(x: 3, y: 6)
+
+print(ccw(points: [p1,p2,p3])) // -1 means ClockWise
+```
+
+Here's how it works. When given an `[Photo]`, `ccw(points:)` calculates the direction of the given points according to the Shoelaces formula.
+
+
+
+`orientation` is less than 0, the direction is clockwise. 
+
+`orientation` is equal to 0, the direction is parallel. 
+
+`orientation` is greater than 0, the direction is counterclockwise. 
+
+
+
+## An example
+
+**In Triangle**
+
+```swift
+var p1 = Point(x: 5, y: 8)
+var p2 = Point(x: 9, y: 1)
+var p3 = Point(x: 3, y: 6)
+
+print(ccw(points: [p1,p2,p3])) // -1 means ClockWise
+```
+
+![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Triangle_img.jpg)
+
+![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/triangle.png)
+
+
+
+**In Quadrilateral**
+
+```swift
+var p4 = Point(x: 5, y: 8)
+var p5 = Point(x: 2, y: 3)
+var p6 = Point(x: 6, y: 1)
+var p7 = Point(x: 9, y: 3)
+
+print(ccw(points: [p4,p5,p6,p7])) // 1 means CounterClockWise
+```
+
+![Quadrilateral](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Quadrilateral_img.jpg)
+
+![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/quadrilateral.png)
+
+
+
+**In Pentagon**
+
+```swift
+var p8 = Point(x: 5, y: 11)
+var p9 = Point(x: 3, y: 4)
+var p10 = Point(x: 5, y: 6)
+var p11 = Point(x: 9, y: 5)
+var p12 = Point(x: 12, y: 8)
+
+print(ccw(points: [p8,p9,p10,p11,p12])) // 1 means CounterClockWise
+```
+
+![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Pentagon_img.png)
+
+![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/pentagon.png)
+
+
+
+You probably won't need to use the CCW in any real-world problems, but it's cool to play around with geometry algorithm. The formula was described by Meister (1724-1788) in 1769 and by Gauss in 1795. It can be verified by dividing the polygon into triangles, and can be considered to be a special case of Green's theorem.
+
+
+
+*Written for Swift Algorithm Club by TaeJoong Yoon*
\ No newline at end of file
diff --git a/README.markdown b/README.markdown
index 90b310752..efe89edc0 100644
--- a/README.markdown
+++ b/README.markdown
@@ -109,6 +109,7 @@ Bad sorting algorithms (don't use these!):
 - [Karatsuba Multiplication](Karatsuba%20Multiplication/). Another take on elementary multiplication.
 - [Haversine Distance](HaversineDistance/). Calculating the distance between 2 points from a sphere.
 - [Strassen's Multiplication Matrix](Strassen%20Matrix%20Multiplication/). Efficient way to handle matrix multiplication.
+- [CounterClockWise](/CounterClockWise/). Determining the area of a simple polygon.
 
 ### Machine learning
 

From e48117cd2cd5efaec539eb83c44d47089edc5054 Mon Sep 17 00:00:00 2001
From: TaeJoong Yoon <tryump225@gmail.com>
Date: Wed, 17 Oct 2018 04:22:34 +0900
Subject: [PATCH 476/643] Update README.md

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

diff --git a/CounterClockWise/README.md b/CounterClockWise/README.md
index 6b6c1a1da..2d15eba53 100644
--- a/CounterClockWise/README.md
+++ b/CounterClockWise/README.md
@@ -70,9 +70,9 @@ var p3 = Point(x: 3, y: 6)
 print(ccw(points: [p1,p2,p3])) // -1 means ClockWise
 ```
 
-![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Triangle_img.jpg)
+![triangle](./Images/Triangle_img.jpg)
 
-![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/triangle.png)
+![triangleExpression](./Images/triangle.png)
 
 
 
@@ -87,9 +87,9 @@ var p7 = Point(x: 9, y: 3)
 print(ccw(points: [p4,p5,p6,p7])) // 1 means CounterClockWise
 ```
 
-![Quadrilateral](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Quadrilateral_img.jpg)
+![Quadrilateral](./Images/Quadrilateral_img.jpg)
 
-![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/quadrilateral.png)
+![triangleExpression](./Images/quadrilateral.png)
 
 
 
@@ -105,9 +105,9 @@ var p12 = Point(x: 12, y: 8)
 print(ccw(points: [p8,p9,p10,p11,p12])) // 1 means CounterClockWise
 ```
 
-![triangle](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/Pentagon_img.png)
+![triangle](./Images/Pentagon_img.png)
 
-![triangleExpression](/Users/taejoongyoon/Developer/Swift/swift-algorithm-club/CounterClockWise/Images/pentagon.png)
+![triangleExpression](./Images/pentagon.png)
 
 
 
@@ -115,4 +115,4 @@ You probably won't need to use the CCW in any real-world problems, but it's cool
 
 
 
-*Written for Swift Algorithm Club by TaeJoong Yoon*
\ No newline at end of file
+*Written for Swift Algorithm Club by TaeJoong Yoon*

From d321542c220e94607b056644c491c7436553103b Mon Sep 17 00:00:00 2001
From: Alex Persian <alex_persian@me.com>
Date: Tue, 16 Oct 2018 22:28:13 -0400
Subject: [PATCH 477/643] Changes class to enum and clarifies the reason why a
 copy is made

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

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 0c8431157..e81e00b9f 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -555,7 +555,7 @@ enum ListNode<T> {
 }
 ```
 
-The big difference with the class-based version is that any modification you make to this list will result in a *new copy* being created. Whether that's what you want or not depends on the application.
+The big difference with the enum-based version is that any modification you make to this list will result in a *new copy* being created because of [Swift's value semantics](https://developer.apple.com/swift/blog/?id=10). Whether that's what you want or not depends on the application.
 
 [I might fill out this section in more detail if there's a demand for it.]
 

From f95093e7338bc66d73ff81b52f959ec0f4fdd2b5 Mon Sep 17 00:00:00 2001
From: Michael Pchelnikov <m.pchelnikov@gmail.com>
Date: Thu, 18 Oct 2018 00:28:16 +0300
Subject: [PATCH 478/643] Update Sorted Set to Swift 4.2

---
 .../Pages/Example 1.xcplaygroundpage/Contents.swift          | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift
index 45af5f99d..c81f4d915 100644
--- a/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
+++ b/Sorted Set/SortedSet.playground/Pages/Example 1.xcplaygroundpage/Contents.swift	
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 //: # Example 1 with type Int
 
 var mySet = SortedSet<Int>()

From 0c93543179946a42b44a11fb79061a6126a8d8b5 Mon Sep 17 00:00:00 2001
From: Erik Strottmann <erik.strottmann@gmail.com>
Date: Wed, 17 Oct 2018 22:01:48 -0700
Subject: [PATCH 479/643] Update Trie to Swift 4.2

Removes `#if swift(>=4.0)` checks and calls to deprecated
`String.characters` property, and enables Xcode 10 recommended warnings.
---
 Trie/ReadMe.md                                |  4 +--
 Trie/Trie/Trie.xcodeproj/project.pbxproj      | 33 +++++++++++++++----
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 Trie/Trie/Trie/Trie.swift                     | 11 ++-----
 Trie/Trie/Trie/ViewController.swift           |  5 ---
 Trie/Trie/TrieTests/TrieTests.swift           |  5 ---
 6 files changed, 39 insertions(+), 27 deletions(-)
 create mode 100644 Trie/Trie/Trie.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 34b9beb9c..8e473a619 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -33,7 +33,7 @@ func contains(word: String) -> Bool {
 	var currentNode = root
   
 	// 2
-	var characters = Array(word.lowercased().characters)
+	var characters = Array(word.lowercased())
 	var currentIndex = 0
  
 	// 3
@@ -74,7 +74,7 @@ func insert(word: String) {
   var currentNode = root
 
   // 2
-  for character in word.lowercased().characters {
+  for character in word.lowercased() {
     // 3
     if let childNode = currentNode.children[character] {
       currentNode = childNode
diff --git a/Trie/Trie/Trie.xcodeproj/project.pbxproj b/Trie/Trie/Trie.xcodeproj/project.pbxproj
index 90c5734cc..1e3602eea 100644
--- a/Trie/Trie/Trie.xcodeproj/project.pbxproj
+++ b/Trie/Trie/Trie.xcodeproj/project.pbxproj
@@ -195,20 +195,23 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0810;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Rick Zaccone";
 				TargetAttributes = {
 					EB798DF91DFEF79900F0628D = {
 						CreatedOnToolsVersion = 8.1;
+						LastSwiftMigration = 1000;
 						ProvisioningStyle = Automatic;
 					};
 					EB798E0A1DFEF79900F0628D = {
 						CreatedOnToolsVersion = 8.1;
+						LastSwiftMigration = 1000;
 						ProvisioningStyle = Automatic;
 						TestTargetID = EB798DF91DFEF79900F0628D;
 					};
 					EB798E151DFEF79900F0628D = {
 						CreatedOnToolsVersion = 8.1;
+						LastSwiftMigration = 1000;
 						ProvisioningStyle = Automatic;
 						TestTargetID = EB798DF91DFEF79900F0628D;
 					};
@@ -326,15 +329,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_SUSPICIOUS_MOVES = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
@@ -376,15 +387,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_SUSPICIOUS_MOVES = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
@@ -418,7 +437,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.Trie;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -431,7 +450,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.Trie;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
@@ -445,7 +464,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.TrieTests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Trie.app/Contents/MacOS/Trie";
 			};
 			name = Debug;
@@ -460,7 +479,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.TrieTests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 				TEST_HOST = "$(BUILT_PRODUCTS_DIR)/Trie.app/Contents/MacOS/Trie";
 			};
 			name = Release;
@@ -474,7 +493,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.TrieUITests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 				TEST_TARGET_NAME = Trie;
 			};
 			name = Debug;
@@ -488,7 +507,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = edu.bucknell.zaccone.TrieUITests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 				TEST_TARGET_NAME = Trie;
 			};
 			name = Release;
diff --git a/Trie/Trie/Trie.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Trie/Trie/Trie.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Trie/Trie/Trie.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index 1a7017c4c..fbc933138 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -6,11 +6,6 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-    print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 /// A node in the trie
@@ -105,7 +100,7 @@ extension Trie {
       return
     }
     var currentNode = root
-    for character in word.lowercased().characters {
+    for character in word.lowercased() {
       if let childNode = currentNode.children[character] {
         currentNode = childNode
       } else {
@@ -130,7 +125,7 @@ extension Trie {
       return false
     }
     var currentNode = root
-    for character in word.lowercased().characters {
+    for character in word.lowercased() {
       guard let childNode = currentNode.children[character] else {
         return false
       }
@@ -148,7 +143,7 @@ extension Trie {
   /// search failed.
   private func findLastNodeOf(word: String) -> Node? {
       var currentNode = root
-      for character in word.lowercased().characters {
+      for character in word.lowercased() {
           guard let childNode = currentNode.children[character] else {
               return nil
           }
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
index 9c5e66163..928b01f4c 100644
--- a/Trie/Trie/Trie/ViewController.swift
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -6,11 +6,6 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-    print("Hello, Swift 4!")
-#endif
-
 import Cocoa
 
 class ViewController: NSViewController {
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index 45be03aad..b69c5666e 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -6,11 +6,6 @@
 //  Copyright © 2016 Rick Zaccone. All rights reserved.
 //
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-    print("Hello, Swift 4!")
-#endif
-
 import XCTest
 @testable import Trie
 

From 5a200e0709ba32a7bd898336502264977b356f77 Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:25:37 +0200
Subject: [PATCH 480/643] renaming Palindromes to Palindrome

also removing one implementation, moving the one on root level to the playground to reduce the number of implementations to maintain
---
 .../Sources/Palindrome.swift                  | 38 +++++++++++++++++++
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++
 .../Palindrome.swift}                         |  2 +-
 Palindromes/Test/Palindromes.swift            | 26 -------------
 .../Test/Test.xcodeproj/project.pbxproj       | 16 +++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++
 6 files changed, 65 insertions(+), 33 deletions(-)
 create mode 100644 Palindromes/Palindromes.playground/Sources/Palindrome.swift
 create mode 100644 Palindromes/Palindromes.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 rename Palindromes/{Palindromes.swift => Test/Palindrome.swift} (93%)
 delete mode 100644 Palindromes/Test/Palindromes.swift
 create mode 100644 Palindromes/Test/Test.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Palindromes/Palindromes.playground/Sources/Palindrome.swift b/Palindromes/Palindromes.playground/Sources/Palindrome.swift
new file mode 100644
index 000000000..a6d2274bf
--- /dev/null
+++ b/Palindromes/Palindromes.playground/Sources/Palindrome.swift
@@ -0,0 +1,38 @@
+import Foundation
+
+/**
+ Validate that a string is a plaindrome
+ - parameter str: The string to validate
+ - returns: `true` if string is plaindrome, `false` if string is not
+ */
+func isPalindrome(_ str: String) -> Bool {
+    let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
+    let length = strippedString.count
+    
+    if length > 1 {
+        return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
+    }
+    return false
+}
+
+/**
+ Compares a strings left side character against right side character following
+ - parameter str: The string to compare characters of
+ - parameter left: Index of left side to compare, must be less than or equal to right
+ - parameter right: Index of right side to compare, must be greater than or equal to left
+ - returns: `true` if left side and right side have all been compared and they all match, `false` if a left and right aren't equal
+ */
+private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
+    if left >= right {
+        return true
+    }
+    
+    let lhs = str[str.index(str.startIndex, offsetBy: left)]
+    let rhs = str[str.index(str.startIndex, offsetBy: right)]
+    
+    if lhs != rhs {
+        return false
+    }
+    
+    return palindrome(str, left: left + 1, right: right - 1)
+}
diff --git a/Palindromes/Palindromes.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Palindromes/Palindromes.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Palindromes/Palindromes.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Palindromes/Palindromes.swift b/Palindromes/Test/Palindrome.swift
similarity index 93%
rename from Palindromes/Palindromes.swift
rename to Palindromes/Test/Palindrome.swift
index 9ddd04c80..16af14fdb 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Test/Palindrome.swift
@@ -2,7 +2,7 @@ import Foundation
 
 func isPalindrome(_ str: String) -> Bool {
     let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-    let length = strippedString.characters.count
+    let length = strippedString.count
 
     if length > 1 {
         return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
diff --git a/Palindromes/Test/Palindromes.swift b/Palindromes/Test/Palindromes.swift
deleted file mode 100644
index 9ddd04c80..000000000
--- a/Palindromes/Test/Palindromes.swift
+++ /dev/null
@@ -1,26 +0,0 @@
-import Foundation
-
-func isPalindrome(_ str: String) -> Bool {
-    let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-    let length = strippedString.characters.count
-
-    if length > 1 {
-        return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
-    }
-    return false
-}
-
-private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
-    if left >= right {
-        return true
-    }
-
-    let lhs = str[str.index(str.startIndex, offsetBy: left)]
-    let rhs = str[str.index(str.startIndex, offsetBy: right)]
-
-    if lhs != rhs {
-        return false
-    }
-
-    return palindrome(str, left: left + 1, right: right - 1)
-}
diff --git a/Palindromes/Test/Test.xcodeproj/project.pbxproj b/Palindromes/Test/Test.xcodeproj/project.pbxproj
index 07aae3e63..6af90d5c2 100644
--- a/Palindromes/Test/Test.xcodeproj/project.pbxproj
+++ b/Palindromes/Test/Test.xcodeproj/project.pbxproj
@@ -8,11 +8,11 @@
 
 /* Begin PBXBuildFile section */
 		9437D8841E0D960A00A38FB8 /* Test.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9437D8831E0D960A00A38FB8 /* Test.swift */; };
-		9437D88B1E0D969500A38FB8 /* Palindromes.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9437D8791E0D948A00A38FB8 /* Palindromes.swift */; };
+		9437D88B1E0D969500A38FB8 /* Palindrome.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9437D8791E0D948A00A38FB8 /* Palindrome.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXFileReference section */
-		9437D8791E0D948A00A38FB8 /* Palindromes.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Palindromes.swift; sourceTree = "<group>"; };
+		9437D8791E0D948A00A38FB8 /* Palindrome.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Palindrome.swift; sourceTree = "<group>"; };
 		9437D8811E0D960A00A38FB8 /* Test.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = Test.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		9437D8831E0D960A00A38FB8 /* Test.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Test.swift; sourceTree = "<group>"; };
 		9437D8851E0D960A00A38FB8 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
@@ -32,7 +32,7 @@
 		9437D8651E0D945200A38FB8 = {
 			isa = PBXGroup;
 			children = (
-				9437D8791E0D948A00A38FB8 /* Palindromes.swift */,
+				9437D8791E0D948A00A38FB8 /* Palindrome.swift */,
 				9437D8821E0D960A00A38FB8 /* Test */,
 				9437D86F1E0D945200A38FB8 /* Products */,
 			);
@@ -87,6 +87,7 @@
 				TargetAttributes = {
 					9437D8801E0D960A00A38FB8 = {
 						CreatedOnToolsVersion = 8.2;
+						LastSwiftMigration = 1000;
 						ProvisioningStyle = Automatic;
 					};
 				};
@@ -123,7 +124,7 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				9437D88B1E0D969500A38FB8 /* Palindromes.swift in Sources */,
+				9437D88B1E0D969500A38FB8 /* Palindrome.swift in Sources */,
 				9437D8841E0D960A00A38FB8 /* Test.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
@@ -229,7 +230,8 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -243,7 +245,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = self.edu.Test;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
@@ -266,6 +269,7 @@
 				9437D8881E0D960A00A38FB8 /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};
diff --git a/Palindromes/Test/Test.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Palindromes/Test/Test.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Palindromes/Test/Test.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 73b0fc92b71fa5a40a8b6ddc6a664ede35d09858 Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:26:50 +0200
Subject: [PATCH 481/643] removing duplicate implementation

---
 .../Palindromes.playground/Contents.swift     | 42 -------------------
 1 file changed, 42 deletions(-)

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index 44662745a..ee43cce33 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -1,49 +1,7 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
-/**
- Validate that a string is a plaindrome
- - parameter str: The string to validate
- - returns: `true` if string is plaindrome, `false` if string is not
- */
-func isPalindrome(_ str: String) -> Bool {
-    let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-    let length = strippedString.characters.count
-
-    if length > 1 {
-        return palindrome(strippedString.lowercased(), left: 0, right: length - 1)
-    }
-    return false
-}
-
-/**
- Compares a strings left side character against right side character following
- - parameter str: The string to compare characters of
- - parameter left: Index of left side to compare, must be less than or equal to right
- - parameter right: Index of right side to compare, must be greater than or equal to left
- - returns: `true` if left side and right side have all been compared and they all match, `false` if a left and right aren't equal
- */
-private func palindrome(_ str: String, left: Int, right: Int) -> Bool {
-    if left >= right {
-        return true
-    }
-
-    let lhs = str[str.index(str.startIndex, offsetBy: left)]
-    let rhs = str[str.index(str.startIndex, offsetBy: right)]
-
-    if lhs != rhs {
-        return false
-    }
-
-    return palindrome(str, left: left + 1, right: right - 1)
-}
-
 //true
 isPalindrome("A man, a plan, a canal, Panama!")
 isPalindrome("abbcbba")

From 66509650d57cd11deeb081359cbc0e4f68877b8e Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:27:09 +0200
Subject: [PATCH 482/643] updating recommended project settings

---
 .../Test/Test.xcodeproj/project.pbxproj        | 18 +++++++++++++++++-
 .../xcshareddata/xcschemes/Test.xcscheme       |  2 +-
 2 files changed, 18 insertions(+), 2 deletions(-)

diff --git a/Palindromes/Test/Test.xcodeproj/project.pbxproj b/Palindromes/Test/Test.xcodeproj/project.pbxproj
index 6af90d5c2..8125d1f8d 100644
--- a/Palindromes/Test/Test.xcodeproj/project.pbxproj
+++ b/Palindromes/Test/Test.xcodeproj/project.pbxproj
@@ -82,7 +82,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0820;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Joshua Alvarado";
 				TargetAttributes = {
 					9437D8801E0D960A00A38FB8 = {
@@ -141,15 +141,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -188,15 +196,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
diff --git a/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme b/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme
index 9a1b39e69..72ae3d696 100644
--- a/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme
+++ b/Palindromes/Test/Test.xcodeproj/xcshareddata/xcschemes/Test.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From e9ed7947a90efd5fb42ed5757df1f89758778351 Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:28:36 +0200
Subject: [PATCH 483/643] setting SWIFT_SWIFT3_OBJC_INFERENCE to default

---
 Palindromes/Test/Test.xcodeproj/project.pbxproj | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Palindromes/Test/Test.xcodeproj/project.pbxproj b/Palindromes/Test/Test.xcodeproj/project.pbxproj
index 8125d1f8d..f01f6f061 100644
--- a/Palindromes/Test/Test.xcodeproj/project.pbxproj
+++ b/Palindromes/Test/Test.xcodeproj/project.pbxproj
@@ -246,7 +246,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
@@ -261,7 +261,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = self.edu.Test;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
 				SWIFT_VERSION = 4.2;
 			};
 			name = Release;

From d3acedfb063b65327d503a50e86dfbaeb545b90e Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:31:39 +0200
Subject: [PATCH 484/643] making isPalindrome(_:) public

---
 Palindromes/Palindromes.playground/Sources/Palindrome.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Palindromes/Palindromes.playground/Sources/Palindrome.swift b/Palindromes/Palindromes.playground/Sources/Palindrome.swift
index a6d2274bf..3652dbb1f 100644
--- a/Palindromes/Palindromes.playground/Sources/Palindrome.swift
+++ b/Palindromes/Palindromes.playground/Sources/Palindrome.swift
@@ -5,7 +5,7 @@ import Foundation
  - parameter str: The string to validate
  - returns: `true` if string is plaindrome, `false` if string is not
  */
-func isPalindrome(_ str: String) -> Bool {
+public func isPalindrome(_ str: String) -> Bool {
     let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
     let length = strippedString.count
     

From 5fe31fff9a5717815cb524b16eb3433fde20926b Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:31:42 +0200
Subject: [PATCH 485/643] cleanup

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

diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index ee43cce33..49f767982 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -2,7 +2,7 @@
 
 import Foundation
 
-//true
+// true
 isPalindrome("A man, a plan, a canal, Panama!")
 isPalindrome("abbcbba")
 isPalindrome("racecar")

From 93a4d2d24689ebc6beec1df55e28dc4e94318a96 Mon Sep 17 00:00:00 2001
From: Florian Heiber <flo@flohei.de>
Date: Thu, 18 Oct 2018 09:55:39 +0200
Subject: [PATCH 486/643] updating README

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

diff --git a/Palindromes/README.markdown b/Palindromes/README.markdown
index 69520a132..e4012d8da 100644
--- a/Palindromes/README.markdown
+++ b/Palindromes/README.markdown
@@ -26,7 +26,7 @@ Here is a recursive implementation of this in Swift:
 ```swift
 func isPalindrome(_ str: String) -> Bool {
   let strippedString = str.replacingOccurrences(of: "\\W", with: "", options: .regularExpression, range: nil)
-  let length = strippedString.characters.count
+  let length = strippedString.count
 
   if length > 1 {
     return palindrome(strippedString.lowercased(), left: 0, right: length - 1)

From c4a89a24bee0269733f2ac8ed9605ae0f1574eaa Mon Sep 17 00:00:00 2001
From: Stefan Pleava <stefan_pleava1@hotmail.com>
Date: Thu, 18 Oct 2018 11:45:46 -0400
Subject: [PATCH 487/643] Update README.markdown

I think it should say minimum not maximum in the description.
---
 Egg Drop Problem/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Egg Drop Problem/README.markdown b/Egg Drop Problem/README.markdown
index b2f45d09e..416984193 100644
--- a/Egg Drop Problem/README.markdown	
+++ b/Egg Drop Problem/README.markdown	
@@ -12,7 +12,7 @@ If the object is incredibly resilient, and you may need to do the testing on the
 
 ## Description
 
-You're in a building with **m** floors and you are given **n** eggs. What is the maximum number of attempts it will take to find out the floor that breaks the egg?
+You're in a building with **m** floors and you are given **n** eggs. What is the minimum number of attempts it will take to find out the floor that breaks the egg?
 
 For convenience, here are a few rules to keep in mind:
 

From 4c718b4023565795675de2b2755db3226b3cd55e Mon Sep 17 00:00:00 2001
From: vp4 <vishwadatha_p@intuit.com>
Date: Fri, 19 Oct 2018 18:24:40 +0530
Subject: [PATCH 488/643] Remove semicolon

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

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 0998349fc..d6f1fc986 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -490,9 +490,9 @@ Recursive Approach:
       return head
     }
     let temp = reverse(head.next)
-    head.next.next = head;
-    head.next = NULL;
-    return temp;
+    head.next.next = head
+    head.next = NULL
+    return temp
   }
 ```
 

From 66d0b867e22378465d83aecce1c30609906538d5 Mon Sep 17 00:00:00 2001
From: Randy the Dev <37282011+RandyTheDev@users.noreply.github.com>
Date: Mon, 22 Oct 2018 03:05:09 +1100
Subject: [PATCH 489/643] Updated Radix Sort to Swift 4.2

---
 Radix Sort/RadixSort.playground/Contents.swift    | 15 ++-------------
 .../RadixSort.playground/Sources/radixSort.swift  |  1 -
 2 files changed, 2 insertions(+), 14 deletions(-)

diff --git a/Radix Sort/RadixSort.playground/Contents.swift b/Radix Sort/RadixSort.playground/Contents.swift
index 941723c37..0b549fc9e 100644
--- a/Radix Sort/RadixSort.playground/Contents.swift	
+++ b/Radix Sort/RadixSort.playground/Contents.swift	
@@ -1,21 +1,10 @@
 //: Playground - noun: a place where people can play
 
-import Cocoa
-
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Test Radix Sort with small array of ten values
 var array: [Int] = [19, 4242, 2, 9, 912, 101, 55, 67, 89, 32]
 radixSort(&array)
 
 // Test Radix Sort with large array of 1000 random values
-var bigArray = [Int](repeating: 0, count: 1000)
-var i = 0
-while i < 1000 {
-  bigArray[i] = Int(arc4random_uniform(1000) + 1)
-  i += 1
-}
+var bigArray = (0..<1000).map { _ in Int.random(in: 1...1000) }
+bigArray
 radixSort(&bigArray)
diff --git a/Radix Sort/RadixSort.playground/Sources/radixSort.swift b/Radix Sort/RadixSort.playground/Sources/radixSort.swift
index 424d33fb9..af382f481 100644
--- a/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
+++ b/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
@@ -3,7 +3,6 @@
  Sorting Algorithm that sorts an input array of integers digit by digit.
  
  */
-import Foundation
 
 // NOTE: This implementation does not handle negative numbers
 public func radixSort(_ array: inout [Int] ) {

From 36ae366ea4faeb4bf96380df3d58ca4da34525c6 Mon Sep 17 00:00:00 2001
From: Randy the Dev <37282011+RandyTheDev@users.noreply.github.com>
Date: Mon, 22 Oct 2018 04:01:21 +1100
Subject: [PATCH 490/643] Updated Radix Sort Tests to Swift 4.2

---
 Radix Sort/Tests/RadixSortTests.swift | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/Radix Sort/Tests/RadixSortTests.swift b/Radix Sort/Tests/RadixSortTests.swift
index 9b881318a..688bcdcb8 100644
--- a/Radix Sort/Tests/RadixSortTests.swift	
+++ b/Radix Sort/Tests/RadixSortTests.swift	
@@ -9,13 +9,6 @@
 import XCTest
 
 class RadixSortTests: XCTestCase {
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-  
   func testCombSort() {
     let expectedSequence: [Int] = [2, 9, 19, 32, 55, 67, 89, 101, 912, 4242]
     var sequence = [19, 4242, 2, 9, 912, 101, 55, 67, 89, 32]

From eab858255456bc4c3be0229cf852d91720ac3361 Mon Sep 17 00:00:00 2001
From: Rahul Sharma <rahulrs0029@gmail.com>
Date: Tue, 23 Oct 2018 18:08:08 +0530
Subject: [PATCH 491/643] [Swift 4.2] Updated Linear Search

The code worked fine in Xcode 10. I removed code snippet at the top of playground file.
---
 Linear Search/LinearSearch.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Linear Search/LinearSearch.playground/Contents.swift b/Linear Search/LinearSearch.playground/Contents.swift
index 8ac0e9a71..8c616ded4 100644
--- a/Linear Search/LinearSearch.playground/Contents.swift	
+++ b/Linear Search/LinearSearch.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
     for (index, obj) in array.enumerated() where obj == object {
         return index

From d4fdc7bfa84715fcae452439e874740fc6759d7f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Simon=20C=2E=20Kr=C3=BCger?= <simon.krueger@intive.com>
Date: Tue, 23 Oct 2018 15:32:33 +0200
Subject: [PATCH 492/643] Adds binary recursive stein algorithm to the GCD
 class

* Improves the LCM by passing the used GCD algorithm into the function.
* Find an easy GCD function if possible.
---
 GCD/GCD.playground/Contents.swift             | 165 +++++++++++++++---
 .../xcshareddata/IDEWorkspaceChecks.plist     |   8 +
 GCD/GCD.playground/timeline.xctimeline        |   6 -
 GCD/GCD.swift                                 | 141 ++++++++++++---
 GCD/README.markdown                           |  68 ++++----
 5 files changed, 296 insertions(+), 92 deletions(-)
 create mode 100644 GCD/GCD.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 GCD/GCD.playground/timeline.xctimeline

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index c44f28310..9dfd7cca9 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -1,39 +1,148 @@
 //: Playground - noun: a place where people can play
 
-// Recursive version
-func gcd(_ a: Int, _ b: Int) -> Int {
-  let r = a % b
-  if r != 0 {
-    return gcd(b, r)
-  } else {
+/*
+ Iterative approach based on the Euclidean algorithm.
+ The Euclidean algorithm is based on the principle that the greatest
+ common divisor of two numbers does not change if the larger number
+ is replaced by its difference with the smaller number.
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd if m and n
+ */
+func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
+    var a: Int = 0
+    var b: Int = max(m, n)
+    var r: Int = min(m, n)
+    
+    while r != 0 {
+        a = b
+        b = r
+        r = a % b
+    }
     return b
-  }
 }
 
 /*
-// Iterative version
-func gcd(m: Int, _ n: Int) -> Int {
-  var a = 0
-  var b = max(m, n)
-  var r = min(m, n)
-
-  while r != 0 {
-    a = b
-    b = r
-    r = a % b
-  }
-  return b
+ Recursive approach based on the Euclidean algorithm.
+ 
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd of m and n
+ - Note: The recursive version makes only tail recursive calls.
+ Most compilers for imperative languages do not optimize these.
+ The swift compiler as well as the obj-c compiler is able to do
+ optimizations for tail recursive calls, even though it still ends
+ up to be the same in terms of complexity. That said, tail call
+ elimination is not mutually exclusive to recursion.
+ */
+func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
+    let r: Int = m % n
+    if r != 0 {
+        return gcdRecursiveEuklid(n, r)
+    } else {
+        return n
+    }
+}
+
+/*
+ The binary GCD algorithm, also known as Stein's algorithm,
+ is an algorithm that computes the greatest common divisor of two
+ nonnegative integers. Stein's algorithm uses simpler arithmetic
+ operations than the conventional Euclidean algorithm; it replaces
+ division with arithmetic shifts, comparisons, and subtraction.
+ 
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd of m and n
+ - Complexity: worst case O(n^2), where n is the number of bits
+ in the larger of the two numbers. Although each step reduces
+ at least one of the operands by at least a factor of 2,
+ the subtract and shift operations take linear time for very
+ large integers
+ */
+func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
+    if let easySolution = findEasySolution(m, n) { return easySolution }
+    
+    if (m & 1) == 0 {
+        // m is even
+        if (n & 1) == 1 {
+            // and n is odd
+            return gcdBinaryRecursiveStein(m >> 1, n)
+        } else {
+            // both m and n are even
+            return gcdBinaryRecursiveStein(m >> 1, n >> 1) << 1
+        }
+    } else if (n & 1) == 0 {
+        // m is odd, n is even
+        return gcdBinaryRecursiveStein(m, n >> 1)
+    } else if (m > n) {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((m - n) >> 1, n)
+    } else {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((n - m) >> 1, m)
+    }
+}
+
+/*
+ Finds an easy solution for the gcd.
+ - Note: It might be relevant for different usecases to
+ try finding an easy solution for the GCD calculation
+ before even starting more difficult operations.
+ */
+func findEasySolution(_ m: Int, _ n: Int) -> Int? {
+    if m == n {
+        return m
+    }
+    if m == 0 {
+        return n
+    }
+    if n == 0 {
+        return m
+    }
+    return nil
 }
-*/
 
-func lcm(_ m: Int, _ n: Int) -> Int {
-  return m / gcd(m, n) * n // we divide before multiplying to avoid integer overflow
+
+enum LCMError: Error {
+    case divisionByZero
+    case lcmEmptyList
+}
+
+/*
+ Calculates the lcm for two given numbers using a specified gcd algorithm.
+ 
+ - Parameter m: First natural number.
+ - Parameter n: Second natural number.
+ - Parameter using: The used gcd algorithm to calculate the lcm.
+ - Throws: Can throw a `divisionByZero` error if one of the given
+ attributes turns out to be zero or less.
+ - Returns: The least common multiplier of the two attributes as
+ an unsigned integer
+ */
+func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
+    guard (m & n) != 0 else { throw LCMError.divisionByZero }
+    return m / gcdAlgorithm(m, n) * n
 }
 
-gcd(52, 39)       // 13
-gcd(228, 36)      // 12
-gcd(51357, 3819)  // 57
-gcd(841, 299)     // 1
+gcdIterativeEuklid(52, 39)       // 13
+gcdIterativeEuklid(228, 36)      // 12
+gcdIterativeEuklid(51357, 3819)  // 57
+gcdIterativeEuklid(841, 299)     // 1
 
-lcm(2, 3)   // 6
-lcm(10, 8)  // 40
+gcdRecursiveEuklid(52, 39)       // 13
+gcdRecursiveEuklid(228, 36)      // 12
+gcdRecursiveEuklid(51357, 3819)  // 57
+gcdRecursiveEuklid(841, 299)     // 1
+
+gcdBinaryRecursiveStein(52, 39)       // 13
+gcdBinaryRecursiveStein(228, 36)      // 12
+gcdBinaryRecursiveStein(51357, 3819)  // 57
+gcdBinaryRecursiveStein(841, 299)     // 1
+
+do {
+    try lcm(2, 3, using: gcdIterativeEuklid)   // 6
+    try lcm(10, 8, using: gcdIterativeEuklid)  // 40
+} catch {
+    dump(error)
+}
diff --git a/GCD/GCD.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/GCD/GCD.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/GCD/GCD.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/GCD/GCD.playground/timeline.xctimeline b/GCD/GCD.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/GCD/GCD.playground/timeline.xctimeline
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Timeline
-   version = "3.0">
-   <TimelineItems>
-   </TimelineItems>
-</Timeline>
diff --git a/GCD/GCD.swift b/GCD/GCD.swift
index bd903e58a..85b7681f0 100644
--- a/GCD/GCD.swift
+++ b/GCD/GCD.swift
@@ -1,34 +1,125 @@
+
 /*
-  Euclid's algorithm for finding the greatest common divisor
-*/
-func gcd(_ m: Int, _ n: Int) -> Int {
-  var a = 0
-  var b = max(m, n)
-  var r = min(m, n)
+ Iterative approach based on the Euclidean algorithm.
+ The Euclidean algorithm is based on the principle that the greatest
+ common divisor of two numbers does not change if the larger number
+ is replaced by its difference with the smaller number.
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd if m and n
+ */
+func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
+    var a: Int = 0
+    var b: Int = max(m, n)
+    var r: Int = min(m, n)
+    
+    while r != 0 {
+        a = b
+        b = r
+        r = a % b
+    }
+    return b
+}
 
-  while r != 0 {
-    a = b
-    b = r
-    r = a % b
-  }
-  return b
+/*
+ Recursive approach based on the Euclidean algorithm.
+ 
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd of m and n
+ - Note: The recursive version makes only tail recursive calls.
+ Most compilers for imperative languages do not optimize these.
+ The swift compiler as well as the obj-c compiler is able to do
+ optimizations for tail recursive calls, even though it still ends
+ up to be the same in terms of complexity. That said, tail call
+ elimination is not mutually exclusive to recursion.
+ */
+func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
+    let r: Int = m % n
+    if r != 0 {
+        return gcdRecursiveEuklid(n, r)
+    } else {
+        return n
+    }
 }
 
 /*
-// Recursive version
-func gcd(_ a: Int, _ b: Int) -> Int {
-  let r = a % b
-  if r != 0 {
-    return gcd(b, r)
-  } else {
-    return b
-  }
+ The binary GCD algorithm, also known as Stein's algorithm,
+ is an algorithm that computes the greatest common divisor of two
+ nonnegative integers. Stein's algorithm uses simpler arithmetic
+ operations than the conventional Euclidean algorithm; it replaces
+ division with arithmetic shifts, comparisons, and subtraction.
+ 
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: The natural gcd of m and n
+ - Complexity: worst case O(n^2), where n is the number of bits
+ in the larger of the two numbers. Although each step reduces
+ at least one of the operands by at least a factor of 2,
+ the subtract and shift operations take linear time for very
+ large integers
+ */
+func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
+    if let easySolution = findEasySolution(m, n) { return easySolution }
+    
+    if (m & 1) == 0 {
+        // m is even
+        if (n & 1) == 1 {
+            // and n is odd
+            return gcdBinaryRecursiveStein(m >> 1, n)
+        } else {
+            // both m and n are even
+            return gcdBinaryRecursiveStein(m >> 1, n >> 1) << 1
+        }
+    } else if (n & 1) == 0 {
+        // m is odd, n is even
+        return gcdBinaryRecursiveStein(m, n >> 1)
+    } else if (m > n) {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((m - n) >> 1, n)
+    } else {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((n - m) >> 1, m)
+    }
+}
+
+/*
+ Finds an easy solution for the gcd.
+ - Note: It might be relevant for different usecases to
+ try finding an easy solution for the GCD calculation
+ before even starting more difficult operations.
+ */
+func findEasySolution(_ m: Int, _ n: Int) -> Int? {
+    if m == n {
+        return m
+    }
+    if m == 0 {
+        return n
+    }
+    if n == 0 {
+        return m
+    }
+    return nil
+}
+
+
+enum LCMError: Error {
+    case divisionByZero
+    case lcmEmptyList
 }
-*/
 
 /*
-  Returns the least common multiple of two numbers.
-*/
-func lcm(_ m: Int, _ n: Int) -> Int {
-  return m / gcd(m, n) * n
+ Calculates the lcm for two given numbers using a specified gcd algorithm.
+ 
+ - Parameter m: First natural number.
+ - Parameter n: Second natural number.
+ - Parameter using: The used gcd algorithm to calculate the lcm.
+ - Throws: Can throw a `divisionByZero` error if one of the given
+ attributes turns out to be zero or less.
+ - Returns: The least common multiplier of the two attributes as
+ an unsigned integer
+ */
+func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
+    guard (m & n) != 0 else { throw LCMError.divisionByZero }
+    return m / gcdAlgorithm(m, n) * n
 }
diff --git a/GCD/README.markdown b/GCD/README.markdown
index d7e9304bd..a23aea190 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -1,8 +1,8 @@
 # Greatest Common Divisor
 
-The *greatest common divisor* (or Greatest Common Factor) of two numbers `a` and `b` is the largest positive integer that divides both `a` and `b` without a remainder.
+The *greatest common divisor* (or Greatest Common Factor) of two numbers `a` and `b` is the largest positive integer that divides both `a` and `b` without a remainder. The GCD.swift file contains three different algorithms of how to calculate the greatest common divisor.
 
-For example, `gcd(39, 52) = 13` because 13 divides 39 (`39/13 = 3`) as well as 52 (`52/13 = 4`). But there is no larger number than 13 that divides them both.
+For example, `gcdIterativeEuklid(39, 52) = 13` because 13 divides 39 (`39/13 = 3`) as well as 52 (`52/13 = 4`). But there is no larger number than 13 that divides them both.
 
 You've probably had to learn about this in school at some point. :-)
 
@@ -17,25 +17,25 @@ where `a % b` calculates the remainder of `a` divided by `b`.
 Here is an implementation of this idea in Swift:
 
 ```swift
-func gcd(_ a: Int, _ b: Int) -> Int {
-  let r = a % b
-  if r != 0 {
-    return gcd(b, r)
-  } else {
-    return b
-  }
+func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
+    let r: Int = m % n
+    if r != 0 {
+        return gcdRecursiveEuklid(n, r)
+    } else {
+        return n
+    }
 }
 ```
 
 Put it in a playground and try it out with these examples:
 
 ```swift
-gcd(52, 39)        // 13
-gcd(228, 36)       // 12
-gcd(51357, 3819)   // 57
+gcdBinaryRecursiveStein(52, 39)        // 13
+gcdRecursiveEuklid(228, 36)       // 12
+gcdIterativeEuklid(51357, 3819)   // 57
 ```
 
-Let's step through the third example:
+Let's step through the third example using gcd as a representation of the gcdRecursiveEuklid here:
 
 	gcd(51357, 3819)
 
@@ -47,10 +47,10 @@ because the remainder of `51357 % 3819` is `1710`. If you work out this division
 
 So `gcd(51357, 3819)` is the same as `gcd(3819, 1710)`. That's useful because we can keep simplifying:
 
-	gcd(3819, 1710) = gcd(1710, 3819 % 1710) = 
-	gcd(1710, 399)  = gcd(399, 1710 % 399)   = 
-	gcd(399, 114)   = gcd(114, 399 % 114)    = 
-	gcd(114, 57)    = gcd(57, 114 % 57)      = 
+	gcd(3819, 1710) = gcd(1710, 3819 % 1710) =
+	gcd(1710, 399)  = gcd(399, 1710 % 399)   =
+	gcd(399, 114)   = gcd(114, 399 % 114)    =
+	gcd(114, 57)    = gcd(57, 114 % 57)      =
 	gcd(57, 0)
 
 And now can't divide any further. The remainder of `114 / 57` is zero because `114 = 57 * 2` exactly. That means we've found the answer:
@@ -68,17 +68,17 @@ gcd(841, 299)     // 1
 Here is a slightly different implementation of Euclid's algorithm. Unlike the first version this doesn't use recursion but only a basic `while` loop.
 
 ```swift
-func gcd(_ m: Int, _ n: Int) -> Int {
-  var a = 0
-  var b = max(m, n)
-  var r = min(m, n)
-
-  while r != 0 {
-    a = b
-    b = r
-    r = a % b
-  }
-  return b
+func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
+    var a: Int = 0
+    var b: Int = max(m, n)
+    var r: Int = min(m, n)
+
+    while r != 0 {
+        a = b
+        b = r
+        r = a % b
+    }
+    return b
 }
 ```
 
@@ -88,9 +88,9 @@ The `max()` and `min()` at the top of the function make sure we always divide th
 
 An idea related to the GCD is the *least common multiple* or LCM.
 
-The least common multiple of two numbers `a` and `b` is the smallest positive integer that is a multiple of both. In other words, the LCM is evenly divisible by `a` and `b`. 
+The least common multiple of two numbers `a` and `b` is the smallest positive integer that is a multiple of both. In other words, the LCM is evenly divisible by `a` and `b`. The example implementation of the LCM takes two numbers and a specification which GCD algorithm is used.
 
-For example: `lcm(2, 3) = 6` because 6 can be divided by 2 and also by 3.
+For example: `lcm(2, 3, using: gcdIterativeEuklid) = 6` because 6 can be divided by 2 and also by 3.
 
