From 1de177535f8facdd188464df0c98e50cc5148504 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Mon, 24 Oct 2016 18:33:25 -0700
Subject: [PATCH 001/862] Init & claim of Strassen's Matrix Multiplication
 Algorithm

---
 Strassen Matrix Multiplication/README.markdown | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Strassen Matrix Multiplication/README.markdown

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
new file mode 100644
index 000000000..d07004bad
--- /dev/null
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -0,0 +1 @@
+## TODO: Examples & Explanation

From 95069fd26cd6c0f5c60f9c980411df72c61ce379 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Wed, 26 Oct 2016 14:12:39 -0700
Subject: [PATCH 002/862] Implementation for Strassen Matrix Multiplication
 Algorithm

---
 .../Contents.swift                            | 316 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 3 files changed, 327 insertions(+)
 create mode 100644 Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
 create mode 100644 Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/contents.xcplayground
 create mode 100644 Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
new file mode 100644
index 000000000..d4b4d8330
--- /dev/null
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -0,0 +1,316 @@
+//: Playground - noun: a place where people can play
+// Reference - http://mathworld.wolfram.com/StrassenFormulas.html
+
+
+import UIKit
+
+enum RowOrColumn {
+  case row, column
+}
+
+protocol Number: Multipliable, Addable {
+  static var zero: Self { get }
+}
+
+protocol Addable {
+  static func +(lhs: Self, rhs: Self) -> Self
+  static func -(lhs: Self, rhs: Self) -> Self
+}
+
+protocol Multipliable {
+  static func *(lhs: Self, rhs: Self) -> Self
+}
+
+extension Int: Number {
+  static var zero: Int {
+    return 0
+  }
+}
+
+extension Double: Number {
+  static var zero: Double {
+    return 0.0
+  }
+}
+
+extension Float: Number {
+  static var zero: Float {
+    return 0.0
+  }
+}
+
+
+extension Array where Element: Number {
+  func dot(_ b: Array<Element>) -> Element {
+    let a = self
+    assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
+    let c = a.indices.map{ a[$0] * b[$0] }
+    return c.reduce(Element.zero, { $0 + $1 })
+  }
+}
+
+struct MatrixSize: Equatable {
+  let rows: Int
+  let columns: Int
+  
+  func forEach(_ body: (Int, Int) throws -> Void) rethrows {
+    for row in 0..<rows {
+      for column in 0..<columns {
+        try? body(row, column)
+      }
+    }
+  }
+}
+
+func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
+  return lhs.columns == rhs.columns && lhs.rows == rhs.rows
+}
+
+
+struct Matrix<T: Number> {
+  
+  // MARK: - Variables
+  
+  let rows: Int, columns: Int
+  var grid: [T]
+  
+  var isSquare: Bool {
+    return rows == columns
+  }
+  
+  var size: MatrixSize {
+    return MatrixSize(rows: rows, columns: columns)
+  }
+  
+  // MARK: - Init
+  
+  init(rows: Int, columns: Int, initialValue: T = T.zero) {
+    self.rows = rows
+    self.columns = columns
+    self.grid = Array(repeating: initialValue, count: rows * columns)
+  }
+  
+  init(size: Int, initialValue: T = T.zero) {
+    self.rows = size
+    self.columns = size
+    self.grid = Array(repeating: initialValue, count: rows * columns)
+  }
+  
+  // MARK: - Subscript
+  
+  subscript(row: Int, column: Int) -> T {
+    get {
+      assert(indexIsValid(row: row, column: column), "Index out of range")
+      return grid[(row * columns) + column]
+    }
+    set {
+      assert(indexIsValid(row: row, column: column), "Index out of range")
+      grid[(row * columns) + column] = newValue
+    }
+  }
+  
+  subscript(type: RowOrColumn, value: Int) -> [T] {
+    get {
+      switch type {
+      case .row:
+        assert(indexIsValid(row: value, column: 0), "Index out of range")
+        return Array(grid[(value * columns)..<(value * columns) + columns])
+      case .column:
+        assert(indexIsValid(row: 0, column: value), "Index out of range")
+        var columns: [T] = []
+        for row in 0..<rows {
+          for column in 0..<self.columns {
+            if column == value {
+              columns.append(grid[(row * self.columns) + value])
+            }
+          }
+        }
+        return columns
+      }
+    } set {
+      switch type {
+      case .row:
+        assert(newValue.count == columns)
+        for (column, element) in newValue.enumerated() {
+          grid[(value * columns) + column] = element
+        }
+      case .column:
+        assert(newValue.count == rows)
+        for (row, element) in newValue.enumerated() {
+          grid[(row * columns) + value] = element
+        }
+      }
+    }
+  }
+  
+  // MARK: - Private Functions
+  
+  private func indexIsValid(row: Int, column: Int) -> Bool {
+    return row >= 0 && row < rows && column >= 0 && column < columns
+  }
+  
+  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.isSquare && B.isSquare, "This function requires square matricies!")
+    guard A.rows > 1 && B.rows > 1 else { return A * B }
+    
+    let n    = A.rows
+    let nBy2 = n / 2
+    
+    var a11 = Matrix(size: nBy2)
+    var a12 = Matrix(size: nBy2)
+    var a21 = Matrix(size: nBy2)
+    var a22 = Matrix(size: nBy2)
+    var b11 = Matrix(size: nBy2)
+    var b12 = Matrix(size: nBy2)
+    var b21 = Matrix(size: nBy2)
+    var b22 = Matrix(size: nBy2)
+    
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        a11[i,j] = A[i,j]
+        a12[i,j] = A[i, j+nBy2]
+        a21[i,j] = A[i+nBy2, j]
+        a22[i,j] = A[i+nBy2, j+nBy2]
+        b11[i,j] = B[i,j]
+        b12[i,j] = B[i, j+nBy2]
+        b21[i,j] = B[i+nBy2, j]
+        b22[i,j] = B[i+nBy2, j+nBy2]
+      }
+    }
+    
+    let q1 = (a11+a22).strassenR(by: b11+b22)    // (a11+a22)(b11+b22)
+    let q2 = (a21+a22).strassenR(by: b11)        // (a21+a22)b11
+    let q3 = a11.strassenR(by: b12-b22)          // a11(b12-b22)
+    let q4 = a22.strassenR(by: b21-b11)          // a22(-b11+b21)
+    let q5 = (a11+a12).strassenR(by: b22)        // (a11+a22)b22
+    let q6 = (a21-a11).strassenR(by: b11+b12)    // (-a11+a21)(b11+b12)
+    let q7 = (a12-a22).strassenR(by: b21+b22)    // (a12-a22)(b21+b22)
+    
+    let c11 = q1 + q4 - q5 + q7
+    let c12 = q3 + q5
+    let c21 = q2 + q4
+    let c22 = q1 + q3 - q2 + q6
+    var C   = Matrix(size: n)
+    
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        C[i, j]           = c11[i,j]
+        C[i, j+nBy2]      = c12[i,j]
+        C[i+nBy2, j]      = c21[i,j]
+        C[i+nBy2, j+nBy2] = c22[i,j]
+      }
+    }
+    
+    return C
+  }
+  
+  private func nextPowerOfTwo(of n: Int) -> Int {
+    return Int(pow(2, ceil(log2(Double(n)))))
+  }
+  
+  // MARK: - Functions
+  
+  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    let n = max(A.rows, A.columns, B.rows, B.columns)
+    let m = nextPowerOfTwo(of: n)
+    
+    var APrep = Matrix(size: m)
+    var BPrep = Matrix(size: m)
+    
+    A.size.forEach { (i, j) in
+      APrep[i,j] = A[i,j]
+    }
+    
+    B.size.forEach { (i, j) in
+      BPrep[i,j] = B[i,j]
+    }
+    
+    let CPrep = APrep.strassenR(by: BPrep)
+    var C = Matrix(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i,j] = CPrep[i,j]
+      }
+    }
+    return C
+  }
+  
+  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    var C = Matrix<T>(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i, j] = A[.row, i].dot(B[.column, j])
+      }
+    }
+    
+    return C
+  }
+}
+
+func *<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] * rhs[row, column]
+    }
+  }
+  return newMatrix
+}
+
+func +<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] + rhs[row, column]
+    }
+  }
+  return newMatrix
+}
+
+func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] - rhs[row, column]
+    }
+  }
+  return newMatrix
+}
+
+var A = Matrix(rows: 2, columns: 4, initialValue: 0)
+A[.row, 0] = [2, 3, -1, 0]
+A[.row, 1] = [-7, 2, 1, 10]
+
+var B = Matrix(rows: 4, columns: 2, initialValue: 0)
+B[.column, 0] = [3, 2, -1, 2]
+B[.column, 1] = [4, 1, 2, 7]
+
+let C = A.matrixMultiply(by: B)
+let D = A.strassenMatrixMultiply(by: B)
+let E = B.matrixMultiply(by: A)
+let F = B.strassenMatrixMultiply(by: A)
+print(C)
+print(D)
+print(E)
+print(F)
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/contents.xcplayground b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/contents.xcplayground
new file mode 100644
index 000000000..9f5f2f40c
--- /dev/null
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.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/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.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 7295526436fa7e8a6dfd16f76f78aaf3a6b72a85 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Fri, 28 Oct 2016 12:44:05 -0700
Subject: [PATCH 003/862] Added File implementations

---
 Strassen Matrix Multiplication/Matrix.swift     | 9 +++++++++
 Strassen Matrix Multiplication/MatrixSize.swift | 9 +++++++++
 Strassen Matrix Multiplication/Number.swift     | 9 +++++++++
 3 files changed, 27 insertions(+)
 create mode 100644 Strassen Matrix Multiplication/Matrix.swift
 create mode 100644 Strassen Matrix Multiplication/MatrixSize.swift
 create mode 100644 Strassen Matrix Multiplication/Number.swift

diff --git a/Strassen Matrix Multiplication/Matrix.swift b/Strassen Matrix Multiplication/Matrix.swift
new file mode 100644
index 000000000..493e27e06
--- /dev/null
+++ b/Strassen Matrix Multiplication/Matrix.swift	
@@ -0,0 +1,9 @@
+//
+//  Matrix.swift
+//  
+//
+//  Created by Richard Ash on 10/28/16.
+//
+//
+
+import Foundation
diff --git a/Strassen Matrix Multiplication/MatrixSize.swift b/Strassen Matrix Multiplication/MatrixSize.swift
new file mode 100644
index 000000000..a01123f3c
--- /dev/null
+++ b/Strassen Matrix Multiplication/MatrixSize.swift	
@@ -0,0 +1,9 @@
+//
+//  MatrixSize.swift
+//  
+//
+//  Created by Richard Ash on 10/28/16.
+//
+//
+
+import Foundation
diff --git a/Strassen Matrix Multiplication/Number.swift b/Strassen Matrix Multiplication/Number.swift
new file mode 100644
index 000000000..1bd6cf634
--- /dev/null
+++ b/Strassen Matrix Multiplication/Number.swift	
@@ -0,0 +1,9 @@
+//
+//  Number.swift
+//  
+//
+//  Created by Richard Ash on 10/28/16.
+//
+//
+
+import Foundation

From 1e23b7f859ed83e21dd37941113102af0d8c4d28 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Tue, 13 Dec 2016 14:30:07 -0800
Subject: [PATCH 004/862] Code updates

---
 Strassen Matrix Multiplication/Matrix.swift   | 237 ++++++++++++++++++
 .../MatrixSize.swift                          |  17 ++
 Strassen Matrix Multiplication/Number.swift   |  41 +++
 3 files changed, 295 insertions(+)

diff --git a/Strassen Matrix Multiplication/Matrix.swift b/Strassen Matrix Multiplication/Matrix.swift
index 493e27e06..657cf3c80 100644
--- a/Strassen Matrix Multiplication/Matrix.swift	
+++ b/Strassen Matrix Multiplication/Matrix.swift	
@@ -7,3 +7,240 @@
 //
 
 import Foundation
+
+enum RowOrColumn {
+  case row, column
+}
+
+struct Matrix<T: Number> {
+  
+  // MARK: - Variables
+  
+  let rows: Int, columns: Int
+  var grid: [T]
+  
+  var isSquare: Bool {
+    return rows == columns
+  }
+  
+  var size: MatrixSize {
+    return MatrixSize(rows: rows, columns: columns)
+  }
+  
+  // MARK: - Init
+  
+  init(rows: Int, columns: Int, initialValue: T = T.zero) {
+    self.rows = rows
+    self.columns = columns
+    self.grid = Array(repeating: initialValue, count: rows * columns)
+  }
+  
+  init(size: Int, initialValue: T = T.zero) {
+    self.rows = size
+    self.columns = size
+    self.grid = Array(repeating: initialValue, count: rows * columns)
+  }
+  
+  // MARK: - Subscript
+  
+  subscript(row: Int, column: Int) -> T {
+    get {
+      assert(indexIsValid(row: row, column: column), "Index out of range")
+      return grid[(row * columns) + column]
+    }
+    set {
+      assert(indexIsValid(row: row, column: column), "Index out of range")
+      grid[(row * columns) + column] = newValue
+    }
+  }
+  
+  subscript(type: RowOrColumn, value: Int) -> [T] {
+    get {
+      switch type {
+      case .row:
+        assert(indexIsValid(row: value, column: 0), "Index out of range")
+        return Array(grid[(value * columns)..<(value * columns) + columns])
+      case .column:
+        assert(indexIsValid(row: 0, column: value), "Index out of range")
+        var columns: [T] = []
+        for row in 0..<rows {
+          for column in 0..<self.columns {
+            if column == value {
+              columns.append(grid[(row * self.columns) + value])
+            }
+          }
+        }
+        return columns
+      }
+    } set {
+      switch type {
+      case .row:
+        assert(newValue.count == columns)
+        for (column, element) in newValue.enumerated() {
+          grid[(value * columns) + column] = element
+        }
+      case .column:
+        assert(newValue.count == rows)
+        for (row, element) in newValue.enumerated() {
+          grid[(row * columns) + value] = element
+        }
+      }
+    }
+  }
+  
+  // MARK: - Private Functions
+  
+  private func indexIsValid(row: Int, column: Int) -> Bool {
+    return row >= 0 && row < rows && column >= 0 && column < columns
+  }
+  
+  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.isSquare && B.isSquare, "This function requires square matricies!")
+    guard A.rows > 1 && B.rows > 1 else { return A * B }
+    
+    let n    = A.rows
+    let nBy2 = n / 2
+    
+    var a11 = Matrix(size: nBy2)
+    var a12 = Matrix(size: nBy2)
+    var a21 = Matrix(size: nBy2)
+    var a22 = Matrix(size: nBy2)
+    var b11 = Matrix(size: nBy2)
+    var b12 = Matrix(size: nBy2)
+    var b21 = Matrix(size: nBy2)
+    var b22 = Matrix(size: nBy2)
+    
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        a11[i,j] = A[i,j]
+        a12[i,j] = A[i, j+nBy2]
+        a21[i,j] = A[i+nBy2, j]
+        a22[i,j] = A[i+nBy2, j+nBy2]
+        b11[i,j] = B[i,j]
+        b12[i,j] = B[i, j+nBy2]
+        b21[i,j] = B[i+nBy2, j]
+        b22[i,j] = B[i+nBy2, j+nBy2]
+      }
+    }
+    
+    let q1 = (a11+a22).strassenR(by: b11+b22)    // (a11+a22)(b11+b22)
+    let q2 = (a21+a22).strassenR(by: b11)        // (a21+a22)b11
+    let q3 = a11.strassenR(by: b12-b22)          // a11(b12-b22)
+    let q4 = a22.strassenR(by: b21-b11)          // a22(-b11+b21)
+    let q5 = (a11+a12).strassenR(by: b22)        // (a11+a22)b22
+    let q6 = (a21-a11).strassenR(by: b11+b12)    // (-a11+a21)(b11+b12)
+    let q7 = (a12-a22).strassenR(by: b21+b22)    // (a12-a22)(b21+b22)
+    
+    let c11 = q1 + q4 - q5 + q7
+    let c12 = q3 + q5
+    let c21 = q2 + q4
+    let c22 = q1 + q3 - q2 + q6
+    var C   = Matrix(size: n)
+    
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        C[i, j]           = c11[i,j]
+        C[i, j+nBy2]      = c12[i,j]
+        C[i+nBy2, j]      = c21[i,j]
+        C[i+nBy2, j+nBy2] = c22[i,j]
+      }
+    }
+    
+    return C
+  }
+  
+  private func nextPowerOfTwo(of n: Int) -> Int {
+    return Int(pow(2, ceil(log2(Double(n)))))
+  }
+  
+  // MARK: - Functions
+  
+  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    let n = max(A.rows, A.columns, B.rows, B.columns)
+    let m = nextPowerOfTwo(of: n)
+    
+    var APrep = Matrix(size: m)
+    var BPrep = Matrix(size: m)
+    
+    A.size.forEach { (i, j) in
+      APrep[i,j] = A[i,j]
+    }
+    
+    B.size.forEach { (i, j) in
+      BPrep[i,j] = B[i,j]
+    }
+    
+    let CPrep = APrep.strassenR(by: BPrep)
+    var C = Matrix(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i,j] = CPrep[i,j]
+      }
+    }
+    return C
+  }
+  
+  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    var C = Matrix<T>(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i, j] = A[.row, i].dot(B[.column, j])
+      }
+    }
+    
+    return C
+  }
+}
+
+// Term-by-term Matrix Math
+
+func *<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] * rhs[row, column]
+    }
+  }
+  return newMatrix
+}
+
+func +<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] + rhs[row, column]
+    }
+  }
+  return newMatrix
+}
+
+func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+  assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
+  let rows = lhs.rows
+  let columns = lhs.columns
+  
+  var newMatrix = Matrix<T>(rows: rows, columns: columns)
+  for row in 0..<rows {
+    for column in 0..<columns {
+      newMatrix[row, column] = lhs[row, column] - rhs[row, column]
+    }
+  }
+  return newMatrix
+}
diff --git a/Strassen Matrix Multiplication/MatrixSize.swift b/Strassen Matrix Multiplication/MatrixSize.swift
index a01123f3c..f1eada931 100644
--- a/Strassen Matrix Multiplication/MatrixSize.swift	
+++ b/Strassen Matrix Multiplication/MatrixSize.swift	
@@ -7,3 +7,20 @@
 //
 
 import Foundation
+
+struct MatrixSize: Equatable {
+  let rows: Int
+  let columns: Int
+  
+  func forEach(_ body: (Int, Int) throws -> Void) rethrows {
+    for row in 0..<rows {
+      for column in 0..<columns {
+        try? body(row, column)
+      }
+    }
+  }
+}
+
+func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
+  return lhs.columns == rhs.columns && lhs.rows == rhs.rows
+}
diff --git a/Strassen Matrix Multiplication/Number.swift b/Strassen Matrix Multiplication/Number.swift
index 1bd6cf634..34c6d5308 100644
--- a/Strassen Matrix Multiplication/Number.swift	
+++ b/Strassen Matrix Multiplication/Number.swift	
@@ -7,3 +7,44 @@
 //
 
 import Foundation
+
+protocol Number: Multipliable, Addable {
+  static var zero: Self { get }
+}
+
+protocol Addable {
+  static func +(lhs: Self, rhs: Self) -> Self
+  static func -(lhs: Self, rhs: Self) -> Self
+}
+
+protocol Multipliable {
+  static func *(lhs: Self, rhs: Self) -> Self
+}
+
+extension Int: Number {
+  static var zero: Int {
+    return 0
+  }
+}
+
+extension Double: Number {
+  static var zero: Double {
+    return 0.0
+  }
+}
+
+extension Float: Number {
+  static var zero: Float {
+    return 0.0
+  }
+}
+
+
+extension Array where Element: Number {
+  func dot(_ b: Array<Element>) -> Element {
+    let a = self
+    assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
+    let c = a.indices.map{ a[$0] * b[$0] }
+    return c.reduce(Element.zero, { $0 + $1 })
+  }
+}

From 548f11791666bb2df3cae77183efda861171a0d0 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Thu, 12 Jan 2017 20:17:41 -0800
Subject: [PATCH 005/862] Code restructuring

- Moved source files Matrix.swift, MatrixSize.swift & Number.swift to the Sources foler in the PLayground
- Restrucutred the code into extensions to make it more organized and readable
- Deleted all the objects from the playground and moved them to the Sources folder
---
 .../MatrixSize.swift                          |  26 --
 .../Contents.swift                            | 297 +-----------------
 .../Sources}/Matrix.swift                     | 183 +++++------
 .../Sources/MatrixSize.swift                  |  33 ++
 .../Sources}/Number.swift                     |  15 +-
 5 files changed, 136 insertions(+), 418 deletions(-)
 delete mode 100644 Strassen Matrix Multiplication/MatrixSize.swift
 rename Strassen Matrix Multiplication/{ => StrassensMatrixMultiplication.playground/Sources}/Matrix.swift (72%)
 create mode 100644 Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift
 rename Strassen Matrix Multiplication/{ => StrassensMatrixMultiplication.playground/Sources}/Number.swift (71%)

diff --git a/Strassen Matrix Multiplication/MatrixSize.swift b/Strassen Matrix Multiplication/MatrixSize.swift
deleted file mode 100644
index f1eada931..000000000
--- a/Strassen Matrix Multiplication/MatrixSize.swift	
+++ /dev/null
@@ -1,26 +0,0 @@
-//
-//  MatrixSize.swift
-//  
-//
-//  Created by Richard Ash on 10/28/16.
-//
-//
-
-import Foundation
-
-struct MatrixSize: Equatable {
-  let rows: Int
-  let columns: Int
-  
-  func forEach(_ body: (Int, Int) throws -> Void) rethrows {
-    for row in 0..<rows {
-      for column in 0..<columns {
-        try? body(row, column)
-      }
-    }
-  }
-}
-
-func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
-  return lhs.columns == rhs.columns && lhs.rows == rhs.rows
-}
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index d4b4d8330..50af60a6f 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -1,302 +1,7 @@
 //: Playground - noun: a place where people can play
 // Reference - http://mathworld.wolfram.com/StrassenFormulas.html
 
-
-import UIKit
-
-enum RowOrColumn {
-  case row, column
-}
-
-protocol Number: Multipliable, Addable {
-  static var zero: Self { get }
-}
-
-protocol Addable {
-  static func +(lhs: Self, rhs: Self) -> Self
-  static func -(lhs: Self, rhs: Self) -> Self
-}
-
-protocol Multipliable {
-  static func *(lhs: Self, rhs: Self) -> Self
-}
-
-extension Int: Number {
-  static var zero: Int {
-    return 0
-  }
-}
-
-extension Double: Number {
-  static var zero: Double {
-    return 0.0
-  }
-}
-
-extension Float: Number {
-  static var zero: Float {
-    return 0.0
-  }
-}
-
-
-extension Array where Element: Number {
-  func dot(_ b: Array<Element>) -> Element {
-    let a = self
-    assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
-    let c = a.indices.map{ a[$0] * b[$0] }
-    return c.reduce(Element.zero, { $0 + $1 })
-  }
-}
-
-struct MatrixSize: Equatable {
-  let rows: Int
-  let columns: Int
-  
-  func forEach(_ body: (Int, Int) throws -> Void) rethrows {
-    for row in 0..<rows {
-      for column in 0..<columns {
-        try? body(row, column)
-      }
-    }
-  }
-}
-
-func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
-  return lhs.columns == rhs.columns && lhs.rows == rhs.rows
-}
-
-
-struct Matrix<T: Number> {
-  
-  // MARK: - Variables
-  
-  let rows: Int, columns: Int
-  var grid: [T]
-  
-  var isSquare: Bool {
-    return rows == columns
-  }
-  
-  var size: MatrixSize {
-    return MatrixSize(rows: rows, columns: columns)
-  }
-  
-  // MARK: - Init
-  
-  init(rows: Int, columns: Int, initialValue: T = T.zero) {
-    self.rows = rows
-    self.columns = columns
-    self.grid = Array(repeating: initialValue, count: rows * columns)
-  }
-  
-  init(size: Int, initialValue: T = T.zero) {
-    self.rows = size
-    self.columns = size
-    self.grid = Array(repeating: initialValue, count: rows * columns)
-  }
-  
-  // MARK: - Subscript
-  
-  subscript(row: Int, column: Int) -> T {
-    get {
-      assert(indexIsValid(row: row, column: column), "Index out of range")
-      return grid[(row * columns) + column]
-    }
-    set {
-      assert(indexIsValid(row: row, column: column), "Index out of range")
-      grid[(row * columns) + column] = newValue
-    }
-  }
-  
-  subscript(type: RowOrColumn, value: Int) -> [T] {
-    get {
-      switch type {
-      case .row:
-        assert(indexIsValid(row: value, column: 0), "Index out of range")
-        return Array(grid[(value * columns)..<(value * columns) + columns])
-      case .column:
-        assert(indexIsValid(row: 0, column: value), "Index out of range")
-        var columns: [T] = []
-        for row in 0..<rows {
-          for column in 0..<self.columns {
-            if column == value {
-              columns.append(grid[(row * self.columns) + value])
-            }
-          }
-        }
-        return columns
-      }
-    } set {
-      switch type {
-      case .row:
-        assert(newValue.count == columns)
-        for (column, element) in newValue.enumerated() {
-          grid[(value * columns) + column] = element
-        }
-      case .column:
-        assert(newValue.count == rows)
-        for (row, element) in newValue.enumerated() {
-          grid[(row * columns) + value] = element
-        }
-      }
-    }
-  }
-  
-  // MARK: - Private Functions
-  
-  private func indexIsValid(row: Int, column: Int) -> Bool {
-    return row >= 0 && row < rows && column >= 0 && column < columns
-  }
-  
-  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.isSquare && B.isSquare, "This function requires square matricies!")
-    guard A.rows > 1 && B.rows > 1 else { return A * B }
-    
-    let n    = A.rows
-    let nBy2 = n / 2
-    
-    var a11 = Matrix(size: nBy2)
-    var a12 = Matrix(size: nBy2)
-    var a21 = Matrix(size: nBy2)
-    var a22 = Matrix(size: nBy2)
-    var b11 = Matrix(size: nBy2)
-    var b12 = Matrix(size: nBy2)
-    var b21 = Matrix(size: nBy2)
-    var b22 = Matrix(size: nBy2)
-    
-    for i in 0..<nBy2 {
-      for j in 0..<nBy2 {
-        a11[i,j] = A[i,j]
-        a12[i,j] = A[i, j+nBy2]
-        a21[i,j] = A[i+nBy2, j]
-        a22[i,j] = A[i+nBy2, j+nBy2]
-        b11[i,j] = B[i,j]
-        b12[i,j] = B[i, j+nBy2]
-        b21[i,j] = B[i+nBy2, j]
-        b22[i,j] = B[i+nBy2, j+nBy2]
-      }
-    }
-    
-    let q1 = (a11+a22).strassenR(by: b11+b22)    // (a11+a22)(b11+b22)
-    let q2 = (a21+a22).strassenR(by: b11)        // (a21+a22)b11
-    let q3 = a11.strassenR(by: b12-b22)          // a11(b12-b22)
-    let q4 = a22.strassenR(by: b21-b11)          // a22(-b11+b21)
-    let q5 = (a11+a12).strassenR(by: b22)        // (a11+a22)b22
-    let q6 = (a21-a11).strassenR(by: b11+b12)    // (-a11+a21)(b11+b12)
-    let q7 = (a12-a22).strassenR(by: b21+b22)    // (a12-a22)(b21+b22)
-    
-    let c11 = q1 + q4 - q5 + q7
-    let c12 = q3 + q5
-    let c21 = q2 + q4
-    let c22 = q1 + q3 - q2 + q6
-    var C   = Matrix(size: n)
-    
-    for i in 0..<nBy2 {
-      for j in 0..<nBy2 {
-        C[i, j]           = c11[i,j]
-        C[i, j+nBy2]      = c12[i,j]
-        C[i+nBy2, j]      = c21[i,j]
-        C[i+nBy2, j+nBy2] = c22[i,j]
-      }
-    }
-    
-    return C
-  }
-  
-  private func nextPowerOfTwo(of n: Int) -> Int {
-    return Int(pow(2, ceil(log2(Double(n)))))
-  }
-  
-  // MARK: - Functions
-  
-  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
-    let n = max(A.rows, A.columns, B.rows, B.columns)
-    let m = nextPowerOfTwo(of: n)
-    
-    var APrep = Matrix(size: m)
-    var BPrep = Matrix(size: m)
-    
-    A.size.forEach { (i, j) in
-      APrep[i,j] = A[i,j]
-    }
-    
-    B.size.forEach { (i, j) in
-      BPrep[i,j] = B[i,j]
-    }
-    
-    let CPrep = APrep.strassenR(by: BPrep)
-    var C = Matrix(rows: A.rows, columns: B.columns)
-    
-    for i in 0..<A.rows {
-      for j in 0..<B.columns {
-        C[i,j] = CPrep[i,j]
-      }
-    }
-    return C
-  }
-  
-  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
-    var C = Matrix<T>(rows: A.rows, columns: B.columns)
-    
-    for i in 0..<A.rows {
-      for j in 0..<B.columns {
-        C[i, j] = A[.row, i].dot(B[.column, j])
-      }
-    }
-    
-    return C
-  }
-}
-
-func *<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
-  
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] * rhs[row, column]
-    }
-  }
-  return newMatrix
-}
-
-func +<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
-  
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] + rhs[row, column]
-    }
-  }
-  return newMatrix
-}
-
-func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
-  
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] - rhs[row, column]
-    }
-  }
-  return newMatrix
-}
+import Foundation
 
 var A = Matrix(rows: 2, columns: 4, initialValue: 0)
 A[.row, 0] = [2, 3, -1, 0]
diff --git a/Strassen Matrix Multiplication/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
similarity index 72%
rename from Strassen Matrix Multiplication/Matrix.swift
rename to Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index 657cf3c80..eba49ce9a 100644
--- a/Strassen Matrix Multiplication/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -8,11 +8,11 @@
 
 import Foundation
 
-enum RowOrColumn {
+public enum RowOrColumn {
   case row, column
 }
 
-struct Matrix<T: Number> {
+public struct Matrix<T: Number> {
   
   // MARK: - Variables
   
@@ -29,20 +29,22 @@ struct Matrix<T: Number> {
   
   // MARK: - Init
   
-  init(rows: Int, columns: Int, initialValue: T = T.zero) {
+  public init(rows: Int, columns: Int, initialValue: T = T.zero) {
     self.rows = rows
     self.columns = columns
     self.grid = Array(repeating: initialValue, count: rows * columns)
   }
   
-  init(size: Int, initialValue: T = T.zero) {
+  public init(size: Int, initialValue: T = T.zero) {
     self.rows = size
     self.columns = size
     self.grid = Array(repeating: initialValue, count: rows * columns)
   }
-  
-  // MARK: - Subscript
-  
+}
+
+// MARK: - Public Functions
+
+public extension Matrix {
   subscript(row: Int, column: Int) -> T {
     get {
       assert(indexIsValid(row: row, column: column), "Index out of range")
@@ -88,13 +90,59 @@ struct Matrix<T: Number> {
     }
   }
   
-  // MARK: - Private Functions
+  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    let n = max(A.rows, A.columns, B.rows, B.columns)
+    let m = nextPowerOfTwo(of: n)
+    
+    var APrep = Matrix(size: m)
+    var BPrep = Matrix(size: m)
+    
+    A.size.forEach { (i, j) in
+      APrep[i,j] = A[i,j]
+    }
+    
+    B.size.forEach { (i, j) in
+      BPrep[i,j] = B[i,j]
+    }
+    
+    let CPrep = APrep.strassenR(by: BPrep)
+    var C = Matrix(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i,j] = CPrep[i,j]
+      }
+    }
+    return C
+  }
   
-  private func indexIsValid(row: Int, column: Int) -> Bool {
+  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    var C = Matrix<T>(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i, j] = A[.row, i].dot(B[.column, j])
+      }
+    }
+    
+    return C
+  }
+}
+
+// MARK: - Private Functions
+
+fileprivate extension Matrix {
+  func indexIsValid(row: Int, column: Int) -> Bool {
     return row >= 0 && row < rows && column >= 0 && column < columns
   }
   
-  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
+  func strassenR(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.isSquare && B.isSquare, "This function requires square matricies!")
     guard A.rows > 1 && B.rows > 1 else { return A * B }
@@ -150,97 +198,56 @@ struct Matrix<T: Number> {
     return C
   }
   
-  private func nextPowerOfTwo(of n: Int) -> Int {
+  func nextPowerOfTwo(of n: Int) -> Int {
     return Int(pow(2, ceil(log2(Double(n)))))
   }
-  
-  // MARK: - Functions
-  
-  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
-    let n = max(A.rows, A.columns, B.rows, B.columns)
-    let m = nextPowerOfTwo(of: n)
-    
-    var APrep = Matrix(size: m)
-    var BPrep = Matrix(size: m)
-    
-    A.size.forEach { (i, j) in
-      APrep[i,j] = A[i,j]
-    }
-    
-    B.size.forEach { (i, j) in
-      BPrep[i,j] = B[i,j]
-    }
-    
-    let CPrep = APrep.strassenR(by: BPrep)
-    var C = Matrix(rows: A.rows, columns: B.columns)
-    
-    for i in 0..<A.rows {
-      for j in 0..<B.columns {
-        C[i,j] = CPrep[i,j]
-      }
-    }
-    return C
-  }
-  
-  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
-    var C = Matrix<T>(rows: A.rows, columns: B.columns)
-    
-    for i in 0..<A.rows {
-      for j in 0..<B.columns {
-        C[i, j] = A[.row, i].dot(B[.column, j])
-      }
-    }
-    
-    return C
-  }
 }
 
+
 // Term-by-term Matrix Math
 
-func *<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
-  
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] * rhs[row, column]
+extension Matrix: Addable {
+  public static func +<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+    assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
+    let rows = lhs.rows
+    let columns = lhs.columns
+    
+    var newMatrix = Matrix<T>(rows: rows, columns: columns)
+    for row in 0..<rows {
+      for column in 0..<columns {
+        newMatrix[row, column] = lhs[row, column] + rhs[row, column]
+      }
     }
+    return newMatrix
   }
-  return newMatrix
-}
-
-func +<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
   
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] + rhs[row, column]
+  public static func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+    assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
+    let rows = lhs.rows
+    let columns = lhs.columns
+    
+    var newMatrix = Matrix<T>(rows: rows, columns: columns)
+    for row in 0..<rows {
+      for column in 0..<columns {
+        newMatrix[row, column] = lhs[row, column] - rhs[row, column]
+      }
     }
+    return newMatrix
   }
-  return newMatrix
 }
 
-func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
-  assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
-  let rows = lhs.rows
-  let columns = lhs.columns
-  
-  var newMatrix = Matrix<T>(rows: rows, columns: columns)
-  for row in 0..<rows {
-    for column in 0..<columns {
-      newMatrix[row, column] = lhs[row, column] - rhs[row, column]
+extension Matrix: Multipliable {
+  public static func *<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
+    assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
+    let rows = lhs.rows
+    let columns = lhs.columns
+    
+    var newMatrix = Matrix<T>(rows: rows, columns: columns)
+    for row in 0..<rows {
+      for column in 0..<columns {
+        newMatrix[row, column] = lhs[row, column] * rhs[row, column]
+      }
     }
+    return newMatrix
   }
-  return newMatrix
 }
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift
new file mode 100644
index 000000000..f4a604ade
--- /dev/null
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift	
@@ -0,0 +1,33 @@
+//
+//  MatrixSize.swift
+//  
+//
+//  Created by Richard Ash on 10/28/16.
+//
+//
+
+import Foundation
+
+public struct MatrixSize: Equatable {
+  let rows: Int
+  let columns: Int
+  
+  public init(rows: Int, columns: Int) {
+    self.rows = rows
+    self.columns = columns
+  }
+  
+  public func forEach(_ body: (Int, Int) throws -> Void) rethrows {
+    for row in 0..<rows {
+      for column in 0..<columns {
+        try? body(row, column)
+      }
+    }
+  }
+}
+
+public extension MatrixSize {
+  static func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
+    return lhs.columns == rhs.columns && lhs.rows == rhs.rows
+  }
+}
diff --git a/Strassen Matrix Multiplication/Number.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift
similarity index 71%
rename from Strassen Matrix Multiplication/Number.swift
rename to Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift
index 34c6d5308..9f4c7f4ab 100644
--- a/Strassen Matrix Multiplication/Number.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
@@ -8,40 +8,39 @@
 
 import Foundation
 
-protocol Number: Multipliable, Addable {
+public protocol Number: Multipliable, Addable {
   static var zero: Self { get }
 }
 
-protocol Addable {
+public protocol Addable {
   static func +(lhs: Self, rhs: Self) -> Self
   static func -(lhs: Self, rhs: Self) -> Self
 }
 
-protocol Multipliable {
+public protocol Multipliable {
   static func *(lhs: Self, rhs: Self) -> Self
 }
 
 extension Int: Number {
-  static var zero: Int {
+  public static var zero: Int {
     return 0
   }
 }
 
 extension Double: Number {
-  static var zero: Double {
+  public static var zero: Double {
     return 0.0
   }
 }
 
 extension Float: Number {
-  static var zero: Float {
+  public static var zero: Float {
     return 0.0
   }
 }
 
-
 extension Array where Element: Number {
-  func dot(_ b: Array<Element>) -> Element {
+  public func dot(_ b: Array<Element>) -> Element {
     let a = self
     assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
     let c = a.indices.map{ a[$0] * b[$0] }

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 006/862] 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 007/862] 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 008/862] 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 009/862] 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 717794dcb7cfaba84bc5f2dbbe3f316e5b7f57f7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Micha=C3=ABl=20Azevedo?= <mazevedo@prynel.com>
Date: Wed, 1 Feb 2017 16:05:06 +0100
Subject: [PATCH 010/862] Fixed the trimming of deques

---
 Deque/Deque-Optimized.swift |  6 ++++--
 Deque/README.markdown       | 12 ++++++++----
 2 files changed, 12 insertions(+), 6 deletions(-)

diff --git a/Deque/Deque-Optimized.swift b/Deque/Deque-Optimized.swift
index 6326b457b..f565458c7 100644
--- a/Deque/Deque-Optimized.swift
+++ b/Deque/Deque-Optimized.swift
@@ -7,9 +7,11 @@ public struct Deque<T> {
   private var array: [T?]
   private var head: Int
   private var capacity: Int
+  private let originalCapacity:Int
 
   public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
+    originalCapacity = self.capacity
     array = [T?](repeating: nil, count: capacity)
     head = capacity
   }
@@ -30,7 +32,7 @@ public struct Deque<T> {
     if head == 0 {
       capacity *= 2
       let emptySpace = [T?](repeating: nil, count: capacity)
-      array.insertContentsOf(emptySpace, at: 0)
+      array.insert(contentsOf: emptySpace, at: 0)
       head = capacity
     }
 
@@ -44,7 +46,7 @@ public struct Deque<T> {
     array[head] = nil
     head += 1
 
-    if capacity > 10 && head >= capacity*2 {
+    if capacity >= originalCapacity && head >= capacity*2 {
       let amountToRemove = capacity + capacity/2
       array.removeFirst(amountToRemove)
       head -= amountToRemove
diff --git a/Deque/README.markdown b/Deque/README.markdown
index 5858f3e6d..d156f9d97 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -119,9 +119,11 @@ public struct Deque<T> {
   private var array: [T?]
   private var head: Int
   private var capacity: Int
+  private let originalCapacity:Int
   
   public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
+    originalCapacity = self.capacity
     array = [T?](repeating: nil, count: capacity)
     head = capacity
   }
@@ -267,7 +269,7 @@ Those empty spots at the front only get used when you call `enqueueFront()`. But
     array[head] = nil
     head += 1
 
-    if capacity > 10 && head >= capacity*2 {
+    if capacity >= originalCapacity && head >= capacity*2 {
       let amountToRemove = capacity + capacity/2
       array.removeFirst(amountToRemove)
       head -= amountToRemove
@@ -279,6 +281,8 @@ Those empty spots at the front only get used when you call `enqueueFront()`. But
 
 Recall that `capacity` is the original number of empty places at the front of the queue. If the `head` has advanced more to the right than twice the capacity, then it's time to trim off a bunch of these empty spots. We reduce it to about 25%.
 
+> **Note:**  he deque will keep at least its original capacity by comparing `capacity` to `originalCapacity`.
+
 For example, this:
 
 	[ x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, 1, 2, 3 ]
@@ -288,9 +292,9 @@ For example, this:
 becomes after trimming:
 
 	[ x, x, x, x, x, 1, 2, 3 ]
-	              |
-	              head
-	              capacity
+	                 |
+	                 head
+	                 capacity
 
 This way we can strike a balance between fast enqueuing and dequeuing at the front and keeping the memory requirements reasonable.
 

From 096eca30aa4a686f4d0839321dd99089d63c6c5a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Micha=C3=ABl=20Azevedo?= <mazevedo@prynel.com>
Date: Wed, 1 Feb 2017 16:07:50 +0100
Subject: [PATCH 011/862] Typo fixed

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

diff --git a/Deque/README.markdown b/Deque/README.markdown
index d156f9d97..67a734576 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -281,7 +281,7 @@ Those empty spots at the front only get used when you call `enqueueFront()`. But
 
 Recall that `capacity` is the original number of empty places at the front of the queue. If the `head` has advanced more to the right than twice the capacity, then it's time to trim off a bunch of these empty spots. We reduce it to about 25%.
 
-> **Note:**  he deque will keep at least its original capacity by comparing `capacity` to `originalCapacity`.
+> **Note:**  The deque will keep at least its original capacity by comparing `capacity` to `originalCapacity`.
 
 For example, this:
 

From 89d84fcd5be39d7a88357b5d6da5de7cec88c8fb Mon Sep 17 00:00:00 2001
From: Jaap <wijnen.jaap@gmail.com>
Date: Sun, 19 Feb 2017 14:58:50 +0100
Subject: [PATCH 012/862] Convex Hull algorithm

---
 .../Convex Hull.xcodeproj/project.pbxproj     | 297 ++++++++++++++++++
 .../contents.xcworkspacedata                  |   7 +
 Convex Hull/Convex Hull/AppDelegate.swift     |  57 ++++
 .../AppIcon.appiconset/Contents.json          |  93 ++++++
 .../Base.lproj/LaunchScreen.storyboard        |  27 ++
 Convex Hull/Convex Hull/Info.plist            |  47 +++
 Convex Hull/Convex Hull/View.swift            | 177 +++++++++++
 Convex Hull/README.md                         |  41 +++
 8 files changed, 746 insertions(+)
 create mode 100644 Convex Hull/Convex Hull.xcodeproj/project.pbxproj
 create mode 100644 Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/contents.xcworkspacedata
 create mode 100644 Convex Hull/Convex Hull/AppDelegate.swift
 create mode 100644 Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json
 create mode 100644 Convex Hull/Convex Hull/Base.lproj/LaunchScreen.storyboard
 create mode 100644 Convex Hull/Convex Hull/Info.plist
 create mode 100644 Convex Hull/Convex Hull/View.swift
 create mode 100644 Convex Hull/README.md

diff --git a/Convex Hull/Convex Hull.xcodeproj/project.pbxproj b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj
new file mode 100644
index 000000000..2f236b013
--- /dev/null
+++ b/Convex Hull/Convex Hull.xcodeproj/project.pbxproj	
@@ -0,0 +1,297 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 46;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		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 PBXFileReference section */
+		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>"; };
+		8E6D68C31E59989400161780 /* Base */ = {isa = PBXFileReference; lastKnownFileType = file.storyboard; name = Base; path = Base.lproj/LaunchScreen.storyboard; sourceTree = "<group>"; };
+		8E6D68C51E59989400161780 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		8E6D68CB1E599CF100161780 /* View.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = View.swift; sourceTree = "<group>"; };
+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		8E6D68B31E59989400161780 /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		8E6D68AD1E59989400161780 = {
+			isa = PBXGroup;
+			children = (
+				8E6D68B81E59989400161780 /* Convex Hull */,
+				8E6D68B71E59989400161780 /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		8E6D68B71E59989400161780 /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				8E6D68B61E59989400161780 /* Convex Hull.app */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		8E6D68B81E59989400161780 /* Convex Hull */ = {
+			isa = PBXGroup;
+			children = (
+				8E6D68B91E59989400161780 /* AppDelegate.swift */,
+				8E6D68CB1E599CF100161780 /* View.swift */,
+				8E6D68C01E59989400161780 /* Assets.xcassets */,
+				8E6D68C21E59989400161780 /* LaunchScreen.storyboard */,
+				8E6D68C51E59989400161780 /* Info.plist */,
+			);
+			path = "Convex Hull";
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		8E6D68B51E59989400161780 /* Convex Hull */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 8E6D68C81E59989400161780 /* Build configuration list for PBXNativeTarget "Convex Hull" */;
+			buildPhases = (
+				8E6D68B21E59989400161780 /* Sources */,
+				8E6D68B31E59989400161780 /* Frameworks */,
+				8E6D68B41E59989400161780 /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = "Convex Hull";
+			productName = "Convex Hull";
+			productReference = 8E6D68B61E59989400161780 /* Convex Hull.app */;
+			productType = "com.apple.product-type.application";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		8E6D68AE1E59989400161780 /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0820;
+				LastUpgradeCheck = 0820;
+				ORGANIZATIONNAME = Workmoose;
+				TargetAttributes = {
+					8E6D68B51E59989400161780 = {
+						CreatedOnToolsVersion = 8.2.1;
+						DevelopmentTeam = 7C4LVS3ZVC;
+						ProvisioningStyle = Automatic;
+					};
+				};
+			};
+			buildConfigurationList = 8E6D68B11E59989400161780 /* Build configuration list for PBXProject "Convex Hull" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 8E6D68AD1E59989400161780;
+			productRefGroup = 8E6D68B71E59989400161780 /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				8E6D68B51E59989400161780 /* Convex Hull */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		8E6D68B41E59989400161780 /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				8E6D68C41E59989400161780 /* LaunchScreen.storyboard in Resources */,
+				8E6D68C11E59989400161780 /* Assets.xcassets in Resources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		8E6D68B21E59989400161780 /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				8E6D68BA1E59989400161780 /* AppDelegate.swift in Sources */,
+				8E6D68CC1E599CF100161780 /* View.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin PBXVariantGroup section */
+		8E6D68C21E59989400161780 /* LaunchScreen.storyboard */ = {
+			isa = PBXVariantGroup;
+			children = (
+				8E6D68C31E59989400161780 /* Base */,
+			);
+			name = LaunchScreen.storyboard;
+			sourceTree = "<group>";
+		};
+/* End PBXVariantGroup section */
+
+/* Begin XCBuildConfiguration section */
+		8E6D68C61E59989400161780 /* 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[sdk=iphoneos*]" = "iPhone Developer";
+				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;
+				IPHONEOS_DEPLOYMENT_TARGET = 10.2;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = iphoneos;
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				TARGETED_DEVICE_FAMILY = "1,2";
+			};
+			name = Debug;
+		};
+		8E6D68C71E59989400161780 /* 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[sdk=iphoneos*]" = "iPhone Developer";
+				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;
+				IPHONEOS_DEPLOYMENT_TARGET = 10.2;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = iphoneos;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+				TARGETED_DEVICE_FAMILY = "1,2";
+				VALIDATE_PRODUCT = YES;
+			};
+			name = Release;
+		};
+		8E6D68C91E59989400161780 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
+				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				INFOPLIST_FILE = "Convex Hull/Info.plist";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Debug;
+		};
+		8E6D68CA1E59989400161780 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
+				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				INFOPLIST_FILE = "Convex Hull/Info.plist";
+				LD_RUNPATH_SEARCH_PATHS = "$(inherited) @executable_path/Frameworks";
+				PRODUCT_BUNDLE_IDENTIFIER = "workmoose.Convex-Hull";
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		8E6D68B11E59989400161780 /* Build configuration list for PBXProject "Convex Hull" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				8E6D68C61E59989400161780 /* Debug */,
+				8E6D68C71E59989400161780 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		8E6D68C81E59989400161780 /* Build configuration list for PBXNativeTarget "Convex Hull" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				8E6D68C91E59989400161780 /* Debug */,
+				8E6D68CA1E59989400161780 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 8E6D68AE1E59989400161780 /* Project object */;
+}
diff --git a/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/contents.xcworkspacedata b/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..dfcd4bc52
--- /dev/null
+++ b/Convex Hull/Convex Hull.xcodeproj/project.xcworkspace/contents.xcworkspacedata	
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:Convex Hull.xcodeproj">
+   </FileRef>
+</Workspace>
diff --git a/Convex Hull/Convex Hull/AppDelegate.swift b/Convex Hull/Convex Hull/AppDelegate.swift
new file mode 100644
index 000000000..1901083a8
--- /dev/null
+++ b/Convex Hull/Convex Hull/AppDelegate.swift	
@@ -0,0 +1,57 @@
+//
+//  AppDelegate.swift
+//  Convex Hull
+//
+//  Created by Jaap Wijnen on 19/02/2017.
+//  Copyright © 2017 Workmoose. All rights reserved.
+//
+
+import UIKit
+
+@UIApplicationMain
+class AppDelegate: UIResponder, UIApplicationDelegate {
+
+    var window: UIWindow?
+
+
+    func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplicationLaunchOptionsKey: Any]?) -> Bool {
+
+        let screenBounds = UIScreen.main.bounds
+        
+        window = UIWindow(frame: screenBounds)
+        
+        let viewController = UIViewController()
+        viewController.view = View(frame: (window?.frame)!)
+        viewController.view.backgroundColor = .white
+        
+        window?.rootViewController = viewController
+        window?.makeKeyAndVisible()
+        
+        return true
+    }
+
+    func applicationWillResignActive(_ application: UIApplication) {
+        // Sent when the application is about to move from active to inactive state. This can occur for certain types of temporary interruptions (such as an incoming phone call or SMS message) or when the user quits the application and it begins the transition to the background state.
+        // Use this method to pause ongoing tasks, disable timers, and invalidate graphics rendering callbacks. Games should use this method to pause the game.
+    }
+
+    func applicationDidEnterBackground(_ application: UIApplication) {
+        // Use this method to release shared resources, save user data, invalidate timers, and store enough application state information to restore your application to its current state in case it is terminated later.
+        // If your application supports background execution, this method is called instead of applicationWillTerminate: when the user quits.
+    }
+
+    func applicationWillEnterForeground(_ application: UIApplication) {
+        // Called as part of the transition from the background to the active state; here you can undo many of the changes made on entering the background.
+    }
+
+    func applicationDidBecomeActive(_ application: UIApplication) {
+        // Restart any tasks that were paused (or not yet started) while the application was inactive. If the application was previously in the background, optionally refresh the user interface.
+    }
+
+    func applicationWillTerminate(_ application: UIApplication) {
+        // Called when the application is about to terminate. Save data if appropriate. See also applicationDidEnterBackground:.
+    }
+
+
+}
+
diff --git a/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json b/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json
new file mode 100644
index 000000000..1d060ed28
--- /dev/null
+++ b/Convex Hull/Convex Hull/Assets.xcassets/AppIcon.appiconset/Contents.json	
@@ -0,0 +1,93 @@
+{
+  "images" : [
+    {
+      "idiom" : "iphone",
+      "size" : "20x20",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "20x20",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "29x29",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "29x29",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "40x40",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "40x40",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "60x60",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "iphone",
+      "size" : "60x60",
+      "scale" : "3x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "20x20",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "20x20",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "29x29",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "29x29",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "40x40",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "40x40",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "76x76",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "76x76",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "ipad",
+      "size" : "83.5x83.5",
+      "scale" : "2x"
+    }
+  ],
+  "info" : {
+    "version" : 1,
+    "author" : "xcode"
+  }
+}
\ No newline at end of file
diff --git a/Convex Hull/Convex Hull/Base.lproj/LaunchScreen.storyboard b/Convex Hull/Convex Hull/Base.lproj/LaunchScreen.storyboard
new file mode 100644
index 000000000..fdf3f97d1
--- /dev/null
+++ b/Convex Hull/Convex Hull/Base.lproj/LaunchScreen.storyboard	
@@ -0,0 +1,27 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="11134" systemVersion="15F34" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" launchScreen="YES" useTraitCollections="YES" colorMatched="YES" initialViewController="01J-lp-oVM">
+    <dependencies>
+        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="11106"/>
+        <capability name="documents saved in the Xcode 8 format" minToolsVersion="8.0"/>
+    </dependencies>
+    <scenes>
+        <!--View Controller-->
+        <scene sceneID="EHf-IW-A2E">
+            <objects>
+                <viewController id="01J-lp-oVM" sceneMemberID="viewController">
+                    <layoutGuides>
+                        <viewControllerLayoutGuide type="top" id="Llm-lL-Icb"/>
+                        <viewControllerLayoutGuide type="bottom" id="xb3-aO-Qok"/>
+                    </layoutGuides>
+                    <view key="view" contentMode="scaleToFill" id="Ze5-6b-2t3">
+                        <rect key="frame" x="0.0" y="0.0" width="375" height="667"/>
+                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
+                        <color key="backgroundColor" red="1" green="1" blue="1" alpha="1" colorSpace="custom" customColorSpace="sRGB"/>
+                    </view>
+                </viewController>
+                <placeholder placeholderIdentifier="IBFirstResponder" id="iYj-Kq-Ea1" userLabel="First Responder" sceneMemberID="firstResponder"/>
+            </objects>
+            <point key="canvasLocation" x="53" y="375"/>
+        </scene>
+    </scenes>
+</document>
diff --git a/Convex Hull/Convex Hull/Info.plist b/Convex Hull/Convex Hull/Info.plist
new file mode 100644
index 000000000..390c5347e
--- /dev/null
+++ b/Convex Hull/Convex Hull/Info.plist	
@@ -0,0 +1,47 @@
+<?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>APPL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>1.0</string>
+	<key>CFBundleVersion</key>
+	<string>1</string>
+	<key>LSRequiresIPhoneOS</key>
+	<true/>
+	<key>UILaunchStoryboardName</key>
+	<string>LaunchScreen</string>
+	<key>UIRequiredDeviceCapabilities</key>
+	<array>
+		<string>armv7</string>
+	</array>
+	<key>UIRequiresFullScreen</key>
+	<true/>
+	<key>UIStatusBarHidden</key>
+	<true/>
+	<key>UISupportedInterfaceOrientations</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+	<key>UISupportedInterfaceOrientations~ipad</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationPortraitUpsideDown</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+</dict>
+</plist>
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
new file mode 100644
index 000000000..2d7157e6f
--- /dev/null
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -0,0 +1,177 @@
+//
+//  View.swift
+//  Convex Hull
+//
+//  Created by Jaap Wijnen on 19/02/2017.
+//  Copyright © 2017 Workmoose. All rights reserved.
+//
+
+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")
+    }
+    
+    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
+        }
+    }
+    
+    func quickHull(points: [CGPoint]) {
+        var pts = points
+                
+        // 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()
+        
+        // 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 p2 to p1
+        var s2 = [CGPoint]()
+        
+        // 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.
+            
+            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)
+    }
+    
+    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
+        }
+        
+        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
+            if dist > maxDist { // if distance is larger than current maxDist remember new point p
+                maxDist = dist
+                maxPoint = p
+            }
+        }
+        
+        convexHull.insert(maxPoint, at: convexHull.index(of: p1)! + 1) // insert point with max distance from line in the convexHull after p1
+        
+        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 p1 to maxPoint
+        var s1 = [CGPoint]()
+        
+        // points to the right of oriented line from maxPoint to p2
+        var s2 = [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)
+        
+        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
+            
+            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
+
+            if sign1 > 0 { // right of p1 maxPoint line
+                s1.append(p)
+            } else if sign2 > 0 { // right of maxPoint p2 line
+                s2.append(p)
+            }
+        }
+        
+        // find new hull points
+        findHull(s1, p1, maxPoint)
+        findHull(s2, maxPoint, p2)
+    }
+
+    override func draw(_ rect: CGRect) {
+        
+        let context = UIGraphicsGetCurrentContext()
+        
+        // Draw hull
+        let lineWidth:CGFloat = 2.0
+        
+        context!.setFillColor(UIColor.black.cgColor)
+        context!.setLineWidth(lineWidth)
+        context!.setStrokeColor(UIColor.red.cgColor)
+        context!.setFillColor(UIColor.black.cgColor)
+        
+        let firstPoint = convexHull.first!
+        context!.move(to: firstPoint)
+        
+        for p in convexHull.dropFirst() {
+            context!.addLine(to: p)
+        }
+        context!.addLine(to: firstPoint)
+        
+        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)
+        }
+    }
+}
diff --git a/Convex Hull/README.md b/Convex Hull/README.md
new file mode 100644
index 000000000..b73f66176
--- /dev/null
+++ b/Convex Hull/README.md	
@@ -0,0 +1,41 @@
+# 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 dimention. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points.
+
+## 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:
+
+`findHull(points: [CGPoint], p1: CGPoint, p2: CGPoint)`
+
+```
+findHull(S1, A, B)
+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`)
+4. Add `maxPoint` to the hull right after `p1`.
+5. Draw a line (`line1`) from `p1` to `maxPoint`.
+6. Draw a line (`line2`) from `maxPoint` to `p2`. (These lines now form a triangle)
+7. All points within this triangle are of course not part of the hull and thus can be ignored. We check which points in `points` are to the right of `line1` these are grouped in an array `s1`.
+8. All points that are to the right of `line2` are grouped in an array `s2`. Note that there are no points that are both to the right of `line1` and `line2` as then `maxPoint` wouldn't be the point furthest away from our initial line between `p1` and `p2`.
+9. We call `findHull(_, _, _)` again on our new groups of points to find more hull points.
+```
+findHull(s1, p1, maxPoint)
+findHull(s2, maxPoint, p2)
+```
+
+This eventually leaves us with an array of points describing the convex hull.
+
+## See also
+
+[Convex Hull on Wikipedia](https://en.wikipedia.org/wiki/Convex_hull_algorithms)
+
+*Written for the Swift Algorithm Club by Jaap Wijnen.*