 We can calculate the LCM using Euclid's algorithm too:
 
@@ -101,17 +101,19 @@ We can calculate the LCM using Euclid's algorithm too:
 In code:
 
 ```swift
-func lcm(_ m: Int, _ n: Int) -> Int {
-  return m / gcd(m, n) * n
+func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
+    guard (m & n) != 0 else { throw LCMError.divisionByZero }
+    return m / gcdAlgorithm(m, n) * n
 }
 ```
 
 And to try it out in a playground:
 
 ```swift
-lcm(10, 8)    // 40
+lcm(10, 8, using: gcdIterativeEuklid)    // 40
 ```
 
 You probably won't need to use the GCD or LCM in any real-world problems, but it's cool to play around with this ancient algorithm. It was first described by Euclid in his [Elements](http://publicdomainreview.org/collections/the-first-six-books-of-the-elements-of-euclid-1847/) around 300 BC. Rumor has it that he discovered this algorithm while he was hacking on his Commodore 64.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
+*Extended by Simon Krüger*
\ No newline at end of file

From 0f08fa9ddb315a55cca92d1fbabecb48a406cee8 Mon Sep 17 00:00:00 2001
From: Rahul <rahulrs0029@gmail.com>
Date: Tue, 23 Oct 2018 19:02:39 +0530
Subject: [PATCH 493/643] [Swift 4.2] Updated Selection Sort

---
 Selection Sort/SelectionSort.playground/Contents.swift       | 5 -----
 .../SelectionSort.playground/Sources/SelectionSort.swift     | 2 +-
 2 files changed, 1 insertion(+), 6 deletions(-)

diff --git a/Selection Sort/SelectionSort.playground/Contents.swift b/Selection Sort/SelectionSort.playground/Contents.swift
index b16dadb8d..a552c9edb 100644
--- a/Selection Sort/SelectionSort.playground/Contents.swift	
+++ b/Selection Sort/SelectionSort.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
 selectionSort(list)
 selectionSort(list, <)
diff --git a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift
index e7c66481d..e157319b4 100644
--- a/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
+++ b/Selection Sort/SelectionSort.playground/Sources/SelectionSort.swift	
@@ -3,7 +3,7 @@
 /// - Parameter array: array of elements that conform to the Comparable protocol
 /// - Returns: an array in ascending order
 public func selectionSort<T: Comparable>(_ array: [T]) -> [T] {
-  return insertionSort(array, <)
+  return selectionSort(array, <)
 }
 
 /// Performs the Selection sort algorithm on a array using the provided comparisson method

From e0c8738b1f1a16184d79158df9b65c6d42fc1568 Mon Sep 17 00:00:00 2001
From: Rahul <rahulrs0029@gmail.com>
Date: Tue, 23 Oct 2018 19:21:46 +0530
Subject: [PATCH 494/643] [Swift 4.2] Updated Linked List

---
 Linked List/LinkedList.playground/Contents.swift | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index cfa3a8b45..76b911310 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -3,10 +3,6 @@
 // For best results, don't forget to select "Show Rendered Markup" from XCode's "Editor" menu
 
 //: Linked List Class Declaration:
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 public final class LinkedList<T> {
     
@@ -459,7 +455,7 @@ var sum = 0
 for element in collection {
     sum += element
 }
-// sum is 15
+sum //15
 
 // Another way of achieving the same result though 'reduce', another method defined in an extension of Sequence. Collections are Sequences.
 let result = collection.reduce(0) {$0 + $1} // 15

From 71b20f41f8e1926a3c4f10a8fc3eca05d98ab193 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 22:25:10 -0500
Subject: [PATCH 495/643] Removes Swift 4.0 checks and updates the Swift
 version to 4.2.

---
 Comb Sort/Comb Sort.playground/Contents.swift |  6 +----
 Comb Sort/Tests/CombSortTests.swift           |  1 +
 .../Tests/Tests.xcodeproj/project.pbxproj     | 22 ++++++++++++++++---
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 4 files changed, 22 insertions(+), 9 deletions(-)

diff --git a/Comb Sort/Comb Sort.playground/Contents.swift b/Comb Sort/Comb Sort.playground/Contents.swift
index 39e24248a..1f7723838 100644
--- a/Comb Sort/Comb Sort.playground/Contents.swift	
+++ b/Comb Sort/Comb Sort.playground/Contents.swift	
@@ -2,11 +2,7 @@
 // Created by Stephen Rutstein
 // 7-16-2016
 
-import Cocoa
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+import Foundation
 
 // Test Comb Sort with small array of ten values
 let array = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
index e972c0a57..783fbd150 100644
--- a/Comb Sort/Tests/CombSortTests.swift	
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -17,6 +17,7 @@ class CombSortTests: XCTestCase {
             print("Hello, Swift 4!")
         #endif
     }
+    
     override func setUp() {
         super.setUp()
         sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
diff --git a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj
index 7530acbdc..14d059271 100644
--- a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -82,7 +82,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0820;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					056E92741E2483D300B30F52 = {
@@ -142,15 +142,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -192,15 +200,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_DOCUMENTATION_COMMENTS = YES;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -235,7 +251,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "Swift-Algorithm-Club.Tests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -248,7 +264,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "Swift-Algorithm-Club.Tests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 55e697ad3..48faa2df7 100644
--- a/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Comb Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 17a1e4c1dec24be6b10cdf8ad7ecddfa520418c1 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 22:40:49 -0500
Subject: [PATCH 496/643] Updates tests to check for Swift 4.2. Updates build
 settings to use Swift 4.2.

---
 Comb Sort/Tests/CombSortTests.swift             | 6 +++---
 Comb Sort/Tests/Tests.xcodeproj/project.pbxproj | 4 ++--
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
index 783fbd150..166065484 100644
--- a/Comb Sort/Tests/CombSortTests.swift	
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -12,9 +12,9 @@ class CombSortTests: XCTestCase {
     var sequence: [Int]!
     let expectedSequence: [Int] = [-12, -10, -1, 2, 9, 32, 55, 67, 89, 101]
 
-    func testSwift4(){
-        #if swift(>=4.0)
-            print("Hello, Swift 4!")
+    func testSwiftVersion(){
+        #if swift(>=4.2)
+            print("Hello, Swift 4.2!")
         #endif
     }
     
diff --git a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj
index 14d059271..4582b3f2d 100644
--- a/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Comb Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -187,7 +187,7 @@
 				SDKROOT = macosx;
 				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -237,7 +237,7 @@
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};

From 8da637c1d1c92cc65ea3eeb63275dc6117432b67 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 23:32:46 -0500
Subject: [PATCH 497/643] Removes Swift 4.0 check. Removes unused import.
 Refactors an if statement into a guard to be more Swift-y.

---
 Slow Sort/SlowSort.playground/Contents.swift | 5 -----
 Slow Sort/SlowSort.swift                     | 7 ++-----
 2 files changed, 2 insertions(+), 10 deletions(-)

diff --git a/Slow Sort/SlowSort.playground/Contents.swift b/Slow Sort/SlowSort.playground/Contents.swift
index 95bf80739..7c686782c 100644
--- a/Slow Sort/SlowSort.playground/Contents.swift	
+++ b/Slow Sort/SlowSort.playground/Contents.swift	
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 var numberList = [1, 12, 9, 17, 13, 12]
 
 slowsort(0, numberList.count-1, &numberList)
diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 9f264a057..c68a53455 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -6,12 +6,9 @@
 //
 //
 
-import Foundation
-
 public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-  if i>=j {
-    return
-  }
+  guard i<j else { return }
+    
   let m = (i+j)/2
   slowsort(i, m, &numberList)
   slowsort(m+1, j, &numberList)

From 1a3a13c94b9ca1fb1ab8c4ec4c4a9b58f700fcdc Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 23:41:43 -0500
Subject: [PATCH 498/643] Removes Swift 4.0 check. Removes unused import.
 Refactors an if statement into a guard to be more Swift-y. Removes
 unnecessarily explicitly defining the function as public.

---
 Slow Sort/SlowSort.playground/Contents.swift | 7 +------
 Slow Sort/SlowSort.swift                     | 8 ++------
 2 files changed, 3 insertions(+), 12 deletions(-)

diff --git a/Slow Sort/SlowSort.playground/Contents.swift b/Slow Sort/SlowSort.playground/Contents.swift
index 95bf80739..54c1e61ea 100644
--- a/Slow Sort/SlowSort.playground/Contents.swift	
+++ b/Slow Sort/SlowSort.playground/Contents.swift	
@@ -1,9 +1,4 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 var numberList = [1, 12, 9, 17, 13, 12]
 
-slowsort(0, numberList.count-1, &numberList)
+slowSort(0, numberList.count-1, &numberList)
 print(numberList)
diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 9f264a057..217733daa 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -6,12 +6,8 @@
 //
 //
 
-import Foundation
-
-public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-  if i>=j {
-    return
-  }
+func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+  guard if i < j else { return }
   let m = (i+j)/2
   slowsort(i, m, &numberList)
   slowsort(m+1, j, &numberList)

From 7add278a6acf10b19e2f8f035441b4a490d0125c Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 23:43:25 -0500
Subject: [PATCH 499/643] Renames function to use camel case.

---
 Slow Sort/SlowSort.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 217733daa..c6e705fc7 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -9,12 +9,12 @@
 func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
   guard if i < j else { return }
   let m = (i+j)/2
-  slowsort(i, m, &numberList)
-  slowsort(m+1, j, &numberList)
+  slowSort(i, m, &numberList)
+  slowSort(m+1, j, &numberList)
   if numberList[j] < numberList[m] {
     let temp = numberList[j]
     numberList[j] = numberList[m]
     numberList[m] = temp
   }
-  slowsort(i, j-1, &numberList)
+  slowSort(i, j-1, &numberList)
 }

From 227d6d9899d7f9abcc120fc04adc4a72119ee4ef Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Tue, 23 Oct 2018 23:50:21 -0500
Subject: [PATCH 500/643] Renames function to use camel case.

---
 Slow Sort/README.markdown                          | 14 ++++++--------
 .../SlowSort.playground/Sources/SlowSort.swift     | 13 ++++++-------
 2 files changed, 12 insertions(+), 15 deletions(-)

diff --git a/Slow Sort/README.markdown b/Slow Sort/README.markdown
index f8cc743cc..f7742b6a3 100644
--- a/Slow Sort/README.markdown	
+++ b/Slow Sort/README.markdown	
@@ -17,19 +17,17 @@ We can decompose the problem of sorting n numbers in ascending order into
 Here is an implementation of slow sort in Swift:
 
 ```swift
-public func slowsort(_ i: Int, _ j: Int) {
-    if i>=j {
-        return
-    }
+func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+    guard if i < j else { return }
     let m = (i+j)/2
-    slowsort(i,m)
-    slowsort(m+1,j)
+    slowSort(i, m, &numberList)
+    slowSort(m+1, j, &numberList)
     if numberList[j] < numberList[m] {
         let temp = numberList[j]
         numberList[j] = numberList[m]
         numberList[m] = temp
     }
-    slowsort(i,j-1)
+    slowSort(i, j-1, &numberList)
 }
 ```
 
@@ -47,4 +45,4 @@ public func slowsort(_ i: Int, _ j: Int) {
 
 *Written for Swift Algorithm Club by Lukas Schramm*
 
-(used the Insertion Sort Readme as template)
\ No newline at end of file
+(used the Insertion Sort Readme as template)
diff --git a/Slow Sort/SlowSort.playground/Sources/SlowSort.swift b/Slow Sort/SlowSort.playground/Sources/SlowSort.swift
index 32bb38505..cf09dcc5d 100644
--- a/Slow Sort/SlowSort.playground/Sources/SlowSort.swift	
+++ b/Slow Sort/SlowSort.playground/Sources/SlowSort.swift	
@@ -1,16 +1,15 @@
 import Foundation
 
-public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-  if i>=j {
-    return
-  }
+public func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+  guard i < j else { return }
+    
   let m = (i+j)/2
-  slowsort(i, m, &numberList)
-  slowsort(m+1, j, &numberList)
+  slowSort(i, m, &numberList)
+  slowSort(m+1, j, &numberList)
   if numberList[j] < numberList[m] {
     let temp = numberList[j]
     numberList[j] = numberList[m]
     numberList[m] = temp
   }
-  slowsort(i, j-1, &numberList)
+  slowSort(i, j-1, &numberList)
 }

From d3de867354ef9f639e991259e8722b9b9bb4e202 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall <lauren.taylor.marshall@gmail.com>
Date: Wed, 24 Oct 2018 18:31:38 -0500
Subject: [PATCH 501/643] Updates build settings to use Swift 4.2. Removes
 references to checking for Swift version 4.0. Removes unused import.

---
 Quicksort/Quicksort.playground/Contents.swift          |  5 -----
 Quicksort/Tests/QuicksortTests.swift                   |  7 -------
 Quicksort/Tests/SortingTestHelpers.swift               |  1 -
 .../Tests/Tests-Quicksort.xcodeproj/project.pbxproj    | 10 +++++++---
 .../xcshareddata/xcschemes/Tests-Quicksort.xcscheme    |  4 +---
 5 files changed, 8 insertions(+), 19 deletions(-)

diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index 94d9f8e45..f0427731f 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 // *** Simple but inefficient version of quicksort ***
diff --git a/Quicksort/Tests/QuicksortTests.swift b/Quicksort/Tests/QuicksortTests.swift
index 0a8f1a2a8..c8d9a62e6 100644
--- a/Quicksort/Tests/QuicksortTests.swift
+++ b/Quicksort/Tests/QuicksortTests.swift
@@ -1,13 +1,6 @@
 import XCTest
 
 class QuicksortTests: XCTestCase {
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-  
   func testQuicksort() {
     checkSortAlgorithm(quicksort)
   }
diff --git a/Quicksort/Tests/SortingTestHelpers.swift b/Quicksort/Tests/SortingTestHelpers.swift
index d699ec1e4..0c47cde4e 100644
--- a/Quicksort/Tests/SortingTestHelpers.swift
+++ b/Quicksort/Tests/SortingTestHelpers.swift
@@ -1,4 +1,3 @@
-import Foundation
 import XCTest
 
 func randomArray(_ size: Int) -> [Int] {
diff --git a/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
index c1b14e727..923195121 100644
--- a/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
+++ b/Quicksort/Tests/Tests-Quicksort.xcodeproj/project.pbxproj
@@ -86,7 +86,7 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0900;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
@@ -149,12 +149,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -187,7 +189,7 @@
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -203,12 +205,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -234,7 +238,7 @@
 				SDKROOT = macosx;
 				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
 				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme b/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
index 5b67c6f70..ec81527d1 100644
--- a/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
+++ b/Quicksort/Tests/Tests-Quicksort.xcodeproj/xcshareddata/xcschemes/Tests-Quicksort.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -10,7 +10,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -31,7 +30,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From b5d5c89353857a26589d2e03bd72f442b45e1aa9 Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 12:17:59 +0200
Subject: [PATCH 502/643] Updated Binary Tree to Swift 4.2

---
 Binary Tree/BinaryTree.playground/Contents.swift          | 5 -----
 Binary Tree/BinaryTree.playground/contents.xcplayground   | 2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 9 insertions(+), 6 deletions(-)
 create mode 100644 Binary Tree/BinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Binary Tree/BinaryTree.playground/Contents.swift b/Binary Tree/BinaryTree.playground/Contents.swift
index 9da194fed..b0bff577a 100644
--- a/Binary Tree/BinaryTree.playground/Contents.swift	
+++ b/Binary Tree/BinaryTree.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 public indirect enum BinaryTree<T> {
   case node(BinaryTree<T>, T, BinaryTree<T>)
   case empty
diff --git a/Binary Tree/BinaryTree.playground/contents.xcplayground b/Binary Tree/BinaryTree.playground/contents.xcplayground
index 06828af92..69d154d1e 100644
--- a/Binary Tree/BinaryTree.playground/contents.xcplayground	
+++ b/Binary Tree/BinaryTree.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Binary Tree/BinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Binary Tree/BinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Binary Tree/BinaryTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 016ae7c90bc525246f925480b6c6aa92eab47e4f Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 12:21:05 +0200
Subject: [PATCH 503/643] Update BitSet to Swift 4.2

---
 Bit Set/BitSet.playground/Contents.swift                  | 5 -----
 Bit Set/BitSet.playground/contents.xcplayground           | 2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 9 insertions(+), 6 deletions(-)
 create mode 100644 Bit Set/BitSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 95253ea27..d11b36e8c 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 // Create a bit set that stores 140 bits
 var bits = BitSet(size: 140)
 
diff --git a/Bit Set/BitSet.playground/contents.xcplayground b/Bit Set/BitSet.playground/contents.xcplayground
index 06828af92..69d154d1e 100644
--- a/Bit Set/BitSet.playground/contents.xcplayground	
+++ b/Bit Set/BitSet.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Bit Set/BitSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bit Set/BitSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bit Set/BitSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 6d8e795377902dc7dbdc6ad0a2231f62ba3a0d49 Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 12:31:47 +0200
Subject: [PATCH 504/643] Update Bounded Priority Queue to Swift 4.2

---
 .../BoundedPriorityQueue.playground/Contents.swift        | 5 -----
 .../BoundedPriorityQueue.playground/contents.xcplayground | 2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../Tests/Tests.xcodeproj/project.pbxproj                 | 6 +++---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 5 files changed, 20 insertions(+), 9 deletions(-)
 create mode 100644 Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift
index f8e219c13..d6204abec 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
@@ -1,8 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 struct Message: Comparable, CustomStringConvertible {
   let name: String
   let priority: Int
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground b/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground
index 06828af92..69d154d1e 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1000'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj
index 842c51695..11f907b47 100644
--- a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.pbxproj	
@@ -86,7 +86,7 @@
 				TargetAttributes = {
 					B80004B21C83E342001FE2D7 = {
 						CreatedOnToolsVersion = 7.2.1;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -226,7 +226,7 @@
 				SDKROOT = macosx;
 				SWIFT_OBJC_BRIDGING_HEADER = "";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -269,7 +269,7 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SDKROOT = macosx;
 				SWIFT_OBJC_BRIDGING_HEADER = "";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Bounded Priority Queue/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 57f25c429638b6a607d3e67f9e70f3633e2a1045 Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 13:16:15 +0200
Subject: [PATCH 505/643] Update Boyer Moore to Swift 4.2

---
 .../BoyerMooreHorspool.playground/Contents.swift   | 11 +++--------
 .../xcshareddata/IDEWorkspaceChecks.plist          |  8 ++++++++
 Boyer-Moore-Horspool/BoyerMooreHorspool.swift      |  6 +++---
 Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift   |  4 ++--
 .../Tests/Tests.xcodeproj/project.pbxproj          | 14 ++++++++------
 .../xcshareddata/IDEWorkspaceChecks.plist          |  8 ++++++++
 .../xcshareddata/xcschemes/Tests.xcscheme          |  4 +---
 .../contents.xcworkspacedata                       |  6 +++---
 8 files changed, 36 insertions(+), 25 deletions(-)
 create mode 100644 Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
index e88a1b93d..1666549c1 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-    print("Hello, Swift 4!")
-#endif
-
 /*
   Boyer-Moore string search
 
@@ -16,13 +11,13 @@ extension String {
     func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
index af8aea9d9..dbd738740 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
@@ -9,13 +9,13 @@ extension String {
     func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
diff --git a/Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift b/Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift
index 9efe60874..436173127 100755
--- a/Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift
+++ b/Boyer-Moore-Horspool/Tests/BoyerMooreTests.swift
@@ -26,8 +26,8 @@ class BoyerMooreTest: XCTestCase {
         XCTAssertNotNil(index)
 
         let startIndex = index!
-        let endIndex = string.index(index!, offsetBy: pattern.characters.count)
-        let match = string.substring(with: startIndex..<endIndex)
+        let endIndex = string.index(index!, offsetBy: pattern.count)
+        let match = String(string[startIndex..<endIndex])
         XCTAssertEqual(match, pattern)
     }
 
diff --git a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
index ab93d46a0..d29ac95f5 100644
--- a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.pbxproj
@@ -78,12 +78,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0900;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0900;
+						LastSwiftMigration = "";
 					};
 				};
 			};
@@ -157,12 +157,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -210,12 +212,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -252,8 +256,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -265,8 +268,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 538a6f4fa..afd69e6a7 100644
--- a/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Boyer-Moore-Horspool/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,7 +26,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -47,7 +46,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 9305ae37c..04d4ac573 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -612,16 +612,16 @@
       location = "group:Boyer-Moore"
       name = "Boyer-Moore">
       <FileRef
-         location = "group:BoyerMoore.playground">
+         location = "group:Boyer-Moore-Horspool/BoyerMooreHorspool.playground">
       </FileRef>
       <FileRef
-         location = "group:BoyerMoore.swift">
+         location = "group:Boyer-Moore-Horspool/BoyerMooreHorspool.swift">
       </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>
       <Group
-         location = "group:Tests"
+         location = "group:Boyer-Moore-Horspool/Tests"
          name = "Tests">
          <FileRef
             location = "group:BoyerMooreHorspoolTests.swift">

From 7384ec29e4e95cbae0b6a93dc6ae2ffe66eecffb Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 13:20:32 +0200
Subject: [PATCH 506/643] Update Boyer Moore to Swift 4.2

---
 .../contents.xcworkspacedata                           | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 04d4ac573..d85d538b3 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -609,19 +609,19 @@
       </Group>
    </Group>
    <Group
-      location = "group:Boyer-Moore"
+      location = "group:Boyer-Moore-Horspool"
       name = "Boyer-Moore">
       <FileRef
-         location = "group:Boyer-Moore-Horspool/BoyerMooreHorspool.playground">
+         location = "group:BoyerMooreHorspool.playground">
       </FileRef>
       <FileRef
-         location = "group:Boyer-Moore-Horspool/BoyerMooreHorspool.swift">
+         location = "group:BoyerMooreHorspool.swift">
       </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>
       <Group
-         location = "group:Boyer-Moore-Horspool/Tests"
+         location = "group:Tests"
          name = "Tests">
          <FileRef
             location = "group:BoyerMooreHorspoolTests.swift">
@@ -633,7 +633,7 @@
             location = "group:Info.plist">
          </FileRef>
          <FileRef
-            location = "group:Tests.xcodeproj">
+            location = "group:/Users/mroedder/workspace/swift-algorithm-club/Boyer-Moore-Horspool/Tests/Tests.xcodeproj">
          </FileRef>
       </Group>
    </Group>

From 402f23669b3f5c06dbd64adfe885d873e3a23f65 Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 13:24:39 +0200
Subject: [PATCH 507/643] Update Boyer Moore to Swift 4.2

---
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index d85d538b3..a37dac494 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -633,7 +633,7 @@
             location = "group:Info.plist">
          </FileRef>
          <FileRef
-            location = "group:/Users/mroedder/workspace/swift-algorithm-club/Boyer-Moore-Horspool/Tests/Tests.xcodeproj">
+            location = "group:Tests/Tests.xcodeproj">
          </FileRef>
       </Group>
    </Group>

From 6ead6d0dcb0e77f51cbda0582a1b6f56c1d0ebd0 Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 13:27:09 +0200
Subject: [PATCH 508/643] Update README to use Swift 4.2

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

diff --git a/Boyer-Moore-Horspool/README.markdown b/Boyer-Moore-Horspool/README.markdown
index f5e21ea41..8879d8df6 100644
--- a/Boyer-Moore-Horspool/README.markdown
+++ b/Boyer-Moore-Horspool/README.markdown
@@ -38,13 +38,13 @@ extension String {
     func index(of pattern: String) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
@@ -162,13 +162,13 @@ extension String {
     func index(of pattern: String) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
+        let patternLength = pattern.count
         guard patternLength > 0, patternLength <= characters.count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 

From 13d152600da95a0864d14edae72c0d93c161781c Mon Sep 17 00:00:00 2001
From: Marc <sticki@sticki.de>
Date: Fri, 26 Oct 2018 13:41:18 +0200
Subject: [PATCH 509/643] Update Breadth First Search to Swift 4.2

---
 .../Contents.swift                            |  4 ---
 .../Sources/Graph.swift                       |  2 +-
 .../contents.xcplayground                     |  2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../Tests/Tests.xcodeproj/project.pbxproj     | 30 +++++++++++++++----
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 7 files changed, 44 insertions(+), 12 deletions(-)
 create mode 100644 Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift
index 3986a0cee..cf22ebb25 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Pages/Simple example.xcplaygroundpage/Contents.swift	
@@ -1,7 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 func breadthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   var queue = Queue<Node>()
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift
index 87e21897c..0343120f8 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/Sources/Graph.swift	
@@ -5,7 +5,7 @@ public class Graph: CustomStringConvertible, Equatable {
     self.nodes = []
   }
 
-  public func addNode(_ label: String) -> Node {
+  @discardableResult public func addNode(_ label: String) -> Node {
     let node = Node(label)
     nodes.append(node)
     return node
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground b/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground
index 513c2e7e9..f635e9804 100644
--- a/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground	
+++ b/Breadth-First Search/BreadthFirstSearch.playground/contents.xcplayground	
@@ -1,2 +1,2 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='6.0' target-platform='ios' display-mode='raw'/>
\ No newline at end of file
+<playground version='6.0' target-platform='ios' display-mode='raw' last-migration='1000'/>
\ No newline at end of file
diff --git a/Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Breadth-First Search/BreadthFirstSearch.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index f86abf86e..a7f04e00a 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -59,7 +59,6 @@
 				7B2BBC941C779E7B0067B71D /* Info.plist */,
 			);
 			name = Tests;
-			path = TestsTests;
 			sourceTree = "<group>";
 		};
 /* End PBXGroup section */
@@ -89,12 +88,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -149,13 +148,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -193,13 +202,23 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
 				CODE_SIGN_IDENTITY = "-";
@@ -218,6 +237,7 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
+				SWIFT_COMPILATION_MODE = wholemodule;
 			};
 			name = Release;
 		};
@@ -231,7 +251,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -244,7 +264,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index dfcf6de42..afd69e6a7 100644
--- a/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Breadth-First Search/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From 56e054717532036d5d42df76295a9633af3e231a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Simon=20C=2E=20Kr=C3=BCger?= <simon.krueger@intive.com>
Date: Fri, 26 Oct 2018 14:33:49 +0200
Subject: [PATCH 510/643] Extended Miller-Rabin Primality test [code]

* Adds a more readable documentation and clear naming for variables to the Miller-Rabin Primality Test example
   * Miller-Rabin can fail under certain situations. These have to throw an error.
* Updates the relevant playground files
* Add name to documentation
---
 .../MRPrimality.playground/Contents.swift     |  46 ++---
 .../Sources/MRPrimality.swift                 | 111 ------------
 .../Sources/MillerRabin.swift                 | 100 +++++++++++
 .../contents.xcworkspacedata                  |   7 +
 .../xcshareddata/IDEWorkspaceChecks.plist     |   8 +
 Miller-Rabin Primality Test/MRPrimality.swift | 169 ++++++++----------
 Miller-Rabin Primality Test/README.markdown   |   5 +-
 7 files changed, 221 insertions(+), 225 deletions(-)
 delete mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/Sources/MillerRabin.swift
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift
index d8fd7fad8..1e4113c15 100644
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
@@ -5,25 +5,27 @@
 print("Hello, Swift 4!")
 #endif
 
-// Real primes
-mrPrimalityTest(5)
-mrPrimalityTest(439)
-mrPrimalityTest(1201)
-mrPrimalityTest(143477)
-mrPrimalityTest(1299869)
-mrPrimalityTest(15487361)
-mrPrimalityTest(179426363)
-mrPrimalityTest(32416187747)
-
-// Fake primes
-mrPrimalityTest(15)
-mrPrimalityTest(435)
-mrPrimalityTest(1207)
-mrPrimalityTest(143473)
-mrPrimalityTest(1291869)
-mrPrimalityTest(15487161)
-mrPrimalityTest(178426363)
-mrPrimalityTest(32415187747)
-
-// With iteration
-mrPrimalityTest(32416190071, iteration: 10)
+do {
+    // Real primes
+    try checkWithMillerRabin(5)
+    try checkWithMillerRabin(439)
+    try checkWithMillerRabin(1201)
+    try checkWithMillerRabin(143477)
+    try checkWithMillerRabin(1299869)
+    try checkWithMillerRabin(15487361)
+    try checkWithMillerRabin(179426363)
+    
+    // Fake primes
+    try checkWithMillerRabin(15)
+    try checkWithMillerRabin(435)
+    try checkWithMillerRabin(1207)
+    try checkWithMillerRabin(143473)
+    try checkWithMillerRabin(1291869)
+    try checkWithMillerRabin(15487161)
+    try checkWithMillerRabin(178426363)
+    
+    // Specifying accuracy
+    try checkWithMillerRabin(179426363, accuracy: 10)
+} catch {
+    dump(error)
+}
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift
deleted file mode 100644
index ee2ace8b9..000000000
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift	
+++ /dev/null
@@ -1,111 +0,0 @@
-//
-//  MRPrimality.swift
-//  
-//
-//  Created by Sahn Cha on 2016. 10. 18..
-//
-//
-
-import Foundation
-
-/*
-  Miller-Rabin Primality Test.
-  One of the most used algorithms for primality testing.
-  Since this is a probabilistic algorithm, it needs to be executed multiple times to increase accuracy.
-  
-  Inputs:
-    n: UInt64 { target integer to be tested for primality }
-    k: Int    { optional. number of iterations }
- 
-  Outputs:
-    true      { probably prime }
-    false     { composite }
- */
-public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
-  guard n > 2 && n % 2 == 1 else { return false }
-
-  var d = n - 1
-  var s = 0
-
-  while d % 2 == 0 {
-    d /= 2
-    s += 1
-  }
-
-  let range = UInt64.max - UInt64.max % (n - 2)
-  var r: UInt64 = 0
-  repeat {
-    arc4random_buf(&r, MemoryLayout.size(ofValue: r))
-  } while r >= range
-
-  r = r % (n - 2) + 2
-
-  for _ in 1 ... k {
-    var x = powmod64(r, d, n)
-    if x == 1 || x == n - 1 { continue }
-
-    if s == 1 { s = 2 }
-
-    for _ in 1 ... s - 1 {
-      x = powmod64(x, 2, n)
-      if x == 1 { return false }
-      if x == n - 1 { break }
-    }
-
-    if x != n - 1 { return false }
-  }
-
-  return true
-}
-
-/*
-  Calculates (base^exp) mod m.
- 
-  Inputs:
-    base: UInt64  { base }
-    exp: UInt64   { exponent }
-    m: UInt64     { modulus }
- 
-  Outputs:
-    the result
- */
-private func powmod64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
-  if m == 1 { return 0 }
-
-  var result: UInt64 = 1
-  var b = base % m
-  var e = exp
-
-  while e > 0 {
-    if e % 2 == 1 { result = mulmod64(result, b, m) }
-    b = mulmod64(b, b, m)
-    e >>= 1
-  }
-
-  return result
-}
-
-/*
-  Calculates (first * second) mod m, hopefully without overflow. :]
- 
-  Inputs:
-    first: UInt64   { first integer }
-    second: UInt64  { second integer }
-    m: UInt64       { modulus }
- 
-  Outputs:
-    the result
- */
-private func mulmod64(_ first: UInt64, _ second: UInt64, _ m: UInt64) -> UInt64 {
-  var result: UInt64 = 0
-  var a = first
-  var b = second
-
-  while a != 0 {
-    if a % 2 == 1 { result = ((result % m) + (b % m)) % m } // This may overflow if 'm' is a 64bit number && both 'result' and 'b' are very close to but smaller than 'm'.
-    a >>= 1
-    b = (b << 1) % m
-  }
-
-  return result
-}
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MillerRabin.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MillerRabin.swift
new file mode 100644
index 000000000..03daac1fa
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MillerRabin.swift	
@@ -0,0 +1,100 @@
+//
+//  MRPrimality.swift
+//
+//
+//  Created by Sahn Cha on 2016. 10. 18..
+//
+//
+
+import Foundation
+
+enum MillerRabinError: Error {
+    case primeLowAccuracy
+    case primeLowerBorder
+    case uIntOverflow
+}
+
+/*
+ The Miller–Rabin test relies on an equality or set of equalities that
+ hold true for prime values, then checks whether or not they hold for
+ a number that we want to test for primality.
+ 
+ - Parameter n: an odd integer to be tested for primality;
+ - Parameter k: a parameter that determines the accuracy of the test
+ - throws: Can throw an error of type `MillerRabinError`.
+ - Returns: composite if n is composite, otherwise probably prime
+ */
+public func checkWithMillerRabin(_ n: UInt, accuracy k: UInt = 1) throws -> Bool {
+    guard k > 0 else { throw MillerRabinError.primeLowAccuracy }
+    guard n > 0 else { throw MillerRabinError.primeLowerBorder }
+    guard n > 3 else { return true }
+    
+    // return false for all even numbers bigger than 2
+    if n % 2 == 0 {
+        return false
+    }
+    
+    let s: UInt = UInt((n - 1).trailingZeroBitCount)
+    let d: UInt = (n - 1) >> s
+    
+    guard UInt(pow(2.0, Double(s))) * d == n - 1 else { throw MillerRabinError.primeLowerBorder }
+    
+    /// Inspect whether a given witness will reveal the true identity of n.
+    func tryComposite(_ a: UInt, d: UInt, n: UInt) throws -> Bool? {
+        var x = try calculateModularExponentiation(base: a, exponent: d, modulus: n)
+        if x == 1 || x == (n - 1) {
+            return nil
+        }
+        for _ in 1..<s {
+            x = try calculateModularExponentiation(base: x, exponent: 2, modulus: n)
+            if x == 1 {
+                return false
+            } else if x == (n - 1) {
+                return nil
+            }
+        }
+        return false
+    }
+    
+    for _ in 0..<k {
+        let a = UInt.random(in: 2..<n-2)
+        if let composite = try tryComposite(a, d: d, n: n) {
+            return composite
+        }
+    }
+    
+    return true
+}
+
+/*
+ Calculates the modular exponentiation based on `Applied Cryptography by Bruce Schneier.`
+ in `Schneier, Bruce (1996). Applied Cryptography: Protocols, Algorithms,
+ and Source Code in C, Second Edition (2nd ed.). Wiley. ISBN 978-0-471-11709-4.`
+ 
+ - Parameter base: The natural base b.
+ - Parameter base: The natural exponent e.
+ - Parameter base: The natural modulus m.
+ - Throws: Can throw a `uIntOverflow` if the modulus' square exceeds the memory
+ limitations of UInt on the current system.
+ - Returns: The modular exponentiation c.
+ */
+private func calculateModularExponentiation(base: UInt, exponent: UInt, modulus: UInt) throws -> UInt {
+    guard modulus > 1 else { return 0 }
+    guard !(modulus-1).multipliedReportingOverflow(by: (modulus-1)).overflow else {
+        throw MillerRabinError.uIntOverflow
+    }
+    
+    var result: UInt = 1
+    var exponentCopy = exponent
+    var baseCopy = base % modulus
+    
+    while exponentCopy > 0 {
+        if exponentCopy % 2 == 1 {
+            result = (result * baseCopy) % modulus
+        }
+        exponentCopy = exponentCopy >> 1
+        baseCopy = (baseCopy * baseCopy) % modulus
+    }
+    
+    return result
+}
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Miller-Rabin Primality Test/MRPrimality.swift b/Miller-Rabin Primality Test/MRPrimality.swift
index ee2ace8b9..24b9c674c 100644
--- a/Miller-Rabin Primality Test/MRPrimality.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.swift	
@@ -1,6 +1,6 @@
 //
 //  MRPrimality.swift
-//  
+//
 //
 //  Created by Sahn Cha on 2016. 10. 18..
 //
@@ -8,104 +8,93 @@
 
 import Foundation
 
-/*
-  Miller-Rabin Primality Test.
-  One of the most used algorithms for primality testing.
-  Since this is a probabilistic algorithm, it needs to be executed multiple times to increase accuracy.
-  
-  Inputs:
-    n: UInt64 { target integer to be tested for primality }
-    k: Int    { optional. number of iterations }
- 
-  Outputs:
-    true      { probably prime }
-    false     { composite }
- */
-public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
-  guard n > 2 && n % 2 == 1 else { return false }
-
-  var d = n - 1
-  var s = 0
-
-  while d % 2 == 0 {
-    d /= 2
-    s += 1
-  }
-
-  let range = UInt64.max - UInt64.max % (n - 2)
-  var r: UInt64 = 0
-  repeat {
-    arc4random_buf(&r, MemoryLayout.size(ofValue: r))
-  } while r >= range
-
-  r = r % (n - 2) + 2
-
-  for _ in 1 ... k {
-    var x = powmod64(r, d, n)
-    if x == 1 || x == n - 1 { continue }
-
-    if s == 1 { s = 2 }
-
-    for _ in 1 ... s - 1 {
-      x = powmod64(x, 2, n)
-      if x == 1 { return false }
-      if x == n - 1 { break }
-    }
-
-    if x != n - 1 { return false }
-  }
-
-  return true
+enum MillerRabinError: Error {
+    case primeLowAccuracy
+    case primeLowerBorder
+    case uIntOverflow
 }
 
 /*
-  Calculates (base^exp) mod m.
- 
-  Inputs:
-    base: UInt64  { base }
-    exp: UInt64   { exponent }
-    m: UInt64     { modulus }
- 
-  Outputs:
-    the result
- */
-private func powmod64(_ base: UInt64, _ exp: UInt64, _ m: UInt64) -> UInt64 {
-  if m == 1 { return 0 }
+ The Miller–Rabin test relies on an equality or set of equalities that
+ hold true for prime values, then checks whether or not they hold for
+ a number that we want to test for primality.
+
+ - Parameter n: an odd integer to be tested for primality;
+ - Parameter k: a parameter that determines the accuracy of the test
+ - throws: Can throw an error of type `MillerRabinError`.
+ - Returns: composite if n is composite, otherwise probably prime
+*/
+func checkWithMillerRabin(_ n: UInt, accuracy k: UInt = 1) throws -> Bool {
+    guard k > 0 else { throw MillerRabinError.primeLowAccuracy }
+    guard n > 0 else { throw MillerRabinError.primeLowerBorder }
+    guard n > 3 else { return true }
+
+    // return false for all even numbers bigger than 2
+    if n % 2 == 0 {
+        return false
+    }
 
-  var result: UInt64 = 1
-  var b = base % m
-  var e = exp
+    let s: UInt = UInt((n - 1).trailingZeroBitCount)
+    let d: UInt = (n - 1) >> s
+
+    guard UInt(pow(2.0, Double(s))) * d == n - 1 else { throw EncryptionError.primeLowerBorder }
+
+    /// Inspect whether a given witness will reveal the true identity of n.
+    func tryComposite(_ a: UInt, d: UInt, n: UInt) throws -> Bool? {
+        var x = try calculateModularExponentiation(base: a, exponent: d, modulus: n)
+        if x == 1 || x == (n - 1) {
+            return nil
+        }
+        for _ in 1..<s {
+            x = try calculateModularExponentiation(base: x, exponent: 2, modulus: n)
+            if x == 1 {
+                return false
+            } else if x == (n - 1) {
+                return nil
+            }
+        }
+        return false
+    }
 
-  while e > 0 {
-    if e % 2 == 1 { result = mulmod64(result, b, m) }
-    b = mulmod64(b, b, m)
-    e >>= 1
-  }
+    for _ in 0..<k {
+        let a = UInt.random(in: 2..<n-2)
+        if let composite = try tryComposite(a, d: d, n: n) {
+            return composite
+        }
+    }
 
-  return result
+    return true
 }
 
 /*
-  Calculates (first * second) mod m, hopefully without overflow. :]
- 
-  Inputs:
-    first: UInt64   { first integer }
-    second: UInt64  { second integer }
-    m: UInt64       { modulus }
- 
-  Outputs:
-    the result
- */
-private func mulmod64(_ first: UInt64, _ second: UInt64, _ m: UInt64) -> UInt64 {
-  var result: UInt64 = 0
-  var a = first
-  var b = second
+ Calculates the modular exponentiation based on `Applied Cryptography by Bruce Schneier.`
+ in `Schneier, Bruce (1996). Applied Cryptography: Protocols, Algorithms,
+ and Source Code in C, Second Edition (2nd ed.). Wiley. ISBN 978-0-471-11709-4.`
+
+ - Parameter base: The natural base b.
+ - Parameter base: The natural exponent e.
+ - Parameter base: The natural modulus m.
+ - Throws: Can throw a `uIntOverflow` if the modulus' square exceeds the memory
+  limitations of UInt on the current system.
+ - Returns: The modular exponentiation c.
+*/
+private func calculateModularExponentiation(base: UInt, exponent: UInt, modulus: UInt) throws -> UInt {
+    guard modulus > 1 else { return 0 }
+    guard !(modulus-1).multipliedReportingOverflow(by: (modulus-1)).overflow else {
+        throw MillerRabinError.uIntOverflow
+    }
 
-  while a != 0 {
-    if a % 2 == 1 { result = ((result % m) + (b % m)) % m } // This may overflow if 'm' is a 64bit number && both 'result' and 'b' are very close to but smaller than 'm'.
-    a >>= 1
-    b = (b << 1) % m
-  }
+    var result: UInt = 1
+    var exponentCopy = exponent
+    var baseCopy = base % modulus
+
+    while exponentCopy > 0 {
+        if exponentCopy % 2 == 1 {
+            result = (result * baseCopy) % modulus
+        }
+        exponentCopy = exponentCopy >> 1
+        baseCopy = (baseCopy * baseCopy) % modulus
+    }
 
-  return result
+    return result
 }
diff --git a/Miller-Rabin Primality Test/README.markdown b/Miller-Rabin Primality Test/README.markdown
index 07acb9e18..9cc677a2e 100644
--- a/Miller-Rabin Primality Test/README.markdown	
+++ b/Miller-Rabin Primality Test/README.markdown	
@@ -27,8 +27,8 @@ The following pseudo code is excerpted from Wikipedia[3]:
 ## Usage
 
 ```swift
-mrPrimalityTest(7)                      // test if 7 is prime. (default iteration = 1)
-mrPrimalityTest(7, iteration: 10)       // test if 7 is prime && iterate 10 times.
+checkWithMillerRabin(7)                      // test if 7 is prime. (default iteration = 1)
+checkWithMillerRabin(7, accuracy: 10)       // test if 7 is prime && iterate 10 times.
 ```
 
 ## Reference
@@ -37,6 +37,7 @@ mrPrimalityTest(7, iteration: 10)       // test if 7 is prime && iterate 10 time
 3. Miller–Rabin primality test - Wikipedia, the free encyclopedia
 
 _Written for Swift Algorithm Club by **Sahn Cha**, @scha00_
+_Code updated by **Simon C. Krüger**._
 
 [1]: https://cs.uwaterloo.ca/research/tr/1975/CS-75-27.pdf
 [2]: http://www.sciencedirect.com/science/article/pii/0022314X80900840

From b47eb3e80afffc20c5e540e33fec66ae7a65bec0 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall
 <44420971+laurentaylormarshall@users.noreply.github.com>
Date: Fri, 26 Oct 2018 18:56:13 -0500
Subject: [PATCH 511/643] Update SlowSort.swift

---
 Slow Sort/SlowSort.swift | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index c68a53455..813f3b7a9 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -5,10 +5,8 @@
 //  Created by Pope Lukas Schramm (Dabendorf Orthodox Religion) on 16-07-16.
 //
 //
-
-public func slowsort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-  guard i<j else { return }
-    
+func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
+  guard if i < j else { return }
   let m = (i+j)/2
   slowsort(i, m, &numberList)
   slowsort(m+1, j, &numberList)

From 231f5629f4147d5808c70607cf9ad94c1cb89152 Mon Sep 17 00:00:00 2001
From: laurentaylormarshall
 <44420971+laurentaylormarshall@users.noreply.github.com>
Date: Fri, 26 Oct 2018 19:11:33 -0500
Subject: [PATCH 512/643] Updates function name.