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 013/862] 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 217cad58d2501c10d040fd72cbcaea96d366fc72 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Mon, 20 Feb 2017 10:25:31 +0800
Subject: [PATCH 014/862] Update README.markdown

add swift version
---
 Shell Sort/README.markdown | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)

diff --git a/Shell Sort/README.markdown b/Shell Sort/README.markdown
index 6cb682035..a2ac843c7 100644
--- a/Shell Sort/README.markdown	
+++ b/Shell Sort/README.markdown	
@@ -111,6 +111,28 @@ This is an old Commodore 64 BASIC version of shell sort that Matthijs used a lon
 	61300 GOTO 61220
 	61310 RETURN
 
+## The Code:
+Here is an implementation of Shell Sort in Swift:
+```
+var arr = [64, 20, 50, 33, 72, 10, 23, -1, 4, 5]
+
+var n = arr.count / 2
+
+repeat
+{
+    for index in 0..<arr.count{
+        
+        if (index + n) < arr.count && arr[index] > arr[index + n]{
+        
+            swap(&arr[index], &arr[index + n])
+        }
+    }
+    
+    n = n / 2
+    
+}while n > 0
+```
+
 ## See also
 
 [Shellsort on Wikipedia](https://en.wikipedia.org/wiki/Shellsort)

From 71bfd719ce6024944e7c17847952d77094be6cc8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Sun, 26 Feb 2017 12:41:50 +0800
Subject: [PATCH 015/862] add file ShellSortExample.swift

update code
---
 Shell Sort/ShellSortExample.swift | 33 +++++++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)
 create mode 100644 Shell Sort/ShellSortExample.swift

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
new file mode 100644
index 000000000..eea80e539
--- /dev/null
+++ b/Shell Sort/ShellSortExample.swift	
@@ -0,0 +1,33 @@
+//
+//  ShellSortExample.swift
+//  
+//
+//  Created by Cheer on 2017/2/26.
+//
+//
+
+import Foundation
+
+public func shellSort(_ list : inout [Int])
+{
+    var sublistCount = list.count / 2
+    
+    while sublistCount > 0
+    {
+        for index in 0..<arr.count{
+            
+            guard index + sublistCount < arr.count else { break }
+            
+            if arr[index] > arr[index + sublistCount]{
+                swap(&arr[index], &arr[index + sublistCount])
+            }
+            
+            guard sublistCount == 1 && index > 0 else { continue }
+            
+            if arr[index - 1] > arr[index]{
+                swap(&arr[index - 1], &arr[index])
+            }
+        }
+        sublistCount = sublistCount / 2
+    }
+}

From 8202cf1668a535b61fbac12962ebc5a639631ee1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Mon, 27 Feb 2017 10:52:37 +0800
Subject: [PATCH 016/862] Update ShellSortExample.swift

Fix my code mistakes
---
 Shell Sort/ShellSortExample.swift | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index eea80e539..68cd9ead1 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -14,18 +14,18 @@ public func shellSort(_ list : inout [Int])
     
     while sublistCount > 0
     {
-        for index in 0..<arr.count{
+        for index in 0..<list.count{
             
-            guard index + sublistCount < arr.count else { break }
+            guard index + sublistCount < list.count else { break }
             
-            if arr[index] > arr[index + sublistCount]{
-                swap(&arr[index], &arr[index + sublistCount])
+            if list[index] > list[index + sublistCount]{
+                swap(&list[index], &list[index + sublistCount])
             }
             
             guard sublistCount == 1 && index > 0 else { continue }
             
-            if arr[index - 1] > arr[index]{
-                swap(&arr[index - 1], &arr[index])
+            if list[index - 1] > list[index]{
+                swap(&list[index - 1], &list[index])
             }
         }
         sublistCount = sublistCount / 2

From 69cb42eef48c610f2f42e6c5d51781fdb3482e6a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Wed, 1 Mar 2017 12:13:54 +0800
Subject: [PATCH 017/862] Update ShellSortExample.swift

let code to suit style guide
---
 Shell Sort/ShellSortExample.swift | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index 68cd9ead1..efa035da3 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -8,23 +8,23 @@
 
 import Foundation
 
-public func shellSort(_ list : inout [Int])
-{
-    var sublistCount = list.count / 2
+public func shellSort(_ list: inout [Int]) {
     
-    while sublistCount > 0
-    {
-        for index in 0..<list.count{
-            
+    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]{
+            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]{
+            if list[index - 1] > list[index] {
                 swap(&list[index - 1], &list[index])
             }
         }

From a69e3d84fcdc3bb8ab1d9e788f8826e5e9ab4254 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Thu, 2 Mar 2017 10:47:14 +0800
Subject: [PATCH 018/862] Update README.markdown

update sample code
---
 Shell Sort/README.markdown | 34 ++++++++++++++++++++++------------
 1 file changed, 22 insertions(+), 12 deletions(-)

diff --git a/Shell Sort/README.markdown b/Shell Sort/README.markdown
index a2ac843c7..9c4bdf076 100644
--- a/Shell Sort/README.markdown	
+++ b/Shell Sort/README.markdown	
@@ -116,21 +116,31 @@ Here is an implementation of Shell Sort in Swift:
 ```
 var arr = [64, 20, 50, 33, 72, 10, 23, -1, 4, 5]
 
-var n = arr.count / 2
-
-repeat
-{
-    for index in 0..<arr.count{
-        
-        if (index + n) < arr.count && arr[index] > arr[index + n]{
+public func shellSort(_ list: inout [Int]) {
+    
+    var sublistCount = list.count / 2
+   
+    while sublistCount > 0 {
         
-            swap(&arr[index], &arr[index + n])
+        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])
+            }
         }
+        sublistCount = sublistCount / 2
     }
-    
-    n = n / 2
-    
-}while n > 0
+}
+
+shellSort(&arr)
 ```
 
 ## See also

From b4e4ef1c8095405c21e69284807095f548fea537 Mon Sep 17 00:00:00 2001
From: John Pham <hprobotic@gmail.com>
Date: Thu, 2 Mar 2017 17:10:59 +0700
Subject: [PATCH 019/862] Update dim func follow syntax change of swift 3

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

diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index 51e77435e..b98a09593 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -36,7 +36,7 @@ var cookies = [[Int]](repeating: [Int](repeating: 0, count: 7), count: 9)
 but that's just ugly. To be fair, you can hide the ugliness in a helper function:
 
 ```swift
-func dim<T>(count: Int, _ value: T) -> [T] {
+func dim<T>(_ count: Int, _ value: T) -> [T] {
   return [T](repeating: value, count: count)
 }
 ```

From 0837113e9e8a0fa69d2e8deb8302bb0a72c5d5b5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Thu, 2 Mar 2017 19:19:18 +0800
Subject: [PATCH 020/862] Add files via upload

upload a radix sort implement,faster than original code
---
 Radix Sort/RadixSortExample.swift | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)
 create mode 100644 Radix Sort/RadixSortExample.swift

diff --git a/Radix Sort/RadixSortExample.swift b/Radix Sort/RadixSortExample.swift
new file mode 100644
index 000000000..7d9461c5c
--- /dev/null
+++ b/Radix Sort/RadixSortExample.swift	
@@ -0,0 +1,29 @@
+//
+//  RadixSortExample.swift
+//  
+//
+//  Created by Cheer on 2017/3/2.
+//
+//
+
+import Foundation
+
+func radixSort1(_ arr: inout [Int]) {
+   
+    var temp = [[Int]](repeating: [], count: 10)
+    
+    for num in arr { temp[num % 10].append(num) }
+    
+    for i in 1...Int(arr.max()!.description.characters.count) {
+        
+        for index in 0..<temp.count {
+           
+            for num in temp[index] {
+                temp[index].remove(at: temp[index].index(of: num)!)
+                temp[(num / Int(pow(10, Double(i)))) % 10].append(num)
+            }
+        }
+    }
+    
+    arr = temp[0]
+}

From 10615dfff7a40ca130d6b2c02a9bedc0c161faac Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Fri, 3 Mar 2017 11:13:22 +0800
Subject: [PATCH 021/862] Update LinearSearch.swift

more swift
---
 Linear Search/LinearSearch.swift | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/Linear Search/LinearSearch.swift b/Linear Search/LinearSearch.swift
index 882795180..c5374d0a4 100644
--- a/Linear Search/LinearSearch.swift	
+++ b/Linear Search/LinearSearch.swift	
@@ -4,3 +4,7 @@ func linearSearch<T: Equatable>(_ array: [T], _ object: T) -> Int? {
   }
   return nil
 }
+
+func linearSearch1<T: Equatable>(_ array: [T], _ object: T) -> Array<T>.Index? {
+    return array.index { $0 == object }
+}

From 12b0bdbb8488f7746edac33623b2f86c57564a31 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Fri, 3 Mar 2017 11:34:04 +0800
Subject: [PATCH 022/862] Update README.markdown

update some details
---
 Select Minimum Maximum/README.markdown | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Select Minimum Maximum/README.markdown b/Select Minimum Maximum/README.markdown
index 09ca97039..fa0f8fed8 100644
--- a/Select Minimum Maximum/README.markdown	
+++ b/Select Minimum Maximum/README.markdown	
@@ -68,6 +68,13 @@ array.minElement()   // This will return 3
 array.maxElement()   // This will return 9
 ```
 
+```
+let array = [ 8, 3, 9, 4, 6 ]
+//swift3
+array.min()   // This will return 3
+array.max()   // This will return 9
+```
+
 ## Maximum and minimum
 
 To find both the maximum and minimum values contained in array while minimizing the number of comparisons we can compare the items in pairs. 

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 023/862] 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 024/862] 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 025/862] 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 026/862] 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 027/862] 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 028/862] 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 029/862] 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 030/862] 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 cae6d08a8c1ea02fdf37c6481e965b74457b0eaa Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Mon, 6 Mar 2017 15:15:06 -0500
Subject: [PATCH 031/862] Update link for radix sort

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

diff --git a/README.markdown b/README.markdown
index e2d99e2bc..dfe451478 100644
--- a/README.markdown
+++ b/README.markdown
@@ -80,7 +80,7 @@ Fast sorts:
 Special-purpose sorts:
 
 - [Counting Sort](Counting Sort/)
-- Radix Sort
+- [Radix Sort](Radix Sort/)
 - [Topological Sort](Topological Sort/)
 
 Bad sorting algorithms (don't use these!):

From ce1ec8842561fb69c02f835278539f4bab287a8e Mon Sep 17 00:00:00 2001
From: "JUNYEONG.YOO" <woody.chiz@gmail.com>
Date: Tue, 7 Mar 2017 19:31:50 +0900
Subject: [PATCH 032/862] Modified typo in README.md of QuickSort

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

diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index e3d284333..d359ecb5c 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -30,7 +30,7 @@ Here's how it works. When given an array, `quicksort()` splits it up into three
 
 All the elements less than the pivot go into a new array called `less`. All the elements equal to the pivot go into the `equal` array. And you guessed it, all elements greater than the pivot go into the third array, `greater`. This is why the generic type `T` must be `Comparable`, so we can compare the elements with `<`, `==`, and `>`.
 
-Once we have these three arrays, `quicksort()` recursively sorts the `less` array and the `right` array, then glues those sorted subarrays back together with the `equal` array to get the final result. 
+Once we have these three arrays, `quicksort()` recursively sorts the `less` array and the `greater` array, then glues those sorted subarrays back together with the `equal` array to get the final result. 
 
 ## An example
 
@@ -44,7 +44,7 @@ First, we pick the pivot element. That is `8` because it's in the middle of the
 	equal:   [ 8, 8 ]
 	greater: [ 10, 9, 14, 27, 26 ]
 
-This is a good split because `less` and `equal` roughly contain the same number of elements. So we've picked a good pivot that chopped the array right down the middle.
+This is a good split because `less` and `greater` roughly contain the same number of elements. So we've picked a good pivot that chopped the array right down the middle.
 
 Note that the `less` and `greater` arrays aren't sorted yet, so we call `quicksort()` again to sort those two subarrays. That does the exact same thing: pick a pivot and split the subarray into three even smaller parts.
 

From 7a5700dbae300b075195842482cb74981ae5fc9e Mon Sep 17 00:00:00 2001
From: Daniel Santos <dsantosp12@gmail.com>
Date: Wed, 8 Mar 2017 19:44:06 -0500
Subject: [PATCH 033/862] added ExpressibleByArrayLiteral to the Linked List
 and wrote test for the new initializer.

---
 .../LinkedList.playground/Contents.swift      | 22 +++++++++++++++++--
 Linked List/LinkedList.swift                  | 10 ++++++++-
 Linked List/Tests/LinkedListTests.swift       | 22 +++++++++++++++++++
 3 files changed, 51 insertions(+), 3 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index a90b7180c..1f7aa7dae 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -10,7 +10,7 @@ public class LinkedListNode<T> {
   }
 }
 
-public class LinkedList<T> {
+public final class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
 
   fileprivate var head: Node?
@@ -187,7 +187,7 @@ extension LinkedList {
   }
 }
 
-extension LinkedList {
+extension LinkedList: ExpressibleByArrayLiteral {
   convenience init(array: Array<T>) {
     self.init()
         
@@ -195,6 +195,14 @@ extension LinkedList {
       self.append(element)
     }
   }
+    
+  public convenience init(arrayLiteral elements: T...) {
+      self.init()
+    
+      for element in elements {
+          self.append(element)
+      }
+  }
 }
 
 let list = LinkedList<String>()
@@ -255,3 +263,13 @@ list[0]                        // "Swift"
 
 list.remove(atIndex: 0)        // "Swift"
 list.count                     // 0
+
+let linkedList: LinkedList<Int> = [1, 2, 3, 4] // [1, 2, 3, 4]
+linkedList.count               // 4
+linkedList[0]                  // 1
+
+// Infer the type from the array
+let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
+listArrayLiteral2.count        // 3
+listArrayLiteral2[0]           // "Swift"
+listArrayLiteral2.removeLast() // "Club"
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 83f898f6c..792215a72 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -8,7 +8,7 @@ public class LinkedListNode<T> {
     }
 }
 
-public class LinkedList<T> {
+public final class LinkedList<T>: ExpressibleByArrayLiteral {
     public typealias Node = LinkedListNode<T>
     
     fileprivate var head: Node?
@@ -203,4 +203,12 @@ extension LinkedList {
             self.append(element)
         }
     }
+  
+    public convenience init(arrayLiteral elements: T...) {
+      self.init()
+    
+      for element in elements {
+        self.append(element)
+      }
+    }
 }
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 367ec8c6b..6f58d9775 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -248,4 +248,26 @@ class LinkedListTest: XCTestCase {
     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)
+  }
 }

From 6863590f96aa24a004af813f6c82272267c5b742 Mon Sep 17 00:00:00 2001
From: Daniel Santos <dsantosp12@gmail.com>
Date: Wed, 8 Mar 2017 19:53:20 -0500
Subject: [PATCH 034/862] implemented the ExpressibleByArrayLiteral for the
 Linked List in a new extension instead of the class declaration for
 readability

---
 .../LinkedList.playground/Contents.swift      | 80 +++++++++++--------
 Linked List/LinkedList.swift                  | 16 ++--
 2 files changed, 55 insertions(+), 41 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 1f7aa7dae..ed46331d8 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -4,7 +4,7 @@ public class LinkedListNode<T> {
   var value: T
   var next: LinkedListNode?
   weak var previous: LinkedListNode?
-
+  
   public init(value: T) {
     self.value = value
   }
@@ -12,17 +12,19 @@ public class LinkedListNode<T> {
 
 public final class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
-
+  
   fileprivate var head: Node?
-
+  
+  public init() {}
+  
   public var isEmpty: Bool {
     return head == nil
   }
-
+  
   public var first: Node? {
     return head
   }
-
+  
   public var last: Node? {
     if var node = head {
       while case let next? = node.next {
@@ -33,7 +35,7 @@ public final class LinkedList<T> {
       return nil
     }
   }
-
+  
   public var count: Int {
     if var node = head {
       var c = 1
@@ -46,7 +48,7 @@ public final class LinkedList<T> {
       return 0
     }
   }
-
+  
   public func node(atIndex index: Int) -> Node? {
     if index >= 0 {
       var node = head
@@ -59,15 +61,19 @@ public final class LinkedList<T> {
     }
     return nil
   }
-
+  
   public subscript(index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
     return node!.value
   }
-
+  
   public func append(_ value: T) {
     let newNode = Node(value: value)
+    self.append(newNode)
+  }
+  
+  public func append(_ newNode: Node) {
     if let lastNode = last {
       newNode.previous = lastNode
       lastNode.next = newNode
@@ -75,64 +81,68 @@ public final class LinkedList<T> {
       head = newNode
     }
   }
-
+  
   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 (prev, next) = nodesBeforeAndAfter(index: index)
-
     let newNode = Node(value: value)
+    self.insert(newNode, atIndex: index)
+  }
+  
+  public func insert(_ newNode: Node, atIndex index: Int) {
+    let (prev, next) = nodesBeforeAndAfter(index: index)
+    
     newNode.previous = prev
     newNode.next = next
     prev?.next = newNode
     next?.previous = newNode
-
+    
     if prev == nil {
       head = newNode
     }
   }
-
+  
   public func removeAll() {
     head = nil
   }
-
-  public func remove(node: Node) -> T {
+  
+  @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
   }
-
-  public func removeLast() -> T {
+  
+  @discardableResult public func removeLast() -> T {
     assert(!isEmpty)
     return remove(node: last!)
   }
-
-  public func remove(atIndex index: Int) -> T {
+  
+  @discardableResult public func remove(atIndex index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
     return remove(node: node!)
@@ -173,7 +183,7 @@ extension LinkedList {
     }
     return result
   }
-
+  
   public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
     let result = LinkedList<T>()
     var node = head
@@ -187,21 +197,23 @@ extension LinkedList {
   }
 }
 
-extension LinkedList: ExpressibleByArrayLiteral {
+extension LinkedList {
   convenience init(array: Array<T>) {
     self.init()
-        
+    
     for element in array {
       self.append(element)
     }
   }
-    
+}
+
+extension LinkedList: ExpressibleByArrayLiteral {
   public convenience init(arrayLiteral elements: T...) {
-      self.init()
+    self.init()
     
-      for element in elements {
-          self.append(element)
-      }
+    for element in elements {
+      self.append(element)
+    }
   }
 }
 
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 792215a72..53dc77a06 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -8,7 +8,7 @@ public class LinkedListNode<T> {
     }
 }
 
-public final class LinkedList<T>: ExpressibleByArrayLiteral {
+public final class LinkedList<T> {
     public typealias Node = LinkedListNode<T>
     
     fileprivate var head: Node?
@@ -203,12 +203,14 @@ extension LinkedList {
             self.append(element)
         }
     }
-  
-    public convenience init(arrayLiteral elements: T...) {
-      self.init()
+}
+
+extension LinkedList: ExpressibleByArrayLiteral {
+  public convenience init(arrayLiteral elements: T...) {
+    self.init()
     
-      for element in elements {
-        self.append(element)
-      }
+    for element in elements {
+      self.append(element)
     }
+  }
 }

From 345f8441b64003258779cd3fed692c5549a4cbd3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Thu, 9 Mar 2017 18:35:26 +0800
Subject: [PATCH 035/862] add SelectionSamplingExample.swift

---
 .../SelectionSamplingExample.swift            | 32 +++++++++++++++++++
 1 file changed, 32 insertions(+)
 create mode 100644 Selection Sampling/SelectionSamplingExample.swift

diff --git a/Selection Sampling/SelectionSamplingExample.swift b/Selection Sampling/SelectionSamplingExample.swift
new file mode 100644
index 000000000..66648a934
--- /dev/null
+++ b/Selection Sampling/SelectionSamplingExample.swift	
@@ -0,0 +1,32 @@
+//
+//  Select.swift
+//  
+//
+//  Created by Cheer on 2017/3/9.
+//
+//
+
+import Foundation
+
+func select<T>(from a: [T], count requested: Int) -> [T] {
+    
+    // if requested > a.count, will throw ==> fatal error: Index out of range
+    
+    if requested < a.count {
+        var arr = a
+        for i in 0..<requested {
+            
+            //arc4random_uniform(n) ==> the range is [0...n-1]
+            //So: arc4random_uniform(UInt32(arr.count - i - 2)) + (i + 1) ==> [0...arr.count - (i + 1) - 1] + (i + 1) ==> the range is [(i + 1)...arr.count - 1]
+            //Why start index is "(i + 1)"?  Because in "swap(&A,&B)", if A's index == B's index, will throw a error: "swapping a location with itself is not supported"
+            
+            let nextIndex = Int(arc4random_uniform(UInt32(arr.count - i - 2))) + (i + 1)
+            swap(&arr[nextIndex], &arr[i])
+        }
+        return Array(arr[0..<requested])
+    }
+    
+    if requested == a.count { return a }
+    
+    return [T]()
+}

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 036/862] 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 5205fc8cf7ac1091448aecd9e7680b25779c9a88 Mon Sep 17 00:00:00 2001
From: Deep Parekh <dparekh@tripadvisor.com>
Date: Thu, 23 Feb 2017 00:08:21 -0500
Subject: [PATCH 037/862] Added checks for subscript and fixed initializer
 compile error

---
 Array2D/Array2D.playground/Contents.swift | 69 +++++++++++++----------
 1 file changed, 40 insertions(+), 29 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 7064de59c..38d4eff23 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -1,31 +1,42 @@
 /*
-  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.
-  Performance is always O(1).
-*/
+ 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.
+ Performance is always O(1).
+ */
 public struct Array2D<T> {
-  public let columns: Int
-  public let rows: Int
-  fileprivate var array: [T]
-
-  public init(columns: Int, rows: Int, initialValue: T) {
-    self.columns = columns
-    self.rows = rows
-    array = .init(repeatElement(initialValue, count: rows*columns))
-  }
-
-  public subscript(column: Int, row: Int) -> T {
-    get {
-      return array[row*columns + column]
+    public let columns: Int
+    public let rows: Int
+    public var array: [T]
+    
+    public init(columns: Int, rows: Int, initialValue: T) {
+        self.columns = columns
+        self.rows = rows
+        array = [T](repeating: initialValue, count: rows*columns)
     }
-    set {
-      array[row*columns + column] = newValue
+    
+    public subscript(column: Int, row: Int) -> T {
+        get {
+            if isValidSubscript(column: column, row: row) {
+                return array[row*columns + column]
+            } else {
+                fatalError("Not a valid subscript")
+            }
+        }
+        set {
+            if isValidSubscript(column: column, row: row) {
+                array[row*columns + column] = newValue
+            } else {
+                fatalError("Not a valid subscript")
+            }
+        }
+    }
+    
+    private func isValidSubscript(column: Int, row: Int) -> Bool {
+        return column < columns && row < rows
     }
-  }
 }
 
 
-
 // initialization
 var matrix = Array2D(columns: 3, rows: 5, initialValue: 0)
 
@@ -51,13 +62,13 @@ print(matrix.array)
 
 // print out the 2D array with a reference around the grid
 for i in 0..<matrix.rows {
-  print("[", terminator: "")
-  for j in 0..<matrix.columns {
-    if j == matrix.columns - 1 {
-      print("\(matrix[j, i])", terminator: "")
-    } else {
-      print("\(matrix[j, i]) ", terminator: "")
+    print("[", terminator: "")
+    for j in 0..<matrix.columns {
+        if j == matrix.columns - 1 {
+            print("\(matrix[j, i])", terminator: "")
+        } else {
+            print("\(matrix[j, i]) ", terminator: "")
+        }
     }
-  }
-  print("]")
+    print("]")
 }

From 40be0d2bbb539fa6d89c2149198a5faa92d66d32 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Wed, 15 Mar 2017 19:48:51 -0700
Subject: [PATCH 038/862] availability check, native array loop for signal

---
 DiningPhilosophers/Sources/main.swift | 46 +++++++++++++--------------
 1 file changed, 22 insertions(+), 24 deletions(-)

diff --git a/DiningPhilosophers/Sources/main.swift b/DiningPhilosophers/Sources/main.swift
index deff344b9..285402d53 100755
--- a/DiningPhilosophers/Sources/main.swift
+++ b/DiningPhilosophers/Sources/main.swift
@@ -7,17 +7,16 @@
 //
 
 
-import Foundation
 import Dispatch
 
 let numberOfPhilosophers = 4
 
 struct ForkPair {
-    static let forksSemaphore:[DispatchSemaphore] = Array(repeating: DispatchSemaphore(value: 1), count: numberOfPhilosophers)
-    
+    static let forksSemaphore: [DispatchSemaphore] = Array(repeating: DispatchSemaphore(value: 1), count: numberOfPhilosophers)
+
     let leftFork: DispatchSemaphore
     let rightFork: DispatchSemaphore
-    
+
     init(leftIndex: Int, rightIndex: Int) {
         //Order forks by index to prevent deadlock
         if leftIndex > rightIndex {
@@ -35,7 +34,7 @@ struct ForkPair {
         leftFork.wait()
         rightFork.wait()
     }
-    
+
     func putDown() {
         //The order does not matter here
         leftFork.signal()
@@ -47,61 +46,60 @@ struct ForkPair {
 struct Philosophers {
     let forkPair: ForkPair
     let philosopherIndex: Int
-    
+
     var leftIndex = -1
     var rightIndex = -1
-    
+
     init(philosopherIndex: Int) {
         leftIndex = philosopherIndex
         rightIndex = philosopherIndex - 1
-        
+
         if rightIndex < 0 {
             rightIndex += numberOfPhilosophers
         }
 
         self.forkPair = ForkPair(leftIndex: leftIndex, rightIndex: rightIndex)
         self.philosopherIndex = philosopherIndex
-        
+
         print("Philosopher: \(philosopherIndex)  left: \(leftIndex)  right: \(rightIndex)")
     }
-    
+
     func run() {
         while true {
-            print("Acquiring lock for Philosofer: \(philosopherIndex) Left:\(leftIndex) Right:\(rightIndex)")
+            print("Acquiring lock for Philosopher: \(philosopherIndex) Left:\(leftIndex) Right:\(rightIndex)")
             forkPair.pickUp()
             print("Start Eating Philosopher: \(philosopherIndex)")
             //sleep(1000)
-            print("Releasing lock for Philosofer: \(philosopherIndex) Left:\(leftIndex) Right:\(rightIndex)")
+            print("Releasing lock for Philosopher: \(philosopherIndex) Left:\(leftIndex) Right:\(rightIndex)")
             forkPair.putDown()
         }
     }
 }
 
 
-// Layout of the table (P = philosopher, f = fork) for 4 Philosopher
+// Layout of the table (P = philosopher, f = fork) for 4 Philosophers
 //          P0
 //       f3    f0
 //     P3        P1
 //       f2    f1
 //          P2
-
 let globalSem = DispatchSemaphore(value: 0)
 
 for i in 0..<numberOfPhilosophers {
-    DispatchQueue.global(qos: .background).async {
-        let p = Philosophers(philosopherIndex: i)
-        
-        p.run()
+    if #available(macOS 10.10, *) {
+        DispatchQueue.global(qos: .background).async {
+            let p = Philosophers(philosopherIndex: i)
+
+            p.run()
+        }
     }
 }
 
-//start the thread signaling the semaphore
-for i in 0..<numberOfPhilosophers {
-    ForkPair.forksSemaphore[i].signal()
+//Start the thread signaling the semaphore
+for semaphore in ForkPair.forksSemaphore {
+    semaphore.signal()
 }
 
 
-//wait forever
+//Wait forever
 globalSem.wait()
-
-

From 8d30d35c4aaaac8ee852437a296859b84eeb2912 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Wed, 15 Mar 2017 19:53:29 -0700
Subject: [PATCH 039/862] links

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

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index 29b5916e9..ec1611c65 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -1,5 +1,5 @@
 # Dining Philosophers
-Dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using GCD and Semaphore in Swift)
+Dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using [GCD](https://apple.github.io/swift-corelibs-libdispatch/) and [Semaphore](https://developer.apple.com/reference/dispatch/dispatchsemaphore) in Swift)
 
 Written for Swift Algorithm Club by Jacopo Mangiavacchi
 

From a9655534e55620364e975cabb78242dca9db0c11 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Fri, 17 Mar 2017 11:06:13 +0800
Subject: [PATCH 040/862] Update ShellSortExample.swift

Fix bug. Origin code probally get wrong answer.My fault.
---
 Shell Sort/ShellSortExample.swift | 27 ++++++++++++++-------------
 1 file changed, 14 insertions(+), 13 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index efa035da3..c41eb8889 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -8,24 +8,25 @@
 
 import Foundation
 
-public func shellSort(_ list: inout [Int]) {
-    
+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 }
+    
+    while sublistCount > 0
+    {
+        for var index in 0..<arr.count{
+            
+            guard index + sublistCount < arr.count else { break }
             
-            if list[index] > list[index + sublistCount] {
-                swap(&list[index], &list[index + sublistCount])
+            if arr[index] > arr[index + sublistCount]{
+                swap(&arr[index], &arr[index + sublistCount])
             }
             
             guard sublistCount == 1 && index > 0 else { continue }
-            
-            if list[index - 1] > list[index] {
-                swap(&list[index - 1], &list[index])
+
+            while arr[index - 1] > arr[index] && index - 1 > 0  {
+                swap(&arr[index - 1], &arr[index])
+                index -= 1
             }
         }
         sublistCount = sublistCount / 2

From beddc9a7f4dd96b9122e849ace3c7dba57caaea7 Mon Sep 17 00:00:00 2001
From: Brandon05 <brandonsanchez05@gmail.com>
Date: Fri, 17 Mar 2017 13:41:49 -0400
Subject: [PATCH 041/862] Updated syntax for Swift 3

Hello, I was recreating this file in playground and I noticed you still had the explicit @noescape . Thought I can lend a hand by removing it. Thanks for this awesome repository!
---
 Binary Tree/BinaryTree.swift | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Binary Tree/BinaryTree.swift b/Binary Tree/BinaryTree.swift
index 61ae696c7..102f23e06 100644
--- a/Binary Tree/BinaryTree.swift	
+++ b/Binary Tree/BinaryTree.swift	
@@ -29,26 +29,26 @@ extension BinaryTree: CustomStringConvertible {
 }
 
 extension BinaryTree {
-  public func traverseInOrder(@noescape process: T -> Void) {
+  public func traverseInOrder(process: T -> Void) {
     if case let .node(left, value, right) = self {
-      left.traverseInOrder(process)
+      left.traverseInOrder(process: process)
       process(value)
-      right.traverseInOrder(process)
+      right.traverseInOrder(process: process)
     }
   }
 
-  public func traversePreOrder(@noescape process: T -> Void) {
+  public func traversePreOrder(process: T -> Void) {
     if case let .node(left, value, right) = self {
       process(value)
-      left.traversePreOrder(process)
-      right.traversePreOrder(process)
+      left.traversePreOrder(process: process)
+      right.traversePreOrder(process: process)
     }
   }
 
-  public func traversePostOrder(@noescape process: T -> Void) {
+  public func traversePostOrder(process: T -> Void) {
     if case let .node(left, value, right) = self {
-      left.traversePostOrder(process)
-      right.traversePostOrder(process)
+      left.traversePostOrder(process: process)
+      right.traversePostOrder(process: process)
       process(value)
     }
   }

From 9677b8c0e6bbd32831b6eca6c69c6f09d64f9f37 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Fri, 17 Mar 2017 20:10:53 -0700
Subject: [PATCH 042/862] Fixed indenting, and changed a scope modifier on the
 array property from public to fileprivate.

---
 Array2D/Array2D.playground/Contents.swift | 72 +++++++++++------------
 Array2D/README.markdown                   | 24 ++++++--
 2 files changed, 54 insertions(+), 42 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 38d4eff23..8b18a333f 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -4,36 +4,36 @@
  Performance is always O(1).
  */
 public struct Array2D<T> {
-    public let columns: Int
-    public let rows: Int
-    public var array: [T]
-    
-    public init(columns: Int, rows: Int, initialValue: T) {
-        self.columns = columns
-        self.rows = rows
-        array = [T](repeating: initialValue, count: rows*columns)
+  public let columns: Int
+  public let rows: Int
+  fileprivate var array: [T]
+  
+  public init(columns: Int, rows: Int, initialValue: T) {
+    self.columns = columns
+    self.rows = rows
+    array = [T](repeating: initialValue, count: rows*columns)
+  }
+  
+  public subscript(column: Int, row: Int) -> T {
+    get {
+      if isValidSubscript(column: column, row: row) {
+        return array[row*columns + column]
+      } else {
+        fatalError("Not a valid subscript")
+      }
     }
-    
-    public subscript(column: Int, row: Int) -> T {
-        get {
-            if isValidSubscript(column: column, row: row) {
-                return array[row*columns + column]
-            } else {
-                fatalError("Not a valid subscript")
-            }
-        }
-        set {
-            if isValidSubscript(column: column, row: row) {
-                array[row*columns + column] = newValue
-            } else {
-                fatalError("Not a valid subscript")
-            }
-        }
-    }
-    
-    private func isValidSubscript(column: Int, row: Int) -> Bool {
-        return column < columns && row < rows
+    set {
+      if isValidSubscript(column: column, row: row) {
+        array[row*columns + column] = newValue
+      } else {
+        fatalError("Not a valid subscript")
+      }
     }
+  }
+  
+  private func isValidSubscript(column: Int, row: Int) -> Bool {
+    return column < columns && row < rows
+  }
 }
 
 
@@ -62,13 +62,13 @@ print(matrix.array)
 
 // print out the 2D array with a reference around the grid
 for i in 0..<matrix.rows {
-    print("[", terminator: "")
-    for j in 0..<matrix.columns {
-        if j == matrix.columns - 1 {
-            print("\(matrix[j, i])", terminator: "")
-        } else {
-            print("\(matrix[j, i]) ", terminator: "")
-        }
+  print("[", terminator: "")
+  for j in 0..<matrix.columns {
+    if j == matrix.columns - 1 {
+      print("\(matrix[j, i])", terminator: "")
+    } else {
+      print("\(matrix[j, i]) ", terminator: "")
     }
-    print("]")
+  }
+  print("]")
 }
diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index 51e77435e..6550dc943 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -67,22 +67,34 @@ So instead let's create our own type that acts like a 2-D array and that is more
 public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
-  private var array: [T]
-
+  fileprivate var array: [T]
+  
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
-    array = .init(repeating: initialValue, count: rows*columns)
+    array = [T](repeating: initialValue, count: rows*columns)
   }
-
+  
   public subscript(column: Int, row: Int) -> T {
     get {
-      return array[row*columns + column]
+      if isValidSubscript(column: column, row: row) {
+        return array[row*columns + column]
+      } else {
+        fatalError("Not a valid subscript")
+      }
     }
     set {
-      array[row*columns + column] = newValue
+      if isValidSubscript(column: column, row: row) {
+        array[row*columns + column] = newValue
+      } else {
+        fatalError("Not a valid subscript")
+      }
     }
   }
+  
+  private func isValidSubscript(column: Int, row: Int) -> Bool {
+    return column < columns && row < rows
+  }
 }
 ```
 

From c4d39ec0dc41060f2ff5b5532e9fa69489c9bbef Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Fri, 17 Mar 2017 20:16:01 -0700
Subject: [PATCH 043/862] Updated the subscript check to use preconditions
 instead of a custom function.

---
 Array2D/Array2D.playground/Contents.swift | 22 +++++++---------------
 Array2D/Array2D.swift                     |  9 +++++----
 Array2D/README.markdown                   | 22 +++++++---------------
 3 files changed, 19 insertions(+), 34 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 8b18a333f..d088c99af 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -11,29 +11,21 @@ public struct Array2D<T> {
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
-    array = [T](repeating: initialValue, count: rows*columns)
+    array = .init(repeating: initialValue, count: rows*columns)
   }
   
   public subscript(column: Int, row: Int) -> T {
     get {
-      if isValidSubscript(column: column, row: row) {
-        return array[row*columns + column]
-      } else {
-        fatalError("Not a valid subscript")
-      }
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      return array[row*columns + column]
     }
     set {
-      if isValidSubscript(column: column, row: row) {
-        array[row*columns + column] = newValue
-      } else {
-        fatalError("Not a valid subscript")
-      }
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      array[row*columns + column] = newValue
     }
   }
-  
-  private func isValidSubscript(column: Int, row: Int) -> Bool {
-    return column < columns && row < rows
-  }
 }
 
 
diff --git a/Array2D/Array2D.swift b/Array2D/Array2D.swift
index 6d6c01902..df4822916 100644
--- a/Array2D/Array2D.swift
+++ b/Array2D/Array2D.swift
@@ -7,21 +7,22 @@ public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
   fileprivate var array: [T]
-
+  
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
     array = .init(repeating: initialValue, count: rows*columns)
   }
-
+  
   public subscript(column: Int, row: Int) -> T {
     get {
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
       return array[row*columns + column]
     }
     set {
-      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
       precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
-        
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
       array[row*columns + column] = newValue
     }
   }
diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index 6550dc943..04afb9510 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -72,29 +72,21 @@ public struct Array2D<T> {
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
-    array = [T](repeating: initialValue, count: rows*columns)
+    array = .init(repeating: initialValue, count: rows*columns)
   }
   