---
 Slow Sort/SlowSort.swift | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 813f3b7a9..3b762042a 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -1,19 +1,19 @@
 //
 //  SlowSort.swift
-//  
+//
 //
 //  Created by Pope Lukas Schramm (Dabendorf Orthodox Religion) on 16-07-16.
 //
 //
 func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-  guard if i < j else { return }
-  let m = (i+j)/2
-  slowsort(i, m, &numberList)
-  slowsort(m+1, j, &numberList)
-  if numberList[j] < numberList[m] {
-    let temp = numberList[j]
-    numberList[j] = numberList[m]
-    numberList[m] = temp
-  }
-  slowsort(i, j-1, &numberList)
+    guard if i < j else { return }
+    let m = (i+j)/2
+    slowSort(i, m, &numberList)
+    slowSort(m+1, j, &numberList)
+    if numberList[j] < numberList[m] {
+        let temp = numberList[j]
+        numberList[j] = numberList[m]
+        numberList[m] = temp
+    }
+    slowSort(i, j-1, &numberList)
 }

From 22efd0d33aa9d3bfacf3c84701dc157bb10e5aa7 Mon Sep 17 00:00:00 2001
From: Erik Strottmann <erik.strottmann@gmail.com>
Date: Sat, 27 Oct 2018 10:26:54 -0700
Subject: [PATCH 513/643] Standardize Trie indentation to 2 spaces

2 spaces is recommended by the Ray Wenderlich Swift Style Guide.
---
 Trie/ReadMe.md                           |  40 +--
 Trie/Trie/Trie.xcodeproj/project.pbxproj |   2 +
 Trie/Trie/Trie/AppDelegate.swift         |  12 +-
 Trie/Trie/Trie/Trie.swift                | 118 ++++----
 Trie/Trie/Trie/ViewController.swift      |  16 +-
 Trie/Trie/TrieTests/TrieTests.swift      | 340 +++++++++++------------
 Trie/Trie/TrieUITests/TrieUITests.swift  |  34 +--
 7 files changed, 280 insertions(+), 282 deletions(-)

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 8e473a619..8d0c45c8a 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -27,29 +27,29 @@ Tries are very useful for certain situations. Here are some of the advantages:
 
 ```swift
 func contains(word: String) -> Bool {
-	guard !word.isEmpty else { return false }
+  guard !word.isEmpty else { return false }
 
-	// 1
-	var currentNode = root
+  // 1
+  var currentNode = root
   
-	// 2
-	var characters = Array(word.lowercased())
-	var currentIndex = 0
+  // 2
+  var characters = Array(word.lowercased())
+  var currentIndex = 0
  
-	// 3
-	while currentIndex < characters.count, 
-	  let child = currentNode.children[characters[currentIndex]] {
-
-	  currentNode = child
-	  currentIndex += 1
-	}
-
-	// 4
-	if currentIndex == characters.count && currentNode.isTerminating {
-	  return true
-	} else {
-	  return false
-	}
+  // 3
+  while currentIndex < characters.count, 
+    let child = currentNode.children[characters[currentIndex]] {
+
+    currentNode = child
+    currentIndex += 1
+  }
+
+  // 4
+  if currentIndex == characters.count && currentNode.isTerminating {
+    return true
+  } else {
+    return false
+  }
 }
 ```
 
diff --git a/Trie/Trie/Trie.xcodeproj/project.pbxproj b/Trie/Trie/Trie.xcodeproj/project.pbxproj
index 1e3602eea..6b7cc9b61 100644
--- a/Trie/Trie/Trie.xcodeproj/project.pbxproj
+++ b/Trie/Trie/Trie.xcodeproj/project.pbxproj
@@ -87,7 +87,9 @@
 				EB798E191DFEF79900F0628D /* TrieUITests */,
 				EB798DFB1DFEF79900F0628D /* Products */,
 			);
+			indentWidth = 2;
 			sourceTree = "<group>";
+			tabWidth = 2;
 		};
 		EB798DFB1DFEF79900F0628D /* Products */ = {
 			isa = PBXGroup;
diff --git a/Trie/Trie/Trie/AppDelegate.swift b/Trie/Trie/Trie/AppDelegate.swift
index b2c46695b..48dc24673 100644
--- a/Trie/Trie/Trie/AppDelegate.swift
+++ b/Trie/Trie/Trie/AppDelegate.swift
@@ -11,12 +11,12 @@ import Cocoa
 @NSApplicationMain
 class AppDelegate: NSObject, NSApplicationDelegate {
 
-    func applicationDidFinishLaunching(_ aNotification: Notification) {
-        // Insert code here to initialize your application
-    }
+  func applicationDidFinishLaunching(_ aNotification: Notification) {
+    // Insert code here to initialize your application
+  }
 
-    func applicationWillTerminate(_ aNotification: Notification) {
-        // Insert code here to tear down your application
-    }
+  func applicationWillTerminate(_ aNotification: Notification) {
+    // Insert code here to tear down your application
+  }
 
 }
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index fbc933138..accc7b61c 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -43,54 +43,53 @@ class TrieNode<T: Hashable> {
 /// A trie data structure containing words.  Each node is a single
 /// character of a word.
 class Trie: NSObject, NSCoding {
-    typealias Node = TrieNode<Character>
-    /// The number of words in the trie
-    public var count: Int {
-        return wordCount
-    }
-    /// Is the trie empty?
-    public var isEmpty: Bool {
-        return wordCount == 0
-    }
-    /// All words currently in the trie
-    public var words: [String] {
-        return wordsInSubtrie(rootNode: root, partialWord: "")
-    }
-    fileprivate let root: Node
-    fileprivate var wordCount: Int
-
-    /// Creates an empty trie.
-    override init() {
-        root = Node()
-        wordCount = 0
-        super.init()
-    }
+  typealias Node = TrieNode<Character>
+  /// The number of words in the trie
+  public var count: Int {
+    return wordCount
+  }
+  /// Is the trie empty?
+  public var isEmpty: Bool {
+    return wordCount == 0
+  }
+  /// All words currently in the trie
+  public var words: [String] {
+    return wordsInSubtrie(rootNode: root, partialWord: "")
+  }
+  fileprivate let root: Node
+  fileprivate var wordCount: Int
+
+  /// Creates an empty trie.
+  override init() {
+    root = Node()
+    wordCount = 0
+    super.init()
+  }
 
-    // MARK: NSCoding
+  // MARK: NSCoding
 
-    /// Initializes the trie with words from an archive
-    ///
-    /// - Parameter decoder: Decodes the archive
-    required convenience init?(coder decoder: NSCoder) {
-        self.init()
-        let words = decoder.decodeObject(forKey: "words") as? [String]
-        for word in words! {
-            self.insert(word: word)
-        }
+  /// Initializes the trie with words from an archive
+  ///
+  /// - Parameter decoder: Decodes the archive
+  required convenience init?(coder decoder: NSCoder) {
+    self.init()
+    let words = decoder.decodeObject(forKey: "words") as? [String]
+    for word in words! {
+      self.insert(word: word)
     }
+  }
 
-    /// Encodes the words in the trie by putting them in an array then encoding
-    /// the array.
-    ///
-    /// - Parameter coder: The object that will encode the array
-    func encode(with coder: NSCoder) {
-        coder.encode(self.words, forKey: "words")
-    }
+  /// Encodes the words in the trie by putting them in an array then encoding
+  /// the array.
+  ///
+  /// - Parameter coder: The object that will encode the array
+  func encode(with coder: NSCoder) {
+    coder.encode(self.words, forKey: "words")
+  }
 }
 
 // MARK: - Adds methods: insert, remove, contains
 extension Trie {
-
   /// Inserts a word into the trie.  If the word is already present,
   /// there is no change.
   ///
@@ -142,14 +141,14 @@ extension Trie {
   /// - Returns: the node where the search ended, nil if the
   /// search failed.
   private func findLastNodeOf(word: String) -> Node? {
-      var currentNode = root
-      for character in word.lowercased() {
-          guard let childNode = currentNode.children[character] else {
-              return nil
-          }
-          currentNode = childNode
+    var currentNode = root
+    for character in word.lowercased() {
+      guard let childNode = currentNode.children[character] else {
+        return nil
       }
-      return currentNode
+      currentNode = childNode
+    }
+    return currentNode
   }
 
   /// Attempts to walk to the terminating node of a word.  The
@@ -160,10 +159,9 @@ extension Trie {
   /// search failed.
   private func findTerminalNodeOf(word: String) -> Node? {
     if let lastNode = findLastNodeOf(word: word) {
-        return lastNode.isTerminating ? lastNode : nil
+      return lastNode.isTerminating ? lastNode : nil
     }
     return nil
-
   }
 
   /// Deletes a word from the trie by starting with the last letter
@@ -237,17 +235,17 @@ extension Trie {
   ///   - prefix: the letters for word prefix
   /// - Returns: the words in the subtrie that start with prefix
   func findWordsWithPrefix(prefix: String) -> [String] {
-      var words = [String]()
-      let prefixLowerCased = prefix.lowercased()
-      if let lastNode = findLastNodeOf(word: prefixLowerCased) {
-          if lastNode.isTerminating {
-              words.append(prefixLowerCased)
-          }
-          for childNode in lastNode.children.values {
-              let childWords = wordsInSubtrie(rootNode: childNode, partialWord: prefixLowerCased)
-              words += childWords
-          }
+    var words = [String]()
+    let prefixLowerCased = prefix.lowercased()
+    if let lastNode = findLastNodeOf(word: prefixLowerCased) {
+      if lastNode.isTerminating {
+        words.append(prefixLowerCased)
+      }
+      for childNode in lastNode.children.values {
+        let childWords = wordsInSubtrie(rootNode: childNode, partialWord: prefixLowerCased)
+        words += childWords
       }
-      return words
+    }
+    return words
   }
 }
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
index 928b01f4c..8ce34f6c7 100644
--- a/Trie/Trie/Trie/ViewController.swift
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -10,16 +10,16 @@ import Cocoa
 
 class ViewController: NSViewController {
 
-    override func viewDidLoad() {
-        super.viewDidLoad()
+  override func viewDidLoad() {
+    super.viewDidLoad()
 
-        // Do any additional setup after loading the view.
-    }
+    // Do any additional setup after loading the view.
+  }
 
-    override var representedObject: Any? {
-        didSet {
-        // Update the view, if already loaded.
-        }
+  override var representedObject: Any? {
+    didSet {
+      // Update the view, if already loaded.
     }
+  }
 
 }
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index b69c5666e..0c5bc69c6 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -10,186 +10,184 @@ import XCTest
 @testable import Trie
 
 class TrieTests: XCTestCase {
-    var wordArray: [String]?
-    var trie = Trie()
-
-    /// Makes sure that the wordArray and trie are initialized before each test.
-    override func setUp() {
-        super.setUp()
-        createWordArray()
-        insertWordsIntoTrie()
+  var wordArray: [String]?
+  var trie = Trie()
+
+  /// Makes sure that the wordArray and trie are initialized before each test.
+  override func setUp() {
+    super.setUp()
+    createWordArray()
+    insertWordsIntoTrie()
+  }
+
+  /// Don't need to do anything here because the wordArray and trie should
+  /// stay around.
+  override func tearDown() {
+    super.tearDown()
+  }
+
+  /// Reads words from the dictionary file and inserts them into an array.  If
+  /// the word array already has words, do nothing.  This allows running all
+  /// tests without repeatedly filling the array with the same values.
+  func createWordArray() {
+    guard wordArray == nil else {
+      return
     }
-
-    /// Don't need to do anything here because the wordArray and trie should
-    /// stay around.
-    override func tearDown() {
-        super.tearDown()
-    }
-
-    /// Reads words from the dictionary file and inserts them into an array.  If
-    /// the word array already has words, do nothing.  This allows running all
-    /// tests without repeatedly filling the array with the same values.
-    func createWordArray() {
-        guard wordArray == nil else {
-            return
-        }
-        let resourcePath = Bundle.main.resourcePath! as NSString
-        let fileName = "dictionary.txt"
-        let filePath = resourcePath.appendingPathComponent(fileName)
-
-        var data: String?
-        do {
-            data = try String(contentsOfFile: filePath, encoding: String.Encoding.utf8)
-        } catch let error as NSError {
-            XCTAssertNil(error)
-        }
-        XCTAssertNotNil(data)
-        let dictionarySize = 162825
-        wordArray = data!.components(separatedBy: "\n")
-        XCTAssertEqual(wordArray!.count, dictionarySize)
-    }
-
-    /// Inserts words into a trie.  If the trie is non-empty, don't do anything.
-    func insertWordsIntoTrie() {
-        guard let wordArray = wordArray, trie.count == 0 else { return }
-        for word in wordArray {
-            trie.insert(word: word)
-        }
-    }
-
-    /// Tests that a newly created trie has zero words.
-    func testCreate() {
-        let trie = Trie()
-        XCTAssertEqual(trie.count, 0)
-    }
-
-    /// Tests the insert method
-    func testInsert() {
-        let trie = Trie()
-        trie.insert(word: "cute")
-        trie.insert(word: "cutie")
-        trie.insert(word: "fred")
-        XCTAssertTrue(trie.contains(word: "cute"))
-        XCTAssertFalse(trie.contains(word: "cut"))
-        trie.insert(word: "cut")
-        XCTAssertTrue(trie.contains(word: "cut"))
-        XCTAssertEqual(trie.count, 4)
-    }
-
-    /// Tests the remove method
-    func testRemove() {
-        let trie = Trie()
-        trie.insert(word: "cute")
-        trie.insert(word: "cut")
-        XCTAssertEqual(trie.count, 2)
-        trie.remove(word: "cute")
-        XCTAssertTrue(trie.contains(word: "cut"))
-        XCTAssertFalse(trie.contains(word: "cute"))
-        XCTAssertEqual(trie.count, 1)
+    let resourcePath = Bundle.main.resourcePath! as NSString
+    let fileName = "dictionary.txt"
+    let filePath = resourcePath.appendingPathComponent(fileName)
+
+    var data: String?
+    do {
+      data = try String(contentsOfFile: filePath, encoding: String.Encoding.utf8)
+    } catch let error as NSError {
+      XCTAssertNil(error)
     }
-
-    /// Tests the words property
-    func testWords() {
-        let trie = Trie()
-        var words = trie.words
-        XCTAssertEqual(words.count, 0)
-        trie.insert(word: "foobar")
-        words = trie.words
-        XCTAssertEqual(words[0], "foobar")
-        XCTAssertEqual(words.count, 1)
+    XCTAssertNotNil(data)
+    let dictionarySize = 162825
+    wordArray = data!.components(separatedBy: "\n")
+    XCTAssertEqual(wordArray!.count, dictionarySize)
+  }
+
+  /// Inserts words into a trie.  If the trie is non-empty, don't do anything.
+  func insertWordsIntoTrie() {
+    guard let wordArray = wordArray, trie.count == 0 else { return }
+    for word in wordArray {
+      trie.insert(word: word)
     }
-
-    /// Tests the performance of the insert method.
-    func testInsertPerformance() {
-        self.measure {
-            let trie = Trie()
-            for word in self.wordArray! {
-                trie.insert(word: word)
-            }
-        }
-        XCTAssertGreaterThan(trie.count, 0)
-        XCTAssertEqual(trie.count, wordArray?.count)
+  }
+
+  /// Tests that a newly created trie has zero words.
+  func testCreate() {
+    let trie = Trie()
+    XCTAssertEqual(trie.count, 0)
+  }
+
+  /// Tests the insert method
+  func testInsert() {
+    let trie = Trie()
+    trie.insert(word: "cute")
+    trie.insert(word: "cutie")
+    trie.insert(word: "fred")
+    XCTAssertTrue(trie.contains(word: "cute"))
+    XCTAssertFalse(trie.contains(word: "cut"))
+    trie.insert(word: "cut")
+    XCTAssertTrue(trie.contains(word: "cut"))
+    XCTAssertEqual(trie.count, 4)
+  }
+
+  /// Tests the remove method
+  func testRemove() {
+    let trie = Trie()
+    trie.insert(word: "cute")
+    trie.insert(word: "cut")
+    XCTAssertEqual(trie.count, 2)
+    trie.remove(word: "cute")
+    XCTAssertTrue(trie.contains(word: "cut"))
+    XCTAssertFalse(trie.contains(word: "cute"))
+    XCTAssertEqual(trie.count, 1)
+  }
+
+  /// Tests the words property
+  func testWords() {
+    let trie = Trie()
+    var words = trie.words
+    XCTAssertEqual(words.count, 0)
+    trie.insert(word: "foobar")
+    words = trie.words
+    XCTAssertEqual(words[0], "foobar")
+    XCTAssertEqual(words.count, 1)
+  }
+
+  /// Tests the performance of the insert method.
+  func testInsertPerformance() {
+    self.measure {
+      let trie = Trie()
+      for word in self.wordArray! {
+        trie.insert(word: word)
+      }
     }
-
-    /// Tests the performance of the insert method when the words are already
-    /// present.
-    func testInsertAgainPerformance() {
-        self.measure {
-            for word in self.wordArray! {
-                self.trie.insert(word: word)
-            }
-        }
+    XCTAssertGreaterThan(trie.count, 0)
+    XCTAssertEqual(trie.count, wordArray?.count)
+  }
+
+  /// Tests the performance of the insert method when the words are already
+  /// present.
+  func testInsertAgainPerformance() {
+    self.measure {
+      for word in self.wordArray! {
+        self.trie.insert(word: word)
+      }
     }
-
-    /// Tests the performance of the contains method.
-    func testContainsPerformance() {
-        self.measure {
-            for word in self.wordArray! {
-                XCTAssertTrue(self.trie.contains(word: word))
-            }
-        }
+  }
+
+  /// Tests the performance of the contains method.
+  func testContainsPerformance() {
+    self.measure {
+      for word in self.wordArray! {
+        XCTAssertTrue(self.trie.contains(word: word))
+      }
     }
+  }
 
-    /// Tests the performance of the remove method.  Since setup has already put
-    /// words into the trie, remove them before measuring performance.
-    func testRemovePerformance() {
-        for word in self.wordArray! {
-            self.trie.remove(word: word)
-        }
-        self.measure {
-            self.insertWordsIntoTrie()
-            for word in self.wordArray! {
-                self.trie.remove(word: word)
-            }
-        }
-        XCTAssertEqual(trie.count, 0)
+  /// Tests the performance of the remove method.  Since setup has already put
+  /// words into the trie, remove them before measuring performance.
+  func testRemovePerformance() {
+    for word in self.wordArray! {
+      self.trie.remove(word: word)
     }
-
-    /// Tests the performance of the words computed property.  Also tests to see
-    /// if it worked properly.
-    func testWordsPerformance() {
-        var words: [String]?
-        self.measure {
-            words = self.trie.words
-        }
-        XCTAssertEqual(words?.count, trie.count)
-        for word in words! {
-            XCTAssertTrue(self.trie.contains(word: word))
-        }
+    self.measure {
+      self.insertWordsIntoTrie()
+      for word in self.wordArray! {
+        self.trie.remove(word: word)
+      }
     }
-
-    /// Tests the archiving and unarchiving of the trie.
-    func testArchiveAndUnarchive() {
-        let resourcePath = Bundle.main.resourcePath! as NSString
-        let fileName = "dictionary-archive"
-        let filePath = resourcePath.appendingPathComponent(fileName)
-        NSKeyedArchiver.archiveRootObject(trie, toFile: filePath)
-        let trieCopy = NSKeyedUnarchiver.unarchiveObject(withFile: filePath) as? Trie
-        XCTAssertEqual(trieCopy?.count, trie.count)
-
+    XCTAssertEqual(trie.count, 0)
+  }
+
+  /// Tests the performance of the words computed property.  Also tests to see
+  /// if it worked properly.
+  func testWordsPerformance() {
+    var words: [String]?
+    self.measure {
+      words = self.trie.words
     }
-
-    func testFindWordsWithPrefix() {
-        let trie = Trie()
-        trie.insert(word: "test")
-        trie.insert(word: "another")
-        trie.insert(word: "exam")
-        let wordsAll = trie.findWordsWithPrefix(prefix: "")
-        XCTAssertEqual(wordsAll.sorted(), ["another", "exam", "test"])
-        let words = trie.findWordsWithPrefix(prefix: "ex")
-        XCTAssertEqual(words, ["exam"])
-        trie.insert(word: "examination")
-        let words2 = trie.findWordsWithPrefix(prefix: "exam")
-        XCTAssertEqual(words2, ["exam", "examination"])
-        let noWords = trie.findWordsWithPrefix(prefix: "tee")
-        XCTAssertEqual(noWords, [])
-        let unicodeWord = "😬😎"
-        trie.insert(word: unicodeWord)
-        let wordsUnicode = trie.findWordsWithPrefix(prefix: "😬")
-        XCTAssertEqual(wordsUnicode, [unicodeWord])
-        trie.insert(word: "Team")
-        let wordsUpperCase = trie.findWordsWithPrefix(prefix: "Te")
-        XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"])
-
+    XCTAssertEqual(words?.count, trie.count)
+    for word in words! {
+      XCTAssertTrue(self.trie.contains(word: word))
     }
+  }
+
+  /// Tests the archiving and unarchiving of the trie.
+  func testArchiveAndUnarchive() {
+    let resourcePath = Bundle.main.resourcePath! as NSString
+    let fileName = "dictionary-archive"
+    let filePath = resourcePath.appendingPathComponent(fileName)
+    NSKeyedArchiver.archiveRootObject(trie, toFile: filePath)
+    let trieCopy = NSKeyedUnarchiver.unarchiveObject(withFile: filePath) as? Trie
+    XCTAssertEqual(trieCopy?.count, trie.count)
+  }
+
+  func testFindWordsWithPrefix() {
+    let trie = Trie()
+    trie.insert(word: "test")
+    trie.insert(word: "another")
+    trie.insert(word: "exam")
+    let wordsAll = trie.findWordsWithPrefix(prefix: "")
+    XCTAssertEqual(wordsAll.sorted(), ["another", "exam", "test"])
+    let words = trie.findWordsWithPrefix(prefix: "ex")
+    XCTAssertEqual(words, ["exam"])
+    trie.insert(word: "examination")
+    let words2 = trie.findWordsWithPrefix(prefix: "exam")
+    XCTAssertEqual(words2, ["exam", "examination"])
+    let noWords = trie.findWordsWithPrefix(prefix: "tee")
+    XCTAssertEqual(noWords, [])
+    let unicodeWord = "😬😎"
+    trie.insert(word: unicodeWord)
+    let wordsUnicode = trie.findWordsWithPrefix(prefix: "😬")
+    XCTAssertEqual(wordsUnicode, [unicodeWord])
+    trie.insert(word: "Team")
+    let wordsUpperCase = trie.findWordsWithPrefix(prefix: "Te")
+    XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"])
+  }
 }
diff --git a/Trie/Trie/TrieUITests/TrieUITests.swift b/Trie/Trie/TrieUITests/TrieUITests.swift
index acb3b1756..380bf3092 100644
--- a/Trie/Trie/TrieUITests/TrieUITests.swift
+++ b/Trie/Trie/TrieUITests/TrieUITests.swift
@@ -10,27 +10,27 @@ import XCTest
 
 class TrieUITests: XCTestCase {
 
-    override func setUp() {
-        super.setUp()
+  override func setUp() {
+    super.setUp()
 
-        // Put setup code here. This method is called before the invocation of each test method in the class.
+    // Put setup code here. This method is called before the invocation of each test method in the class.
 
-        // In UI tests it is usually best to stop immediately when a failure occurs.
-        continueAfterFailure = false
-        // UI tests must launch the application that they test. Doing this in setup will make sure it happens for each test method.
-        XCUIApplication().launch()
+    // In UI tests it is usually best to stop immediately when a failure occurs.
+    continueAfterFailure = false
+    // UI tests must launch the application that they test. Doing this in setup will make sure it happens for each test method.
+    XCUIApplication().launch()
 
-        // In UI tests it’s important to set the initial state - such as interface orientation - required for your tests before they run. The setUp method is a good place to do this.
-    }
+    // In UI tests it’s important to set the initial state - such as interface orientation - required for your tests before they run. The setUp method is a good place to do this.
+  }
 
-    override func tearDown() {
-        // Put teardown code here. This method is called after the invocation of each test method in the class.
-        super.tearDown()
-    }
+  override func tearDown() {
+    // Put teardown code here. This method is called after the invocation of each test method in the class.
+    super.tearDown()
+  }
 
-    func testExample() {
-        // Use recording to get started writing UI tests.
-        // Use XCTAssert and related functions to verify your tests produce the correct results.
-    }
+  func testExample() {
+    // Use recording to get started writing UI tests.
+    // Use XCTAssert and related functions to verify your tests produce the correct results.
+  }
 
 }

From 41eb9c1ee1591472c24b49108295261f698a3f1b Mon Sep 17 00:00:00 2001
From: Samwel Charles <younggeeks101@gmail.com>
Date: Mon, 29 Oct 2018 00:22:43 +0300
Subject: [PATCH 514/643] update union-find to swift 4.2

---
 Union-Find/UnionFind.playground/Contents.swift            | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Union-Find/UnionFind.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 6ac3b4c4e..b1f7fb4e1 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 var dsu = UnionFindQuickUnion<Int>()
 
 for i in 1...10 {
diff --git a/Union-Find/UnionFind.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Union-Find/UnionFind.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Union-Find/UnionFind.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From cb76b97e3f295d171267044ca599d27db113a7ee Mon Sep 17 00:00:00 2001
From: Samwel Charles <younggeeks101@gmail.com>
Date: Mon, 29 Oct 2018 01:01:09 +0300
Subject: [PATCH 515/643] add link to merge sort algorithm in buble sort
 algorith README.md file

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

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index e55129d93..c4b2c37c8 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -117,7 +117,7 @@ There is no Fifth pass
 
 #### Conclusion
 
-Even with the proposed optimizations, this is still a terribly inefficient sorting algorithm. A good alternative is [Merge Sort](), that not only is better performing, has a similar degree of dificulty to implement.
+Even with the proposed optimizations, this is still a terribly inefficient sorting algorithm. A good alternative is [Merge Sort](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Merge%20Sort), that not only is better performing, has a similar degree of dificulty to implement.
 
 *Updated for the Swift Algorithm Club by Julio Brazil*
 

From 299a67caeb984577561aaf1921271015558bfd6e Mon Sep 17 00:00:00 2001
From: Julio Brazil <julio_bbl@hotmail.com>
Date: Mon, 29 Oct 2018 11:45:21 -0300
Subject: [PATCH 516/643] addition of convenience method

---
 Bubble Sort/MyPlayground.playground/Contents.swift     |  4 +++-
 .../MyPlayground.playground/Sources/BubbleSort.swift   | 10 +++++++---
 2 files changed, 10 insertions(+), 4 deletions(-)

diff --git a/Bubble Sort/MyPlayground.playground/Contents.swift b/Bubble Sort/MyPlayground.playground/Contents.swift
index 8d27d801e..6188a0763 100644
--- a/Bubble Sort/MyPlayground.playground/Contents.swift	
+++ b/Bubble Sort/MyPlayground.playground/Contents.swift	
@@ -3,4 +3,6 @@ import Foundation
 var array = [4,2,1,3]
 
 print("before:",array)
-print("after:",BubbleSort(array))
+print("after:", bubbleSort(array))
+print("after:", bubbleSort(array, <))
+print("after:", bubbleSort(array, >))
diff --git a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift
index 9c091b661..09e01542b 100644
--- a/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
+++ b/Bubble Sort/MyPlayground.playground/Sources/BubbleSort.swift	
@@ -23,14 +23,18 @@ import Foundation
 
 /// Performs the bubble sort algorithm in the array
 ///
-/// - Parameter elements: the array to be sorted
+/// - Parameter elements: a array of elements that implement the Comparable protocol
 /// - Returns: an array with the same elements but in order
-public func BubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
+public func bubbleSort<T> (_ elements: [T]) -> [T] where T: Comparable {
+  return bubbleSort(elements, <)
+}
+
+public func bubbleSort<T> (_ elements: [T], _ comparison: (T,T) -> Bool) -> [T]  {
   var array = elements
   
   for i in 0..<array.count {
     for j in 1..<array.count-i {
-      if array[j] < array[j-1] {
+      if comparison(array[j], array[j-1]) {
         let tmp = array[j-1]
         array[j-1] = array[j]
         array[j] = tmp

From 7793fb4582dedafaa65f9de78bd9fcb96f9dd5d5 Mon Sep 17 00:00:00 2001
From: cr0ss <kayoslab@users.noreply.github.com>
Date: Tue, 30 Oct 2018 10:11:48 +0100
Subject: [PATCH 517/643] Removing unnecessary Error case for empty list

* Was intended to be a second example, but is not yet implemented
---
 GCD/GCD.playground/Contents.swift | 1 -
 1 file changed, 1 deletion(-)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index 9dfd7cca9..175d26639 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -106,7 +106,6 @@ func findEasySolution(_ m: Int, _ n: Int) -> Int? {
 
 enum LCMError: Error {
     case divisionByZero
-    case lcmEmptyList
 }
 
 /*

From 34a6067355c2596754500ad309eb79bf540f135c Mon Sep 17 00:00:00 2001
From: cr0ss <kayoslab@users.noreply.github.com>
Date: Tue, 30 Oct 2018 10:12:34 +0100
Subject: [PATCH 518/643] Also removes the lcmEmptyList from the actual code
 file

---
 GCD/GCD.swift | 1 -
 1 file changed, 1 deletion(-)

diff --git a/GCD/GCD.swift b/GCD/GCD.swift
index 85b7681f0..f4b390e63 100644
--- a/GCD/GCD.swift
+++ b/GCD/GCD.swift
@@ -105,7 +105,6 @@ func findEasySolution(_ m: Int, _ n: Int) -> Int? {
 
 enum LCMError: Error {
     case divisionByZero
-    case lcmEmptyList
 }
 
 /*

From 1e8e231d3cceb8d57a5bdf6838b4f8b544cdfe65 Mon Sep 17 00:00:00 2001
From: Randy the Dev <37282011+RandyTheDev@users.noreply.github.com>
Date: Thu, 1 Nov 2018 06:55:11 +1100
Subject: [PATCH 519/643] Updated Run-Length Encoding to Swift 4.2

---
 Run-Length Encoding/RLE.playground/Contents.swift | 7 +------
 1 file changed, 1 insertion(+), 6 deletions(-)

diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
index fc2d82505..8d6a0a403 100644
--- a/Run-Length Encoding/RLE.playground/Contents.swift	
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Foundation
 
 let originalString = "aaaaabbbcdeeeeeeef"
@@ -64,7 +59,7 @@ func testBufferWithoutSpans() -> Bool {
     // data ends up being longer.
     var bytes: [UInt8] = []
     for i in 0..<1024 {
-        bytes.append(UInt8(i%256))
+        bytes.append(UInt8(i % 256))
     }
     return encodeAndDecode(bytes)
 }

From d454cf1e1b3a9b60bc005a8b3051be1d328d1932 Mon Sep 17 00:00:00 2001
From: Randy the Dev <37282011+RandyTheDev@users.noreply.github.com>
Date: Thu, 1 Nov 2018 07:25:19 +1100
Subject: [PATCH 520/643] Confirmed Linear Regression to work with Swift 4.2

---
 .../LinearRegression.playground/Contents.swift             | 7 +------
 Linear Regression/README.markdown                          | 2 +-
 2 files changed, 2 insertions(+), 7 deletions(-)

diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 3e4135794..a093ef566 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -2,11 +2,6 @@
 
 import Foundation
 
-// last checked with Xcode 4.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let carAge: [Double] = [10, 8, 3, 3, 2, 1]
 let carPrice: [Double] = [500, 400, 7000, 8500, 11000, 10500]
 var intercept = 0.0
@@ -22,7 +17,7 @@ let numberOfCarAdvertsWeSaw = carPrice.count
 let numberOfIterations = 100
 let alpha = 0.0001
 
-for n in 1...numberOfIterations {
+for _ in 1...numberOfIterations {
     for i in 0..<numberOfCarAdvertsWeSaw {
         let difference = carPrice[i] - predictedCarPrice(carAge[i])
         intercept += alpha * difference
diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 29ac2e321..4f9d030db 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -62,7 +62,7 @@ let numberOfCarAdvertsWeSaw = carPrice.count
 let numberOfIterations = 100
 let alpha = 0.0001
 
-for n in 1...numberOfIterations {
+for _ in 1...numberOfIterations {
     for i in 0..<numberOfCarAdvertsWeSaw {
         let difference = carPrice[i] - predictedCarPrice(carAge[i])
         intercept += alpha * difference

From 8683fb16eee6102c207694f96beadbb63438ee75 Mon Sep 17 00:00:00 2001
From: Randy the Dev <37282011+RandyTheDev@users.noreply.github.com>
Date: Thu, 1 Nov 2018 07:35:17 +1100
Subject: [PATCH 521/643] Updated Minimum Edit Distance Playground for Swift
 4.2

---
 .../MinimumEditDistance.playground/Contents.swift    | 12 ++++--------
 Minimum Edit Distance/README.markdown                |  4 ++--
 2 files changed, 6 insertions(+), 10 deletions(-)

diff --git a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
index 967e73182..5db0aeb0d 100644
--- a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
@@ -1,15 +1,11 @@
 
 // Minimum Edit Distance
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 extension String {
     
     public func minimumEditDistance(other: String) -> Int {
-        let m = self.characters.count
-        let n = other.characters.count
+        let m = self.count
+        let n = other.count
         var matrix = [[Int]](repeating: [Int](repeating: 0, count: n + 1), count: m + 1)
         
         // initialize matrix
@@ -24,8 +20,8 @@ extension String {
         }
         
         // compute Levenshtein distance
-        for (i, selfChar) in self.characters.enumerated() {
-            for (j, otherChar) in other.characters.enumerated() {
+        for (i, selfChar) in self.enumerated() {
+            for (j, otherChar) in other.enumerated() {
                 if otherChar == selfChar {
                     // substitution of equal symbols with cost 0
                     matrix[i + 1][j + 1] = matrix[i][j]
diff --git a/Minimum Edit Distance/README.markdown b/Minimum Edit Distance/README.markdown
index b8880b2d4..c8e5e2f6d 100755
--- a/Minimum Edit Distance/README.markdown	
+++ b/Minimum Edit Distance/README.markdown	
@@ -37,8 +37,8 @@ Then in each cell the minimum of the cost of insertion, deletion, or substitutio
 
 ```swift
 // compute Levenshtein distance
-for (i, selfChar) in self.characters.enumerated() {
-    for (j, otherChar) in other.characters.enumerated() {
+for (i, selfChar) in self.enumerated() {
+    for (j, otherChar) in other.enumerated() {
         if otherChar == selfChar {
             // substitution of equal symbols with cost 0
             matrix[i + 1][j + 1] = matrix[i][j]

From eea4cfc6eaba53d86c3a383b1dce9c3c374b3ebd Mon Sep 17 00:00:00 2001
From: iillx <iill@cin.ufpe.br>
Date: Wed, 31 Oct 2018 22:56:29 -0300
Subject: [PATCH 522/643] Counting Sort working with Swift 4.2

---
 Counting Sort/CountingSort.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index 4d918e384..dc375512a 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 enum CountingSortError: Error {
   case arrayEmpty
 }

From 43e76adfc53c5cadde2511e9fc80fa3c59114be9 Mon Sep 17 00:00:00 2001
From: iillx <iill@cin.ufpe.br>
Date: Wed, 31 Oct 2018 23:10:55 -0300
Subject: [PATCH 523/643] Union Find working with Swift 4.2 and Xcode 10

---
 Union-Find/UnionFind.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 6ac3b4c4e..b1f7fb4e1 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 var dsu = UnionFindQuickUnion<Int>()
 
 for i in 1...10 {

From 6707ce26934addaceff3d54ee417632e210443df Mon Sep 17 00:00:00 2001
From: iillx <iill@cin.ufpe.br>
Date: Wed, 31 Oct 2018 23:16:04 -0300
Subject: [PATCH 524/643] Shunting Yard working fine with Swift 4.2 and Xcode
 10

---
 Shunting Yard/ShuntingYard.playground/Contents.swift      | 5 -----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 5 deletions(-)
 create mode 100644 Shunting Yard/ShuntingYard.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index ddd73de59..38431f5e2 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 internal enum OperatorAssociativity {
   case leftAssociative
   case rightAssociative
diff --git a/Shunting Yard/ShuntingYard.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Shunting Yard/ShuntingYard.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Shunting Yard/ShuntingYard.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From a1d65fcba404f8a59897c46480e54cadbe491b63 Mon Sep 17 00:00:00 2001
From: iillx <iill@cin.ufpe.br>
Date: Wed, 31 Oct 2018 23:25:54 -0300
Subject: [PATCH 525/643] Updated random number generation to Swift 4.2

---
 Set Cover (Unweighted)/SetCover.playground/Contents.swift  | 7 ++-----
 .../SetCover.playground/Sources/RandomArrayOfSets.swift    | 4 ++--
 2 files changed, 4 insertions(+), 7 deletions(-)

diff --git a/Set Cover (Unweighted)/SetCover.playground/Contents.swift b/Set Cover (Unweighted)/SetCover.playground/Contents.swift
index d61b9c84a..065f5fd4d 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Contents.swift	
@@ -1,10 +1,5 @@
 // SetCover
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 let universe1 = Set(1...7)
 let array1 = randomArrayOfSets(covering: universe1)
 let cover1 = universe1.cover(within: array1)
@@ -36,3 +31,5 @@ let emptySet = Set<Int>()
 let coverTest1 = emptySet.cover(within: array1)
 let coverTest2 = universe1.cover(within: Array<Set<Int>>())
 let coverTest3 = emptySet.cover(within: Array<Set<Int>>())
+
+
diff --git a/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift b/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift
index 9454c6383..ac4ff063e 100644
--- a/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift	
+++ b/Set Cover (Unweighted)/SetCover.playground/Sources/RandomArrayOfSets.swift	
@@ -14,10 +14,10 @@ public func randomArrayOfSets<T>(covering universe: Set<T>,
 
   while true {
     var generatedSet = Set<T>()
-    let targetSetSize = Int(arc4random_uniform(UInt32(maxSetSize)) + 1)
+    let targetSetSize = Int.random(in: 0...maxSetSize) + 1
 
     while true {
-      let randomUniverseIndex = Int(arc4random_uniform(UInt32(universe.count)))
+      let randomUniverseIndex = Int.random(in: 0...universe.count)
       for (setIndex, value) in universe.enumerated() {
         if setIndex == randomUniverseIndex {
           generatedSet.insert(value)

From f37fb19f054c95b654e07186d5f6fc5cf56bb12d Mon Sep 17 00:00:00 2001
From: Bruno Scheele <bruno@noodlewerk.com>
Date: Thu, 1 Nov 2018 20:55:17 +0100
Subject: [PATCH 526/643] Update README according to comments.

---
 Bloom Filter/README.markdown | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
index 4364db857..5f2ede069 100644
--- a/Bloom Filter/README.markdown	
+++ b/Bloom Filter/README.markdown	
@@ -102,7 +102,9 @@ If you're coming from another imperative language, you might notice the unusual
 
 ## Another approach
 
-Another approach to create different hashes of an element for use in the Bloom filter, is to use the same hash function for every iteration, but combine it with different random numbers. This can help, because finding good hashing functions is hard, but combining them is equally non-trivial.
+In the previous section, you learnt about how using multiple different hash functions can help reduce the chance of collisions in the bloom filter. However, good hash functions are difficult to design. A simple alternative to multiple hash functions is to use a set of random numbers.
+
+As an example, let's say a bloom filter wants to hash each element 15 times during insertion. Instead of using 15 different hash functions, you can rely on just one hash function. The hash value can then be combined with 15 different values to form the indices for flipping. This bloom filter would initialize a set of 15 random numbers ahead of time and use these values during each insertion.
 
 ```
 hash("Hello world!") >> hash(987654321) // would flip bit 8

From f9133844436bd6336595e0f6b66038f676dd3b3a Mon Sep 17 00:00:00 2001
From: gmotzespina <gmotzespina@icloud.com>
Date: Mon, 5 Nov 2018 19:00:34 -0600
Subject: [PATCH 527/643] Swift 4.2 Migration #748 - Depth First Search
 migrated to Swift 4.2

---
 .../APSP/APSP.xcodeproj/project.pbxproj                   | 8 +++++---
 .../Pages/Simple Example.xcplaygroundpage/Contents.swift  | 5 +----
 Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj  | 4 ++--
 3 files changed, 8 insertions(+), 9 deletions(-)

diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj
index 78df3fb76..908d32785 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
@@ -196,7 +196,7 @@
 					};
 					493D8DF01CDD5B960089795A = {
 						CreatedOnToolsVersion = 7.3;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1010;
 					};
 				};
 			};
@@ -420,7 +420,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
@@ -442,7 +443,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = On;
+				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
 			};
diff --git a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift
index 99f20a729..c83f52af8 100644
--- a/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
+++ b/Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift	
@@ -1,7 +1,4 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+// last checked with Xcode 10.1
 
 func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
     var nodesExplored = [source.label]
diff --git a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj
index 8f6058600..2b433bd96 100644
--- a/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Depth-First Search/Tests/Tests.xcodeproj/project.pbxproj	
@@ -234,7 +234,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -247,7 +247,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};

From 0f739b5230f7fe0df655fac82941e9111d346b90 Mon Sep 17 00:00:00 2001
From: gmotzespina <gmotzespina@icloud.com>
Date: Mon, 5 Nov 2018 19:08:43 -0600
Subject: [PATCH 528/643] Swift 4.2 support Depth-First Search

---
 .../DepthFirstSearch.playground/Edge.o          | Bin 0 -> 7016 bytes
 .../DepthFirstSearch.playground/Graph.o         | Bin 0 -> 21488 bytes
 .../DepthFirstSearch.playground/Node.o          | Bin 0 -> 19288 bytes
 .../xcshareddata/IDEWorkspaceChecks.plist       |   8 ++++++++
 .../xcshareddata/WorkspaceSettings.xcsettings   |   8 ++++++++
 5 files changed, 16 insertions(+)
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Edge.o
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Graph.o
 create mode 100644 Depth-First Search/DepthFirstSearch.playground/Node.o
 create mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

diff --git a/Depth-First Search/DepthFirstSearch.playground/Edge.o b/Depth-First Search/DepthFirstSearch.playground/Edge.o
new file mode 100644
index 0000000000000000000000000000000000000000..ab1e89b3aa83ed547413ba061a5edfd5dc918137
GIT binary patch
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diff --git a/Depth-First Search/DepthFirstSearch.playground/Graph.o b/Depth-First Search/DepthFirstSearch.playground/Graph.o
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diff --git a/Depth-First Search/DepthFirstSearch.playground/Node.o b/Depth-First Search/DepthFirstSearch.playground/Node.o
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zdn4O)*&7!BxPaD!T|qy-*OEc(d{Yg|(PllO$3yKqLdggUSBvDza-{dfl6_ixu)SNS
z($l!zv(1m6VB5Vb2R8kbzc@Er_%9&Gg_Q3CqB1t(-yfjjXYc&neH+`cr^8;(67Awb
znMf8FDH6=$13HTs)Q1h~Z|`ikH@EnX^>}<m#?XEzUN)=R5HvIFG*6~x1mFLxI||3h
z_Z{g*QOFZJQB)wo^FQj7i2E~N1x>VjEmHDw3V@i+reDlN{h4(a4zqbF({{JzW>ZgJ
zvNNFByULPJ7ZS^4)P;nK<kW?RtdHwG(LH)!<`lBY-{#r0)64ey{bu>bDa`Lj0hi%V
z__uD`7xreDbPv%y8=0TuH{sR`rD4L;U~~7_Vec-=go1mDklh&FvE33oybhZm8JT7U
zuhnAzw7~|vW~+Ba=snw(ZDNt3;zlQSG)s{O3MLWDE$H^`^oaqscd5*7YAVoXy#os_
z6?mV#vehMdg#jqmUwn<&jhhSX$?it*GW*2-U?CUG304zK_WDCwauf9?Ty<I}y*@48
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zk>u?)+oewHlFhWl$yyk!c^Y`)+jTyT^z97$yF|tcgK9Qt;@KdW)B_QEX`PSNo_IXi
z*Czs`ZHy&1?hT6tSSOQH_(VUBQQlho>lk`(?cQ$uGd#78biH+-zsujY!5h|l^hk2+
zzWaB2wdDOp6cuhr`yg~S2><$P*5mmJZ>Yl;dOQ{l!%sMW>0LCH-`}ex+lz-7TR7EO
zFZ2XmH9=Zy6W&IT2g72;y&V|Me81}syLoE-R+$=?)|Lu|lc9)=6f1LWNF_V#>hXL9
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WO2$%2gh>zf&_PY60#Acy_5T4cZe^PQ

literal 0
HcmV?d00001

diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
new file mode 100644
index 000000000..08de0be8d
--- /dev/null
+++ b/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
+	<false/>
+</dict>
+</plist>

From 07732e85027602ed909f9afbd9ebb2869ba18632 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Francisco=20Salda=C3=B1a?= <pako7797@icloud.com>
Date: Mon, 5 Nov 2018 19:18:53 -0600
Subject: [PATCH 529/643] fix deprecated methods and return type

---
 .../BoyerMooreHorspool.playground/Contents.swift       | 10 +++++-----
 .../xcshareddata/IDEWorkspaceChecks.plist              |  8 ++++++++
 .../BoyerMooreHorspool.playground/timeline.xctimeline  |  6 +++---
 Boyer-Moore-Horspool/BoyerMooreHorspool.swift          | 10 +++++-----
 4 files changed, 21 insertions(+), 13 deletions(-)
 create mode 100644 Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
index e88a1b93d..c51070caf 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
@@ -13,16 +13,16 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
+    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Int? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= self.count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
@@ -57,7 +57,7 @@ extension String {
             if c == lastChar {
 
                 // There is a possible match. Do a brute-force search backwards.
-                if let k = backwards() { return k }
+                if let k = backwards() { return k.encodedOffset }
 
                 if !usingHorspoolImprovement {
                     // If no match, we can only safely skip one character ahead.
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
index 89bc76f90..431d4a349 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=37&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.616217"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.556089"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=26&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.61657"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.5563149"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=25&amp;EndingLineNumber=3&amp;StartingColumnNumber=9&amp;StartingLineNumber=3&amp;Timestamp=503226447.616725"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.556504"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
index af8aea9d9..92d2ee4c1 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
@@ -6,16 +6,16 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
+    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Int? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
-        let patternLength = pattern.characters.count
-        guard patternLength > 0, patternLength <= characters.count else { return nil }
+        let patternLength = pattern.count
+        guard patternLength > 0, patternLength <= self.count else { return nil }
 
         // Make the skip table. This table determines how far we skip ahead
         // when a character from the pattern is found.
         var skipTable = [Character: Int]()
-        for (i, c) in pattern.characters.enumerated() {
+        for (i, c) in pattern.enumerated() {
             skipTable[c] = patternLength - i - 1
         }
 
@@ -50,7 +50,7 @@ extension String {
             if c == lastChar {
 
                 // There is a possible match. Do a brute-force search backwards.
-                if let k = backwards() { return k }
+                if let k = backwards() { return k.encodedOffset }
 
                 if !usingHorspoolImprovement {
                     // If no match, we can only safely skip one character ahead.