   public subscript(column: Int, row: Int) -> T {
     get {
-      if isValidSubscript(column: column, row: row) {
-        return array[row*columns + column]
-      } else {
-        fatalError("Not a valid subscript")
-      }
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      return array[row*columns + column]
     }
     set {
-      if isValidSubscript(column: column, row: row) {
-        array[row*columns + column] = newValue
-      } else {
-        fatalError("Not a valid subscript")
-      }
+      precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      precondition(row < rows, "Row \(row) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
+      array[row*columns + column] = newValue
     }
   }
-  
-  private func isValidSubscript(column: Int, row: Int) -> Bool {
-    return column < columns && row < rows
-  }
 }
 ```
 

From 162c3453bab7fa216cd3f11a9a45488ce9515c5c Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Tue, 21 Mar 2017 11:21:59 +0100
Subject: [PATCH 044/862] Exchanged old red-black tree implementation with new
 one, also updated redmea

---
 Red-Black Tree/README.markdown                | 259 +++---
 .../RedBlackTree.playground/Contents.swift    |  22 +
 .../Sources/RedBlackTree.swift                | 740 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 4 files changed, 930 insertions(+), 95 deletions(-)
 create mode 100644 Red-Black Tree/RedBlackTree.playground/Contents.swift
 create mode 100644 Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
 create mode 100644 Red-Black Tree/RedBlackTree.playground/contents.xcplayground

diff --git a/Red-Black Tree/README.markdown b/Red-Black Tree/README.markdown
index 05993f016..74fffa415 100644
--- a/Red-Black Tree/README.markdown	
+++ b/Red-Black Tree/README.markdown	
@@ -1,120 +1,189 @@
 # Red-Black Tree
 
-A Red-Black tree is a special version of a [Binary Search  Tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Binary%20Search%20Tree). Binary search trees(BSTs) can become unbalanced after a lot of insertions/deletions. The only difference between a node from a BST and a Red-Black Tree(RBT) is that RBT nodes have a color property added to them which can either be red or black. A RBT rebalances itself by making sure the following properties hold:
+A red-black tree (RBT) is a balanced version of a [Binary Search Tree](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Binary%20Search%20Tree) guaranteeing that the basic operations (search, predecessor, successor, minimum, maximum, insert and delete) have a logarithmic worst case performance.
 
-## Properties
-1. A node is either red or black
-2. The root is always black
-3. All leaves are black
-4. If a node is red, both of its children are black
-5. Every path to a leaf contains the same number of black nodes (The amount of black nodes met when going down a RBT is called the black-depth of the tree.)
-
-## Methods
-* `insert(_ value: T)` inserts the value into the tree
-* `insert(_ values: [T])` inserts an array of values into the tree
-* `delete(_ value: T)` deletes the value from the tree
-* `find(_ value: T) -> RBTNode<T>` looks for a node in the tree with given value and returns it
-* `minimum(n: RBTNode<T>) -> RBTNode<T>` looks for the maximum value of a subtree starting at the given node
-* `maximum(n: RBTNode<T>) -> RBTNode<T>` looks for the minimum value of a subtree starting at the given node
-* `func verify()` verifies if the tree is still valid. Prints warning messages if this is not the case
-
-## Rotation
+Binary search trees (BSTs) have the disadvantage that they can become unbalanced after some insert or delete operations. In the worst case, this could lead to a tree where the nodes build a linked list as shown in the following example:
 
-In order to rebalance their nodes RBTs use an operation known as rotation. You can either left or right rotate a node and its child. Rotating a node and its child swaps the nodes and interchanges their subtrees. Left rotation swaps the parent node with its right child. while right rotation swaps the parent node with its left child.
-
-Left rotation:
-```
-before left rotating p       after left rotating p  
-     p                         b
-   /   \                     /   \
-  a     b          ->       p     n
- / \   / \                 / \   
-n   n  n  n               a   n
-                         / \
-                        n   n
-```
-Right rotation:
 ```
-before right rotating p       after right rotating p  
-     p                         a
-   /   \                     /   \
-  a     b          ->       n     p
- / \   / \                       / \   
-n   n  n  n                     n   b
-                                   / \
-                                  n   n
+a
+  \
+   b
+    \
+     c
+      \
+       d
 ```
+To prevent this issue, RBTs perform rebalancing operations after an insert or delete and store an additional color property at each node which can either be red or black. After each operation a RBT satisfies the following properties:
 
-## Insertion
-
-We create a new node with the value to be inserted into the tree. The color of this new node is always red.
-We perform a standard BST insert with this node. Now the three might not be a valid RBT anymore.
-We now go through several insertion steps in order to make the tree valid again. We call the just inserted node n.  
-
-**Step 1**: We check if n is the rootNode, if so we paint it black and we are done. If not we go to Step 2.
-
-We now know that n at least has a parent as it is not the rootNode.
-
-**Step 2**: We check if the parent of n is black if so we are done. If not we go to Step 3.
-
-We now know the parent is also not the root node as the parent is red. Thus n also has a grandparent and thus also an uncle as every node has two children. This uncle may however be a nullLeaf
-
-**Step 3**: We check if n's uncle is red. If not we go to Step 4. If n's uncle is indeed red we recolor uncle and parent to black and n's grandparent to red. We now go back to step 1 performing the same logic on n's grandparent.
-
-From here there are four cases:
-- **The left left case.** n's parent is the left child of its parent and n is the left child of its parent.
-- **The left right case** n's parent is the left child of its parent and n is the right child of its parent.
-- **The right right case** n's parent is the right child of its parent and n is the right child of its parent.
-- **The right left case** n's parent is the right child of its parent and n is the left child of its parent.
-
-**Step 4**: checks if either the **left right** case or the **right left** case applies to the current situation.
-  - If we find the **left right case**, we left rotate n's parent and go to Step 5 while setting n to n's parent. (This transforms the **left right** case into the **left left** case)
-  - If we find the **right left case**, we right rotate n's parent and go to Step 5 while setting n to n's parent. (This transforms the **right left** case into the **right right** case)
-  - If we find neither of these two we proceed to Step 5.
+## Properties
 
-n's parent is now red, while n's grandparent is black.
+1. Every node is either red or black
+2. The root is black
+3. Every leaf (nullLeaf) is black
+4. If a node is red, then both its children are black
+5. For each node, all paths from the node to descendant leaves contain the same number of black nodes
 
-**Step 5**: We swap the colors of n's parent and grandparent.
-  - We either right rotate n's grandparent in case of the **left left** case
-  - Or we left rotate n's grandparent in case of the **right right** case
+Property 5 includes the definition of the black-height of a node x, bh(x), which is the number of black nodes on a path from this node down to a leaf not counting the node itself.
+From [CLRS]
 
-Reaching the end we have successfully made the tree valid again.
+## Methods
 
-# Deletion
+Nodes:
+* `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
+Tree:
+* `search(input:)` Returns the node with the given key value
+* `minValue()` Returns the minimum key value of the whole tree
+* `maxValue()` Returns the maximum key value of the whole 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
 
-Deletion is a little more complicated than insertion. In the following we call del the node to be deleted.
-First we try and find the node to be deleted using find()
-we send the result of find to del.
-We now go through the following steps in order to delete the node del.
+The rotation, insertion and deletion algorithms are implemented based on the pseudo-code provided in [CLRS]
 
-First we do a few checks:
-- Is del the rootNode if so set the root to a nullLeaf and we are done.
-- If del has 2 nullLeaf children and is red. We check if del is either a left or a right child and set del's parent left or right to a nullLeaf.
-- If del has two non nullLeaf children we look for the maximum value in del's left subtree. We set del's value to this maximum value and continue to instead delete this maximum node. Which we will now call del.
+## Implementation Details
 
-Because of these checks we now know that del has at most 1 non nullLeaf child. It has either two nullLeaf children or one nullLeaf and one regular red child. (The child is red otherwise the black-depth wouldn't be the same for every leaf)
+For convenience, all nil-pointers to children or the parent (except the parent of the root) of a node are exchanged with a nullLeaf. This is an ordinary node object, like all other nodes in the tree, but with a black color, and in this case a nil value for its children, parent and key. Therefore, an empty tree consists of exactly one nullLeaf at the root.
 
-We now call the non nullLeaf child of del, child. If del has two nullLeaf children child will be a nullLeaf. This means child can either be a nullLeaf or a red node.
+## Rotation
 
-We now have three options
+Left rotation (around 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]
+```
+Right rotation (around 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]
+```
+As rotation is a local operation only exchanging pointers it's runtime is O(1).
 
-- If del is red its child is a nullLeaf and we can just delete it as it doesn't change the black-depth of the tree. We are done
+## Insertion
 
-- If child is red we recolor it black and child's parent to del's parent. del is now deleted and we are done.
+We create a node with the given key and set its color to red. Then we insert it into the the tree by performing a standard insert into a BST. After this, the tree might not be a valid RBT anymore, so we fix the red-black properties by calling the insertFixup algorithm.
+The only violation of the red-black properties occurs at the inserted node z and its parent. Either both are red, or the parent does not exist (so there is a violation since the root must be black).
+We have three distinct cases:
+**Case 1:** The uncle of z is red. If z.parent is left child, z's uncle is z.grandparent's right child. If this is the case, we recolor and move z to z.grandparent, then we check again for this new z. In the following cases, we denote a red node with (x) and a black node with {x}, p = parent, gp = grandparent and u = uncle
+```
+         |                   |
+        {gp}               (newZ)
+       /    \     ~>       /    \
+    (p)     (u)         {p}     {u}
+    / \     / \         / \     / \
+  (z)  [C] [D] [E]    (z) [C] [D] [E]
+  / \                 / \
+[A] [B]             [A] [B]
 
-- Both del and child are black we go through
+```
+**Case 2a:** The uncle of z is black and z is right child. Here, we move z upwards, so z's parent is the newZ and then we rotate around this newZ. After this, we have Case 2b.
+```
+         |                   |
+        {gp}                {gp}
+       /    \     ~>       /    \
+    (p)      {u}         (z)     {u}
+    / \      / \         / \     / \
+  [A]  (z)  [D] [E]  (newZ) [C] [D] [E]
+       / \            / \
+     [B] [C]        [A] [B]
 
-If both del and child are black we introduce a new variable sibling. Which is del's sibling. We also replace del with child and recolor it doubleBlack. del is now deleted and child and sibling are siblings.
+```
+**Case 2b:** The uncle of z is black and z is left child. In this case, we recolor z.parent to black and z.grandparent to red. Then we rotate around z's grandparent. Afterwards we have valid red-black tree.
+```
+         |                   |
+        {gp}                {p}
+       /    \     ~>       /    \
+    (p)      {u}         (z)    (gp)
+    / \      / \         / \     / \
+  (z)  [C] [D] [E]    [A] [B]  [C]  {u}
+  / \                               / \
+[A] [B]                           [D] [E]
 
-We now have to go through a lot of steps in order to remove this doubleBlack color. Which are hard to explain in text without just writing the full code in text. This is due the many possible combination of nodes and colors. The code is commented, but if you don't quite understand please leave me a message. Also part of the deletion is described by the final link in the Also See section.
+```
+Running time of this algorithm: 
+* Only case 1 may repeat, but this only h/2 steps, where h is the height of the tree
+* Case 2a -> Case 2b -> red-black tree
+* Case 2b -> red-black tree
+As we perform case 1 at most O(log n) times and all other cases at most once, we have O(log n) recolorings and at most 2 rotations. 
+The overall runtime of insert is O(log n).
+
+## Deletion
+
+We search for the node with the given key, and if it exists we delete it by performing a standard delete from a BST. If the deleted nodes' color was red everything is fine, otherwise red-black properties may be violated so we call the fixup procedure deleteFixup.
+Violations can be that the parent and child of the deleted node x where red, so we now have two adjacent red nodes, or if we deleted the root, the root could now be red, or the black height property is violated.
+We have 4 cases: We call deleteFixup on node x
+**Case 1:** The sibling of x is red. The sibling is the other child of x's parent, which is not x itself. In this case, we recolor the parent of x and x.sibling then we left rotate around x's parent. In the following cases s = sibling of x, (x) = red, {x} = black, |x| = red/black.
+```
+        |                   |
+       {p}                 {s}
+      /    \     ~>       /    \
+    {x}    (s)         (p)     [D]
+    / \    / \         / \     
+  [A] [B] [C] [D]    {x} [C]
+                     / \  
+                   [A] [B]
 
-## Also see
+```
+**Case 2:** The sibling of x is black and has two black children. Here, we recolor x.sibling to red, move x upwards to x.parent and check again for this newX.
+```
+        |                    |
+       |p|                 |newX|
+      /    \     ~>       /     \
+    {x}     {s}          {x}     (s)
+    / \    /   \          / \   /   \
+  [A] [B] {l}  {r}     [A] [B] {l}  {r}
+          / \  / \             / \  / \
+        [C][D][E][F]         [C][D][E][F]
 
-* [Wikipedia](https://en.wikipedia.org/wiki/Red–black_tree)
-* [GeeksforGeeks - introduction](http://www.geeksforgeeks.org/red-black-tree-set-1-introduction-2/)
-* [GeeksforGeeks - insertion](http://www.geeksforgeeks.org/red-black-tree-set-2-insert/)
-* [GeeksforGeeks - deletion](http://www.geeksforgeeks.org/red-black-tree-set-3-delete-2/)
+```
+**Case 3:** The sibling of x is black with one black child to the right. In this case, we recolor the sibling to red and sibling.leftChild to black, then we right rotate around the sibling. After this we have case 4.
+```
+        |                    |
+       |p|                  |p|
+      /    \     ~>       /     \
+    {x}     {s}          {x}     {l}
+    / \    /   \         / \    /   \
+  [A] [B] (l)  {r}     [A] [B] [C]  (s)
+          / \  / \                  / \
+        [C][D][E][F]               [D]{e}
+                                      / \
+                                    [E] [F]
 
-Important to note is that GeeksforGeeks doesn't mention a few deletion cases that do occur. The code however does implement these.
+```
+**Case 4:** The sibling of x is black with one red child to the right. Here, we recolor the sibling to the color of x.parent and x.parent and sibling.rightChild to black. Then we left rotate around x.parent. After this operation we have a valid red-black tree. Here, ||x|| denotes that x can have either color red or black, but that this can be different to |x| color. This is important, as s gets the same color as p.
+```
+        |                        |
+       ||p||                   ||s||
+      /    \     ~>           /     \
+    {x}     {s}              {p}     {r}
+    / \    /   \            /  \     /  \
+  [A] [B] |l|  (r)        {x}  |l|  [E] [F]
+          / \  / \        / \  / \
+        [C][D][E][F]    [A][B][C][D]
 
-*Written for Swift Algorithm Club by Jaap Wijnen. Updated from Ashwin Raghuraman's contribution.*
+```
+Running time of this algorithm:
+* Only case 2 can repeat, but this only h many times, 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
+As we perform case 2 at most O(log n) times and all other steps at most once, we have O(log n) recolorings and at most 3 rotations.
+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.*
diff --git a/Red-Black Tree/RedBlackTree.playground/Contents.swift b/Red-Black Tree/RedBlackTree.playground/Contents.swift
new file mode 100644
index 000000000..5b19f9bd1
--- /dev/null
+++ b/Red-Black Tree/RedBlackTree.playground/Contents.swift	
@@ -0,0 +1,22 @@
+//: Playground - noun: a place where people can play
+// Test for  the RedBlackTree implementation provided in the Source folder of this Playground
+import Foundation
+
+let redBlackTree = RedBlackTree<Double>()
+
+let randomMax = Double(0x10000000)
+var values = [Double]()
+for _ in 0..<1000 {
+  let value = Double(arc4random()) / randomMax
+  values.append(value)
+  redBlackTree.insert(key: value)
+}
+redBlackTree.verify()
+
+for _ in 0..<1000 {
+  let rand = arc4random_uniform(UInt32(values.count))
+  let index = Int(rand)
+  let value = values.remove(at: index)
+  redBlackTree.delete(key: value)
+}
+redBlackTree.verify()
diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
new file mode 100644
index 000000000..057909b07
--- /dev/null
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -0,0 +1,740 @@
+//
+//  RedBlackTree.swift
+//
+//  Created by Ute Schiehlen on 14.03.17.
+//  Copyright © 2017 Ute Schiehlen. All rights reserved.
+//
+
+import Foundation
+
+private enum RBTreeColor {
+  case red
+  case black
+}
+
+private enum rotationDirection {
+  case left
+  case right
+}
+
+// MARK: - RBNode
+
+public class RBTreeNode<Key: Comparable>: Equatable {
+  public typealias RBNode = RBTreeNode<Key>
+  
+  fileprivate var color: RBTreeColor = .black
+  fileprivate var key: Key?
+  fileprivate var isNullLeaf = true
+  var leftChild: RBNode?
+  var rightChild: RBNode?
+  fileprivate weak var parent: RBNode?
+  
+  public init(key: Key?, 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: Key?) {
+    self.init(key: key, leftChild: RBNode(), rightChild: RBNode(), parent: RBNode())
+    self.isNullLeaf = false
+  }
+  
+  // For initialising the nullLeaf
+  public convenience init() {
+    self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
+    self.color = .black
+    self.isNullLeaf = true
+  }
+  
+  var isRoot: Bool {
+    return parent == nil
+  }
+  
+  var isLeaf: Bool {
+    return rightChild == nil && leftChild == nil
+  }
+  
+  var isLeftCild: Bool {
+    return parent?.leftChild === self
+  }
+  
+  var isRightChild: Bool {
+    return parent?.rightChild === self
+  }
+  
+  var grandparent: RBNode? {
+    return parent?.parent
+  }
+  
+  var sibling: RBNode? {
+    if isLeftCild {
+      return parent?.rightChild
+    } else {
+      return parent?.leftChild
+    }
+  }
+  
+  var uncle: RBNode? {
+    return parent?.sibling
+  }
+}
+
+// MARK: - RedBlackTree
+
+public class RedBlackTree<Key: Comparable> {
+  public typealias RBNode = RBTreeNode<Key>
+  
+  fileprivate(set) var root: RBNode
+  fileprivate(set) var size = 0
+  fileprivate let nullLeaf = RBNode()
+  
+  public init() {
+    root = nullLeaf
+  }
+}
+
+// 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: Key) -> RBNode? {
+    return search(key: input, node: root)
+  }
+  
+  /*
+   * Returns the node with given |key| in subtree of |node|
+   */
+  fileprivate func search(key: Key, 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() -> Key? {
+    if let minNode = root.minimum() {
+       return minNode.key
+    } else {
+      return nil
+    }
+  }
+  
+  /*
+   * Returns the maximum key value of the whole tree
+   */
+  public func maxValue() -> Key? {
+      if let maxNode = root.maximum() {
+        return maxNode.key
+      } else {
+        return nil
+    }
+  }
+}
+
+// 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: Key) {
+    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.isLeftCild && z.isRightChild {
+            zNew = parentZ
+            leftRotate(node: zNew)
+          } else if parentZ.isRightChild && z.isLeftCild {
+            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.isLeftCild {
+              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: Key) {
+    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.isLeftCild {
+          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.isLeftCild {
+            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.isLeftCild && 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.isLeftCild {
+            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.isLeftCild {
+      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 \(node.key ?? nil) has red left child")
+          return false
+        }
+        if !rightChild.isNullLeaf && rightChild.color == .red {
+          print("Property-Error: Red node with key \(node.key ?? nil) 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 \(node.key ?? nil)")
+      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: \(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
+    }
+  }
+}
diff --git a/Red-Black Tree/RedBlackTree.playground/contents.xcplayground b/Red-Black Tree/RedBlackTree.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Red-Black Tree/RedBlackTree.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 cf91833f5688398045bb7b76150bc988df747580 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 045/862] Deleted old version

---
 .../Contents.swift                            |  20 -
 .../Sources/RBTree.swift                      | 521 ------------------
 .../contents.xcplayground                     |   4 -
 .../contents.xcworkspacedata                  |   0
 4 files changed, 545 deletions(-)
 delete mode 100644 Red-Black Tree/Red-Black Tree 2.playground/Contents.swift
 delete mode 100644 Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
 delete mode 100644 Red-Black Tree/Red-Black Tree 2.playground/contents.xcplayground
 rename Red-Black Tree/{Red-Black Tree 2.playground => RedBlackTree.playground}/playground.xcworkspace/contents.xcworkspacedata (100%)

diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift b/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift
deleted file mode 100644
index d55c153d5..000000000
--- a/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift	
+++ /dev/null
@@ -1,20 +0,0 @@
-//: Playground - noun: a place where people can play
-import Foundation
-
-let tree = RBTree<Double>()
-let randomMax = Double(0x100000000)
-var values = [Double]()
-for _ in 0..<1000 {
-    let value = Double(arc4random()) / randomMax
-    values.append(value)
-    tree.insert(value)
-}
-tree.verify()
- 
-for _ in 0..<1000 {
-    let rand = arc4random_uniform(UInt32(values.count))
-    let index = Int(rand)
-    let value = values.remove(at: index)
-    tree.delete(value)
-}
-tree.verify()
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
deleted file mode 100644
index 1735798d5..000000000
--- a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ /dev/null
@@ -1,521 +0,0 @@
-
-private enum RBTColor {
-    case red
-    case black
-    case doubleBlack
-}
-
-public class RBTNode<T: Comparable>: CustomStringConvertible {
-    fileprivate var color: RBTColor = .red
-    public var value: T! = nil
-    public var right:  RBTNode<T>!
-    public var left:  RBTNode<T>!
-    public var parent:  RBTNode<T>!
-    
-    public var description: String {
-        if self.value == nil {
-            return "null"
-        } else {
-            var nodeValue: String
-            
-            // If the value is encapsulated by parentheses it is red
-            // If the value is encapsulated by pipes it is black
-            // If the value is encapsulated by double pipes it is double black (This should not occur in a verified RBTree)
-            if self.isRed {
-                nodeValue = "(\(self.value!))"
-            } else if self.isBlack{
-                nodeValue = "|\(self.value!)|"
-            } else {
-                nodeValue = "||\(self.value!)||"
-            }
-            
-            return "(\(self.left.description)<-\(nodeValue)->\(self.right.description))"
-        }
-    }
-    
-    init(tree: RBTree<T>) {
-        right = tree.nullLeaf
-        left = tree.nullLeaf
-        parent = tree.nullLeaf
-    }
-    
-    init() {
-        //This method is here to support the creation of a nullLeaf
-    }
-    
-    public var isLeftChild: Bool {
-        return self.parent.left === self
-    }
-    
-    public var isRightChild: Bool {
-        return self.parent.right === self
-    }
-    
-    public var grandparent: RBTNode<T> {
-        return parent.parent
-    }
-    
-    public var sibling: RBTNode<T> {
-        if isLeftChild {
-            return self.parent.right
-        } else {
-            return self.parent.left
-        }
-    }
-    
-    public var uncle: RBTNode<T> {
-        return parent.sibling
-    }
-    
-    fileprivate var isRed: Bool {
-        return color == .red
-    }
-    
-    fileprivate var isBlack: Bool {
-        return color == .black
-    }
-    
-    fileprivate var isDoubleBlack: Bool {
-        return color == .doubleBlack
-    }
-}
-
-public class RBTree<T: Comparable>: CustomStringConvertible {
-    public var root: RBTNode<T>
-    fileprivate let nullLeaf: RBTNode<T>
-    
-    public var description: String {
-        return root.description
-    }
-    
-    public init() {
-        nullLeaf = RBTNode<T>()
-        nullLeaf.color = .black
-        root = nullLeaf
-    }
-    
-    public convenience init(withValue value: T) {
-        self.init()
-        insert(value)
-    }
-    
-    public convenience init(withArray array: [T]) {
-        self.init()
-        insert(array)
-    }
-    
-    public func insert(_ value: T) {
-        let newNode = RBTNode<T>(tree: self)
-        newNode.value = value
-        insertNode(n: newNode)
-    }
-    
-    public func insert(_ values: [T]) {
-        for value in values {
-            print(value)
-            insert(value)
-        }
-    }
-    
-    public func delete(_ value: T) {
-        let nodeToDelete = find(value)
-        if nodeToDelete !== nullLeaf {
-            deleteNode(n: nodeToDelete)
-        }
-    }
-    
-    public func find(_ value: T) -> RBTNode<T> {
-        let foundNode = findNode(rootNode: root, value: value)
-        return foundNode
-    }
-    
-    public func minimum(n: RBTNode<T>) -> RBTNode<T> {
-        var min = n
-        if n.left !== nullLeaf {
-            min = minimum(n: n.left)
-        }
-        
-        return min
-    }
-    
-    public func maximum(n: RBTNode<T>) -> RBTNode<T> {
-        var max = n
-        if n.right !== nullLeaf {
-            max = maximum(n: n.right)
-        }
-        
-        return max
-    }
-    
-    public func verify() {
-        if self.root === nullLeaf {
-            print("The tree is empty")
-            return
-        }
-        property1()
-        property2(n: self.root)
-        property3()
-    }
-    
-    private func findNode(rootNode: RBTNode<T>, value: T) -> RBTNode<T> {
-        var nextNode = rootNode
-        if rootNode !== nullLeaf && value != rootNode.value {
-            if value < rootNode.value {
-                nextNode = findNode(rootNode: rootNode.left, value: value)
-            } else {
-                nextNode = findNode(rootNode: rootNode.right, value: value)
-            }
-        }
-        
-        return nextNode
-    }
-    
-    private func insertNode(n: RBTNode<T>) {
-        BSTInsertNode(n: n, parent: root)
-        insertCase1(n: n)
-    }
-    
-    private func BSTInsertNode(n: RBTNode<T>, parent: RBTNode<T>) {
-        if parent === nullLeaf {
-            self.root = n
-        } else if n.value < parent.value {
-            if parent.left !== nullLeaf {
-                BSTInsertNode(n: n, parent: parent.left)
-            } else {
-                parent.left = n
-                parent.left.parent = parent
-            }
-        } else {
-            if parent.right !== nullLeaf {
-                BSTInsertNode(n: n, parent: parent.right)
-            } else {
-                parent.right = n
-                parent.right.parent = parent
-            }
-        }
-    }
-    
-    // if node is root change color to black, else move on
-    private func insertCase1(n: RBTNode<T>) {
-        if n === root {
-            n.color = .black
-        } else {
-            insertCase2(n: n)
-        }
-    }
-    
-    // if parent of node is not black, and node is not root move on
-    private func insertCase2(n: RBTNode<T>) {
-        if !n.parent.isBlack {
-            insertCase3(n: n)
-        }
-    }
-    
-    // if uncle is red do stuff otherwise move to 4
-    private func insertCase3(n: RBTNode<T>) {
-        if n.uncle.isRed { // node must have grandparent as children of root have a black parent
-            // both parent and uncle are red, so grandparent must be black.
-            n.parent.color = .black
-            n.uncle.color = .black
-            n.grandparent.color = .red
-            // now both parent and uncle are black and grandparent is red.
-            // we repeat for the grandparent
-            insertCase1(n: n.grandparent)
-        } else {
-            insertCase4(n: n)
-        }
-    }
-    
-    // parent is red, grandparent is black, uncle is black
-    // There are 4 cases left:
-    // - left left
-    // - left right
-    // - right right
-    // - right left
-    
-    // the cases "left right" and "right left" can be rotated into the other two
-    // so if either of the two is detected we apply a rotation and then move on to
-    // deal with the final two cases, if neither is detected we move on to those cases anyway
-    private func insertCase4(n: RBTNode<T>) {
-        if n.parent.isLeftChild && n.isRightChild { // left right case
-            leftRotate(n: n.parent)
-            insertCase5(n: n.left)
-        } else if n.parent.isRightChild && n.isLeftChild { // right left case
-            rightRotate(n: n.parent)
-            insertCase5(n: n.right)
-        } else {
-            insertCase5(n: n)
-        }
-    }
-    
-    private func insertCase5(n: RBTNode<T>) {
-        // swap color of parent and grandparent
-        // parent is red grandparent is black
-        n.parent.color = .black
-        n.grandparent.color = .red
-        
-        if n.isLeftChild { // left left case
-            rightRotate(n: n.grandparent)
-        } else { // right right case
-            leftRotate(n: n.grandparent)
-        }
-    }
-    
-    private func deleteNode(n: RBTNode<T>) {
-        var toDel = n
-        
-        if toDel.left === nullLeaf && toDel.right === nullLeaf && toDel.parent === nullLeaf {
-            self.root = nullLeaf
-            return
-        }
-        
-        if toDel.left === nullLeaf && toDel.right === nullLeaf && toDel.isRed {
-            if toDel.isLeftChild {
-                toDel.parent.left = nullLeaf
-            } else {
-                toDel.parent.right = nullLeaf
-            }
-            return
-        }
-        
-        if toDel.left !== nullLeaf && toDel.right !== nullLeaf {
-            let pred = maximum(n: toDel.left)
-            toDel.value = pred.value
-            toDel = pred
-        }
-        
-        // from here toDel has at most 1 non nullLeaf child
-        
-        var child: RBTNode<T>
-        if toDel.left !== nullLeaf {
-            child = toDel.left
-        } else {
-            child = toDel.right
-        }
-        
-        if toDel.isRed || child.isRed {
-            child.color = .black
-            
-            if toDel.isLeftChild {
-                toDel.parent.left = child
-            } else {
-                toDel.parent.right = child
-            }
-            
-            if child !== nullLeaf {
-                child.parent = toDel.parent
-            }
-        } else { // both toDel and child are black
-            
-            var sibling = toDel.sibling
-            
-            if toDel.isLeftChild {
-                toDel.parent.left = child
-            } else {
-                toDel.parent.right = child
-            }
-            if child !== nullLeaf {
-                child.parent = toDel.parent
-            }
-            child.color = .doubleBlack
-            
-            while child.isDoubleBlack || (child.parent !== nullLeaf && child.parent != nil) {
-                if sibling.isBlack {
-                    
-                    var leftRedChild: RBTNode<T>! = nil
-                    if sibling.left.isRed {
-                        leftRedChild = sibling.left
-                    }
-                    var rightRedChild: RBTNode<T>! = nil
-                    if sibling.right.isRed {
-                        rightRedChild = sibling.right
-                    }
-                    
-                    if leftRedChild != nil || rightRedChild != nil { // at least one of sibling's children are red
-                        child.color = .black
-                        if sibling.isLeftChild {
-                            if leftRedChild != nil { // left left case
-                                sibling.left.color = .black
-                                let tempColor = sibling.parent.color
-                                sibling.parent.color = sibling.color
-                                sibling.color = tempColor
-                                rightRotate(n: sibling.parent)
-                            } else { // left right case
-                                if sibling.parent.isRed {
-                                    sibling.parent.color = .black
-                                } else {
-                                    sibling.right.color = .black
-                                }
-                                leftRotate(n: sibling)
-                                rightRotate(n: sibling.grandparent)
-                            }
-                        } else {
-                            if rightRedChild != nil { // right right case
-                                sibling.right.color = .black
-                                let tempColor = sibling.parent.color
-                                sibling.parent.color = sibling.color
-                                sibling.color = tempColor
-                                leftRotate(n: sibling.parent)
-                            } else { // right left case
-                                if sibling.parent.isRed {
-                                    sibling.parent.color = .black
-                                } else {
-                                    sibling.left.color = .black
-                                }
-                                rightRotate(n: sibling)
-                                leftRotate(n: sibling.grandparent)
-                            }
-                        }
-                        break
-                    } else { // both sibling's children are black
-                        child.color = .black
-                        sibling.color = .red
-                        if sibling.parent.isRed {
-                            sibling.parent.color = .black
-                            break
-                        }
-                        /*
-                        sibling.parent.color = .doubleBlack
-                        child = sibling.parent
-                        sibling = child.sibling
-                        */
-                        if sibling.parent.parent === nullLeaf { // parent of child is root
-                            break
-                        } else {
-                            sibling.parent.color = .doubleBlack
-                            child = sibling.parent
-                            sibling = child.sibling // can become nill if child is root as parent is nullLeaf
-                        }
-                        //---------------
-                    }
-                } else { // sibling is red
-                    sibling.color = .black
-                    
-                    if sibling.isLeftChild { // left case
-                        rightRotate(n: sibling.parent)
-                        sibling = sibling.right.left
-                        sibling.parent.color = .red
-                    } else { // right case
-                        leftRotate(n: sibling.parent)
-                        sibling = sibling.left.right
-                        sibling.parent.color = .red
-                    }
-                }
-                
-                // sibling check is here for when child is a nullLeaf and thus does not have a parent.
-                // child is here as sibling can become nil when child is the root
-                if (sibling.parent === nullLeaf) || (child !== nullLeaf && child.parent === nullLeaf) {
-                    child.color = .black
-                }
-            }
-        }
-    }
-    
-    private func property1() {
-        
-        if self.root.isRed {
-            print("Root is not black")
-        }
-    }
-    
-    private func property2(n: RBTNode<T>) {
-        if n === nullLeaf {
-            return
-        }
-        if n.isRed {
-            if n.left !== nullLeaf && n.left.isRed {
-                print("Red node: \(n.value), has red left child")
-            } else if n.right !== nullLeaf && n.right.isRed {
-                print("Red node: \(n.value), has red right child")
-            }
-        }
-        property2(n: n.left)
-        property2(n: n.right)
-    }
-    
-    private func property3() {
-        let bDepth = blackDepth(root: self.root)
-        
-        let leaves:[RBTNode<T>] = getLeaves(n: self.root)
-        
-        for leaflet in leaves {
-            var leaf = leaflet
-            var i = 0
-            
-            while leaf !== nullLeaf {
-                if leaf.isBlack {
-                    i = i + 1
-                }
-                leaf = leaf.parent
-            }
-            
-            if i != bDepth {
-                print("black depth: \(bDepth), is not equal (depth: \(i)) for leaf with value: \(leaflet.value)")
-            }
-        }
-        
-    }
-    
-    private func getLeaves(n: RBTNode<T>) -> [RBTNode<T>] {
-        var leaves = [RBTNode<T>]()
-        
-        if n !== nullLeaf {
-            if n.left === nullLeaf && n.right === nullLeaf {
-                leaves.append(n)
-            } else {
-                let leftLeaves = getLeaves(n: n.left)
-                let rightLeaves = getLeaves(n: n.right)
-                
-                leaves.append(contentsOf: leftLeaves)
-                leaves.append(contentsOf: rightLeaves)
-            }
-        }
-        
-        return leaves
-    }
-    
-    private func blackDepth(root: RBTNode<T>) -> Int {
-        if root === nullLeaf {
-            return 0
-        } else {
-            let returnValue = root.isBlack ? 1 : 0
-            return returnValue + (max(blackDepth(root: root.left), blackDepth(root: root.right)))
-        }
-    }
-    
-    private func leftRotate(n: RBTNode<T>) {
-        let newRoot = n.right!
-        n.right = newRoot.left!
-        if newRoot.left !== nullLeaf {
-            newRoot.left.parent = n
-        }
-        newRoot.parent = n.parent
-        if n.parent === nullLeaf {
-            self.root = newRoot
-        } else if n.isLeftChild {
-            n.parent.left = newRoot
-        } else {
-            n.parent.right = newRoot
-        }
-        newRoot.left = n
-        n.parent = newRoot
-    }
-    
-    private func rightRotate(n: RBTNode<T>) {
-        let newRoot = n.left!
-        n.left = newRoot.right!
-        if newRoot.right !== nullLeaf {
-            newRoot.right.parent = n
-        }
-        newRoot.parent = n.parent
-        if n.parent === nullLeaf {
-            self.root = newRoot
-        } else if n.isRightChild {
-            n.parent.right = newRoot
-        } else {
-            n.parent.left = newRoot
-        }
-        newRoot.right = n
-        n.parent = newRoot
-    }
-}
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/contents.xcplayground b/Red-Black Tree/Red-Black Tree 2.playground/contents.xcplayground
deleted file mode 100644
index 5da2641c9..000000000
--- a/Red-Black Tree/Red-Black Tree 2.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/Red-Black Tree/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata b/Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/contents.xcworkspacedata
similarity index 100%
rename from Red-Black Tree/Red-Black Tree 2.playground/playground.xcworkspace/contents.xcworkspacedata
rename to Red-Black Tree/RedBlackTree.playground/playground.xcworkspace/contents.xcworkspacedata

From dc460542ffe226bbb0175fec35a9195eac87d9a3 Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Tue, 21 Mar 2017 11:30:51 +0100
Subject: [PATCH 046/862] Added licence to file

---
 .../Sources/RedBlackTree.swift                | 19 ++++++++++++++++---
 1 file changed, 16 insertions(+), 3 deletions(-)

diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index 057909b07..a588ea6bc 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -1,9 +1,22 @@
+//Copyright (c) 2016 Matthijs Hollemans and contributors
 //
-//  RedBlackTree.swift
+//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:
 //
-//  Created by Ute Schiehlen on 14.03.17.
-//  Copyright © 2017 Ute Schiehlen. All rights reserved.
+//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
 

From 37d7300627bda5538381127db68571bf7b38f57e Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Tue, 21 Mar 2017 11:51:08 +0100
Subject: [PATCH 047/862] Incorporated major swiftlint warnings

---
 .../Sources/RedBlackTree.swift                     | 14 ++++++--------
 1 file changed, 6 insertions(+), 8 deletions(-)

diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index a588ea6bc..6f3b16b86 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -25,7 +25,7 @@ private enum RBTreeColor {
   case black
 }
 
-private enum rotationDirection {
+private enum RotationDirection {
   case left
   case right
 }
@@ -114,7 +114,7 @@ public class RedBlackTree<Key: Comparable> {
 // MARK: - Equatable protocol
 
 extension RBTreeNode {
-  static public func ==<T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
+  static public func == <T>(lhs: RBTreeNode<T>, rhs: RBTreeNode<T>) -> Bool {
     return lhs.key == rhs.key
   }
 }
@@ -309,8 +309,8 @@ extension RedBlackTree {
    * - case 2b -> red-black tree
    */
   private func insertFixup(node z: RBNode) {
-    if(!z.isNullLeaf) {
-      guard let parentZ = z.parent else{
+    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
@@ -539,7 +539,6 @@ extension RedBlackTree {
     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,
@@ -561,7 +560,7 @@ extension RedBlackTree {
    * 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) {
+  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
@@ -616,7 +615,6 @@ extension RedBlackTree {
   // 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 {
@@ -746,7 +744,7 @@ extension RedBlackTree: CustomStringConvertible {
   public var description: String {
     if root.isNullLeaf {
       return "[]"
-    } else{
+    } else {
       return root.description
     }
   }

From 306ef65bd3ef8b652b1120bc8a5b6770583c3e35 Mon Sep 17 00:00:00 2001
From: kyungkoo <mc2e.dev@gmail.com>
Date: Fri, 24 Mar 2017 17:29:41 +0900
Subject: [PATCH 048/862] fixed broken link

---
 README.markdown | 100 ++++++++++++++++++++++++------------------------
 1 file changed, 50 insertions(+), 50 deletions(-)

diff --git a/README.markdown b/README.markdown
index dfe451478..fc034f71b 100644
--- a/README.markdown
+++ b/README.markdown
@@ -34,31 +34,31 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 
 - [Stack](Stack/)
 - [Queue](Queue/)
-- [Insertion Sort](Insertion Sort/)
-- [Binary Search](Binary Search/) and [Binary Search Tree](Binary Search Tree/)
-- [Merge Sort](Merge Sort/)
+- [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/)
 
 ## The algorithms
 
 ### Searching
 
-- [Linear Search](Linear Search/). Find an element in an array.
-- [Binary Search](Binary Search/). Quickly find elements in a sorted array.
-- [Count Occurrences](Count Occurrences/). Count how often a value appears in an array.
-- [Select Minimum / Maximum](Select Minimum Maximum). Find the minimum/maximum value in an array.
-- [k-th Largest Element](Kth Largest Element/). Find the *k*-th largest element in an array, such as the median.
-- [Selection Sampling](Selection Sampling/). Randomly choose a bunch of items from a collection.
+- [Linear Search](Linear%20Search/). Find an element in an array.
+- [Binary Search](Binary%20Search/). Quickly find elements in a sorted array.
+- [Count Occurrences](Count%20Occurrences/). Count how often a value appears in an array.
+- [Select Minimum / Maximum](Select%20Minimum%20Maximum). Find the minimum/maximum value in an array.
+- [k-th Largest Element](Kth%20Largest%20Element/). Find the *k*-th largest element in an array, such as the median.
+- [Selection Sampling](Selection%20Sampling/). Randomly choose a bunch of items from a collection.
 - [Union-Find](Union-Find/). Keeps track of disjoint sets and lets you quickly merge them.
 
 
 ### String Search
 
-- [Brute-Force String Search](Brute-Force String Search/). A naive method.
+- [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.
 - Knuth-Morris-Pratt
 - [Rabin-Karp](Rabin-Karp/)  Faster search by using hashing.
-- [Longest Common Subsequence](Longest Common Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
+- [Longest Common Subsequence](Longest%20Common%20Subsequence/). Find the longest sequence of characters that appear in the same order in both strings.
 - [Z-Algorithm](Z-Algorithm/). Finds all instances of a pattern in a String, and returns the indexes of where the pattern starts within the String.
 
 ### Sorting
@@ -67,51 +67,51 @@ It's fun to see how sorting algorithms work, but in practice you'll almost never
 
 Basic sorts:
 
-- [Insertion Sort](Insertion Sort/)
-- [Selection Sort](Selection Sort/)
-- [Shell Sort](Shell Sort/)
+- [Insertion Sort](Insertion%20Sort/)
+- [Selection Sort](Selection%20Sort/)
+- [Shell Sort](Shell%20Sort/)
 
 Fast sorts:
 
 - [Quicksort](Quicksort/)
-- [Merge Sort](Merge Sort/)
-- [Heap Sort](Heap Sort/)
+- [Merge Sort](Merge%20Sort/)
+- [Heap Sort](Heap%20Sort/)
 
 Special-purpose sorts:
 
-- [Counting Sort](Counting Sort/)
-- [Radix Sort](Radix Sort/)
-- [Topological Sort](Topological Sort/)
+- [Counting Sort](Counting%20Sort/)
+- [Radix Sort](Radix%20Sort/)
+- [Topological Sort](Topological%20Sort/)
 
 Bad sorting algorithms (don't use these!):
 
-- [Bubble Sort](Bubble Sort/)
-- [Slow Sort](Slow Sort/)
+- [Bubble Sort](Bubble%20Sort/)
+- [Slow Sort](Slow%20Sort/)
 
 ### Compression
 
-- [Run-Length Encoding (RLE)](Run-Length Encoding/). Store repeated values as a single byte and a count.
-- [Huffman Coding](Huffman Coding/). Store more common elements using a smaller number of bits.
+- [Run-Length Encoding (RLE)](Run-Length%20Encoding/). Store repeated values as a single byte and a count.
+- [Huffman Coding](Huffman%20Coding/). Store more common elements using a smaller number of bits.
 
 ### Miscellaneous
 
 - [Shuffle](Shuffle/). Randomly rearranges the contents of an array.
-- [Comb Sort](Comb Sort/). An improve upon the Bubble Sort algorithm.
+- [Comb Sort](Comb%20Sort/). An improve upon the Bubble Sort algorithm.
 
 ### Mathematics
 
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.
 - [Permutations and Combinations](Combinatorics/). Get your combinatorics on!
-- [Shunting Yard Algorithm](Shunting Yard/). Convert infix expressions to postfix.
+- [Shunting Yard Algorithm](Shunting%20Yard/). Convert infix expressions to postfix.
 - Statistics
-- [Karatsuba Multiplication](Karatsuba Multiplication/). Another take on elementary multiplication.
+- [Karatsuba Multiplication](Karatsuba%20Multiplication/). Another take on elementary multiplication.
 - [Haversine Distance](HaversineDistance/). Calculating the distance between 2 points from a sphere.
 
 ### Machine learning
 
 - [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
 - k-Nearest Neighbors
-- [Linear Regression](Linear Regression/)
+- [Linear Regression](Linear%20Regression/)
 - Logistic Regression
 - Neural Networks
 - PageRank
@@ -129,33 +129,33 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 ### Variations on arrays
 
 - [Array2D](Array2D/). A two-dimensional array with fixed dimensions. Useful for board games.
-- [Bit Set](Bit Set/). A fixed-size sequence of *n* bits.
-- [Fixed Size Array](Fixed Size Array/). When you know beforehand how large your data will be, it might be more efficient to use an old-fashioned array with a fixed size.
-- [Ordered Array](Ordered Array/). An array that is always sorted.
-- [Rootish Array Stack](Rootish Array Stack/). A space and time efficient variation on Swift arrays.
+- [Bit Set](Bit%20Set/). A fixed-size sequence of *n* bits.
+- [Fixed Size Array](Fixed%20Size%20Array/). When you know beforehand how large your data will be, it might be more efficient to use an old-fashioned array with a fixed size.
+- [Ordered Array](Ordered%20Array/). An array that is always sorted.
+- [Rootish Array Stack](Rootish%20Array%20Stack/). A space and time efficient variation on Swift arrays.
 
 ### Queues
 
 - [Stack](Stack/). Last-in, first-out!
 - [Queue](Queue/). First-in, first-out!
 - [Deque](Deque/). A double-ended queue.
-- [Priority Queue](Priority Queue). A queue where the most important element is always at the front.
-- [Ring Buffer](Ring Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
+- [Priority Queue](Priority%20Queue). A queue where the most important element is always at the front.
+- [Ring Buffer](Ring%20Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
 
 ### Lists
 
-- [Linked List](Linked List/). A sequence of data items connected through links. Covers both singly and doubly linked 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.
 
 ### Trees
 
 - [Tree](Tree/). A general-purpose tree structure.
-- [Binary Tree](Binary Tree/). A tree where each node has at most two children.
-- [Binary Search Tree (BST)](Binary Search Tree/). A binary tree that orders its nodes in a way that allows for fast queries.
+- [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
 - Splay Tree
 - Threaded Binary Tree
-- [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
+- [Segment Tree](Segment%20Tree/). Can quickly compute a function over a portion of an array.
 - kd-Tree
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
 - Fibonacci Heap
@@ -164,33 +164,33 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 
 ### Hashing
 
-- [Hash Table](Hash Table/). Allows you to store and retrieve objects by a key. This is how the dictionary type is usually implemented.
+- [Hash Table](Hash%20Table/). Allows you to store and retrieve objects by a key. This is how the dictionary type is usually implemented.
 - Hash Functions
 
 ### Sets
 
-- [Bloom Filter](Bloom Filter/). A constant-memory data structure that probabilistically tests whether an element is in a set.
-- [Hash Set](Hash Set/). A set implemented using a hash table.
+- [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
-- [Ordered Set](Ordered Set/). A set where the order of items matters.
+- [Ordered Set](Ordered%20Set/). A set where the order of items matters.
 
 ### Graphs
 
 - [Graph](Graph/)
-- [Breadth-First Search (BFS)](Breadth-First Search/)
-- [Depth-First Search (DFS)](Depth-First Search/)
-- [Shortest Path](Shortest Path %28Unweighted%29/) on an unweighted tree
-- [Single-Source Shortest Paths](Single-Source Shortest Paths (Weighted)/)
-- [Minimum Spanning Tree](Minimum Spanning Tree %28Unweighted%29/) on an unweighted tree
-- [All-Pairs Shortest Paths](All-Pairs Shortest Paths/)
+- [Breadth-First Search (BFS)](Breadth-First%20Search/)
+- [Depth-First Search (DFS)](Depth-First%20Search/)
+- [Shortest Path](Shortest%20Path%20%28Unweighted%29/) on an unweighted tree
+- [Single-Source Shortest Paths](Single-Source%20Shortest%20Paths%20(Weighted)/)
+- [Minimum Spanning Tree](Minimum%20Spanning%20Tree%20%28Unweighted%29/) on an unweighted tree
+- [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
 
 ## Puzzles
 
 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 Problem/)
-- [Fizz Buzz](Fizz Buzz/)
-- [Monty Hall Problem](Monty Hall Problem/)
+- [Two-Sum Problem](Two-Sum%20Problem/)
+- [Fizz Buzz](Fizz%20Buzz/)
+- [Monty Hall Problem](Monty%20Hall%20Problem/)
 - [Finding Palindromes](Palindromes/)
 - [Dining Philosophers](DiningPhilosophers/)
 

From 943ad7e48fe966f7679c4addfafa7baa5fb81fb2 Mon Sep 17 00:00:00 2001
From: kyungkoo <mc2e.dev@gmail.com>
Date: Fri, 24 Mar 2017 18:25:24 +0900
Subject: [PATCH 049/862] fixed important links section link

---
 README.markdown | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/README.markdown b/README.markdown
index fc034f71b..023f151fb 100644
--- a/README.markdown
+++ b/README.markdown
@@ -16,17 +16,17 @@ This is a work in progress. More algorithms will be added soon. :-)
 
 ## Important links
 
-[What are algorithms and data structures?](What are Algorithms.markdown) Pancakes!
+[What are algorithms and data structures?](What%20are%20Algorithms.markdown) Pancakes!
 
-[Why learn algorithms?](Why Algorithms.markdown) Worried this isn't your cup of tea? Then read this.
+[Why learn algorithms?](Why%20Algorithms.markdown) Worried this isn't your cup of tea? Then read this.
 
-[Big-O notation](Big-O Notation.markdown). We often say things like, "This algorithm is **O(n)**." If you don't know what that means, read this first.
+[Big-O notation](Big-O%20Notation.markdown). We often say things like, "This algorithm is **O(n)**." If you don't know what that means, read this first.
 
-[Algorithm design techniques](Algorithm Design.markdown). How do you create your own algorithms?
+[Algorithm design techniques](Algorithm%20Design.markdown). How do you create your own algorithms?
 
-[How to contribute](How to Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
+[How to contribute](How%20to%20Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
 
-[Under construction](Under Construction.markdown). Algorithms that are under construction.
+[Under construction](Under%20Construction.markdown). Algorithms that are under construction.
 
 ## Where to start?
 

From a54e722b035ffc5eeba63fcd5b1648e56f732ec0 Mon Sep 17 00:00:00 2001
From: Jake Romer <jkrmr.io@gmail.com>
Date: Fri, 24 Mar 2017 07:58:19 -0700
Subject: [PATCH 050/862] Fix links to related articles

Fixes links to Linked List, Ring Buffer, and Priority Queue directories.
---
 Queue/README.markdown | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Queue/README.markdown b/Queue/README.markdown
index f8259c31c..9efce66b9 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -255,8 +255,8 @@ The `nil` objects at the front have been removed and the array is no longer wast
 
 ## See also
 
-There are many other ways to create a queue. Alternative implementations use a [linked list](../Linked List/), a [circular buffer](../Ring Buffer/), or a [heap](../Heap/). 
+There are many other ways to create a queue. Alternative implementations use a [linked list](../Linked%20List/), a [circular buffer](../Ring%20Buffer/), or a [heap](../Heap/). 
 
-Variations on this theme are [deque](../Deque/), a double-ended queue where you can enqueue and dequeue at both ends, and [priority queue](../Priority Queue/), a sorted queue where the "most important" item is always at the front.
+Variations on this theme are [deque](../Deque/), a double-ended queue where you can enqueue and dequeue at both ends, and [priority queue](../Priority%20Queue/), a sorted queue where the "most important" item is always at the front.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 3d033740b0d3b727d488a14121da68f822b578a2 Mon Sep 17 00:00:00 2001
From: Jake Romer <jkrmr.io@gmail.com>
Date: Sat, 25 Mar 2017 07:47:49 -0700
Subject: [PATCH 051/862] URL encode links in Markdown files

There are a ton of broken markdown links in the READMEs throughout this
repo because the files and directories they refer to have spaces in
their names but these aren't HTML encoded in their links. This commit
just replaces spaces with %20 to fix these.
---
 AVL Tree/README.markdown                   |  8 ++++----
 Big-O Notation.markdown                    |  2 +-
 Binary Search Tree/README.markdown         | 10 +++++-----
 Binary Search/README.markdown              |  2 +-
 Binary Tree/README.markdown                |  2 +-
 Bloom Filter/README.markdown               |  2 +-
 Bounded Priority Queue/README.markdown     |  2 +-
 Boyer-Moore/README.markdown                |  2 +-
 Breadth-First Search/README.markdown       |  4 ++--
 Count Occurrences/README.markdown          |  4 ++--
 Hash Set/README.markdown                   |  2 +-
 How to Contribute.markdown                 |  2 +-
 Ordered Array/README.markdown              |  2 +-
 Ordered Set/README.markdown                |  2 +-
 Selection Sort/README.markdown             |  6 +++---
 Shell Sort/README.markdown                 |  2 +-
 Shortest Path (Unweighted)/README.markdown |  8 ++++----
 Threaded Binary Tree/README.markdown       | 10 +++++-----
 Topological Sort/README.markdown           |  2 +-
 Tree/README.markdown                       |  4 ++--
 Under Construction.markdown                | 20 ++++++++++----------
 21 files changed, 49 insertions(+), 49 deletions(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index 355204587..a9218203a 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -1,6 +1,6 @@
 # AVL Tree
 
-An AVL tree is a self-balancing form of a [binary search tree](../Binary Search Tree/), in which the height of subtrees differ at most by only 1.
+An AVL tree is a self-balancing form of a [binary search tree](../Binary%20Search%20Tree/), in which the height of subtrees differ at most by only 1.
 
 A binary tree is *balanced* when its left and right subtrees contain roughly the same number of nodes. That is what makes searching the tree really fast. But if a binary search tree is unbalanced, searching can become really slow.
 
@@ -8,7 +8,7 @@ This is an example of an unbalanced tree:
 
 ![Unbalanced tree](Images/Unbalanced.png)
 
-All the children are in the left branch and none are in the right. This is essentially the same as a [linked list](../Linked List/). As a result, searching takes **O(n)** time instead of the much faster **O(log n)** that you'd expect from a binary search tree.
+All the children are in the left branch and none are in the right. This is essentially the same as a [linked list](../Linked%20List/). As a result, searching takes **O(n)** time instead of the much faster **O(log n)** that you'd expect from a binary search tree.
 
 A balanced version of that tree would look like this:
 
@@ -78,7 +78,7 @@ Insertion never needs more than 2 rotations. Removal might require up to __log(n
 
 Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary search tree](../Binary Search Tree/) stuff. You'll find this in any implementation of a binary search tree. For example, searching the tree is exactly the same. The only things that an AVL tree does slightly differently are inserting and deleting the nodes.
 
-> **Note:** If you're a bit fuzzy on the regular operations of a binary search tree, I suggest you [catch up on those first](../Binary Search Tree/). It will make the rest of the AVL tree easier to understand.
+> **Note:** If you're a bit fuzzy on the regular operations of a binary search tree, I suggest you [catch up on those first](../Binary%20Search%20Tree/). It will make the rest of the AVL tree easier to understand.
 
 The interesting bits are in the `balance()` method which is called after inserting or deleting a node.
 
@@ -86,6 +86,6 @@ The interesting bits are in the `balance()` method which is called after inserti
 
 [AVL tree on Wikipedia](https://en.wikipedia.org/wiki/AVL_tree)
 
-AVL tree was the first self-balancing binary tree. These days, the [red-black tree](../Red-Black Tree/) seems to be more popular.
+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*
diff --git a/Big-O Notation.markdown b/Big-O Notation.markdown
index 8cb988168..09fbb04aa 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -19,6 +19,6 @@ Big-O | Name | Description
 
 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 Sort/) algorithm is **O(n^2)**. In theory that is worse than the running time for [merge sort](Merge Sort/), 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!
+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 Sort/), 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!
 
 If you find this confusing, don't let this Big-O stuff bother you too much. It's mostly useful when comparing two algorithms to figure out which one is better. But in the end you still want to test in practice which one really is the best. And if the amount of data is relatively small, then even a slow algorithm will be fast enough for practical use.
diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index bd2a00c9e..a3a84c03d 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -1,6 +1,6 @@
 # Binary Search Tree (BST)
 
-A binary search tree is a special kind of [binary tree](../Binary Tree/) (a tree in which each node has at most two children) that performs insertions and deletions such that the tree is always sorted.
+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.
 
 If you don't know what a tree is or what it is for, then [read this first](../Tree/).
 
@@ -49,7 +49,7 @@ If we were looking for the value `5` in the example, it would go as follows:
 
 ![Searching the tree](Images/Searching.png)
 
-Thanks to the structure of the tree, searching is really fast. It runs in **O(h)** time. If you have a well-balanced tree with a million nodes, it only takes about 20 steps to find anything in this tree. (The idea is very similar to [binary search](../Binary Search) in an array.)
+Thanks to the structure of the tree, searching is really fast. It runs in **O(h)** time. If you have a well-balanced tree with a million nodes, it only takes about 20 steps to find anything in this tree. (The idea is very similar to [binary search](../Binary%20Search) in an array.)
 
 ## Traversing the tree
 
@@ -535,7 +535,7 @@ The code for `successor()` works the exact same way but mirrored:
 
 Both these methods run in **O(h)** time.
 
-> **Note:** There is a cool variation called a ["threaded" binary tree](../Threaded Binary Tree) where "unused" left and right pointers are repurposed to make direct links between predecessor and successor nodes. Very clever!
+> **Note:** There is a cool variation called a ["threaded" binary tree](../Threaded%20Binary%20Tree) where "unused" left and right pointers are repurposed to make direct links between predecessor and successor nodes. Very clever!
 
 ### Is the search tree valid?
 
@@ -713,11 +713,11 @@ The root node is in the middle; a dot means there is no child at that position.
 
 A binary search tree is *balanced* when its left and right subtrees contain roughly the same number of nodes. In that case, the height of the tree is *log(n)*, where *n* is the number of nodes. That's the ideal situation.
 
-However, if one branch is significantly longer than the other, searching becomes very slow. We end up checking way more values than we'd ideally have to. In the worst case, the height of the tree can become *n*. Such a tree acts more like a [linked list](../Linked List/) than a binary search tree, with performance degrading to **O(n)**. Not good!
+However, if one branch is significantly longer than the other, searching becomes very slow. We end up checking way more values than we'd ideally have to. In the worst case, the height of the tree can become *n*. Such a tree acts more like a [linked list](../Linked%20List/) than a binary search tree, with performance degrading to **O(n)**. Not good!
 
 One way to make the binary search tree balanced is to insert the nodes in a totally random order. On average that should balance out the tree quite nicely. But it doesn't guarantee success, nor is it always practical.
 
-The other solution is to use a *self-balancing* binary tree. This type of data structure adjusts the tree to keep it balanced after you insert or delete nodes. See [AVL tree](../AVL Tree) and [red-black tree](../Red-Black Tree) for examples.
+The other solution is to use a *self-balancing* binary tree. This type of data structure adjusts the tree to keep it balanced after you insert or delete nodes. See [AVL tree](../AVL%20Tree) and [red-black tree](../Red-Black%20Tree) for examples.
 
 ## See also
 
diff --git a/Binary Search/README.markdown b/Binary Search/README.markdown
index c65d0b5fd..09b141e04 100644
--- a/Binary Search/README.markdown	
+++ b/Binary Search/README.markdown	
@@ -12,7 +12,7 @@ let numbers = [11, 59, 3, 2, 53, 17, 31, 7, 19, 67, 47, 13, 37, 61, 29, 43, 5, 4
 numbers.indexOf(43)  // returns 15
 ```
 
-The built-in `indexOf()` function performs a [linear search](../Linear Search/). In code that looks something like this:
+The built-in `indexOf()` function performs a [linear search](../Linear%20Search/). In code that looks something like this:
 
 ```swift
 func linearSearch<T: Equatable>(_ a: [T], _ key: T) -> Int? {
diff --git a/Binary Tree/README.markdown b/Binary Tree/README.markdown
index 896116dda..8ce398804 100644
--- a/Binary Tree/README.markdown	
+++ b/Binary Tree/README.markdown	
@@ -8,7 +8,7 @@ The child nodes are usually called the *left* child and the *right* child. If a
 
 Often nodes will have a link back to their parent but this is not strictly necessary.
 
-Binary trees are often used as [binary search trees](../Binary Search Tree/). In that case, the nodes must be in a specific order (smaller values on the left, larger values on the right). But this is not a requirement for all binary trees.
+Binary trees are often used as [binary search trees](../Binary%20Search%20Tree/). In that case, the nodes must be in a specific order (smaller values on the left, larger values on the right). But this is not a requirement for all binary trees.
 
 For example, here is a binary tree that represents a sequence of arithmetical operations, `(5 * (a - 10)) + (-4 * (3 / b))`:
 
diff --git a/Bloom Filter/README.markdown b/Bloom Filter/README.markdown
index a85d71be4..3fff0a379 100644
--- a/Bloom Filter/README.markdown	
+++ b/Bloom Filter/README.markdown	
@@ -18,7 +18,7 @@ An advantage of the Bloom Filter over a hash table is that the former maintains
 
 ## Inserting objects into the set
 
-A Bloom Filter is essentially a fixed-length [bit vector](../Bit Set/), an array of bits. When we insert objects, we set some of these bits to `1`, and when we query for objects we check if certain bits are `0` or `1`. Both operations use hash functions.
+A Bloom Filter is essentially a fixed-length [bit vector](../Bit%20Set/), an array of bits. When we insert objects, we set some of these bits to `1`, and when we query for objects we check if certain bits are `0` or `1`. Both operations use hash functions.
 
 To insert an element in the filter, the element is hashed with several different hash functions. Each hash function returns a value that we map to an index in the array. We then set the bits at these indices to `1` or true.
 
diff --git a/Bounded Priority Queue/README.markdown b/Bounded Priority Queue/README.markdown
index 8d47adefb..4e4c89272 100644
--- a/Bounded Priority Queue/README.markdown	
+++ b/Bounded Priority Queue/README.markdown	
@@ -1,6 +1,6 @@
 # Bounded Priority queue
 
-A bounded priority queue is similar to a regular [priority queue](../Priority Queue/), except that there is a fixed upper bound on the number of elements that can be stored. When a new element is added to the queue while the queue is at capacity, the element with the highest priority value is ejected from the queue.
+A bounded priority queue is similar to a regular [priority queue](../Priority%20Queue/), except that there is a fixed upper bound on the number of elements that can be stored. When a new element is added to the queue while the queue is at capacity, the element with the highest priority value is ejected from the queue.
 
 ## Example
 
diff --git a/Boyer-Moore/README.markdown b/Boyer-Moore/README.markdown
index e821b812e..5b3841eca 100644
--- a/Boyer-Moore/README.markdown
+++ b/Boyer-Moore/README.markdown
@@ -24,7 +24,7 @@ animals.indexOf(pattern: "🐮")
 
 > **Note:** The index of the cow is 6, not 3 as you might expect, because the string uses more storage per character for emoji. The actual value of the `String.Index` is not so important, just that it points at the right character in the string.
 
-The [brute-force approach](../Brute-Force String Search/) works OK, but it's not very efficient, especially on large chunks of text. As it turns out, you don't need to look at _every_ character from the source string -- you can often skip ahead multiple characters.
+The [brute-force approach](../Brute-Force%20String%20Search/) works OK, but it's not very efficient, especially on large chunks of text. As it turns out, you don't need to look at _every_ character from the source string -- you can often skip ahead multiple characters.
 
 The skip-ahead algorithm is called [Boyer-Moore](https://en.wikipedia.org/wiki/Boyer–Moore_string_search_algorithm) and it has been around for a long time. It is considered the benchmark for all string search algorithms.
 
diff --git a/Breadth-First Search/README.markdown b/Breadth-First Search/README.markdown
index 084f4611a..2ef92fd73 100644
--- a/Breadth-First Search/README.markdown	
+++ b/Breadth-First Search/README.markdown	
@@ -148,7 +148,7 @@ 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 Path/) between a source node and each of the other nodes (only for unweighted graphs).
-* Calculating the [minimum spanning tree](../Minimum Spanning Tree (Unweighted)/) on an unweighted graph.
+* Computing the [shortest path](../Shortest%20Path/) 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*
diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 90a9ec2f3..4c65c4219 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -2,9 +2,9 @@
 
 Goal: Count how often a certain value appears in an array.
 
-The obvious way to do this is with a [linear search](../Linear Search/) from the beginning of the array until the end, keeping count of how often you come across the value. That is an **O(n)** algorithm.
+The obvious way to do this is with a [linear search](../Linear%20Search/) from the beginning of the array until the end, keeping count of how often you come across the value. That is an **O(n)** algorithm.
 
-However, if the array is sorted you can do it much faster, in **O(log n)** time, by using a modification of [binary search](../Binary Search/).
+However, if the array is sorted you can do it much faster, in **O(log n)** time, by using a modification of [binary search](../Binary%20Search/).
 
 Let's say we have the following array:
 
diff --git a/Hash Set/README.markdown b/Hash Set/README.markdown
index 368920a1c..fb829c313 100644
--- a/Hash Set/README.markdown	
+++ b/Hash Set/README.markdown	
@@ -196,7 +196,7 @@ difference2.allElements()                // [5, 6]
 
 If you look at the [documentation](http://swiftdoc.org/v2.1/type/Set/) for Swift's own `Set`, you'll notice it has tons more functionality. An obvious extension would be to make `HashSet` conform to `SequenceType` so that you can iterate it with a `for`...`in` loop.
 
-Another thing you could do is replace the `Dictionary` with an actual [hash table](../Hash Table), but one that just stores the keys and doesn't associate them with anything. So you wouldn't need the `Bool` values anymore.
+Another thing you could do is replace the `Dictionary` with an actual [hash table](../Hash%20Table), but one that just stores the keys and doesn't associate them with anything. So you wouldn't need the `Bool` values anymore.
 
 If you often need to look up whether an element belongs to a set and perform unions, then the [union-find](../Union-Find/) data structure may be more suitable. It uses a tree structure instead of a dictionary to make the find and union operations very efficient.
 
diff --git a/How to Contribute.markdown b/How to Contribute.markdown
index 258357e8b..1235f07ff 100644
--- a/How to Contribute.markdown	
+++ b/How to Contribute.markdown	
@@ -6,7 +6,7 @@ Want to help out with the Swift Algorithm Club? Great!
 
 Take a look at the [list](README.markdown). Any algorithms or data structures that don't have a link yet are up for grabs.
 
-Algorithms in the [Under construction](Under Construction.markdown) area are being worked on. Suggestions and feedback is welcome!
+Algorithms in the [Under construction](Under%20Construction.markdown) area are being worked on. Suggestions and feedback is welcome!
 
 New algorithms and data structures are always welcome (even if they aren't on the list).
 
diff --git a/Ordered Array/README.markdown b/Ordered Array/README.markdown
index ca088c325..974a42cae 100644
--- a/Ordered Array/README.markdown	
+++ b/Ordered Array/README.markdown	
@@ -83,7 +83,7 @@ a              // [-2, -1, 1, 3, 4, 5, 7, 9, 10]
 
 The array's contents will always be sorted from low to high, now matter what.
 
-Unfortunately, the current `findInsertionPoint()` function is a bit slow. In the worst case, it needs to scan through the entire array. We can speed this up by using a [binary search](../Binary Search) to find the insertion point.
+Unfortunately, the current `findInsertionPoint()` function is a bit slow. In the worst case, it needs to scan through the entire array. We can speed this up by using a [binary search](../Binary%20Search) to find the insertion point.
 
 Here is the new version:
 
diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
index 0525a31ed..1c0d5a8ac 100644
--- a/Ordered Set/README.markdown	
+++ b/Ordered Set/README.markdown	
@@ -115,7 +115,7 @@ The next function is `indexOf()`, which takes in an object of type `T` and retur
   }
 ```
 
-> **Note:** If you are not familiar with the concept of binary search, we have an [article that explains all about it](../Binary Search).
+> **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.
 
diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index c583b47ea..e95749d14 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -6,7 +6,7 @@ You are given an array of numbers and need to put them in the right order. The s
 
 	[ ...sorted numbers... | ...unsorted numbers... ]
 
-This is similar to [insertion sort](../Insertion Sort/), but the difference is in how new numbers are added to the sorted portion.
+This is similar to [insertion sort](../Insertion%20Sort/), but the difference is in how new numbers are added to the sorted portion.
 
 It works as follows:
 
@@ -108,9 +108,9 @@ The source file [SelectionSort.swift](SelectionSort.swift) has a version of this
 
 ## Performance
 
-Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion Sort/) but better than [bubble sort](../Bubble Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
+Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
 
-[Heap sort](../Heap Sort/) uses the same principle as selection sort but has a really fast method for finding the minimum value in the rest of the array. Its performance is **O(n log n)**.
+[Heap sort](../Heap%20Sort/) uses the same principle as selection sort but has a really fast method for finding the minimum value in the rest of the array. Its performance is **O(n log n)**.
 
 ## See also
 
diff --git a/Shell Sort/README.markdown b/Shell Sort/README.markdown
index 9c4bdf076..c21c29685 100644
--- a/Shell Sort/README.markdown	
+++ b/Shell Sort/README.markdown	
@@ -39,7 +39,7 @@ As you can see, each sublist contains only every 4th item from the original arra
 
 We now call `insertionSort()` once on each sublist.
 
-This particular version of [insertion sort](../Insertion Sort/) sorts from the back to the front. Each item in the sublist is compared against the others. If they're in the wrong order, the value is swapped and travels all the way down until we reach the start of the sublist.
+This particular version of [insertion sort](../Insertion%20Sort/) sorts from the back to the front. Each item in the sublist is compared against the others. If they're in the wrong order, the value is swapped and travels all the way down until we reach the start of the sublist.
 
 So for sublist 0, we swap `4` with `72`, then swap `4` with `64`. After sorting, this sublist looks like:
 
diff --git a/Shortest Path (Unweighted)/README.markdown b/Shortest Path (Unweighted)/README.markdown
index a16519260..4c3c34d9c 100644
--- a/Shortest Path (Unweighted)/README.markdown	
+++ b/Shortest Path (Unweighted)/README.markdown	
@@ -12,11 +12,11 @@ If the [graph is unweighed](../Graph/), then finding the shortest path is easy:
 
 ## Unweighted graph: breadth-first search
 
-[Breadth-first search](../Breadth-First Search/) is a method for traversing a tree or graph data structure. It starts at a source node and explores the immediate neighbor nodes first, before moving to the next level neighbors. As a convenient side effect, it automatically computes the shortest path between a source node and each of the other nodes in the tree or graph.
+[Breadth-first search](../Breadth-First%20Search/) is a method for traversing a tree or graph data structure. It starts at a source node and explores the immediate neighbor nodes first, before moving to the next level neighbors. As a convenient side effect, it automatically computes the shortest path between a source node and each of the other nodes in the tree or graph.
 
 The result of the breadth-first search can be represented with a tree:
 
-![The BFS tree](../Breadth-First Search/Images/TraversalTree.png)
+![The BFS tree](../Breadth-First%20Search/Images/TraversalTree.png)
 
 The root of the tree is the node you started the breadth-first search from. To find the distance from node `A` to any other node, we simply count the number of edges in the tree. And so we find that the shortest path between `A` and `F` is 2. The tree not only tells you how long that path is, but also how to actually get from `A` to `F` (or any of the other nodes).
 
@@ -57,7 +57,7 @@ queue.enqueue(element: G)
 G.distance = C.distance + 1   // result: 2
 ```
 
-This continues until the queue is empty and we've visited all the nodes. Each time we discover a new node, it gets the `distance` of its parent plus 1. As you can see, this is exactly what the [breadth-first search](../Breadth-First Search/) algorithm does, except that we now also keep track of the distance travelled.
+This continues until the queue is empty and we've visited all the nodes. Each time we discover a new node, it gets the `distance` of its parent plus 1. As you can see, this is exactly what the [breadth-first search](../Breadth-First%20Search/) algorithm does, except that we now also keep track of the distance travelled.
 
 Here's the code:
 
@@ -97,6 +97,6 @@ This will output:
 	Node(label: d, distance: 2), Node(label: e, distance: 2), Node(label: f, distance: 2),
 	Node(label: g, distance: 2), Node(label: h, distance: 3)
 
-> **Note:** This version of `breadthFirstSearchShortestPath()` does not actually produce the tree, it only computes the distances. See [minimum spanning tree](../Minimum Spanning Tree (Unweighted)/) on how you can convert the graph into a tree by removing edges.
+> **Note:** This version of `breadthFirstSearchShortestPath()` does not actually produce the tree, it only computes the distances. See [minimum spanning tree](../Minimum%20Spanning%20Tree%20(Unweighted)/) on how you can convert the graph into a tree by removing edges.
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*
diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index fd05113d8..8a1c518f1 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -1,6 +1,6 @@
 # Threaded Binary Tree
 
-A threaded binary tree is a special kind of [binary tree](../Binary Tree/) (a
+A threaded binary tree is a special kind of [binary tree](../Binary%20Tree/) (a
 tree in which each node has at most two children) that maintains a few extra
 variables to allow cheap and fast **in-order traversal** of the tree.  We will
 explore the general structure of threaded binary trees, as well as
@@ -17,7 +17,7 @@ The main motivation behind using a threaded binary tree over a simpler and
 smaller standard binary tree is to increase the speed of an in-order traversal
 of the tree.  An in-order traversal of a binary tree visits the nodes in the
 order in which they are stored, which matches the underlying ordering of a
-[binary search tree](../Binary Search Tree/).  This means most threaded binary
+[binary search tree](../Binary%20Search%20Tree/).  This means most threaded binary
 trees are also binary search trees.  The idea is to visit all the left children
 of a node first, then visit the node itself, and then visit the right children
 last.
@@ -47,7 +47,7 @@ tree, to **O(n)** to a very unbalanced tree.
 
 A threaded binary tree fixes this problem.
 
-> For more information about in-order traversals [see here](../Binary Tree/).
+> For more information about in-order traversals [see here](../Binary%20Tree/).
 
 
 ## Predecessors and successors
@@ -222,7 +222,7 @@ walking through some boring code, it is best to explain this with an example
 (although you can read through [the implementation](ThreadedBinaryTree.swift)
 if you want to know the finer details).  Please note that this requires
 knowledge of binary search trees, so make sure you have
-[read this first](../Binary Search Tree/).
+[read this first](../Binary%20Search%20Tree/).
 
 > Note: we do allow duplicate nodes in this implementation of a threaded binary
 > tree.  We break ties by defaulting insertion to the right.
@@ -339,7 +339,7 @@ such as `searching()` for a node in the tree, finding the `depth()` or
 `height()` of a node, etc.  You can check
 [the implementation](ThreadedBinaryTree.swift) for the full technical details.
 Many of these methods are inherent to binary search trees as well, so you can
-find [further documentation here](../Binary Search Tree/).
+find [further documentation here](../Binary%20Search%20Tree/).
 
 
 ## See also
diff --git a/Topological Sort/README.markdown b/Topological Sort/README.markdown
index 4429a0754..5659dc3fd 100644
--- a/Topological Sort/README.markdown	
+++ b/Topological Sort/README.markdown	
@@ -22,7 +22,7 @@ The following is not a valid topological sort for this graph, since **X** and **
 
 Let's consider that you want to learn all the algorithms and data structures from the Swift Algorithm Club. This might seem daunting at first but we can use topological sort to get things organized.
 
-Since you're learning about topological sort, let's take this topic as an example. What else do you need to learn first before you can fully understand topological sort? Well, topological sort uses [depth-first search](../Depth-First Search/) as well as a [stack](../Stack/). But before you can learn about the depth-first search algorithm, you need to know what a [graph](../Graph/) is, and it helps to know what a [tree](../Tree/) is. In turn, graphs and trees use the idea of linking objects together, so you may need to read up on that first. And so on...
+Since you're learning about topological sort, let's take this topic as an example. What else do you need to learn first before you can fully understand topological sort? Well, topological sort uses [depth-first search](../Depth-First%20Search/) as well as a [stack](../Stack/). But before you can learn about the depth-first search algorithm, you need to know what a [graph](../Graph/) is, and it helps to know what a [tree](../Tree/) is. In turn, graphs and trees use the idea of linking objects together, so you may need to read up on that first. And so on...
 
 If we were to represent these objectives in the form of a graph it would look as follows:
 
diff --git a/Tree/README.markdown b/Tree/README.markdown
index 529a68cf1..440d9c9a4 100644
--- a/Tree/README.markdown
+++ b/Tree/README.markdown
@@ -16,7 +16,7 @@ The pointers in a tree do not form cycles. This is not a tree:
 
 ![Not a tree](Images/Cycles.png)
 
-Such a structure is called a [graph](../Graph/). A tree is really a very simple form of a graph. (In a similar vein, a [linked list](../Linked List/) is a simple version of a tree. Think about it!)
+Such a structure is called a [graph](../Graph/). A tree is really a very simple form of a graph. (In a similar vein, a [linked list](../Linked%20List/) is a simple version of a tree. Think about it!)
 
 This article talks about a general-purpose tree. That's a tree without any kind of restrictions on how many children each node may have, or on the order of the nodes in the tree.
 
@@ -119,7 +119,7 @@ We often use the following definitions when talking about trees:
 
 - **Depth of a node.** The number of links between this node and the root node. For example, the depth of `tea` is 2 because it takes two jumps to reach the root. (The root itself has depth 0.)
 
-There are many different ways to construct trees. For example, sometimes you don't need to have a `parent` property at all. Or maybe you only need to give each node a maximum of two children -- such a tree is called a [binary tree](../Binary Tree/). A very common type of tree is the [binary search tree](../Binary Search Tree/) (or BST), a stricter version of a binary tree where the nodes are ordered in a particular way to speed up searches.
+There are many different ways to construct trees. For example, sometimes you don't need to have a `parent` property at all. Or maybe you only need to give each node a maximum of two children -- such a tree is called a [binary tree](../Binary%20Tree/). A very common type of tree is the [binary search tree](../Binary%20Search%20Tree/) (or BST), a stricter version of a binary tree where the nodes are ordered in a particular way to speed up searches.
 
 The general purpose tree I've shown here is great for describing hierarchical data, but it really depends on your application what kind of extra functionality it needs to have.
 
diff --git a/Under Construction.markdown b/Under Construction.markdown
index 0c59d90c1..be53e01b0 100644
--- a/Under Construction.markdown	
+++ b/Under Construction.markdown	
@@ -5,27 +5,27 @@ Here you'll find algorithms that are currently under construction. Suggestions a
 ### Sorting
 
 Special-purpose sorts:
- - [Radix Sort](Radix Sort/)
+ - [Radix Sort](Radix%20Sort/)
 
 ### Special-purpose sorts:
 
-- [Bucket Sort](Bucket Sort/)
+- [Bucket Sort](Bucket%20Sort/)
 
 ### Queues
 
-- [Bounded Priority Queue](Bounded Priority Queue). A queue that is bounded to have a limited number of elements.
+- [Bounded Priority Queue](Bounded%20Priority%20Queue). A queue that is bounded to have a limited number of elements.
 
 ### Trees
 
-- [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations.
-- [Red-Black Tree](Red-Black Tree/)
-- [Threaded Binary Tree](Threaded Binary Tree/)
-- [Ternary Search Tree](Ternary Search Tree/)
+- [AVL Tree](AVL%20Tree/). A binary search tree that balances itself using rotations.
+- [Red-Black Tree](Red-Black%20Tree/)
+- [Threaded Binary Tree](Threaded%20Binary%20Tree/)
+- [Ternary Search Tree](Ternary%20Search%20Tree/)
 - [Trie](Trie/)
-- [Radix Tree](Radix Tree/)
+- [Radix Tree](Radix%20Tree/)
 
 ### Miscellaneous
 
-- [Minimum Edit Distance](Minimum Edit Distance/). Measure the similarity of two strings by counting the number of operations required to transform one string into the other.
+- [Minimum Edit Distance](Minimum%20Edit%20Distance/). Measure the similarity of two strings by counting the number of operations required to transform one string into the other.
 - [Treap](Treap/)
-- [Set Cover (Unweighted)](Set Cover (Unweighted)/)
+- [Set Cover (Unweighted)](Set%20Cover%20(Unweighted)/)

From bd35ff8f1bb984bf5cf5eeb8375539dfcdd248ad Mon Sep 17 00:00:00 2001
From: Hunter Maximillion Monk <hunter.monk@gmail.com>
Date: Sat, 25 Mar 2017 21:57:12 -0500
Subject: [PATCH 052/862] Fix binary search tree link

Just need to convert spaces into %20 for relative URLs
with spaces to work.
---
 Binary Tree/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Binary Tree/README.markdown b/Binary Tree/README.markdown
index 896116dda..8ce398804 100644
--- a/Binary Tree/README.markdown	
+++ b/Binary Tree/README.markdown	
@@ -8,7 +8,7 @@ The child nodes are usually called the *left* child and the *right* child. If a
 
 Often nodes will have a link back to their parent but this is not strictly necessary.
 
-Binary trees are often used as [binary search trees](../Binary Search Tree/). In that case, the nodes must be in a specific order (smaller values on the left, larger values on the right). But this is not a requirement for all binary trees.
+Binary trees are often used as [binary search trees](../Binary%20Search%20Tree/). In that case, the nodes must be in a specific order (smaller values on the left, larger values on the right). But this is not a requirement for all binary trees.
 
 For example, here is a binary tree that represents a sequence of arithmetical operations, `(5 * (a - 10)) + (-4 * (3 / b))`:
 

From eb68b1d69836d3d2d1bb1cba269466a94f837aea Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Sun, 26 Mar 2017 15:38:26 -0700
Subject: [PATCH 053/862] updated readme

---
 .../README.markdown                           | 459 +++++++++++++++++-
 .../Contents.swift                            |   2 +
 .../Sources/Matrix.swift                      | 180 ++++---
 .../Sources/MatrixSize.swift                  |  19 +-
 .../Sources/Number.swift                      |  12 +-
 5 files changed, 571 insertions(+), 101 deletions(-)

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
index d07004bad..e4222b4f4 100644
--- a/Strassen Matrix Multiplication/README.markdown	
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -1 +1,458 @@
-## TODO: Examples & Explanation
+# Strassen Matrix Multiplication
+
+## Goal
++ To quickly perform a matrix multiplication operation on two matricies
+
+## What is Matrix Multiplication??
+
+> Note: If you are already familiar with Linear Algebra/Matrix Multiplication, feel free to skip this section
+
+Before we begin, you may ask what is matrix multiplication? Great question! It is **NOT** multiplying two matricies term-by-term. Matrix multiplication is a mathematical operation that combines two matricies into a single one. Sounds like multiplying term-by-term huh? It's not... our lives would be much easier if it were. To see how matrix multiplcation works, let's look at an example.
+
+### Example: Matrix Multiplication
+
+	matrix A = |1 2|
+	           |3 4|
+				 
+	matrix B = |5 6|
+	           |7 8|
+	
+	A * B = C
+	
+	|1 2| * |5 6| = |1*5+2*7 1*6+2*8| = |19 22|
+	|3 4|   |7 8|   |3*5+4*7 3*6+4*8|   |43 48|
+	
+What's going on here? To start, we're multiplying matricies A & B. Our new matrix, C's, elements `[i, j]` are determined by the dot product of the first matrix's ith row and the second matrix's jth column. See [here](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/vector-dot-product-and-vector-length) for a refresher on the dot product.
+
+So the upper left element `[i=1, j=1]` of our new matrix is a combination of A's 1st row and B's 1st column.
+
+	A's first row = [1, 2]
+	B's first column = [5, 7]
+
+	[1, 2] dot [5, 7] = [1*5 + 2*7] = [19] = C[1, 1]
+
+Now let's try this for `[i=1, j=2]`. Because `i=1` and `j=2`, this will represent the upper right element in our new matrix, C.
+
+	A's first row = [1, 2]
+	B's second column = [6, 8]
+	
+	[1, 2] dot [6, 8] = [1*6 + 2*8] = [22] = C[1, 2]
+
+If we do this for each row & column of A & B we'll get our result matrix C!
+
+Here's a great graphic that visually shows you what's going on.
+
+![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Matrix_multiplication_principle.svg/1024px-Matrix_multiplication_principle.svg.png)
+
+[Source](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Matrix_multiplication_principle.svg/1024px-Matrix_multiplication_principle.svg.png)
+
+
+## Matix Multiplication Algorithm
+
+So how do we implement matrix multiplication in an algoirthm? We'll start with the basic version and from there move on to Strassen's Algorithm.
+
++ [Basic Version](#basic-version)
++ [Strassen's Algorithm](#strassens-algorithm)
+
+### Basic Version
+
+Remember the method we used to solve matrix multiplication [above](#what-is-matrix-multiplication??)? Let's try to implement that first! We first assert that the two matricies are the right size. 
+
+`assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")`
+
+> **NOTE:** A's # of columns HAS to equal B's # of rows for matrix multiplication to work
+
+Next, we loop over A's columns and B's rows. Because we know both A's columns & B's rows are the same length, we set that length equal to `n`.
+
+```swift
+for i in 0..<n {
+	for j in 0..<n {
+```
+
+Then, for each row in A and column in B, we take the dot product of the ith row in A with the jth column in B and set that result equal to the `[i, j]` element in C. Or `C[i, j]`.
+
+```swift
+for k in 0..<n {
+	C[i, j] = A[i, k] * B[k, j]
+}
+```
+
+Finally, we return our new matrix C!
+
+Here's the full implementation:
+
+```swift
+public func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+	let A = self
+	assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+	let n = A.columns
+	var C = Matrix<T>(rows: A.rows, columns: B.columns)
+    
+	for i in 0..<n {
+		for j in 0..<n {
+			for k in 0..<n {
+				C[i, j] = A[i, k] * B[k, j]
+			}
+		}
+	}
+    
+	return C
+}
+```
+
+This algorithm has a runtime of **O(n^3)**. The **O(n^3)** comes from the three `for` loops. Two from the loop over the rows & columns and one from the dot product!
+
+Now, **O(n^3)** is not very fast and a great question we should ask is can we do better? Indeed we can!
+
+### Strassens Algorithm
+
+Volker Strassen first published his algorithm in 1969. It was the first algorithm to prove that the basic **O(n^3)** runtime was not optiomal. 
+
+The basic idea behind Strassen's algorithm is to split A & B into 8 submatricies and then recursively compute the submatricies of C. This strategy is called *Divide and Conquer*.
+
+	matrix A = |a b|
+	  		   |c d|
+	matrix B = |e f|
+			   |g h|
+
+*There will be 8 recursive calls:*
+
+1. a * e
+2. b * g
+3. a * f 
+4. b * h
+5. c * e
+6. d * g 
+7. c * f 
+8. d * h
+
+We then use these results to compute C's submatricies.
+
+	matrix C = |ae+bg af+bh|
+			   |ce+dg cf+dh| 
+
+![http://d1hyf4ir1gqw6c.cloudfront.net//wp-content/uploads/strassen_new.png](http://d1hyf4ir1gqw6c.cloudfront.net//wp-content/uploads/strassen_new.png)
+
+This step alone, however, doesn't help our runtime at all. Using the [Master Theorem](https://en.wikipedia.org/wiki/Master_theorem) with `T(n) = 8T(n/2) + O(n^2)` we still get a runtime of `O(n^3)`.
+
+Strassen's insight was that we don't actually need **8** recursive calls to complete this process. We can finish the call with **7** recursive calls and a little bit of addition and subtraction.
+
+Strassen's **7** calls are as follows:
+
+1. a * (f - h)
+2. (a + b) * h
+3. (c + d) * e
+4. d * (g - e)
+5. (a + d) * (e + h)
+6. (b - d) * (g + h)
+7. (a - c) * (e + f)
+
+Now we can compute our new matrix C's new quardents!
+
+	matrix C = |p5+p4-p2+p6    p1+p2   |
+			   |   p3+p4    p1+p5-p3-p7|    
+
+
+A great reaction right now would be !!??!?!?!!?! How does this even work??
+
+Let's prove it!
+
+**First** Submatrix:
+
+	p5+p4-p2+p6 = (a+d)*(e+h) + d*(g-e) - (a+b)*h + (b-d)*(g+h)
+				= (ae+de+ah+dh) + (dg-de) - (ah+bh) + (bg-dg+bh-dh)
+				= ae+bg ✅
+				
+Exactly what we got the first time!
+
+Now let's prove the others.
+
+**Second** submatrix:
+
+	p1+p2 = a*(f-h) + (a+b)*h
+		  = (af-ah) + (ah+bh)
+		  = af+bh ✅
+		  
+**Third** submatrix:
+
+	p3+p4 = (c+d)*e + d*(g-e)
+		  = (ce+de) + (dg-de)
+		  = ce+dg ✅
+
+**Fourth** submatrix: 
+
+	p1+p5-p3-p7 = a*(f-h) + (a+d)*(e+h) - (c+d)*e - (a-c)*(e+f)
+				= (af-ah) + (ae+de+ah+dh) -(ce+de) - (ae-ce+af-cf)
+				= cf+dh ✅
+
+Great! The math checks out!
+
+Here's the process in action.
+
+![](http://d1hyf4ir1gqw6c.cloudfront.net//wp-content/uploads/stressen_formula_new_new.png)
+
+[Source](http://www.geeksforgeeks.org/strassens-matrix-multiplication/)
+
+#### Implementation
+
+Ok so now to the implementation. We'll start with the same first step from the basic implementation. We need to assert that A's # of columns are equal to B's number of rows.
+
+	assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+	
+Now time for some prep work! We make each matrix a square and increase it's size to the next power of two. This ensures makes Strassen's Algorithm much easier to manage. We now only need to deal with square matricies that can be broken up an even number of times!
+
+```swift
+let n = max(A.rows, A.columns, B.rows, B.columns)
+let m = nextPowerOfTwo(after: n)
+    
+var APrep = Matrix(size: m)
+var BPrep = Matrix(size: m)
+   
+for i in A.rows {
+	for j in A.columns {
+		APrep[i, j] = A[i,j]
+	}
+}
+
+for i in B.rows {
+	for j in B.columns {
+		BPrep[i, j] = B[i, j]
+	}
+}
+```
+
+Finally, we recusrisvely compute the matrix using Strassen's algorithm and the transform our new matrix `C` back to the correct dimensions!
+
+```swift
+let CPrep = APrep.strassenR(by: BPrep)
+var C = Matrix(rows: A.rows, columns: B.columns)
+    
+for i in 0..<A.rows {
+	for j in 0..<B.columns {
+		C[i,j] = CPrep[i,j]
+	}
+}
+```
+
+#### Recursively Computing the Matrix Multiplication
+
+Next let's explore this recursive function `strassenR`.
+
+We start by initializing 8 submatricies.
+
+```swift
+var a = Matrix(size: nBy2)
+var b = Matrix(size: nBy2)
+var c = Matrix(size: nBy2)
+var d = Matrix(size: nBy2)
+var e = Matrix(size: nBy2)
+var f = Matrix(size: nBy2)
+var g = Matrix(size: nBy2)
+var h = Matrix(size: nBy2)
+    
+for i in 0..<nBy2 {
+	for j in 0..<nBy2 {
+		a[i,j] = A[i,j]
+       b[i,j] = A[i, j+nBy2]
+       c[i,j] = A[i+nBy2, j]
+       d[i,j] = A[i+nBy2, j+nBy2]
+       e[i,j] = B[i,j]
+       f[i,j] = B[i, j+nBy2]
+       g[i,j] = B[i+nBy2, j]
+       h[i,j] = B[i+nBy2, j+nBy2]
+	}
+}
+```
+
+We next recursively compute the 7 matrix multiplications.
+
+```swift
+let p1 = a.strassenR(by: f-h)       // a * (f - h)
+let p2 = (a+b).strassenR(by: h)     // (a + b) * h
+let p3 = (c+d).strassenR(by: e)     // (c + d) * e
+let p4 = d.strassenR(by: g-e)       // d * (g - e)
+let p5 = (a+d).strassenR(by: e+h)   // (a + d) * (e + h)
+let p6 = (b-d).strassenR(by: g+h)   // (b - d) * (g + h)
+let p7 = (a-c).strassenR(by: e+f)   // (a - c) * (e + f)
+```
+
+Next, we compute the submatricies of C.
+
+```swift
+let c11 = p5 + p4 - p2 + p6         // p5 + p4 - p2 + p6
+let c12 = p1 + p2                   // p1 + p2
+let c21 = p3 + p4                   // p3 + p4
+let c22 = p1 + p5 - p3 - p7         // p1 + p5 - p3 - p7
+```
+
+And finally, we combine these submatricies into our new matrix C!
+
+```swift
+var C = Matrix(size: n)    
+for i in 0..<nBy2 {
+	for j in 0..<nBy2 {
+		C[i, j]           = c11[i,j]
+		C[i, j+nBy2]      = c12[i,j]
+		C[i+nBy2, j]      = c21[i,j]
+		C[i+nBy2, j+nBy2] = c22[i,j]
+	}
+}
+```
+
+As before, we can analyze the time completxity using the [Master Theorem](https://en.wikipedia.org/wiki/Master_theorem). `T(n) = 7T(n/2) +  O(n^2)` which leads to `O(n^log(7))` runtime. This comes out to approxiamtely `O(n^2.8074)` which is better than `O(n^3)`!
+
+And that's Strassen's algorithm! Here's the full implementation:
+
+```swift
+// MARK: - Strassen Multiplication
+
+extension Matrix {
+  public func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    let n = max(A.rows, A.columns, B.rows, B.columns)
+    let m = nextPowerOfTwo(after: n)
+    
+    var APrep = Matrix(size: m)
+    var BPrep = Matrix(size: m)
+    
+    A.forEach { (i, j) in
+      APrep[i,j] = A[i,j]
+    }
+    
+    B.forEach { (i, j) in
+      BPrep[i,j] = B[i,j]
+    }
+    
+    let CPrep = APrep.strassenR(by: BPrep)
+    var C = Matrix(rows: A.rows, columns: B.columns)
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i,j] = CPrep[i,j]
+      }
+    }
+    
+    return C
+  }
+  
+  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.isSquare && B.isSquare, "This function requires square matricies!")
+    guard A.rows > 1 && B.rows > 1 else { return A * B }
+    
+    let n    = A.rows
+    let nBy2 = n / 2
+    
+    /*
+    Assume submatricies are allocated as follows
+    
+     matrix A = |a b|,    matrix B = |e f|
+                |c d|                |g h|
+    */
+    
+    var a = Matrix(size: nBy2)
+    var b = Matrix(size: nBy2)
+    var c = Matrix(size: nBy2)
+    var d = Matrix(size: nBy2)
+    var e = Matrix(size: nBy2)
+    var f = Matrix(size: nBy2)
+    var g = Matrix(size: nBy2)
+    var h = Matrix(size: nBy2)
+    
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        a[i,j] = A[i,j]
+        b[i,j] = A[i, j+nBy2]
+        c[i,j] = A[i+nBy2, j]
+        d[i,j] = A[i+nBy2, j+nBy2]
+        e[i,j] = B[i,j]
+        f[i,j] = B[i, j+nBy2]
+        g[i,j] = B[i+nBy2, j]
+        h[i,j] = B[i+nBy2, j+nBy2]
+      }
+    }
+    
+    let p1 = a.strassenR(by: f-h)       // a * (f - h)
+    let p2 = (a+b).strassenR(by: h)     // (a + b) * h
+    let p3 = (c+d).strassenR(by: e)     // (c + d) * e
+    let p4 = d.strassenR(by: g-e)       // d * (g - e)
+    let p5 = (a+d).strassenR(by: e+h)   // (a + d) * (e + h)
+    let p6 = (b-d).strassenR(by: g+h)   // (b - d) * (g + h)
+    let p7 = (a-c).strassenR(by: e+f)   // (a - c) * (e + f)
+    
+    let c11 = p5 + p4 - p2 + p6         // p5 + p4 - p2 + p6
+    let c12 = p1 + p2                   // p1 + p2
+    let c21 = p3 + p4                   // p3 + p4
+    let c22 = p1 + p5 - p3 - p7         // p1 + p5 - p3 - p7
+    
+    var C = Matrix(size: n)
+    for i in 0..<nBy2 {
+      for j in 0..<nBy2 {
+        C[i, j]           = c11[i,j]
+        C[i, j+nBy2]      = c12[i,j]
+        C[i+nBy2, j]      = c21[i,j]
+        C[i+nBy2, j+nBy2] = c22[i,j]
+      }
+    }
+    
+    return C
+  }
+  
+  private func nextPowerOfTwo(after n: Int) -> Int {
+    return Int(pow(2, ceil(log2(Double(n)))))
+  }
+}
+```
+
+
+## Appendix
+
+### Number Protocol
+
+I use a number protocol to enable by Matrix to be generic. 
+
+The Number protocol ensures three things:
+
+1. Everything that is a number can be multiplied
+2. Everything that is a number can be added/subtracted
+3. Everything that is a number has a zero value
+
+Extending `Int`, `Float`, and `Double` to conform to this protocol is now very straightforward. All you need to do is implement the `static var zero`! 
+
+```swift
+public protocol Number: Multipliable, Addable {
+  static var zero: Self { get }
+}
+
+public protocol Addable {
+  static func +(lhs: Self, rhs: Self) -> Self
+  static func -(lhs: Self, rhs: Self) -> Self
+}
+
+public protocol Multipliable {
+  static func *(lhs: Self, rhs: Self) -> Self
+}
+```
+
+### Dot Product
+
+I extend `Array` to include a dot product function for when the Array's element conform to the `Number` protocol.
+
+```swift
+extension Array where Element: Number {
+  public func dot(_ b: Array<Element>) -> Element {
+    let a = self
+    assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
+    let c = a.indices.map{ a[$0] * b[$0] }
+    return c.reduce(Element.zero, { $0 + $1 })
+  }
+}
+```
+
+##Resources
++ [Intro to Matrix Multiplication | Khan Academy](https://www.khanacademy.org/math/precalculus/precalc-matrices/multiplying-matrices-by-matrices/v/matrix-multiplication-intro)
++ [Matrix Multiplication | Wikipedia](https://en.wikipedia.org/wiki/Matrix_multiplication)
++ [Strassen Algorithm | Wikipedia](https://en.wikipedia.org/wiki/Strassen_algorithm)
++ [Strassen Algorithm | Wolfram MathWorld](http://mathworld.wolfram.com/StrassenFormulas.html)
++ [Strassens Algorithm | Geeks for Geeks](http://www.geeksforgeeks.org/strassens-matrix-multiplication/)
\ No newline at end of file
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index 50af60a6f..5d82244a3 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -8,9 +8,11 @@ A[.row, 0] = [2, 3, -1, 0]
 A[.row, 1] = [-7, 2, 1, 10]
 
 var B = Matrix(rows: 4, columns: 2, initialValue: 0)
+print(B)
 B[.column, 0] = [3, 2, -1, 2]
 B[.column, 1] = [4, 1, 2, 7]
 
+
 let C = A.matrixMultiply(by: B)
 let D = A.strassenMatrixMultiply(by: B)
 let E = B.matrixMultiply(by: A)
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index eba49ce9a..77ced4632 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -40,23 +40,26 @@ public struct Matrix<T: Number> {
     self.columns = size
     self.grid = Array(repeating: initialValue, count: rows * columns)
   }
-}
-
-// MARK: - Public Functions
-
-public extension Matrix {
-  subscript(row: Int, column: Int) -> T {
+  
+  // MARK: - Private Functions
+  
+  fileprivate func indexIsValid(row: Int, column: Int) -> Bool {
+    return row >= 0 && row < rows && column >= 0 && column < columns
+  }
+  
+  // MARK: - Subscript
+  
+  public subscript(row: Int, column: Int) -> T {
     get {
       assert(indexIsValid(row: row, column: column), "Index out of range")
       return grid[(row * columns) + column]
-    }
-    set {
+    } set {
       assert(indexIsValid(row: row, column: column), "Index out of range")
       grid[(row * columns) + column] = newValue
     }
   }
   
-  subscript(type: RowOrColumn, value: Int) -> [T] {
+  public subscript(type: RowOrColumn, value: Int) -> [T] {
     get {
       switch type {
       case .row:
@@ -64,15 +67,11 @@ public extension Matrix {
         return Array(grid[(value * columns)..<(value * columns) + columns])
       case .column:
         assert(indexIsValid(row: 0, column: value), "Index out of range")
-        var columns: [T] = []
-        for row in 0..<rows {
-          for column in 0..<self.columns {
-            if column == value {
-              columns.append(grid[(row * self.columns) + value])
-            }
-          }
+        let column = (0..<rows).map { (currentRow) -> T in
+          let currentColumnIndex = currentRow * columns + value
+          return grid[currentColumnIndex]
         }
-        return columns
+        return column
       }
     } set {
       switch type {
@@ -90,59 +89,84 @@ public extension Matrix {
     }
   }
   
-  func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+  // MARK: - Public Functions
+  
+  public func row(for columnIndex: Int) -> [T] {
+    assert(indexIsValid(row: columnIndex, column: 0), "Index out of range")
+    return Array(grid[(columnIndex * columns)..<(columnIndex * columns) + columns])
+  }
+  
+  public func column(for rowIndex: Int) -> [T] {
+    assert(indexIsValid(row: 0, column: rowIndex), "Index out of range")
+    
+    let column = (0..<rows).map { (currentRow) -> T in
+      let currentColumnIndex = currentRow * columns + rowIndex
+      return grid[currentColumnIndex]
+    }
+    return column
+  }
+  
+  public func forEach(_ body: (Int, Int) throws -> Void) rethrows {
+    for row in 0..<rows {
+      for column in 0..<columns {
+        try body(row, column)
+      }
+    }
+  }
+}
+
+// MARK: - Matrix Multiplication Function
+
+extension Matrix {
+  public func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
+    let A = self
+    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+    
+    var C = Matrix<T>(rows: A.rows, columns: B.columns)
+    
+    for i in 0..<A.rows {
+      for j in 0..<B.columns {
+        C[i, j] = A[.row, i].dot(B[.column, j])
+      }
+    }
+    
+    return C
+  }
+}
+
+// MARK: - Strassen Multiplication
+
+extension Matrix {
+  public func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
     
     let n = max(A.rows, A.columns, B.rows, B.columns)
-    let m = nextPowerOfTwo(of: n)
+    let m = nextPowerOfTwo(after: n)
     
     var APrep = Matrix(size: m)
     var BPrep = Matrix(size: m)
     
-    A.size.forEach { (i, j) in
+    A.forEach { (i, j) in
       APrep[i,j] = A[i,j]
     }
     
-    B.size.forEach { (i, j) in
+    B.forEach { (i, j) in
       BPrep[i,j] = B[i,j]
     }
     
     let CPrep = APrep.strassenR(by: BPrep)
     var C = Matrix(rows: A.rows, columns: B.columns)
-    
     for i in 0..<A.rows {
       for j in 0..<B.columns {
         C[i,j] = CPrep[i,j]
       }
     }
-    return C
-  }
-  
-  func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-    let A = self
-    assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
-    var C = Matrix<T>(rows: A.rows, columns: B.columns)
-    
-    for i in 0..<A.rows {
-      for j in 0..<B.columns {
-        C[i, j] = A[.row, i].dot(B[.column, j])
-      }
-    }
     
     return C
   }
-}
-
-// MARK: - Private Functions
-
-fileprivate extension Matrix {
-  func indexIsValid(row: Int, column: Int) -> Bool {
-    return row >= 0 && row < rows && column >= 0 && column < columns
-  }
   
-  func strassenR(by B: Matrix<T>) -> Matrix<T> {
+  private func strassenR(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.isSquare && B.isSquare, "This function requires square matricies!")
     guard A.rows > 1 && B.rows > 1 else { return A * B }
@@ -150,42 +174,49 @@ fileprivate extension Matrix {
     let n    = A.rows
     let nBy2 = n / 2
     
-    var a11 = Matrix(size: nBy2)
-    var a12 = Matrix(size: nBy2)
-    var a21 = Matrix(size: nBy2)
-    var a22 = Matrix(size: nBy2)
-    var b11 = Matrix(size: nBy2)
-    var b12 = Matrix(size: nBy2)
-    var b21 = Matrix(size: nBy2)
-    var b22 = Matrix(size: nBy2)
+    /*
+    Assume submatricies are allocated as follows
+    
+     matrix A = |a b|,    matrix B = |e f|
+                |c d|                |g h|
+    */
+    
+    var a = Matrix(size: nBy2)
+    var b = Matrix(size: nBy2)
+    var c = Matrix(size: nBy2)
+    var d = Matrix(size: nBy2)
+    var e = Matrix(size: nBy2)
+    var f = Matrix(size: nBy2)
+    var g = Matrix(size: nBy2)
+    var h = Matrix(size: nBy2)
     
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
-        a11[i,j] = A[i,j]
-        a12[i,j] = A[i, j+nBy2]
-        a21[i,j] = A[i+nBy2, j]
-        a22[i,j] = A[i+nBy2, j+nBy2]
-        b11[i,j] = B[i,j]
-        b12[i,j] = B[i, j+nBy2]
-        b21[i,j] = B[i+nBy2, j]
-        b22[i,j] = B[i+nBy2, j+nBy2]
+        a[i,j] = A[i,j]
+        b[i,j] = A[i, j+nBy2]
+        c[i,j] = A[i+nBy2, j]
+        d[i,j] = A[i+nBy2, j+nBy2]
+        e[i,j] = B[i,j]
+        f[i,j] = B[i, j+nBy2]
+        g[i,j] = B[i+nBy2, j]
+        h[i,j] = B[i+nBy2, j+nBy2]
       }
     }
     
-    let q1 = (a11+a22).strassenR(by: b11+b22)    // (a11+a22)(b11+b22)
-    let q2 = (a21+a22).strassenR(by: b11)        // (a21+a22)b11
-    let q3 = a11.strassenR(by: b12-b22)          // a11(b12-b22)
-    let q4 = a22.strassenR(by: b21-b11)          // a22(-b11+b21)
-    let q5 = (a11+a12).strassenR(by: b22)        // (a11+a22)b22
-    let q6 = (a21-a11).strassenR(by: b11+b12)    // (-a11+a21)(b11+b12)
-    let q7 = (a12-a22).strassenR(by: b21+b22)    // (a12-a22)(b21+b22)
+    let p1 = a.strassenR(by: f-h)       // a * (f - h)
+    let p2 = (a+b).strassenR(by: h)     // (a + b) * h
+    let p3 = (c+d).strassenR(by: e)     // (c + d) * e
+    let p4 = d.strassenR(by: g-e)       // d * (g - e)
+    let p5 = (a+d).strassenR(by: e+h)   // (a + d) * (e + h)
+    let p6 = (b-d).strassenR(by: g+h)   // (b - d) * (g + h)
+    let p7 = (a-c).strassenR(by: e+f)   // (a - c) * (e + f)
     
-    let c11 = q1 + q4 - q5 + q7
-    let c12 = q3 + q5
-    let c21 = q2 + q4
-    let c22 = q1 + q3 - q2 + q6
-    var C   = Matrix(size: n)
+    let c11 = p5 + p4 - p2 + p6         // p5 + p4 - p2 + p6
+    let c12 = p1 + p2                   // p1 + p2
+    let c21 = p3 + p4                   // p3 + p4
+    let c22 = p1 + p5 - p3 - p7         // p1 + p5 - p3 - p7
     
+    var C = Matrix(size: n)
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
         C[i, j]           = c11[i,j]
@@ -198,12 +229,11 @@ fileprivate extension Matrix {
     return C
   }
   
-  func nextPowerOfTwo(of n: Int) -> Int {
+  private func nextPowerOfTwo(after n: Int) -> Int {
     return Int(pow(2, ceil(log2(Double(n)))))
   }
 }
 
-
 // Term-by-term Matrix Math
 
 extension Matrix: Addable {
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift
index f4a604ade..e0d957607 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift	
@@ -8,26 +8,13 @@
 
 import Foundation
 
-public struct MatrixSize: Equatable {
+public struct MatrixSize {
   let rows: Int
   let columns: Int
-  
-  public init(rows: Int, columns: Int) {
-    self.rows = rows
-    self.columns = columns
-  }
-  
-  public func forEach(_ body: (Int, Int) throws -> Void) rethrows {
-    for row in 0..<rows {
-      for column in 0..<columns {
-        try? body(row, column)
-      }
-    }
-  }
 }
 
-public extension MatrixSize {
-  static func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
+extension MatrixSize: Equatable {
+  public static func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
     return lhs.columns == rhs.columns && lhs.rows == rhs.rows
   }
 }
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift
index 9f4c7f4ab..7da1eee60 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
@@ -22,21 +22,15 @@ public protocol Multipliable {
 }
 
 extension Int: Number {
-  public static var zero: Int {
-    return 0
-  }
+  public static var zero: Int { return 0 }
 }
 
 extension Double: Number {
-  public static var zero: Double {
-    return 0.0
-  }
+  public static var zero: Double { return 0.0 }
 }
 
 extension Float: Number {
-  public static var zero: Float {
-    return 0.0
-  }
+  public static var zero: Float { return 0.0 }
 }
 
 extension Array where Element: Number {

From c94fbab56dcd0b3f483ec8a1fec718de7ef97ba2 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Sun, 26 Mar 2017 15:53:58 -0700
Subject: [PATCH 054/862] added authorship to readme

---
 Strassen Matrix Multiplication/README.markdown | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
index e4222b4f4..6949f906c 100644
--- a/Strassen Matrix Multiplication/README.markdown	
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -405,7 +405,6 @@ extension Matrix {
 }
 ```
 
-
 ## Appendix
 
 ### Number Protocol
@@ -455,4 +454,6 @@ extension Array where Element: Number {
 + [Matrix Multiplication | Wikipedia](https://en.wikipedia.org/wiki/Matrix_multiplication)
 + [Strassen Algorithm | Wikipedia](https://en.wikipedia.org/wiki/Strassen_algorithm)
 + [Strassen Algorithm | Wolfram MathWorld](http://mathworld.wolfram.com/StrassenFormulas.html)
-+ [Strassens Algorithm | Geeks for Geeks](http://www.geeksforgeeks.org/strassens-matrix-multiplication/)
\ No newline at end of file
++ [Strassens Algorithm | Geeks for Geeks](http://www.geeksforgeeks.org/strassens-matrix-multiplication/)
+
+*Written for Swift Algorithm Club by Richard Ash*
\ No newline at end of file

From 09848a79e92c266b3e33006781732c1e288d7f6f Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Sun, 26 Mar 2017 15:55:13 -0700
Subject: [PATCH 055/862] fixed the display of the resources header

---
 Strassen Matrix Multiplication/README.markdown | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
index 6949f906c..713ab1801 100644
--- a/Strassen Matrix Multiplication/README.markdown	
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -449,7 +449,8 @@ extension Array where Element: Number {
 }
 ```
 
-##Resources
+## Resources
+
 + [Intro to Matrix Multiplication | Khan Academy](https://www.khanacademy.org/math/precalculus/precalc-matrices/multiplying-matrices-by-matrices/v/matrix-multiplication-intro)
 + [Matrix Multiplication | Wikipedia](https://en.wikipedia.org/wiki/Matrix_multiplication)
 + [Strassen Algorithm | Wikipedia](https://en.wikipedia.org/wiki/Strassen_algorithm)

From ab37359616c210f84363b885ef0308b17cadc202 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Sun, 26 Mar 2017 16:05:27 -0700
Subject: [PATCH 056/862] fixed layout of code in readme

---
 .../README.markdown                           | 142 +++++++++---------
 1 file changed, 75 insertions(+), 67 deletions(-)

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
index 713ab1801..fa822d310 100644
--- a/Strassen Matrix Multiplication/README.markdown	
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -11,17 +11,16 @@ Before we begin, you may ask what is matrix multiplication? Great question! It i
 
 ### Example: Matrix Multiplication
 
-	matrix A = |1 2|
-	           |3 4|
-				 
-	matrix B = |5 6|
-	           |7 8|
-	
-	A * B = C
+```
+matrix A = |1 2|, matrix B = |5 6|
+           |3 4|             |7 8|
 	
-	|1 2| * |5 6| = |1*5+2*7 1*6+2*8| = |19 22|
-	|3 4|   |7 8|   |3*5+4*7 3*6+4*8|   |43 48|
+A * B = C
 	
+|1 2| * |5 6| = |1*5+2*7 1*6+2*8| = |19 22|
+|3 4|   |7 8|   |3*5+4*7 3*6+4*8|   |43 48|
+```
+
 What's going on here? To start, we're multiplying matricies A & B. Our new matrix, C's, elements `[i, j]` are determined by the dot product of the first matrix's ith row and the second matrix's jth column. See [here](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/vector-dot-product-and-vector-length) for a refresher on the dot product.
 
 So the upper left element `[i=1, j=1]` of our new matrix is a combination of A's 1st row and B's 1st column.
@@ -66,14 +65,14 @@ Next, we loop over A's columns and B's rows. Because we know both A's columns &
 
 ```swift
 for i in 0..<n {
-	for j in 0..<n {
+  for j in 0..<n {
 ```
 
 Then, for each row in A and column in B, we take the dot product of the ith row in A with the jth column in B and set that result equal to the `[i, j]` element in C. Or `C[i, j]`.
 