From 17990d8b52ae03bae0570f5e97e18d5f75485136 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Francisco=20Salda=C3=B1a?= <pako7797@icloud.com>
Date: Mon, 5 Nov 2018 19:37:55 -0600
Subject: [PATCH 530/643] change return type

---
 .../BoyerMooreHorspool.playground/Contents.swift            | 4 ++--
 .../BoyerMooreHorspool.playground/timeline.xctimeline       | 6 +++---
 Boyer-Moore-Horspool/BoyerMooreHorspool.swift               | 4 ++--
 3 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
index c51070caf..eba2a5806 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
@@ -13,7 +13,7 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Int? {
+    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.count
@@ -57,7 +57,7 @@ extension String {
             if c == lastChar {
 
                 // There is a possible match. Do a brute-force search backwards.
-                if let k = backwards() { return k.encodedOffset }
+                if let k = backwards() { return k }
 
                 if !usingHorspoolImprovement {
                     // If no match, we can only safely skip one character ahead.
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
index 431d4a349..5eb7f2337 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/timeline.xctimeline
@@ -3,17 +3,17 @@
    version = "3.0">
    <TimelineItems>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.556089"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563161016.665907"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.5563149"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563161016.666045"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
       <LoggerValueHistoryTimelineItem
-         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563159867.556504"
+         documentLocation = "file:///Users/francisco_saldana/Documents/Nearsoft/Open%20source/swift-algorithm-club/Boyer-Moore-Horspool/BoyerMooreHorspool.playground#CharacterRangeLen=0&amp;CharacterRangeLoc=75&amp;EndingColumnNumber=21&amp;EndingLineNumber=2&amp;StartingColumnNumber=21&amp;StartingLineNumber=2&amp;Timestamp=563161016.666169"
          selectedRepresentationIndex = "0"
          shouldTrackSuperviewWidth = "NO">
       </LoggerValueHistoryTimelineItem>
diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
index 92d2ee4c1..1dd37873a 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.swift
@@ -6,7 +6,7 @@
   http://www.drdobbs.com/database/faster-string-searches/184408171
 */
 extension String {
-    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Int? {
+    func index(of pattern: String, usingHorspoolImprovement: Bool = false) -> Index? {
         // Cache the length of the search pattern because we're going to
         // use it a few times and it's expensive to calculate.
         let patternLength = pattern.count
@@ -50,7 +50,7 @@ extension String {
             if c == lastChar {
 
                 // There is a possible match. Do a brute-force search backwards.
-                if let k = backwards() { return k.encodedOffset }
+                if let k = backwards() { return k }
 
                 if !usingHorspoolImprovement {
                     // If no match, we can only safely skip one character ahead.

From a7047d8bbb8cbdc023c8979dcfa22d15ba6ed21f Mon Sep 17 00:00:00 2001
From: Morgan Davison <morgan.davison@gmail.com>
Date: Tue, 6 Nov 2018 20:09:29 -0500
Subject: [PATCH 531/643] Compile for Swift 4.2

---
 B-Tree/BTree.playground/Contents.swift        |  5 +---
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++++
 B-Tree/Tests/Tests.xcodeproj/project.pbxproj  | 24 +++++++++++++++----
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  2 +-
 5 files changed, 38 insertions(+), 9 deletions(-)
 create mode 100644 B-Tree/BTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 B-Tree/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/B-Tree/BTree.playground/Contents.swift b/B-Tree/BTree.playground/Contents.swift
index a0643586f..f6325513a 100644
--- a/B-Tree/BTree.playground/Contents.swift
+++ b/B-Tree/BTree.playground/Contents.swift
@@ -2,10 +2,7 @@
 
 import Foundation
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
+// last checked with Xcode 10.0
 
 let bTree = BTree<Int, Int>(order: 1)!
 
diff --git a/B-Tree/BTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/B-Tree/BTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/B-Tree/BTree.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/B-Tree/Tests/Tests.xcodeproj/project.pbxproj b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
index 3e12b9ac3..66eb85190 100644
--- a/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
+++ b/B-Tree/Tests/Tests.xcodeproj/project.pbxproj
@@ -85,12 +85,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 1000;
 				ORGANIZATIONNAME = "Viktor Szilárd Simkó";
 				TargetAttributes = {
 					C66702771D0EEE25008CD769 = {
 						CreatedOnToolsVersion = 7.3.1;
-						LastSwiftMigration = 0800;
+						LastSwiftMigration = 1000;
 					};
 				};
 			};
@@ -144,14 +144,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -192,14 +200,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -234,7 +250,7 @@
 				PRODUCT_BUNDLE_IDENTIFIER = viktorsimko.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -247,7 +263,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = viktorsimko.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/B-Tree/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/B-Tree/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/B-Tree/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 9d6c542ae..d1555acfb 100644
--- a/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/B-Tree/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0800"
+   LastUpgradeVersion = "1000"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From b4ec5b84731a4cef0319e74d8109bbf8bc101a0e Mon Sep 17 00:00:00 2001
From: alextakahashi <alextakahashi@berkeley.edu>
Date: Wed, 7 Nov 2018 22:38:11 -0800
Subject: [PATCH 532/643] Added Markdown Documentation to Stack playground

This might be overkill for such a small file, but I wish I started using Swift Markdown early in my iOS career.  Option click is too convenient to ignore!
---
 Stack/Stack.playground/Contents.swift | 28 +++++++++++++++++++++++++--
 1 file changed, 26 insertions(+), 2 deletions(-)

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 1eb705f20..13774d7d1 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -1,4 +1,4 @@
-/*
+/**
   Stack
 
   A stack is like an array but with limited functionality. You can only push
@@ -9,27 +9,51 @@
   last is the first one to come off with the next pop.
 
   Push and pop are O(1) operations.
+ 
+  ## Usage
+  ```
+  var myStack = Stack(array: [])
+  myStack.push(10)
+  myStack.push(3)
+  myStack.push(57)
+  myStack.pop() // 57
+  myStack.pop() // 3
+ ```
 */
-
 public struct Stack<T> {
+    
+  /// Datastructure consisting of a generic item.
   fileprivate var array = [T]()
 
+  /// The number of items in the stack.
   public var count: Int {
     return array.count
   }
 
+  /// Verifies if the stack is empty.
   public var isEmpty: Bool {
     return array.isEmpty
   }
 
+  /**
+     Pushes an item to the top of the stack.
+     
+     - Parameter element: The item being pushed.
+  */
   public mutating func push(_ element: T) {
     array.append(element)
   }
 
+  /**
+     Removes and returns the item at the top of the sack.
+     
+     - Returns: The item at the top of the stack.
+  */
   public mutating func pop() -> T? {
     return array.popLast()
   }
 
+  /// Returns the item at the top of the stack.
   public var top: T? {
     return array.last
   }

From eb228cc1d18d860ad825c7d79063524121555bce Mon Sep 17 00:00:00 2001
From: Kelvin Reid <codesmithk@gmail.com>
Date: Sun, 11 Nov 2018 21:24:07 -0500
Subject: [PATCH 533/643] [Swift 4.2] Updated Hash Set

---
 Hash Set/HashSet.playground/Contents.swift                | 4 ----
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 16 insertions(+), 4 deletions(-)
 create mode 100644 Hash Set/HashSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Hash Set/HashSet.playground/Contents.swift b/Hash Set/HashSet.playground/Contents.swift
index 5edb76bb4..551c6dc86 100644
--- a/Hash Set/HashSet.playground/Contents.swift	
+++ b/Hash Set/HashSet.playground/Contents.swift	
@@ -1,8 +1,4 @@
 //: Playground - noun: a place where people can play
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 
 var set = HashSet<String>()
 
diff --git a/Hash Set/HashSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Hash Set/HashSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Hash Set/HashSet.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 67ecddaafb2e7637da0b24787ece79cadd82603c Mon Sep 17 00:00:00 2001
From: Kelvin Reid <codesmithk@gmail.com>
Date: Sun, 11 Nov 2018 21:37:44 -0500
Subject: [PATCH 534/643] [Swift 4.2] Updated Hash Table

---
 Hash Table/HashTable.playground/Contents.swift            | 3 ---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 2 files changed, 8 insertions(+), 3 deletions(-)
 create mode 100644 Hash Table/HashTable.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Hash Table/HashTable.playground/Contents.swift b/Hash Table/HashTable.playground/Contents.swift
index 273113440..121fb6032 100644
--- a/Hash Table/HashTable.playground/Contents.swift	
+++ b/Hash Table/HashTable.playground/Contents.swift	
@@ -1,8 +1,5 @@
 //: Playground - noun: a place where people can play
 
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
 // Playing with hash values
 
 "firstName".hashValue
diff --git a/Hash Table/HashTable.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Hash Table/HashTable.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Hash Table/HashTable.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 70d26fccdea4e655986b0fe36cec2d2dae2ab8e8 Mon Sep 17 00:00:00 2001
From: Kelvin Reid <codesmithk@gmail.com>
Date: Sun, 11 Nov 2018 21:44:55 -0500
Subject: [PATCH 535/643] [Swift 4.2] Updated Heap Sort

---
 Heap Sort/Tests/HeapSortTests.swift           |  6 ----
 .../Tests/Tests.xcodeproj/project.pbxproj     | 31 +++++++++++++------
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 +--
 4 files changed, 31 insertions(+), 18 deletions(-)
 create mode 100644 Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Heap Sort/Tests/HeapSortTests.swift b/Heap Sort/Tests/HeapSortTests.swift
index b36f605e3..dae1f8a68 100644
--- a/Heap Sort/Tests/HeapSortTests.swift	
+++ b/Heap Sort/Tests/HeapSortTests.swift	
@@ -1,12 +1,6 @@
 import XCTest
 
 class HeapSortTests: XCTestCase {
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
   
   func testSort() {
     var h1 = Heap(array: [5, 13, 2, 25, 7, 17, 20, 8, 4], sort: >)
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj
index ff1f4937f..62e6d4e3f 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -3,7 +3,7 @@
 	archiveVersion = 1;
 	classes = {
 	};
-	objectVersion = 46;
+	objectVersion = 51;
 	objects = {
 
 /* Begin PBXBuildFile section */
@@ -86,17 +86,17 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0900;
+				LastUpgradeCheck = 1010;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1010;
 					};
 				};
 			};
 			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
-			compatibilityVersion = "Xcode 3.2";
+			compatibilityVersion = "Xcode 10.0";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
@@ -149,12 +149,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -201,12 +203,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -230,7 +234,8 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
-				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_COMPILATION_MODE = wholemodule;
+				SWIFT_OPTIMIZATION_LEVEL = "-O";
 			};
 			name = Release;
 		};
@@ -239,10 +244,14 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -251,10 +260,14 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Heap Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 538a6f4fa..1608804f9 100644
--- a/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
+++ b/Heap Sort/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0900"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,7 +26,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -47,7 +46,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 0a2793fa925812cb71458c8447b988b897e126bb Mon Sep 17 00:00:00 2001
From: Kelvin Reid <codesmithk@gmail.com>
Date: Sun, 11 Nov 2018 21:49:37 -0500
Subject: [PATCH 536/643] [Swift 4.2] Updated Heap

---
 Heap/Tests/HeapTests.swift                    |  7 -----
 Heap/Tests/Tests.xcodeproj/project.pbxproj    | 31 +++++++++++++------
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 +++++
 .../xcshareddata/xcschemes/Tests.xcscheme     |  4 +--
 4 files changed, 31 insertions(+), 19 deletions(-)
 create mode 100644 Heap/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index 1ed15c726..ecf143778 100755
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -7,13 +7,6 @@ import XCTest
 
 class HeapTests: XCTestCase {
   
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-  
   fileprivate func verifyMaxHeap(_ h: Heap<Int>) -> Bool {
     for i in 0..<h.count {
       let left = h.leftChildIndex(ofIndex: i)
diff --git a/Heap/Tests/Tests.xcodeproj/project.pbxproj b/Heap/Tests/Tests.xcodeproj/project.pbxproj
index 51433ee64..0ab48ba3b 100755
--- a/Heap/Tests/Tests.xcodeproj/project.pbxproj
+++ b/Heap/Tests/Tests.xcodeproj/project.pbxproj
@@ -3,7 +3,7 @@
 	archiveVersion = 1;
 	classes = {
 	};
-	objectVersion = 46;
+	objectVersion = 51;
 	objects = {
 
 /* Begin PBXBuildFile section */
@@ -83,17 +83,17 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0720;
-				LastUpgradeCheck = 0920;
+				LastUpgradeCheck = 1010;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					7B2BBC7F1C779D720067B71D = {
 						CreatedOnToolsVersion = 7.2;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1010;
 					};
 				};
 			};
 			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Tests" */;
-			compatibilityVersion = "Xcode 3.2";
+			compatibilityVersion = "Xcode 10.0";
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
@@ -145,12 +145,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -197,12 +199,14 @@
 				CLANG_WARN_BOOL_CONVERSION = YES;
 				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
 				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
 				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
 				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
@@ -226,7 +230,8 @@
 				MACOSX_DEPLOYMENT_TARGET = 10.11;
 				MTL_ENABLE_DEBUG_INFO = NO;
 				SDKROOT = macosx;
-				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				SWIFT_COMPILATION_MODE = wholemodule;
+				SWIFT_OPTIMIZATION_LEVEL = "-O";
 			};
 			name = Release;
 		};
@@ -235,10 +240,14 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -247,10 +256,14 @@
 			buildSettings = {
 				COMBINE_HIDPI_IMAGES = YES;
 				INFOPLIST_FILE = Info.plist;
-				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
diff --git a/Heap/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Heap/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Heap/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
index 77d01bebc..1608804f9 100755
--- a/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
+++ b/Heap/Tests/Tests.xcodeproj/xcshareddata/xcschemes/Tests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0920"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
@@ -26,7 +26,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       shouldUseLaunchSchemeArgsEnv = "YES">
       <Testables>
          <TestableReference
@@ -47,7 +46,6 @@
       buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
-      language = ""
       launchStyle = "0"
       useCustomWorkingDirectory = "NO"
       ignoresPersistentStateOnLaunch = "NO"

From 9374c513f34170a1fd5db63398718507a8937c70 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 11 Nov 2018 23:00:22 -0500
Subject: [PATCH 537/643] Update Contents.swift

---
 HaversineDistance/HaversineDistance.playground/Contents.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index 7aa686645..3d8d60f54 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -1,8 +1,4 @@
 import UIKit
-// last checked with Xcode 9.04
-#if swift(>=4)
-print("Hello, Swift 4!")
-#endif
 
 func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
     

From ef4e890fd9f5b0ddf15cfa289fc2993ee46a9e04 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 11 Nov 2018 23:01:46 -0500
Subject: [PATCH 538/643] Updates Contents.swift

---
 .../BoyerMooreHorspool.playground/Contents.swift             | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
index 5817cc41f..1666549c1 100644
--- a/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
+++ b/Boyer-Moore-Horspool/BoyerMooreHorspool.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-    print("Hello, Swift 4!")
-#endif
-
 /*
   Boyer-Moore string search
 

From 9ba8b54dc580cc6cb3803a1a2cd2a9efcd5bf6ab Mon Sep 17 00:00:00 2001
From: gmotzespina <gmotzespina@icloud.com>
Date: Mon, 12 Nov 2018 19:53:38 -0600
Subject: [PATCH 539/643] Bubble Sort Readme Code Issue #838 solved

---
 Bubble Sort/README.markdown | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Bubble Sort/README.markdown b/Bubble Sort/README.markdown
index e55129d93..648b9f324 100644
--- a/Bubble Sort/README.markdown	
+++ b/Bubble Sort/README.markdown	
@@ -57,9 +57,9 @@ This is the same for the forth and fifth passes.
 ```swift
 for i in 0..<array.count {
   for j in 1..<array.count {
-    if array[j] < array[i] {
-      let tmp = array[i]
-      array[i] = array[j]
+    if array[j] < array[j-1] {
+      let tmp = array[j-1]
+      array[j-1] = array[j]
       array[j] = tmp
     }
   }
@@ -73,9 +73,9 @@ The bubble sort algorithm can be easily optimized by observing that the `n-th` p
 ```swift
 for i in 0..<array.count {
   for j in 1..<array.count - i {
-    if array[j] < array[i] {
-      let tmp = array[i]
-      array[i] = array[j]
+    if array[j] < array[j-1] {
+      let tmp = array[j-1]
+      array[j-1] = array[j]
       array[j] = tmp
     }
   }

From 71c228a2b63a091a7bd521dc6f2c3bf219a9b6c7 Mon Sep 17 00:00:00 2001
From: Daniel Chick <daniel.chick@hotmail.com>
Date: Tue, 27 Nov 2018 14:22:02 -0600
Subject: [PATCH 540/643] Removing version check

---
 Tree/Tree.playground/Contents.swift | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index 06f992fa8..1fad157a0 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.2)
-print("Hello, Swift 4.2!")
-#endif
-
 let tree = TreeNode<String>(value: "beverages")
 
 let hotNode = TreeNode<String>(value: "hot")

From f1363dd983ccacf1e48d9d393022f3ce68ba3c39 Mon Sep 17 00:00:00 2001
From: Francesco Scalise <f.scalise@eco-mind.eu>
Date: Tue, 4 Dec 2018 19:31:26 +0100
Subject: [PATCH 541/643] [Swift 4.2] Count occurences

---
 Count Occurrences/CountOccurrences.playground/Contents.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/Count Occurrences/CountOccurrences.playground/Contents.swift b/Count Occurrences/CountOccurrences.playground/Contents.swift
index 6138b74ac..a34e3485f 100644
--- a/Count Occurrences/CountOccurrences.playground/Contents.swift	
+++ b/Count Occurrences/CountOccurrences.playground/Contents.swift	
@@ -1,7 +1,3 @@
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-  print("Hello, Swift 4!")
-#endif
 
 func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
   func leftBoundary() -> Int {

From a2953343f16129995f90cfc6cf49236b3bcb9ae5 Mon Sep 17 00:00:00 2001
From: Morgan Kan <heraldk@gmail.com>
Date: Sun, 16 Dec 2018 21:46:06 +0000
Subject: [PATCH 542/643] Implement bit shift operations in BitSet

---
 Bit Set/BitSet.playground/Contents.swift      | 20 ++++++++
 .../BitSet.playground/Sources/BitSet.swift    | 46 +++++++++++++++++-
 Bit Set/BitSet.swift                          | 47 ++++++++++++++++++-
 3 files changed, 111 insertions(+), 2 deletions(-)

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index d11b36e8c..2c5edcd84 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -89,3 +89,23 @@ z.all1()        // false
 
 //var bigBits = BitSet(size: 10000)
 //print(bigBits)
+
+var smallBitSet = BitSet(size: 16)
+smallBitSet[5] = true
+smallBitSet[10] = true
+print( smallBitSet >> 3 )
+print( smallBitSet << 6 ) // one bit shifts off the end
+
+var bigBitSet = BitSet( size: 120 )
+bigBitSet[1] = true
+bigBitSet[3] = true
+bigBitSet[7] = true
+bigBitSet[32] = true
+bigBitSet[55] = true
+bigBitSet[64] = true
+bigBitSet[80] = true
+print( bigBitSet )
+print( bigBitSet << 32 )
+print( bigBitSet << 64 )
+print( bigBitSet >> 32 )
+print( bigBitSet >> 64 )
diff --git a/Bit Set/BitSet.playground/Sources/BitSet.swift b/Bit Set/BitSet.playground/Sources/BitSet.swift
index 59306f5a5..85f5da505 100644
--- a/Bit Set/BitSet.playground/Sources/BitSet.swift	
+++ b/Bit Set/BitSet.playground/Sources/BitSet.swift	
@@ -9,7 +9,7 @@ public struct BitSet {
     We store the bits in a list of unsigned 64-bit integers.
     The first entry, `words[0]`, is the least significant word.
   */
-  private let N = 64
+  fileprivate let N = 64
   public typealias Word = UInt64
   fileprivate(set) public var words: [Word]
 
@@ -221,6 +221,50 @@ prefix public func ~ (rhs: BitSet) -> BitSet {
   return out
 }
 
+// MARK: - Bit shift operations
+
+/*
+ Note: For bitshift operations, the assumption is that any bits that are
+ shifted off the end of the end of the declared size are not still set.
+ In other words, we are maintaining the original number of bits.
+ */
+
+public func << (lhs: BitSet, numBitsLeft: Int) -> BitSet {
+    var out = lhs
+    let offset = numBitsLeft / lhs.N
+    let shift = numBitsLeft % lhs.N
+    for i in 0..<lhs.words.count {
+        out.words[i] = 0
+        if( i - offset >= 0 ) {
+            out.words[i] = lhs.words[i - offset] << shift
+        }
+        if( i - offset - 1 >= 0 ) {
+            out.words[i] |= lhs.words[i - offset - 1] >> (lhs.N - shift)
+        }
+    }
+    
+    out.clearUnusedBits()
+    return out
+}
+
+public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
+    var out = lhs
+    let offset = numBitsRight / lhs.N
+    let shift = numBitsRight % lhs.N
+    for i in 0..<lhs.words.count {
+        out.words[i] = 0
+        if( i + offset < lhs.words.count ) {
+            out.words[i] = lhs.words[i + offset] >> shift
+        }
+        if( i + offset + 1 < lhs.words.count ) {
+            out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
+        }
+    }
+    
+    out.clearUnusedBits()
+    return out
+}
+
 // MARK: - Debugging
 
 extension UInt64 {
diff --git a/Bit Set/BitSet.swift b/Bit Set/BitSet.swift
index cfe8517b5..83829c6c5 100644
--- a/Bit Set/BitSet.swift	
+++ b/Bit Set/BitSet.swift	
@@ -9,7 +9,7 @@ public struct BitSet {
    We store the bits in a list of unsigned 64-bit integers.
    The first entry, `words[0]`, is the least significant word.
    */
-  private let N = 64
+  fileprivate let N = 64
   public typealias Word = UInt64
   fileprivate(set) public var words: [Word]
   
@@ -221,6 +221,51 @@ prefix public func ~ (rhs: BitSet) -> BitSet {
   return out
 }
 
+// MARK: - Bit shift operations
+
+/*
+ Note: For bitshift operations, the assumption is that any bits that are
+ shifted off the end of the end of the declared size are not still set.
+ In other words, we are maintaining the original number of bits.
+ */
+
+public func << (lhs: BitSet, numBitsLeft: Int) -> BitSet {
+    var out = lhs
+    let offset = numBitsLeft / lhs.N
+    let shift = numBitsLeft % lhs.N
+    for i in 0..<lhs.words.count {
+        out.words[i] = 0
+        if( i - offset >= 0 ) {
+            out.words[i] = lhs.words[i - offset] << shift
+        }
+        if( i - offset - 1 >= 0 ) {
+            out.words[i] |= lhs.words[i - offset - 1] >> (lhs.N - shift)
+        }
+    }
+    
+    out.clearUnusedBits()
+    return out
+}
+
+public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
+    var out = lhs
+    let offset = numBitsRight / lhs.N
+    let shift = numBitsRight % lhs.N
+    for i in 0..<lhs.words.count {
+        out.words[i] = 0
+        if( i + offset < lhs.words.count ) {
+            out.words[i] = lhs.words[i + offset] >> shift
+        }
+        if( i + offset + 1 < lhs.words.count ) {
+            out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
+        }
+    }
+    
+    out.clearUnusedBits()
+    return out
+}
+
+
 // MARK: - Debugging
 
 extension UInt64 {

From dd182db605004ecdea85cf9b95de13b4006d52e3 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 20 Dec 2018 19:36:18 -0500
Subject: [PATCH 543/643] Fixes a typo

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

diff --git a/A-Star/README.md b/A-Star/README.md
index f362bb61e..b373d25fc 100644
--- a/A-Star/README.md
+++ b/A-Star/README.md
@@ -16,7 +16,7 @@ On the first step we expand the root node on the left (blue). We set the cost `g
 
 ![Step 1](Images/step1.png)
 
-We put the first not in the closed list (light blue) so that we don't try expanding it again if there were to be loops in the graph. Next we take the node on the open list with the smallest value of `g + h` where `g` is the current cost (0) plus the edge cost (1). Since all nodes in the open list have the same value we choose the top one.
+We put the first node in the closed list (light blue) so that we don't try expanding it again if there were to be loops in the graph. Next we take the node on the open list with the smallest value of `g + h` where `g` is the current cost (0) plus the edge cost (1). Since all nodes in the open list have the same value we choose the top one.
 
 ![Step 2](Images/step2.png)
 

From 1f15eda576530fdf76bb8245eecb99a5b4233a48 Mon Sep 17 00:00:00 2001
From: Andrzej Michnia <amichnia@gmail.com>
Date: Sun, 16 Dec 2018 22:44:30 +0100
Subject: [PATCH 544/643] Fixed error in description

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

diff --git a/Comb Sort/README.markdown b/Comb Sort/README.markdown
index d30d429b3..20c939307 100644
--- a/Comb Sort/README.markdown	
+++ b/Comb Sort/README.markdown	
@@ -64,8 +64,8 @@ This will sort the values of the array into ascending order -- increasing in val
 ## Performance
 
 Comb Sort was created to improve upon the worst case time complexity of Bubble Sort. With Comb 
-Sort, the worst case scenario for performance is exponential -- O(n^2). At best though, Comb Sort 
-performs at O(n logn) time complexity. This creates a drastic improvement over Bubble Sort's performance. 
+Sort, the worst case scenario for performance is polynomial -- O(n^2). At best though, Comb Sort 
+performs at O(n logn) time complexity -- loglinear. This creates a drastic improvement over Bubble Sort's performance. 
 
 Similar to Bubble Sort, the space complexity for Comb Sort is constant -- O(1). 
 This is extremely space efficient as it sorts the array in place. 

From a9c311588b2ecee2420af4cfee91217db427f450 Mon Sep 17 00:00:00 2001
From: Mac Bellingrath <macbellingrath@users.noreply.github.com>
Date: Wed, 26 Dec 2018 15:27:08 -0500
Subject: [PATCH 545/643] Update README.md

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

diff --git a/Convex Hull/README.md b/Convex Hull/README.md
index d27027a45..ab263f00d 100644
--- a/Convex Hull/README.md	
+++ b/Convex Hull/README.md	
@@ -2,7 +2,7 @@
 
 Given a group of points on a plane. The Convex Hull algorithm calculates the shape (made up from the points itself) containing all these points. It can also be used on a collection of points of different dimensions. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points. In comparing different solutions to this problem we can describe each algorithm in terms of it's big-O time complexity.
 
-There are multiple Convex Hull algorithms but this solution is called Quickhull, is comes from the work of both W. Eddy in 1977 and also separately A. Bykat in 1978, this algorithm has an expected time complexity of O(n log n), but it's worst-case time-complexity can be O(n^2) . With average conditions the algorithm has ok efficiency, but it's time-complexity can start to head become more exponential in cases of high symmetry or where there are points lying on the circumference of a circle for example.
+There are multiple Convex Hull algorithms but this solution is called Quickhull, is comes from the work of both W. Eddy in 1977 and also separately A. Bykat in 1978, this algorithm has an expected time complexity of O(n log n), but it's worst-case time-complexity can be O(n^2) . With average conditions the algorithm has ok efficiency, but it's time-complexity can start to become more exponential in cases of high symmetry or where there are points lying on the circumference of a circle for example.
 
 ## Quickhull
 

From c1b704dfbe27b96a67a34949055bcc55a47ca7c3 Mon Sep 17 00:00:00 2001
From: Mac Bellingrath <macbellingrath@users.noreply.github.com>
Date: Thu, 27 Dec 2018 09:14:45 -0500
Subject: [PATCH 546/643] Update README.md

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

diff --git a/Convex Hull/README.md b/Convex Hull/README.md
index d27027a45..71a470f56 100644
--- a/Convex Hull/README.md	
+++ b/Convex Hull/README.md	
@@ -17,7 +17,7 @@ The quickhull algorithm works as follows:
 - Keep on doing so on until no more points are left, the recursion has come to an end and the points selected constitute the convex hull.
 
 
-Our functioni will have the following defininition:
+Our function will have the following defininition:
 
 `findHull(points: [CGPoint], p1: CGPoint, p2: CGPoint)`
 

From 611253f617661d54280dd2861dfe57b3e4568b4e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Simon=20C=2E=20Kr=C3=BCger?= <simon.krueger@intive.com>
Date: Fri, 11 Jan 2019 10:43:51 +0100
Subject: [PATCH 547/643] GCD improvements after review

- Default parameter values
- umbrella for different gcd implementations with generic gcd(_: _:) function
- better structure of readme file including all 3 algorithms
---
 GCD/GCD.playground/Contents.swift          | 154 ++-------------------
 GCD/{ => GCD.playground/Sources}/GCD.swift |  35 +++--
 GCD/README.markdown                        | 146 ++++++++++++++-----
 3 files changed, 151 insertions(+), 184 deletions(-)
 rename GCD/{ => GCD.playground/Sources}/GCD.swift (73%)

diff --git a/GCD/GCD.playground/Contents.swift b/GCD/GCD.playground/Contents.swift
index 175d26639..bb8d49055 100644
--- a/GCD/GCD.playground/Contents.swift
+++ b/GCD/GCD.playground/Contents.swift
@@ -1,147 +1,21 @@
-//: Playground - noun: a place where people can play
+gcd(52, 39)       // 13
+gcd(228, 36)      // 12
+gcd(51357, 3819)  // 57
+gcd(841, 299)     // 1
 
-/*
- Iterative approach based on the Euclidean algorithm.
- The Euclidean algorithm is based on the principle that the greatest
- common divisor of two numbers does not change if the larger number
- is replaced by its difference with the smaller number.
- - Parameter m: First natural number
- - Parameter n: Second natural number
- - Returns: The natural gcd if m and n
- */
-func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
-    var a: Int = 0
-    var b: Int = max(m, n)
-    var r: Int = min(m, n)
-    
-    while r != 0 {
-        a = b
-        b = r
-        r = a % b
-    }
-    return b
-}
-
-/*
- Recursive approach based on the Euclidean algorithm.
- 
- - Parameter m: First natural number
- - Parameter n: Second natural number
- - Returns: The natural gcd of m and n
- - Note: The recursive version makes only tail recursive calls.
- Most compilers for imperative languages do not optimize these.
- The swift compiler as well as the obj-c compiler is able to do
- optimizations for tail recursive calls, even though it still ends
- up to be the same in terms of complexity. That said, tail call
- elimination is not mutually exclusive to recursion.
- */
-func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
-    let r: Int = m % n
-    if r != 0 {
-        return gcdRecursiveEuklid(n, r)
-    } else {
-        return n
-    }
-}
-
-/*
- The binary GCD algorithm, also known as Stein's algorithm,
- is an algorithm that computes the greatest common divisor of two
- nonnegative integers. Stein's algorithm uses simpler arithmetic
- operations than the conventional Euclidean algorithm; it replaces
- division with arithmetic shifts, comparisons, and subtraction.
- 
- - Parameter m: First natural number
- - Parameter n: Second natural number
- - Returns: The natural gcd of m and n
- - Complexity: worst case O(n^2), where n is the number of bits
- in the larger of the two numbers. Although each step reduces
- at least one of the operands by at least a factor of 2,
- the subtract and shift operations take linear time for very
- large integers
- */
-func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
-    if let easySolution = findEasySolution(m, n) { return easySolution }
-    
-    if (m & 1) == 0 {
-        // m is even
-        if (n & 1) == 1 {
-            // and n is odd
-            return gcdBinaryRecursiveStein(m >> 1, n)
-        } else {
-            // both m and n are even
-            return gcdBinaryRecursiveStein(m >> 1, n >> 1) << 1
-        }
-    } else if (n & 1) == 0 {
-        // m is odd, n is even
-        return gcdBinaryRecursiveStein(m, n >> 1)
-    } else if (m > n) {
-        // reduce larger argument
-        return gcdBinaryRecursiveStein((m - n) >> 1, n)
-    } else {
-        // reduce larger argument
-        return gcdBinaryRecursiveStein((n - m) >> 1, m)
-    }
-}
-
-/*
- Finds an easy solution for the gcd.
- - Note: It might be relevant for different usecases to
- try finding an easy solution for the GCD calculation
- before even starting more difficult operations.
- */
-func findEasySolution(_ m: Int, _ n: Int) -> Int? {
-    if m == n {
-        return m
-    }
-    if m == 0 {
-        return n
-    }
-    if n == 0 {
-        return m
-    }
-    return nil
-}
-
-
-enum LCMError: Error {
-    case divisionByZero
-}
-
-/*
- Calculates the lcm for two given numbers using a specified gcd algorithm.
- 
- - Parameter m: First natural number.
- - Parameter n: Second natural number.
- - Parameter using: The used gcd algorithm to calculate the lcm.
- - Throws: Can throw a `divisionByZero` error if one of the given
- attributes turns out to be zero or less.
- - Returns: The least common multiplier of the two attributes as
- an unsigned integer
- */
-func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
-    guard (m & n) != 0 else { throw LCMError.divisionByZero }
-    return m / gcdAlgorithm(m, n) * n
-}
-
-gcdIterativeEuklid(52, 39)       // 13
-gcdIterativeEuklid(228, 36)      // 12
-gcdIterativeEuklid(51357, 3819)  // 57
-gcdIterativeEuklid(841, 299)     // 1
-
-gcdRecursiveEuklid(52, 39)       // 13
-gcdRecursiveEuklid(228, 36)      // 12
-gcdRecursiveEuklid(51357, 3819)  // 57
-gcdRecursiveEuklid(841, 299)     // 1
+gcd(52, 39, using: gcdRecursiveEuklid)       // 13
+gcd(228, 36, using:  gcdRecursiveEuklid)      // 12
+gcd(51357, 3819, using: gcdRecursiveEuklid)  // 57
+gcd(841, 299, using: gcdRecursiveEuklid)     // 1
 
-gcdBinaryRecursiveStein(52, 39)       // 13
-gcdBinaryRecursiveStein(228, 36)      // 12
-gcdBinaryRecursiveStein(51357, 3819)  // 57
-gcdBinaryRecursiveStein(841, 299)     // 1
+gcd(52, 39, using: gcdBinaryRecursiveStein)       // 13
+gcd(228, 36, using: gcdBinaryRecursiveStein)      // 12
+gcd(51357, 3819, using: gcdBinaryRecursiveStein)  // 57
+gcd(841, 299, using: gcdBinaryRecursiveStein)     // 1
 
 do {
-    try lcm(2, 3, using: gcdIterativeEuklid)   // 6
-    try lcm(10, 8, using: gcdIterativeEuklid)  // 40
+    try lcm(2, 3)   // 6
+    try lcm(10, 8, using: gcdRecursiveEuklid)  // 40
 } catch {
     dump(error)
 }
diff --git a/GCD/GCD.swift b/GCD/GCD.playground/Sources/GCD.swift
similarity index 73%
rename from GCD/GCD.swift
rename to GCD/GCD.playground/Sources/GCD.swift
index f4b390e63..4eb0c7621 100644
--- a/GCD/GCD.swift
+++ b/GCD/GCD.playground/Sources/GCD.swift
@@ -1,3 +1,17 @@
+/*
+ Finds the largest positive integer that divides both
+ m and n without a remainder.
+
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Parameter using: The used algorithm to calculate the gcd.
+                    If nothing provided, the Iterative Euclidean
+                    algorithm is used.
+ - Returns: The natural gcd of m and n.
+ */
+public func gcd(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int) = gcdIterativeEuklid) -> Int {
+    return gcdAlgorithm(m, n)
+}
 
 /*
  Iterative approach based on the Euclidean algorithm.
@@ -6,9 +20,9 @@
  is replaced by its difference with the smaller number.
  - Parameter m: First natural number
  - Parameter n: Second natural number
- - Returns: The natural gcd if m and n
+ - Returns: The natural gcd of m and n.
  */
-func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
+public func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
     var a: Int = 0
     var b: Int = max(m, n)
     var r: Int = min(m, n)
@@ -26,7 +40,7 @@ func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
  
  - Parameter m: First natural number
  - Parameter n: Second natural number
- - Returns: The natural gcd of m and n
+ - Returns: The natural gcd of m and n.
  - Note: The recursive version makes only tail recursive calls.
  Most compilers for imperative languages do not optimize these.
  The swift compiler as well as the obj-c compiler is able to do
@@ -34,7 +48,7 @@ func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
  up to be the same in terms of complexity. That said, tail call
  elimination is not mutually exclusive to recursion.
  */
-func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
+public func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
     let r: Int = m % n
     if r != 0 {
         return gcdRecursiveEuklid(n, r)
@@ -59,7 +73,7 @@ func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
  the subtract and shift operations take linear time for very
  large integers
  */
-func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
+public func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
     if let easySolution = findEasySolution(m, n) { return easySolution }
     
     if (m & 1) == 0 {
@@ -85,6 +99,9 @@ func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
 
 /*
  Finds an easy solution for the gcd.
+ - Parameter m: First natural number
+ - Parameter n: Second natural number
+ - Returns: A natural gcd of m and n if possible.
  - Note: It might be relevant for different usecases to
  try finding an easy solution for the GCD calculation
  before even starting more difficult operations.
@@ -103,7 +120,7 @@ func findEasySolution(_ m: Int, _ n: Int) -> Int? {
 }
 
 
-enum LCMError: Error {
+public enum LCMError: Error {
     case divisionByZero
 }
 
@@ -113,12 +130,14 @@ enum LCMError: Error {
  - Parameter m: First natural number.
  - Parameter n: Second natural number.
  - Parameter using: The used gcd algorithm to calculate the lcm.
+                    If nothing provided, the Iterative Euclidean
+                    algorithm is used.
  - Throws: Can throw a `divisionByZero` error if one of the given
  attributes turns out to be zero or less.
  - Returns: The least common multiplier of the two attributes as
  an unsigned integer
  */
-func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
-    guard (m & n) != 0 else { throw LCMError.divisionByZero }
+public func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int) = gcdIterativeEuklid) throws -> Int {
+    guard m & n != 0 else { throw LCMError.divisionByZero }
     return m / gcdAlgorithm(m, n) * n
 }
diff --git a/GCD/README.markdown b/GCD/README.markdown
index a23aea190..07a3f0f4d 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -1,14 +1,19 @@
 # Greatest Common Divisor
 
 The *greatest common divisor* (or Greatest Common Factor) of two numbers `a` and `b` is the largest positive integer that divides both `a` and `b` without a remainder. The GCD.swift file contains three different algorithms of how to calculate the greatest common divisor.
+For example, `gcd(39, 52) = 13` because 13 divides 39 (`39 / 13 = 3`) as well as 52 (`52 / 13 = 4`). But there is no larger number than 13 that divides them both.
+You've probably had to learn about this in school at some point. :-)
 
-For example, `gcdIterativeEuklid(39, 52) = 13` because 13 divides 39 (`39/13 = 3`) as well as 52 (`52/13 = 4`). But there is no larger number than 13 that divides them both.
+You probably won't need to use the GCD or LCM in any real-world problems, but it's cool to play around with this ancient algorithm. It was first described by Euklid in his [Elements](http://publicdomainreview.org/collections/the-first-six-books-of-the-elements-of-euclid-1847/) around 300 BC. Rumor has it that he discovered this algorithm while he was hacking on his Commodore 64.
 
-You've probably had to learn about this in school at some point. :-)
+## Different Algorithms
 
-The laborious way to find the GCD of two numbers is to first figure out the factors of both numbers, then take the greatest number they have in common. The problem is that factoring numbers is quite difficult, especially when they get larger. (On the plus side, that difficulty is also what keeps your online payments secure.)
+This example includes three different algorithms to find the same result. 
 
-There is a smarter way to calculate the GCD: Euclid's algorithm. The big idea here is that,
+### Iterative Euklidean
+
+The laborious way to find the GCD of two numbers is to first figure out the factors of both numbers, then take the greatest number they have in common. The problem is that factoring numbers is quite difficult, especially when they get larger. (On the plus side, that difficulty is also what keeps your online payments secure.)
+There is a smarter way to calculate the GCD: Euklid's algorithm. The big idea here is that,
 
 	gcd(a, b) = gcd(b, a % b)
 
@@ -16,6 +21,33 @@ where `a % b` calculates the remainder of `a` divided by `b`.
 
 Here is an implementation of this idea in Swift:
 
+```swift
+func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
+    var a: Int = 0
+    var b: Int = max(m, n)
+    var r: Int = min(m, n)
+
+    while r != 0 {
+        a = b
+        b = r
+        r = a % b
+    }
+    return b
+}
+```
+
+Put it in a playground and try it out with these examples:
+
+```swift
+gcd(52, 39, using: gcdIterativeEuklid)        // 13
+gcd(228, 36, using: gcdIterativeEuklid)       // 12
+gcd(51357, 3819, using: gcdIterativeEuklid)   // 57
+```
+
+### Recursive Euklidean
+
+Here is a slightly different implementation of Euklid's algorithm. Unlike the first version this doesn't use a `while` loop, but leverages recursion.
+
 ```swift
 func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
     let r: Int = m % n
@@ -27,19 +59,21 @@ func gcdRecursiveEuklid(_ m: Int, _ n: Int) -> Int {
 }
 ```
 
-Put it in a playground and try it out with these examples:
+Put it in a playground and compare it with the results of the iterative Eulidean gcd. They should return the same results:
 
 ```swift
-gcdBinaryRecursiveStein(52, 39)        // 13
-gcdRecursiveEuklid(228, 36)       // 12
-gcdIterativeEuklid(51357, 3819)   // 57
+gcd(52, 39, using: gcdRecursiveEuklid)        // 13
+gcd(228, 36, using: gcdRecursiveEuklid)       // 12
+gcd(51357, 3819, using: gcdRecursiveEuklid)   // 57
 ```
 
-Let's step through the third example using gcd as a representation of the gcdRecursiveEuklid here:
+The `max()` and `min()` at the top of the function make sure we always divide the larger number by the smaller one.
+
+Let's step through the third example using the *recursive Euklidean algorithm* here:
 
 	gcd(51357, 3819)
 
-According to Euclid's rule, this is equivalent to,
+According to Euklid's rule, this is equivalent to,
 
 	gcd(3819, 51357 % 3819) = gcd(3819, 1710)
 
@@ -57,7 +91,7 @@ And now can't divide any further. The remainder of `114 / 57` is zero because `1
 
 	gcd(3819, 51357) = gcd(57, 0) = 57
 
-So in each step of Euclid's algorithm the numbers become smaller and at some point it ends when one of them becomes zero.
+So in each step of Euklid's algorithm the numbers become smaller and at some point it ends when one of them becomes zero.
 
 By the way, it's also possible that two numbers have a GCD of 1. They are said to be *relatively prime*. This happens when there is no number that divides them both, for example:
 
@@ -65,55 +99,95 @@ By the way, it's also possible that two numbers have a GCD of 1. They are said t
 gcd(841, 299)     // 1
 ```
 
-Here is a slightly different implementation of Euclid's algorithm. Unlike the first version this doesn't use recursion but only a basic `while` loop.
+### Binary Recursive Stein
+
+The binary GCD algorithm, also known as Stein's algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein's algorithm is very similar to the recursive Eulidean algorithm, but uses arithmetical operations, which are simpler for computers to perform, than the conventional Euclidean algorithm does. It replaces division with arithmetic shifts, comparisons, and subtraction.
 