 ```swift
 for k in 0..<n {
-	C[i, j] = A[i, k] * B[k, j]
+  C[i, j] = A[i, k] * B[k, j]
 }
 ```
 
@@ -83,20 +82,20 @@ Here's the full implementation:
 
 ```swift
 public func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
-	let A = self
-	assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-	let n = A.columns
-	var C = Matrix<T>(rows: A.rows, columns: B.columns)
+  let A = self
+  assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
+  let n = A.columns
+  var C = Matrix<T>(rows: A.rows, columns: B.columns)
     
-	for i in 0..<n {
-		for j in 0..<n {
-			for k in 0..<n {
-				C[i, j] = A[i, k] * B[k, j]
-			}
-		}
-	}
+  for i in 0..<n {
+    for j in 0..<n {
+      for k in 0..<n {
+        C[i, j] = A[i, k] * B[k, j]
+      }
+    }
+  }
     
-	return C
+  return C
 }
 ```
 
@@ -110,10 +109,10 @@ Volker Strassen first published his algorithm in 1969. It was the first algorith
 
 The basic idea behind Strassen's algorithm is to split A & B into 8 submatricies and then recursively compute the submatricies of C. This strategy is called *Divide and Conquer*.
 
-	matrix A = |a b|
-	  		   |c d|
-	matrix B = |e f|
-			   |g h|
+```
+matrix A = |a b|, matrix B = |e f|
+           |c d|             |g h|
+```
 
 *There will be 8 recursive calls:*
 
@@ -149,9 +148,10 @@ Strassen's **7** calls are as follows:
 
 Now we can compute our new matrix C's new quardents!
 
-	matrix C = |p5+p4-p2+p6    p1+p2   |
-			   |   p3+p4    p1+p5-p3-p7|    
-
+```
+matrix C = |p5+p4-p2+p6    p1+p2   |
+           |   p3+p4    p1+p5-p3-p7|    
+```
 
 A great reaction right now would be !!??!?!?!!?! How does this even work??
 
@@ -159,9 +159,11 @@ Let's prove it!
 
 **First** Submatrix:
 
-	p5+p4-p2+p6 = (a+d)*(e+h) + d*(g-e) - (a+b)*h + (b-d)*(g+h)
-				= (ae+de+ah+dh) + (dg-de) - (ah+bh) + (bg-dg+bh-dh)
-				= ae+bg ✅
+```
+p5+p4-p2+p6 = (a+d)*(e+h) + d*(g-e) - (a+b)*h + (b-d)*(g+h)
+            = (ae+de+ah+dh) + (dg-de) - (ah+bh) + (bg-dg+bh-dh)
+            = ae+bg ✅
+```
 				
 Exactly what we got the first time!
 
@@ -169,21 +171,27 @@ Now let's prove the others.
 
 **Second** submatrix:
 
-	p1+p2 = a*(f-h) + (a+b)*h
-		  = (af-ah) + (ah+bh)
-		  = af+bh ✅
+```
+p1+p2 = a*(f-h) + (a+b)*h
+      = (af-ah) + (ah+bh)
+      = af+bh ✅
+```
 		  
 **Third** submatrix:
 
-	p3+p4 = (c+d)*e + d*(g-e)
-		  = (ce+de) + (dg-de)
-		  = ce+dg ✅
+```
+p3+p4 = (c+d)*e + d*(g-e)
+      = (ce+de) + (dg-de)
+      = ce+dg ✅
+```
 
 **Fourth** submatrix: 
 
-	p1+p5-p3-p7 = a*(f-h) + (a+d)*(e+h) - (c+d)*e - (a-c)*(e+f)
-				= (af-ah) + (ae+de+ah+dh) -(ce+de) - (ae-ce+af-cf)
-				= cf+dh ✅
+```
+p1+p5-p3-p7 = a*(f-h) + (a+d)*(e+h) - (c+d)*e - (a-c)*(e+f)
+            = (af-ah) + (ae+de+ah+dh) -(ce+de) - (ae-ce+af-cf)
+            = cf+dh ✅
+```
 
 Great! The math checks out!
 
@@ -209,15 +217,15 @@ var APrep = Matrix(size: m)
 var BPrep = Matrix(size: m)
    
 for i in A.rows {
-	for j in A.columns {
-		APrep[i, j] = A[i,j]
-	}
+  for j in A.columns {
+    APrep[i, j] = A[i,j]
+  }
 }
 
 for i in B.rows {
-	for j in B.columns {
-		BPrep[i, j] = B[i, j]
-	}
+  for j in B.columns {
+    BPrep[i, j] = B[i, j]
+  }
 }
 ```
 
@@ -228,9 +236,9 @@ let CPrep = APrep.strassenR(by: BPrep)
 var C = Matrix(rows: A.rows, columns: B.columns)
     
 for i in 0..<A.rows {
-	for j in 0..<B.columns {
-		C[i,j] = CPrep[i,j]
-	}
+  for j in 0..<B.columns {
+    C[i,j] = CPrep[i,j]
+  }
 }
 ```
 
@@ -251,16 +259,16 @@ var g = Matrix(size: nBy2)
 var h = Matrix(size: nBy2)
     
 for i in 0..<nBy2 {
-	for j in 0..<nBy2 {
-		a[i,j] = A[i,j]
-       b[i,j] = A[i, j+nBy2]
-       c[i,j] = A[i+nBy2, j]
-       d[i,j] = A[i+nBy2, j+nBy2]
-       e[i,j] = B[i,j]
-       f[i,j] = B[i, j+nBy2]
-       g[i,j] = B[i+nBy2, j]
-       h[i,j] = B[i+nBy2, j+nBy2]
-	}
+  for j in 0..<nBy2 {
+    a[i,j] = A[i,j]
+    b[i,j] = A[i, j+nBy2]
+    c[i,j] = A[i+nBy2, j]
+    d[i,j] = A[i+nBy2, j+nBy2]
+    e[i,j] = B[i,j]
+    f[i,j] = B[i, j+nBy2]
+    g[i,j] = B[i+nBy2, j]
+    h[i,j] = B[i+nBy2, j+nBy2]
+  }
 }
 ```
 
@@ -290,12 +298,12 @@ And finally, we combine these submatricies into our new matrix C!
 ```swift
 var C = Matrix(size: n)    
 for i in 0..<nBy2 {
-	for j in 0..<nBy2 {
-		C[i, j]           = c11[i,j]
-		C[i, j+nBy2]      = c12[i,j]
-		C[i+nBy2, j]      = c21[i,j]
-		C[i+nBy2, j+nBy2] = c22[i,j]
-	}
+  for j in 0..<nBy2 {
+    C[i, j]           = c11[i,j]
+    C[i, j+nBy2]      = c12[i,j]
+    C[i+nBy2, j]      = c21[i,j]
+    C[i+nBy2, j+nBy2] = c22[i,j]
+  }
 }
 ```
 

From ae1da6fc3c88d84ae4620f3c58500816fac10499 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Mon, 27 Mar 2017 16:33:26 +0800
Subject: [PATCH 057/862] Delete SelectionSamplingExample.swift

---
 .../SelectionSamplingExample.swift            | 32 -------------------
 1 file changed, 32 deletions(-)
 delete mode 100644 Selection Sampling/SelectionSamplingExample.swift

diff --git a/Selection Sampling/SelectionSamplingExample.swift b/Selection Sampling/SelectionSamplingExample.swift
deleted file mode 100644
index 66648a934..000000000
--- a/Selection Sampling/SelectionSamplingExample.swift	
+++ /dev/null
@@ -1,32 +0,0 @@
-//
-//  Select.swift
-//  
-//
-//  Created by Cheer on 2017/3/9.
-//
-//
-
-import Foundation
-
-func select<T>(from a: [T], count requested: Int) -> [T] {
-    
-    // if requested > a.count, will throw ==> fatal error: Index out of range
-    
-    if requested < a.count {
-        var arr = a
-        for i in 0..<requested {
-            
-            //arc4random_uniform(n) ==> the range is [0...n-1]
-            //So: arc4random_uniform(UInt32(arr.count - i - 2)) + (i + 1) ==> [0...arr.count - (i + 1) - 1] + (i + 1) ==> the range is [(i + 1)...arr.count - 1]
-            //Why start index is "(i + 1)"?  Because in "swap(&A,&B)", if A's index == B's index, will throw a error: "swapping a location with itself is not supported"
-            
-            let nextIndex = Int(arc4random_uniform(UInt32(arr.count - i - 2))) + (i + 1)
-            swap(&arr[nextIndex], &arr[i])
-        }
-        return Array(arr[0..<requested])
-    }
-    
-    if requested == a.count { return a }
-    
-    return [T]()
-}

From 7dd9de00802ea1ff0d03e3fb09d547c867f83a81 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Tue, 28 Mar 2017 15:54:51 +0800
Subject: [PATCH 058/862] Update ShellSortExample.swift

fix code. And apologize for my carelessness.
---
 Shell Sort/ShellSortExample.swift | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index c41eb8889..0beac00a3 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -14,18 +14,18 @@ public func shellSort(_ list : inout [Int])
     
     while sublistCount > 0
     {
-        for var index in 0..<arr.count{
+        for var index in 0..<list.count{
             
-            guard index + sublistCount < arr.count else { break }
+            guard index + sublistCount < list.count else { break }
             
-            if arr[index] > arr[index + sublistCount]{
-                swap(&arr[index], &arr[index + sublistCount])
+            if list[index] > list[index + sublistCount]{
+                swap(&list[index], &list[index + sublistCount])
             }
             
             guard sublistCount == 1 && index > 0 else { continue }
-
-            while arr[index - 1] > arr[index] && index - 1 > 0  {
-                swap(&arr[index - 1], &arr[index])
+            
+            while list[index - 1] > list[index] && index - 1 > 0  {
+                swap(&list[index - 1], &list[index])
                 index -= 1
             }
         }

From 14fe78745ccceb2de88ed2a3dc05835d99317e90 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Tue, 28 Mar 2017 15:55:45 +0800
Subject: [PATCH 059/862] Update ShellSortExample.swift

---
 Shell Sort/ShellSortExample.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index 0beac00a3..05ab2518b 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -14,11 +14,11 @@ public func shellSort(_ list : inout [Int])
     
     while sublistCount > 0
     {
-        for var index in 0..<list.count{
+        for var index in 0..<list.count {
             
             guard index + sublistCount < list.count else { break }
             
-            if list[index] > list[index + sublistCount]{
+            if list[index] > list[index + sublistCount] {
                 swap(&list[index], &list[index + sublistCount])
             }
             

From cf1561f885c414d8c4bb260cd21720c109468b9e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E6=A9=98=E5=AD=90?= <726451484@qq.com>
Date: Tue, 28 Mar 2017 15:56:26 +0800
Subject: [PATCH 060/862] Update ShellSortExample.swift

---
 Shell Sort/ShellSortExample.swift | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index 05ab2518b..9174b935b 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -8,12 +8,10 @@
 
 import Foundation
 
-public func shellSort(_ list : inout [Int])
-{
+public func shellSort(_ list : inout [Int]) {
     var sublistCount = list.count / 2
     
-    while sublistCount > 0
-    {
+    while sublistCount > 0 {
         for var index in 0..<list.count {
             
             guard index + sublistCount < list.count else { break }

From 3be78947ea3dba5905e6526776ab6cee13861159 Mon Sep 17 00:00:00 2001
From: Kevin VanderLugt <kevin.vanderlugt@gmail.com>
Date: Tue, 28 Mar 2017 20:01:36 -0700
Subject: [PATCH 061/862] Update How to Contribute link

Super simple but just something I noticed while getting started.
Cheers!
---
 README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.markdown b/README.markdown
index 023f151fb..5e6cfbfe4 100644
--- a/README.markdown
+++ b/README.markdown
@@ -227,7 +227,7 @@ The Swift Algorithm Club was originally created by [Matthijs Hollemans](https://
 
 It is now maintained by [Vincent Ngo](https://www.raywenderlich.com/u/jomoka) 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](How to Contribute.markdown)? :]
+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](How%20to%20Contribute.markdown)? :]
 
 ## License
 

From edee6981d7e77ff88186439b2536b8cc212354c5 Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Tue, 28 Mar 2017 21:31:33 -0700
Subject: [PATCH 062/862] =?UTF-8?q?updated=20syntax=20for=20Swift=203.1!?=
 =?UTF-8?q?=20=F0=9F=98=81=F0=9F=94=A5?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../Contents.swift                            |  1 -
 .../Sources/Matrix.swift                      | 31 ++++++++++++-------
 .../Sources/MatrixSize.swift                  | 20 ------------
 3 files changed, 19 insertions(+), 33 deletions(-)
 delete mode 100644 Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift

diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index 5d82244a3..9e11cb6a1 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -1,5 +1,4 @@
 //: Playground - noun: a place where people can play
-// Reference - http://mathworld.wolfram.com/StrassenFormulas.html
 
 import Foundation
 
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index 77ced4632..c13b3eeee 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -8,37 +8,44 @@
 
 import Foundation
 
-public enum RowOrColumn {
-  case row, column
-}
-
 public struct Matrix<T: Number> {
   
+  // MARK: - Martix Objects
+  
+  public enum Index {
+    case row, column
+  }
+  
+  public struct Size: Equatable {
+    let rows: Int, columns: Int
+    
+    public static func ==(lhs: Size, rhs: Size) -> Bool {
+      return lhs.columns == rhs.columns && lhs.rows == rhs.rows
+    }
+  }
+  
   // MARK: - Variables
   
   let rows: Int, columns: Int
+  let size: Size
+  
   var grid: [T]
   
   var isSquare: Bool {
     return rows == columns
   }
   
-  var size: MatrixSize {
-    return MatrixSize(rows: rows, columns: columns)
-  }
-  
   // MARK: - Init
   
   public init(rows: Int, columns: Int, initialValue: T = T.zero) {
     self.rows = rows
     self.columns = columns
+    self.size = Size(rows: rows, columns: columns)
     self.grid = Array(repeating: initialValue, count: rows * columns)
   }
   
   public init(size: Int, initialValue: T = T.zero) {
-    self.rows = size
-    self.columns = size
-    self.grid = Array(repeating: initialValue, count: rows * columns)
+    self.init(rows: size, columns: size, initialValue: initialValue)
   }
   
   // MARK: - Private Functions
@@ -59,7 +66,7 @@ public struct Matrix<T: Number> {
     }
   }
   
-  public subscript(type: RowOrColumn, value: Int) -> [T] {
+  public subscript(type: Matrix.Index, value: Int) -> [T] {
     get {
       switch type {
       case .row:
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift
deleted file mode 100644
index e0d957607..000000000
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/MatrixSize.swift	
+++ /dev/null
@@ -1,20 +0,0 @@
-//
-//  MatrixSize.swift
-//  
-//
-//  Created by Richard Ash on 10/28/16.
-//
-//
-
-import Foundation
-
-public struct MatrixSize {
-  let rows: Int
-  let columns: Int
-}
-
-extension MatrixSize: Equatable {
-  public static func ==(lhs: MatrixSize, rhs: MatrixSize) -> Bool {
-    return lhs.columns == rhs.columns && lhs.rows == rhs.rows
-  }
-}

From 4d1b9ff02cb46640b55f8b462be8d4536ca182bf Mon Sep 17 00:00:00 2001
From: Jim Rhoades <jim@crushapps.com>
Date: Wed, 29 Mar 2017 18:02:32 -0400
Subject: [PATCH 063/862] Update Big-O Notation.markdown

Fixed the link to "merge sort".
---
 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 09fbb04aa..746cba8a3 100644
--- a/Big-O Notation.markdown	
+++ b/Big-O Notation.markdown	
@@ -19,6 +19,6 @@ Big-O | Name | Description
 
 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 Sort/), 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!
+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!
 
 If you find this confusing, don't let this Big-O stuff bother you too much. It's mostly useful when comparing two algorithms to figure out which one is better. But in the end you still want to test in practice which one really is the best. And if the amount of data is relatively small, then even a slow algorithm will be fast enough for practical use.

From 6d4a1eec73c92713e2e4e880b486694da545dbf9 Mon Sep 17 00:00:00 2001
From: darrellhz <zh0521@gmail.com>
Date: Thu, 30 Mar 2017 14:30:01 +0900
Subject: [PATCH 064/862] Update README.markdown

updated to swift 3 syntax
---
 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 a3a84c03d..b3b955c61 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -195,7 +195,7 @@ For convenience, let's add an init method that calls `insert()` for all the elem
     precondition(array.count > 0)
     self.init(value: array.first!)
     for v in array.dropFirst() {
-      insert(v, parent: self)
+      insert(value: v)
     }
   }
 ```

From da0be01444b4dfc2cdbd2259a3e5c524e9d37434 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Sat, 1 Apr 2017 14:29:56 -0700
Subject: [PATCH 065/862] Update README.markdown

Hello,
I have revised one of your documents for my assignment. I still need to revise more documents (10 in total). I hope it will be fine if I choose some documents from your account.
Thanks,
Parvaneh
---
 Heap/README.markdown | 116 +++++++++++++++++++++----------------------
 1 file changed, 58 insertions(+), 58 deletions(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 88ea25eeb..3935950a6 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -1,19 +1,19 @@
 # Heap
 
-A heap is a [binary tree](../Binary Tree/) that lives inside an array, so it doesn't use parent/child pointers. The tree is partially sorted according to something called the "heap property" that determines the order of the nodes in the tree.
+A heap is a [binary tree](../Binary Tree/) inside an array, so it doesn't 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:
 
-- For building [priority queues](../Priority Queue/).
-- The heap is the data structure supporting [heap sort](../Heap Sort/).
-- Heaps are fast for when you often need to compute the minimum (or maximum) element of a collection.
-- Impressing your non-programmer friends.
+- To build [priority queues](../Priority Queue/).
+- To support [heap sorts](../Heap Sort/).
+- To compute the minimum (or maximum) element of a collection quickly.
+- To impress your non-programmer friends.
 
 ## The heap property
 
-There are two kinds of heaps: a *max-heap* and a *min-heap*. They are identical, except that the order in which they store the tree nodes is opposite.
+There are two kinds of heaps: a *max-heap* and a *min-heap* which are different by the order in which they store the tree nodes.
 
-In a max-heap, parent nodes must always have a greater value than each of their children. For a min-heap it's the other way around: every parent node has a smaller value than its child nodes. This is called the "heap property" and it is true for every single node in the tree.
+In a max-heap, parent nodes have a greater value than each of their children. In a min-heap, every parent node has a smaller value than its child nodes. This is called the "heap property", and it is true for every single node in the tree.
 
 An example:
 
@@ -21,33 +21,33 @@ An example:
 
 This is a max-heap because every parent node is greater than its children. `(10)` is greater than `(7)` and `(2)`. `(7)` is greater than `(5)` and `(1)`.
 
-As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. That is very useful because heaps are often used as a [priority queue](../Priority Queue/) where you want to quickly access the "most important" element.
+As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. The heap property is useful because heaps are often used as a [priority queue](../Priority Queue/)to access the "most important" element quickly.
 
-> **Note:** You can't really say anything else about the sort order of the heap. For example, in a max-heap the maximum element is always at index 0 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.
+> **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 heap compare to regular trees?
+## How does a heap can be compared to regular trees?
 
-A heap isn't intended to be a replacement for a binary search tree. But there are many similarities between the two and also some differences. Here are some of the bigger differences:
+A heap is not a replacement for a binary search tree, and there are similarities and differnces between them. Here are some main differences:
 
-**Order of the nodes.** In a [binary search tree (BST)](../Binary Search Tree/), the left child must always be smaller than its parent and the right child must be greater. This is not true for a heap. In max-heap both children must be smaller; in a min-heap they both must be greater.
+**Order of the nodes.** In a [binary search tree (BST)](../Binary Search Tree/), 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; in a min-heap they both must be greater.
 
 **Memory.** Traditional trees take up more memory than just the data they store. You need to allocate additional storage for the node objects and pointers to the left/right child nodes. A heap only uses a plain array for storage and uses no pointers.
 
-**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 Tree/) or [red-black tree](../Red-Black Tree/). But with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, and so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
+**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 Tree/) or [red-black tree](../Red-Black Tree/), 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.** Searching a binary tree is really fast -- that's its whole purpose. In a heap, searching is slow. The purpose of a heap is to always put the largest (or smallest) node at the front, and to allow relatively fast inserts and deletes. Searching isn't a top priority.
+**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 that lived in an array
+## The tree inside an array
 
-An array may seem like an odd way to implement a tree-like structure but it is very efficient in both time and space.
+An array may seem like an odd way to implement a tree-like structure, but it is efficient in both time and space.
 
-This is how we're going to store the tree from the above example:
+This is how we are going to store the tree from the above example:
 
 	[ 10, 7, 2, 5, 1 ]
 
 That's all there is to it! We don't need any more storage than just this simple array.
 
-So how do we know which nodes are the parents and which are the children if we're not allowed to use any pointers? Good question! There is a well-defined relationship between the array index of a tree node and the array indices of its parent and children.
+So how do we know which nodes are the parents and which are the children if we are not allowed to use any pointers? Good question! There is a well-defined relationship between the array index of a tree node and the array indices of its parent and children.
 
 If `i` is the index of a node, then the following formulas give the array indices of its parent and child nodes:
 
@@ -69,7 +69,7 @@ Let's use these formulas on the example. Fill in the array index and we should g
 
 Verify for yourself that these array indices indeed correspond to the picture of the tree.
 
-> **Note:** The root node `(10)` doesn't have a parent because `-1` is not a valid array index. Likewise, nodes `(2)`, `(5)`, and `(1)` don't have children because those indices are greater than the array size. So we always have to make sure the indices we calculate are actually valid before we use them.
+> **Note:** The root node `(10)` does not have a parent because `-1` is not a valid array index. Likewise, nodes `(2)`, `(5)`, and `(1)` do not have children because those indices are greater than the array size, so we always have to make sure the indices we calculate are actually valid before we use them.
 
 Recall that in a max-heap, the parent's value is always greater than (or equal to) the values of its children. This means the following must be true for all array indices `i`:
 
@@ -79,27 +79,27 @@ array[parent(i)] >= array[i]
 	
 Verify that this heap property holds for the array from the example heap.
 
-As you can see, these equations let us find the parent or child index for any node without the need for pointers. True, it's slightly more complicated than just dereferencing a pointer but that's 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 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's important to understand this relationship between array index and position in the tree. Here's a slightly larger heap, this tree has 15 nodes divided over four levels:
+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:
 
 ![Large heap](Images/LargeHeap.png)
 
-The numbers in this picture aren't the values of the nodes but the array indices that store the nodes! Those array indices correspond to the different levels of the tree like this:
+The numbers in this picture are not the values of the nodes but the array indices that store the nodes! Here is the array indices correspond to the different levels of the tree:
 
 ![The heap array](Images/Array.png)
 
-For the formulas to work, parent nodes must always appear before child nodes in the array. You can see that in the above picture.
+For the formulas to work, parent nodes must appear before child nodes in the array. You can see that in the above picture.
 
 Note that this scheme has limitations. You can do the following with a regular binary tree but not with a heap:
 
 ![Impossible with a heap](Images/RegularTree.png)
 
-You can’t start a new level unless the current lowest level is completely full. So heaps always have this kind of shape:
+You can not start a new level unless the current lowest level is completely full, so heaps always have this kind of shape:
 
 ![The shape of a heap](Images/HeapShape.png)
 
-> **Note:** Technically speaking you *could* emulate a regular binary tree with a heap, but it would waste a lot of space and you’d need some way to mark array indices as being empty.
+> **Note:** You *could* emulate a regular binary tree with a heap, but it would be a waste of space, and you would need to mark array indices as being empty.
 
 Pop quiz! Let's say we have the array:
 
@@ -111,15 +111,15 @@ Is this a valid heap? The answer is yes! A sorted array from low-to-high is a va
 
 The heap property holds for each node because a parent is always smaller than its children. (Verify for yourself that an array sorted from high-to-low is always a valid max-heap.)
 
-> **Note:** But not every min-heap is necessarily a sorted array! It only works one way... To turn a heap back into a sorted array, you need to use [heap sort](../Heap Sort/).
+> **Note:** But not every min-heap is necessarily a sorted array! It only works one way. To turn a heap back into a sorted array, you need to use [heap sort](../Heap Sort/).
 
 ## More math!
 
-In case you are curious, here are a few more formulas that describe certain properties of a heap. You don't need to know these by heart but they come in handy sometimes. Feel free to skip this section!
+In case you are curious, here are a few more formulas that describe certain properties of a heap. You do not need to know these by heart, but they come in handy sometimes. Feel free to skip this section!
 
-The *height* of a tree is defined as the number of steps it takes to go from the root node to the lowest leaf node. Or more formally: the height is the maximum number of edges between the nodes. A heap of height *h* has *h + 1* levels.
+The *height* of a tree is defined as the number of steps it takes to go from the root node to the lowest leaf node, or more formally: the height is the maximum number of edges between the nodes. A heap of height *h* has *h + 1* levels.
 
-This heap has height 3 and therefore has 4 levels:
+This heap has height 3, so it has 4 levels:
 
 ![Large heap](Images/LargeHeap.png)
 
@@ -145,31 +145,31 @@ 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.
 
-The other operations are built on these primitives. They are:
+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.
 
-- `remove()`: Removes and returns the maximum value (max-heap) or the minimum value (min-heap). To fill up the hole that's left by removing the element, the very last element is moved to the root position and then `shiftDown()` fixes up the heap. (This is sometimes called "extract min" or "extract max".)
+- `remove()`: Removes and returns the maximum value (max-heap) or the minimum value (min-heap). To fill up the hole left by removing the element, the very last element is moved to the root position and then `shiftDown()` fixes up the heap. (This is sometimes called "extract min" or "extract max".)
 
-- `removeAtIndex(index)`: Just like `remove()` except it lets you remove any item from the heap, not just the root. This calls both `shiftDown()`, in case the new element is out-of-order with its children, and `shiftUp()`, in case the element is out-of-order with its parents.
+- `removeAtIndex(index)`: Just like `remove()` with the exception that it allows you to remove any item from the heap, not just the root. This calls both `shiftDown()`, in case the new element is out-of-order with its children, and `shiftUp()`, in case the element is out-of-order with its parents.
 
-- `replace(index, value)`: Assigns a smaller (min-heap) or larger (max-heap)  value to a node. Because this invalidates the heap property, it uses `shiftUp()` to patch things up. (Also called "decrease key" and "increase key".)
+- `replace(index, value)`: Assigns a smaller (min-heap) or larger (max-heap) value to a node. Because this invalidates the heap property, it uses `shiftUp()` to patch things up. (Also called "decrease key" and "increase key".)
 
-All of the above take time **O(log n)** because shifting up or down is the most expensive thing they do. There are also a few operations that take more time:
+All of the above take time **O(log n)** because shifting up or down is expensive. There are also a few operations that take more time:
 
-- `search(value)`. Heaps aren't built for efficient searches but the `replace()` and `removeAtIndex()` operations require the array index of the node, so you need to find that index somehow. Time: **O(n)**.
+- `search(value)`. Heaps are not built for efficient searches, but the `replace()` and `removeAtIndex()` operations require the array index of the node, so you need to find that index. Time: **O(n)**.
 
-- `buildHeap(array)`: Converts an (unsorted) array into a heap by repeatedly calling `insert()`. If you’re smart about this, it can be done in **O(n)** time.
+- `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 Sort/). Since the heap is really an array, we can use its unique properties to sort the array from low to high. Time: **O(n lg n).**
+- [Heap sort](../Heap Sort/). 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).**
 
 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)**.
 
-> **Note:** By far the most common things you'll do with a heap are inserting new values with `insert()` and removing the maximum or minimum value with `remove()`. Both take **O(log n)** time. The other operations exist to support more advanced usage, such as building a priority queue where the "importance" of items can change after they've been added to the queue.
+> **Note:** By far the most common things you will do with a heap are inserting new values with `insert()` and removing the maximum or minimum value with `remove()`. Both take **O(log n)** time. The other operations exist to support more advanced usage, such as building a priority queue where the "importance" of items can change after they have been added to the queue.
 
 ## Inserting into the heap
 
-Let's go through an example insertion to see in more detail how this works. We'll insert the value `16` into this heap:
+Let's go through an example of insertion to see in details how this works. We will insert the value `16` into this heap:
 
 ![The heap before insertion](Images/Heap1.png)
 
@@ -185,13 +185,13 @@ This corresponds to the following tree:
 
 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.)
+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're going to swap `(16)` and `(2)`. 
+To restore the heap property, we are going to swap `(16)` and `(2)`. 
 
 ![The heap before insertion](Images/Insert2.png)
 
-We're not done yet because `(10)` is also smaller than `(16)`. We keep swapping our inserted value with its parent, until the parent is larger or we reach the top of the tree. This is called **shift-up** or **sifting** and is done after every insertion. It makes a number that is too large or too small "float up" the tree.
+We are not done yet because `(10)` is also smaller than `(16)`. We keep swapping our inserted value with its parent, until the parent is larger or we reach the top of the tree. This is called **shift-up** or **sifting** and is done after every insertion. It makes a number that is too large or too small "float up" the tree.
 
 Finally, we get:
 
@@ -199,7 +199,7 @@ Finally, we get:
 
 And now every parent is greater than its children again.
 
-The time required for shifting up is proportional to the height of the tree so it takes **O(log n)** time. (The time it takes to append the node to the end of the array is only **O(1)**, so that doesn't slow it down.)
+The time required for shifting up is proportional to the height of the tree, so it takes **O(log n)** time. (The time it takes to append the node to the end of the array is only **O(1)**, so that does not slow it down.)
 
 ## Removing the root
 
@@ -211,7 +211,7 @@ 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'll do the opposite: we're going to 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 will do the opposite: we are going to 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)
 
@@ -219,19 +219,19 @@ Let's look at how to **shift-down** `(1)`. To maintain the heap property for thi
 
 ![The last node goes to the root](Images/Remove3.png)
 
-Keep shifting down until the node doesn't have any children or it is larger than both its children. For our heap we only need one more swap to restore the heap property:
+Keep shifting down until the node does not have any children or it is larger than both its children. For our heap, we only need one more swap to restore the heap property:
 
 ![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 so it takes **O(log n)** time. 
+The time required for shifting all the way down is proportional to the height of the tree, so it 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.
 
 ## Removing any node
 
-The vast majority of the time you'll be removing the object at the root of the heap because that's what heaps are designed for.
+The vast majority of the time you will be removing the object at the root of the heap because that is what heaps are designed for.
 
-However, it can be useful to remove an arbitrary element. This is a more general version of `remove()` and may involve either `shiftDown()` or `shiftUp()`.
+However, it can be useful to remove an arbitrary element. This is a general version of `remove()` and may involve either `shiftDown()` or `shiftUp()`.
 
 Let's take the example tree again and remove `(7)`:
 
@@ -241,13 +241,13 @@ As a reminder, the array is:
 
 	[ 10, 7, 2, 5, 1 ]
 
-As you know, removing an element could potentially invalidate the max-heap or min-heap property. To fix this, we swap the node that we're removing with the last element:
+As you know, removing an element could potentially invalidate the max-heap or min-heap property. To fix this, we swap the node that we are removing with the last element:
 
 	[ 10, 1, 2, 5, 7 ]
 
-The last element is the one that we'll return; we'll call `removeLast()` to remove it from the heap. The `(1)` is now out-of-order because it's smaller than its child, `(5)`, but sits higher in the tree. We call `shiftDown()` to repair this.
+The last element is the one that we will return; we will call `removeLast()` to remove it from the heap. The `(1)` is now out-of-order because it is smaller than its child, `(5)` but sits higher in the tree. We call `shiftDown()` to repair this.
 
-However, shifting down is not the only situation we need to handle -- it may also happen that the new element must be shifted up. Consider what happens if you remove `(5)` from the following heap:
+However, shifting down is not the only situation we need to handle. It may also happen that the new element must be shifted up. Consider what happens if you remove `(5)` from the following heap:
 
 ![We need to shift up](Images/Remove5.png)
 
@@ -267,7 +267,7 @@ In code it would look like this:
   }
 ```
 
-We simply call `insert()` for each of the values in the array. Simple enough, but not very efficient. This takes **O(n log n)** time in total because there are **n** elements and each insertion takes **log n** time.
+We simply call `insert()` for each of the values in the array. Simple enough but not very efficient. This takes **O(n log n)** time in total because there are **n** elements and each insertion takes **log n** time.
 
 If you didn't gloss over the math section, you'd have seen that for any heap the elements at array indices *n/2* to *n-1* are the leaves of the tree. We can simply skip those leaves. We only have to process the other nodes, since they are parents with one or more children and therefore may be in the wrong order. 
 
@@ -286,9 +286,9 @@ Here, `elements` is the heap's own array. We walk backwards through this array,
 
 ## Searching the heap
 
-Heaps aren't made for fast searches, but if you want to remove an arbitrary element using `removeAtIndex()` or change the value of an element with `replace()`, then you need to obtain the index of that element somehow. Searching is one way to do this but it's kind of slow.
+Heaps are not made for fast searches, but if you want to remove an arbitrary element using `removeAtIndex()` or change the value of an element with `replace()`, then you need to obtain the index of that element. Searching is one way to do this, but it is slow.
 
-In a [binary search tree](../Binary Search Tree/) you can depend on the order of the nodes to guarantee a fast search. A heap orders its nodes differently and so a binary search won't work. You'll potentially have to look at every node in the tree.
+In a [binary search tree](../Binary Search Tree/) you can depend on the order of the nodes to guarantee a fast search. A heap orders its nodes differently, so a binary search will not work. You need to look at every node in the tree.
 
 Let's take our example heap again:
 
@@ -296,9 +296,9 @@ Let's take our example heap again:
 
 If we want to search for the index of node `(1)`, we could just step through the array `[ 10, 7, 2, 5, 1 ]` with a linear search.
 
-But even though the heap property wasn't conceived with searching in mind, we can still take advantage of it. We know that in a max-heap a parent node is always larger than its children, so we can ignore those children (and their children, and so on...) if the parent is already smaller than the value we're looking for.
+Even though the heap property was not conceived with searching in mind, we can still take advantage of it. We know that in a max-heap a parent node is always larger than its children, so we can ignore those children (and their children, and so on...) if the parent is already smaller than the value we are looking for.
 
-Let's say we want to see if the heap contains the value `8` (it doesn't). We start at the root `(10)`. This is obviously not what we're looking for, so we recursively look at its left and right child. The left child is `(7)`. That is also not what we want, but since this is a max-heap, we know there's no point in looking at the children of `(7)`. They will always be smaller than `7` and are therefore never equal to `8`. Likewise for the right child, `(2)`.
+Let's say we want to see if the heap contains the value `8` (it doesn't). We start at the root `(10)`. This is not what we are looking for, so we recursively look at its left and right child. The left child is `(7)`. That is also not what we want, but since this is a max-heap, we know there is no point in looking at the children of `(7)`. They will always be smaller than `7` and are therefore never equal to `8`; likewise, for the right child, `(2)`.
 
 Despite this small optimization, searching is still an **O(n)** operation.
 
@@ -308,9 +308,9 @@ Despite this small optimization, searching is still an **O(n)** operation.
 
 See [Heap.swift](Heap.swift) for the implementation of these concepts in Swift. Most of the code is quite straightforward. The only tricky bits are in `shiftUp()` and `shiftDown()`.
 
-You've seen that there are two types of heaps: a max-heap and a min-heap. The only difference between them is in how they order their nodes: largest value first or smallest value first.
+You have seen that there are two types of heaps: a max-heap and a min-heap. The only difference between them is in how they order their nodes: largest value first or smallest value first.
 
-Rather than create two different versions, `MaxHeap` and `MinHeap`, there is just one `Heap` object and it takes an `isOrderedBefore` closure. This closure contains the logic that determines the order of two values. You've probably seen this before because it's also how Swift's `sort()` works.
+Rather than create two different versions, `MaxHeap` and `MinHeap`, there is just one `Heap` object and it takes an `isOrderedBefore` closure. This closure contains the logic that determines the order of two values. You have probably seen this before because it is also how Swift's `sort()` works.
 
 To make a max-heap of integers, you write:
 

From 52855ccbd3fb95704cd6375d44f1fa22512d04e1 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Sat, 1 Apr 2017 19:38:22 -0700
Subject: [PATCH 066/862] Update README.markdown

For an assignment in technical writings, I have revised this document.

Thanks,
Parvaneh
---
 Hash Table/README.markdown | 69 +++++++++++++++++++-------------------
 1 file changed, 34 insertions(+), 35 deletions(-)

diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index 4399b0f86..958c3595a 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -2,13 +2,13 @@
 
 A hash table allows you to store and retrieve objects by a "key".
 
-Also called dictionary, map, associative array. There are other ways to implement these, such as with a tree or even a plain array, but hash table is the most common.
+A hash table is used to implement structures, such as a dictionary, a map, and an associative array. These structures can be implemented by a tree or a plain array, but it is efficient to use a hash table.
 
-This should explain why Swift's built-in `Dictionary` type requires that keys conform to the `Hashable` protocol: internally it uses a hash table, just like the one you'll learn about here.
+This should explain why Swift's built-in `Dictionary` type requires that keys conform to the `Hashable` protocol: internally it uses a hash table, like the one you will learn about here.
 
 ## How it works
 
-At its most basic, a hash table is nothing more than an array. Initially, this array is empty. When you put a value into the hash table under a certain key, it uses that key to calculate an index in the array, like so:
+A hash table is nothing more than an array. Initially, this array is empty. When you put a value into the hash table under a certain key, it uses that key to calculate an index in the array. Here is an example:
 
 ```swift
 hashTable["firstName"] = "Steve"
@@ -48,33 +48,33 @@ hashTable["hobbies"] = "Programming Swift"
 	+--------------+
 ```
 
-The trick is in how the hash table calculates those array indices. That's where the hashing comes in. When you write,
+The trick is how the hash table calculates those array indices. That is where the hashing comes in. When you write the following statement,
 
 ```swift
 hashTable["firstName"] = "Steve"
 ```
 
-the hash table takes the key `"firstName"` and asks it for its `hashValue` property. That's why keys must be `Hashable`. 
+the hash table takes the key `"firstName"` and asks it for its `hashValue` property. Hence, keys must be `Hashable`.
 
-When you do `"firstName".hashValue`, it returns a big integer: -4799450059917011053. Likewise, `"hobbies".hashValue` has the hash value 4799450060928805186. (The values you see may vary.)
+When you write `"firstName".hashValue`, it returns a big integer: -4799450059917011053. Likewise, `"hobbies".hashValue` has the hash value 4799450060928805186. (The values you see may vary.)
 
-Of course, these numbers are way too big to be used as indices into our array. One of them is even negative! A common way to make these big numbers more suitable is to first make the hash positive and then take the modulo with the array size.
+These numbers are big to be used as indices into our array, and one of them is even negative! A common way to make these big numbers  suitable is to first make the hash positive and then take the modulo with the array size.
 
-Our array has size 5, so the index for the `"firstName"` key becomes `abs(-4799450059917011053) % 5 = 3`. You can calculate for yourself that the array index for `"hobbies"` is 1.
+Our array has size 5, so the index for the `"firstName"` key becomes `abs(-4799450059917011053) % 5 = 3`. You can calculate that the array index for `"hobbies"` is 1.
 
-Using hashes in this manner is what makes the dictionary so efficient: to find an element in the hash table you only have to hash the key to get an array index and then look up the element in the underlying array. All these operations take a constant amount of time, so inserting, retrieving, and removing are all **O(1)**.
+Using hashes in this manner is what makes the dictionary efficient: to find an element in the hash table, you must hash the key to get an array index and then look up the element in the underlying array. All these operations take a constant amount of time, so inserting, retrieving, and removing are all **O(1)**.
 
-> **Note:** As you can see, it's hard to predict where in the array your objects end up. That's why dictionaries do not guarantee any particular order of the elements in the hash table.
+> **Note:** It is difficult to predict where in the array your objects end up. Hence, dictionaries do not guarantee any particular order of the elements in the hash table.
 
 ## Avoiding collisions
 
 There is one problem: because we take the modulo of the hash value with the size of the array, it can happen that two or more keys get assigned the same array index. This is called a collision.
 
-One way to avoid collisions is to have a very large array. That reduces the likelihood of two keys mapping to the same index. Another trick is to use a prime number for the array size. However, collisions are bound to occur so you need some way to handle them.
+One way to avoid collisions is to have a large array which reduces the likelihood of two keys mapping to the same index. Another trick is to use a prime number for the array size. However, collisions are bound to occur, so you need to find a way to handle them.
 
-Because our table is so small it's easy to show a collision. For example, the array index for the key `"lastName"` is also 3. That's a problem, as we don't want to overwrite the value that's already at this array index.
+Because our table is small, it is easy to show a collision. For example, the array index for the key `"lastName"` is also 3, but we do not want to overwrite the value that is already at this array index.
 
-There are a few ways to handle collisions. A common one is to use chaining. The array now looks as follows:
+A common way to handle collisions is to use chaining. The array looks as follows:
 
 ```swift
 	buckets:
@@ -91,25 +91,25 @@ There are a few ways to handle collisions. A common one is to use chaining. The
 	+-----+
 ```
 
-With chaining, keys and their values are not stored directly in the array. Instead, each array element is really a list of zero or more key/value pairs. The array elements are usually called the *buckets* and the lists are called the *chains*. So here we have 5 buckets and two of these buckets have chains. The other three buckets are empty.
+With chaining, keys and their values are not stored directly in the array. Instead, each array element is a list of zero or more key/value pairs. The array elements are usually called the *buckets* and the lists are called the *chains*. Here we have 5 buckets, and two of these buckets have chains. The other three buckets are empty.
 
-If we now write the following to retrieve an item from the hash table,
+If we write the following statement to retrieve an item from the hash table,
 
 ```swift
 let x = hashTable["lastName"]
 ```
 
-then this first hashes the key `"lastName"` to calculate the array index, which is 3. Bucket 3 has a chain, so we step through that list to find the value with the key `"lastName"`. That is done by comparing the keys, so here that involves a string comparison. The hash table sees that this key belongs to the last item in the chain and returns the corresponding value, `"Jobs"`.
+it first hashes the key `"lastName"` to calculate the array index, which is 3. Since bucket 3 has a chain, we step through the list to find the value with the key `"lastName"`. This is done by comparing the keys using a string comparison. The hash table checks that the key belongs to the last item in the chain and returns the corresponding value, `"Jobs"`.
 
-Common ways to implement this chaining mechanism are to use a linked list or another array. Technically speaking the order of the items in the chain doesn't matter, so you also can think of it as a set instead of a list. (Now you can also imagine where the term "bucket" comes from; we just dump all the objects together into the bucket.)
+Common ways to implement this chaining mechanism are to use a linked list or another array. Since the order of the items in the chain does not matter, you can think of it as a set instead of a list. (Now you can also imagine where the term "bucket" comes from; we just dump all the objects together into the bucket.)
 
-It's important that chains do not become too long or looking up items in the hash table becomes really slow. Ideally, we would have no chains at all but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets and by using high-quality hash functions.
+Chains should not become long becasuse the slow process of looking up items in the hash table. Ideally, we would have no chains at all, but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets using high-quality hash functions.
 
-> **Note:** An alternative to chaining is "open addressing". The idea is this: if an array index is already taken, we put the element in the next unused bucket. Of course, this approach has its own upsides and downsides.
+> **Note:** An alternative to chaining is "open addressing". The idea is this: if an array index is already taken, we put the element in the next unused bucket. This approach has its own upsides and downsides.
 
 ## The code
 
-Let's look at a basic implementation of a hash table in Swift. We'll build it up step-by-step.
+Let's look at a basic implementation of a hash table in Swift. We will build it up step-by-step.
 
 ```swift
 public struct HashTable<Key: Hashable, Value> {
@@ -127,9 +127,9 @@ public struct HashTable<Key: Hashable, Value> {
   }
 ```
 
-The `HashTable` is a generic container and the two generic types are named `Key` (which must be `Hashable`) and `Value`. We also define two other types: `Element` is a key/value pair for use in a chain and `Bucket` is an array of such `Elements`.
+The `HashTable` is a generic container, and the two generic types are named `Key` (which must be `Hashable`) and `Value`. We also define two other types: `Element` is a key/value pair for useing in a chain, and `Bucket` is an array of such `Elements`.
 
-The main array is named `buckets`. It has a fixed size, the so-called capacity, provided by the `init(capacity)` method. We're also keeping track of how many items have been added to the hash table using the `count` variable.
+The main array is named `buckets`. It has a fixed size, the so-called capacity, provided by the `init(capacity)` method. We are also keeping track of how many items have been added to the hash table using the `count` variable.
 
 An example of how to create a new hash table object:
 
@@ -137,7 +137,7 @@ An example of how to create a new hash table object:
 var hashTable = HashTable<String, String>(capacity: 5)
 ```
 
-Currently the hash table doesn't do anything yet, so let's add the remaining functionality. First, add a helper method that calculates the array index for a given key:
+The hash table does not do anything yet, so let's add the remaining functionality. First, add a helper method that calculates the array index for a given key:
 
 ```swift
   private func index(forKey key: Key) -> Int {
@@ -145,9 +145,9 @@ Currently the hash table doesn't do anything yet, so let's add the remaining fun
   }
 ```
 
-This performs the calculation you saw earlier: it takes the absolute value of the key's `hashValue` modulo the size of the buckets array. We've put this in a function of its own because it gets used in a few different places.
+This performs the calculation you saw earlier: it takes the absolute value of the key's `hashValue` modulo the size of the buckets array. We have put this in a function of its own because it gets used in a few different places.
 
-There are four common things you'll do with a hash table or dictionary: 
+There are four common things you will do with a hash table or dictionary: 
 
 - insert a new element
 - look up an element
@@ -180,7 +180,7 @@ We can do all these things with a `subscript` function:
   }
 ```
 
-This calls three helper functions to do the actual work. Let's take a look at `value(forKey:)` first, which retrieves an object from the hash table.
+This calls three helper functions to do the actual work. Let's take a look at `value(forKey:)`which retrieves an object from the hash table.
 
 ```swift
   public func value(forKey key: Key) -> Value? {
@@ -193,10 +193,9 @@ This calls three helper functions to do the actual work. Let's take a look at `v
     return nil  // key not in hash table
   }
 ```
+First it calls `index(forKey:)` to convert the key into an array index. That gives us the bucket number, but this bucket may be used by more than one key if there were collisions. The `value(forKey:)` loops through the chain from that bucket and compares the keys one-by-one. If found, it returns the corresponding value, otherwise it returns `nil`.
 
-First it calls `index(forKey:)` to convert the key into an array index. That gives us the bucket number, but if there were collisions this bucket may be used by more than one key. So `value(forKey:)` loops through the chain from that bucket and compares the keys one-by-one. If found, it returns the corresponding value, otherwise it returns `nil`.
-
-The code to insert a new element or update an existing element lives in `updateValue(_:forKey:)`. It's a little bit more complicated:
+The code to insert a new element or update an existing element lives in `updateValue(_:forKey:)`. This is more complicated:
 
 ```swift
   public mutating func updateValue(_ value: Value, forKey key: Key) -> Value? {
@@ -218,9 +217,9 @@ The code to insert a new element or update an existing element lives in `updateV
   }
 ```
 
-Again, the first thing we do is convert the key into an array index to find the bucket. Then we loop through the chain for that bucket. If we find the key in the chain, it means we must update it with the new value. If the key is not in the chain, we insert the new key/value pair to the end of the chain.
+Again, the first step is to convert the key into an array index to find the bucket. Then we loop through the chain for that bucket. If we find the key in the chain, we must update it with the new value. If the key is not in the chain, we insert the new key/value pair to the end of the chain.
 
-As you can see, it's important that chains are kept short (by making the hash table large enough). Otherwise, you spend a lot of time in these `for`...`in` loops and the performance of the hash table will no longer be **O(1)** but more like **O(n)**.
+As you can see, it is important to keep the chains short (by making the hash table large enough). Otherwise, you spend excessive time in these `for`...`in` loops and the performance of the hash table will no longer be **O(1)** but more like **O(n)**.
 
 Removing is similar in that again it loops through the chain:
 
@@ -246,16 +245,16 @@ Try this stuff out in a playground. It should work just like a standard Swift `D
 
 ## Resizing the hash table
 
-This version of `HashTable` always uses an array of a fixed size or capacity. That's fine if you've got a good idea of many items you'll be storing in the hash table. For the capacity, choose a prime number that is greater than the maximum number of items you expect to store and you're good to go.
+This version of `HashTable` always uses an array of a fixed size or capacity. If you have many items to store in the hash table, for the capacity, choose a prime number greater than the maximum number of items.
 
 The *load factor* of a hash table is the percentage of the capacity that is currently used. If there are 3 items in a hash table with 5 buckets, then the load factor is `3/5 = 60%`.
 
-If the hash table is too small and the chains are long, the load factor can become greater than 1. That's not a good idea.
+If the hash table is small, and the chains are long, the load factor can become greater than 1, that is not a good idea.
 
-If the load factor becomes too high, say > 75%, you can resize the hash table. Adding the code for this is left as an exercise for the reader. Keep in mind that making the buckets array larger will change the array indices that the keys map to! To account for this, you'll have to insert all the elements again after resizing the array.
+If the load factor becomes high, greater than 75%, you can resize the hash table. Adding the code for this condition is left as an exercise for the reader. Keep in mind that making the buckets array larger will change the array indices that the keys map to! This requires you to insert all the elements again after resizing the array.
 