 ```swift
-func gcdIterativeEuklid(_ m: Int, _ n: Int) -> Int {
-    var a: Int = 0
-    var b: Int = max(m, n)
-    var r: Int = min(m, n)
+func gcdBinaryRecursiveStein(_ m: Int, _ n: Int) -> Int {
+    if let easySolution = findEasySolution(m, n) { return easySolution }
+
+    if (m & 1) == 0 {
+        // m is even
+        if (n & 1) == 1 {
+            // and n is odd
+            return gcdBinaryRecursiveStein(m >> 1, n)
+        } else {
+            // both m and n are even
+            return gcdBinaryRecursiveStein(m >> 1, n >> 1) << 1
+        }
+    } else if (n & 1) == 0 {
+        // m is odd, n is even
+        return gcdBinaryRecursiveStein(m, n >> 1)
+    } else if (m > n) {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((m - n) >> 1, n)
+    } else {
+        // reduce larger argument
+        return gcdBinaryRecursiveStein((n - m) >> 1, m)
+    }
+}
+```
 
-    while r != 0 {
-        a = b
-        b = r
-        r = a % b
+Depending on your application and your input expectations, it might be reasonable to also search for an "easy solution" using the other gcd implementations:
+
+```swift
+func findEasySolution(_ m: Int, _ n: Int) -> Int? {
+    if m == n {
+        return m
     }
-    return b
+    if m == 0 {
+        return n
+    }
+    if n == 0 {
+        return m
+    }
+    return nil
 }
+
 ```
 
-The `max()` and `min()` at the top of the function make sure we always divide the larger number by the smaller one.
+Put it in a playground and compare it with the results of the other gcd implementations:
+
+```swift
+gcd(52, 39, using: gcdBinaryRecursiveStein)        // 13
+gcd(228, 36, using: gcdBinaryRecursiveStein)       // 12
+gcd(51357, 3819, using: gcdBinaryRecursiveStein)   // 57
+```
 
-## Least Common Multiple
+### Least Common Multiple
 
-An idea related to the GCD is the *least common multiple* or LCM.
+Another algorithm related to the GCD is the *least common multiple* or LCM.
 
-The least common multiple of two numbers `a` and `b` is the smallest positive integer that is a multiple of both. In other words, the LCM is evenly divisible by `a` and `b`. The example implementation of the LCM takes two numbers and a specification which GCD algorithm is used.
+The least common multiple of two numbers `a` and `b` is the smallest positive integer that is a multiple of both. In other words, the LCM is evenly divisible by `a` and `b`. The example implementation of the LCM takes two numbers and an optional specification which GCD algorithm is used.
 
-For example: `lcm(2, 3, using: gcdIterativeEuklid) = 6` because 6 can be divided by 2 and also by 3.
+For example: `lcm(2, 3, using: gcdRecursiveEuklid) = 6` , which tells us that 6 is the smallest number that can be devided by 2 as well as 3.
 
-We can calculate the LCM using Euclid's algorithm too:
+We can calculate the LCM using Euklid's algorithm too:
 
-	              a * b
-	lcm(a, b) = ---------
-	            gcd(a, b)
+a * b
+lcm(a, b) = ---------
+gcd(a, b)
 
 In code:
 
 ```swift
-func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int)) throws -> Int {
-    guard (m & n) != 0 else { throw LCMError.divisionByZero }
-    return m / gcdAlgorithm(m, n) * n
+func lcm(_ m: Int, _ n: Int, using gcdAlgorithm: (Int, Int) -> (Int) = gcdIterativeEuklid) throws -> Int {
+guard (m & n) != 0 else { throw LCMError.divisionByZero }
+return m / gcdAlgorithm(m, n) * n
 }
 ```
 
 And to try it out in a playground:
 
 ```swift
-lcm(10, 8, using: gcdIterativeEuklid)    // 40
+lcm(10, 8)    // 40
 ```
 
-You probably won't need to use the GCD or LCM in any real-world problems, but it's cool to play around with this ancient algorithm. It was first described by Euclid in his [Elements](http://publicdomainreview.org/collections/the-first-six-books-of-the-elements-of-euclid-1847/) around 300 BC. Rumor has it that he discovered this algorithm while he was hacking on his Commodore 64.
+## Discussion
+
+While these algorithms all calculate the same result, comparing their plane complexity might not be enough to decide for one of them, though. The original iterative Euklidean algorithm is easier to understand. The recursive Euklidean and Stein's algorithm, while being generally faster, their runtime is heavily dependend on the environment they are running on.
+_If a fast calculation of the gcd is necessary, a runtime comparison for the specific platform and compiler optimization level should be done for the rekursive Euklidean and Stein's algorithm._
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
-*Extended by Simon Krüger*
\ No newline at end of file
+*Extended by Simon C. Krüger*

From 15f27793c56cd27788576deb0ef2c8ed901385d2 Mon Sep 17 00:00:00 2001
From: cr0ss <kayoslab@users.noreply.github.com>
Date: Fri, 11 Jan 2019 10:51:27 +0100
Subject: [PATCH 548/643] Linebreak in README

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

diff --git a/GCD/README.markdown b/GCD/README.markdown
index 07a3f0f4d..4c459eff0 100644
--- a/GCD/README.markdown
+++ b/GCD/README.markdown
@@ -190,4 +190,5 @@ While these algorithms all calculate the same result, comparing their plane comp
 _If a fast calculation of the gcd is necessary, a runtime comparison for the specific platform and compiler optimization level should be done for the rekursive Euklidean and Stein's algorithm._
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*
+
 *Extended by Simon C. Krüger*

From c5ff4084bd0f42ef7106a3139c217454aca28015 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Tue, 15 Jan 2019 15:27:38 -0800
Subject: [PATCH 549/643] Fix typo in Stack playground

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

diff --git a/Stack/Stack.playground/Contents.swift b/Stack/Stack.playground/Contents.swift
index 13774d7d1..e0632f8b4 100644
--- a/Stack/Stack.playground/Contents.swift
+++ b/Stack/Stack.playground/Contents.swift
@@ -45,7 +45,7 @@ public struct Stack<T> {
   }
 
   /**
-     Removes and returns the item at the top of the sack.
+     Removes and returns the item at the top of the stack.
      
      - Returns: The item at the top of the stack.
   */

From 0f2e9e1ebc22de221f508504c6e10bd34a76d919 Mon Sep 17 00:00:00 2001
From: Mike <mitghi@me.com>
Date: Mon, 28 Jan 2019 07:57:44 +0100
Subject: [PATCH 550/643] Update hyperlinks

Link to author profiles were missing
---
 AVL Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index e7515d99f..4e974ba71 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -88,4 +88,4 @@ The interesting bits are in the `balance()` method which is called after inserti
 
 AVL tree was the first self-balancing binary tree. These days, the [red-black tree](../Red-Black%20Tree/) seems to be more popular.
 
-*Written for Swift Algorithm Club by Mike Taghavi and Matthijs Hollemans*
+*Written for Swift Algorithm Club by [Mike Taghavi](https://github.com/mitghi) and [Matthijs Hollemans](https://github.com/hollance)*

From ff780b6ff7d25b2aa79cbeef5ac72de6ce76b77e Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Wed, 30 Jan 2019 17:16:49 -0800
Subject: [PATCH 551/643] Update README

Updated supported Xcode version to 10 and swift version to 4.2
---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index ff8bfe778..88ea35949 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,7 +8,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-Code is compatible with **Xcode 9** and **Swift 4**. We'll keep this updated with the latest version of Swift.
+Code is compatible with **Xcode 10** and **Swift 4.2**. We'll keep this updated with the latest version of Swift.
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 

From fa656f090ec4de0b7c9e8bd8eeb2e808c3d7f32c Mon Sep 17 00:00:00 2001
From: Andriy Makukha <andriy.makukha@gmail.com>
Date: Fri, 1 Feb 2019 10:20:10 +0800
Subject: [PATCH 552/643] reserveCapacity was missing in README (11% faster
 with it)

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

diff --git a/Merge Sort/README.markdown b/Merge Sort/README.markdown
index 7ad6fd95e..d86f062f4 100644
--- a/Merge Sort/README.markdown	
+++ b/Merge Sort/README.markdown	
@@ -79,6 +79,7 @@ func merge(leftPile: [Int], rightPile: [Int]) -> [Int] {
 
   // 2
   var orderedPile = [Int]()
+  orderedPile.reserveCapacity(leftPile.count + rightPile.count)
 
   // 3
   while leftIndex < leftPile.count && rightIndex < rightPile.count {
@@ -115,7 +116,7 @@ This method may look scary, but it is quite straightforward:
 
 1. You need two indexes to keep track of your progress for the two arrays while merging.
 
-2. This is the merged array. It is empty right now, but you will build it up in subsequent steps by appending elements from the other arrays.
+2. This is the merged array. It is empty right now, but you will build it up in subsequent steps by appending elements from the other arrays. Since you already know number of elements that will end up in this array, you reserve capacity to avoid reallocation overhead later.
 
 3. This while-loop will compare the elements from the left and right sides and append them into the `orderedPile` while making sure that the result stays in order.
 

From d4b9091af6f83f55e9681a5a11b6374bd2ac8cff Mon Sep 17 00:00:00 2001
From: Morgan Davison <morgan.davison@gmail.com>
Date: Sun, 3 Feb 2019 20:45:28 -0500
Subject: [PATCH 553/643] Check with Xcode 10.1

No changes needed
---
 3Sum and 4Sum/3Sum.playground/Contents.swift              | 4 ++++
 .../playground.xcworkspace/contents.xcworkspacedata       | 7 +++++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3Sum and 4Sum/4Sum.playground/Contents.swift              | 5 +++++
 .../playground.xcworkspace/contents.xcworkspacedata       | 7 +++++++
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 6 files changed, 39 insertions(+)
 create mode 100644 3Sum and 4Sum/3Sum.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 3Sum and 4Sum/3Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 3Sum and 4Sum/4Sum.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 3Sum and 4Sum/4Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/3Sum and 4Sum/3Sum.playground/Contents.swift b/3Sum and 4Sum/3Sum.playground/Contents.swift
index 2581da6e7..d172aed1f 100644
--- a/3Sum and 4Sum/3Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/3Sum.playground/Contents.swift	
@@ -1,3 +1,7 @@
+// last checked with Xcode 10.1
+#if swift(>=4.2)
+print("Hello, Swift 4.2!")
+#endif
 
 extension Collection where Element: Equatable {
   
diff --git a/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/contents.xcworkspacedata b/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/3Sum and 4Sum/3Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/3Sum and 4Sum/4Sum.playground/Contents.swift b/3Sum and 4Sum/4Sum.playground/Contents.swift
index 86b530224..37f75918c 100644
--- a/3Sum and 4Sum/4Sum.playground/Contents.swift	
+++ b/3Sum and 4Sum/4Sum.playground/Contents.swift	
@@ -1,3 +1,8 @@
+// last checked with Xcode 10.1
+#if swift(>=4.2)
+print("Hello, Swift 4.2!")
+#endif
+
 extension Collection where Element: Equatable {
   
   /// In a sorted collection, replaces the given index with a successor mapping to a unique element.
diff --git a/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/contents.xcworkspacedata b/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>
diff --git a/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/3Sum and 4Sum/4Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From 2f92aef01b0d7e6b57e4ae8a9de79467dd7598d9 Mon Sep 17 00:00:00 2001
From: Morgan Kan <heraldk@gmail.com>
Date: Wed, 6 Feb 2019 21:34:53 +0000
Subject: [PATCH 554/643] fix bracket formatting

---
 Bit Set/BitSet.playground/Contents.swift       | 14 +++++++-------
 Bit Set/BitSet.playground/Sources/BitSet.swift |  8 ++++----
 Bit Set/BitSet.swift                           |  8 ++++----
 3 files changed, 15 insertions(+), 15 deletions(-)

diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 2c5edcd84..70d5ca5e8 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -93,8 +93,8 @@ z.all1()        // false
 var smallBitSet = BitSet(size: 16)
 smallBitSet[5] = true
 smallBitSet[10] = true
-print( smallBitSet >> 3 )
-print( smallBitSet << 6 ) // one bit shifts off the end
+print(smallBitSet >> 3)
+print(smallBitSet << 6) // one bit shifts off the end
 
 var bigBitSet = BitSet( size: 120 )
 bigBitSet[1] = true
@@ -104,8 +104,8 @@ bigBitSet[32] = true
 bigBitSet[55] = true
 bigBitSet[64] = true
 bigBitSet[80] = true
-print( bigBitSet )
-print( bigBitSet << 32 )
-print( bigBitSet << 64 )
-print( bigBitSet >> 32 )
-print( bigBitSet >> 64 )
+print(bigBitSet)
+print(bigBitSet << 32)
+print(bigBitSet << 64)
+print(bigBitSet >> 32)
+print(bigBitSet >> 64)
diff --git a/Bit Set/BitSet.playground/Sources/BitSet.swift b/Bit Set/BitSet.playground/Sources/BitSet.swift
index 85f5da505..258bce457 100644
--- a/Bit Set/BitSet.playground/Sources/BitSet.swift	
+++ b/Bit Set/BitSet.playground/Sources/BitSet.swift	
@@ -235,10 +235,10 @@ public func << (lhs: BitSet, numBitsLeft: Int) -> BitSet {
     let shift = numBitsLeft % lhs.N
     for i in 0..<lhs.words.count {
         out.words[i] = 0
-        if( i - offset >= 0 ) {
+        if (i - offset >= 0) {
             out.words[i] = lhs.words[i - offset] << shift
         }
-        if( i - offset - 1 >= 0 ) {
+        if (i - offset - 1 >= 0) {
             out.words[i] |= lhs.words[i - offset - 1] >> (lhs.N - shift)
         }
     }
@@ -253,10 +253,10 @@ public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
     let shift = numBitsRight % lhs.N
     for i in 0..<lhs.words.count {
         out.words[i] = 0
-        if( i + offset < lhs.words.count ) {
+        if (i + offset < lhs.words.count) {
             out.words[i] = lhs.words[i + offset] >> shift
         }
-        if( i + offset + 1 < lhs.words.count ) {
+        if (i + offset + 1 < lhs.words.count) {
             out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
         }
     }
diff --git a/Bit Set/BitSet.swift b/Bit Set/BitSet.swift
index 83829c6c5..19413f424 100644
--- a/Bit Set/BitSet.swift	
+++ b/Bit Set/BitSet.swift	
@@ -235,10 +235,10 @@ public func << (lhs: BitSet, numBitsLeft: Int) -> BitSet {
     let shift = numBitsLeft % lhs.N
     for i in 0..<lhs.words.count {
         out.words[i] = 0
-        if( i - offset >= 0 ) {
+        if (i - offset >= 0) {
             out.words[i] = lhs.words[i - offset] << shift
         }
-        if( i - offset - 1 >= 0 ) {
+        if (i - offset - 1 >= 0) {
             out.words[i] |= lhs.words[i - offset - 1] >> (lhs.N - shift)
         }
     }
@@ -253,10 +253,10 @@ public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
     let shift = numBitsRight % lhs.N
     for i in 0..<lhs.words.count {
         out.words[i] = 0
-        if( i + offset < lhs.words.count ) {
+        if (i + offset < lhs.words.count) {
             out.words[i] = lhs.words[i + offset] >> shift
         }
-        if( i + offset + 1 < lhs.words.count ) {
+        if (i + offset + 1 < lhs.words.count) {
             out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
         }
     }

From 27efddaa9ceaa4f1675dc69433d253ce028596f1 Mon Sep 17 00:00:00 2001
From: Larissa Laich <llaich@ethz.ch>
Date: Thu, 7 Feb 2019 20:47:01 +0100
Subject: [PATCH 555/643] fixed error in linear regression formula

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

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 4f9d030db..db04bf8a2 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -75,7 +75,7 @@ for _ in 1...numberOfIterations {
 
 The program loops through each data point (each car age and car price). For each data point it adjusts the intercept and the slope to bring them closer to the correct values. The equations used in the code to adjust the intercept and the slope are based on moving in the direction of the maximal reduction of these variables. This is a *gradient descent*.
 
-We want to minimise the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proportional to `((slope.carAge + intercept) - carPrice)) ^ 2`.
+We want to minimise the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proportional to `((slope * carAge + intercept) - carPrice)) ^ 2`.
 
 In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope, and similarly for the intercept. We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
 

From 6d936e461435783e2a19afcf6b817e1b9c0ceb5f Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Tue, 12 Feb 2019 14:38:02 +0530
Subject: [PATCH 556/643] Update Karatsuba README

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

diff --git a/Karatsuba Multiplication/README.markdown b/Karatsuba Multiplication/README.markdown
index aef0d744a..02e54a1bf 100644
--- a/Karatsuba Multiplication/README.markdown	
+++ b/Karatsuba Multiplication/README.markdown	
@@ -115,10 +115,10 @@ What about the running time of this algorithm? Is all this extra work worth it?
  
 ## Resources
 
-[Wikipedia] (https://en.wikipedia.org/wiki/Karatsuba_algorithm)
+[Wikipedia](https://en.wikipedia.org/wiki/Karatsuba_algorithm)
 
-[WolframMathWorld] (http://mathworld.wolfram.com/KaratsubaMultiplication.html) 
+[WolframMathWorld](http://mathworld.wolfram.com/KaratsubaMultiplication.html) 
 
-[Master Theorem] (https://en.wikipedia.org/wiki/Master_theorem)
+[Master Theorem](https://en.wikipedia.org/wiki/Master_theorem)
 
 *Written for Swift Algorithm Club by Richard Ash*

From deae79c2010d1e7341b24314819c9736cdfc4387 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Tue, 12 Feb 2019 15:07:50 +0530
Subject: [PATCH 557/643] Update README

Replace "minimise" with "minimize"
---
 Linear Regression/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index db04bf8a2..d07bf1497 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -21,7 +21,7 @@ Let's start by looking at the data plotted out:
 
 We could imagine a straight line drawn through the points on this graph. It's not (in this case) going to go exactly through every point, but we could place the line so that it goes as close to all the points as possible.
 
-To say this in another way, we want to make the distance from the line to each point as small as possible. This is most often done by minimising the square of the distance from the line to each point.
+To say this in another way, we want to make the distance from the line to each point as small as possible. This is most often done by minimizing the square of the distance from the line to each point.
 
 We can describe the straight line in terms of two variables:
 
@@ -75,7 +75,7 @@ for _ in 1...numberOfIterations {
 
 The program loops through each data point (each car age and car price). For each data point it adjusts the intercept and the slope to bring them closer to the correct values. The equations used in the code to adjust the intercept and the slope are based on moving in the direction of the maximal reduction of these variables. This is a *gradient descent*.
 
-We want to minimise the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proportional to `((slope * carAge + intercept) - carPrice)) ^ 2`.
+We want to minimize the square of the distance between the line and the points. We define a function `J` which represents this distance - for simplicity we consider only one point here. This function `J` is proportional to `((slope * carAge + intercept) - carPrice)) ^ 2`.
 
 In order to move in the direction of maximal reduction, we take the partial derivative of this function with respect to the slope, and similarly for the intercept. We multiply these derivatives by our factor alpha and then use them to adjust the values of slope and intercept on each iteration.
 

From a88c984a388c456de27302af796180bf25b15529 Mon Sep 17 00:00:00 2001
From: Morgan Kan <heraldk@gmail.com>
Date: Fri, 15 Feb 2019 18:19:58 +0000
Subject: [PATCH 558/643] remove duplicate source file, update README

---
 Bit Set/BitSet.swift    | 293 ----------------------------------------
 Bit Set/README.markdown |  84 ++++++++++++
 2 files changed, 84 insertions(+), 293 deletions(-)
 delete mode 100644 Bit Set/BitSet.swift

diff --git a/Bit Set/BitSet.swift b/Bit Set/BitSet.swift
deleted file mode 100644
index 19413f424..000000000
--- a/Bit Set/BitSet.swift	
+++ /dev/null
@@ -1,293 +0,0 @@
-/*
- A fixed-size sequence of n bits. Bits have indices 0 to n-1.
- */
-public struct BitSet {
-  /* How many bits this object can hold. */
-  private(set) public var size: Int
-  
-  /*
-   We store the bits in a list of unsigned 64-bit integers.
-   The first entry, `words[0]`, is the least significant word.
-   */
-  fileprivate let N = 64
-  public typealias Word = UInt64
-  fileprivate(set) public var words: [Word]
-  
-  private let allOnes = ~Word()
-  
-  /* Creates a bit set that can hold `size` bits. All bits are initially 0. */
-  public init(size: Int) {
-    precondition(size > 0)
-    self.size = size
-    
-    // Round up the count to the next multiple of 64.
-    let n = (size + (N-1)) / N
-    words = [Word](repeating: 0, count: n)
-  }
-  
-  /* Converts a bit index into an array index and a mask inside the word. */
-  private func indexOf(_ i: Int) -> (Int, Word) {
-    precondition(i >= 0)
-    precondition(i < size)
-    let o = i / N
-    let m = Word(i - o*N)
-    return (o, 1 << m)
-  }
-  
-  /* Returns a mask that has 1s for all bits that are in the last word. */
-  private func lastWordMask() -> Word {
-    let diff = words.count*N - size
-    if diff > 0 {
-      // Set the highest bit that's still valid.
-      let mask = 1 << Word(63 - diff)
-      // Subtract 1 to turn it into a mask, and add the high bit back in.
-      return (Word)(mask | (mask - 1))
-    } else {
-      return allOnes
-    }
-  }
-  
-  /*
-   If the size is not a multiple of N, then we have to clear out the bits
-   that we're not using, or bitwise operations between two differently sized
-   BitSets will go wrong.
-   */
-  fileprivate mutating func clearUnusedBits() {
-    words[words.count - 1] &= lastWordMask()
-  }
-  
-  /* So you can write bitset[99] = ... */
-  public subscript(i: Int) -> Bool {
-    get { return isSet(i) }
-    set { if newValue { set(i) } else { clear(i) } }
-  }
-  
-  /* Sets the bit at the specified index to 1. */
-  public mutating func set(_ i: Int) {
-    let (j, m) = indexOf(i)
-    words[j] |= m
-  }
-  
-  /* Sets all the bits to 1. */
-  public mutating func setAll() {
-    for i in 0..<words.count {
-      words[i] = allOnes
-    }
-    clearUnusedBits()
-  }
-  
-  /* Sets the bit at the specified index to 0. */
-  public mutating func clear(_ i: Int) {
-    let (j, m) = indexOf(i)
-    words[j] &= ~m
-  }
-  
-  /* Sets all the bits to 0. */
-  public mutating func clearAll() {
-    for i in 0..<words.count {
-      words[i] = 0
-    }
-  }
-  
-  /* Changes 0 into 1 and 1 into 0. Returns the new value of the bit. */
-  public mutating func flip(_ i: Int) -> Bool {
-    let (j, m) = indexOf(i)
-    words[j] ^= m
-    return (words[j] & m) != 0
-  }
-  
-  /* Determines whether the bit at the specific index is 1 (true) or 0 (false). */
-  public func isSet(_ i: Int) -> Bool {
-    let (j, m) = indexOf(i)
-    return (words[j] & m) != 0
-  }
-  
-  /*
-   Returns the number of bits that are 1. Time complexity is O(s) where s is
-   the number of 1-bits.
-   */
-  public var cardinality: Int {
-    var count = 0
-    for var x in words {
-      while x != 0 {
-        let y = x & ~(x - 1)  // find lowest 1-bit
-        x = x ^ y             // and erase it
-        count += 1
-      }
-    }
-    return count
-  }
-  
-  /* Checks if all the bits are set. */
-  public func all1() -> Bool {
-    for i in 0..<words.count - 1 {
-      if words[i] != allOnes { return false }
-    }
-    return words[words.count - 1] == lastWordMask()
-  }
-  
-  /* Checks if any of the bits are set. */
-  public func any1() -> Bool {
-    for x in words {
-      if x != 0 { return true }
-    }
-    return false
-  }
-  
-  /* Checks if none of the bits are set. */
-  public func all0() -> Bool {
-    for x in words {
-      if x != 0 { return false }
-    }
-    return true
-  }
-}
-
-// MARK: - Equality
-
-extension BitSet: Equatable {
-}
-
-public func == (lhs: BitSet, rhs: BitSet) -> Bool {
-  return lhs.words == rhs.words
-}
-
-// MARK: - Hashing
-
-extension BitSet: Hashable {
-  /* Based on the hashing code from Java's BitSet. */
-  public var hashValue: Int {
-    var h = Word(1234)
-    for i in stride(from: words.count, to: 0, by: -1) {
-      h ^= words[i - 1] &* Word(i)
-    }
-    return Int((h >> 32) ^ h)
-  }
-}
-
-// MARK: - Bitwise operations
-
-extension BitSet {
-  public static var allZeros: BitSet {
-    return BitSet(size: 64)
-  }
-}
-
-private func copyLargest(_ lhs: BitSet, _ rhs: BitSet) -> BitSet {
-  return (lhs.words.count > rhs.words.count) ? lhs : rhs
-}
-
-/*
- Note: In all of these bitwise operations, lhs and rhs are allowed to have a
- different number of bits. The new BitSet always has the larger size.
- The extra bits that get added to the smaller BitSet are considered to be 0.
- That will strip off the higher bits from the larger BitSet when doing &.
- */
-
-public func & (lhs: BitSet, rhs: BitSet) -> BitSet {
-  let m = max(lhs.size, rhs.size)
-  var out = BitSet(size: m)
-  let n = min(lhs.words.count, rhs.words.count)
-  for i in 0..<n {
-    out.words[i] = lhs.words[i] & rhs.words[i]
-  }
-  return out
-}
-
-public func | (lhs: BitSet, rhs: BitSet) -> BitSet {
-  var out = copyLargest(lhs, rhs)
-  let n = min(lhs.words.count, rhs.words.count)
-  for i in 0..<n {
-    out.words[i] = lhs.words[i] | rhs.words[i]
-  }
-  return out
-}
-
-public func ^ (lhs: BitSet, rhs: BitSet) -> BitSet {
-  var out = copyLargest(lhs, rhs)
-  let n = min(lhs.words.count, rhs.words.count)
-  for i in 0..<n {
-    out.words[i] = lhs.words[i] ^ rhs.words[i]
-  }
-  return out
-}
-
-prefix public func ~ (rhs: BitSet) -> BitSet {
-  var out = BitSet(size: rhs.size)
-  for i in 0..<rhs.words.count {
-    out.words[i] = ~rhs.words[i]
-  }
-  out.clearUnusedBits()
-  return out
-}
-
-// MARK: - Bit shift operations
-
-/*
- Note: For bitshift operations, the assumption is that any bits that are
- shifted off the end of the end of the declared size are not still set.
- In other words, we are maintaining the original number of bits.
- */
-
-public func << (lhs: BitSet, numBitsLeft: Int) -> BitSet {
-    var out = lhs
-    let offset = numBitsLeft / lhs.N
-    let shift = numBitsLeft % lhs.N
-    for i in 0..<lhs.words.count {
-        out.words[i] = 0
-        if (i - offset >= 0) {
-            out.words[i] = lhs.words[i - offset] << shift
-        }
-        if (i - offset - 1 >= 0) {
-            out.words[i] |= lhs.words[i - offset - 1] >> (lhs.N - shift)
-        }
-    }
-    
-    out.clearUnusedBits()
-    return out
-}
-
-public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
-    var out = lhs
-    let offset = numBitsRight / lhs.N
-    let shift = numBitsRight % lhs.N
-    for i in 0..<lhs.words.count {
-        out.words[i] = 0
-        if (i + offset < lhs.words.count) {
-            out.words[i] = lhs.words[i + offset] >> shift
-        }
-        if (i + offset + 1 < lhs.words.count) {
-            out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
-        }
-    }
-    
-    out.clearUnusedBits()
-    return out
-}
-
-
-// MARK: - Debugging
-
-extension UInt64 {
-  /* Writes the bits in little-endian order, LSB first. */
-  public func bitsToString() -> String {
-    var s = ""
-    var n = self
-    for _ in 1...64 {
-      s += ((n & 1 == 1) ? "1" : "0")
-      n >>= 1
-    }
-    return s
-  }
-}
-
-extension BitSet: CustomStringConvertible {
-  public var description: String {
-    var s = ""
-    for x in words {
-      s += x.bitsToString() + " "
-    }
-    return s
-  }
-}
-
diff --git a/Bit Set/README.markdown b/Bit Set/README.markdown
index 6bb6e7c89..365950d06 100644
--- a/Bit Set/README.markdown	
+++ b/Bit Set/README.markdown	
@@ -329,6 +329,90 @@ This is the original value but with the lowest 1-bit removed.
 
 We keep repeating this process until the value consists of all zeros. The time complexity is **O(s)** where **s** is the number of 1-bits.
 
+## Bit Shift Operations
+
+Bit shifts are a common and very useful mechanism when dealing with bitsets. Here is the right-shift function:
+
+```
+public func >> (lhs: BitSet, numBitsRight: Int) -> BitSet {
+    var out = lhs
+    let offset = numBitsRight / lhs.N
+    let shift = numBitsRight % lhs.N
+    for i in 0..<lhs.words.count {
+        out.words[i] = 0
+        
+        if (i + offset < lhs.words.count) {
+            out.words[i] = lhs.words[i + offset] >> shift
+        }
+        
+        if (i + offset + 1 < lhs.words.count) {
+            out.words[i] |= lhs.words[i + offset + 1] << (lhs.N - shift)
+        }
+    }
+
+    out.clearUnusedBits()
+    return out
+}
+```
+
+Let's start with this line:
+
+```swift
+for i in 0..<lhs.words.count {
+```
+
+This indicates our strategy: we want to go through each word of the result and assign the correct bits.
+
+The two internal if-statements inside this loop are assigning some bits from one place in the source number and bitwise OR-ing them with some bits from a second place in the source number. The key insight here is that the bits for any one word of the result comes from at most two source words in the input. So the only remaining trick is to calculate which ones. For this, we need these two numbers:
+
+```swift
+let offset = numBitsRight / lhs.N
+let shift = numBitsRight % lhs.N
+```
+
+Offset gives us how many words away from the source word we start getting our bits (with the remainder coming from it's neighbour). Shift gives us how many bits we need to shift within that word. Note that both of these are calcuated using the word size `lhs.N`.
+
+All that's left if a little bit of protection against reading outside the bounds of the input. So these two if conditions protect against that:
+```swift
+if (i + offset < lhs.words.count) {
+```
+and
+```swift
+if (i + offset + 1 < lhs.words.count) {
+```
+
+Let's work through an example. Suppose our word length has been reduced to 8 bits, and we'd like to right-shift the following number by 10 bits:
+
+    01000010 11000000 00011100      >> 10
+
+I've grouped each part of the number by word to make it easier to see what happens. The for-loop goes from least significant word to most significant. So for index zero we're want to know what bits will make up our least significant word. Let's calculate our offset and shift values:
+
+    offset = 10 / 8 = 1     (remember this is integer division)
+    shift = 10 % 8 = 2
+
+So we consult the word at offset 1 to get some of our bits:
+
+    11000000 >> 2 = 00110000
+
+And we get the rest of them from the word one further away:
+
+    01000010 << (8 - 2) = 10000000
+    
+And we bitwise OR these together to get our least significant term
+
+    00110000
+    10000000
+    -------- OR
+    10110000
+
+We repeat this for the 2nd least significant term and obtain:
+
+    00010000
+
+The last term can't get any bits because they are past the end of our number so those are all zeros. Our result is:
+
+    00000000 00010000 10110000
+
 ## See also
 
 [Bit Twiddling Hacks](http://graphics.stanford.edu/~seander/bithacks.html)

From a10a15bab9934520d1762b5a71f357e6b112bc2a Mon Sep 17 00:00:00 2001
From: Morgan Kan <heraldk@gmail.com>
Date: Sat, 16 Feb 2019 09:49:47 +0000
Subject: [PATCH 559/643] remove reference to old source file

---
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index a37dac494..12be3d827 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -549,9 +549,6 @@
       <FileRef
          location = "group:BitSet.playground">
       </FileRef>
-      <FileRef
-         location = "group:BitSet.swift">
-      </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>

From aa2a318bfbf24223a26a609d8a23dba3accba935 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad@yelp.com>
Date: Sun, 24 Feb 2019 14:53:47 -0800
Subject: [PATCH 560/643] [Swift 4.2] Update All-Pairs Shortest Paths to Swift
 4.2

---
 .../APSP/APSP.playground/Contents.swift       |  5 ----
 .../APSP.playground/contents.xcplayground     |  2 +-
 .../APSP/APSP.xcodeproj/project.pbxproj       | 26 ++++++++++++++-----
 .../xcshareddata/xcschemes/APSP.xcscheme      |  2 +-
 .../xcshareddata/xcschemes/APSPTests.xcscheme |  2 +-
 .../xcshareddata/IDEWorkspaceChecks.plist     |  8 ++++++
 .../APSP/APSPTests/APSPTests.swift            |  8 ------
 .../xcshareddata/xcschemes/Graph.xcscheme     |  2 +-
 .../xcschemes/GraphTests.xcscheme             |  2 +-
 9 files changed, 33 insertions(+), 24 deletions(-)
 create mode 100644 All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift
index b1b499b39..24c27cac8 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/Contents.swift	
@@ -1,10 +1,5 @@
 //: Playground - noun: a place where people can play
 
-// last checked with Xcode 9.0b4
-#if swift(>=4.0)
-print("Hello, Swift 4!")
-#endif
-
 import Graph
 import APSP
 
diff --git a/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground b/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground
index 06828af92..d5a8d0e3f 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground	
+++ b/All-Pairs Shortest Paths/APSP/APSP.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx'>
+<playground version='5.0' target-platform='osx' last-migration='1010'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj
index 908d32785..dc8e509a1 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/project.pbxproj	
@@ -187,12 +187,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0820;
+				LastUpgradeCheck = 1010;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					493D8DDF1CDD2A1C0089795A = {
 						CreatedOnToolsVersion = 7.3;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 1010;
 					};
 					493D8DF01CDD5B960089795A = {
 						CreatedOnToolsVersion = 7.3;
@@ -302,14 +302,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -349,14 +357,22 @@
 				CLANG_CXX_LIBRARY = "libc++";
 				CLANG_ENABLE_MODULES = YES;
 				CLANG_ENABLE_OBJC_ARC = YES;
+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
 				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
 				CLANG_WARN_CONSTANT_CONVERSION = YES;
+				CLANG_WARN_DEPRECATED_OBJC_IMPLEMENTATIONS = YES;
 				CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;
 				CLANG_WARN_EMPTY_BODY = YES;
 				CLANG_WARN_ENUM_CONVERSION = YES;
 				CLANG_WARN_INFINITE_RECURSION = YES;
 				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
 				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
 				CLANG_WARN_SUSPICIOUS_MOVE = YES;
 				CLANG_WARN_UNREACHABLE_CODE = YES;
 				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
@@ -388,7 +404,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Debug;
 		};
@@ -400,7 +416,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSPTests";
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 4.0;
+				SWIFT_VERSION = 4.2;
 			};
 			name = Release;
 		};
@@ -420,7 +436,6 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
 				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
@@ -443,7 +458,6 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.APSP";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_SWIFT3_OBJC_INFERENCE = On;
 				SWIFT_VERSION = 4.2;
 				VERSIONING_SYSTEM = "apple-generic";
 				VERSION_INFO_PREFIX = "";
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme
index e313c4b88..944957d8f 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSP.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme
index 5797cbf9c..481baffd8 100644
--- a/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme	
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcodeproj/xcshareddata/xcschemes/APSPTests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "0820"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/All-Pairs Shortest Paths/APSP/APSP.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift
index c2f64e239..ce0dfcf32 100644
--- a/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSPTests/APSPTests.swift	
@@ -19,14 +19,6 @@ struct TestCase<T> where T: Hashable {
 }
 
 class APSPTests: XCTestCase {
-
-  func testSwift4() {
-    // last checked with Xcode 9.0b4
-    #if swift(>=4.0)
-      print("Hello, Swift 4!")
-    #endif
-  }
-
   /**
    See Figure 25.1 of “Introduction to Algorithms” by Cormen et al, 3rd ed., pg 690
    */
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
index 73524effc..84c688e66 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "1000"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
index 873f1d7b4..7aa65b0e4 100644
--- a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
+++ b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/GraphTests.xcscheme
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "1000"
+   LastUpgradeVersion = "1010"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From d89bf25bba0367bab880a3f18f2c78ec39fcd179 Mon Sep 17 00:00:00 2001
From: bbvch13531 <bbvch13531@gmail.com>
Date: Mon, 25 Feb 2019 22:08:56 +0900
Subject: [PATCH 561/643] Fix wrong description

Signed-off-by: bbvch13531 <bbvch13531@gmail.com>
---
 Linked List/LinkedList.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 7c2cbb3b1..de8a42c93 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -67,7 +67,7 @@ public final class LinkedList<T> {
     /// - Returns: LinkedListNode
     public func node(at index: Int) -> Node {
         assert(head != nil, "List is empty")
-        assert(index >= 0, "index must be greater than 0")
+        assert(index >= 0, "index must be greater or equal to 0")
         
         if index == 0 {
             return head!

From 8a6d99aa19f0888b51969bc10c0463aa98c1a94e Mon Sep 17 00:00:00 2001
From: bbvch13531 <bbvch13531@gmail.com>
Date: Mon, 25 Feb 2019 22:09:44 +0900
Subject: [PATCH 562/643] Fix typo

Signed-off-by: bbvch13531 <bbvch13531@gmail.com>
---
 Insertion Sort/InsertionSort.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 9faf9dc42..2ad607ac8 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -22,7 +22,7 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
 /// Performs the Insertion sort algorithm to a given array
 ///
-/// - Parameter array: the array to be sorted, conatining elements that conform to the Comparable protocol
+/// - Parameter array: the array to be sorted, containing elements that conform to the Comparable protocol
 /// - Returns: a sorted array containing the same elements
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
     guard array.count > 1 else { return array }

From de935b700ab32492791dbd9771a3fc841ad4044c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 5 Mar 2019 22:37:29 -0500
Subject: [PATCH 563/643] Updates README.markdown

* now using new `random` API from the Swift collection protocols, instead of creating a new function that uses `arc4random`
* updates code to Swift 4.2
* fixes some inconsistencies between terms begin used - such as `MAX_GENERATIONS` and `GENERATIONS`
---
 Genetic/README.markdown | 60 ++++++++++++++++-------------------------
 1 file changed, 23 insertions(+), 37 deletions(-)

diff --git a/Genetic/README.markdown b/Genetic/README.markdown
index 18afb9639..5dc4747f2 100644
--- a/Genetic/README.markdown
+++ b/Genetic/README.markdown
@@ -5,7 +5,7 @@
 A genetic algorithm (GA) is process inspired by natural selection to find high quality solutions. Most commonly used for optimization. GAs rely on the bio-inspired processes of natural selection, more specifically the process of selection (fitness), crossover and mutation. To understand more, let's walk through these processes in terms of biology:
 
 ### Selection
->**Selection**, in biology, the preferential survival and reproduction or preferential elimination of individuals with certain genotypes (genetic compositions), by means of natural or artificial controlling factors. [Britannica](britannica)
+>**Selection**, in biology, the preferential survival and reproduction or preferential elimination of individuals with certain genotypes (genetic compositions), by means of natural or artificial controlling factors.
 
 In other words, survival of the fittest. Organisms that survive in their environment tend to reproduce more. With GAs we generate a fitness model that will rank individuals and give them a better chance for reproduction.
 
@@ -60,35 +60,23 @@ extension String {
 let OPTIMAL:[UInt8] = "Hello, World".unicodeArray
 let DNA_SIZE = OPTIMAL.count
 let POP_SIZE = 50
-let MAX_GENERATIONS = 5000
+let GENERATIONS = 5000
 let MUTATION_CHANCE = 100
  ```
 
- The last piece we need for set up is a function to give us a random unicode value from our lexicon:
-
- ```swift
- func randomChar(from lexicon: [UInt8]) -> UInt8 {
-     let len = UInt32(lexicon.count-1)
-     let rand = Int(arc4random_uniform(len))
-     return lexicon[rand]
- }
- ```
-
- **Note**: `arc4random_uniform` is strictly used in this example. It would be fun to play around with some of the [randomization in GameKit](https://developer.apple.com/library/content/documentation/General/Conceptual/GameplayKit_Guide/RandomSources.html)
-
  ### Population Zero
 
 Before selecting, crossover and mutation, we need a population to start with. Now that we have the universe defined we can write that function:
 
  ```swift
  func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
-
+    guard lexicon.count > 1 else { return [] }
     var pop = [[UInt8]]()
 
     (0..<populationSize).forEach { _ in
         var dna = [UInt8]()
         (0..<dnaSize).forEach { _ in
-            let char = randomChar(from: lexicon)
+            let char = lexicon.randomElement()! // guaranteed to be non-nil by initial guard statement
             dna.append(char)
         }
         pop.append(dna)
@@ -102,10 +90,11 @@ Before selecting, crossover and mutation, we need a population to start with. No
 There are two parts to the selection process, the first is calculating the fitness, which will assign a rating to a individual. We do this by simply calculating how close the individual is to the optimal string using unicode values:
 
 ```swift
-func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
+func calculateFitness(dna: [UInt8], optimal: [UInt8]) -> Int {
+    guard dna.count == optimal.count else { return -1 }
     var fitness = 0
-    (0...dna.count-1).forEach { c in
-        fitness += abs(Int(dna[c]) - Int(optimal[c]))
+    for index in dna.indices {
+        fitness += abs(Int(dna[index]) - Int(optimal[index]))
     }
     return fitness
 }
@@ -121,13 +110,11 @@ Let's take a second and ask why on this one. Why would you not always want to se
 
 With all that, here is our weight choice function:
 
-```swift
-func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weight:Double) {
-
-    let total = items.reduce(0.0) { return $0 + $1.weight}
-
-    var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
-
+func weightedChoice(items: [(dna: [UInt8], weight: Double)]) -> (dna: [UInt8], weight: Double) {
+    
+    let total = items.reduce(0) { $0 + $1.weight }
+    var n = Double.random(in: 0..<(total * 1000000)) / 1000000.0
+    
     for item in items {
         if n < item.weight {
             return item
@@ -136,25 +123,24 @@ func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weigh
     }
     return items[1]
 }
-```
 
-The above function takes a list of individuals with their calculated fitness. Then selects one at random offset by their fitness value. The horrible 1,000,000 multiplication and division is to insure precision by calculating decimals. `arc4random` only uses integers so this is required to convert to a precise Double, it's not perfect, but enough for our example.
+
+The above function takes a list of individuals with their calculated fitness. Then selects one at random offset by their fitness value. The horrible 1,000,000 multiplication and division is to insure precision by calculating decimals. `Double.random` only uses integers so this is required to convert to a precise Double, it's not perfect, but enough for our example.
 