 ## Where to go from here?
 
-`HashTable` is quite basic. It might be fun to integrate it better with the Swift standard library by making it a `SequenceType`, for example.
+`HashTable` is quite basic. It might be efficient to integrate it with the Swift standard library by making it a `SequenceType`.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 7010d4ff4e28871cd06067aad15dcde031e745c8 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Sun, 2 Apr 2017 18:28:48 -0400
Subject: [PATCH 067/862] Fixed an issue with links that has spaces in the
 address

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

diff --git a/Graph/README.markdown b/Graph/README.markdown
index 1ff1a82ac..a2531e808 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -28,7 +28,7 @@ The following are also graphs:
 
 ![Tree and linked list](Images/TreeAndList.png)
 
-On the left is a [tree](../Tree/) structure, on the right a [linked list](../Linked List/). Both can be considered graphs, but in a simpler form. After all, they have vertices (nodes) and edges (links).
+On the left is a [tree](../Tree/) structure, on the right a [linked list](../Linked%20List/). Both can be considered graphs, but in a simpler form. After all, they have vertices (nodes) and edges (links).
 
 The very first graph I showed you contained *cycles*, where you can start off at a vertex, follow a path, and come back to the original vertex. A tree is a graph without such cycles.
 
@@ -42,7 +42,7 @@ Like a tree this does not have any cycles in it (no matter where you start, ther
 
 Maybe you're shrugging your shoulders and thinking, what's the big deal? Well, it turns out that graphs are an extremely useful data structure.
 
-If you have some programming problem where you can represent some of your data as vertices and some of it as edges between those vertices, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First Search/) or [depth-first search](../Depth-First Search) to find a solution.
+If you have some programming problem where you can represent some of your data as vertices and some of it as edges between those vertices, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First%20Search/) or [depth-first search](../Depth-First%20Search) to find a solution.
 
 For example, let's say you have a list of tasks where some tasks have to wait on others before they can begin. You can model this using an acyclic directed graph:
 
@@ -50,7 +50,7 @@ For example, let's say you have a list of tasks where some tasks have to wait on
 
 Each vertex represents a task. Here, an edge between two vertices means that the source task must be completed before the destination task can start. So task C cannot start before B and D are finished, and B nor D can start before A is finished.
 
-Now that the problem is expressed using a graph, you can use a depth-first search to perform a [topological sort](../Topological Sort/). This will put the tasks in an optimal order so that you minimize the time spent waiting for tasks to complete. (One possible order here is A, B, D, E, C, F, G, H, I, J, K.)
+Now that the problem is expressed using a graph, you can use a depth-first search to perform a [topological sort](../Topological%20Sort/). This will put the tasks in an optimal order so that you minimize the time spent waiting for tasks to complete. (One possible order here is A, B, D, E, C, F, G, H, I, J, K.)
 
 Whenever you're faced with a tough programming problem, ask yourself, "how can I express this problem using a graph?" Graphs are all about representing relationships between your data. The trick is in how you define "relationship".
 

From 79255d2bb83cfbbcab0fb3f983bdc96e25c0bd4b Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Sun, 2 Apr 2017 19:43:48 -0400
Subject: [PATCH 068/862] Fixed white-space encoding in markdown links

---
 Heap/README.markdown | 40 ++++++++++++++++++++--------------------
 1 file changed, 20 insertions(+), 20 deletions(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 88ea25eeb..1bcb05e1b 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -1,11 +1,11 @@
 # Heap
 
-A heap is a [binary tree](../Binary Tree/) that lives inside an array, so it doesn't use parent/child pointers. The tree is partially sorted according to something called the "heap property" that determines the order of the nodes in the tree.
+A heap is a [binary tree](../Binary%20Tree/) that lives inside an array, so it doesn't use parent/child pointers. The tree is partially sorted according to something called the "heap property" that determines the order of the nodes in the tree.
 
 Common uses for heap:
 
-- For building [priority queues](../Priority Queue/).
-- The heap is the data structure supporting [heap sort](../Heap Sort/).
+- For building [priority queues](../Priority%20Queue/).
+- The heap is the data structure supporting [heap sort](../Heap%20Sort/).
 - Heaps are fast for when you often need to compute the minimum (or maximum) element of a collection.
 - Impressing your non-programmer friends.
 
@@ -21,7 +21,7 @@ An example:
 
 This is a max-heap because every parent node is greater than its children. `(10)` is greater than `(7)` and `(2)`. `(7)` is greater than `(5)` and `(1)`.
 
-As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. That is very useful because heaps are often used as a [priority queue](../Priority Queue/) where you want to quickly access the "most important" element.
+As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. That is very useful because heaps are often used as a [priority queue](../Priority%20Queue/) where you want to quickly access the "most important" element.
 
 > **Note:** You can't really say anything else about the sort order of the heap. For example, in a max-heap the maximum element is always at index 0 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.
 
@@ -29,11 +29,11 @@ As a result of this heap property, a max-heap always stores its largest item at
 
 A heap isn't intended to be a replacement for a binary search tree. But there are many similarities between the two and also some differences. Here are some of the bigger differences:
 
-**Order of the nodes.** In a [binary search tree (BST)](../Binary Search Tree/), the left child must always be smaller than its parent and the right child must be greater. This is not true for a heap. In max-heap both children must be smaller; in a min-heap they both must be greater.
+**Order of the nodes.** In a [binary search tree (BST)](../Binary%20Search%20Tree/), the left child must always be smaller than its parent and the right child must be greater. This is not true for a heap. In max-heap both children must be smaller; in a min-heap they both must be greater.
 
 **Memory.** Traditional trees take up more memory than just the data they store. You need to allocate additional storage for the node objects and pointers to the left/right child nodes. A heap only uses a plain array for storage and uses no pointers.
 
-**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 Tree/) or [red-black tree](../Red-Black Tree/). But with heaps we don't actually need the entire tree to be sorted. We just want the heap property to be fulfilled, and so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
+**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, and so balancing isn't an issue. Because of the way the heap is structured, heaps can guarantee **O(log n)** performance.
 
 **Searching.** Searching a binary tree is really fast -- that's its whole purpose. In a heap, searching is slow. The purpose of a heap is to always put the largest (or smallest) node at the front, and to allow relatively fast inserts and deletes. Searching isn't a top priority.
 
@@ -54,7 +54,7 @@ If `i` is the index of a node, then the following formulas give the array indice
     parent(i) = floor((i - 1)/2)
     left(i)   = 2i + 1
     right(i)  = 2i + 2
-    
+
 Note that `right(i)` is simply `left(i) + 1`. The left and right nodes are always stored right next to each other.
 
 Let's use these formulas on the example. Fill in the array index and we should get the positions of the parent and child nodes in the array:
@@ -63,7 +63,7 @@ Let's use these formulas on the example. Fill in the array index and we should g
 |------|-------------|--------------|------------|-------------|
 | 10 | 0 | -1 | 1 | 2 |
 | 7 | 1 | 0 | 3 | 4 |
-| 2 | 2 | 0 | 5 | 6 | 
+| 2 | 2 | 0 | 5 | 6 |
 | 5 | 3 | 1 | 7 | 8 |
 | 1 | 4 | 1 | 9 | 10 |
 
@@ -76,7 +76,7 @@ Recall that in a max-heap, the parent's value is always greater than (or equal t
 ```swift
 array[parent(i)] >= array[i]
 ```
-	
+
 Verify that this heap property holds for the array from the example heap.
 
 As you can see, these equations let us find the parent or child index for any node without the need for pointers. True, it's slightly more complicated than just dereferencing a pointer but that's the tradeoff: we save memory space but pay with extra computations. Fortunately, the computations are fast and only take **O(1)** time.
@@ -104,14 +104,14 @@ You can’t start a new level unless the current lowest level is completely full
 Pop quiz! Let's say we have the array:
 
 	[ 10, 14, 25, 33, 81, 82, 99 ]
-	
+
 Is this a valid heap? The answer is yes! A sorted array from low-to-high is a valid min-heap. We can draw this heap as follows:
 
 ![A sorted array is a valid heap](Images/SortedArray.png)
 
 The heap property holds for each node because a parent is always smaller than its children. (Verify for yourself that an array sorted from high-to-low is always a valid max-heap.)
 
-> **Note:** But not every min-heap is necessarily a sorted array! It only works one way... To turn a heap back into a sorted array, you need to use [heap sort](../Heap Sort/).
+> **Note:** But not every min-heap is necessarily a sorted array! It only works one way... To turn a heap back into a sorted array, you need to use [heap sort](../Heap%20Sort/).
 
 ## More math!
 
@@ -129,7 +129,7 @@ If the lowest level is completely full, then that level contains *2^h* nodes. Th
 
 The total number of nodes *n* in the entire heap is therefore *2^(h+1) - 1*. In the example, `2^4 - 1 = 16 - 1 = 15`.
 
-There are at most *ceil(n/2^(h+1))* nodes of height *h* in an *n*-element heap. 
+There are at most *ceil(n/2^(h+1))* nodes of height *h* in an *n*-element heap.
 
 The leaf nodes are always located at array indices *floor(n/2)* to *n-1*. We will make use of this fact to quickly build up the heap from an array. Verify this for the example if you don't believe it. ;-)
 
@@ -141,7 +141,7 @@ There are two primitive operations necessary to make sure the heap is a valid ma
 
 - `shiftUp()`: If the element is greater (max-heap) or smaller (min-heap) than its parent, it needs to be swapped with the parent. This makes it move up the tree.
 
-- `shiftDown()`. If the element is smaller (max-heap) or greater (min-heap) than its children, it needs to move down the tree. This operation is also called "heapify". 
+- `shiftDown()`. If the element is smaller (max-heap) or greater (min-heap) than its children, it needs to move down the tree. This operation is also called "heapify".
 
 Shifting up or down is a recursive procedure that takes **O(log n)** time.
 
@@ -161,7 +161,7 @@ All of the above take time **O(log n)** because shifting up or down is the most
 
 - `buildHeap(array)`: Converts an (unsorted) array into a heap by repeatedly calling `insert()`. If you’re smart about this, it can be done in **O(n)** time.
 
-- [Heap sort](../Heap Sort/). Since the heap is really 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 really an array, we can use its unique properties to sort the array from low to high. Time: **O(n lg 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)**.
 
@@ -187,7 +187,7 @@ 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're going to swap `(16)` and `(2)`. 
+To restore the heap property, we're going to swap `(16)` and `(2)`.
 
 ![The heap before insertion](Images/Insert2.png)
 
@@ -211,7 +211,7 @@ 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'll do the opposite: we're going to 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'll do the opposite: we're going to 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)
 
@@ -223,7 +223,7 @@ Keep shifting down until the node doesn't have any children or it is larger than
 
 ![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 so it takes **O(log n)** time. 
+The time required for shifting all the way down is proportional to the height of the tree so it 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.
 
@@ -269,7 +269,7 @@ In code it would look like this:
 
 We simply call `insert()` for each of the values in the array. Simple enough, but not very efficient. This takes **O(n log n)** time in total because there are **n** elements and each insertion takes **log n** time.
 
-If you didn't gloss over the math section, you'd have seen that for any heap the elements at array indices *n/2* to *n-1* are the leaves of the tree. We can simply skip those leaves. We only have to process the other nodes, since they are parents with one or more children and therefore may be in the wrong order. 
+If you didn't gloss over the math section, you'd have seen that for any heap the elements at array indices *n/2* to *n-1* are the leaves of the tree. We can simply skip those leaves. We only have to process the other nodes, since they are parents with one or more children and therefore may be in the wrong order.
 
 In code:
 
@@ -288,7 +288,7 @@ Here, `elements` is the heap's own array. We walk backwards through this array,
 
 Heaps aren't made for fast searches, but if you want to remove an arbitrary element using `removeAtIndex()` or change the value of an element with `replace()`, then you need to obtain the index of that element somehow. Searching is one way to do this but it's kind of slow.
 
-In a [binary search tree](../Binary Search Tree/) you can depend on the order of the nodes to guarantee a fast search. A heap orders its nodes differently and so a binary search won't work. You'll potentially have to look at every node in the tree.
+In a [binary search tree](../Binary%20Search%20Tree/) you can depend on the order of the nodes to guarantee a fast search. A heap orders its nodes differently and so a binary search won't work. You'll potentially have to look at every node in the tree.
 
 Let's take our example heap again:
 
@@ -302,7 +302,7 @@ Let's say we want to see if the heap contains the value `8` (it doesn't). We sta
 
 Despite this small optimization, searching is still an **O(n)** operation.
 
-> **Note:** There is away to turn lookups into a **O(1)** operation by keeping an additional dictionary that maps node values to indices. This may be worth doing if you often need to call `replace()` to change the "priority" of objects in a [priority queue](../Priority Queue/) that's built on a heap.
+> **Note:** There is away to turn lookups into a **O(1)** operation by keeping an additional dictionary that maps node values to indices. This may be worth doing if you often need to call `replace()` to change the "priority" of objects in a [priority queue](../Priority%20Queue/) that's built on a heap.
 
 ## The code
 

From bdb1b157cc2698b3e211069475399ef19958261e Mon Sep 17 00:00:00 2001
From: Jacopo <jmangia@kywix.com>
Date: Mon, 3 Apr 2017 21:26:14 +0100
Subject: [PATCH 069/862] Minimum Coin Change Problem - Dynamic Programming in
 Swift

---
 MinimumCoinChange/LICENSE                     | 201 ++++++++++++++++++
 MinimumCoinChange/Package.swift               |   7 +
 MinimumCoinChange/README.md                   |  41 ++++
 .../Sources/MinimumCoinChange.swift           |  76 +++++++
 MinimumCoinChange/Tests/LinuxMain.swift       |   6 +
 .../MinimumCoinChangeTests.swift              |  21 ++
 MinimumCoinChange/eurocoins.gif               | Bin 0 -> 90051 bytes
 7 files changed, 352 insertions(+)
 create mode 100755 MinimumCoinChange/LICENSE
 create mode 100644 MinimumCoinChange/Package.swift
 create mode 100755 MinimumCoinChange/README.md
 create mode 100644 MinimumCoinChange/Sources/MinimumCoinChange.swift
 create mode 100644 MinimumCoinChange/Tests/LinuxMain.swift
 create mode 100644 MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
 create mode 100644 MinimumCoinChange/eurocoins.gif

diff --git a/MinimumCoinChange/LICENSE b/MinimumCoinChange/LICENSE
new file mode 100755
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--- /dev/null
+++ b/MinimumCoinChange/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/MinimumCoinChange/Package.swift b/MinimumCoinChange/Package.swift
new file mode 100644
index 000000000..749073782
--- /dev/null
+++ b/MinimumCoinChange/Package.swift
@@ -0,0 +1,7 @@
+// swift-tools-version:3.1
+
+import PackageDescription
+
+let package = Package(
+    name: "MinimumCoinChange"
+)
diff --git a/MinimumCoinChange/README.md b/MinimumCoinChange/README.md
new file mode 100755
index 000000000..c9cd71cd1
--- /dev/null
+++ b/MinimumCoinChange/README.md
@@ -0,0 +1,41 @@
+# Minimum Coin Change
+Minimum Coin Change problem algorithm implemented in Swift comparing dynamic programming algorithm design to traditional greedy approach.
+
+Written for Swift Algorithm Club by Jacopo Mangiavacchi
+
+![Coins](eurocoins.gif)
+
+# Introduction
+
+In the traditional coin change problem you have to find all the different ways to change some given money in a particular amount of coins using a given amount of set of coins (i.e. 1 cent, 2 cents, 5 cents, 10 cents etc.).
+
+For example using Euro cents the total of 4 cents value of money can be changed in these possible ways:
+
+- Four 1 cent coins
+- Two 2 cent coins
+- One 2 cent coin and two 1 cent coins
+
+The minimum coin change problem is a variation of the generic coin change problem where you need to find the best option for changing the money returning the less number of coins.
+
+For example using Euro cents the best possible change for 4 cents are two 2 cent coins with a total of two coins.
+
+
+# Greedy Solution
+
+A simple approach for implementing the Minimum Coin Change algorithm in a very efficient way is to start subtracting from the input value the greater possible coin value from the given amount of set of coins available and iterate subtracting the next greater possible coin value on the resulting difference.
+
+For example from the total of 4 Euro cents of the example above you can subtract initially 2 cents as  the other biggest coins value (from 5 cents to above) are to bigger for the current 4 Euro cent value. Once used the first 2 cents coin you iterate again with the same logic for the rest of 2 cents and select another 2 cents coin and finally return the two 2 cents coins as the best change.
+
+Most of the time the result for this greedy approach is optimal but for some set of coins the result will not be the optimal.
+
+Indeed, if we use the a set of these three different coins set with values 1, 3 and 4 and execute this  greedy algorithm for asking the best change for the value 6 we will get one coin of 4 and two coins of 1 instead of two coins of 3.
+
+
+# Dynamic Programming Solution
+
+A classic dynamic programming strategy will iterate selecting in order a possible coin from the given amount of set of coins and finding using recursive calls the minimum coin change on the difference from the passed value and the selected coin. For any interaction the algorithm select from all possible combinations the one with the less number of coins used.
+
+The dynamic programming approach will always select the optimal change but it will require a number of steps that is at least quadratic in the goal amount to change.
+
+In this Swift implementation in order to optimize the overall performance we use an internal data structure for caching the result for best minimum coin change for previous values.
+
diff --git a/MinimumCoinChange/Sources/MinimumCoinChange.swift b/MinimumCoinChange/Sources/MinimumCoinChange.swift
new file mode 100644
index 000000000..db7edecbe
--- /dev/null
+++ b/MinimumCoinChange/Sources/MinimumCoinChange.swift
@@ -0,0 +1,76 @@
+//
+//  Minimum Coin Change Problem 
+//  Compare Greedy Algorithm and Dynamic Programming Algorithm in Swift
+//
+//  Created by Jacopo Mangiavacchi on 04/03/17.
+//
+
+import Foundation
+
+public struct MinimumCoinChange {
+    private let sortedCoinSet: [Int]
+    private var cache: [Int : [Int]]
+    
+    public init(coinSet: [Int]) {
+        self.sortedCoinSet = coinSet.sorted(by: { $0 > $1} )
+        self.cache = [:]
+    }
+
+    //Greedy Algorithm
+    public func changeGreedy(_ value: Int) -> [Int] {
+        var change:  [Int] = []
+        var newValue = value
+        
+        for coin in sortedCoinSet {
+            while newValue - coin >= 0 {
+                change.append(coin)
+                newValue -= coin
+            }
+
+            if newValue  == 0 {
+                break
+            }
+        }
+        
+        return change
+    }
+
+    //Dynamic Programming Algorithm
+    public mutating func changeDynamic(_ value: Int) -> [Int] {
+        if value <= 0 {
+            return []
+        }
+        
+        if let cached = cache[value] {
+            return cached
+        }
+        
+        var change:  [Int] = []
+        
+        var potentialChangeArray: [[Int]] = []
+        
+        for coin in sortedCoinSet {
+            if value - coin >= 0 {
+                var potentialChange: [Int] = []
+                 potentialChange.append(coin)
+                let newPotentialValue = value - coin
+
+                if value  > 0 {
+                    potentialChange.append(contentsOf: changeDynamic(newPotentialValue))
+                }
+
+                //print("value: \(value) coin: \(coin) potentialChange: \(potentialChange)")
+                potentialChangeArray.append(potentialChange)
+            }
+        }
+        
+        if potentialChangeArray.count > 0 {
+            let sortedPotentialChangeArray = potentialChangeArray.sorted(by: { $0.count < $1.count })
+            change = sortedPotentialChangeArray[0]
+        }
+        
+        cache[value] = change
+        return change
+    }
+}
+
diff --git a/MinimumCoinChange/Tests/LinuxMain.swift b/MinimumCoinChange/Tests/LinuxMain.swift
new file mode 100644
index 000000000..db61c6011
--- /dev/null
+++ b/MinimumCoinChange/Tests/LinuxMain.swift
@@ -0,0 +1,6 @@
+import XCTest
+@testable import MinimumCoinChangeTests
+
+XCTMain([
+    testCase(MinimumCoinChangeTests.allTests),
+])
diff --git a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
new file mode 100644
index 000000000..86c9007ba
--- /dev/null
+++ b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
@@ -0,0 +1,21 @@
+import XCTest
+@testable import MinimumCoinChange
+
+class MinimumCoinChangeTests: XCTestCase {
+    func testExample() {
+        var mcc = MinimumCoinChange(coinSet: [1, 2, 5, 10, 20, 25])
+
+        for i in 0..<100 {
+            let greedy = mcc.changeGreedy(i)
+            let dynamic = mcc.changeDynamic(i)
+
+            if greedy.count != dynamic.count {
+                print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
+            }
+        }
+    }
+
+    static var allTests = [
+        ("testExample", testExample),
+    ]
+}
diff --git a/MinimumCoinChange/eurocoins.gif b/MinimumCoinChange/eurocoins.gif
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From 3f7aaa2799db7c94076bb3155a83811a7c596708 Mon Sep 17 00:00:00 2001
From: Weihang Lo <weihanglotw@gmail.com>
Date: Tue, 4 Apr 2017 09:19:14 +0800
Subject: [PATCH 070/862] fix: broken links

---
 AVL Tree/README.markdown                      |  4 +-
 Bounded Priority Queue/README.markdown        |  2 +-
 Count Occurrences/README.markdown             |  6 +--
 Depth-First Search/README.markdown            |  6 +--
 Deque/README.markdown                         | 42 +++++++++----------
 Heap Sort/README.markdown                     |  2 +-
 Huffman Coding/README.markdown                | 28 ++++++-------
 Knuth-Morris-Pratt/README.markdown            | 32 +++++++-------
 Kth Largest Element/README.markdown           |  6 +--
 .../README.markdown                           |  4 +-
 Priority Queue/README.markdown                |  6 +--
 Quicksort/README.markdown                     | 24 +++++------
 Segment Tree/README.markdown                  | 12 +++---
 Selection Sort/README.markdown                | 10 ++---
 14 files changed, 92 insertions(+), 92 deletions(-)

diff --git a/AVL Tree/README.markdown b/AVL Tree/README.markdown
index a9218203a..c8d8d4628 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -53,7 +53,7 @@ For the rotation we're using the terminology:
 * *RotationSubtree* - subtree of the *Pivot* upon the side of rotation
 * *OppositeSubtree* - subtree of the *Pivot* opposite the side of rotation
 
-Let take an example of balancing the unbalanced tree using *Right* (clockwise direction) rotation: 
+Let take an example of balancing the unbalanced tree using *Right* (clockwise direction) rotation:
 
 ![Rotation1](Images/RotationStep1.jpg) ![Rotation2](Images/RotationStep2.jpg) ![Rotation3](Images/RotationStep3.jpg)
 
@@ -76,7 +76,7 @@ Insertion never needs more than 2 rotations. Removal might require up to __log(n
 
 ## The code
 
-Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary search tree](../Binary Search Tree/) stuff. You'll find this in any implementation of a binary search tree. For example, searching the tree is exactly the same. The only things that an AVL tree does slightly differently are inserting and deleting the nodes.
+Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary search tree](../Binary%20Search%20Tree/) stuff. You'll find this in any implementation of a binary search tree. For example, searching the tree is exactly the same. The only things that an AVL tree does slightly differently are inserting and deleting the nodes.
 
 > **Note:** If you're a bit fuzzy on the regular operations of a binary search tree, I suggest you [catch up on those first](../Binary%20Search%20Tree/). It will make the rest of the AVL tree easier to understand.
 
diff --git a/Bounded Priority Queue/README.markdown b/Bounded Priority Queue/README.markdown
index 4e4c89272..8cbaa85b2 100644
--- a/Bounded Priority Queue/README.markdown	
+++ b/Bounded Priority Queue/README.markdown	
@@ -26,7 +26,7 @@ Suppose that we wish to insert the element `G` with priority 0.1 into this BPQ.
 
 ## Implementation
 
-While a [heap](../Heap/) may be a really simple implementation for a priority queue, a sorted [linked list](../Linked List/) allows for **O(k)** insertion and **O(1)** deletion, where **k** is the bounding number of elements.
+While a [heap](../Heap/) may be a really simple implementation for a priority queue, a sorted [linked list](../Linked%20List/) allows for **O(k)** insertion and **O(1)** deletion, where **k** is the bounding number of elements.
 
 Here's how you could implement it in Swift:
 
diff --git a/Count Occurrences/README.markdown b/Count Occurrences/README.markdown
index 4c65c4219..85b77d2d0 100644
--- a/Count Occurrences/README.markdown	
+++ b/Count Occurrences/README.markdown	
@@ -36,7 +36,7 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     }
     return low
   }
-  
+
   func rightBoundary() -> Int {
     var low = 0
     var high = a.count
@@ -50,12 +50,12 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
     }
     return low
   }
-  
+
   return rightBoundary() - leftBoundary()
 }
 ```
 
-Notice that the helper functions `leftBoundary()` and `rightBoundary()` are very similar to the [binary search](../Binary Search/) algorithm. The big difference is that they don't stop when they find the search key, but keep going.
+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.
 
 To test this algorithm, copy the code to a playground and then do:
 
diff --git a/Depth-First Search/README.markdown b/Depth-First Search/README.markdown
index 9e1a5112d..98a19e0cb 100644
--- a/Depth-First Search/README.markdown	
+++ b/Depth-First Search/README.markdown	
@@ -40,7 +40,7 @@ func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
 }
 ```
 
-Where a [breadth-first search](../Breadth-First Search/) visits all immediate neighbors first, a depth-first search tries to go as deep down the tree or graph as it can.
+Where a [breadth-first search](../Breadth-First%20Search/) visits all immediate neighbors first, a depth-first search tries to go as deep down the tree or graph as it can.
 
 Put this code in a playground and test it like so:
 
@@ -71,13 +71,13 @@ print(nodesExplored)
 ```
 
 This will output: `["a", "b", "d", "e", "h", "f", "g", "c"]`
-   
+
 ## What is DFS good for?
 
 Depth-first search can be used to solve many problems, for example:
 
 * Finding connected components of a sparse graph
-* [Topological sorting](../Topological Sort/) of nodes in a graph
+* [Topological sorting](../Topological%20Sort/) of nodes in a graph
 * Finding bridges of a graph (see: [Bridges](https://en.wikipedia.org/wiki/Bridge_(graph_theory)#Bridge-finding_algorithm))
 * And lots of others!
 
diff --git a/Deque/README.markdown b/Deque/README.markdown
index 67a734576..fda1de5f8 100644
--- a/Deque/README.markdown
+++ b/Deque/README.markdown
@@ -9,23 +9,23 @@ Here is a very basic implementation of a deque in Swift:
 ```swift
 public struct Deque<T> {
   private var array = [T]()
-  
+
   public var isEmpty: Bool {
     return array.isEmpty
   }
-  
+
   public var count: Int {
     return array.count
   }
-  
+
   public mutating func enqueue(_ element: T) {
     array.append(element)
   }
-  
+
   public mutating func enqueueFront(_ element: T) {
     array.insert(element, atIndex: 0)
   }
-  
+
   public mutating func dequeue() -> T? {
     if isEmpty {
       return nil
@@ -33,7 +33,7 @@ public struct Deque<T> {
       return array.removeFirst()
     }
   }
-  
+
   public mutating func dequeueBack() -> T? {
     if isEmpty {
       return nil
@@ -41,11 +41,11 @@ public struct Deque<T> {
       return array.removeLast()
     }
   }
-  
+
   public func peekFront() -> T? {
     return array.first
   }
-  
+
   public func peekBack() -> T? {
     return array.last
   }
@@ -73,7 +73,7 @@ deque.dequeue()       // 5
 This particular implementation of `Deque` is simple but not very efficient. Several operations are **O(n)**, notably `enqueueFront()` and `dequeue()`. I've included it only to show the principle of what a deque does.
 
 ## A more efficient version
-  
+
 The reason that `dequeue()` and `enqueueFront()` are **O(n)** is that they work on the front of the array. If you remove an element at the front of an array, what happens is that all the remaining elements need to be shifted in memory.
 
 Let's say the deque's array contains the following items:
@@ -92,7 +92,7 @@ Likewise, inserting an element at the front of the array is expensive because it
 
 First, the elements `2`, `3`, and `4` are moved up by one position in the computer's memory, and then the new element `5` is inserted at the position where `2` used to be.
 
-Why is this not an issue at for `enqueue()` and `dequeueBack()`? Well, these operations are performed at the end of the array. The way resizable arrays are implemented in Swift is by reserving a certain amount of free space at the back. 
+Why is this not an issue at for `enqueue()` and `dequeueBack()`? Well, these operations are performed at the end of the array. The way resizable arrays are implemented in Swift is by reserving a certain amount of free space at the back.
 
 Our initial array `[ 1, 2, 3, 4]` actually looks like this in memory:
 
@@ -120,26 +120,26 @@ public struct Deque<T> {
   private var head: Int
   private var capacity: Int
   private let originalCapacity:Int
-  
+
   public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
     originalCapacity = self.capacity
     array = [T?](repeating: nil, count: capacity)
     head = capacity
   }
-  
+
   public var isEmpty: Bool {
     return count == 0
   }
-  
+
   public var count: Int {
     return array.count - head
   }
-  
+
   public mutating func enqueue(_ element: T) {
     array.append(element)
   }
-  
+
   public mutating func enqueueFront(_ element: T) {
     // this is explained below
   }
@@ -155,7 +155,7 @@ public struct Deque<T> {
       return array.removeLast()
     }
   }
-  
+
   public func peekFront() -> T? {
     if isEmpty {
       return nil
@@ -163,7 +163,7 @@ public struct Deque<T> {
       return array[head]
     }
   }
-  
+
   public func peekBack() -> T? {
     if isEmpty {
       return nil
@@ -176,7 +176,7 @@ public struct Deque<T> {
 
 It still largely looks the same -- `enqueue()` and `dequeueBack()` haven't changed -- but there are also a few important differences. The array now stores objects of type `T?` instead of just `T` because we need some way to mark array elements as being empty.
 
-The `init` method allocates a new array that contains a certain number of `nil` values. This is the free room we have to work with at the beginning of the array. By default this creates 10 empty spots. 
+The `init` method allocates a new array that contains a certain number of `nil` values. This is the free room we have to work with at the beginning of the array. By default this creates 10 empty spots.
 
 The `head` variable is the index in the array of the front-most object. Since the queue is currently empty, `head` points at an index beyond the end of the array.
 
@@ -219,7 +219,7 @@ Notice how the array has resized itself. There was no room to add the `1`, so Sw
 	                          |
 	                          head
 
-> **Note:** You won't see those empty spots at the back of the array when you `print(deque.array)`. This is because Swift hides them from you. Only the ones at the front of the array show up. 
+> **Note:** You won't see those empty spots at the back of the array when you `print(deque.array)`. This is because Swift hides them from you. Only the ones at the front of the array show up.
 
 The `dequeue()` method does the opposite of `enqueueFront()`, it reads the value at `head`, sets the array element back to `nil`, and then moves `head` one position to the right:
 
@@ -250,7 +250,7 @@ There is one tiny problem... If you enqueue a lot of objects at the front, you'r
   }
 ```
 
-If `head` equals 0, there is no room left at the front. When that happens, we add a whole bunch of new `nil` elements to the array. This is an **O(n)** operation but since this cost gets divided over all the `enqueueFront()`s, each individual call to `enqueueFront()` is still **O(1)** on average. 
+If `head` equals 0, there is no room left at the front. When that happens, we add a whole bunch of new `nil` elements to the array. This is an **O(n)** operation but since this cost gets divided over all the `enqueueFront()`s, each individual call to `enqueueFront()` is still **O(1)** on average.
 
 > **Note:** We also multiply the capacity by 2 each time this happens, so if your queue grows bigger and bigger, the resizing happens less often. This is also what Swift arrays automatically do at the back.
 
@@ -302,7 +302,7 @@ This way we can strike a balance between fast enqueuing and dequeuing at the fro
 
 ## See also
 
-Other ways to implement deque are by using a [doubly linked list](../Linked List/), a [circular buffer](../Ring Buffer/), or two [stacks](../Stack/) facing opposite directions.
+Other ways to implement deque are by using a [doubly linked list](../Linked%20List/), a [circular buffer](../Ring%20Buffer/), or two [stacks](../Stack/) facing opposite directions.
 
 [A fully-featured deque implementation in Swift](https://github.com/lorentey/Deque)
 
diff --git a/Heap Sort/README.markdown b/Heap Sort/README.markdown
index 5f047f82b..7fdd8d2ca 100644
--- a/Heap Sort/README.markdown	
+++ b/Heap Sort/README.markdown	
@@ -40,7 +40,7 @@ And fix up the heap to make it valid max-heap again:
 
 As you can see, the largest items are making their way to the back. We repeat this process until we arrive at the root node and then the whole array is sorted.
 
-> **Note:** This process is very similar to [selection sort](../Selection Sort/), 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.
+> **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.
 
diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 6b2c0d245..4e6f75514 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -16,7 +16,7 @@ If you count how often each byte appears, you can clearly see that some bytes oc
 	    c: 2	              p: 1
 	    r: 2	              e: 1
 	    n: 2	              i: 1
-	
+
 We can assign bit strings to each of these bytes. The more common a byte is, the fewer bits we assign to it. We might get something like this:
 
 	space: 5    010           u: 1    11001
@@ -30,12 +30,12 @@ We can assign bit strings to each of these bytes. The more common a byte is, the
 
 Now if we replace the original bytes with these bit strings, the compressed output becomes:
 
-	101 000 010 111 11001 0011 10001 010 0010 000 1001 11010 101 
+	101 000 010 111 11001 0011 10001 010 0010 000 1001 11010 101
 	s   o   _   m   u     c    h     _   w    o   r    d     s
-	
+
 	010 0010 000 0010 010 111 11011 0110 01111 010 0011 000 111
 	_   w    o   w    _   m   a     n    y     _   c    o   m
-	
+
 	11000 1001 01110 101 101 10000 000 0110 0
 	p     r    e     s   s   i     o   n
 
@@ -57,7 +57,7 @@ The edges between the nodes either say "1" or "0". These correspond to the bit-e
 
 Compression is then a matter of looping through the input bytes, and for each byte traverse the tree from the root node to that byte's leaf node. Every time we take a left branch, we emit a 1-bit. When we take a right branch, we emit a 0-bit.
 
-For example, to go from the root node to `c`, we go right (`0`), right again (`0`), left (`1`), and left again (`1`). So the Huffman code for `c` is `0011`. 
+For example, to go from the root node to `c`, we go right (`0`), right again (`0`), left (`1`), and left again (`1`). So the Huffman code for `c` is `0011`.
 
 Decompression works in exactly the opposite way. It reads the compressed bits one-by-one and traverses the tree until we get to a leaf node. The value of that leaf node is the uncompressed byte. For example, if the bits are `11010`, we start at the root and go left, left again, right, left, and a final right to end up at `d`.
 
@@ -137,7 +137,7 @@ Here are the definitions we need:
 ```swift
 class Huffman {
   typealias NodeIndex = Int
- 
+
   struct Node {
     var count = 0
     var index: NodeIndex = -1
@@ -152,7 +152,7 @@ class Huffman {
 }
 ```
 
-The tree structure is stored in the `tree` array and will be made up of `Node` objects. Since this is a [binary tree](../Binary Tree/), each node needs two children, `left` and `right`, and a reference back to its `parent` node. Unlike a typical binary tree, however, these nodes don't to use pointers to refer to each other but simple integer indices in the `tree` array. (We also store the array `index` of the node itself; the reason for this will become clear later.)
+The tree structure is stored in the `tree` array and will be made up of `Node` objects. Since this is a [binary tree](../Binary%20Tree/), each node needs two children, `left` and `right`, and a reference back to its `parent` node. Unlike a typical binary tree, however, these nodes don't to use pointers to refer to each other but simple integer indices in the `tree` array. (We also store the array `index` of the node itself; the reason for this will become clear later.)
 
 Note that `tree` currently has room for 256 entries. These are for the leaf nodes because there are 256 possible byte values. Of course, not all of those may end up being used, depending on the input data. Later, we'll add more nodes as we build up the actual tree. For the moment there isn't a tree yet, just 256 separate leaf nodes with no connections between them. All the node counts are 0.
 
@@ -183,7 +183,7 @@ Instead, we'll add a method to export the frequency table without all the pieces
     var byte: UInt8 = 0
     var count = 0
   }
-  
+
   func frequencyTable() -> [Freq] {
     var a = [Freq]()
     for i in 0..<256 where tree[i].count > 0 {
@@ -209,7 +209,7 @@ To build the tree, we do the following:
 2. Create a new parent node that links these two nodes together.
 3. This repeats over and over until only one node with no parent remains. This becomes the root node of the tree.
 
-This is an ideal place to use a [priority queue](../Priority Queue/). A priority queue is a data structure that is optimized so that finding the minimum value is always very fast. Here, we repeatedly need to find the node with the smallest count.
+This is an ideal place to use a [priority queue](../Priority%20Queue/). A priority queue is a data structure that is optimized so that finding the minimum value is always very fast. Here, we repeatedly need to find the node with the smallest count.
 
 The function `buildTree()` then becomes:
 
@@ -233,7 +233,7 @@ The function `buildTree()` then becomes:
 
       tree[node1.index].parent = parentNode.index    // 4
       tree[node2.index].parent = parentNode.index
-      
+
       queue.enqueue(parentNode)                      // 5
     }
 
@@ -286,7 +286,7 @@ Now that we know how to build the compression tree from the frequency table, we
   }
 ```
 
-This first calls `countByteFrequency()` to build the frequency table, then `buildTree()` to put together the compression tree. It also creates a `BitWriter` object for writing individual bits. 
+This first calls `countByteFrequency()` to build the frequency table, then `buildTree()` to put together the compression tree. It also creates a `BitWriter` object for writing individual bits.
 
 Then it loops through the entire input and for each byte calls `traverseTree()`. That method will step through the tree nodes and for each node write a 1 or 0 bit. Finally, we return the `BitWriter`'s data object.
 
@@ -309,7 +309,7 @@ The interesting stuff happens in `traverseTree()`. This is a recursive method:
   }
 ```
 
-When we call this method from `compressData()`, the `nodeIndex` parameter is the array index of the leaf node for the byte that we're about to encode. This method recursively walks the tree from a leaf node up to the root, and then back again. 
+When we call this method from `compressData()`, the `nodeIndex` parameter is the array index of the leaf node for the byte that we're about to encode. This method recursively walks the tree from a leaf node up to the root, and then back again.
 
 As we're going back from the root to the leaf node, we write a 1 bit or a 0 bit for every node we encounter. If a child is the left node, we emit a 1; if it's the right node, we emit a 0.
 
@@ -395,10 +395,10 @@ Here's how you would use the decompression method:
 
 ```swift
   let frequencyTable = huffman1.frequencyTable()
-  
+
   let huffman2 = Huffman()
   let decompressedData = huffman2.decompressData(compressedData, frequencyTable: frequencyTable)
-  
+
   let s2 = String(data: decompressedData, encoding: NSUTF8StringEncoding)!
 ```
 
diff --git a/Knuth-Morris-Pratt/README.markdown b/Knuth-Morris-Pratt/README.markdown
index f01b87b3d..95fdea9e9 100644
--- a/Knuth-Morris-Pratt/README.markdown
+++ b/Knuth-Morris-Pratt/README.markdown
@@ -1,9 +1,9 @@
 # Knuth-Morris-Pratt String Search
 
-Goal: Write a linear-time string matching algorithm in Swift that returns the indexes of all the occurrencies of a given pattern. 
- 
+Goal: Write a linear-time string matching algorithm in Swift that returns the indexes of all the occurrencies of a given pattern.
+
 In other words, we want to implement an `indexesOf(pattern: String)` extension on `String` that returns an array `[Int]` of integers, representing all occurrences' indexes of the search pattern, or `nil` if the pattern could not be found inside the string.
- 
+
 For example:
 
 ```swift
@@ -16,7 +16,7 @@ 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 idea behind the algorithm is not too different from the [naive string search](../Brute-Force String Search/) 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.
+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.
 
 The pre-processing stage produces an array (called `suffixPrefix` in the code) of integers in which every element `suffixPrefix[i]` records the length of the longest proper suffix of `P[0...i]` (where `P` is the pattern) that matches a prefix of `P`. In other words, `suffixPrefix[i]` is the longest proper substring of `P` that ends at position `i` and that is a prefix of `P`. Just a quick example. Consider `P = "abadfryaabsabadffg"`, then `suffixPrefix[4] = 0`, `suffixPrefix[9] = 2`, `suffixPrefix[14] = 4`.
 There are different ways to obtain the values of `SuffixPrefix` array. We will use the method based on the [Z-Algorithm](../Z-Algorithm/). This function takes in input the pattern and produces an array of integers. Each element represents the length of the longest substring starting at position `i` of `P` and that matches a prefix of `P`. You can notice that the two arrays are similar, they record the same informations but on the different places. We only have to find a method to map `Z[i]` to `suffixPrefix[j]`. It is not that difficult and this is the code that will do for us:
@@ -93,10 +93,10 @@ extension String {
 ```
 
 Let's make an example reasoning with the code above. Let's consider the string `P = ACTGACTA"`, the consequentially obtained `suffixPrefix` array equal to `[0, 0, 0, 0, 0, 0, 3, 1]`, and the text `T = "GCACTGACTGACTGACTAG"`. The algorithm begins with the text and the pattern aligned like below. We have to compare `T[0]` with `P[0]`.  
-  
+
                               1       
                     0123456789012345678
-    text:           GCACTGACTGACTGACTAG 
+    text:           GCACTGACTGACTGACTAG
     textIndex:      ^
     pattern:        ACTGACTA
     patternIndex:   ^
@@ -104,54 +104,54 @@ Let's make an example reasoning with the code above. Let's consider the string `
     suffixPrefix:   00000031
 
 We have a mismatch and we move on comparing `T[1]` and `P[0]`. We have to check if a pattern occurrence is present but there is not. So, we have to shift the pattern right and by doing so we have to check `suffixPrefix[1 - 1]`. Its value is `0` and we restart by comparing `T[1]` with `P[0]`. Again a mismath occurs, so we go on with `T[2]` and `P[0]`.
-  
+
                               1      
                     0123456789012345678
     text:           GCACTGACTGACTGACTAG
-    textIndex:        ^ 
+    textIndex:        ^
     pattern:          ACTGACTA
     patternIndex:     ^
     suffixPrefix:     00000031
 
 This time we have a match. And it continues until position `8`. Unfortunately the length of the match is not equal to the pattern length, we cannot report an occurrence. But we are still lucky because we can use the values computed in the `suffixPrefix` array now. In fact, the length of the match is `7`, and if we look at the element `suffixPrefix[7 - 1]` we discover that is `3`. This information tell us that that the prefix of `P` matches the suffix of the susbtring `T[0...8]`. So the `suffixPrefix` array guarantees us that the two substring match and that we do not have to compare their characters, so we can shift right the pattern for more than one character!
 The comparisons restart from `T[9]` and `P[3]`.  
-      
+
                               1       
                     0123456789012345678
-    text:           GCACTGACTGACTGACTAG 
+    text:           GCACTGACTGACTGACTAG
     textIndex:               ^
     pattern:              ACTGACTA
     patternIndex:            ^
     suffixPrefix:         00000031
 
 They match so we continue the compares until position `13` where a misatch occurs beetwen charcter `G` and `A`. Just like before, we are lucky and we can use the `suffixPrefix` array to shift right the pattern.
-      
+
                               1       
                     0123456789012345678
-    text:           GCACTGACTGACTGACTAG 
+    text:           GCACTGACTGACTGACTAG
     textIndex:                   ^
     pattern:                  ACTGACTA
     patternIndex:                ^
     suffixPrefix:             00000031
 
 Again, we have to compare. But this time the comparisons finally take us to an occurrence, at position `17 - 7 = 10`.
-      
+
                               1       
                     0123456789012345678
-    text:           GCACTGACTGACTGACTAG 
+    text:           GCACTGACTGACTGACTAG
     textIndex:                       ^
     pattern:                  ACTGACTA
     patternIndex:                    ^
     suffixPrefix:             00000031
 
 The algorithm than tries to compare `T[18]` with `P[1]` (because we used the element `suffixPrefix[8 - 1] = 1`) but it fails and at the next iteration it ends its work.
- 
+
 
 The pre-processing stage involves only the pattern. The running time of the Z-Algorithm is linear and takes `O(n)`, where `n` is the length of the pattern `P`. After that, the search stage does not "overshoot" the length of the text `T` (call it `m`). It can be be proved that number of comparisons of the search stage is bounded by `2 * m`. The final running time of the Knuth-Morris-Pratt algorithm is `O(n + m)`.
 
 
 > **Note:** To execute the code in the [KnuthMorrisPratt.swift](./KnuthMorrisPratt.swift) you have to copy the [ZAlgorithm.swift](../Z-Algorithm/ZAlgorithm.swift) file contained in the [Z-Algorithm](../Z-Algorithm/) folder. The [KnuthMorrisPratt.playground](./KnuthMorrisPratt.playground) already includes the definition of the `Zeta` function.
 
-Credits: This code is based on the handbook ["Algorithm on String, Trees and Sequences: Computer Science and Computational Biology"](https://books.google.it/books/about/Algorithms_on_Strings_Trees_and_Sequence.html?id=Ofw5w1yuD8kC&redir_esc=y) by Dan Gusfield, Cambridge University Press, 1997. 
+Credits: This code is based on the handbook ["Algorithm on String, Trees and Sequences: Computer Science and Computational Biology"](https://books.google.it/books/about/Algorithms_on_Strings_Trees_and_Sequence.html?id=Ofw5w1yuD8kC&redir_esc=y) by Dan Gusfield, Cambridge University Press, 1997.
 
 *Written for Swift Algorithm Club by Matteo Dunnhofer*
diff --git a/Kth Largest Element/README.markdown b/Kth Largest Element/README.markdown
index d50d691a1..53bec1c1c 100644
--- a/Kth Largest Element/README.markdown	
+++ b/Kth Largest Element/README.markdown	
@@ -44,7 +44,7 @@ Of course, if you were looking for the k-th *smallest* element, you'd use `a[k]`
 
 ## A faster solution
 
-There is a clever algorithm that combines the ideas of [binary search](../Binary Search/) and [quicksort](../Quicksort/) to arrive at an **O(n)** solution.
+There is a clever algorithm that combines the ideas of [binary search](../Binary%20Search/) and [quicksort](../Quicksort/) to arrive at an **O(n)** solution.
 
 Recall that binary search splits the array in half over and over again, to quickly narrow in on the value you're searching for. That's what we'll do here too.
 
@@ -86,7 +86,7 @@ The following function implements these ideas:
 ```swift
 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 {
     let pivotIndex = random(min: low, max: high)
     swap(&a, pivotIndex, high)
@@ -120,7 +120,7 @@ public func randomizedSelect<T: Comparable>(array: [T], order k: Int) -> T {
       return a[low]
     }
   }
-  
+
   precondition(a.count > 0)
   return randomizedSelect(&a, 0, a.count - 1, k)
 }
diff --git a/Minimum Spanning Tree (Unweighted)/README.markdown b/Minimum Spanning Tree (Unweighted)/README.markdown
index cfd29c987..23f18c335 100644
--- a/Minimum Spanning Tree (Unweighted)/README.markdown	
+++ b/Minimum Spanning Tree (Unweighted)/README.markdown	
@@ -16,7 +16,7 @@ Drawn as a more conventional tree it looks like this:
 
 ![An actual tree](Images/Tree.png)
 
-To calculate the minimum spanning tree on an unweighted graph, we can use the [breadth-first search](../Breadth-First Search/) algorithm. Breadth-first search starts at a source node and traverses the graph by exploring the immediate neighbor nodes first, before moving to the next level neighbors. If we tweak this algorithm by selectively removing edges, then it can convert the graph into the minimum spanning tree.
+To calculate the minimum spanning tree on an unweighted graph, we can use the [breadth-first search](../Breadth-First%20Search/) algorithm. Breadth-first search starts at a source node and traverses the graph by exploring the immediate neighbor nodes first, before moving to the next level neighbors. If we tweak this algorithm by selectively removing edges, then it can convert the graph into the minimum spanning tree.
 
 Let's step through the example. We start with the source node `a`, add it to a queue and mark it as visited.
 
@@ -185,6 +185,6 @@ print(minimumSpanningTree) // [node: a edges: ["b", "h"]]
                            // [node: h edges: ["g", "i"]]
 ```
 
-> **Note:** On an unweighed graph, any spanning tree is always a minimal spanning tree. This means you can also use a [depth-first search](../Depth-First Search) to find the minimum spanning tree.
+> **Note:** On an unweighed graph, any spanning tree is always a minimal spanning tree. This means you can also use a [depth-first search](../Depth-First%20Search) to find the minimum spanning tree.
 
 *Written by [Chris Pilcher](https://github.com/chris-pilcher) and Matthijs Hollemans*
diff --git a/Priority Queue/README.markdown b/Priority Queue/README.markdown
index 8308ec16f..fbbcaa0f3 100644
--- a/Priority Queue/README.markdown	
+++ b/Priority Queue/README.markdown	
@@ -12,7 +12,7 @@ Examples of algorithms that can benefit from a priority queue:
 
 - Event-driven simulations. Each event is given a timestamp and you want events to be performed in order of their timestamps. The priority queue makes it easy to find the next event that needs to be simulated.
 - Dijkstra's algorithm for graph searching uses a priority queue to calculate the minimum cost.
-- [Huffman coding](../Huffman Coding/) for data compression. This algorithm builds up a compression tree. It repeatedly needs to find the two nodes with the smallest frequencies that do not have a parent node yet.
+- [Huffman coding](../Huffman%20Coding/) for data compression. This algorithm builds up a compression tree. It repeatedly needs to find the two nodes with the smallest frequencies that do not have a parent node yet.
 - A* pathfinding for artificial intelligence.
 - Lots of other places!
 
@@ -31,8 +31,8 @@ Common operations on a priority queue:
 
 There are different ways to implement priority queues:
 
-- As a [sorted array](../Ordered Array/). The most important item is at the end of the array. Downside: inserting new items is slow because they must be inserted in sorted order.
-- As a balanced [binary search tree](../Binary Search Tree/). This is great for making a double-ended priority queue because it implements both "find minimum" and "find maximum" efficiently.
+- As a [sorted array](../Ordered%20Array/). The most important item is at the end of the array. Downside: inserting new items is slow because they must be inserted in sorted order.
+- As a balanced [binary search tree](../Binary%20Search%20Tree/). This is great for making a double-ended priority queue because it implements both "find minimum" and "find maximum" efficiently.
 - As a [heap](../Heap/). The heap is a natural data structure for a priority queue. In fact, the two terms are often used as synonyms. A heap is more efficient than a sorted array because a heap only has to be partially sorted. All heap operations are **O(log n)**.
 
 Here's a Swift priority queue based on a heap:
diff --git a/Quicksort/README.markdown b/Quicksort/README.markdown
index d359ecb5c..e0bd8e604 100644
--- a/Quicksort/README.markdown
+++ b/Quicksort/README.markdown
@@ -14,7 +14,7 @@ func quicksort<T: Comparable>(_ a: [T]) -> [T] {
   let less = a.filter { $0 < pivot }
   let equal = a.filter { $0 == pivot }
   let greater = a.filter { $0 > pivot }
-  
+
   return quicksort(less) + equal + quicksort(greater)
 }
 ```
@@ -30,7 +30,7 @@ Here's how it works. When given an array, `quicksort()` splits it up into three
 
 All the elements less than the pivot go into a new array called `less`. All the elements equal to the pivot go into the `equal` array. And you guessed it, all elements greater than the pivot go into the third array, `greater`. This is why the generic type `T` must be `Comparable`, so we can compare the elements with `<`, `==`, and `>`.
 