 ## Mutation
 
 The all powerful mutation, the thing that introduces otherwise non existent fitness variance. It can either hurt of improve a individuals fitness but over time it will cause evolution towards more fit populations. Imagine if our initial random population was missing the charachter `H`, in that case we need to rely on mutation to introduce that character into the population in order to achieve the optimal solution.
 
 ```swift
-func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
+func mutate(lexicon: [UInt8], dna: [UInt8], mutationChance: Int) -> [UInt8] {
     var outputDna = dna
-
     (0..<dna.count).forEach { i in
-        let rand = Int(arc4random_uniform(UInt32(mutationChance)))
+        let rand = Int.random(in: 0..<mutationChance)
         if rand == 1 {
-            outputDna[i] = randomChar(from: lexicon)
+            outputDna[i] = lexicon.randomElement()!
         }
     }
-
+    
     return outputDna
 }
 ```
@@ -168,12 +154,12 @@ This allows for a population to explore all the possibilities of it's building b
 Crossover, the sexy part of a GA, is how offspring are created from 2 selected individuals in the current population. This is done by splitting the parents into 2 parts, then combining 1 part from each parent to create the offspring. To promote diversity, we randomly select a index to split the parents.
 
 ```swift
-func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> [UInt8] {
-    let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
-
+func crossover(dna1: [UInt8], dna2: [UInt8], dnaSize: Int) -> [UInt8] {
+    let pos = Int.random(in: 0..<dnaSize)
+    
     let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
     let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
-
+    
     return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
 }
 ```

From a1e2e9d03ba34c7e9f74cebea34258dce5bdac00 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 5 Mar 2019 22:38:53 -0500
Subject: [PATCH 564/643] Updates code to Swift 4.2

---
 Genetic/gen.playground/Contents.swift | 192 +++++++++++---------------
 1 file changed, 84 insertions(+), 108 deletions(-)

diff --git a/Genetic/gen.playground/Contents.swift b/Genetic/gen.playground/Contents.swift
index 79a398ceb..d76342f56 100644
--- a/Genetic/gen.playground/Contents.swift
+++ b/Genetic/gen.playground/Contents.swift
@@ -1,14 +1,12 @@
-//: Playground - noun: a place where people can play
 
-import Foundation
 
 extension String {
-    var unicodeArray: [UInt8] {
-        return [UInt8](self.utf8)
-    }
+  
+  var unicodeArray: [UInt8] {
+    return [UInt8](self.utf8)
+  }
 }
 
-
 let lex: [UInt8] = " !\"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~".unicodeArray
 
 // This is the end goal and what we will be using to rate fitness. In the real world this will not exist
@@ -17,132 +15,110 @@ let OPTIMAL:[UInt8] = "Hello, World".unicodeArray
 // The length of the string in our population. Organisms need to be similar
 let DNA_SIZE = OPTIMAL.count
 
-// size of each generation
+// Size of each generation
 let POP_SIZE = 50
 
-// max number of generations, script will stop when it reach 5000 if the optimal value is not found
+// Max number of generations, script will stop when it reaches 5000 if the optimal value is not found
 let GENERATIONS = 5000
 
 // The chance in which a random nucleotide can mutate (1/n)
 let MUTATION_CHANCE = 100
 
-func randomChar(from lexicon: [UInt8]) -> UInt8 {
-    let len = UInt32(lexicon.count-1)
-    let rand = Int(arc4random_uniform(len))
-    return lexicon[rand]
-}
-
 func randomPopulation(from lexicon: [UInt8], populationSize: Int, dnaSize: Int) -> [[UInt8]] {
-    
-    var pop = [[UInt8]]()
-    
-    (0..<populationSize).forEach { _ in
-        var dna = [UInt8]()
-        (0..<dnaSize).forEach { _ in
-            let char = randomChar(from: lexicon)
-            dna.append(char)
-        }
-        pop.append(dna)
+  var pop = [[UInt8]]()
+  
+  (0..<populationSize).forEach { _ in
+    var dna = [UInt8]()
+    (0..<dnaSize).forEach { _ in
+      let char = lexicon.randomElement()!
+      dna.append(char)
     }
-    return pop
+    pop.append(dna)
+  }
+  return pop
 }
 
-func calculateFitness(dna:[UInt8], optimal:[UInt8]) -> Int {
-    var fitness = 0
-    (0...dna.count-1).forEach { c in
-        fitness += abs(Int(dna[c]) - Int(optimal[c]))
-    }
-    return fitness
+func calculateFitness(dna: [UInt8], optimal: [UInt8]) -> Int {
+  var fitness = 0
+  for index in dna.indices {
+    fitness += abs(Int(dna[index]) - Int(optimal[index]))
+  }
+  return fitness
 }
 
-func weightedChoice(items:[(dna:[UInt8], weight:Double)]) -> (dna:[UInt8], weight:Double) {
-    
-    let total = items.reduce(0.0) { return $0 + $1.weight}
-    
-    var n = Double(arc4random_uniform(UInt32(total * 1000000.0))) / 1000000.0
-    
-    for item in items {
-        if n < item.weight {
-            return item
-        }
-        n = n - item.weight
+func weightedChoice(items: [(dna: [UInt8], weight: Double)]) -> (dna: [UInt8], weight: Double) {
+  
+  let total = items.reduce(0) { $0 + $1.weight }
+  var n = Double.random(in: 0..<(total * 1000000)) / 1000000.0
+  
+  for item in items {
+    if n < item.weight {
+      return item
     }
-    return items[1]
+    n = n - item.weight
+  }
+  return items[1]
 }
 
-func mutate(lexicon: [UInt8], dna:[UInt8], mutationChance:Int) -> [UInt8] {
-    var outputDna = dna
-    
-    (0..<dna.count).forEach { i in
-        let rand = Int(arc4random_uniform(UInt32(mutationChance)))
-        if rand == 1 {
-            outputDna[i] = randomChar(from: lexicon)
-        }
+func mutate(lexicon: [UInt8], dna: [UInt8], mutationChance: Int) -> [UInt8] {
+  var outputDna = dna
+  (0..<dna.count).forEach { i in
+    let rand = Int.random(in: 0..<mutationChance)
+    if rand == 1 {
+      outputDna[i] = lexicon.randomElement()!
     }
-    
-    return outputDna
+  }
+  
+  return outputDna
 }
 
-
-func crossover(dna1:[UInt8], dna2:[UInt8], dnaSize:Int) -> [UInt8] {
-    let pos = Int(arc4random_uniform(UInt32(dnaSize-1)))
-    
-    let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
-    let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
-    
-    return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
+func crossover(dna1: [UInt8], dna2: [UInt8], dnaSize: Int) -> [UInt8] {
+  let pos = Int.random(in: 0..<dnaSize)
+  
+  let dna1Index1 = dna1.index(dna1.startIndex, offsetBy: pos)
+  let dna2Index1 = dna2.index(dna2.startIndex, offsetBy: pos)
+  
+  return [UInt8](dna1.prefix(upTo: dna1Index1) + dna2.suffix(from: dna2Index1))
 }
 
+var population: [[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
+var fittest = population[0]
+import Foundation
+
 func main() {
+  for generation in 0...GENERATIONS {
+    var weightedPopulation = [(dna: [UInt8], weight: Double)]()
+    
+    for individual in population {
+      let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
+      let pair = (individual, fitnessValue == 0 ? 1.0 : 1.0/Double(fitnessValue))
+      weightedPopulation.append(pair)
+    }
+    
+    population = []
+    
+    (0...POP_SIZE).forEach { _ in
+      let ind1 = weightedChoice(items: weightedPopulation)
+      let ind2 = weightedChoice(items: weightedPopulation)
+      
+      let offspring = crossover(dna1: ind1.dna, dna2: ind2.dna, dnaSize: DNA_SIZE)
+      population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
+    }
     
-    // generate the starting random population
-    var population:[[UInt8]] = randomPopulation(from: lex, populationSize: POP_SIZE, dnaSize: DNA_SIZE)
-    // print("population: \(population), dnaSize: \(DNA_SIZE) ")
-    var fittest = [UInt8]()
+    fittest = population[0]
+    var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
     
-    for generation in 0...GENERATIONS {
-        
-        var weightedPopulation = [(dna:[UInt8], weight:Double)]()
-        
-        // calulcated the fitness of each individual in the population
-        // and add it to the weight population (weighted = 1.0/fitness)
-        for individual in population {
-            let fitnessValue = calculateFitness(dna: individual, optimal: OPTIMAL)
-            
-            let pair = ( individual, fitnessValue == 0 ? 1.0 : Double(100/POP_SIZE)/Double( fitnessValue ) )
-            
-            weightedPopulation.append(pair)
-        }
-        
-        population = []
-        
-        // create a new generation using the individuals in the origional population
-        (0...POP_SIZE).forEach { _ in
-            let ind1 = weightedChoice(items: weightedPopulation)
-            let ind2 = weightedChoice(items: weightedPopulation)
-            
-            let offspring = crossover(dna1: ind1.dna, dna2: ind2.dna, dnaSize: DNA_SIZE)
-            
-            // append to the population and mutate
-            population.append(mutate(lexicon: lex, dna: offspring, mutationChance: MUTATION_CHANCE))
-        }
-        
-        fittest = population[0]
-        var minFitness = calculateFitness(dna: fittest, optimal: OPTIMAL)
-        
-        // parse the population for the fittest string
-        population.forEach { indv in
-            let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
-            if indvFitness < minFitness {
-                fittest = indv
-                minFitness = indvFitness
-            }
-        }
-        if minFitness == 0 { break; }
-        print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
-        
+    population.forEach { indv in
+      let indvFitness = calculateFitness(dna: indv, optimal: OPTIMAL)
+      if indvFitness < minFitness {
+        fittest = indv
+        minFitness = indvFitness
+      }
     }
-    print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
+    
+    if minFitness == 0 { break }
+    print("\(generation): \(String(bytes: fittest, encoding: .utf8)!)")
+  }
+  print("fittest string: \(String(bytes: fittest, encoding: .utf8)!)")
 }
-
 main()

From b41a01d824674cb6efc9859e4e3fbadf05e622cc Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 5 Mar 2019 22:46:10 -0500
Subject: [PATCH 565/643] Update README.markdown

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

diff --git a/README.markdown b/README.markdown
index 88ea35949..064a4616c 100644
--- a/README.markdown
+++ b/README.markdown
@@ -100,7 +100,7 @@ Bad sorting algorithms (don't use these!):
 - [Convex Hull](Convex%20Hull/).
 - [Miller-Rabin Primality Test](Miller-Rabin%20Primality%20Test/). Is the number a prime number?
 - [MinimumCoinChange](MinimumCoinChange/). A showcase for dynamic programming.
-
+- [Genetic](Genetic/). A simple example on how to slowly mutate a value to its ideal form, in the context of biological evolution.
 ### Mathematics
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.

From 04b2d3010b3db16b1bfd472e9686364bbf785a94 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Fri, 8 Mar 2019 23:13:13 -0500
Subject: [PATCH 566/643] Updates for Swift 5.0

Removes unnecessary equatable implementations, since default implementations of `Equatable` has identical result.
---
 .../Points Lines Planes/2D/Line2D.swift       | 20 -------------------
 1 file changed, 20 deletions(-)

diff --git a/Points Lines Planes/Points Lines Planes/2D/Line2D.swift b/Points Lines Planes/Points Lines Planes/2D/Line2D.swift
index c92cbdbed..c23040b14 100644
--- a/Points Lines Planes/Points Lines Planes/2D/Line2D.swift	
+++ b/Points Lines Planes/Points Lines Planes/2D/Line2D.swift	
@@ -14,27 +14,11 @@ struct Line2D: Equatable {
     enum Slope: Equatable {
         case finite(slope: Double)
         case infinite(offset: Double)
-        
-        static func ==(lhs: Slope, rhs: Slope) -> Bool {
-            switch (lhs, rhs) {
-            case (.finite(let slope1), .finite(let slope2)): return slope1 == slope2
-            case (.infinite(let offset1), .infinite(let offset2)): return offset1 == offset2
-            default: return false
-            }
-        }
     }
     
     enum Direction: Equatable {
         case increasing
         case decreasing
-        
-        static func ==(lhs: Direction, rhs: Direction) -> Bool {
-            switch (lhs, rhs) {
-            case (.increasing, .increasing): return true
-            case (.decreasing, .decreasing): return true
-            default: return false
-            }
-        }
     }
     
     init(from p1: Point2D, to p2: Point2D) {
@@ -154,8 +138,4 @@ struct Line2D: Equatable {
             return Line2D(slope: .finite(slope: 0), offset: p.y, direction: dir)
         }
     }
-    
-    static func ==(lhs: Line2D, rhs: Line2D) -> Bool {
-        return lhs.slope == rhs.slope && lhs.offset == rhs.offset && lhs.direction == rhs.direction
-    }
 }

From 339cc1489b3b70e7464db4af7e8f398d45ce50db Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Fri, 8 Mar 2019 23:13:42 -0500
Subject: [PATCH 567/643] Updates to Swift 5.0

Removes `Equatable` impl.
---
 Points Lines Planes/Points Lines Planes/2D/Point2D.swift | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/Points Lines Planes/Points Lines Planes/2D/Point2D.swift b/Points Lines Planes/Points Lines Planes/2D/Point2D.swift
index f51ffd64d..bbd8305f8 100644
--- a/Points Lines Planes/Points Lines Planes/2D/Point2D.swift	
+++ b/Points Lines Planes/Points Lines Planes/2D/Point2D.swift	
@@ -9,10 +9,6 @@ struct Point2D: Equatable {
     var x: Double
     var y: Double
     
-    static func ==(lhs: Point2D, rhs: Point2D) -> Bool {
-        return lhs.x == rhs.x && lhs.y == rhs.y
-    }
-    
     // returns true if point is on or right of line
     func isRight(of line: Line2D) -> Bool {
         switch line.slope {

From 5e55f9261bc4095df3424fdd9f238513e0eae8e5 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 9 Mar 2019 19:39:32 -0500
Subject: [PATCH 568/643] Adds Myers Difference Algorithm to Readme

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

diff --git a/README.markdown b/README.markdown
index 064a4616c..97917a320 100644
--- a/README.markdown
+++ b/README.markdown
@@ -101,6 +101,7 @@ Bad sorting algorithms (don't use these!):
 - [Miller-Rabin Primality Test](Miller-Rabin%20Primality%20Test/). Is the number a prime number?
 - [MinimumCoinChange](MinimumCoinChange/). A showcase for dynamic programming.
 - [Genetic](Genetic/). A simple example on how to slowly mutate a value to its ideal form, in the context of biological evolution.
+- [Myers Difference Algorithm](Myers\ Difference\ Algorithm/). Finding the longest common subsequence of two sequences.
 ### Mathematics
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.

From 46c22ac590f580268a5c1fce288f6f8a720b37bb Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 9 Mar 2019 19:40:06 -0500
Subject: [PATCH 569/643] Update README.markdown

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

diff --git a/README.markdown b/README.markdown
index 97917a320..c94716242 100644
--- a/README.markdown
+++ b/README.markdown
@@ -101,7 +101,7 @@ Bad sorting algorithms (don't use these!):
 - [Miller-Rabin Primality Test](Miller-Rabin%20Primality%20Test/). Is the number a prime number?
 - [MinimumCoinChange](MinimumCoinChange/). A showcase for dynamic programming.
 - [Genetic](Genetic/). A simple example on how to slowly mutate a value to its ideal form, in the context of biological evolution.
-- [Myers Difference Algorithm](Myers\ Difference\ Algorithm/). Finding the longest common subsequence of two sequences.
+- [Myers Difference Algorithm](Myers Difference Algorithm/). Finding the longest common subsequence of two sequences.
 ### Mathematics
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.

From 3849a1d6113ddb7d8ac24be2a1e9fc4b7677efd6 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sat, 9 Mar 2019 19:41:21 -0500
Subject: [PATCH 570/643] Update README.markdown

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

diff --git a/README.markdown b/README.markdown
index c94716242..d66eee5d8 100644
--- a/README.markdown
+++ b/README.markdown
@@ -101,7 +101,7 @@ Bad sorting algorithms (don't use these!):
 - [Miller-Rabin Primality Test](Miller-Rabin%20Primality%20Test/). Is the number a prime number?
 - [MinimumCoinChange](MinimumCoinChange/). A showcase for dynamic programming.
 - [Genetic](Genetic/). A simple example on how to slowly mutate a value to its ideal form, in the context of biological evolution.
-- [Myers Difference Algorithm](Myers Difference Algorithm/). Finding the longest common subsequence of two sequences.
+- [Myers Difference Algorithm](Myers%20Difference%20Algorithm/). Finding the longest common subsequence of two sequences.
 ### Mathematics
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.

From 0d5e1b94e49311607fc0b30cc379304fe2123798 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 14 Mar 2019 22:44:36 -0400
Subject: [PATCH 571/643] Update README.markdown

Adds a reference to the GitHub page via #720
---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index d66eee5d8..44879e8f8 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,7 +8,7 @@ If you're a computer science student who needs to learn this stuff for exams --
 
 The goal of this project is to **explain how algorithms work**. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
 
-Code is compatible with **Xcode 10** and **Swift 4.2**. We'll keep this updated with the latest version of Swift.
+Code is compatible with **Xcode 10** and **Swift 4.2**. We'll keep this updated with the latest version of Swift. If you're interested in a GitHub pages version of the repo, check out [this](https://aquarchitect.github.io/swift-algorithm-club/).
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 

From 56e2fc9047a4523d62d3f1fe4eac679b20382509 Mon Sep 17 00:00:00 2001
From: bbvch13531 <bbvch13531@gmail.com>
Date: Fri, 15 Mar 2019 19:52:09 +0900
Subject: [PATCH 572/643] Change return type to brief type.

Fixes :#865

Signed-off-by: bbvch13531 <bbvch13531@gmail.com>
---
 .../Sources/BinarySearchTree.swift                            | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift
index 34ade3896..2d0eb7e57 100644
--- a/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
+++ b/Binary Search Tree/Solution 1/BinarySearchTree.playground/Sources/BinarySearchTree.swift	
@@ -235,7 +235,7 @@ extension BinarySearchTree {
   /*
     Finds the node whose value precedes our value in sorted order.
   */
-  public func predecessor() -> BinarySearchTree<T>? {
+  public func predecessor() -> BinarySearchTree? {
     if let left = left {
       return left.maximum()
     } else {
@@ -251,7 +251,7 @@ extension BinarySearchTree {
   /*
     Finds the node whose value succeeds our value in sorted order.
   */
-  public func successor() -> BinarySearchTree<T>? {
+  public func successor() -> BinarySearchTree? {
     if let right = right {
       return right.minimum()
     } else {

From 7065c1a2d0aa0633188cdb27de69c11ab8d740d5 Mon Sep 17 00:00:00 2001
From: Dmitry Cherednikov <dmitry.cherednikov@tachos.ru>
Date: Sat, 16 Mar 2019 15:44:00 +0400
Subject: [PATCH 573/643] Implement getPredecessor().

---
 Red-Black Tree/README.markdown                |  1 +
 .../Sources/RedBlackTree.swift                | 27 ++++++++++++++++++-
 2 files changed, 27 insertions(+), 1 deletion(-)

diff --git a/Red-Black Tree/README.markdown b/Red-Black Tree/README.markdown
index fd6c4db18..352588056 100644
--- a/Red-Black Tree/README.markdown	
+++ b/Red-Black Tree/README.markdown	
@@ -29,6 +29,7 @@ From [CLRS]
 ## Methods
 
 Nodes:
+* `nodeX.getPredecessor()` Returns the inorder predecessor of nodeX
 * `nodeX.getSuccessor()` Returns the inorder successor of nodeX
 * `nodeX.minimum()` Returns the node with the minimum key of the subtree of nodeX
 * `nodeX.maximum()` Returns the node with the maximum key of the subtree of nodeX
diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index 59633031d..b88cd7cf5 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -60,6 +60,10 @@ public class RBTreeNode<T: Comparable>: Equatable {
     self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
     self.color = .black
   }
+
+  public func getKey() -> T? {
+    return key
+  }
   
   var isRoot: Bool {
     return parent == nil
@@ -120,9 +124,30 @@ extension RBTreeNode {
   }
 }
 
-// MARK: - Finding a nodes successor
+// MARK: - Finding a nodes successor and predecessor
 
 extension RBTreeNode {
+  /*
+  * Returns the inorder predecessor node of a node
+  * The predecessor is a node with the next smaller key value of the current node
+  */
+  public func getPredecessor() -> RBNode? {
+    // if node has left child: predecessor is min of this left tree
+    if let leftChild = leftChild, !leftChild.isNullLeaf {
+      return leftChild.maximum()
+    }
+    // else go upward while node is left child
+    var currentNode = self
+    var parent = currentNode.parent
+    while currentNode.isLeftChild {
+      if let parent = parent {
+        currentNode = parent
+      }
+      parent = currentNode.parent
+    }
+    return parent
+  }
+
   /*
    * Returns the inorder successor node of a node
    * The successor is a node with the next larger key value of the current node

From 6e8b5cdc37324a4120abee841d89cef36ab6352f Mon Sep 17 00:00:00 2001
From: TL <tommylohz@gmail.com>
Date: Wed, 20 Mar 2019 16:09:34 +0800
Subject: [PATCH 574/643] Update Shuffle
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

according to https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle

`checks if j ≠ i may be omitted`, and also remove checking logic will optimise performance(tested by 100000 times random).
---
 Shuffle/README.markdown | 3 ---
 Shuffle/Shuffle.swift   | 3 ---
 2 files changed, 6 deletions(-)

diff --git a/Shuffle/README.markdown b/Shuffle/README.markdown
index 63868767b..d8ab7ff78 100644
--- a/Shuffle/README.markdown
+++ b/Shuffle/README.markdown
@@ -96,9 +96,6 @@ public func shuffledArray(_ n: Int) -> [Int] {
   var a = [Int](repeating: 0, count: n)
   for i in 0..<n {
     let j = Int.random(in: 0...i)
-    if i != j {
-      a[i] = a[j]
-    }
     a[j] = i
   }
   return a
diff --git a/Shuffle/Shuffle.swift b/Shuffle/Shuffle.swift
index 3e4292d56..a921e5ec3 100644
--- a/Shuffle/Shuffle.swift
+++ b/Shuffle/Shuffle.swift
@@ -30,9 +30,6 @@ public func shuffledArray(_ n: Int) -> [Int] {
   var a = Array(repeating: 0, count: n)
   for i in 0..<n {
     let j = random(i + 1)
-    if i != j {
-      a[i] = a[j]
-    }
     a[j] = i  // insert next number from the sequence
   }
   return a

From 91b7bb1d1d16f4cbe64399de156b2045ebf6d5be Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 21 Mar 2019 10:17:06 -0400
Subject: [PATCH 575/643] Update SlowSort.swift

---
 Slow Sort/SlowSort.swift | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index bd8288b18..546a36395 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -7,14 +7,14 @@
 //
 
 func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
-    guard if i < j else { return }
-    let m = (i+j)/2
-    slowSort(i, m, &numberList)
-    slowSort(m+1, j, &numberList)
-    if numberList[j] < numberList[m] {
-        let temp = numberList[j]
-        numberList[j] = numberList[m]
-        numberList[m] = temp
-    }
-    slowSort(i, j-1, &numberList)
+  guard if i < j else { return }
+  let m = (i+j)/2
+  slowSort(i, m, &numberList)
+  slowSort(m+1, j, &numberList)
+  if numberList[j] < numberList[m] {
+      let temp = numberList[j]
+      numberList[j] = numberList[m]
+      numberList[m] = temp
+  }
+  slowSort(i, j-1, &numberList)
 }

From 7457ceb7e9ec688ac11db158ac3d32118df49b0f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 21 Mar 2019 10:25:04 -0400
Subject: [PATCH 576/643] Two-spaced indents

---
 Comb Sort/Tests/CombSortTests.swift | 32 ++++++++++++-----------------
 1 file changed, 13 insertions(+), 19 deletions(-)

diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
index 166065484..1d83af002 100644
--- a/Comb Sort/Tests/CombSortTests.swift	
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -9,26 +9,20 @@
 import XCTest
 
 class CombSortTests: XCTestCase {
-    var sequence: [Int]!
-    let expectedSequence: [Int] = [-12, -10, -1, 2, 9, 32, 55, 67, 89, 101]
-
-    func testSwiftVersion(){
-        #if swift(>=4.2)
-            print("Hello, Swift 4.2!")
-        #endif
-    }
+  var sequence: [Int]!
+  let expectedSequence: [Int] = [-12, -10, -1, 2, 9, 32, 55, 67, 89, 101]
     
-    override func setUp() {
-        super.setUp()
-        sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
-    }
+  override func setUp() {
+    super.setUp()
+    sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
+  }
 
-    override func tearDown() {
-        super.tearDown()
-    }
+  override func tearDown() {
+    super.tearDown()
+  }
 
-    func testCombSort() {
-        let sortedSequence = combSort(sequence)
-        XCTAssertEqual(sortedSequence, expectedSequence)
-    }
+  func testCombSort() {
+    let sortedSequence = combSort(sequence)
+    XCTAssertEqual(sortedSequence, expectedSequence)
+  }
 }

From fdab1a2d7a9f9797ed7be27c5023f284c47f38ea Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Thu, 21 Mar 2019 10:25:24 -0400
Subject: [PATCH 577/643] two spaced indents

---
 Slow Sort/SlowSort.swift | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index 546a36395..968f6841b 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -12,9 +12,9 @@ func slowSort(_ i: Int, _ j: Int, _ numberList: inout [Int]) {
   slowSort(i, m, &numberList)
   slowSort(m+1, j, &numberList)
   if numberList[j] < numberList[m] {
-      let temp = numberList[j]
-      numberList[j] = numberList[m]
-      numberList[m] = temp
+    let temp = numberList[j]
+    numberList[j] = numberList[m]
+    numberList[m] = temp
   }
   slowSort(i, j-1, &numberList)
 }

From 7405c64e2cf7c035dce15207bba0fe7434010b55 Mon Sep 17 00:00:00 2001
From: Priyanka- <khiladis@Priyankas-MacBook-Pro.local>
Date: Sun, 24 Mar 2019 12:20:31 -0700
Subject: [PATCH 578/643] Kth Largest Element: updated to use Int.random API
 which has been introduced with Swift 4.2

---
 .../kthLargest.playground/Sources/kthLargest.swift        | 8 +-------
 1 file changed, 1 insertion(+), 7 deletions(-)

diff --git a/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift b/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift
index 397c43a38..aad15eac6 100644
--- a/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift	
+++ b/Kth Largest Element/kthLargest.playground/Sources/kthLargest.swift	
@@ -16,12 +16,6 @@ public func kthLargest(_ a: [Int], _ k: Int) -> Int? {
 
 // MARK: - Randomized selection
 
-/* Returns a random integer in the range min...max, inclusive. */
-public func random(min: Int, max: Int) -> Int {
-  assert(min < max)
-  return min + Int(arc4random_uniform(UInt32(max - min + 1)))
-}
-
 /*
   Returns the i-th smallest element from the array.
 
@@ -39,7 +33,7 @@ public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
   var a = array
 
   func randomPivot<T: Comparable>(_ a: inout [T], _ low: Int, _ high: Int) -> T {
-    let pivotIndex = random(min: low, max: high)
+    let pivotIndex = Int.random(in: low...high)
     a.swapAt(pivotIndex, high)
     return a[high]
   }

From b6e9a40652d489605772f284ad2dac4a033fd216 Mon Sep 17 00:00:00 2001
From: TL <tommylohz@gmail.com>
Date: Tue, 26 Mar 2019 15:34:12 +0800
Subject: [PATCH 579/643] Update Shuffle

---
 Shuffle/README.markdown | 4 ++++
 Shuffle/Shuffle.swift   | 1 +
 2 files changed, 5 insertions(+)

diff --git a/Shuffle/README.markdown b/Shuffle/README.markdown
index d8ab7ff78..5a2a07a98 100644
--- a/Shuffle/README.markdown
+++ b/Shuffle/README.markdown
@@ -96,6 +96,8 @@ public func shuffledArray(_ n: Int) -> [Int] {
   var a = [Int](repeating: 0, count: n)
   for i in 0..<n {
     let j = Int.random(in: 0...i)
+    // for the Fisher–Yates_shuffle's pseudo code implement in wiki, it will check if i != j
+    a[i] = a[j]
     a[j] = i
   }
   return a
@@ -112,6 +114,8 @@ This returns something like `[3, 0, 9, 1, 8, 5, 2, 6, 7, 4]`. As you can see, ev
 
 The `shuffledArray()` function first creates a new array with `n` zeros. Then it loops `n` times and in each step adds the next number from the sequence to a random position in the array. The trick is to make sure that none of these numbers gets overwritten with the next one, so it moves the previous number out of the way first!
 
+For this function, `The condition that checks if j ≠ i may be omitted in languages that have no problems accessing uninitialized array values, and for which assigning is cheaper than comparing.`, you can check it in wiki. And also remove checking logic will optimise performance.
+
 The algoritm is quite clever and I suggest you walk through an example yourself, either on paper or in the playground. (Hint: Again it splits the array into two regions.)
 
 ## See also
diff --git a/Shuffle/Shuffle.swift b/Shuffle/Shuffle.swift
index a921e5ec3..1d2758c11 100644
--- a/Shuffle/Shuffle.swift
+++ b/Shuffle/Shuffle.swift
@@ -30,6 +30,7 @@ public func shuffledArray(_ n: Int) -> [Int] {
   var a = Array(repeating: 0, count: n)
   for i in 0..<n {
     let j = random(i + 1)
+    a[i] = a[j]
     a[j] = i  // insert next number from the sequence
   }
   return a

From 114becb9f856a765e58ebf890b2140a73899ce08 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Sun, 28 Apr 2019 13:19:59 -0400
Subject: [PATCH 580/643] Adds Closest Pair

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

diff --git a/README.markdown b/README.markdown
index 44879e8f8..3e0174576 100644
--- a/README.markdown
+++ b/README.markdown
@@ -208,6 +208,7 @@ A lot of software developer interview questions consist of algorithmic puzzles.
 - [Dining Philosophers](DiningPhilosophers/)
 - [Egg Drop Problem](Egg%20Drop%20Problem/)
 - [Encoding and Decoding Binary Tree](Encode%20and%20Decode%20Tree/)
+- [Closest Pair](Closest%20Pair/)
 
 ## Learn more!
 

From 721af5d569661effa976e88fc65a14fd3961b826 Mon Sep 17 00:00:00 2001
From: Vladislav Badulin <vladislav@badulin.com>
Date: Mon, 29 Apr 2019 21:24:24 +0200
Subject: [PATCH 581/643] This fixes the unlikely event that the generated
 hashValue happens to be the equal to Int.min, in which case the abs value of
 it would be Int.max + 1 causing overflow.

---
 Hash Table/HashTable.playground/Sources/HashTable.swift | 2 +-
 Hash Table/README.markdown                              | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Hash Table/HashTable.playground/Sources/HashTable.swift b/Hash Table/HashTable.playground/Sources/HashTable.swift
index 476a51174..f2a1be040 100644
--- a/Hash Table/HashTable.playground/Sources/HashTable.swift	
+++ b/Hash Table/HashTable.playground/Sources/HashTable.swift	
@@ -131,7 +131,7 @@ public struct HashTable<Key: Hashable, Value> {
      Returns the given key's array index.
      */
     private func index(forKey key: Key) -> Int {
-        return abs(key.hashValue) % buckets.count
+        return abs(key.hashValue % buckets.count)
     }
 }
 
diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index 9c4065a51..fb0bda788 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -141,7 +141,7 @@ The hash table does not do anything yet, so let's add the remaining functionalit
 
 ```swift
   private func index(forKey key: Key) -> Int {
-    return abs(key.hashValue) % buckets.count
+    return abs(key.hashValue % buckets.count)
   }
 ```
 

From 15db2b6d953d1130acb711a358a79f5237979d02 Mon Sep 17 00:00:00 2001
From: Vanderlei Alves <39912609+vzanshin@users.noreply.github.com>
Date: Fri, 3 May 2019 15:47:53 -0300
Subject: [PATCH 582/643] Fix typo and grammar

---
 .github/CONTRIBUTING.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index e5d00c17b..29f4ca7e1 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -6,7 +6,7 @@ Want to help out with the Swift Algorithm Club? Great! While we don't have stric
 
 Our repo is all about learning. The `README` file is the cake, and the sample code is the cherry on top. A good contribution has succinct explanations supported by diagrams. Code is best introduced in chunks, weaved into the explanations where relevant. 
 
-> When choosing between brievity and performance, err to the side of brievity as long as the time complexity of the particular implementation is the same. You can make a note afterwards suggesting a more performant way of doing things. 
+> When choosing between brevity and performance, err to the side of brevity as long as the time complexity of the particular implementation is the same. You can make a note afterwards suggesting a more performant way of doing things. 
 
 **API Design Guidelines**
 
@@ -22,7 +22,7 @@ We follow the following Swift [style guide](https://github.com/raywenderlich/swi
 
 Unit tests. Fixes for typos. No contribution is too small. :-)
 
-The repository has over 100 different data structures and algorithms. We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library is most welcomed. 
+The repository has over 100 different data structures and algorithms. We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library are most welcome.
 
 ### New Contributions
 

From 3f1d661b2d95eb0349d824277447c63c0aa3ecf1 Mon Sep 17 00:00:00 2001
From: Vanderlei Alves <39912609+vzanshin@users.noreply.github.com>
Date: Wed, 8 May 2019 16:39:15 -0300
Subject: [PATCH 583/643] Fix minor typo at Heap/README

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

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 76d2bee39..6c65fe9c8 100755
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -29,7 +29,7 @@ As a result of this heap property, a max-heap always stores its largest item at
 
 ## How does a heap compare to regular trees?
 
-A heap is not a replacement for a binary search tree, and there are similarities and differnces between them. Here are some main differences:
+A heap is not a replacement for a binary search tree, and there are similarities and differences between them. Here are some main differences:
 
 
 **Order of the nodes.** In a [binary search tree (BST)](../Binary%20Search%20Tree/), the left child must be smaller than its parent, and the right child must be greater. This is not true for a heap. In a max-heap both children must be smaller than the parent, while in a min-heap they both must be greater.

From 78a7ceeff6c59a740428c6fae41a79f660c5a58c Mon Sep 17 00:00:00 2001
From: Kenny Schlagel <schlagelk@aetna.com>
Date: Sun, 7 Jul 2019 19:52:11 -0600
Subject: [PATCH 584/643] Improvements to Count Occurrences

---
 .../Contents.swift                            | 20 +++++++--------
 Count Occurrences/CountOccurrences.swift      | 25 ++++++++++---------
 Count Occurrences/README.markdown             | 12 ++++-----
 3 files changed, 29 insertions(+), 28 deletions(-)

diff --git a/Count Occurrences/CountOccurrences.playground/Contents.swift b/Count Occurrences/CountOccurrences.playground/Contents.swift
index a34e3485f..6ab4c00f3 100644
--- a/Count Occurrences/CountOccurrences.playground/Contents.swift	
+++ b/Count Occurrences/CountOccurrences.playground/Contents.swift	
@@ -1,11 +1,11 @@
 
-func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
-  func leftBoundary() -> Int {
+func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
+  var leftBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] < key {
+      if array[midIndex] < key {
         low = midIndex + 1
       } else {
         high = midIndex
@@ -14,12 +14,12 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  func rightBoundary() -> Int {
+  var rightBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] > key {
+      if array[midIndex] > key {
         high = midIndex
       } else {
         low = midIndex + 1
@@ -28,13 +28,13 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  return rightBoundary() - leftBoundary()
+  return rightBoundary - leftBoundary
 }
 
 // Simple test
 
 let a = [ 0, 1, 1, 3, 3, 3, 3, 6, 8, 10, 11, 11 ]
-countOccurrencesOfKey(3, inArray: a)
+countOccurrences(of: 3, in: a)
 
 // Test with arrays of random size and contents (see debug output)
 
@@ -59,6 +59,6 @@ for _ in 0..<10 {
 
   // Note: we also test -1 and 6 to check the edge cases.
   for k in -1...6 {
-    print("\t\(k): \(countOccurrencesOfKey(k, inArray: a))")
+    print("\t\(k): \(countOccurrences(of: k, in: a))")
   }
 }
diff --git a/Count Occurrences/CountOccurrences.swift b/Count Occurrences/CountOccurrences.swift
index 10dd12c4f..532e3810e 100644
--- a/Count Occurrences/CountOccurrences.swift	
+++ b/Count Occurrences/CountOccurrences.swift	
@@ -1,14 +1,15 @@
-/*
-  Counts the number of times a value appears in an array in O(lg n) time.
-  The array must be sorted from low to high.
-*/
-func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
-  func leftBoundary() -> Int {
+/// Counts the number of times a value appears in an array in O(log n) time.  The array must be sorted from low to high.
+///
+/// - Parameter key: the key to be searched for in the array
+/// - Parameter array: the array to search
+/// - Returns: the count of occurences of the key in the given array
+func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
+  var leftBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] < key {
+      if array[midIndex] < key {
         low = midIndex + 1
       } else {
         high = midIndex
@@ -17,12 +18,12 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  func rightBoundary() -> Int {
+  var rightBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] > key {
+      if array[midIndex] > key {
         high = midIndex
       } else {
         low = midIndex + 1
@@ -31,5 +32,5 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  return rightBoundary() - leftBoundary()
+  return rightBoundary - leftBoundary
 }
diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 85b77d2d0..297bc4b0f 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -22,8 +22,8 @@ The trick is to use two binary searches, one to find where the `3`s start (the l
 In code this looks as follows:
 
 ```swift
-func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
-  func leftBoundary() -> Int {
+func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
+  var leftBoundary: Int {
     var low = 0
     var high = a.count
     while low < high {
@@ -37,7 +37,7 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  func rightBoundary() -> Int {
+  var rightBoundary: Int {
     var low = 0
     var high = a.count
     while low < high {
@@ -51,11 +51,11 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     return low
   }
 
-  return rightBoundary() - leftBoundary()
+  return rightBoundary - leftBoundary
 }
 ```
 
-Notice that the helper functions `leftBoundary()` and `rightBoundary()` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.
+Notice that the variables `leftBoundary` and `rightBoundary` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.  Also, notice that we constrain the type `T` to be Comparable so that the algorithm can be applied to an array of Strings, Ints or other types that conform to the Swift Comparable protocol.
 
 To test this algorithm, copy the code to a playground and then do:
 
@@ -113,7 +113,7 @@ The right boundary is at index 7. The difference between the two boundaries is 7
 
 Each binary search took 4 steps, so in total this algorithm took 8 steps. Not a big gain on an array of only 12 items, but the bigger the array, the more efficient this algorithm becomes. For a sorted array with 1,000,000 items, it only takes 2 x 20 = 40 steps to count the number of occurrences for any particular value.
 
-By the way, if the value you're looking for is not in the array, then `rightBoundary()` and `leftBoundary()` return the same value and so the difference between them is 0.
+By the way, if the value you're looking for is not in the array, then `rightBoundary` and `leftBoundary` return the same value and so the difference between them is 0.
 
 This is an example of how you can modify the basic binary search to solve other algorithmic problems as well. Of course, it does require that the array is sorted.
 

From 6e64f07b43971ba04b85887bf3bf2d616243c21a Mon Sep 17 00:00:00 2001
From: ygit <ygit@users.noreply.github.com>
Date: Wed, 10 Jul 2019 02:38:29 +0530
Subject: [PATCH 585/643] added Big O computation comparison graph

---
 Big-O Notation.markdown | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 257f80462..9509331a5 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -18,6 +18,11 @@ Big-O | Name | Description
 **O(n!)** | factorial | **Intolerably slow.** It literally takes a million years to do anything.  
 
 
+
+![Comparison of Big O computations](https://upload.wikimedia.org/wikipedia/commons/7/7e/Comparison_computational_complexity.svg)
+
+
+
 Below are some examples for each category of performance:
 
 **O(1)**

From 762de527ad71e07f36ca9fd417819d733d298bdd Mon Sep 17 00:00:00 2001
From: markgz <markgzpccw@gmail.com>
Date: Thu, 8 Aug 2019 17:09:28 +0800
Subject: [PATCH 586/643] The code of O(2^n) isn't correct which is O(n)

Need solve two smaller problems in one recursive call
---
 Big-O Notation.markdown | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 9509331a5..c3f020df2 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -124,9 +124,8 @@ Below are some examples for each category of performance:
   func solveHanoi(n: Int, from: String, to: String, spare: String) {
     guard n >= 1 else { return }
     if n > 1 {
-      solveHanoi(n: n - 1, from: from, to: spare, spare: to)
-    } else {
-      solveHanoi(n: n - 1, from: spare, to: to, spare: from)
+        solveHanoi(n: n - 1, from: from, to: spare, spare: to)
+        solveHanoi(n: n - 1, from: spare, to: to, spare: from)
     }
   }
   ```

From eb9424d3f69d18a311c474907c2775f2a07d2852 Mon Sep 17 00:00:00 2001
From: abuzeid ibrahim <abuzeid7@gmail.com>
Date: Thu, 15 Aug 2019 14:21:38 +0200
Subject: [PATCH 587/643] rename variables with convenience names

---
 Insertion Sort/InsertionSort.swift | 42 +++++++++++++++---------------
 1 file changed, 21 insertions(+), 21 deletions(-)

diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 2ad607ac8..926dad302 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -2,22 +2,22 @@
 ///
 /// - Parameters:
 ///   - array: the array of elements to be sorted
+///   - sortedArray: copy the array to save stability
 ///   - isOrderedBefore: returns true if the elements provided are in the corect order
 /// - Returns: a sorted array containing the same elements
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
-  guard array.count > 1 else { return array }
-
-  var a = array
-  for x in 1..<a.count {
-    var y = x
-    let temp = a[y]
-    while y > 0 && isOrderedBefore(temp, a[y - 1]) {
-      a[y] = a[y - 1]
-      y -= 1
+    guard array.count > 1 else { return array }
+    var sortedArray = array
+    for index in 1..<sortedArray.count {
+        var currentIndex = index
+        let temp = sortedArray[currentIndex]
+        while currentIndex > 0, isOrderedBefore(temp, sortedArray[currentIndex - 1]) {
+            sortedArray[currentIndex] = sortedArray[currentIndex - 1]
+            currentIndex -= 1
+        }
+        sortedArray[currentIndex] = temp
     }
-    a[y] = temp
-  }
-  return a
+    return sortedArray
 }
 
 /// Performs the Insertion sort algorithm to a given array
@@ -27,15 +27,15 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
     guard array.count > 1 else { return array }
 
-    var a = array
-    for x in 1..<a.count {
-        var y = x
-        let temp = a[y]
-        while y > 0 && temp < a[y - 1] {
-            a[y] = a[y - 1]
-            y -= 1
+    var sortedArray = array
+    for index in 1..<sortedArray.count {
+        var currentIndex = index
+        let temp = sortedArray[currentIndex]
+        while currentIndex > 0, temp < sortedArray[currentIndex - 1] {
+            sortedArray[currentIndex] = sortedArray[currentIndex - 1]
+            currentIndex -= 1
         }
-        a[y] = temp
+        sortedArray[currentIndex] = temp
     }
-    return a
+    return sortedArray
 }

From 92e797ac998b3f7a00cb1c2247c01d927cfa5414 Mon Sep 17 00:00:00 2001
From: abuzeid ibrahim <abuzeid7@gmail.com>
Date: Thu, 15 Aug 2019 14:31:22 +0200
Subject: [PATCH 588/643] rename variables in the playground

---
 .../InsertionSort.playground/Contents.swift   | 36 +++++++++----------
 .../contents.xcplayground                     |  2 +-
 2 files changed, 19 insertions(+), 19 deletions(-)

diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index 184fc36e4..e1d3a312e 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -9,17 +9,17 @@
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
     guard array.count > 1 else { return array }
     
-    var a = array
-    for x in 1..<a.count {
-        var y = x
-        let temp = a[y]
-        while y > 0 && isOrderedBefore(temp, a[y - 1]) {
-            a[y] = a[y - 1]
-            y -= 1
+    var sortedArray = array
+    for index in 1..<sortedArray.count {
+        var currentIndex = index
+        let temp = sortedArray[currentIndex]
+        while currentIndex > 0 && isOrderedBefore(temp, sortedArray[currentIndex - 1]) {
+            sortedArray[currentIndex] = sortedArray[currentIndex - 1]
+            currentIndex -= 1
         }
-        a[y] = temp
+        sortedArray[currentIndex] = temp
     }
-    return a
+    return sortedArray
 }
 
 /// Performs the Insertion sort algorithm to a given array
@@ -27,17 +27,17 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 /// - Parameter array: the array to be sorted, conatining elements that conform to the Comparable protocol
 /// - Returns: a sorted array containing the same elements
 func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
-    var a = array
-    for x in 1..<a.count {
-        var y = x
-        let temp = a[y]
-        while y > 0 && temp < a[y - 1] {
-            a[y] = a[y - 1]
-            y -= 1
+    var sortedArray = array
+    for index in 1..<sortedArray.count {
+        var currentIndex = index
+        let temp = sortedArray[currentIndex]
+        while currentIndex > 0 && temp < sortedArray[currentIndex - 1] {
+            sortedArray[currentIndex] = sortedArray[currentIndex - 1]
+            currentIndex -= 1
         }
-        a[y] = temp
+        sortedArray[currentIndex] = temp
     }
-    return a
+    return sortedArray
 }
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
diff --git a/Insertion Sort/InsertionSort.playground/contents.xcplayground b/Insertion Sort/InsertionSort.playground/contents.xcplayground
index 9f9eecc96..06828af92 100644
--- a/Insertion Sort/InsertionSort.playground/contents.xcplayground	
+++ b/Insertion Sort/InsertionSort.playground/contents.xcplayground	
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='osx' executeOnSourceChanges='false'>
+<playground version='5.0' target-platform='osx'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 6dc91c4a7bee34ff2b4fe9f4f2d5d77d3d42e55c Mon Sep 17 00:00:00 2001
From: Abuzeid-Ibrahim <abuzeid7@gmail.com>
Date: Thu, 15 Aug 2019 14:35:33 +0200
Subject: [PATCH 589/643] Update README.markdown

---
 Insertion Sort/README.markdown | 32 ++++++++++++++++----------------
 1 file changed, 16 insertions(+), 16 deletions(-)

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index 4bad29aa1..8c2a5c1a0 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -91,15 +91,15 @@ Here is an implementation of insertion sort in Swift:
 
 ```swift
 func insertionSort(_ array: [Int]) -> [Int] {
-    var a = array			 // 1
-    for x in 1..<a.count {		 // 2
-        var y = x
-        while y > 0 && a[y] < a[y - 1] { // 3
-            a.swapAt(y - 1, y)
-            y -= 1
+    var sortedArray = array			 // 1
+    for index in 1..<sortedArray.count {		 // 2
+        var currentIndex = index
+        while currentIndex > 0 && sortedArray[currentIndex] < sortedArray[currentIndex - 1] { // 3
+            sortedArray.swapAt(currentIndex - 1, currentIndex)
+            currentIndex -= 1
         }
     }
-    return a
+    return sortedArray
 }
 
 
@@ -154,17 +154,17 @@ In code that looks like this:
 
 ```swift
 func insertionSort(_ array: [Int]) -> [Int] {
-  var a = array
-  for x in 1..<a.count {
-    var y = x
-    let temp = a[y]
-    while y > 0 && temp < a[y - 1] {
-      a[y] = a[y - 1]                // 1
-      y -= 1
+  var sortedArray = array
+  for index in 1..<sortedArray.count {
+    var currentIndex = index
+    let temp = sortedArray[currentIndex]
+    while currentIndex > 0 && temp < sortedArray[currentIndex - 1] {
+      sortedArray[currentIndex] = sortedArray[currentIndex - 1]                // 1
+      currentIndex -= 1
     }
-    a[y] = temp                      // 2
+    sortedArray[currentIndex] = temp                      // 2
   }
-  return a
+  return sortedArray
 }
 ```
 

From dfea1d68dd6151f88221c6be34a0a78002c50537 Mon Sep 17 00:00:00 2001
From: Pavel <Peeoner174@gmail.com>
Date: Sat, 31 Aug 2019 11:12:51 +0500
Subject: [PATCH 590/643] Update Queue-Optimized.swift

---
 Queue/Queue-Optimized.swift | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

diff --git a/Queue/Queue-Optimized.swift b/Queue/Queue-Optimized.swift
index 7dff91698..aedf9c67f 100644
--- a/Queue/Queue-Optimized.swift
+++ b/Queue/Queue-Optimized.swift
@@ -23,7 +23,7 @@ public struct Queue<T> {
   }
 
   public mutating func dequeue() -> T? {
-    guard head < array.count, let element = array[head] else { return nil }
+    guard let element = array[guarded: head] else { return nil }
 
     array[head] = nil
     head += 1
@@ -45,3 +45,14 @@ public struct Queue<T> {
     }
   }
 }
+
+extension Array {
+    
+    subscript(guarded idx: Int) -> Element? {
+        guard (startIndex..<endIndex).contains(idx) else {
+            return nil
+        }
+        return self[idx]
+    }
+    
+}

From 70fdd27222f6ed42f958b78d906b4a0b0d4fb66f Mon Sep 17 00:00:00 2001
From: abuzeid ibrahim <abuzeid7@gmail.com>
Date: Tue, 3 Sep 2019 16:14:28 +0200
Subject: [PATCH 591/643] move documentation to func body

---
 Insertion Sort/InsertionSort.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index 926dad302..e24ede905 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -2,11 +2,11 @@
 ///
 /// - Parameters:
 ///   - array: the array of elements to be sorted
-///   - sortedArray: copy the array to save stability
 ///   - isOrderedBefore: returns true if the elements provided are in the corect order
 /// - Returns: a sorted array containing the same elements
 func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
     guard array.count > 1 else { return array }
+    ///   - sortedArray: copy the array to save stability
     var sortedArray = array
     for index in 1..<sortedArray.count {
         var currentIndex = index

From 0299a1cb92c516ade55a0095467376a79d116f86 Mon Sep 17 00:00:00 2001
From: PavelKochenda
 <kpa@napoleonit.rukpa@napoleonit.rukpa@napoleonit.rukpa@napoleonit.rukpa@napoleonit.ru>
Date: Fri, 6 Sep 2019 11:39:57 +0500
Subject: [PATCH 592/643] Added changed by opened discussions

---
 Queue/Queue-Optimized.swift | 2 --
 1 file changed, 2 deletions(-)

diff --git a/Queue/Queue-Optimized.swift b/Queue/Queue-Optimized.swift
index aedf9c67f..3b17b98cb 100644
--- a/Queue/Queue-Optimized.swift
+++ b/Queue/Queue-Optimized.swift
@@ -47,12 +47,10 @@ public struct Queue<T> {
 }
 
 extension Array {
-    
     subscript(guarded idx: Int) -> Element? {
         guard (startIndex..<endIndex).contains(idx) else {
             return nil
         }
         return self[idx]
     }
-    
 }

From adc0360746e75aa6922c9a7bc1e65139d9c36204 Mon Sep 17 00:00:00 2001
From: Perris Davis <WikipediaBrown@users.noreply.github.com>
Date: Fri, 6 Sep 2019 13:18:40 -0700
Subject: [PATCH 593/643] Updated broken link

Updated link to Boyer-Moore-Horspool algorithm.
---
 Knuth-Morris-Pratt/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Knuth-Morris-Pratt/README.markdown b/Knuth-Morris-Pratt/README.markdown
index 95fdea9e9..2e4d5360b 100644
--- a/Knuth-Morris-Pratt/README.markdown
+++ b/Knuth-Morris-Pratt/README.markdown
@@ -14,7 +14,7 @@ let concert = "🎼🎹🎹🎸🎸🎻🎻🎷🎺🎤👏👏👏"
 concert.indexesOf(ptnr: "🎻🎷")   // Output: [6]
 ```
 
-The [Knuth-Morris-Pratt algorithm](https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm) is considered one of the best algorithms for solving the pattern matching problem. Although in practice [Boyer-Moore](../Boyer-Moore/) is usually preferred, the algorithm that we will introduce is simpler, and has the same (linear) running time.
+The [Knuth-Morris-Pratt algorithm](https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm) is considered one of the best algorithms for solving the pattern matching problem. Although in practice [Boyer-Moore](../Boyer-Moore-Horspool/) is usually preferred, the algorithm that we will introduce is simpler, and has the same (linear) running time.
 
 The idea behind the algorithm is not too different from the [naive string search](../Brute-Force%20String%20Search/) procedure. As it, Knuth-Morris-Pratt aligns the text with the pattern and goes with character comparisons from left to right. But, instead of making a shift of one character when a mismatch occurs, it uses a more intelligent way to move the pattern along the text. In fact, the algorithm features a pattern pre-processing stage where it acquires all the informations that will make the algorithm skip redundant comparisons, resulting in larger shifts.
 

From da2085fc5bd7b08aec0b061301218e90fdf3d35e Mon Sep 17 00:00:00 2001
From: Joe Soultanis <jsoultanis@uber.com>
Date: Tue, 29 Oct 2019 16:55:50 -0700
Subject: [PATCH 594/643] updaing incorrect big-O performance documentation of
 heap removal

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

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index cf39fb8a5..7560bc7b9 100755
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -212,7 +212,7 @@ extension Heap where T: Equatable {
     return nodes.index(where: { $0 == node })
   }
   
-  /** Removes the first occurrence of a node from the heap. Performance: O(n log n). */
+  /** Removes the first occurrence of a node from the heap. Performance: O(n). */
   @discardableResult public mutating func remove(node: T) -> T? {
     if let index = index(of: node) {
       return remove(at: index)

From 519a57ae2946033608bda0fe24d428e189212df4 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Tue, 29 Oct 2019 22:35:24 -0400
Subject: [PATCH 595/643] Removes the workspace.

---
 .../contents.xcworkspacedata                  | 2914 -----------------
 .../xcshareddata/IDEWorkspaceChecks.plist     |    8 -
 .../xcshareddata/WorkspaceSettings.xcsettings |    8 -
 3 files changed, 2930 deletions(-)
 delete mode 100644 swift-algorithm-club.xcworkspace/contents.xcworkspacedata
 delete mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 delete mode 100644 swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
deleted file mode 100644
index 03d06d2f7..000000000
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ /dev/null
@@ -1,2914 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Workspace
-   version = "1.0">
-   <Group
-      location = "container:"
-      name = "Sorted Set">
-      <FileRef
-         location = "group:Sorted Set/README.markdown">
-      </FileRef>
-      <FileRef
-         location = "group:Sorted Set/SortedSet.playground">
-      </FileRef>
-      <FileRef
-         location = "group:Sorted Set/SortedSet.swift">
-      </FileRef>
-   </Group>
-   <Group
-      location = "group:Egg Drop Problem"
-      name = "Egg Drop Problem">
-      <FileRef
-         location = "group:/Users/arkalyk/Desktop/SwiftAlgorithmClub/swift-algorithm-club/Egg Drop Problem/EggDrop.swift">
-      </FileRef>
-      <FileRef
-         location = "group:EggDrop.playground">
-      </FileRef>
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-   </Group>
-   <FileRef
-      location = "group:README.markdown">
-   </FileRef>
-   <FileRef
-      location = "group:LICENSE.txt">
-   </FileRef>
-   <FileRef
-      location = "group:Algorithm Design.markdown">
-   </FileRef>
-   <FileRef
-      location = "group:Big-O Notation.markdown">
-   </FileRef>
-   <FileRef
-      location = "group:.github/CONTRIBUTING.md">
-   </FileRef>
-   <FileRef
-      location = "group:Under Construction.markdown">
-   </FileRef>
-   <FileRef
-      location = "group:What are Algorithms.markdown">
-   </FileRef>
-   <FileRef
-      location = "group:Why Algorithms.markdown">
-   </FileRef>
-   <Group
-      location = "group:Myers Difference Algorithm"
-      name = "Myers Difference Algorithm">
-      <Group
-         location = "container:"
-         name = "Images">
-         <FileRef
-            location = "group:Myers Difference Algorithm/Images/EditGraph_k_move.png">
-         </FileRef>
-         <FileRef
-            location = "group:Myers Difference Algorithm/Images/EditGraph.png">
-         </FileRef>
-      </Group>
-      <FileRef
-         location = "group:/Users/a14757/Documents/Commiter/swift-algorithm-club/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift">
-      </FileRef>
-      <FileRef
-         location = "group:MyersDifferenceAlgorithm.playground">
-      </FileRef>
-      <FileRef
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-   </Group>
-   <Group
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-      </FileRef>
-   </Group>
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-      location = "container:"
-      name = "Dijkstra">
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-         </FileRef>
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-      name = "Trie">
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-         name = "images">
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-         name = "Images">
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-      <FileRef
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-      <FileRef
-         location = "group:ZetaAlgorithm.playground">
-      </FileRef>
-      <FileRef
-         location = "group:ZetaAlgorithm.swift">
-      </FileRef>
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-</Workspace>
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/swift-algorithm-club.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>
diff --git a/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings b/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
deleted file mode 100644
index 08de0be8d..000000000
--- a/swift-algorithm-club.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
-	<false/>
-</dict>
-</plist>

From ed5fca001429674c1f13557a166a19b73e7ba5e0 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.lau@instacart.com>
Date: Wed, 30 Oct 2019 14:43:34 -0400
Subject: [PATCH 596/643] Removes travis.yml

---
 .travis.yml | 55 -----------------------------------------------------
 1 file changed, 55 deletions(-)
 delete mode 100644 .travis.yml

diff --git a/.travis.yml b/.travis.yml
deleted file mode 100644
index 56e205656..000000000
--- a/.travis.yml
+++ /dev/null
@@ -1,55 +0,0 @@
-language: objective-c
-osx_image: xcode9
-# sudo: false
-
-install:
-
-- gem install xcpretty-travis-formatter
-# - ./install_swiftlint.sh
-
-script:
-
-- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Boyer-Moore-Horspool/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Bounded\ Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./B-Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Comb\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Convex\ Hull/Convex\ Hull.xcodeproj -scheme Tests -destination 'platform=iOS Simulator,name=iPhone 7,OS=11.0' | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Counting\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Depth-First\ Search/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Graph/Graph.xcodeproj -scheme GraphTests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Singly\ Linked\ List/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Minimum\ Spanning\ Tree\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Quicksort/Tests/Tests-Quicksort.xcodeproj -scheme Test-Quicksort | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Radix\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Rootish\ Array\ Stack/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Shortest\ Path\ \(Unweighted\)/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Topological\ Sort/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Treap/Treap/Treap.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Palindromes/Test/Test.xcodeproj -scheme Test | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Ternary\ Search\ Tree/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-- xcodebuild test -project ./Karatsuba\ Multiplication/Tests/Tests.xcodeproj -scheme Tests | xcpretty -f `xcpretty-travis-formatter`
-
-after_success:
-
-- if [[ "$TRAVIS_BRANCH" == "master" ]]; then ./gfm-render.sh; fi

From 7b08311b01bb7f4f2a261286e93e9cf7abe6da1b Mon Sep 17 00:00:00 2001
From: Robert Manson <robmanson@gmail.com>
Date: Sun, 3 Nov 2019 17:36:22 -0800
Subject: [PATCH 597/643] Fix infinite recursion in DFS

Fixes infinite recursion in the DFS algorithm for topological sort caused by graphs with cycles.
For example the following graph would previously have recursed indefinitely `a->b->a`.
---
 Topological Sort/TopologicalSort1.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
index 2ad9b51a0..05f1ab887 100644
--- a/Topological Sort/TopologicalSort1.swift	
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -1,6 +1,7 @@
 extension Graph {
   private func depthFirstSearch(_ source: Node, visited: inout [Node : Bool]) -> [Node] {
     var result = [Node]()
+    visited[source] = true
 
     if let adjacencyList = adjacencyList(forNode: source) {
       for nodeInAdjacencyList in adjacencyList {
@@ -10,7 +11,6 @@ extension Graph {
       }
     }
 
-    visited[source] = true
     return [source] + result
   }
 

From 0904c23f746bbbbfc5525ce32cf5c181c1eafe8e Mon Sep 17 00:00:00 2001
From: freak4pc <freak4pc@gmail.com>
Date: Sat, 9 Nov 2019 18:58:19 +0200
Subject: [PATCH 598/643] Use swapAt for Lomuto's partitioning

---
 Quicksort/Quicksort.playground/Contents.swift | 4 ++--
 Quicksort/README.markdown                     | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index 94d9f8e45..bbe5d9b7d 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -42,12 +42,12 @@ func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int
   var i = low
   for j in low..<high {
     if a[j] <= pivot {
-      (a[i], a[j]) = (a[j], a[i])
+      a.swapAt(i, j)
       i += 1
     }
   }
 
-  (a[i], a[high]) = (a[high], a[i])
+  a.swapAt(i, high)
   return i
 }
 
diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index f4145af5b..120ddc346 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -137,12 +137,12 @@ func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int
   var i = low
   for j in low..<high {
     if a[j] <= pivot {
-      (a[i], a[j]) = (a[j], a[i])
+	  a.swapAt(i, j)
       i += 1
     }
   }
 
-  (a[i], a[high]) = (a[high], a[i])
+  a.swapAt(i, high)
   return i
 }
 ```

From ce280b64b2315cef04b5c0b0924d4ca9d9a6599e Mon Sep 17 00:00:00 2001
From: Fabian Terh <fabianterh@gmail.com>
Date: Wed, 27 Nov 2019 17:22:04 +0800
Subject: [PATCH 599/643] Update Heap.swift

Time complexity of remove() is O(n + log n), which simplifies to O(n).
---
 Heap/Heap.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index cf39fb8a5..7560bc7b9 100755
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -212,7 +212,7 @@ extension Heap where T: Equatable {
     return nodes.index(where: { $0 == node })
   }
   
-  /** Removes the first occurrence of a node from the heap. Performance: O(n log n). */
+  /** Removes the first occurrence of a node from the heap. Performance: O(n). */
   @discardableResult public mutating func remove(node: T) -> T? {
     if let index = index(of: node) {
       return remove(at: index)

From 7762f6a884daa51e4acdb5677c664bec38273f5c Mon Sep 17 00:00:00 2001
From: TL <tommylohz@gmail.com>
Date: Fri, 29 Nov 2019 18:52:19 +0800
Subject: [PATCH 600/643] fix: add use case

---
 Skip-List/SkipList.playground/Contents.swift        | 13 +++++++++++++
 .../SkipList.playground/Sources/SkipList.swift      |  2 +-
 Skip-List/SkipList.swift                            |  2 +-
 3 files changed, 15 insertions(+), 2 deletions(-)

diff --git a/Skip-List/SkipList.playground/Contents.swift b/Skip-List/SkipList.playground/Contents.swift
index 1b4847c0e..55b9d3a23 100644
--- a/Skip-List/SkipList.playground/Contents.swift
+++ b/Skip-List/SkipList.playground/Contents.swift
@@ -5,3 +5,16 @@ print("Hello, Swift 4!")
 
 // SkipList is ready for Swift 4.
 // TODO: Add Test
+
+let k = SkipList<Int, String>()
+k.insert(key: 10, data: "10")
+k.insert(key: 12, data: "12")
+k.insert(key: 13, data: "13")
+k.insert(key: 20, data: "20")
+k.insert(key: 24, data: "24")
+
+if let value = k.get(key: 20) {
+  print(value)
+} else {
+  print("not found!")
+}
diff --git a/Skip-List/SkipList.playground/Sources/SkipList.swift b/Skip-List/SkipList.playground/Sources/SkipList.swift
index f626da0f8..186286977 100644
--- a/Skip-List/SkipList.playground/Sources/SkipList.swift
+++ b/Skip-List/SkipList.playground/Sources/SkipList.swift
@@ -212,7 +212,7 @@ extension SkipList {
     }
   }
 
-  func insert(key: Key, data: Payload) {
+  public func insert(key: Key, data: Payload) {
     if head != nil {
       if let node = findNode(key: key) {
         // replace, in case of key already exists.
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index fc635d0f2..8a1959f70 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -212,7 +212,7 @@ extension SkipList {
     }
   }
 
-  func insert(key: Key, data: Payload) {
+  public func insert(key: Key, data: Payload) {
     if head != nil {
       if let node = findNode(key: key) {
         // replace, in case of key already exists.

From b513c0331b79a520cd30569913a624eaae8fa7bb Mon Sep 17 00:00:00 2001
From: Kyle Nicol <54515183+TRGoCPftF@users.noreply.github.com>
Date: Tue, 10 Dec 2019 12:30:45 -0500
Subject: [PATCH 601/643] Update simann_example.swift

Corrected definition where shuffle() was invoking self.shuffle() instead of self.tour.shuffle(), which would left the example in a infinite loop of shuffle() invocation
---
 Simulated annealing/simann_example.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Simulated annealing/simann_example.swift b/Simulated annealing/simann_example.swift
index 0e07e0024..e7933c89a 100644
--- a/Simulated annealing/simann_example.swift	
+++ b/Simulated annealing/simann_example.swift	
@@ -138,7 +138,7 @@ extension Tour {
   }
 
   func shuffle() {
-    self.shuffle()
+    self.tour.shuffle()
   }
 }
 

From 809cb974dc0b105407500f42e675c55f55e1588b Mon Sep 17 00:00:00 2001
From: "G. Moraleda" <guille.moraleda@gmail.com>
Date: Wed, 22 Jan 2020 17:51:05 +0100
Subject: [PATCH 602/643] Typos corrected

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

diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 297bc4b0f..95f020e90 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -25,10 +25,10 @@ In code this looks as follows:
 func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
   var leftBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] < key {
+      if array[midIndex] < key {
         low = midIndex + 1
       } else {
         high = midIndex
@@ -39,10 +39,10 @@ func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
 
   var rightBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if a[midIndex] > key {
+      if array[midIndex] > key {
         high = midIndex
       } else {
         low = midIndex + 1
@@ -62,7 +62,7 @@ To test this algorithm, copy the code to a playground and then do:
 ```swift
 let a = [ 0, 1, 1, 3, 3, 3, 3, 6, 8, 10, 11, 11 ]
 
-countOccurrencesOfKey(3, inArray: a)  // returns 4
+countOccurrences(of: 3, in: a)  // returns 4
 ```
 
 > **Remember:** If you use your own array, make sure it is sorted first!

From 8a7db67f4f0e1706a3a91054f1b7aecc6ac95761 Mon Sep 17 00:00:00 2001
From: "G. Moraleda" <guille.moraleda@gmail.com>
Date: Wed, 22 Jan 2020 19:57:53 +0100
Subject: [PATCH 603/643] Update README.markdown

---
 Count Occurrences/README.markdown | 14 ++++++++------
 1 file changed, 8 insertions(+), 6 deletions(-)

diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 95f020e90..2e48d1020 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -22,13 +22,13 @@ The trick is to use two binary searches, one to find where the `3`s start (the l
 In code this looks as follows:
 
 ```swift
-func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
+func countOccurrences<T: Comparable>(of key: T, in a: [T]) -> Int {
   var leftBoundary: Int {
     var low = 0
-    var high = array.count
+    var high = a.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if array[midIndex] < key {
+      if a[midIndex] < key {
         low = midIndex + 1
       } else {
         high = midIndex
@@ -39,10 +39,10 @@ func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
 
   var rightBoundary: Int {
     var low = 0
-    var high = array.count
+    var high = a.count
     while low < high {
       let midIndex = low + (high - low)/2
-      if array[midIndex] > key {
+      if a[midIndex] > key {
         high = midIndex
       } else {
         low = midIndex + 1
@@ -55,7 +55,9 @@ func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
 }
 ```
 
-Notice that the variables `leftBoundary` and `rightBoundary` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.  Also, notice that we constrain the type `T` to be Comparable so that the algorithm can be applied to an array of Strings, Ints or other types that conform to the Swift Comparable protocol.
+Notice that the variables `leftBoundary` and `rightBoundary` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.  Also, notice that we constrain the type `T` to be Comparable so that the algorithm can be applied to an 
+
+y of Strings, Ints or other types that conform to the Swift Comparable protocol.
 
 To test this algorithm, copy the code to a playground and then do:
 

From 467503c623c0fa781ea337b68a2ee5251d9a20bc Mon Sep 17 00:00:00 2001
From: "G. Moraleda" <guille.moraleda@gmail.com>
Date: Wed, 22 Jan 2020 19:58:38 +0100
Subject: [PATCH 604/643] Update README.markdown

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

diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 2e48d1020..4deb9990e 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -55,9 +55,7 @@ func countOccurrences<T: Comparable>(of key: T, in a: [T]) -> Int {
 }
 ```
 
-Notice that the variables `leftBoundary` and `rightBoundary` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.  Also, notice that we constrain the type `T` to be Comparable so that the algorithm can be applied to an 
-
-y of Strings, Ints or other types that conform to the Swift Comparable protocol.
+Notice that the variables `leftBoundary` and `rightBoundary` are very similar to the [binary search](../Binary%20Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.  Also, notice that we constrain the type `T` to be Comparable so that the algorithm can be applied to an array of Strings, Ints or other types that conform to the Swift Comparable protocol.
 
 To test this algorithm, copy the code to a playground and then do:
 

From 43181f5b4c8790fa887c4a6bd5ea8e94b0279eb5 Mon Sep 17 00:00:00 2001
From: Satveer Singh <satveer.y.singh@gmail.com>
Date: Thu, 6 Feb 2020 19:30:24 +1100
Subject: [PATCH 605/643] Fix typo in Heap Sort README lg -> log

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

diff --git a/Heap Sort/README.markdown b/Heap Sort/README.markdown
index a45dad6f9..5bec58626 100644
--- a/Heap Sort/README.markdown	
+++ b/Heap Sort/README.markdown	
@@ -42,7 +42,7 @@ As you can see, the largest items are making their way to the back. We repeat th
 
 > **Note:** This process is very similar to [selection sort](../Selection%20Sort/), which repeatedly looks for the minimum item in the remainder of the array. Extracting the minimum or maximum value is what heaps are good at.
 
-Performance of heap sort is **O(n lg n)** in best, worst, and average case. Because we modify the array directly, heap sort can be performed in-place. But it is not a stable sort: the relative order of identical elements is not preserved.
+Performance of heap sort is **O(n log n)** in best, worst, and average case. Because we modify the array directly, heap sort can be performed in-place. But it is not a stable sort: the relative order of identical elements is not preserved.
 
 Here's how you can implement heap sort in Swift:
 

From f664af1f502ec7f6692e8dcb34d5848ce3af4e60 Mon Sep 17 00:00:00 2001
From: "G. Moraleda" <guille.moraleda@gmail.com>
Date: Mon, 10 Feb 2020 20:01:47 +0100
Subject: [PATCH 606/643] Renamed array

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

diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 4deb9990e..8e935ea58 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -22,10 +22,10 @@ The trick is to use two binary searches, one to find where the `3`s start (the l
 In code this looks as follows:
 
 ```swift
-func countOccurrences<T: Comparable>(of key: T, in a: [T]) -> Int {
+func countOccurrences<T: Comparable>(of key: T, in array: [T]) -> Int {
   var leftBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
       if a[midIndex] < key {
@@ -39,7 +39,7 @@ func countOccurrences<T: Comparable>(of key: T, in a: [T]) -> Int {
 
   var rightBoundary: Int {
     var low = 0
-    var high = a.count
+    var high = array.count
     while low < high {
       let midIndex = low + (high - low)/2
       if a[midIndex] > key {

From 901aaeac47c2275d0e5facbf9c5525882eb4f7ea Mon Sep 17 00:00:00 2001
From: Paul Anguiano <paul@gentleworks.com>
Date: Thu, 5 Mar 2020 18:10:39 -0800
Subject: [PATCH 607/643] Modified Trie to add prefix support to boolean
 contains(), plus unit tests.

---
 Trie/Trie/Trie/Trie.swift           |  9 ++++++---
 Trie/Trie/TrieTests/TrieTests.swift | 27 ++++++++++++++++++++++++++-
 2 files changed, 32 insertions(+), 4 deletions(-)

diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index accc7b61c..3d5031cf3 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -117,9 +117,12 @@ extension Trie {
 
   /// Determines whether a word is in the trie.
   ///
-  /// - Parameter word: the word to check for
+  /// - Parameters:
+  ///   - word: the word to check for
+  ///   - matchPrefix: whether the search word should match
+  ///   if it is only a prefix of other nodes in the trie
   /// - Returns: true if the word is present, false otherwise.
-  func contains(word: String) -> Bool {
+  func contains(word: String, matchPrefix: Bool = false) -> Bool {
     guard !word.isEmpty else {
       return false
     }
@@ -130,7 +133,7 @@ extension Trie {
       }
       currentNode = childNode
     }
-    return currentNode.isTerminating
+    return matchPrefix || currentNode.isTerminating
   }
 
   /// Attempts to walk to the last node of a word.  The
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index 0c5bc69c6..59da2cd9b 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -167,7 +167,8 @@ class TrieTests: XCTestCase {
     let trieCopy = NSKeyedUnarchiver.unarchiveObject(withFile: filePath) as? Trie
     XCTAssertEqual(trieCopy?.count, trie.count)
   }
-
+  
+  /// Tests whether word prefixes are properly found and returned.
   func testFindWordsWithPrefix() {
     let trie = Trie()
     trie.insert(word: "test")
@@ -190,4 +191,28 @@ class TrieTests: XCTestCase {
     let wordsUpperCase = trie.findWordsWithPrefix(prefix: "Te")
     XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"])
   }
+
+  /// Tests whether word prefixes are properly detected on a boolean contains() check.
+  func testContainsWordMatchPrefix() {
+    let trie = Trie()
+    trie.insert(word: "test")
+    trie.insert(word: "another")
+    trie.insert(word: "exam")
+    let wordsAll = trie.contains(word: "", matchPrefix: true)
+    XCTAssertEqual(wordsAll, true)
+    let words = trie.contains(word: "ex", matchPrefix: true)
+    XCTAssertEqual(words, true)
+    trie.insert(word: "examination")
+    let words2 = trie.contains(word: "exam", matchPrefix: true)
+    XCTAssertEqual(words2, true)
+    let noWords = trie.contains(word: "tee", matchPrefix: true)
+    XCTAssertEqual(noWords, false)
+    let unicodeWord = "😬😎"
+    trie.insert(word: unicodeWord)
+    let wordsUnicode = trie.contains(word: "😬", matchPrefix: true)
+    XCTAssertEqual(wordsUnicode, true)
+    trie.insert(word: "Team")
+    let wordsUpperCase = trie.contains(word: "Te", matchPrefix: true)
+    XCTAssertEqual(wordsUpperCase, true)
+  }
 }

From 510f3da1a0e445c3c1ec4aec69f1731a86acfbc4 Mon Sep 17 00:00:00 2001
From: Mick Bennett <mjbennett31@gmail.com>
Date: Fri, 27 Mar 2020 00:00:03 -0700
Subject: [PATCH 608/643] updated depricated hashable values to hash into
 methods

---
 Graph/Graph/Edge.swift   | 10 ++++------
 Graph/Graph/Vertex.swift |  5 +++--
 2 files changed, 7 insertions(+), 8 deletions(-)

diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index ac5ed6a25..b69937895 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -29,12 +29,10 @@ extension Edge: CustomStringConvertible {
 
 extension Edge: Hashable {
 
-  public var hashValue: Int {
-    var string = "\(from.description)\(to.description)"
-    if weight != nil {
-      string.append("\(weight!)")
-    }
-    return string.hashValue
+  public func hash(into hasher: inout Hasher) {
+    hasher.combine(from.description)
+    hasher.combine(to.description)
+    hasher.combine(weight)
   }
 }
 
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index 758a367bb..47499dcc6 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -24,8 +24,9 @@ extension Vertex: CustomStringConvertible {
 
 extension Vertex: Hashable {
 
-  public var hashValue: Int {
-    return "\(data)\(index)".hashValue
+  public func hash(into hasher: inout Hasher) {
+    hasher.combine(data)
+    hasher.combine(index)
   }
 
 }

From 47356447f47fc353cb95dcdcc9a4d296b1a1b816 Mon Sep 17 00:00:00 2001
From: Mick Bennett <mjbennett31@gmail.com>
Date: Thu, 9 Apr 2020 16:47:58 -0700
Subject: [PATCH 609/643] updated lcs string extension to access string
 directly

---
 .../Contents.swift                                 | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift
index c8d413e7f..0e78b7043 100644
--- a/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
+++ b/Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift	
@@ -1,4 +1,4 @@
-// last checked with Xcode 9.0b4
+// last checked with Xcode 11.4
 #if swift(>=4.0)
 print("Hello, Swift 4!")
 #endif
@@ -7,10 +7,10 @@ extension String {
   public func longestCommonSubsequence(_ other: String) -> String {
 
     func lcsLength(_ other: String) -> [[Int]] {
-      var matrix = [[Int]](repeating: [Int](repeating: 0, count: other.characters.count+1), count: self.characters.count+1)
+      var matrix = [[Int]](repeating: [Int](repeating: 0, count: other.count+1), count: self.count+1)
 
-      for (i, selfChar) in self.characters.enumerated() {
-        for (j, otherChar) in other.characters.enumerated() {
+      for (i, selfChar) in self.enumerated() {
+        for (j, otherChar) in other.enumerated() {
           if otherChar == selfChar {
             matrix[i+1][j+1] = matrix[i][j] + 1
           } else {
@@ -22,8 +22,8 @@ extension String {
     }
 
     func backtrack(_ matrix: [[Int]]) -> String {
-      var i = self.characters.count
-      var j = other.characters.count
+      var i = self.count
+      var j = other.count
       var charInSequence = self.endIndex
 
       var lcs = String()
@@ -41,7 +41,7 @@ extension String {
           lcs.append(self[charInSequence])
         }
       }
-      return String(lcs.characters.reversed())
+      return String(lcs.reversed())
     }
 
     return backtrack(lcsLength(other))

From 5b0861c2eca8ec37ed3f2667ada5de7e850cd75e Mon Sep 17 00:00:00 2001
From: Azhar Anwar <azharcodes@gmail.com>
Date: Tue, 28 Apr 2020 15:52:03 +0530
Subject: [PATCH 610/643] fixes: typo and punctuation

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

diff --git a/Shuffle/README.markdown b/Shuffle/README.markdown
index 5a2a07a98..d9c35868a 100644
--- a/Shuffle/README.markdown
+++ b/Shuffle/README.markdown
@@ -37,7 +37,7 @@ This code works just fine but it's not very efficient. Removing an element from
 
 ## The Fisher-Yates / Knuth shuffle
 
-Here is a much improved version of the shuffle algorithm:
+Here is a much-improved version of the shuffle algorithm:
 
 ```swift
 extension Array {
@@ -52,7 +52,7 @@ extension Array {
 }
 ```
 
-Again, this picks objects at random. In the naive version we placed those objects into a new temporary array so we could keep track of which objects were already shuffled and which still remained to be done. In this improved algorithm, however, we'll move the shuffled objects to the end of the original array. 
+Again, this picks objects at random. In the naive version, we placed those objects into a new temporary array so we could keep track of which objects were already shuffled and which still remained to be done. In this improved algorithm, however, we'll move the shuffled objects to the end of the original array. 
 
 Let's walk through the example. We have the array:
 
@@ -116,7 +116,7 @@ The `shuffledArray()` function first creates a new array with `n` zeros. Then it
 
 For this function, `The condition that checks if j ≠ i may be omitted in languages that have no problems accessing uninitialized array values, and for which assigning is cheaper than comparing.`, you can check it in wiki. And also remove checking logic will optimise performance.
 
-The algoritm is quite clever and I suggest you walk through an example yourself, either on paper or in the playground. (Hint: Again it splits the array into two regions.)
+The algorithm is quite clever and I suggest you walk through an example yourself, either on paper or in the playground. (Hint: Again it splits the array into two regions.)
 
 ## See also
 

From 409ffd6921441afb56a7ea68c73a0f2c9516c809 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sarp=20G=C3=BCney=20Ba=C5=9Faraner?=
 <sarpbasaraner@gmail.com>
Date: Thu, 7 May 2020 10:35:45 +0300
Subject: [PATCH 611/643] fix typo

Dinstance -> Distance
---
 HaversineDistance/HaversineDistance.playground/Contents.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index 3d8d60f54..ed89b4462 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -1,6 +1,6 @@
 import UIKit
 
-func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
+func haversineDistance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
     
     let haversin = { (angle: Double) -> Double in
         return (1 - cos(angle))/2
@@ -27,4 +27,4 @@ let amsterdam = (52.3702, 4.8952)
 let newYork = (40.7128, -74.0059)
 
 // Google says it's 5857 km so our result is only off by 2km which could be due to all kinds of things, not sure how google calculates the distance or which latitude and longitude google uses to calculate the distance.
-haversineDinstance(la1: amsterdam.0, lo1: amsterdam.1, la2: newYork.0, lo2: newYork.1)
+haversineDistance(la1: amsterdam.0, lo1: amsterdam.1, la2: newYork.0, lo2: newYork.1)

From 7a77f3fa8abbdc0ee68b77b84d56b3e1eaf61087 Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 11:57:00 -0500
Subject: [PATCH 612/643] Update Readme for code modification

Update to reflect alternative of using .isMultiple(of:) method instead of modulo (%) operator
---
 Fizz Buzz/README.markdown | 97 ++++++++++++++++++++++++++++-----------
 1 file changed, 69 insertions(+), 28 deletions(-)

diff --git a/Fizz Buzz/README.markdown b/Fizz Buzz/README.markdown
index 8c250da27..be516bd46 100644
--- a/Fizz Buzz/README.markdown	
+++ b/Fizz Buzz/README.markdown	
@@ -16,46 +16,48 @@ The modulus operator `%` is the key to solving fizz buzz.
 
 The modulus operator returns the remainder after an integer division. Here is an example of the modulus operator:
 
-| Division      | Division Result            | Modulus         | Modulus Result  |
-| ------------- | -------------------------- | --------------- | ---------------:|
-| 1 / 3       | 0 with a remainder of 3  | 1 % 3         | 1             |
-| 5 / 3       | 1 with a remainder of 2  | 5 % 3         | 2             |
-| 16 / 3      | 5 with a remainder of 1  | 16 % 3        | 1             |
+| Division    | Division Result       | Modulus       | Modulus Result|
+| ----------- | --------------------- | ------------- | :-----------: |
+| 1 / 3       | 0 with a remainder of 3 | 1 % 3         | 1             |
+| 5 / 3       | 1 with a remainder of 2 | 5 % 3         | 2             |
+| 16 / 3      | 5 with a remainder of 1 | 16 % 3        | 1             |
 
 A common approach to determine if a number is even or odd is to use the modulus operator:
 
-| Modulus       | Result          | Swift Code                      | Swift Code Result | Comment                                       |
-| ------------- | ---------------:| ------------------------------- | -----------------:| --------------------------------------------- |
-| 6 % 2       | 0               | `let isEven = (number % 2 == 0)`  | `true`            | If a number is divisible by 2 it is *even*    |
-| 5 % 2       | 1               | `let isOdd = (number % 2 != 0)`   | `true`            | If a number is not divisible by 2 it is *odd* |
+| Modulus  | Result | Swift Code                       | Swift Code<br>Result | Comment                                    |
+| -------- | :-----:| -------------------------------- | :----------------:| --------------------------------------------- |
+| 6 % 2    | 0      | `let isEven = (number % 2 == 0)` | `true`            | If a number is divisible by 2 it is *even*    |
+| 5 % 2    | 1      | `let isOdd = (number % 2 != 0)`  | `true`            | If a number is not divisible by 2 it is *odd* |
+
+Alternatively, Swift's built in function .isMultiple(of:) can be used, i.e. 6.isMultiple(of: 2) will return true, 5.isMultiple(of: 2) will return false
 
 ## Solving fizz buzz
 
-Now we can use the modulus operator `%` to solve fizz buzz.
+Now we can use the modulus operator `%` or .isMultiple(of:) method to solve fizz buzz.
 
 Finding numbers divisible by three:
 
-| Modulus | Modulus Result | Swift Code    | Swift Code Result |
-| ------- | --------------:| ------------- |------------------:|
-| 1 % 3 | 1            | `1 % 3 == 0`  | `false`           |
-| 2 % 3 | 2            | `2 % 3 == 0`  | `false`           |
-| 3 % 3 | 0            | `3 % 3 == 0`  | `true`            |
-| 4 % 3 | 1            | `4 % 3 == 0`  | `false`           |
+| Modulus | Modulus<br>Result | Swift Code<br>using Modulo | Swift Code<br>using .isMultiple(of:) | Swift Code<br>Result |
+| ------- | :---------------: | -------------------------- | ------------------------------------ | ------------------- |
+|1 % 3    | 1                 | `1 % 3 == 0`               | `1.isMultiple(of: 3)`                | `false`              |
+|2 % 3    | 2                 | `2 % 3 == 0`               | `2.isMultiple(of: 3)`                | `false`              |
+|3 % 3    | 0                 | `3 % 3 == 0`               | `3.isMultiple(of: 3)`                | `true`               |
+|4 % 3    | 1                 | `4 % 3 == 0`               | `4.isMultiple(of: 3)`                | `false`              |
 
 Finding numbers divisible by five:
 
-| Modulus | Modulus Result | Swift Code    | Swift Code Result |
-| ------- | --------------:| ------------- |------------------:|
-| 1 % 5 | 1            | `1 % 5 == 0`  | `false`           |
-| 2 % 5 | 2            | `2 % 5 == 0`  | `false`           |
-| 3 % 5 | 3            | `3 % 5 == 0`  | `false`           |
-| 4 % 5 | 4            | `4 % 5 == 0`  | `false`           |
-| 5 % 5 | 0            | `5 % 5 == 0`  | `true`            |
-| 6 % 5 | 1            | `6 % 5 == 0`  | `false`           |
+| Modulus | Modulus<br>Result | Swift Code<br>using Modulo | Swift Code<br>using .isMultiple(of:) | Swift Code<br>Result |
+| ------- | :---------------: | -------------------------- | ------------------------------------ | -------------------- |
+| 1 % 5   | 1                 | `1 % 5 == 0`               | `1.isMultiple(of: 5)`                | `false`              |
+| 2 % 5   | 2                 | `2 % 5 == 0`               | `2.isMultiple(of: 5)`                | `false`              |
+| 3 % 5   | 3                 | `3 % 5 == 0`               | `3.isMultiple(of: 5)`                | `false`              |
+| 4 % 5   | 4                 | `4 % 5 == 0`               | `4.isMultiple(of: 5)`                | `false`              |
+| 5 % 5   | 0                 | `5 % 5 == 0`               | `5.isMultiple(of: 5)`                | `true`               |
+| 6 % 5   | 1                 | `6 % 5 == 0`               | `6.isMultiple(of: 5)`                | `false`              |
 
 ## The code
 
-Here is a simple implementation in Swift:
+Here is a simple implementation in Swift using Modulus approach
 
 ```swift
 func fizzBuzz(_ numberOfTurns: Int) {
@@ -79,7 +81,31 @@ func fizzBuzz(_ numberOfTurns: Int) {
 }
 ```
 
-Put this code in a playground and test it like so:
+Here is simple implementation in Swift using .isMultiple(of:) and switch statement
+
+```swift
+func fizzBuzz(_ numberOfTurns: Int) {
+    guard numberOfTurns >= 1 else {
+        print("Number of turns must be >= 1")
+        return
+    }
+    
+    for i in 1...numberOfTurns {
+        switch (i.isMultiple(of: 3), i.isMultiple(of: 5)) {
+        case (false, false):
+            print("\(i)")
+        case (true, false):
+            print("Fizz")
+        case (false, true):
+            print("Buzz")
+        case (true, true):
+            print("Fizz Buzz")
+        }
+    }
+}
+```
+
+Put either code in a playground and test it like so:
 
 ```swift
 fizzBuzz(15)
@@ -87,10 +113,25 @@ fizzBuzz(15)
 
 This will output:
 
-	1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, Fizz Buzz
+1    
+2   
+Fizz   
+4   
+Buzz    
+Fizz  
+7   
+8   
+Fizz   
+Buzz   
+11   
+Fizz  
+13   
+14    
+Fizz Buzz  
 
 ## See also
 
 [Fizz buzz on Wikipedia](https://en.wikipedia.org/wiki/Fizz_buzz)
 
-*Written by [Chris Pilcher](https://github.com/chris-pilcher)*
+*Originally written by [Chris Pilcher](https://github.com/chris-pilcher)*<br>
+*Updated by [Lance Rettberg](https://github.com/l-rettberg)*

From 99d769d03c0cfee1b92b63aeeb1b203811eaddc8 Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 12:02:06 -0500
Subject: [PATCH 613/643] Update FizzBuzz

Update to 1) add guard, 2) use .isMultiple(of:), 3) use switch statement
---
 Fizz Buzz/FizzBuzz.swift | 32 +++++++++++++++++---------------
 1 file changed, 17 insertions(+), 15 deletions(-)

diff --git a/Fizz Buzz/FizzBuzz.swift b/Fizz Buzz/FizzBuzz.swift
index b6bb410e7..704ea7c6b 100644
--- a/Fizz Buzz/FizzBuzz.swift	
+++ b/Fizz Buzz/FizzBuzz.swift	
@@ -1,19 +1,21 @@
-func fizzBuzz(_ numberOfTurns: Int) {
-  for i in 1...numberOfTurns {
-    var result = ""
+// Updated for Xcode Version 11.4.1 (11E503a)
 
-    if i % 3 == 0 {
-      result += "Fizz"
+func fizzBuzz2(_ numberOfTurns: Int) {
+    guard numberOfTurns >= 1 else {
+        print("Number of turns must be >= 1")
+        return
     }
-
-    if i % 5 == 0 {
-      result += (result.isEmpty ? "" : " ") + "Buzz"
-    }
-
-    if result.isEmpty {
-      result += "\(i)"
+    
+    for i in 1...numberOfTurns {
+        switch (i.isMultiple(of: 3), i.isMultiple(of: 5)) {
+        case (false, false):
+            print("\(i)")
+        case (true, false):
+            print("Fizz")
+        case (false, true):
+            print("Buzz")
+        case (true, true):
+            print("Fizz Buzz")
+        }
     }
-
-    print(result)
-  }
 }

From 71431b12042a2dc17eb9c170a9fa5c731942462d Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 12:09:54 -0500
Subject: [PATCH 614/643] Update

---
 Fizz Buzz/FizzBuzz.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Fizz Buzz/FizzBuzz.swift b/Fizz Buzz/FizzBuzz.swift
index 704ea7c6b..2e66b26f4 100644
--- a/Fizz Buzz/FizzBuzz.swift	
+++ b/Fizz Buzz/FizzBuzz.swift	
@@ -1,6 +1,6 @@
 // Updated for Xcode Version 11.4.1 (11E503a)
 
-func fizzBuzz2(_ numberOfTurns: Int) {
+func fizzBuzz(_ numberOfTurns: Int) {
     guard numberOfTurns >= 1 else {
         print("Number of turns must be >= 1")
         return

From f94bccc68d017bbc61cb774f7642dd25b25f1d4a Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 14:41:39 -0500
Subject: [PATCH 615/643] Updates to 1) add guard, 2) use .isMultiple(of:) and
 3) use switch statement

---
 Fizz Buzz/FizzBuzz.playground/Contents.swift | 34 ++++++++++----------
 Fizz Buzz/FizzBuzz.swift                     |  4 +--
 2 files changed, 19 insertions(+), 19 deletions(-)

diff --git a/Fizz Buzz/FizzBuzz.playground/Contents.swift b/Fizz Buzz/FizzBuzz.playground/Contents.swift
index ae966bbcc..2ab13b362 100644
--- a/Fizz Buzz/FizzBuzz.playground/Contents.swift	
+++ b/Fizz Buzz/FizzBuzz.playground/Contents.swift	
@@ -1,23 +1,23 @@
-// last checked with Xcode 10.0 (10A255)
+// Last checked with Xcode Version 11.4.1 (11E503a)
 
 func fizzBuzz(_ numberOfTurns: Int) {
-  for i in 1...numberOfTurns {
-    var result = ""
-
-    if i % 3 == 0 {
-      result += "Fizz"
+    guard numberOfTurns >= 1 else {
+        print("Number of turns must be >= 1")
+        return
     }
-
-    if i % 5 == 0 {
-      result += (result.isEmpty ? "" : " ") + "Buzz"
+    
+    for i in 1...numberOfTurns {
+        switch (i.isMultiple(of: 3), i.isMultiple(of: 5)) {
+        case (false, false):
+            print("\(i)")
+        case (true, false):
+            print("Fizz")
+        case (false, true):
+            print("Buzz")
+        case (true, true):
+            print("Fizz Buzz")
+        }
     }
-
-    if result.isEmpty {
-      result += "\(i)"
-    }
-
-    print(result)
-  }
 }
 
-fizzBuzz(100)
+fizzBuzz(15)
diff --git a/Fizz Buzz/FizzBuzz.swift b/Fizz Buzz/FizzBuzz.swift
index 2e66b26f4..bf753e648 100644
--- a/Fizz Buzz/FizzBuzz.swift	
+++ b/Fizz Buzz/FizzBuzz.swift	
@@ -1,4 +1,4 @@
-// Updated for Xcode Version 11.4.1 (11E503a)
+// Last checked with Xcode Version 11.4.1 (11E503a)
 
 func fizzBuzz(_ numberOfTurns: Int) {
     guard numberOfTurns >= 1 else {
@@ -18,4 +18,4 @@ func fizzBuzz(_ numberOfTurns: Int) {
             print("Fizz Buzz")
         }
     }
-}
+}
\ No newline at end of file

From 6a9ec9628099601714655ad42237d8948b2cfc05 Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 16:45:31 -0500
Subject: [PATCH 616/643] Remove file

---
 Fizz Buzz/FizzBuzz.playground/contents.xcplayground | 4 ----
 1 file changed, 4 deletions(-)
 delete mode 100644 Fizz Buzz/FizzBuzz.playground/contents.xcplayground

diff --git a/Fizz Buzz/FizzBuzz.playground/contents.xcplayground b/Fizz Buzz/FizzBuzz.playground/contents.xcplayground
deleted file mode 100644
index 5da2641c9..000000000
--- a/Fizz Buzz/FizzBuzz.playground/contents.xcplayground	
+++ /dev/null
@@ -1,4 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
-<playground version='5.0' target-platform='ios'>
-    <timeline fileName='timeline.xctimeline'/>
-</playground>
\ No newline at end of file

From e3b3126f819ec57b9759cd4b80f639b1d39b440a Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 16:47:18 -0500
Subject: [PATCH 617/643] Delete IDEWorkspaceChecks.plist

---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 --------
 1 file changed, 8 deletions(-)
 delete mode 100644 Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
deleted file mode 100644
index 18d981003..000000000
--- a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-<dict>
-	<key>IDEDidComputeMac32BitWarning</key>
-	<true/>
-</dict>
-</plist>

From 51b0c2b5a2abed1a90241e64869ccd173b54a1e7 Mon Sep 17 00:00:00 2001
From: L Rettberg <lrettberg@outlook.com>
Date: Sat, 9 May 2020 16:47:30 -0500
Subject: [PATCH 618/643] Delete contents.xcworkspacedata

---
 .../playground.xcworkspace/contents.xcworkspacedata        | 7 -------
 1 file changed, 7 deletions(-)
 delete mode 100644 Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata b/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata
deleted file mode 100644
index 919434a62..000000000
--- a/Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata	
+++ /dev/null
@@ -1,7 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<Workspace
-   version = "1.0">
-   <FileRef
-      location = "self:">
-   </FileRef>
-</Workspace>

From 4617d9401be60101c12e100f428c0b460de0a210 Mon Sep 17 00:00:00 2001
From: jinthislife <8064873+jinthislife@users.noreply.github.com>
Date: Mon, 11 May 2020 15:30:38 +1000
Subject: [PATCH 619/643] Update README.markdown

remove duplicate parameter
---
 Binary Search Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index 0b382f204..57d1f4bff 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -557,7 +557,7 @@ As a result, doing `tree.search(100)` gives nil.
 You can check whether a tree is a valid binary search tree with the following method:
 
 ```swift
-  public func isBST(minValue minValue: T, maxValue: T) -> Bool {
+  public func isBST(minValue: T, maxValue: T) -> Bool {
     if value < minValue || value > maxValue { return false }
     let leftBST = left?.isBST(minValue: minValue, maxValue: value) ?? true
     let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true

From bf3f3d5d690fe0a6e3cd7fc549781551477a8c6b Mon Sep 17 00:00:00 2001
From: Jagdeep Matharu <jagdeepmatharu88@gmail.com>
Date: Sun, 31 May 2020 19:54:14 -0400
Subject: [PATCH 620/643] Updating Counting sort for stability

---
 Counting Sort/CountingSort.playground/Contents.swift | 7 ++++++-
 Counting Sort/CountingSort.swift                     | 5 ++++-
 Counting Sort/README.markdown                        | 7 +++++--
 3 files changed, 15 insertions(+), 4 deletions(-)

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index dc375512a..839b16bc8 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -29,12 +29,17 @@ func countingSort(array: [Int]) throws -> [Int] {
 
   // Step 3
   // Place the element in the final array as per the number of elements before it
+  // Loop through the array in reverse to keep the stability of the new array
+  // (i.e. 7, is at index 3 and 6, thus in sortedArray the position of 7 at index 3 should be before 7 at index 6
   var sortedArray = [Int](repeating: 0, count: array.count)
-  for element in array {
+  for index in stride(from: array.count - 1, through: 0, by: -1) {
+    let element = array[index]
     countArray[element] -= 1
     sortedArray[countArray[element]] = element
   }
+    
   return sortedArray
 }
 
 try countingSort(array: [10, 9, 8, 7, 1, 2, 7, 3])
+
diff --git a/Counting Sort/CountingSort.swift b/Counting Sort/CountingSort.swift
index 725a634a4..68dcf5c0d 100644
--- a/Counting Sort/CountingSort.swift	
+++ b/Counting Sort/CountingSort.swift	
@@ -29,8 +29,11 @@ func countingSort(_ array: [Int])-> [Int] {
 
   // Step 3
   // Place the element in the final array as per the number of elements before it
+  // Loop through the array in reverse to keep the stability of the new sorted array
+  // (For Example: 7 is at index 3 and 6, thus in sortedArray the position of 7 at index 3 should be before 7 at index 6
   var sortedArray = [Int](repeating: 0, count: array.count)
-  for element in array {
+  for index in stride(from: array.count - 1, through: 0, by: -1) {
+    let element = array[index]
     countArray[element] -= 1
     sortedArray[countArray[element]] = element
   }
diff --git a/Counting Sort/README.markdown b/Counting Sort/README.markdown
index 959becc8c..93d6635bd 100644
--- a/Counting Sort/README.markdown	
+++ b/Counting Sort/README.markdown	
@@ -50,7 +50,9 @@ The code for step 2 is:
 
 ### Step 3:
 
-This is the last step in the algorithm. Each element in the original array is placed at the position defined by the output of step 2. For example, the number 10 would be placed at an index of 7 in the output array. Also, as you place the elements you need to reduce the count by 1 as those many elements are reduced from the array.
+This is the last step in the algorithm. Each element in the original array is placed at the position defined by the output of step 2. For example, the number 10 would be placed at an index of 7 in the output array. Also, as you place the elements you need to reduce the count by 1 as those many elements are reduced from the array. 
+We also have to loop through the array in reverse to keep the stability of the new sorted array.
+For Example: 7 is at index 3 and 6, thus in sortedArray the position of 7 at index 3 should be before 7 at index 6.
 