-Once we have these three arrays, `quicksort()` recursively sorts the `less` array and the `greater` array, then glues those sorted subarrays back together with the `equal` array to get the final result. 
+Once we have these three arrays, `quicksort()` recursively sorts the `less` array and the `greater` array, then glues those sorted subarrays back together with the `equal` array to get the final result.
 
 ## An example
 
@@ -73,7 +73,7 @@ The `less` array is empty because there was no value smaller than `-1`; the othe
 That `greater` array was:
 
 	[ 3, 2, 5 ]
-	
+
 This works just the same way as before: we pick the middle element `2` as the pivot and fill up the subarrays:
 
 	less:    [ ]
@@ -122,7 +122,7 @@ There is no guarantee that partitioning keeps the elements in the same relative
 
 	[ 3, 0, 5, 2, -1, 1, 8, 8, 14, 26, 10, 27, 9 ]
 
-The only guarantee is that to the left of the pivot are all the smaller elements and to the right are all the larger elements. Because partitioning can change the original order of equal elements, quicksort does not produce a "stable" sort (unlike [merge sort](../Merge Sort/), for example). Most of the time that's not a big deal.
+The only guarantee is that to the left of the pivot are all the smaller elements and to the right are all the larger elements. Because partitioning can change the original order of equal elements, quicksort does not produce a "stable" sort (unlike [merge sort](../Merge%20Sort/), for example). Most of the time that's not a big deal.
 
 ## Lomuto's partitioning scheme
 
@@ -133,7 +133,7 @@ Here's an implementation of Lomuto's partitioning scheme in Swift:
 ```swift
 func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
   let pivot = a[high]
-  
+
   var i = low
   for j in low..<high {
     if a[j] <= pivot {
@@ -141,7 +141,7 @@ func partitionLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int
       i += 1
     }
   }
-  
+
   (a[i], a[high]) = (a[high], a[i])
   return i
 }
@@ -168,7 +168,7 @@ After partitioning, the array looks like this:
 
 The variable `p` contains the return value of the call to `partitionLomuto()` and is 7. This is the index of the pivot element in the new array (marked with a star).
 
-The left partition goes from 0 to `p-1` and is `[ 0, 3, 2, 1, 5, 8, -1 ]`. The right partition goes from `p+1` to the end, and is `[ 9, 10, 14, 26, 27 ]` (the fact that the right partition is already sorted is a coincidence). 
+The left partition goes from 0 to `p-1` and is `[ 0, 3, 2, 1, 5, 8, -1 ]`. The right partition goes from `p+1` to the end, and is `[ 9, 10, 14, 26, 27 ]` (the fact that the right partition is already sorted is a coincidence).
 
 You may notice something interesting... The value `8` occurs more than once in the array. One of those `8`s did not end up neatly in the middle but somewhere in the left partition. That's a small downside of the Lomuto algorithm as it makes quicksort slower if there are a lot of duplicate elements.
 
@@ -281,11 +281,11 @@ func partitionHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) -> Int {
   let pivot = a[low]
   var i = low - 1
   var j = high + 1
-  
+
   while true {
     repeat { j -= 1 } while a[j] > pivot
     repeat { i += 1 } while a[i] < pivot
-    
+
     if i < j {
       swap(&a[i], &a[j])
     } else {
@@ -309,9 +309,9 @@ The result is:
 
 	[ -1, 0, 3, 8, 2, 5, 1, 27, 10, 14, 9, 8, 26 ]
 
-Note that this time the pivot isn't in the middle at all. Unlike with Lomuto's scheme, the return value is not necessarily the index of the pivot element in the new array. 
+Note that this time the pivot isn't in the middle at all. Unlike with Lomuto's scheme, the return value is not necessarily the index of the pivot element in the new array.
 
-Instead, the array is partitioned into the regions `[low...p]` and `[p+1...high]`. Here, the return value `p` is 6, so the two partitions are `[ -1, 0, 3, 8, 2, 5, 1 ]` and `[ 27, 10, 14, 9, 8, 26 ]`. 
+Instead, the array is partitioned into the regions `[low...p]` and `[p+1...high]`. Here, the return value `p` is 6, so the two partitions are `[ -1, 0, 3, 8, 2, 5, 1 ]` and `[ 27, 10, 14, 9, 8, 26 ]`.
 
 The pivot is placed somewhere inside one of the two partitions, but the algorithm doesn't tell you which one or where. If the pivot value occurs more than once, then some instances may appear in the left partition and others may appear in the right partition.
 
@@ -357,7 +357,7 @@ And again:
 
 And so on...
 
-That's no good, because this pretty much reduces quicksort to the much slower insertion sort. For quicksort to be efficient, it needs to split the array into roughly two halves. 
+That's no good, because this pretty much reduces quicksort to the much slower insertion sort. For quicksort to be efficient, it needs to split the array into roughly two halves.
 
 The optimal pivot for this example would have been `4`, so we'd get:
 
diff --git a/Segment Tree/README.markdown b/Segment Tree/README.markdown
index 15b1a3227..9897c9c3b 100644
--- a/Segment Tree/README.markdown	
+++ b/Segment Tree/README.markdown	
@@ -18,7 +18,7 @@ var a = [ 20, 3, -1, 101, 14, 29, 5, 61, 99 ]
 We want to query this array on the interval from 3 to 7 for the function "sum". That means we do the following:
 
 	101 + 14 + 29 + 5 + 61 = 210
-	
+
 because `101` is at index 3 in the array and `61` is at index 7. So we pass all the numbers between `101` and `61` to the sum function, which adds them all up. If we had used the "min" function, the result would have been `5` because that's the smallest number in the interval from 3 to 7.
 
 Here's naive approach if our array's type is `Int` and **f** is just the sum of two integers:
@@ -43,7 +43,7 @@ The main idea of segment trees is simple: we precalculate some segments in our a
 
 ## Structure of segment tree
 
-A segment tree is just a [binary tree](../Binary Tree/) where each node is an instance of the `SegmentTree` class:
+A segment tree is just a [binary tree](../Binary%20Tree/) where each node is an instance of the `SegmentTree` class:
 
 ```swift
 public class SegmentTree<T> {
@@ -116,18 +116,18 @@ Here's the code:
     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") }
-    
+
     // 2
     if leftChild.rightBound < leftBound {
       return rightChild.query(withLeftBound: leftBound, rightBound: rightBound)
-      
+
     // 3
     } else if rightChild.leftBound > rightBound {
       return leftChild.query(withLeftBound: leftBound, rightBound: rightBound)
-      
+
     // 4
     } else {
       let leftResult = leftChild.query(withLeftBound: leftBound, rightBound: leftChild.rightBound)
diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index e95749d14..cb8ed59c2 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -2,7 +2,7 @@
 
 Goal: Sort an array from low to high (or high to low).
 
-You are given an array of numbers and need to put them in the right order. The selection sort algorithm divides the array into two parts: the beginning of the array is sorted, while the rest of the array consists of the numbers that still remain to be sorted. 
+You are given an array of numbers and need to put them in the right order. The selection sort algorithm divides the array into two parts: the beginning of the array is sorted, while the rest of the array consists of the numbers that still remain to be sorted.
 
 	[ ...sorted numbers... | ...unsorted numbers... ]
 
@@ -23,7 +23,7 @@ It's called a "selection" sort, because at every step you search through the res
 
 ## An example
 
-Let's say the numbers to sort are `[ 5, 8, 3, 4, 6 ]`. We also keep track of where the sorted portion of the array ends, denoted by the `|` symbol. 
+Let's say the numbers to sort are `[ 5, 8, 3, 4, 6 ]`. We also keep track of where the sorted portion of the array ends, denoted by the `|` symbol.
 
 Initially, the sorted portion is empty:
 
@@ -65,14 +65,14 @@ func selectionSort(_ array: [Int]) -> [Int] {
   var a = array                    // 2
 
   for x in 0 ..< a.count - 1 {     // 3
-    
+
     var lowest = x
     for y in x + 1 ..< a.count {   // 4
       if a[y] < a[lowest] {
         lowest = y
       }
     }
-    
+
     if x != lowest {               // 5
       swap(&a[x], &a[lowest])
     }
@@ -108,7 +108,7 @@ The source file [SelectionSort.swift](SelectionSort.swift) has a version of this
 
 ## Performance
 
-Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
+Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble%20Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
 
 [Heap sort](../Heap%20Sort/) uses the same principle as selection sort but has a really fast method for finding the minimum value in the rest of the array. Its performance is **O(n log n)**.
 

From 93cbde7ae9f22d800bb30050b504e13a652ce5a2 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Tue, 4 Apr 2017 02:46:04 -0400
Subject: [PATCH 071/862] Fixed a bug when appending or inserting a node

---
 .../LinkedList.playground/Contents.swift      | 27 ++++++++++---------
 1 file changed, 14 insertions(+), 13 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index ed46331d8..6e743ba89 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -73,7 +73,8 @@ public final class LinkedList<T> {
     self.append(newNode)
   }
   
-  public func append(_ newNode: Node) {
+  public func append(_ node: Node) {
+    let newNode = LinkedListNode(value: node.value)
     if let lastNode = last {
       newNode.previous = lastNode
       lastNode.next = newNode
@@ -104,9 +105,9 @@ public final class LinkedList<T> {
     self.insert(newNode, atIndex: index)
   }
   
-  public func insert(_ newNode: Node, atIndex index: Int) {
+  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
@@ -264,16 +265,16 @@ f    // [Universe, Swifty]
 //list.removeAll()
 //list.isEmpty
 
-list.remove(node: list.first!) // "Hello"
+list.remove(node: list.first!) // "Universe"
 list.count                     // 2
-list[0]                        // "Swift"
-list[1]                        // "World"
+list[0]                        // "Swifty"
+list[1]                        // "Hello"
 
-list.removeLast()              // "World"
+list.removeLast()              // "Hello"
 list.count                     // 1
-list[0]                        // "Swift"
+list[0]                        // "Swifty"
 
-list.remove(atIndex: 0)        // "Swift"
+list.remove(atIndex: 0)        // "Swifty"
 list.count                     // 0
 
 let linkedList: LinkedList<Int> = [1, 2, 3, 4] // [1, 2, 3, 4]
@@ -281,7 +282,7 @@ linkedList.count               // 4
 linkedList[0]                  // 1
 
 // Infer the type from the array
-let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
-listArrayLiteral2.count        // 3
-listArrayLiteral2[0]           // "Swift"
-listArrayLiteral2.removeLast() // "Club"
+let listArrayLiteral2: LinkedList? = ["Swift", "Algorithm", "Club"]
+listArrayLiteral2?.count        // 3
+listArrayLiteral2?[0]           // "Swift"
+listArrayLiteral2?.removeLast()  // "Club"

From 3028c6500f4b2bf8ac4fe899f238b32f946fa879 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Tue, 4 Apr 2017 03:07:05 -0400
Subject: [PATCH 072/862] Corrected comments in playground. Fixed a logic bug
 when inserting/appending a node

---
 Linked List/LinkedList.playground/Contents.swift | 8 ++++----
 Linked List/LinkedList.swift                     | 7 ++++---
 2 files changed, 8 insertions(+), 7 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 6e743ba89..abbb90467 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -282,7 +282,7 @@ linkedList.count               // 4
 linkedList[0]                  // 1
 
 // Infer the type from the array
-let listArrayLiteral2: LinkedList? = ["Swift", "Algorithm", "Club"]
-listArrayLiteral2?.count        // 3
-listArrayLiteral2?[0]           // "Swift"
-listArrayLiteral2?.removeLast()  // "Club"
+let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
+listArrayLiteral2.count        // 3
+listArrayLiteral2[0]           // "Swift"
+listArrayLiteral2.removeLast()  // "Club"
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 53dc77a06..55593cdc9 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -71,7 +71,8 @@ public final class LinkedList<T> {
         self.append(newNode)
     }
     
-    public func append(_ newNode: Node) {
+    public func append(_ node: Node) {
+        let newNode = Node(value: node.value)
         if let lastNode = last {
             newNode.previous = lastNode
             lastNode.next = newNode
@@ -102,9 +103,9 @@ public final class LinkedList<T> {
         self.insert(newNode, atIndex: index)
     }
     
-    public func insert(_ newNode: Node, atIndex index: Int) {
+    public func insert(_ node: Node, atIndex index: Int) {
         let (prev, next) = nodesBeforeAndAfter(index: index)
-        
+        let newNode = Node(value: node.value)
         newNode.previous = prev
         newNode.next = next
         prev?.next = newNode

From b0204d3e0a9a84c8ddb4fdce3fa9dc8276e755ed Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Tue, 4 Apr 2017 10:08:48 +0300
Subject: [PATCH 073/862] Dijkstra's algorithm

---
 .../Dijkstra.playground/Contents.swift        | 122 +++++++
 .../Dijkstra.playground/contents.xcplayground |   4 +
 .../contents.xcworkspacedata                  |   7 +
 Dijkstra Algorithm/README.md                  |  23 ++
 .../Screenshots/screenshot1.jpg               | Bin 0 -> 214771 bytes
 .../Screenshots/screenshot2.jpg               | Bin 0 -> 225916 bytes
 .../Screenshots/screenshot3.jpg               | Bin 0 -> 224243 bytes
 .../Contents.swift                            |  57 ++++
 .../Resources/Pause.png                       | Bin 0 -> 712 bytes
 .../Resources/Start.png                       | Bin 0 -> 1044 bytes
 .../Resources/Stop.png                        | Bin 0 -> 498 bytes
 .../Sources/CustomUI/EdgeRepresentation.swift | 109 ++++++
 .../Sources/CustomUI/ErrorView.swift          |  30 ++
 .../Sources/CustomUI/MyShapeLayer.swift       |   7 +
 .../Sources/CustomUI/RoundedButton.swift      |  20 ++
 .../Sources/CustomUI/VertexView.swift         |  63 ++++
 .../Sources/Graph.swift                       | 308 +++++++++++++++++
 .../Sources/GraphColors.swift                 |  15 +
 .../Sources/GraphView.swift                   | 246 ++++++++++++++
 .../Sources/SimpleObjects/Edge.swift          |  12 +
 .../Sources/SimpleObjects/Vertex.swift        |  62 ++++
 .../Sources/Window.swift                      | 319 ++++++++++++++++++
 .../contents.xcplayground                     |   4 +
 .../contents.xcworkspacedata                  |   7 +
 .../timeline.xctimeline                       |   6 +
 README.markdown                               |   1 +
 26 files changed, 1422 insertions(+)
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/Contents.swift
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/contents.xcplayground
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Dijkstra Algorithm/README.md
 create mode 100644 Dijkstra Algorithm/Screenshots/screenshot1.jpg
 create mode 100644 Dijkstra Algorithm/Screenshots/screenshot2.jpg
 create mode 100644 Dijkstra Algorithm/Screenshots/screenshot3.jpg
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Resources/Pause.png
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Resources/Start.png
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Resources/Stop.png
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphColors.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Edge.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/contents.xcplayground
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/contents.xcworkspacedata
 create mode 100644 Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
new file mode 100644
index 000000000..8d600d577
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -0,0 +1,122 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+import UIKit
+
+open class ProductVertex: Vertex {}
+
+open class Vertex: Hashable, Equatable {
+
+    open var identifier: String!
+    open var neighbors: [(Vertex, Double)] = []
+    open var pathLengthFromStart: Double = Double.infinity
+    open var pathVerticesFromStart: [Vertex] = []
+//    open var point: CGPoint!
+
+    public init(identifier: String/*, point: CGPoint*/) {
+        self.identifier = identifier
+//        self.point = point
+    }
+
+    open var hashValue: Int {
+        return self.identifier.hashValue
+    }
+
+    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
+        if lhs.hashValue == rhs.hashValue {
+            return true
+        }
+        return false
+    }
+
+    open func clearCache() {
+        self.pathLengthFromStart = Double.infinity
+        self.pathVerticesFromStart = []
+    }
+}
+
+public class Dijkstra {
+    private var totalVertices: Set<Vertex>
+
+    public init(vertices: Set<Vertex>) {
+        self.totalVertices = vertices
+    }
+
+    private func clearCache() {
+        self.totalVertices.forEach { $0.clearCache() }
+    }
+
+    public func findShortestPaths(from startVertex: Vertex) {
+        self.clearCache()
+        startVertex.pathLengthFromStart = 0
+        startVertex.pathVerticesFromStart.append(startVertex)
+        var currentVertex: Vertex! = startVertex
+        while currentVertex != nil {
+            totalVertices.remove(currentVertex)
+            let filteredNeighbors = currentVertex.neighbors.filter { totalVertices.contains($0.0) }
+            for neighbor in filteredNeighbors {
+                let neighborVertex = neighbor.0
+                let weight = neighbor.1
+
+                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
+                if theoreticNewWeight < neighborVertex.pathLengthFromStart {
+                    neighborVertex.pathLengthFromStart = theoreticNewWeight
+                    neighborVertex.pathVerticesFromStart = currentVertex.pathVerticesFromStart
+                    neighborVertex.pathVerticesFromStart.append(neighborVertex)
+                }
+            }
+            if totalVertices.isEmpty {
+                currentVertex = nil
+                break
+            }
+            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
+        }
+    }
+}
+
+var _vertices: Set<Vertex> = Set()
+
+func createNotConnectedVertices() {
+    for i in 0..<15 {
+        let vertex = Vertex(identifier: "\(i)")
+        _vertices.insert(vertex)
+    }
+}
+
+func setupConnections() {
+    for vertex in _vertices {
+        let randomEdgesCount = arc4random_uniform(4) + 1
+        for _ in 0..<randomEdgesCount {
+            let randomWeight = Double(arc4random_uniform(10))
+            let neighborVertex = randomVertex(except: vertex)
+            if vertex.neighbors.contains(where: { $0.0 == neighborVertex }) {
+                continue
+            }
+            let neighbor1 = (neighborVertex, randomWeight)
+            let neighbor2 = (vertex, randomWeight)
+            vertex.neighbors.append(neighbor1)
+            neighborVertex.neighbors.append(neighbor2)
+        }
+    }
+}
+
+func randomVertex(except vertex: Vertex) -> Vertex {
+    var newSet = _vertices
+    newSet.remove(vertex)
+    let offset = Int(arc4random_uniform(UInt32(newSet.count)))
+    let index = newSet.index(newSet.startIndex, offsetBy: offset)
+    return newSet[index]
+}
+
+createNotConnectedVertices()
+setupConnections()
+let dijkstra = Dijkstra(vertices: _vertices)
+let offset = Int(arc4random_uniform(UInt32(_vertices.count)))
+let index = _vertices.index(_vertices.startIndex, offsetBy: offset)
+let startVertex = _vertices[index]
+dijkstra.findShortestPaths(from: startVertex)
+let destinationVertex = randomVertex(except: startVertex)
+destinationVertex.pathLengthFromStart
+destinationVertex.pathVerticesFromStart
+
+
diff --git a/Dijkstra Algorithm/Dijkstra.playground/contents.xcplayground b/Dijkstra Algorithm/Dijkstra.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.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/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/contents.xcworkspacedata b/Dijkstra Algorithm/Dijkstra.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.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/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
new file mode 100644
index 000000000..872e9f851
--- /dev/null
+++ b/Dijkstra Algorithm/README.md	
@@ -0,0 +1,23 @@
+# Dijkstra-algorithm
+WWDC 2017 Scholarship Project
+Created by [Taras Nikulin](https://github.com/crabman448)
+
+## About
+Dijkstra's algorithm is used for finding shortest paths from start vertex in graph(with weighted vertices) to all other vertices. 
+More algorithm's description can be found in playground or on wikipedia:
+[Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
+
+To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
+
+If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
+
+## Demo video
+Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
+
+## Screenshots
+
+<img src="Screenshots/screenshot1.jpg" height="400" />
+
+<img src="Screenshots/screenshot2.jpg" height="400" />
+
+<img src="Screenshots/screenshot3.jpg" height="400" />
diff --git a/Dijkstra Algorithm/Screenshots/screenshot1.jpg b/Dijkstra Algorithm/Screenshots/screenshot1.jpg
new file mode 100644
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diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift
new file mode 100644
index 000000000..e4b3e6732
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Contents.swift	
@@ -0,0 +1,57 @@
+/*:
+ ## Dijkstra's algorithm visualization
+ This playground is about the [Dijkstra's algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm).
+ Plyground works in 2 modes:
+ * Auto visualization
+ * Interactive visualization
+
+ */
+import UIKit
+import PlaygroundSupport
+/*:
+ 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.
+ */
+GraphColors.sharedInstance.visitedColor = #colorLiteral(red: 0, green: 0.5898008943, blue: 1, alpha: 1)
+GraphColors.sharedInstance.checkingColor = #colorLiteral(red: 0.9411764741, green: 0.4980392158, blue: 0.3529411852, alpha: 1)
+GraphColors.sharedInstance.defaultEdgeColor = #colorLiteral(red: 0.721568644, green: 0.8862745166, blue: 0.5921568871, alpha: 1)
+GraphColors.sharedInstance.defaultVertexColor = #colorLiteral(red: 0.721568644, green: 0.8862745166, blue: 0.5921568871, alpha: 1)
+
+GraphColors.sharedInstance.mainWindowBackgroundColor = #colorLiteral(red: 0.921431005, green: 0.9214526415, blue: 0.9214410186, alpha: 1)
+GraphColors.sharedInstance.topViewBackgroundColor = #colorLiteral(red: 1, green: 0.4932718873, blue: 0.4739984274, alpha: 1)
+GraphColors.sharedInstance.buttonsBackgroundColor = #colorLiteral(red: 0, green: 0.3285208941, blue: 0.5748849511, alpha: 1)
+GraphColors.sharedInstance.graphBackgroundColor = #colorLiteral(red: 1, green: 1, blue: 1, alpha: 1)
+/*:
+ Now, we need to create some graph. You can create graph with any vertices amount but I aware you from setting up too many, otherwise it will be hard to place all of them nicely on the screen. Also, you can change the animations' duration: slow down or speed up.
+ */
+let graph = Graph(verticesCount: 6)
+graph.interactiveNeighborCheckAnimationDuration = 1.2
+graph.visualizationNeighborCheckAnimationDuration = 1.2
+/*:
+ Now, let's configure the graph's visual representation by passing the virtual graph to our window. For better perception open live view in full screen.
+ */
+let screenBounds = UIScreen.main.bounds
+let frame = CGRect(x: 0, y: 0, width: screenBounds.width * 0.8, height: screenBounds.height * 0.8)
+let window = Window(frame: frame)
+window.configure(graph: graph)
+PlaygroundPage.current.liveView = window
+/*:
+ **Great!**
+
+ Now we have graph on the screen. It is beautiful, isn't it? ;) Before the visualization starts, I recommend you to move vertices around the screen using you finger to be sure that all vertices and edges are properly visible.
+ 
+ And a final step! Before you will see the visualization **(by pressing "Visualization" button),** please, read explanation of how the Dijkstra's algorithm works.
+
+ Algorithm's flow:
+ First of all, this program randomly decides which vertex will be the start one, then the program assigns a zero value to the start vertex path length from the start.
+
+ Then the algorithm repeats following cycle until all vertices are marked as visited.
+ Cycle:
+ 1) From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
+ 2) The algorithm marks picked vertex as visited.
+ 3) The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
+ When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
+ 
+ Now, try yourself at the Dijkstra's algorithm. Press **"Interactive" button.** The program will mark the start vertex as visited and calculate new paths for its neighbors. You have to pick next vertex for the algorithm to check. If you are wrong, you will see a message on the screen.
+ 
+ Good luck and have fun! ;)
+ */
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Resources/Pause.png b/Dijkstra Algorithm/VisualizedDijkstra.playground/Resources/Pause.png
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diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift
new file mode 100644
index 000000000..5ff656dab
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift	
@@ -0,0 +1,109 @@
+import UIKit
+
+public class EdgeRepresentation: Equatable {
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+
+    public private(set)var label: UILabel!
+    public private(set)var layer: MyShapeLayer!
+
+    public init(from vertex1: Vertex, to vertex2: Vertex, weight: Double) {
+        guard let vertex1View = vertex1.view, let vertex2View = vertex2.view else {
+            assertionFailure("passed vertices without configured views")
+            return
+        }
+        let x1 = vertex1View.frame.origin.x
+        let y1 = vertex1View.frame.origin.y
+        let width1 = vertex1View.frame.width
+        let height1 = vertex1View.frame.height
+
+        let x2 = vertex2View.frame.origin.x
+        let y2 = vertex2View.frame.origin.y
+        let width2 = vertex2View.frame.width
+        let height2 = vertex2View.frame.height
+
+        var startPoint: CGPoint
+        var endPoint: CGPoint
+
+        if y1 == y2 {
+            if x1 < x2 {
+                startPoint = CGPoint(x: x1 + width1, y: y1 + height1 / 2)
+                endPoint = CGPoint(x: x2, y: y2 + height2 / 2)
+            } else {
+                startPoint = CGPoint(x: x1, y: y1 + height1 / 2)
+                endPoint = CGPoint(x: x2 + width2, y: y2 + height2 / 2)
+            }
+        } else {
+            startPoint = CGPoint(x: x1 + width1 / 2, y: y1 + height1)
+            endPoint = CGPoint(x: x2 + width2 / 2, y: y2)
+        }
+
+        let arcDiameter: CGFloat = 20
+        var circleOrigin: CGPoint!
+
+        if endPoint.x == startPoint.x {
+            startPoint.y -= 1
+            endPoint.y += 1
+            let x = startPoint.x - arcDiameter / 2
+            let y = startPoint.y + ((endPoint.y - startPoint.y) / 2 * 1.25 - arcDiameter / 2)
+            circleOrigin = CGPoint(x: x, y: y)
+        } else if endPoint.y == startPoint.y {
+            let x = startPoint.x + ((endPoint.x - startPoint.x) / 2 * 1.25 - arcDiameter / 2)
+            let y = startPoint.y + ((endPoint.y - startPoint.y) / 2 * 1.25 - arcDiameter / 2)
+            circleOrigin = CGPoint(x: x, y: y)
+        } else {
+            startPoint.x -= 1
+            endPoint.x += 1
+            startPoint.y -= 1
+            endPoint.y += 1
+            let x = startPoint.x + ((endPoint.x - startPoint.x) / 2 * 1.25 - arcDiameter / 2)
+            let y = startPoint.y + ((endPoint.y - startPoint.y) / 2 * 1.25 - arcDiameter / 2)
+            circleOrigin = CGPoint(x: x, y: y)
+        }
+
+
+        let path = UIBezierPath()
+        path.move(to: startPoint)
+        path.addLine(to: endPoint)
+
+        let label = UILabel(frame: CGRect(origin: circleOrigin, size: CGSize(width: arcDiameter, height: arcDiameter)))
+        label.textAlignment = .center
+        label.backgroundColor = self.graphColors.defaultEdgeColor
+        label.clipsToBounds = true
+        label.adjustsFontSizeToFitWidth = true
+        label.layer.cornerRadius = arcDiameter / 2
+        label.text = ""
+
+        let shapeLayer = MyShapeLayer()
+        shapeLayer.path = path.cgPath
+        shapeLayer.strokeColor = self.graphColors.defaultEdgeColor.cgColor
+        shapeLayer.fillColor = UIColor.clear.cgColor
+        shapeLayer.lineWidth = 2.0
+        shapeLayer.startPoint = startPoint
+        shapeLayer.endPoint = endPoint
+        shapeLayer.actions = ["position" : NSNull(), "bounds" : NSNull(), "path" : NSNull()]
+        self.layer = shapeLayer
+        self.label = label
+        self.label.text = "\(weight)"
+    }
+
+    public func setCheckingColor() {
+        self.layer.strokeColor = self.graphColors.checkingColor.cgColor
+        self.label.backgroundColor = self.graphColors.checkingColor
+    }
+
+    public func setDefaultColor() {
+        self.layer.strokeColor = self.graphColors.defaultEdgeColor.cgColor
+        self.label.backgroundColor = self.graphColors.defaultEdgeColor
+    }
+
+    public func setText(text: String) {
+        self.label.text = text
+    }
+
+    public static func ==(lhs: EdgeRepresentation, rhs: EdgeRepresentation) -> Bool {
+        if lhs.label.hashValue == rhs.label.hashValue && lhs.layer.hashValue == rhs.layer.hashValue {
+            return true
+        }
+        return false
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift
new file mode 100644
index 000000000..69874e5d7
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift	
@@ -0,0 +1,30 @@
+import UIKit
+
+public class ErrorView: UIView {
+    private var label: UILabel!
+    public override init(frame: CGRect) {
+        super.init(frame: frame)
+        self.commonInit()
+    }
+
+    public required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    }
+
+    private func commonInit() {
+        self.backgroundColor = UIColor(red: 242/255, green: 156/255, blue: 84/255, alpha: 1)
+        self.layer.cornerRadius = 10
+
+        let labelFrame = CGRect(x: 10, y: 10, width: self.frame.width - 20, height: self.frame.height - 20)
+        self.label = UILabel(frame: labelFrame)
+        self.label.numberOfLines = 0
+        self.label.adjustsFontSizeToFitWidth = true
+        self.label.textAlignment = .center
+        self.label.textColor = UIColor.white
+        self.addSubview(self.label)
+    }
+
+    public func setText(text: String) {
+        self.label.text = text
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift
new file mode 100644
index 000000000..54147f5e1
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift	
@@ -0,0 +1,7 @@
+import Foundation
+import UIKit
+
+public class MyShapeLayer: CAShapeLayer {
+    public var startPoint: CGPoint?
+    public var endPoint: CGPoint?
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift
new file mode 100644
index 000000000..2647c4525
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift	
@@ -0,0 +1,20 @@
+import UIKit
+
+public class RoundedButton: UIButton {
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+    
+    public override init(frame: CGRect) {
+        super.init(frame: frame)
+        self.commonInit()
+    }
+    
+    public required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    }
+
+    private func commonInit() {
+        self.backgroundColor = self.graphColors.buttonsBackgroundColor
+        self.titleLabel?.adjustsFontSizeToFitWidth = true
+        self.layer.cornerRadius = 7
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift
new file mode 100644
index 000000000..29c971411
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift	
@@ -0,0 +1,63 @@
+import UIKit
+
+public class VertexView: UIButton {
+
+    public var vertex: Vertex?
+    private var idLabel: UILabel!
+    private var pathLengthLabel: UILabel!
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+
+    public required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    }
+
+    public override init(frame: CGRect) {
+        precondition(frame.height == frame.width)
+        precondition(frame.height >= 30)
+        super.init(frame: frame)
+        self.backgroundColor = self.graphColors.defaultVertexColor
+        self.layer.cornerRadius = frame.width / 2
+        self.clipsToBounds = true
+        self.setupIdLabel()
+        self.setupPathLengthFromStartLabel()
+    }
+
+    private func setupIdLabel() {
+        let x: CGFloat = self.frame.width * 0.2
+        let y: CGFloat = 0
+        let width: CGFloat = self.frame.width * 0.6
+        let height: CGFloat = self.frame.height / 2
+        let idLabelFrame = CGRect(x: x, y: y, width: width, height: height)
+
+        self.idLabel = UILabel(frame: idLabelFrame)
+        self.idLabel.textAlignment = .center
+        self.idLabel.adjustsFontSizeToFitWidth = true
+        self.addSubview(self.idLabel)
+    }
+
+    private func setupPathLengthFromStartLabel() {
+        let x: CGFloat = self.frame.width * 0.2
+        let y: CGFloat = self.frame.height / 2
+        let width: CGFloat = self.frame.width * 0.6
+        let height: CGFloat = self.frame.height / 2
+        let pathLengthLabelFrame = CGRect(x: x, y: y, width: width, height: height)
+
+        self.pathLengthLabel = UILabel(frame: pathLengthLabelFrame)
+        self.pathLengthLabel.textAlignment = .center
+        self.pathLengthLabel.adjustsFontSizeToFitWidth = true
+        self.addSubview(self.pathLengthLabel)
+    }
+
+    public func setIdLabel(text: String) {
+        self.idLabel.text = text
+    }
+
+    public func setPathLengthLabel(text: String) {
+        self.pathLengthLabel.text = text
+    }
+
+    public func setLabelsTextColor(color: UIColor) {
+        self.idLabel.textColor = color
+        self.pathLengthLabel.textColor = color
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift
new file mode 100644
index 000000000..0b0b97b92
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
@@ -0,0 +1,308 @@
+import Foundation
+import UIKit
+
+public enum GraphState {
+    case initial
+    case autoVisualization
+    case interactiveVisualization
+    case parsing
+    case completed
+}
+
+public class Graph {
+    private init() { }
+
+    private var verticesCount: UInt!
+    private var _vertices: Set<Vertex> = Set()
+    public weak var delegate: GraphDelegate?
+    public var nextVertices: [Vertex] = []
+    public var state: GraphState = .initial
+    public var pauseVisualization: Bool = false
+    public var stopVisualization: Bool = false
+    public var startVertex: Vertex!
+    public var interactiveNeighborCheckAnimationDuration: Double = 1.8 {
+        didSet {
+            self._interactiveOneSleepDuration = UInt32(self.interactiveNeighborCheckAnimationDuration * 1000000.0 / 3.0)
+        }
+    }
+    private var _interactiveOneSleepDuration: UInt32 = 600000
+
+    public var visualizationNeighborCheckAnimationDuration: Double = 2.25 {
+        didSet {
+            self._visualizationOneSleepDuration = UInt32(self.visualizationNeighborCheckAnimationDuration * 1000000.0 / 3.0)
+        }
+    }
+    private var _visualizationOneSleepDuration: UInt32 = 750000
+
+    public var vertices: Set<Vertex> {
+        return self._vertices
+    }
+
+    public init(verticesCount: UInt) {
+        self.verticesCount = verticesCount
+    }
+
+    public func removeGraph() {
+        self._vertices.removeAll()
+        self.startVertex = nil
+    }
+
+    public func createNewGraph() {
+        guard self._vertices.isEmpty, self.startVertex == nil else {
+            assertionFailure("Clear graph before creating new one")
+            return
+        }
+        self.createNotConnectedVertices()
+        self.setupConnections()
+        let offset = Int(arc4random_uniform(UInt32(self._vertices.count)))
+        let index = self._vertices.index(self._vertices.startIndex, offsetBy: offset)
+        self.startVertex =  self._vertices[index]
+        self.setVertexLevels()
+    }
+    
+    private func clearCache() {
+        self._vertices.forEach { $0.clearCache() }
+    }
+
+    public func reset() {
+        for vertex in self._vertices {
+            vertex.clearCache()
+        }
+    }
+
+    private func createNotConnectedVertices() {
+        for i in 0..<self.verticesCount {
+            let vertex = Vertex(identifier: "\(i)")
+            self._vertices.insert(vertex)
+        }
+    }
+
+    private func setupConnections() {
+        for vertex in self._vertices {
+            let randomEdgesCount = arc4random_uniform(4) + 1
+            for _ in 0..<randomEdgesCount {
+                let randomWeight = Double(arc4random_uniform(10))
+                let neighbor = self.randomVertex(except: vertex)
+                let edge1 = Edge(vertex: neighbor, weight: randomWeight)
+                if vertex.edges.contains(where: { $0.neighbor == neighbor }) {
+                    continue
+                }
+                let edge2 = Edge(vertex: vertex, weight: randomWeight)
+                vertex.edges.append(edge1)
+                neighbor.edges.append(edge2)
+            }
+        }
+    }
+
+    private func randomVertex(except vertex: Vertex) -> Vertex {
+        var newSet = self._vertices
+        newSet.remove(vertex)
+        let offset = Int(arc4random_uniform(UInt32(newSet.count)))
+        let index = newSet.index(newSet.startIndex, offsetBy: offset)
+        return newSet[index]
+    }
+
+    private func setVertexLevels() {
+        self._vertices.forEach { $0.clearLevelInfo() }
+        guard let startVertex = self.startVertex else {
+            assertionFailure()
+            return
+        }
+        var queue: [Vertex] = [startVertex]
+        startVertex.levelChecked = true
+
+        //BFS
+        while !queue.isEmpty {
+            let currentVertex = queue.first!
+            for edge in currentVertex.edges {
+                let neighbor = edge.neighbor
+                if !neighbor.levelChecked {
+                    neighbor.levelChecked = true
+                    neighbor.level = currentVertex.level + 1
+                    queue.append(neighbor)
+                }
+            }
+            queue.removeFirst()
+        }
+    }
+
+    public func findShortestPathsWithVisualization(completion: () -> Void) {
+        self.clearCache()
+        startVertex.pathLengthFromStart = 0
+        startVertex.pathVerticesFromStart.append(self.startVertex)
+        var currentVertex: Vertex! = self.startVertex
+
+        var totalVertices = self._vertices
+
+        breakableLoop: while currentVertex != nil {
+            totalVertices.remove(currentVertex)
+            while self.pauseVisualization == true {
+                if self.stopVisualization == true {
+                    break breakableLoop
+                }
+            }
+            if self.stopVisualization == true {
+                break breakableLoop
+            }
+            DispatchQueue.main.async {
+                currentVertex.setVisitedColor()
+            }
+            usleep(750000)
+            currentVertex.visited = true
+            let filteredEdges = currentVertex.edges.filter { !$0.neighbor.visited }
+            for edge in filteredEdges {
+                let neighbor = edge.neighbor
+                let weight = edge.weight
+                let edgeRepresentation = edge.edgeRepresentation
+
+                while self.pauseVisualization == true {
+                    if self.stopVisualization == true {
+                        break breakableLoop
+                    }
+                }
+                if self.stopVisualization == true {
+                    break breakableLoop
+                }
+                DispatchQueue.main.async {
+                    edgeRepresentation?.setCheckingColor()
+                    neighbor.setCheckingPathColor()
+                    self.delegate?.willCompareVertices(startVertexPathLength: currentVertex.pathLengthFromStart,
+                                                       edgePathLength: weight,
+                                                       endVertexPathLength: neighbor.pathLengthFromStart)
+                }
+                usleep(self._visualizationOneSleepDuration)
+
+
+                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
+
+                if theoreticNewWeight < neighbor.pathLengthFromStart {
+                    while self.pauseVisualization == true {
+                        if self.stopVisualization == true {
+                            break breakableLoop
+                        }
+                    }
+                    if self.stopVisualization == true {
+                        break breakableLoop
+                    }
+                    neighbor.pathLengthFromStart = theoreticNewWeight
+                    neighbor.pathVerticesFromStart = currentVertex.pathVerticesFromStart
+                    neighbor.pathVerticesFromStart.append(neighbor)
+                }
+                usleep(self._visualizationOneSleepDuration)
+
+                DispatchQueue.main.async {
+                    self.delegate?.didFinishCompare()
+                    edge.edgeRepresentation?.setDefaultColor()
+                    edge.neighbor.setDefaultColor()
+                }
+                usleep(self._visualizationOneSleepDuration)
+            }
+            if totalVertices.isEmpty {
+                currentVertex = nil
+                break
+            }
+            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
+        }
+        if self.stopVisualization == true {
+            DispatchQueue.main.async {
+                self.delegate?.didStop()
+            }
+        } else {
+            completion()
+        }
+    }
+
+    public func parseNeighborsFor(vertex: Vertex, completion: @escaping () -> ()) {
+        DispatchQueue.main.async {
+            vertex.setVisitedColor()
+        }
+        DispatchQueue.global(qos: .background).async {
+            vertex.visited = true
+
+            let nonVisitedVertices = self._vertices.filter { $0.visited == false }
+            if nonVisitedVertices.isEmpty {
+                self.state = .completed
+                DispatchQueue.main.async {
+                    self.delegate?.didCompleteGraphParsing()
+                }
+                return
+            }
+
+            let filteredEdges = vertex.edges.filter { !$0.neighbor.visited }
+            breakableLoop: for edge in filteredEdges {
+                while self.pauseVisualization == true {
+                    if self.stopVisualization == true {
+                        break breakableLoop
+                    }
+                }
+                if self.stopVisualization == true {
+                    break breakableLoop
+                }
+                let weight = edge.weight
+                let neighbor = edge.neighbor
+
+                DispatchQueue.main.async {
+                    edge.neighbor.setCheckingPathColor()
+                    edge.edgeRepresentation?.setCheckingColor()
+                    self.delegate?.willCompareVertices(startVertexPathLength: vertex.pathLengthFromStart,
+                                                       edgePathLength: weight,
+                                                       endVertexPathLength: neighbor.pathLengthFromStart)
+                }
+                usleep(self._interactiveOneSleepDuration)
+                
+                let theoreticNewWeight = vertex.pathLengthFromStart + weight
+                if theoreticNewWeight < neighbor.pathLengthFromStart {
+                    while self.pauseVisualization == true {
+                        if self.stopVisualization == true {
+                            break breakableLoop
+                        }
+                    }
+                    if self.stopVisualization == true {
+                        break breakableLoop
+                    }
+                    neighbor.pathLengthFromStart = theoreticNewWeight
+                    neighbor.pathVerticesFromStart = vertex.pathVerticesFromStart
+                    neighbor.pathVerticesFromStart.append(neighbor)
+                }
+
+                usleep(self._interactiveOneSleepDuration)
+                while self.pauseVisualization == true {
+                    if self.stopVisualization == true {
+                        break breakableLoop
+                    }
+                }
+                if self.stopVisualization == true {
+                    break breakableLoop
+                }
+                DispatchQueue.main.async {
+                    self.delegate?.didFinishCompare()
+                    edge.neighbor.setDefaultColor()
+                    edge.edgeRepresentation?.setDefaultColor()
+                }
+                usleep(self._interactiveOneSleepDuration)
+            }
+            if self.stopVisualization == true {
+                DispatchQueue.main.async {
+                    self.delegate?.didStop()
+                }
+            } else {
+                let nextVertexPathLength = nonVisitedVertices.sorted { $0.pathLengthFromStart < $1.pathLengthFromStart }.first!.pathLengthFromStart
+                self.nextVertices = nonVisitedVertices.filter { $0.pathLengthFromStart == nextVertexPathLength }
+                completion()
+            }
+        }
+    }
+
+    public func didTapVertex(vertex: Vertex) {
+        if self.nextVertices.contains(vertex) {
+            self.delegate?.willStartVertexNeighborsChecking()
+            self.state = .parsing
+            self.parseNeighborsFor(vertex: vertex) {
+                self.state = .interactiveVisualization
+                self.delegate?.didFinishVertexNeighborsChecking()
+            }
+        } else {
+            self.delegate?.didTapWrongVertex()
+        }
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphColors.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphColors.swift
new file mode 100644
index 000000000..95e9b8d74
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphColors.swift	
@@ -0,0 +1,15 @@
+import UIKit
+
+public class GraphColors {
+    public static let sharedInstance: GraphColors = GraphColors()
+    private init() { }
+
+    public var mainWindowBackgroundColor: UIColor = #colorLiteral(red: 0.921431005, green: 0.9214526415, blue: 0.9214410186, alpha: 1)
+    public var topViewBackgroundColor: UIColor = #colorLiteral(red: 1, green: 0.4932718873, blue: 0.4739984274, alpha: 1)
+    public var graphBackgroundColor: UIColor = #colorLiteral(red: 1, green: 1, blue: 1, alpha: 1)
+    public var defaultVertexColor: UIColor = #colorLiteral(red: 0.721568644, green: 0.8862745166, blue: 0.5921568871, alpha: 1)
+    public var defaultEdgeColor: UIColor = #colorLiteral(red: 0.721568644, green: 0.8862745166, blue: 0.5921568871, alpha: 1)
+    public var checkingColor: UIColor = #colorLiteral(red: 0.9411764741, green: 0.4980392158, blue: 0.3529411852, alpha: 1)
+    public var visitedColor: UIColor = #colorLiteral(red: 0, green: 0.5898008943, blue: 1, alpha: 1)
+    public var buttonsBackgroundColor: UIColor = #colorLiteral(red: 0, green: 0.3285208941, blue: 0.5748849511, alpha: 1)
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift
new file mode 100644
index 000000000..49bc6853f
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift	
@@ -0,0 +1,246 @@
+import UIKit
+
+public class GraphView: UIView {
+    private var graph: Graph!
+    private var panningView: VertexView? = nil
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+
+    public override init(frame: CGRect) {
+        super.init(frame: frame)
+        self.backgroundColor = self.graphColors.graphBackgroundColor
+    }
+    
+    public required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    
+    }
+
+    public func configure(graph: Graph) {
+        self.graph = graph
+    }
+
+    public func removeGraph() {
+        for vertex in self.graph.vertices {
+            if let view = vertex.view {
+                view.removeFromSuperview()
+                vertex.view = nil
+            }
+        }
+        for vertex in self.graph.vertices {
+            for edge in vertex.edges {
+                if let edgeRepresentation = edge.edgeRepresentation {
+                    edgeRepresentation.layer.removeFromSuperlayer()
+                    edgeRepresentation.label.removeFromSuperview()
+                    edge.edgeRepresentation = nil
+                }
+            }
+        }
+    }
+
+    public func createNewGraph() {
+        self.setupVertexViews()
+        self.setupEdgeRepresentations()
+        self.addGraph()
+    }
+
+    public func reset() {
+        for vertex in self.graph.vertices {
+            vertex.edges.forEach { $0.edgeRepresentation?.setDefaultColor() }
+            vertex.setDefaultColor()
+        }
+    }
+
+    private func addGraph() {
+        for vertex in self.graph.vertices {
+            for edge in vertex.edges {
+                if let edgeRepresentation = edge.edgeRepresentation {
+                    self.layer.addSublayer(edgeRepresentation.layer)
+                    self.addSubview(edgeRepresentation.label)
+                }
+            }
+        }
+        for vertex in self.graph.vertices {
+            if let view = vertex.view {
+                self.addSubview(view)
+            }
+        }
+    }
+
+    private func setupVertexViews() {
+        var level = 0
+        var buildViewQueue = [self.graph.startVertex!]
+        let itemWidth: CGFloat = 40
+        while !buildViewQueue.isEmpty {
+            let levelItemsCount = CGFloat(buildViewQueue.count)
+            let xStep = (self.frame.width - levelItemsCount * itemWidth) / (levelItemsCount + 1)
+            var previousVertexMaxX: CGFloat = 0.0
+            for vertex in buildViewQueue {
+                let x: CGFloat = previousVertexMaxX + xStep
+                let y: CGFloat = CGFloat(level * 100)
+                previousVertexMaxX = x + itemWidth
+                let frame = CGRect(x: x, y: y, width: itemWidth, height: itemWidth)
+                let vertexView = VertexView(frame: frame)
+                vertex.view = vertexView
+                vertexView.vertex = vertex
+                vertex.view?.setIdLabel(text: vertex.identifier)
+                vertex.view?.setPathLengthLabel(text: "\(vertex.pathLengthFromStart)")
+                vertex.view?.addTarget(self, action: #selector(self.didTapVertex(sender:)), for: .touchUpInside)
+                let panGesture = UIPanGestureRecognizer(target: self, action: #selector(self.handlePan(recognizer:)))
+                vertex.view?.addGestureRecognizer(panGesture)
+            }
+            level += 1
+            buildViewQueue = self.graph.vertices.filter { $0.level == level }
+        }
+    }
+
+    private var movingVertexInputEdges: [EdgeRepresentation] = []
+    private var movingVertexOutputEdges: [EdgeRepresentation] = []
+
+    @objc private func handlePan(recognizer: UIPanGestureRecognizer) {
+        guard let vertexView = recognizer.view as? VertexView, let vertex = vertexView.vertex else {
+            return
+        }
+        if self.panningView != nil {
+            if self.panningView != vertexView {
+                return
+            }
+        }
+
+        switch recognizer.state {
+        case .began:
+            let movingVertexViewFrame = vertexView.frame
+            let sizedVertexView = CGRect(x: movingVertexViewFrame.origin.x - 10,
+                                         y: movingVertexViewFrame.origin.y - 10,
+                                         width: movingVertexViewFrame.width + 20,
+                                         height: movingVertexViewFrame.height + 20)
+            vertex.edges.forEach { edge in
+                if let edgeRepresentation = edge.edgeRepresentation{
+                    if sizedVertexView.contains(edgeRepresentation.layer.startPoint!) {
+                        movingVertexOutputEdges.append(edgeRepresentation)
+                    } else {
+                        movingVertexInputEdges.append(edgeRepresentation)
+                    }
+                }
+            }
+            self.panningView = vertexView
+        case .changed:
+            if self.movingVertexOutputEdges.isEmpty && self.movingVertexInputEdges.isEmpty {
+                return
+            }
+            let translation = recognizer.translation(in: self)
+            if vertexView.frame.origin.x + translation.x <= 0
+                || vertexView.frame.origin.y + translation.y <= 0
+                || (vertexView.frame.origin.x + vertexView.frame.width + translation.x) >= self.frame.width
+                || (vertexView.frame.origin.y + vertexView.frame.height + translation.y) >= self.frame.height {
+                break
+            }
+            self.movingVertexInputEdges.forEach { edgeRepresentation in
+                let originalLabelCenter = edgeRepresentation.label.center
+                edgeRepresentation.label.center = CGPoint(x: originalLabelCenter.x + translation.x * 0.625,
+                                                          y: originalLabelCenter.y + translation.y * 0.625)
+
+                CATransaction.begin()
+                CATransaction.setValue(kCFBooleanTrue, forKey: kCATransactionDisableActions)
+                let newPath = self.path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: false)
+                edgeRepresentation.layer.path = newPath
+                CATransaction.commit()
+
+            }
+
+            self.movingVertexOutputEdges.forEach { edgeRepresentation in
+                let originalLabelCenter = edgeRepresentation.label.center
+                edgeRepresentation.label.center = CGPoint(x: originalLabelCenter.x + translation.x * 0.375,
+                                                          y: originalLabelCenter.y + translation.y * 0.375)
+
+                CATransaction.begin()
+                CATransaction.setValue(kCFBooleanTrue, forKey: kCATransactionDisableActions)
+                let newPath = self.path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: true)
+                edgeRepresentation.layer.path = newPath
+                CATransaction.commit()
+            }
+
+            vertexView.center = CGPoint(x: vertexView.center.x + translation.x,
+                                        y: vertexView.center.y + translation.y)
+            recognizer.setTranslation(CGPoint.zero, in: self)
+        case .ended:
+            self.movingVertexInputEdges = []
+            self.movingVertexOutputEdges = []
+            self.panningView = nil
+        default:
+            break
+        }
+    }
+
+    private func path(fromEdgeRepresentation edgeRepresentation: EdgeRepresentation, movingVertex: Vertex, translation: CGPoint, outPath: Bool) -> CGPath {
+        let bezier = UIBezierPath()
+
+        if outPath == true {
+            bezier.move(to: edgeRepresentation.layer.endPoint!)
+            let startPoint = CGPoint(x: edgeRepresentation.layer.startPoint!.x + translation.x,
+                                     y: edgeRepresentation.layer.startPoint!.y + translation.y)
+            edgeRepresentation.layer.startPoint = startPoint
+            bezier.addLine(to: startPoint)
+        } else {
+            bezier.move(to: edgeRepresentation.layer.startPoint!)
+            let endPoint = CGPoint(x: edgeRepresentation.layer.endPoint!.x + translation.x,
+                                   y: edgeRepresentation.layer.endPoint!.y + translation.y)
+            edgeRepresentation.layer.endPoint = endPoint
+            bezier.addLine(to: endPoint)
+        }
+        return bezier.cgPath
+    }
+
+    @objc private func didTapVertex(sender: AnyObject) {
+        DispatchQueue.main.async {
+            if self.graph.state == .completed {
+                for vertex in self.graph.vertices {
+                    vertex.edges.forEach { $0.edgeRepresentation?.setDefaultColor() }
+                    vertex.setVisitedColor()
+                }
+                if let vertexView = sender as? VertexView, let vertex = vertexView.vertex {
+                    for (index, pathVertex) in vertex.pathVerticesFromStart.enumerated() {
+                        pathVertex.setCheckingPathColor()
+                        if vertex.pathVerticesFromStart.count > index + 1 {
+                            let nextVertex = vertex.pathVerticesFromStart[index + 1]
+
+                            if let edge = pathVertex.edges.filter({ $0.neighbor == nextVertex }).first {
+                                edge.edgeRepresentation?.setCheckingColor()
+                            }
+                        }
+
+                    }
+                }
+            } else if self.graph.state == .interactiveVisualization {
+                if let vertexView = sender as? VertexView, let vertex = vertexView.vertex {
+                    if vertex.visited {
+                        return
+                    } else {
+                        self.graph.didTapVertex(vertex: vertex)
+                    }
+                }
+            }
+        }
+    }
+
+    private func setupEdgeRepresentations() {
+        var edgeQueue: [Vertex] = [self.graph.startVertex!]
+
+        //BFS
+        while !edgeQueue.isEmpty {
+            let currentVertex = edgeQueue.first!
+            currentVertex.haveAllEdges = true
+            for edge in currentVertex.edges {
+                let neighbor = edge.neighbor
+                let weight = edge.weight
+                if !neighbor.haveAllEdges {
+                    let edgeRepresentation = EdgeRepresentation(from: currentVertex, to: neighbor, weight: weight)
+                    edge.edgeRepresentation = edgeRepresentation
+                    let index = neighbor.edges.index(where: { $0.neighbor == currentVertex })!
+                    neighbor.edges[index].edgeRepresentation = edgeRepresentation
+                    edgeQueue.append(neighbor)
+                }
+            }
+            edgeQueue.removeFirst()
+        }
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Edge.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Edge.swift
new file mode 100644
index 000000000..6f4493bbe
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Edge.swift	
@@ -0,0 +1,12 @@
+import Foundation
+
+public class Edge {
+    public var neighbor: Vertex
+    public var weight: Double
+    public var edgeRepresentation: EdgeRepresentation?
+
+    public init(vertex: Vertex, weight: Double) {
+        self.neighbor = vertex
+        self.weight = weight
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift
new file mode 100644
index 000000000..c9270b0df
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift	
@@ -0,0 +1,62 @@
+import UIKit
+
+public class Vertex: Hashable, Equatable {
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+
+    public var identifier: String
+    public var edges: [Edge] = []
+    public var pathLengthFromStart: Double = Double.infinity {
+        didSet {
+            DispatchQueue.main.async {
+                self.view?.setPathLengthLabel(text: "\(self.pathLengthFromStart)")
+            }
+        }
+    }
+    public var pathVerticesFromStart: [Vertex] = []
+    public var level: Int = 0
+    public var levelChecked: Bool = false
+    public var haveAllEdges: Bool = false
+    public var visited: Bool = false
+
+    public var view: VertexView?
+
+    public init(identifier: String) {
+        self.identifier = identifier
+    }
+
+    public var hashValue: Int {
+        return self.identifier.hashValue
+    }
+
+    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
+        if lhs.hashValue == rhs.hashValue {
+            return true
+        }
+        return false
+    }
+
+    public func clearCache() {
+        self.pathLengthFromStart = Double.infinity
+        self.pathVerticesFromStart = []
+        self.visited = false
+    }
+
+    public func clearLevelInfo() {
+        self.level = 0
+        self.levelChecked = false
+    }
+
+    public func setVisitedColor() {
+        self.view?.backgroundColor = self.graphColors.visitedColor
+        self.view?.setLabelsTextColor(color: UIColor.white)
+    }
+
+    public func setCheckingPathColor() {
+        self.view?.backgroundColor = self.graphColors.checkingColor
+    }
+
+    public func setDefaultColor() {
+        self.view?.backgroundColor = self.graphColors.defaultVertexColor
+        self.view?.setLabelsTextColor(color: UIColor.black)
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift
new file mode 100644
index 000000000..e8aabad27
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
@@ -0,0 +1,319 @@
+import Foundation
+import UIKit
+
+public protocol GraphDelegate: class {
+    func willCompareVertices(startVertexPathLength: Double, edgePathLength: Double, endVertexPathLength: Double)
+    func didFinishCompare()
+    func didCompleteGraphParsing()
+    func didTapWrongVertex()
+    func didStop()
+    func willStartVertexNeighborsChecking()
+    func didFinishVertexNeighborsChecking()
+}
+
+public class Window: UIView, GraphDelegate {
+    public var graphView: GraphView!
+
+    private var topView: UIView!
+    private var createGraphButton: RoundedButton!
+    private var startVisualizationButton: RoundedButton!
+    private var startInteractiveVisualizationButton: RoundedButton!
+    private var startButton: UIButton!
+    private var pauseButton: UIButton!
+    private var stopButton: UIButton!
+    private var comparisonLabel: UILabel!
+    private var activityIndicator: UIActivityIndicatorView!
+    private var graph: Graph!
+    private var numberOfVertices: UInt!
+    private var graphColors: GraphColors = GraphColors.sharedInstance
+
+    public override init(frame: CGRect) {
+        super.init(frame: frame)
+        self.frame = frame
+        self.backgroundColor = self.graphColors.mainWindowBackgroundColor
+    }
+    
+    public required init?(coder aDecoder: NSCoder) {
+        fatalError("init(coder:) has not been implemented")
+    }
+
+    public func configure(graph: Graph) {
+        self.graph = graph
+        self.graph.createNewGraph()
+        self.graph.delegate = self
+        let frame = CGRect(x: 10, y: 170, width: self.frame.width - 20, height: self.frame.height - 180)
+        self.graphView = GraphView(frame: frame)
+        self.graphView.layer.cornerRadius = 15
+
+        self.graphView.configure(graph: self.graph)
+        self.graphView.createNewGraph()
+        self.addSubview(self.graphView)
+
+        self.configureCreateGraphButton()
+        self.configureStartVisualizationButton()
+        self.configureStartInteractiveVisualizationButton()
+        self.configureStartButton()
+        self.configurePauseButton()
+        self.configureStopButton()
+        self.configureComparisonLabel()
+        self.configureActivityIndicator()
+
+        self.topView = UIView(frame: CGRect(x: 10, y: 10, width: self.frame.width - 20, height: 150))
+        self.topView.backgroundColor = self.graphColors.topViewBackgroundColor
+        self.topView.layer.cornerRadius = 15
+        self.addSubview(self.topView)
+
+        self.topView.addSubview(self.createGraphButton)
+        self.topView.addSubview(self.startVisualizationButton)
+        self.topView.addSubview(self.startInteractiveVisualizationButton)
+        self.topView.addSubview(self.startButton)
+        self.topView.addSubview(self.pauseButton)
+        self.topView.addSubview(self.stopButton)
+        self.topView.addSubview(self.comparisonLabel)
+        self.topView.addSubview(self.activityIndicator)
+    }
+
+    private func configureCreateGraphButton() {
+        let frame = CGRect(x: self.center.x - 200, y: 12, width: 100, height: 34)
+        self.createGraphButton = RoundedButton(frame: frame)
+        self.createGraphButton.setTitle("New graph", for: .normal)
+        self.createGraphButton.addTarget(self, action: #selector(self.createGraphButtonTap), for: .touchUpInside)
+    }
+
+    private func configureStartVisualizationButton() {
+        let frame = CGRect(x: self.center.x - 50, y: 12, width: 100, height: 34)
+        self.startVisualizationButton = RoundedButton(frame: frame)
+        self.startVisualizationButton.setTitle("Auto", for: .normal)
+        self.startVisualizationButton.addTarget(self, action: #selector(self.startVisualizationButtonDidTap), for: .touchUpInside)
+    }
+
+    private func configureStartInteractiveVisualizationButton() {
+        let frame = CGRect(x: self.center.x + 100, y: 12, width: 100, height: 34)
+        self.startInteractiveVisualizationButton = RoundedButton(frame: frame)
+        self.startInteractiveVisualizationButton.setTitle("Interactive", for: .normal)
+        self.startInteractiveVisualizationButton.addTarget(self, action: #selector(self.startInteractiveVisualizationButtonDidTap), for: .touchUpInside)
+    }
+
+    private func configureStartButton() {
+        let frame = CGRect(x: self.center.x - 65, y: 56, width: 30, height: 30)
+        self.startButton = UIButton(frame: frame)
+        let playImage = UIImage(named: "Start.png")
+        self.startButton.setImage(playImage, for: .normal)
+        self.startButton.isEnabled = false
+        self.startButton.addTarget(self, action: #selector(self.didTapStartButton), for: .touchUpInside)
+    }
+
+    private func configurePauseButton() {
+        let frame = CGRect(x: self.center.x - 15, y: 56, width: 30, height: 30)
+        self.pauseButton = UIButton(frame: frame)
+        let pauseImage = UIImage(named: "Pause.png")
+        self.pauseButton.setImage(pauseImage, for: .normal)
+        self.pauseButton.isEnabled = false
+        self.pauseButton.addTarget(self, action: #selector(self.didTapPauseButton), for: .touchUpInside)
+    }
+
+    private func configureStopButton() {
+        let frame = CGRect(x: self.center.x + 35, y: 56, width: 30, height: 30)
+        self.stopButton = UIButton(frame: frame)
+        let stopImage = UIImage(named: "Stop.png")
+        self.stopButton.setImage(stopImage, for: .normal)
+        self.stopButton.isEnabled = false
+        self.stopButton.addTarget(self, action: #selector(self.didTapStopButton), for: .touchUpInside)
+    }
+
+    private func configureComparisonLabel() {
+        let size = CGSize(width: 250, height: 42)
+        let origin = CGPoint(x: self.center.x - 125, y: 96)
+        let frame = CGRect(origin: origin, size: size)
+        self.comparisonLabel = UILabel(frame: frame)
+        self.comparisonLabel.textAlignment = .center
+        self.comparisonLabel.text = "Have fun!"
+    }
+
+    private func configureActivityIndicator() {
+        let size = CGSize(width: 50, height: 42)
+        let origin = CGPoint(x: self.center.x - 25, y: 100)
+        let activityIndicatorFrame = CGRect(origin: origin, size: size)
+        self.activityIndicator = UIActivityIndicatorView(frame: activityIndicatorFrame)
+        self.activityIndicator.activityIndicatorViewStyle = .whiteLarge
+    }
+
+    @objc private func createGraphButtonTap() {
+        self.comparisonLabel.text = ""
+        self.graphView.removeGraph()
+        self.graph.removeGraph()
+        self.graph.createNewGraph()
+        self.graphView.createNewGraph()
+        self.graph.state = .initial
+    }
+
+    @objc private func startVisualizationButtonDidTap() {
+        self.comparisonLabel.text = ""
+        self.pauseButton.isEnabled = true
+        self.stopButton.isEnabled = true
+        self.createGraphButton.isEnabled = false
+        self.startVisualizationButton.isEnabled = false
+        self.startInteractiveVisualizationButton.isEnabled = false
+        self.createGraphButton.alpha = 0.5
+        self.startVisualizationButton.alpha = 0.5
+        self.startInteractiveVisualizationButton.alpha = 0.5
+
+        if self.graph.state == .completed {
+            self.graphView.reset()
+            self.graph.reset()
+        }
+        self.graph.state = .autoVisualization
+        DispatchQueue.global(qos: .background).async {
+            self.graph.findShortestPathsWithVisualization {
+                self.graph.state = .completed
+
+                DispatchQueue.main.async {
+                    self.startButton.isEnabled = false
+                    self.pauseButton.isEnabled = false
+                    self.stopButton.isEnabled = false
+                    self.createGraphButton.isEnabled = true
+                    self.startVisualizationButton.isEnabled = true
+                    self.startInteractiveVisualizationButton.isEnabled = true
+                    self.createGraphButton.alpha = 1
+                    self.startVisualizationButton.alpha = 1
+                    self.startInteractiveVisualizationButton.alpha = 1
+                    self.comparisonLabel.text = "Completed!"
+                }
+            }
+        }
+    }
+
+    @objc private func startInteractiveVisualizationButtonDidTap() {
+        self.comparisonLabel.text = ""
+        self.pauseButton.isEnabled = true
+        self.stopButton.isEnabled = true
+        self.createGraphButton.isEnabled = false
+        self.startVisualizationButton.isEnabled = false
+        self.startInteractiveVisualizationButton.isEnabled = false
+        self.createGraphButton.alpha = 0.5
+        self.startVisualizationButton.alpha = 0.5
+        self.startInteractiveVisualizationButton.alpha = 0.5
+
+        if self.graph.state == .completed {
+            self.graphView.reset()
+            self.graph.reset()
+        }
+        
+        self.graph.startVertex.pathLengthFromStart = 0
+        self.graph.startVertex.pathVerticesFromStart.append(self.graph.startVertex)
+        self.graph.state = .parsing
+        self.graph.parseNeighborsFor(vertex: self.graph.startVertex) {
+            self.graph.state = .interactiveVisualization
+            DispatchQueue.main.async {
+                self.comparisonLabel.text = "Pick next vertex"
+            }
+        }
+    }
+
+    @objc private func didTapStartButton() {
+        self.startButton.isEnabled = false
+        self.pauseButton.isEnabled = true
+        DispatchQueue.global(qos: .utility).async {
+            self.graph.pauseVisualization = false
+        }
+    }
+
+    @objc private func didTapPauseButton() {
+        self.startButton.isEnabled = true
+        self.pauseButton.isEnabled = false
+        DispatchQueue.global(qos: .utility).async {
+            self.graph.pauseVisualization = true
+        }
+    }
+
+    @objc private func didTapStopButton() {
+        self.startButton.isEnabled = false
+        self.pauseButton.isEnabled = false
+        self.comparisonLabel.text = ""
+        self.activityIndicator.startAnimating()
+        if self.graph.state == .parsing || self.graph.state == .autoVisualization {
+            self.graph.stopVisualization = true
+        } else if self.graph.state == .interactiveVisualization {
+            self.didStop()
+        }
+    }
+
+    private func setButtonsToInitialState() {
+        self.createGraphButton.isEnabled = true
+        self.startVisualizationButton.isEnabled = true
+        self.startInteractiveVisualizationButton.isEnabled = true
+        self.startButton.isEnabled = false
+        self.pauseButton.isEnabled = false
+        self.stopButton.isEnabled = false
+        self.createGraphButton.alpha = 1
+        self.startVisualizationButton.alpha = 1
+        self.startInteractiveVisualizationButton.alpha = 1
+    }
+
+    private func showError(error: String) {
+        DispatchQueue.main.async {
+            let size = CGSize(width: 250, height: 42)
+            let origin = CGPoint(x: self.topView.center.x - 125, y: 96)
+            let frame = CGRect(origin: origin, size: size)
+            let errorView = ErrorView(frame: frame)
+            errorView.setText(text: error)
+            self.topView.addSubview(errorView)
+            UIView.animate(withDuration: 2, animations: {
+                errorView.alpha = 0
+            }, completion: { _ in
+                errorView.removeFromSuperview()
+            })
+        }
+    }
+
+    // MARK: GraphDelegate
+    public func didCompleteGraphParsing() {
+        self.graph.state = .completed
+        self.setButtonsToInitialState()
+        self.comparisonLabel.text = "Completed!"
+    }
+
+    public func didTapWrongVertex() {
+        if !self.subviews.contains { $0 is ErrorView } {
+            self.showError(error: "You have picked wrong next vertex")
+        }
+    }
+
+    public func willCompareVertices(startVertexPathLength: Double, edgePathLength: Double, endVertexPathLength: Double) {
+        DispatchQueue.main.async {
+            if startVertexPathLength + edgePathLength < endVertexPathLength {
+                self.comparisonLabel.text = "\(startVertexPathLength) + \(edgePathLength) < \(endVertexPathLength) 👍"
+            } else {
+                self.comparisonLabel.text = "\(startVertexPathLength) + \(edgePathLength) >= \(endVertexPathLength) 👎"
+            }
+        }
+    }
+
+    public func didFinishCompare() {
+        DispatchQueue.main.async {
+            self.comparisonLabel.text = ""
+        }
+    }
+
+    public func didStop() {
+        self.graph.state = .initial
+        self.graph.stopVisualization = false
+        self.graph.pauseVisualization = false
+        self.graphView.reset()
+        self.graph.reset()
+        self.setButtonsToInitialState()
+        self.activityIndicator.stopAnimating()
+    }
+
+    public func willStartVertexNeighborsChecking() {
+        DispatchQueue.main.async {
+            self.comparisonLabel.text = ""
+        }
+    }
+
+    public func didFinishVertexNeighborsChecking() {
+        DispatchQueue.main.async {
+            self.comparisonLabel.text = "Pick next vertex"
+        }
+    }
+}
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/contents.xcplayground b/Dijkstra Algorithm/VisualizedDijkstra.playground/contents.xcplayground
new file mode 100644
index 000000000..35968656f
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' display-mode='raw'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/contents.xcworkspacedata b/Dijkstra Algorithm/VisualizedDijkstra.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.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/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline b/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline
new file mode 100644
index 000000000..bf468afec
--- /dev/null
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/timeline.xctimeline	
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>
diff --git a/README.markdown b/README.markdown
index 5e6cfbfe4..eee5cbb46 100644
--- a/README.markdown
+++ b/README.markdown
@@ -183,6 +183,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Single-Source Shortest Paths](Single-Source%20Shortest%20Paths%20(Weighted)/)
 - [Minimum Spanning Tree](Minimum%20Spanning%20Tree%20%28Unweighted%29/) on an unweighted tree
 - [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
+- [Dijkstra's shortest path algorithm](Dijkstra%20Algorithm/)
 