 The final output would be:
 
@@ -63,7 +65,8 @@ Here is the code for this final step:
 
 ```swift
   var sortedArray = [Int](repeating: 0, count: array.count)
-  for element in array {
+  for index in stride(from: array.count - 1, through: 0, by: -1) {
+    let element = array[index]
     countArray[element] -= 1
     sortedArray[countArray[element]] = element
   }

From d06b7e3c5e45a65b2f275a7dd81bfc77520788c6 Mon Sep 17 00:00:00 2001
From: Jagdeep Matharu <jagdeepmatharu88@gmail.com>
Date: Sun, 31 May 2020 19:54:43 -0400
Subject: [PATCH 621/643] Updating Counting sort tests project to support Swift
 5

---
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 Counting Sort/Tests/Tests.xcodeproj/project.pbxproj       | 5 +++--
 .../xcshareddata/IDEWorkspaceChecks.plist                 | 8 ++++++++
 3 files changed, 19 insertions(+), 2 deletions(-)
 create mode 100644 Counting Sort/CountingSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Counting Sort/CountingSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Counting Sort/CountingSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Counting Sort/CountingSort.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj b/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj
index 5cbb0d4aa..aaa6c1b6b 100644
--- a/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj	
+++ b/Counting Sort/Tests/Tests.xcodeproj/project.pbxproj	
@@ -97,6 +97,7 @@
 			developmentRegion = English;
 			hasScannedForEncodings = 0;
 			knownRegions = (
+				English,
 				en,
 				Base,
 			);
@@ -226,7 +227,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 5.0;
 			};
 			name = Debug;
 		};
@@ -238,7 +239,7 @@
 				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks";
 				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
 				PRODUCT_NAME = "$(TARGET_NAME)";
-				SWIFT_VERSION = 3.0;
+				SWIFT_VERSION = 5.0;
 			};
 			name = Release;
 		};
diff --git a/Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Counting Sort/Tests/Tests.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist	
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

From bf38b12ddc30c6e396a50e61e3dc342ced28e538 Mon Sep 17 00:00:00 2001
From: Jagdeep Matharu <jagdeepmatharu88@gmail.com>
Date: Sun, 31 May 2020 19:58:21 -0400
Subject: [PATCH 622/643] Minor change in comment

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

diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index 839b16bc8..99178f85d 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -30,7 +30,7 @@ func countingSort(array: [Int]) throws -> [Int] {
   // Step 3
   // Place the element in the final array as per the number of elements before it
   // Loop through the array in reverse to keep the stability of the new array
-  // (i.e. 7, is at index 3 and 6, thus in sortedArray the position of 7 at index 3 should be before 7 at index 6
+  // i.e. 7, is at index 3 and 6, thus in sortedArray the position of 7 at index 3 should be before 7 at index 6
   var sortedArray = [Int](repeating: 0, count: array.count)
   for index in stride(from: array.count - 1, through: 0, by: -1) {
     let element = array[index]

From d8d165208465c8c725eda950e8cb2ddb3d7cfdca Mon Sep 17 00:00:00 2001
From: Yossa Bourne <cybercanonx@gmail.com>
Date: Thu, 11 Jun 2020 09:56:40 +0700
Subject: [PATCH 623/643] Fix Swift (language) typos

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

diff --git a/Introsort/README.markdown b/Introsort/README.markdown
index 376703cf7..3e596ee89 100644
--- a/Introsort/README.markdown
+++ b/Introsort/README.markdown
@@ -2,7 +2,7 @@
 
 Goal: Sort an array from low to high (or high to low).
 
-IntroSort is the algorithm used by swift to sort a collection. Introsort is an hybrid algorithm invented by David Musser  in 1993 with the purpose of giving a generic sorting algorithm for the C++ standard library. The classic implementation of introsort expect a recursive Quicksort with fallback to Heapsort in case the recursion depth level reached a certain max. The maximum depends on the number of elements in the collection and it is usually 2 * log(n). The reason behind this “fallback” is that if Quicksort was not able to get the solution after 2 * log(n) recursions for a branch, probably it hit its worst case and it is degrading to complexity O( n^2 ). To optimise even further this algorithm, the swift implementation introduce an extra step in each recursion where the partition is sorted using InsertionSort if the count of the partition is less than 20.
+IntroSort is the algorithm used by Swift to sort a collection. Introsort is an hybrid algorithm invented by David Musser  in 1993 with the purpose of giving a generic sorting algorithm for the C++ standard library. The classic implementation of introsort expect a recursive Quicksort with fallback to Heapsort in case the recursion depth level reached a certain max. The maximum depends on the number of elements in the collection and it is usually 2 * log(n). The reason behind this “fallback” is that if Quicksort was not able to get the solution after 2 * log(n) recursions for a branch, probably it hit its worst case and it is degrading to complexity O( n^2 ). To optimise even further this algorithm, the Swift implementation introduce an extra step in each recursion where the partition is sorted using InsertionSort if the count of the partition is less than 20.
 
 The number 20 is an empiric number obtained observing the behaviour of InsertionSort with lists of this size.
 

From 9bc6aad9aaa56ce53ea7319f52c25585651e737a Mon Sep 17 00:00:00 2001
From: Roberto Efrain Hernandez <reh9019@gmail.com>
Date: Wed, 10 Jun 2020 23:44:40 -0700
Subject: [PATCH 624/643] Updating how String can be casted into an Array.

Just wanted to update the syntax from Array(self.characters) to Array(self). Similarly for casting of the ptnr String.
---
 Knuth-Morris-Pratt/KnuthMorrisPratt.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
index 81bc65278..be0cd961d 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
@@ -12,8 +12,8 @@ extension String {
   
   func indexesOf(ptnr: String) -> [Int]? {
     
-    let text = Array(self.characters)
-    let pattern = Array(ptnr.characters)
+    let text = Array(self)
+    let pattern = Array(ptnr)
     
     let textLength: Int = text.count
     let patternLength: Int = pattern.count

From abfa66b02d35b6320a5e404241db94d4317386d6 Mon Sep 17 00:00:00 2001
From: msalvacion <mcsalvacion@gmail.com>
Date: Thu, 11 Jun 2020 15:32:05 -0700
Subject: [PATCH 625/643] Fix: Typos in Heap README.markdown

Added missing word and fixed a typo
---
 Heap/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 6c65fe9c8..fee881129 100755
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -82,7 +82,7 @@ array[parent(i)] >= array[i]
 
 Verify that this heap property holds for the array from the example heap.
 
-As you can see, these equations allow us to find the parent or child index for any node without the need for pointers. It is complicated than just dereferencing a pointer, but that is the tradeoff: we save memory space but pay with extra computations. Fortunately, the computations are fast and only take **O(1)** time.
+As you can see, these equations allow us to find the parent or child index for any node without the need for pointers. It is more complicated than just dereferencing a pointer, but that is the tradeoff: we save memory space but pay with extra computations. Fortunately, the computations are fast and only take **O(1)** time.
 
 It is important to understand this relationship between array index and position in the tree. Here is a larger heap which has 15 nodes divided over four levels:
 
@@ -164,7 +164,7 @@ All of the above take time **O(log n)** because shifting up or down is expensive
 
 - `buildHeap(array)`: Converts an (unsorted) array into a heap by repeatedly calling `insert()`. If you are smart about this, it can be done in **O(n)** time.
 
-- [Heap sort](../Heap%20Sort/). Since the heap is an array, we can use its unique properties to sort the array from low to high. Time: **O(n lg n).**
+- [Heap sort](../Heap%20Sort/). Since the heap is an array, we can use its unique properties to sort the array from low to high. Time: **O(n log n).**
 
 The heap also has a `peek()` function that returns the maximum (max-heap) or minimum (min-heap) element, without removing it from the heap. Time: **O(1)**.
 

From f30e53c3cb45af31f8b80c35a8c4ee781d1ee311 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Mon, 15 Jun 2020 18:23:10 -0400
Subject: [PATCH 626/643] Fixes a few typos

---
 Introsort/README.markdown | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/Introsort/README.markdown b/Introsort/README.markdown
index 3e596ee89..280950928 100644
--- a/Introsort/README.markdown
+++ b/Introsort/README.markdown
@@ -2,7 +2,9 @@
 
 Goal: Sort an array from low to high (or high to low).
 
-IntroSort is the algorithm used by Swift to sort a collection. Introsort is an hybrid algorithm invented by David Musser  in 1993 with the purpose of giving a generic sorting algorithm for the C++ standard library. The classic implementation of introsort expect a recursive Quicksort with fallback to Heapsort in case the recursion depth level reached a certain max. The maximum depends on the number of elements in the collection and it is usually 2 * log(n). The reason behind this “fallback” is that if Quicksort was not able to get the solution after 2 * log(n) recursions for a branch, probably it hit its worst case and it is degrading to complexity O( n^2 ). To optimise even further this algorithm, the Swift implementation introduce an extra step in each recursion where the partition is sorted using InsertionSort if the count of the partition is less than 20.
+IntroSort is the algorithm used by Swift to sort a collection. Introsort is an hybrid algorithm invented by David Musser in 1993 with the purpose of giving a generic sorting algorithm for the C++ standard library. 
+
+The classic implementation of introsort uses a recursive Quicksort with a fallback to Heapsort in the case where the recursion depth level reached a certain maximum value. The maximum depends on the number of elements in the collection and it is usually 2 * log(n). The reason behind this “fallback” is that if Quicksort was not able to get the solution after 2 * log(n) recursions for a branch, probably it hit its worst case and it is degrading to complexity O( n^2 ). To optimise even further this algorithm, the Swift implementation introduce an extra step in each recursion where the partition is sorted using InsertionSort if the count of the partition is less than 20.
 
 The number 20 is an empiric number obtained observing the behaviour of InsertionSort with lists of this size.
 

From f4fb2fc0eb04ab6a7862ae903f258741896f9ec1 Mon Sep 17 00:00:00 2001
From: nghiahoang <vannghia.hoang@ocha.vn>
Date: Thu, 25 Jun 2020 13:17:01 +0700
Subject: [PATCH 627/643] fix: SplayTree.remove is broken

---
 .../SplayTree.playground/Contents.swift       |  33 +----
 .../Sources/SplayTree.swift                   | 122 ++++-------------
 Splay Tree/SplayTree.swift                    | 124 ++++--------------
 Splay Tree/readme.md                          |   7 +-
 4 files changed, 57 insertions(+), 229 deletions(-)

diff --git a/Splay Tree/SplayTree.playground/Contents.swift b/Splay Tree/SplayTree.playground/Contents.swift
index a8a0bc5c6..28a201b37 100644
--- a/Splay Tree/SplayTree.playground/Contents.swift	
+++ b/Splay Tree/SplayTree.playground/Contents.swift	
@@ -5,29 +5,10 @@
 print("Hello, Swift 4!")
 #endif
 
-let splayTree = SplayTree(value: 1)
-splayTree.insert(value: 2)
-splayTree.insert(value: 10)
-splayTree.insert(value: 6)
-
-splayTree.remove(value: 10)
-splayTree.remove(value: 6)
-
-splayTree.insert(value: 55)
-splayTree.insert(value: 559)
-splayTree.remove(value: 2)
-splayTree.remove(value: 1)
-splayTree.remove(value: 55)
-splayTree.remove(value: 559)
-
-splayTree.insert(value: 1843000)
-splayTree.insert(value: 1238)
-splayTree.insert(value: -1)
-splayTree.insert(value: 87)
-
-splayTree.minimum()
-splayTree.maximum()
-
-
-
-
+var tree = SplayTree<Int>(value: 0)
+tree.insert(value: 2)
+tree.insert(value: 3)
+tree.insert(value: 4)
+tree.insert(value: 7)
+_ = tree.search(value: 2)
+tree.remove(value: 2)
diff --git a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift
index 9e484129c..f450eaced 100644
--- a/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
+++ b/Splay Tree/SplayTree.playground/Sources/SplayTree.swift	
@@ -289,120 +289,42 @@ extension Node {
      - Node     Resulting from the deletion and the splaying of the removed node
      
      */
-    public func remove(value: T) -> Node<T>? {
-        let replacement: Node<T>?
+    fileprivate func remove(value: T) -> Node<T>? {
+        guard let target = search(value: value) else { return self }
         
-        if let v = self.value, v == value {
+        if let left = target.left, let right = target.right {
+            let largestOfLeftChild = left.maximum()
+            left.parent = nil
+            right.parent = nil
             
-            var parentToSplay: Node<T>?
-            if let left = left {
-                if let right = right {
-                    
-                    replacement = removeNodeWithTwoChildren(left, right)
-                    
-                    if let replacement = replacement,
-                        let replacementParent = replacement.parent,
-                        replacementParent.value != self.value {
-                        
-                        parentToSplay = replacement.parent
-                        
-                    } else if self.parent != nil {
-                        parentToSplay = self.parent
-                    } else {
-                        parentToSplay = replacement
-                    }
-                    
-                } else {
-                    // This node only has a left child. The left child replaces the node.
-                    replacement = left
-                    if self.parent != nil {
-                        parentToSplay = self.parent
-                    } else {
-                        parentToSplay = replacement
-                    }
-                }
-            } else if let right = right {
-                // This node only has a right child. The right child replaces the node.
-                replacement = right
-                if self.parent != nil {
-                    parentToSplay = self.parent
-                } else {
-                    parentToSplay = replacement
-                }
-            } else {
-                // This node has no children. We just disconnect it from its parent.
-                replacement = nil
-                parentToSplay = parent
-            }
-            
-            reconnectParentTo(node: replacement)
+            SplayOperation.splay(node: largestOfLeftChild)
+            largestOfLeftChild.right = right
             
-            // performs the splay operation
-            if let parentToSplay = parentToSplay {
-                SplayOperation.splay(node: parentToSplay)
-            }
+            return largestOfLeftChild
             
-            // The current node is no longer part of the tree, so clean it up.
-            parent = nil
-            left = nil
-            right = nil
+        } else if let left = target.left {
+            replace(node: target, with: left)
+            return left
             
-            return parentToSplay
+        } else if let right = target.right {
+            replace(node: target, with: right)
+            return right
             
-        } else if let v = self.value, value < v {
-            if left != nil {
-                return left!.remove(value: value)
-            } else {
-                let node = self
-                SplayOperation.splay(node: node)
-                return node
-                
-            }
         } else {
-            if right != nil {
-                return right?.remove(value: value)
-            } else {
-                let node = self
-                SplayOperation.splay(node: node)
-                return node
-                
-            }
+            return nil
         }
     }
     
-    private func removeNodeWithTwoChildren(_ left: Node, _ right: Node) -> Node {
-        // This node has two children. It must be replaced by the smallest
-        // child that is larger than this node's value, which is the leftmost
-        // descendent of the right child.
-        let successor = right.minimum()
+    private func replace(node: Node<T>, with newNode: Node<T>?) {
+        guard let sourceParent = sourceNode.parent else { return }
         
-        // Connect our left child with the new node.
-        successor.left = left
-        left.parent = successor
-        
-        // Connect our right child with the new node. If the right child does
-        // not have any left children of its own, then the in-order successor
-        // *is* the right child.
-        if right !== successor {
-            successor.right = right
-            right.parent = successor
+        if sourceNode.isLeftChild {
+            sourceParent.left = newNode
         } else {
-            successor.right = nil
+            sourceParent.right = newNode
         }
         
-        // And finally, connect the successor node to our parent.
-        return successor
-    }
-    
-    private func reconnectParentTo(node: Node?) {
-        if let parent = parent {
-            if isLeftChild {
-                parent.left = node
-            } else {
-                parent.right = node
-            }
-        }
-        node?.parent = parent
+        newNode?.parent = sourceParent
     }
 }
 
diff --git a/Splay Tree/SplayTree.swift b/Splay Tree/SplayTree.swift
index a7b20743d..0f1fa48f0 100644
--- a/Splay Tree/SplayTree.swift	
+++ b/Splay Tree/SplayTree.swift	
@@ -44,7 +44,7 @@ public enum SplayOperation {
         - Returns
             - Operation     Case zigZag - zigZig - zig
      */
-    public static func operation<T: Comparable>(forNode node: Node<T>) -> SplayOperation {
+    public static func operation<T>(forNode node: Node<T>) -> SplayOperation {
         
         if let parent = node.parent, let _ = parent.parent {
             if (node.isLeftChild && parent.isRightChild) || (node.isRightChild && parent.isLeftChild) {
@@ -289,120 +289,42 @@ extension Node {
             - Node     Resulting from the deletion and the splaying of the removed node
      
      */
-    public func remove(value: T) -> Node<T>? {
-        let replacement: Node<T>?
+    fileprivate func remove(value: T) -> Node<T>? {
+        guard let target = search(value: value) else { return self }
         
-        if let v = self.value, v == value {
+        if let left = target.left, let right = target.right {
+            let largestOfLeftChild = left.maximum()
+            left.parent = nil
+            right.parent = nil
             
-            var parentToSplay: Node<T>?
-            if let left = left {
-                if let right = right {
-                    
-                    replacement = removeNodeWithTwoChildren(left, right)
-                    
-                    if let replacement = replacement,
-                        let replacementParent = replacement.parent,
-                        replacementParent.value != self.value {
-                        
-                        parentToSplay = replacement.parent
-                        
-                    } else if self.parent != nil {
-                        parentToSplay = self.parent
-                    } else {
-                        parentToSplay = replacement
-                    }
-                    
-                } else {
-                    // This node only has a left child. The left child replaces the node.
-                    replacement = left
-                    if self.parent != nil {
-                        parentToSplay = self.parent
-                    } else {
-                        parentToSplay = replacement
-                    }
-                }
-            } else if let right = right {
-                // This node only has a right child. The right child replaces the node.
-                replacement = right
-                if self.parent != nil {
-                    parentToSplay = self.parent
-                } else {
-                    parentToSplay = replacement
-                }
-            } else {
-                // This node has no children. We just disconnect it from its parent.
-                replacement = nil
-                parentToSplay = parent
-            }
+            SplayOperation.splay(node: largestOfLeftChild)
+            largestOfLeftChild.right = right
             
-            reconnectParentTo(node: replacement)
+            return largestOfLeftChild
             
-            // performs the splay operation
-            if let parentToSplay = parentToSplay {
-                SplayOperation.splay(node: parentToSplay)
-            }
+        } else if let left = target.left {
+            replace(node: target, with: left)
+            return left
             
-            // The current node is no longer part of the tree, so clean it up.
-            parent = nil
-            left = nil
-            right = nil
-
-            return parentToSplay
+        } else if let right = target.right {
+            replace(node: target, with: right)
+            return right
             
-        } else if let v = self.value, value < v {
-            if left != nil {
-                return left!.remove(value: value)
-            } else {
-                let node = self
-                SplayOperation.splay(node: node)
-                return node
-                
-            }
         } else {
-            if right != nil {
-                return right?.remove(value: value)
-            } else {
-                let node = self
-                SplayOperation.splay(node: node)
-                return node
-                
-            }
+            return nil
         }
     }
     
-    private func removeNodeWithTwoChildren(_ left: Node, _ right: Node) -> Node {
-        // This node has two children. It must be replaced by the smallest
-        // child that is larger than this node's value, which is the leftmost
-        // descendent of the right child.
-        let successor = right.minimum()
+    private func replace(node: Node<T>, with newNode: Node<T>?) {
+        guard let sourceParent = sourceNode.parent else { return }
         
-        // Connect our left child with the new node.
-        successor.left = left
-        left.parent = successor
-        
-        // Connect our right child with the new node. If the right child does
-        // not have any left children of its own, then the in-order successor
-        // *is* the right child.
-        if right !== successor {
-            successor.right = right
-            right.parent = successor
+        if sourceNode.isLeftChild {
+            sourceParent.left = newNode
         } else {
-            successor.right = nil
+            sourceParent.right = newNode
         }
         
-        // And finally, connect the successor node to our parent.
-        return successor
-    }
-    
-    private func reconnectParentTo(node: Node?) {
-        if let parent = parent {
-            if isLeftChild {
-                parent.left = node
-            } else {
-                parent.right = node
-            }
-        }
-        node?.parent = parent
+        newNode?.parent = sourceParent
     }
 }
 
diff --git a/Splay Tree/readme.md b/Splay Tree/readme.md
index 75c3c0389..8a852c950 100644
--- a/Splay Tree/readme.md	
+++ b/Splay Tree/readme.md	
@@ -102,8 +102,11 @@ To insert a value:
 
 To delete a value: 
 
-- Delete it as in a binary search tree 
-- Splay the parent of the removed node to the root 
+- Perform search for the value, after performed search function if the tree contains the value, it'll be the root of the new tree.
+- If the tree has only left child, change left child to the root of the tree, remove the old root node
+- If the tree has only right child, change right child to the root of the tree, remove the old root node
+- Else, the tree has both two children, set parent of two children to nil, so that they're two new trees (left-tree and right-tree).
+- Splay the minimum node of right-tree (or minimum node of left-tree), then set left-tree as left child of new root of right-tree (or set right-tree as right child of new root of left-tree), return right-tree
 
 ### Search 
 

From 73f009209e99eaed53a6c81bf72dae83a5397cb4 Mon Sep 17 00:00:00 2001
From: Ahmed Abdulkareem Rezik <ahmedrezq100@hotmail.com>
Date: Thu, 9 Jul 2020 14:33:03 +0200
Subject: [PATCH 628/643] Fixed Hashable Conformance to hash(into:)

---
 Graph/Graph/Edge.swift   | 14 +++++++-------
 Graph/Graph/Vertex.swift |  6 ++++--
 2 files changed, 11 insertions(+), 9 deletions(-)

diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index ac5ed6a25..61cb576d1 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -29,13 +29,13 @@ extension Edge: CustomStringConvertible {
 
 extension Edge: Hashable {
 
-  public var hashValue: Int {
-    var string = "\(from.description)\(to.description)"
-    if weight != nil {
-      string.append("\(weight!)")
-    }
-    return string.hashValue
-  }
+    public func hash(into hasher: inout Hasher) {
+           hasher.combine(from)
+           hasher.combine(to)
+        if weight != nil {
+             hasher.combine(weight)
+          }
+         }
 }
 
 public func == <T>(lhs: Edge<T>, rhs: Edge<T>) -> Bool {
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index 758a367bb..cdf39ba62 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -24,8 +24,10 @@ extension Vertex: CustomStringConvertible {
 
 extension Vertex: Hashable {
 
-  public var hashValue: Int {
-    return "\(data)\(index)".hashValue
+  public func hasher(into hasher: inout Hasher){
+      
+      hasher.combine(data)
+      hasher.combine(index)
   }
 
 }

From 0513f7d1d0432d844357f5b931bfc5e0d1940870 Mon Sep 17 00:00:00 2001
From: Ahmed Abdulkareem Rezik <ahmedrezq100@hotmail.com>
Date: Thu, 9 Jul 2020 14:37:37 +0200
Subject: [PATCH 629/643] Fixed Conformance to Hashable Protocol in Vertex and
 Edge structs

---
 Graph/Graph/Edge.swift   | 14 ++++++++------
 Graph/Graph/Vertex.swift | 12 +++++++-----
 2 files changed, 15 insertions(+), 11 deletions(-)

diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index 61cb576d1..1f29e07dd 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -29,13 +29,15 @@ extension Edge: CustomStringConvertible {
 
 extension Edge: Hashable {
 
+
     public func hash(into hasher: inout Hasher) {
-           hasher.combine(from)
-           hasher.combine(to)
-        if weight != nil {
-             hasher.combine(weight)
-          }
-         }
+              hasher.combine(from)
+              hasher.combine(to)
+           if weight != nil {
+                hasher.combine(weight)
+             }
+            }
+    
 }
 
 public func == <T>(lhs: Edge<T>, rhs: Edge<T>) -> Bool {
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index cdf39ba62..45b2c3088 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -24,11 +24,13 @@ extension Vertex: CustomStringConvertible {
 
 extension Vertex: Hashable {
 
-  public func hasher(into hasher: inout Hasher){
-      
-      hasher.combine(data)
-      hasher.combine(index)
-  }
+
+    
+    public func hasher(into hasher: inout Hasher){
+        
+        hasher.combine(data)
+        hasher.combine(index)
+    }
 
 }
 

From 4311cad2e332b9454c1189bddcbbca5f156a3d4c Mon Sep 17 00:00:00 2001
From: Samuel Huang <samhuang91@gmail.com>
Date: Wed, 22 Jul 2020 13:26:35 -0700
Subject: [PATCH 630/643] Update BTree.swift

Fix spelling of swift markers - rename `Travelsals` to `Traversals`
---
 B-Tree/BTree.playground/Sources/BTree.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/B-Tree/BTree.playground/Sources/BTree.swift b/B-Tree/BTree.playground/Sources/BTree.swift
index 2693eb308..2ed0b2593 100644
--- a/B-Tree/BTree.playground/Sources/BTree.swift
+++ b/B-Tree/BTree.playground/Sources/BTree.swift
@@ -86,7 +86,7 @@ extension BTreeNode {
   }
 }
 
-// MARK: BTreeNode extension: Travelsals
+// MARK: BTreeNode extension: Traversals
 
 extension BTreeNode {
 
@@ -443,7 +443,7 @@ public class BTree<Key: Comparable, Value> {
   }
 }
 
-// MARK: BTree extension: Travelsals
+// MARK: BTree extension: Traversals
 
 extension BTree {
   /**

From 617187bf4c36ab57948592d403e295cf8127d664 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 13:37:23 -0700
Subject: [PATCH 631/643] Update style of Graph

---
 .../xcshareddata/IDEWorkspaceChecks.plist         |  8 ++++++++
 .../xcshareddata/IDEWorkspaceChecks.plist         |  8 ++++++++
 Graph/Graph/Edge.swift                            | 15 +++++++--------
 3 files changed, 23 insertions(+), 8 deletions(-)
 create mode 100644 Graph/Graph.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
 create mode 100644 Graph/Graph.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

diff --git a/Graph/Graph.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Graph/Graph.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Graph/Graph.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Graph/Graph.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist b/Graph/Graph.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
new file mode 100644
index 000000000..18d981003
--- /dev/null
+++ b/Graph/Graph.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>
diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index 3c95f9666..9ddd4e23d 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -29,14 +29,13 @@ extension Edge: CustomStringConvertible {
 
 extension Edge: Hashable {
 
-    public func hash(into hasher: inout Hasher) {
-              hasher.combine(from)
-              hasher.combine(to)
-           if weight != nil {
-                hasher.combine(weight)
-             }
-            }
-    
+  public func hash(into hasher: inout Hasher) {
+    hasher.combine(from)
+    hasher.combine(to)
+    if weight != nil {
+      hasher.combine(weight)
+    }
+  }
 
 }
 

From d951e67ec24167c9518bcab4e91946ce956978f3 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 13:57:25 -0700
Subject: [PATCH 632/643] Update README.markdown

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

diff --git a/README.markdown b/README.markdown
index 3e0174576..093c5b9e7 100644
--- a/README.markdown
+++ b/README.markdown
@@ -195,6 +195,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Minimum Spanning Tree](Minimum%20Spanning%20Tree/)
 - [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
 - [Dijkstra's shortest path algorithm](Dijkstra%20Algorithm/)
+- [A*](A-star/)
 
 ## Puzzles
 

From 7bba2b28da53b3764f24c7fa455fe37065948530 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 13:58:06 -0700
Subject: [PATCH 633/643] Update README.markdown

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

diff --git a/README.markdown b/README.markdown
index 093c5b9e7..b8b59bbcc 100644
--- a/README.markdown
+++ b/README.markdown
@@ -195,7 +195,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Minimum Spanning Tree](Minimum%20Spanning%20Tree/)
 - [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
 - [Dijkstra's shortest path algorithm](Dijkstra%20Algorithm/)
-- [A*](A-star/)
+- [A-star](A-star/)
 
 ## Puzzles
 

From cf518c04b31013a4f1b468648967eb7a7a3694b6 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 13:58:47 -0700
Subject: [PATCH 634/643] Update README.markdown

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

diff --git a/README.markdown b/README.markdown
index b8b59bbcc..e87fe0335 100644
--- a/README.markdown
+++ b/README.markdown
@@ -195,7 +195,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Minimum Spanning Tree](Minimum%20Spanning%20Tree/)
 - [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
 - [Dijkstra's shortest path algorithm](Dijkstra%20Algorithm/)
-- [A-star](A-star/)
+- [A-Star](A-Star/)
 
 ## Puzzles
 

From e515919e305371cbff38319e00d21c90b35188e4 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 14:24:59 -0700
Subject: [PATCH 635/643] Update Vertex.swift

---
 Graph/Graph/Vertex.swift | 14 ++++----------
 1 file changed, 4 insertions(+), 10 deletions(-)

diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index f74b38396..48645f0fa 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -24,16 +24,10 @@ extension Vertex: CustomStringConvertible {
 
 extension Vertex: Hashable {
 
-
-
-    
-    public func hasher(into hasher: inout Hasher){
-        
-        hasher.combine(data)
-        hasher.combine(index)
-    }
-
-
+  public func hasher(into hasher: inout Hasher) {
+    hasher.combine(data)
+    hasher.combine(index)
+  }
 
 }
 

From 81e2726f03ea14a5f92ddafe2e093cba9bee84c1 Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 14:35:34 -0700
Subject: [PATCH 636/643] Update Linked List/README.markdown

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

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index d6f1fc986..c80b11d6f 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -491,7 +491,7 @@ Recursive Approach:
     }
     let temp = reverse(head.next)
     head.next.next = head
-    head.next = NULL
+    head.next = nil
     return temp
   }
 ```

From 15229cf1b57bd5bd95e81a19a0fd7de9abe0bb6f Mon Sep 17 00:00:00 2001
From: Richard Ash <r.ash8347@gmail.com>
Date: Sat, 29 Aug 2020 14:38:06 -0700
Subject: [PATCH 637/643] Update Linked List/README.markdown

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

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index c80b11d6f..fdbc2ee84 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -486,7 +486,7 @@ Iterative Approach:
 Recursive Approach:
 ```swift
   public func reverse(node: head) {
-    if (!head || !(head.next)) {
+    if !head || !head.next {
       return head
     }
     let temp = reverse(head.next)

From d664df8cb4fea0aad54d2e693f01684cec0590f9 Mon Sep 17 00:00:00 2001
From: Hashem <hashemp206@yahoo.com>
Date: Mon, 29 Mar 2021 15:58:37 +0400
Subject: [PATCH 638/643] Update README.markdown

`sort()` is in place sort. in reveres `sorted()` returns a sorted copy of the original array
---
 Insertion Sort/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index 8c2a5c1a0..1c41aa91d 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -114,7 +114,7 @@ insertionSort(list)
 
 Here is how the code works.
 
-1. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly. Like Swift's own `sort()`, the `insertionSort()` function will return a sorted *copy* of the original array.
+1. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly. Like Swift's own `sorted()`, the `insertionSort()` function will return a sorted *copy* of the original array.
 
 2. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what picks the top-most number from the pile. The variable `x` is the index of where the sorted portion ends and the pile begins (the position of the `|` bar). Remember, at any given moment the beginning of the array -- from index 0 up to `x` -- is always sorted. The rest, from index `x` until the last element, is the unsorted pile.
 

From 90e23a6790f1f0a0e3704314a08be02114bcdf11 Mon Sep 17 00:00:00 2001
From: Coskun Deniz <c.deniz@gmail.com>
Date: Sat, 21 Aug 2021 19:44:58 +0100
Subject: [PATCH 639/643] declare 'index' as variable

---
 Insertion Sort/InsertionSort.swift | 13 ++++++-------
 1 file changed, 6 insertions(+), 7 deletions(-)

diff --git a/Insertion Sort/InsertionSort.swift b/Insertion Sort/InsertionSort.swift
index e24ede905..5f0b6c2b4 100644
--- a/Insertion Sort/InsertionSort.swift	
+++ b/Insertion Sort/InsertionSort.swift	
@@ -28,14 +28,13 @@ func insertionSort<T: Comparable>(_ array: [T]) -> [T] {
     guard array.count > 1 else { return array }
 
     var sortedArray = array
-    for index in 1..<sortedArray.count {
-        var currentIndex = index
-        let temp = sortedArray[currentIndex]
-        while currentIndex > 0, temp < sortedArray[currentIndex - 1] {
-            sortedArray[currentIndex] = sortedArray[currentIndex - 1]
-            currentIndex -= 1
+    for var index in 1..<sortedArray.count {
+        let temp = sortedArray[index]
+        while index > 0, temp < sortedArray[index - 1] {
+            sortedArray[index] = sortedArray[index - 1]
+            index -= 1
         }
-        sortedArray[currentIndex] = temp
+        sortedArray[index] = temp
     }
     return sortedArray
 }

From 5ad2c68e359c6676df6b3b95315fe8d2b8d70d81 Mon Sep 17 00:00:00 2001
From: Aaron Watkins <ac.watkins80@gmail.com>
Date: Fri, 26 Nov 2021 16:35:21 -0500
Subject: [PATCH 640/643] legacy variables names correct legacy variable name
 `x` to be `index` so reader isnt wasting time scratching their head and can
 focus more on understanding the insertion sort algorithm.

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

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index 1c41aa91d..f37bfeaef 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -116,9 +116,9 @@ Here is how the code works.
 
 1. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly. Like Swift's own `sorted()`, the `insertionSort()` function will return a sorted *copy* of the original array.
 
-2. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what picks the top-most number from the pile. The variable `x` is the index of where the sorted portion ends and the pile begins (the position of the `|` bar). Remember, at any given moment the beginning of the array -- from index 0 up to `x` -- is always sorted. The rest, from index `x` until the last element, is the unsorted pile.
+2. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what picks the top-most number from the pile. The variable `index` is the index of where the sorted portion ends and the pile begins (the position of the `|` bar). Remember, at any given moment the beginning of the array -- from index 0 up to `index` -- is always sorted. The rest, from index `index` until the last element, is the unsorted pile.
 
-3. The inner loop looks at the element at position `x`. This is the number at the top of the pile, and it may be smaller than any of the previous elements. The inner loop steps backwards through the sorted array; every time it finds a previous number that is larger, it swaps them. When the inner loop completes, the beginning of the array is sorted again, and the sorted portion has grown by one element.
+3. The inner loop looks at the element at position `index`. This is the number at the top of the pile, and it may be smaller than any of the previous elements. The inner loop steps backwards through the sorted array; every time it finds a previous number that is larger, it swaps them. When the inner loop completes, the beginning of the array is sorted again, and the sorted portion has grown by one element.
 
 > **Note:** The outer loop starts at index 1, not 0. Moving the very first element from the pile to the sorted portion doesn't actually change anything, so we might as well skip it. 
 

From eb4e151b55ff846c28be5d2357b7ab2f776a9dce Mon Sep 17 00:00:00 2001
From: Aaron Watkins <ac.watkins80@gmail.com>
Date: Fri, 26 Nov 2021 16:45:21 -0500
Subject: [PATCH 641/643] correct index to currentIndex

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

diff --git a/Insertion Sort/README.markdown b/Insertion Sort/README.markdown
index f37bfeaef..f7b933b92 100644
--- a/Insertion Sort/README.markdown	
+++ b/Insertion Sort/README.markdown	
@@ -116,9 +116,9 @@ Here is how the code works.
 
 1. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly. Like Swift's own `sorted()`, the `insertionSort()` function will return a sorted *copy* of the original array.
 
-2. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what picks the top-most number from the pile. The variable `index` is the index of where the sorted portion ends and the pile begins (the position of the `|` bar). Remember, at any given moment the beginning of the array -- from index 0 up to `index` -- is always sorted. The rest, from index `index` until the last element, is the unsorted pile.
+2. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what picks the top-most number from the pile. The variable `currentIndex` is the index of where the sorted portion ends and the pile begins (the position of the `|` bar). Remember, at any given moment the beginning of the array -- from index 0 up to `currentIndex` -- is always sorted. The rest, from index `currentIndex` until the last element, is the unsorted pile.
 
-3. The inner loop looks at the element at position `index`. This is the number at the top of the pile, and it may be smaller than any of the previous elements. The inner loop steps backwards through the sorted array; every time it finds a previous number that is larger, it swaps them. When the inner loop completes, the beginning of the array is sorted again, and the sorted portion has grown by one element.
+3. The inner loop looks at the element at position `currentIndex`. This is the number at the top of the pile, and it may be smaller than any of the previous elements. The inner loop steps backwards through the sorted array; every time it finds a previous number that is larger, it swaps them. When the inner loop completes, the beginning of the array is sorted again, and the sorted portion has grown by one element.
 
 > **Note:** The outer loop starts at index 1, not 0. Moving the very first element from the pile to the sorted portion doesn't actually change anything, so we might as well skip it. 
 

From 6af57a839d59db84ded9e95315d4a9aeff8a9d64 Mon Sep 17 00:00:00 2001
From: Namratha2604 <gundanamratha@gmail.com>
Date: Thu, 26 Sep 2024 14:25:05 +0530
Subject: [PATCH 642/643] #986-corrected the comment

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

diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index 7a3719d57..8ed808a06 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -79,4 +79,4 @@ bloom.insert("Bloom Filterz")
 print(bloom.array)
 
 bloom.query("Bloom Filterz")   // true
-bloom.query("Hello WORLD")     // true
+bloom.query("Hello WORLD")     // false or true: It may return true due to a false positive, but it's not guaranteed.

From 5e8c02913c04d86d3b41ebf47210b9f974ad7d26 Mon Sep 17 00:00:00 2001
From: Nitesh J <jnitesh1463@gmail.com>
Date: Mon, 7 Oct 2024 14:05:17 +0530
Subject: [PATCH 643/643] issue resolved  #997 and #998

Correction of the README.markdown and Selection Sampling code improvement #998
---
 Selection Sampling/README.markdown         | 2 +-
 Selection Sampling/SelectionSampling.swift | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Selection Sampling/README.markdown b/Selection Sampling/README.markdown
index 741f592f4..5c2ff5e25 100644
--- a/Selection Sampling/README.markdown	
+++ b/Selection Sampling/README.markdown	
@@ -12,7 +12,7 @@ func select<T>(from a: [T], count k: Int) -> [T] {
   for i in 0..<k {
     let r = random(min: i, max: a.count - 1)
     if i != r {
-      swap(&a[i], &a[r])
+      a.swapAt(i, r) // Corrected line in README
     }
   }
   return Array(a[0..<k])
diff --git a/Selection Sampling/SelectionSampling.swift b/Selection Sampling/SelectionSampling.swift
index 52aa5988b..711460f47 100644
--- a/Selection Sampling/SelectionSampling.swift	
+++ b/Selection Sampling/SelectionSampling.swift	
@@ -17,7 +17,7 @@ func select<T>(from a: [T], count k: Int) -> [T] {
   for i in 0..<k {
     let r = random(min: i, max: a.count - 1)
     if i != r {
-      swap(&a[i], &a[r])
+      a.swapAt(i, r) // Corrected line
     }
   }
   return Array(a[0..<k])