 ## Puzzles
 

From 8efb7354645763fce0823ec74c2fe3ffb904f4df Mon Sep 17 00:00:00 2001
From: Jacopo Mangiavacchi <jacopo.mangiavacchi@uk.ibm.com>
Date: Tue, 4 Apr 2017 10:25:36 +0100
Subject: [PATCH 074/862] MIT License

---
 MinimumCoinChange/LICENSE | 222 ++++----------------------------------
 1 file changed, 21 insertions(+), 201 deletions(-)

diff --git a/MinimumCoinChange/LICENSE b/MinimumCoinChange/LICENSE
index 8dada3eda..fda6e6146 100755
--- a/MinimumCoinChange/LICENSE
+++ b/MinimumCoinChange/LICENSE
@@ -1,201 +1,21 @@
-                                 Apache License
-                           Version 2.0, January 2004
-                        http://www.apache.org/licenses/
-
-   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
-
-   1. Definitions.
-
-      "License" shall mean the terms and conditions for use, reproduction,
-      and distribution as defined by Sections 1 through 9 of this document.
-
-      "Licensor" shall mean the copyright owner or entity authorized by
-      the copyright owner that is granting the License.
-
-      "Legal Entity" shall mean the union of the acting entity and all
-      other entities that control, are controlled by, or are under common
-      control with that entity. For the purposes of this definition,
-      "control" means (i) the power, direct or indirect, to cause the
-      direction or management of such entity, whether by contract or
-      otherwise, or (ii) ownership of fifty percent (50%) or more of the
-      outstanding shares, or (iii) beneficial ownership of such entity.
-
-      "You" (or "Your") shall mean an individual or Legal Entity
-      exercising permissions granted by this License.
-
-      "Source" form shall mean the preferred form for making modifications,
-      including but not limited to software source code, documentation
-      source, and configuration files.
-
-      "Object" form shall mean any form resulting from mechanical
-      transformation or translation of a Source form, including but
-      not limited to compiled object code, generated documentation,
-      and conversions to other media types.
-
-      "Work" shall mean the work of authorship, whether in Source or
-      Object form, made available under the License, as indicated by a
-      copyright notice that is included in or attached to the work
-      (an example is provided in the Appendix below).
-
-      "Derivative Works" shall mean any work, whether in Source or Object
-      form, that is based on (or derived from) the Work and for which the
-      editorial revisions, annotations, elaborations, or other modifications
-      represent, as a whole, an original work of authorship. For the purposes
-      of this License, Derivative Works shall not include works that remain
-      separable from, or merely link (or bind by name) to the interfaces of,
-      the Work and Derivative Works thereof.
-
-      "Contribution" shall mean any work of authorship, including
-      the original version of the Work and any modifications or additions
-      to that Work or Derivative Works thereof, that is intentionally
-      submitted to Licensor for inclusion in the Work by the copyright owner
-      or by an individual or Legal Entity authorized to submit on behalf of
-      the copyright owner. For the purposes of this definition, "submitted"
-      means any form of electronic, verbal, or written communication sent
-      to the Licensor or its representatives, including but not limited to
-      communication on electronic mailing lists, source code control systems,
-      and issue tracking systems that are managed by, or on behalf of, the
-      Licensor for the purpose of discussing and improving the Work, but
-      excluding communication that is conspicuously marked or otherwise
-      designated in writing by the copyright owner as "Not a Contribution."
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-      "Contributor" shall mean Licensor and any individual or Legal Entity
-      on behalf of whom a Contribution has been received by Licensor and
-      subsequently incorporated within the Work.
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-   2. Grant of Copyright License. Subject to the terms and conditions of
-      this License, each Contributor hereby grants to You a perpetual,
-      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
-      copyright license to reproduce, prepare Derivative Works of,
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-   you may not use this file except in compliance with the License.
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-   distributed under the License is distributed on an "AS IS" BASIS,
-   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-   See the License for the specific language governing permissions and
-   limitations under the License.
+MIT License
+
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+
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+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
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+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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+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.

From 63257f629f99ba76a7997a1e0b18b8236cefa57b Mon Sep 17 00:00:00 2001
From: Richard <r.ash8347@gmail.com>
Date: Tue, 4 Apr 2017 13:37:53 -0700
Subject: [PATCH 075/862] fixed typos in readme

---
 Strassen Matrix Multiplication/README.markdown | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Strassen Matrix Multiplication/README.markdown b/Strassen Matrix Multiplication/README.markdown
index fa822d310..07ce534b2 100644
--- a/Strassen Matrix Multiplication/README.markdown	
+++ b/Strassen Matrix Multiplication/README.markdown	
@@ -18,7 +18,7 @@ matrix A = |1 2|, matrix B = |5 6|
 A * B = C
 	
 |1 2| * |5 6| = |1*5+2*7 1*6+2*8| = |19 22|
-|3 4|   |7 8|   |3*5+4*7 3*6+4*8|   |43 48|
+|3 4|   |7 8|   |3*5+4*7 3*6+4*8|   |43 50|
 ```
 
 What's going on here? To start, we're multiplying matricies A & B. Our new matrix, C's, elements `[i, j]` are determined by the dot product of the first matrix's ith row and the second matrix's jth column. See [here](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/vector-dot-product-and-vector-length) for a refresher on the dot product.
@@ -72,7 +72,7 @@ Then, for each row in A and column in B, we take the dot product of the ith row
 
 ```swift
 for k in 0..<n {
-  C[i, j] = A[i, k] * B[k, j]
+  C[i, j] += A[i, k] * B[k, j]
 }
 ```
 
@@ -90,7 +90,7 @@ public func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
   for i in 0..<n {
     for j in 0..<n {
       for k in 0..<n {
-        C[i, j] = A[i, k] * B[k, j]
+        C[i, j] += A[i, k] * B[k, j]
       }
     }
   }
@@ -229,7 +229,7 @@ for i in B.rows {
 }
 ```
 
-Finally, we recusrisvely compute the matrix using Strassen's algorithm and the transform our new matrix `C` back to the correct dimensions!
+Finally, we recursively compute the matrix using Strassen's algorithm and the transform our new matrix `C` back to the correct dimensions!
 
 ```swift
 let CPrep = APrep.strassenR(by: BPrep)

From e8c256eae82b8c30ca32ba28acce5c792edfe79c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 4 Apr 2017 14:07:19 -0700
Subject: [PATCH 076/862] Update README.markdown

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

diff --git a/README.markdown b/README.markdown
index 5e6cfbfe4..067de2418 100644
--- a/README.markdown
+++ b/README.markdown
@@ -106,6 +106,7 @@ Bad sorting algorithms (don't use these!):
 - Statistics
 - [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%20Multiplication%20Matrix). Efficient way to handle matrix multiplication.
 
 ### Machine learning
 

From bbba068205500a62943a601540d4dfba205586f2 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 4 Apr 2017 14:09:02 -0700
Subject: [PATCH 077/862] Updated a link to Strassen Multiplication Matrix.

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

diff --git a/README.markdown b/README.markdown
index 067de2418..29fc9d748 100644
--- a/README.markdown
+++ b/README.markdown
@@ -106,7 +106,7 @@ Bad sorting algorithms (don't use these!):
 - Statistics
 - [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%20Multiplication%20Matrix). Efficient way to handle matrix multiplication.
+- [Strassen's Multiplication Matrix](Strassen%20Matrix%20Multiplication/). Efficient way to handle matrix multiplication.
 
 ### Machine learning
 

From 20d7c1fd66b93c2a3933abe5d048169cea888ced Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Tue, 4 Apr 2017 17:46:46 -0700
Subject: [PATCH 078/862] Revisions in README.md

# Coherence & Sentence structures
# Grammar and spelling
---
 DiningPhilosophers/README.md | 29 +++++++++++++----------------
 1 file changed, 13 insertions(+), 16 deletions(-)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index ec1611c65..0bf4f28ce 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -1,22 +1,22 @@
 # Dining Philosophers
-Dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using [GCD](https://apple.github.io/swift-corelibs-libdispatch/) and [Semaphore](https://developer.apple.com/reference/dispatch/dispatchsemaphore) in Swift)
+The dining philosophers problem Algorithm implemented in Swift (concurrent algorithm design to illustrate synchronization issues and techniques for resolving them using [GCD](https://apple.github.io/swift-corelibs-libdispatch/) and [Semaphore](https://developer.apple.com/reference/dispatch/dispatchsemaphore) in Swift)
 
 Written for Swift Algorithm Club by Jacopo Mangiavacchi
 
 
 # Introduction
 
-In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them.
+In computer science, the dining philosophers problem is often used in the concurrent algorithm design to illustrate synchronization issues and techniques for resolving them.
 
 It was originally formulated in 1965 by Edsger Dijkstra as a student exam exercise, presented in terms of computers competing for access to tape drive peripherals. Soon after, Tony Hoare gave the problem its present formulation.
 
-This Swift implementation is based on the Chandy/Misra solution and it use GCD Dispatch and Semaphone on Swift cross platform
+This Swift implementation is based on the Chandy/Misra solution, and it uses the GCD Dispatch and Semaphone on the Swift cross platform.
 
 # Problem statement
 
 Five silent philosophers sit at a round table with bowls of spaghetti. Forks are placed between each pair of adjacent philosophers.
 
-Each philosopher must alternately think and eat. However, a philosopher can only eat spaghetti when they have both left and right forks. Each fork can be held by only one philosopher and so a philosopher can use the fork only if it is not being used by another philosopher. After an individual philosopher finishes eating, they need to put down both forks so that the forks become available to others. A philosopher can take the fork on their right or the one on their left as they become available, but cannot start eating before getting both forks.
+Each philosopher must alternately think and eat. A philosopher can only eat spaghetti when they have both left and right forks. Since each fork can be held by only one philosopher, a philosopher can use the fork only if it is not being used by another philosopher. When a philosopher finishes eating, they need to put down both forks so that the forks become available to others. A philosopher can take the fork on their right or the one on their left as they become available, but they cannot start eating before getting both forks.
 
 Eating is not limited by the remaining amounts of spaghetti or stomach space; an infinite supply and an infinite demand are assumed.
 
@@ -26,35 +26,32 @@ This is an illustration of an dinining table:
 
 ![Dining Philosophers table](https://upload.wikimedia.org/wikipedia/commons/7/7b/An_illustration_of_the_dining_philosophers_problem.png)
 
-
 # Solution
-There are different solutions for this classic algorithm and this Swift implementation is based on the on the Chandy/Misra solution that more generally allows for arbitrary agents to contend for an arbitrary number of resources in a completely distributed scenario with no needs for a central authority to control the locking and serialization of resources. 
-
-However, it is very important to note here that this solution violates the requirement that "the philosophers do not speak to each other" (due to the request messages).
+There are different solutions for this classic algorithm, and this Swift implementation is based on the Chandy/Misra solution. This implementation allows agents to contend for an arbitrary number of resources in a completely distributed scenario with no needs for a central authority to control the locking and serialization of resources. 
 
+However, this solution violates the requirement that "the philosophers do not speak to each other" (due to the request messages).
 
 # Description
 For every pair of philosophers contending for a resource, create a fork and give it to the philosopher with the lower ID (n for agent Pn). Each fork can either be dirty or clean. Initially, all forks are dirty.
-When a philosopher wants to use a set of resources (i.e. eat), said philosopher must obtain the forks from their contending neighbors. For all such forks the philosopher does not have, they send a request message.
-When a philosopher with a fork receives a request message, they keep the fork if it is clean, but give it up when it is dirty. If the philosopher sends the fork over, they clean the fork before doing so.
+When a philosopher wants to use a set of resources (i.e. eat), said philosopher must obtain the forks from their contending neighbors. The philospher send a message for all such forks needed. When a philosopher with a fork receives a request message, they keep the fork if it is clean, but give it up when it is dirty. If the philosopher sends the fork over, they clean the fork before doing so.
 After a philosopher is done eating, all their forks become dirty. If another philosopher had previously requested one of the forks, the philosopher that has just finished eating cleans the fork and sends it.
-This solution also allows for a large degree of concurrency, and will solve an arbitrarily large problem.
+This solution also allows for a large degree of concurrency, and it will solve an arbitrarily large problem.
 
-It also solves the starvation problem. The clean / dirty labels act as a way of giving preference to the most "starved" processes, and a disadvantage to processes that have just "eaten". One could compare their solution to one where philosophers are not allowed to eat twice in a row without letting others use the forks in between. Chandy and Misra's solution is more flexible than that, but has an element tending in that direction.
+In addition, it solves the starvation problem. The clean / dirty labels give a preference to the most "starved" processes and a disadvantage to processes that have just "eaten". One could compare their solution to one where philosophers are not allowed to eat twice in a row without letting others use the forks in between. The Chandy and Misra's solution is more flexible but has an element tending in that direction.
 
-In their analysis they derive a system of preference levels from the distribution of the forks and their clean/dirty states. They show that this system may describe an acyclic graph, and if so, the operations in their protocol cannot turn that graph into a cyclic one. This guarantees that deadlock cannot occur. However, if the system is initialized to a perfectly symmetric state, like all philosophers holding their left side forks, then the graph is cyclic at the outset, and their solution cannot prevent a deadlock. Initializing the system so that philosophers with lower IDs have dirty forks ensures the graph is initially acyclic.
+Based on the Chandy and Misra's analysis, a system of preference levels is derived from the distribution of the forks and their clean/dirty states. This system may describe an acyclic graph, and if so, the solution's protocol cannot turn that graph into a cyclic one. This guarantees that deadlock cannot occur. However, if the system is initialized to a perfectly symmetric state, such as all philosophers holding their left side forks, then the graph is cyclic at the outset, and the solution cannot prevent a deadlock. Initializing the system so that philosophers with lower IDs have dirty forks ensures the graph is initially acyclic.
 
 
 # Swift implementation
 
-This Swift 3.0 implementation of the Chandy/Misra solution is based on GCD and Semaphore tecnique and it could be built on both macOS and Linux.
+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.
 
 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.
 
 The ForkPair DispatchSemaphore static array is used for waking the neighbour Philosophers any time a fork pair is put down on the table.
 
-A background DispatchQueue is then used to let any Philosopher run asyncrounosly on the background and a global DispatchSemaphore is simply used in order to keep the main thread on wait forever and let the Philosophers contienue forever in their alternate think and eat cycle.
-
+A background DispatchQueue is then used to let any Philosopher run asyncrounosly on the background, and a global DispatchSemaphore is used to keep the main thread on wait forever and let the Philosophers continue forever in their alternate think and eat cycle.
+  
 # See also
 
 Dining Philosophers on Wikipedia https://en.wikipedia.org/wiki/Dining_philosophers_problem

From 56c5ecf2c5c6baf4b7442dbf46db5c9d13fda523 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Tue, 4 Apr 2017 19:31:26 -0700
Subject: [PATCH 079/862] Revisions in README.markdown

1- Coherence, Sentence structure, & Consistency
2- Grammar, Word choice, & Spelling
---
 Huffman Coding/README.markdown | 82 +++++++++++++++++-----------------
 1 file changed, 41 insertions(+), 41 deletions(-)

diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 4e6f75514..69e105c87 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -1,12 +1,12 @@
 # Huffman Coding
 
-The idea: Encode objects that occur often with a smaller number of bits than objects that occur less frequently.
+The idea: To encode objects that occur with a smaller number of bits than objects that occur less frequently.
 
-Although you can encode any type of objects with this scheme, it's most common to compress a stream of bytes. Let's say you have the following text, where each character is one byte:
+Although any type of objects can be encoded with this scheme, it is common to compress a stream of bytes. Suppose you have the following text, where each character is one byte:
 
 	so much words wow many compression
 
-If you count how often each byte appears, you can clearly see that some bytes occur more than others:
+If you count how often each byte appears, you can see some bytes occur more than others:
 
 	space: 5                  u: 1
 	    o: 5	              h: 1
@@ -41,11 +41,11 @@ Now if we replace the original bytes with these bit strings, the compressed outp
 
 The extra 0-bit at the end is there to make a full number of bytes. We were able to compress the original 34 bytes into merely 16 bytes, a space savings of over 50%!
 
-But hold on... to be able to decode these bits we need to have the original frequency table. That table needs to be transmitted or saved along with the compressed data, otherwise the decoder doesn't know how to interpret the bits. Because of the overhead of this frequency table (about 1 kilobyte), it doesn't really pay to use Huffman encoding on very small inputs.
+To be able to decode these bits, we need to have the original frequency table. That table needs to be transmitted or saved along with the compressed data. Otherwise, the decoder does not know how to interpret the bits. Because of the overhead of this frequency table (about 1 kilobyte), it is not beneficial to use Huffman encoding on small inputs.
 
 ## How it works
 
-When compressing a stream of bytes, the algorithm first creates a frequency table that counts how often each byte occurs. Based on this table it creates a binary tree that describes the bit strings for each of the input bytes.
+When compressing a stream of bytes, the algorithm first creates a frequency table that counts how often each byte occurs. Based on this table, the algorithm creates a binary tree that describes the bit strings for each of the input bytes.
 
 For our example, the tree looks like this:
 
@@ -53,17 +53,17 @@ For our example, the tree looks like this:
 
 Note that the tree has 16 leaf nodes (the grey ones), one for each byte value from the input. Each leaf node also shows the count of how often it occurs. The other nodes are "intermediate" nodes. The number shown in these nodes is the sum of the counts of their child nodes. The count of the root node is therefore the total number of bytes in the input.
 
-The edges between the nodes either say "1" or "0". These correspond to the bit-encodings of the leaf nodes. Notice how each left branch is always 1 and each right branch is always 0.
+The edges between the nodes are either "1" or "0". These correspond to the bit-encodings of the leaf nodes. Notice how each left branch is always 1 and each right branch is always 0.
 
-Compression is then a matter of looping through the input bytes, and for each byte traverse the tree from the root node to that byte's leaf node. Every time we take a left branch, we emit a 1-bit. When we take a right branch, we emit a 0-bit.
+Compression is then a matter of looping through the input bytes and for each byte traversing the tree from the root node to that byte's leaf node. Every time we take a left branch, we emit a 1-bit. When we take a right branch, we emit a 0-bit.
 
-For example, to go from the root node to `c`, we go right (`0`), right again (`0`), left (`1`), and left again (`1`). So the Huffman code for `c` is `0011`.
+For example, to go from the root node to `c`, we go right (`0`), right again (`0`), left (`1`), and left again (`1`). This gives the Huffman code as `0011` for `c`.
 
-Decompression works in exactly the opposite way. It reads the compressed bits one-by-one and traverses the tree until we get to a leaf node. The value of that leaf node is the uncompressed byte. For example, if the bits are `11010`, we start at the root and go left, left again, right, left, and a final right to end up at `d`.
+Decompression works in exactly the opposite way. It reads the compressed bits one-by-one and traverses the tree until it reaches to a leaf node. The value of that leaf node is the uncompressed byte. For example, if the bits are `11010`, we start at the root and go left, left again, right, left, and a final right to end up at `d`.
 
 ## The code
 
-Before we get to the actual Huffman coding scheme, it's useful to have some helper code that can write individual bits to an `NSData` object. The smallest piece of data that `NSData` understands is the byte, but we're dealing in bits, so we need to translate between the two.
+Before we get to the actual Huffman coding scheme, it is useful to have some helper code that can write individual bits to an `NSData` object. The smallest piece of data that `NSData` understands is the byte, but we are dealing in bits, so we need to translate between the two.
 
 ```swift
 public class BitWriter {
@@ -92,11 +92,11 @@ public class BitWriter {
 }
 ```
 
-To add a bit to the `NSData` you call `writeBit()`. This stuffs each new bit into the `outByte` variable. Once you've written 8 bits, `outByte` gets added to the `NSData` object for real.
+To add a bit to the `NSData`, you can call `writeBit()`. This helper object stuffs each new bit into the `outByte` variable. Once you have written 8 bits, `outByte` gets added to the `NSData` object for real.
 
 The `flush()` method is used for outputting the very last byte. There is no guarantee that the number of compressed bits is a nice round multiple of 8, in which case there may be some spare bits at the end. If so, `flush()` adds a few 0-bits to make sure that we write a full byte.
 
-We'll use a similar helper object for reading individual bits from `NSData`:
+Here is a similar helper object for reading individual bits from `NSData`:
 
 ```swift
 public class BitReader {
@@ -122,15 +122,15 @@ public class BitReader {
 }
 ```
 
-This works in a similar fashion. We read one whole byte from the `NSData` object and put it in `inByte`. Then `readBit()` returns the individual bits from that byte. Once `readBit()` has been called 8 times, we read the next byte from the `NSData`.
+By using this helper object, we can read one whole byte from the `NSData` object and put it in `inByte`. Then, `readBit()` returns the individual bits from that byte. Once `readBit()` has been called 8 times, we read the next byte from the `NSData`.
 
-> **Note:** It's no big deal if you're unfamiliar with this sort of bit manipulation. Just know that these two helper objects make it simple for us to write and read bits and not worry about all the messy stuff of making sure they end up in the right place.
+> **Note:** If you are unfamiliar with this type of bit manipulation, just know that these two helper objects make it simple for us to write and read bits.
 
 ## The frequency table
 
-The first step in Huffman compression is to read the entire input stream and build a frequency table. This table contains a list of all 256 possible byte values and how often each of these bytes occurs in the input data.
+The first step in the Huffman compression is to read the entire input stream and build a frequency table. This table contains a list of all 256 possible byte values and shows how often each of these bytes occurs in the input data.
 
-We could store this frequency information in a dictionary or an array, but since we're going to need to build a tree anyway, we might as well store the frequency table as the leaves of the tree.
+We could store this frequency information in a dictionary or an array, but since we need to build a tree, we might store the frequency table as the leaves of the tree.
 
 Here are the definitions we need:
 
@@ -152,9 +152,9 @@ class Huffman {
 }
 ```
 
-The tree structure is stored in the `tree` array and will be made up of `Node` objects. Since this is a [binary tree](../Binary%20Tree/), each node needs two children, `left` and `right`, and a reference back to its `parent` node. Unlike a typical binary tree, however, these nodes don't to use pointers to refer to each other but simple integer indices in the `tree` array. (We also store the array `index` of the node itself; the reason for this will become clear later.)
+The tree structure is stored in the `tree` array and will be made up of `Node` objects. Since this is a [binary tree](../Binary%20Tree/), each node needs two children, `left` and `right`, and a reference back to its `parent` node. Unlike a typical binary tree, these nodes do not use pointers to refer to each other but use simple integer indices in the `tree` array. (We also store the array `index` of the node itself; the reason for this will become clear later.)
 
-Note that `tree` currently has room for 256 entries. These are for the leaf nodes because there are 256 possible byte values. Of course, not all of those may end up being used, depending on the input data. Later, we'll add more nodes as we build up the actual tree. For the moment there isn't a tree yet, just 256 separate leaf nodes with no connections between them. All the node counts are 0.
+Note that the `tree` currently has room for 256 entries. These are for the leaf nodes because there are 256 possible byte values. Of course, not all of those may end up being used, depending on the input data. Later, we will add more nodes as we build up the actual tree. For the moment, there is not a tree yet. It includes 256 separate leaf nodes with no connections between them. All the node counts are 0.
 
 We use the following method to count how often each byte occurs in the input data:
 
@@ -170,13 +170,13 @@ We use the following method to count how often each byte occurs in the input dat
   }
 ```
 
-This steps through the `NSData` object from beginning to end and for each byte increments the `count` of the corresponding leaf node. That's all there is to it. After `countByteFrequency()` completes, the first 256 `Node` objects in the `tree` array represent the frequency table.
+This steps through the `NSData` object from beginning to end and for each byte increments the `count` of the corresponding leaf node. After `countByteFrequency()` completes, the first 256 `Node` objects in the `tree` array represent the frequency table.
 
-Now, I mentioned that in order to decompress a Huffman-encoded block of data, you also need to have the original frequency table. If you were writing the compressed data to a file, then somewhere in the file you'd include the frequency table.
+To decompress a Huffman-encoded block of data, we need to have the original frequency table. If we were writing the compressed data to a file, then somewhere in the file we should include the frequency table.
 
-You could simply dump the first 256 elements from the `tree` array but that's not very efficient. It's likely that not all of these 256 elements will be used, plus you don't need to serialize the `parent`, `right`, and `left` pointers. All we need is the frequency information, not the entire tree.
+We could dump the first 256 elements from the `tree` array, but that is not efficient. Not all of these 256 elements will be used, and we do not need to serialize the `parent`, `right`, and `left` pointers. All we need is the frequency information and not the entire tree.
 
-Instead, we'll add a method to export the frequency table without all the pieces we don't need:
+Instead, we will add a method to export the frequency table without all the pieces we do not need:
 
 ```swift
   struct Freq {
@@ -193,7 +193,7 @@ Instead, we'll add a method to export the frequency table without all the pieces
   }
 ```
 
-The `frequencyTable()` method looks at those first 256 nodes from the tree but keeps only those that are actually used, without the `parent`, `left`, and `right` pointers. It returns an array of `Freq` objects. You have to serialize this array along with the compressed data so that it can be properly decompressed later.
+The `frequencyTable()` method looks at those first 256 nodes from the tree but keeps only those that are used, without the `parent`, `left`, and `right` pointers. It returns an array of `Freq` objects. You have to serialize this array along with the compressed data, so that it can be properly decompressed later.
 
 ## The tree
 
@@ -201,7 +201,7 @@ As a reminder, there is the compression tree for the example:
 
 ![The compression tree](Images/Tree.png)
 
-The leaf nodes represent the actual bytes that are present in the input data. The intermediary nodes connect the leaves in such a way that the path from the root to a frequently-used byte value is shorter than the path to a less common byte value. As you can see, `m`, `s`, space, and `o` are the most common letters in our input data and therefore they are highest up in the tree.
+The leaf nodes represent the actual bytes that are present in the input data. The intermediary nodes connect the leaves in such a way that the path from the root to a frequently-used byte value is shorter than the path to a less common byte value. As you can see, `m`, `s`, space, and `o` are the most common letters in our input data and the highest up in the tree.
 
 To build the tree, we do the following:
 
@@ -209,7 +209,7 @@ To build the tree, we do the following:
 2. Create a new parent node that links these two nodes together.
 3. This repeats over and over until only one node with no parent remains. This becomes the root node of the tree.
 
-This is an ideal place to use a [priority queue](../Priority%20Queue/). A priority queue is a data structure that is optimized so that finding the minimum value is always very fast. Here, we repeatedly need to find the node with the smallest count.
+This is an ideal place to use a [priority queue](../Priority%20Queue/). A priority queue is a data structure that is optimized, so that finding the minimum value is always fast. Here, we repeatedly need to find the node with the smallest count.
 
 The function `buildTree()` then becomes:
 
@@ -252,15 +252,15 @@ Here is how it works step-by-step:
 
 4. Link the two nodes into their new parent node. Now this new intermediate node has become part of the tree.
 
-5. Put the new intermediate node back into the queue. At this point we're done with `node1` and `node2`, but the `parentNode` still need to be connected to other nodes in the tree.
+5. Put the new intermediate node back into the queue. At this point we are done with `node1` and `node2`, but the `parentNode` still needs to be connected to other nodes in the tree.
 
-6. Repeat steps 2-5 until there is only one node left in the queue. This becomes the root node of the tree, and we're done.
+6. Repeat steps 2-5 until there is only one node left in the queue. This becomes the root node of the tree, and we are done.
 
 The animation shows what the process looks like:
 
 ![Building the tree](Images/BuildTree.gif)
 
-> **Note:** Instead of using a priority queue, you can repeatedly iterate through the `tree` array to find the next two smallest nodes, but that makes the compressor quite slow, **O(n^2)**. Using the priority queue, the running time is only **O(n log n)** where **n** is the number of nodes.
+> **Note:** Instead of using a priority queue, you can repeatedly iterate through the `tree` array to find the next two smallest nodes, but that makes the compressor slow as **O(n^2)**. Using the priority queue, the running time is only **O(n log n)** where **n** is the number of nodes.
 
 > **Fun fact:** Due to the nature of binary trees, if we have *x* leaf nodes we can at most add *x - 1* additional nodes to the tree. Given that at most there will be 256 leaf nodes, the tree will never contain more than 511 nodes total.
 
@@ -286,11 +286,11 @@ Now that we know how to build the compression tree from the frequency table, we
   }
 ```
 
-This first calls `countByteFrequency()` to build the frequency table, then `buildTree()` to put together the compression tree. It also creates a `BitWriter` object for writing individual bits.
+This first calls `countByteFrequency()` to build the frequency table and then calls `buildTree()` to put together the compression tree. It also creates a `BitWriter` object for writing individual bits.
 
-Then it loops through the entire input and for each byte calls `traverseTree()`. That method will step through the tree nodes and for each node write a 1 or 0 bit. Finally, we return the `BitWriter`'s data object.
+Then, it loops through the entire input and calls `traverseTree()`for each byte. This method will step through the tree nodes and for each node write a 1 or 0 bit. Finally, we return the `BitWriter`'s data object.
 
-> **Note:** Compression always requires two passes through the entire input data: first to build the frequency table, second to convert the bytes to their compressed bit sequences.
+> **Note:** Compression always requires two passes through the entire input data: first to build the frequency table, and second to convert the bytes to their compressed bit sequences.
 
 The interesting stuff happens in `traverseTree()`. This is a recursive method:
 
@@ -309,15 +309,15 @@ The interesting stuff happens in `traverseTree()`. This is a recursive method:
   }
 ```
 
-When we call this method from `compressData()`, the `nodeIndex` parameter is the array index of the leaf node for the byte that we're about to encode. This method recursively walks the tree from a leaf node up to the root, and then back again.
+When we call this method from `compressData()`, the `nodeIndex` parameter is the array index of the leaf node for the byte that we need to encode. This method recursively walks the tree from a leaf node up to the root and then back again.
 
-As we're going back from the root to the leaf node, we write a 1 bit or a 0 bit for every node we encounter. If a child is the left node, we emit a 1; if it's the right node, we emit a 0.
+As we are going back from the root to the leaf node, we write a 1 bit or a 0 bit for every node we encounter. If a child is the left node, we emit a 1; if it is the right node, we emit a 0.
 
 In a picture:
 
 ![How compression works](Images/Compression.png)
 
-Even though the illustration of the tree shows a 0 or 1 for each edge between the nodes, the bit values 0 and 1 aren't actually stored in the tree! The rule is that we write a 1 bit if we take the left branch and a 0 bit if we take the right branch, so just knowing the direction we're going in is enough to determine what bit value to write.
+Even though the illustration of the tree shows a 0 or 1 for each edge between the nodes, the bit values 0 and 1 are not actually stored in the tree! The rule is that we write a 1 bit if we take the left branch and a 0 bit if we take the right branch, so just knowing the direction we are going in is enough to determine what bit value to write.
 
 You use the `compressData()` method as follows:
 
@@ -332,9 +332,9 @@ if let originalData = s1.dataUsingEncoding(NSUTF8StringEncoding) {
 
 ## Decompression
 
-Decompression is pretty much compression in reverse. However, the compressed bits are useless to us without the frequency table. Earlier you saw the `frequencyTable()` method that returns an array of `Freq` objects. The idea is that if you were saving the compressed data into a file or sending it across the network, you'd also save that `[Freq]` array along with it.
+Decompression is the compression in reverse. However, the compressed bits are useless without the frequency table. As mentioned, the `frequencyTable()` method returns an array of `Freq` objects. If we were saving the compressed data into a file or sending it across the network, we'd also save that `[Freq]` array along with it.
 
-We first need some way to turn the `[Freq]` array back into a compression tree. Fortunately, this is pretty easy:
+We first need some way to turn the `[Freq]` array back into a compression tree:
 
 ```swift
   fileprivate func restoreTree(fromTable frequencyTable: [Freq]) {
@@ -349,7 +349,7 @@ We first need some way to turn the `[Freq]` array back into a compression tree.
 
 We convert the `Freq` objects into leaf nodes and then call `buildTree()` to do the rest.
 
-Here is the code for `decompressData()`, which takes an `NSData` object with Huffman-encoded bits and a frequency table, and returns the original data:
+Here is the code for `decompressData()`, which takes an `NSData` object with Huffman-encoded bits and a frequency table, and it returns the original data:
 
 ```swift
   func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
@@ -385,13 +385,13 @@ This also uses a helper method to traverse the tree:
   }
 ```
 
-`findLeafNode()` walks the tree from the root down to the leaf node given by `nodeIndex`. At each intermediate node we read a new bit and then step to the left (bit is 1) or the right (bit is 0). When we get to the leaf node, we simply return its index, which is equal to the original byte value.
+`findLeafNode()` walks the tree from the root down to the leaf node given by `nodeIndex`. At each intermediate node, we read a new bit and then step to the left (bit is 1) or the right (bit is 0). When we get to the leaf node, we simply return its index, which is equal to the original byte value.
 
 In a picture:
 
 ![How decompression works](Images/Decompression.png)
 
-Here's how you would use the decompression method:
+Here is how we use the decompression method:
 
 ```swift
   let frequencyTable = huffman1.frequencyTable()
@@ -402,9 +402,9 @@ Here's how you would use the decompression method:
   let s2 = String(data: decompressedData, encoding: NSUTF8StringEncoding)!
 ```
 
-First you get the frequency table from somewhere (in this case the `Huffman` object we used to encode the data) and then call `decompressData()`. The string that results should be equal to the one you compressed in the first place.
+First we get the frequency table from somewhere (in this case the `Huffman` object we used to encode the data) and then call `decompressData()`. The string that results should be equal to the one we compressed in the first place.
 
-You can see how this works in more detail in the Playground.
+we can see how this works in more detail in the Playground.
 
 ## See also
 

From d70f40ed8668e60584dc1bd9d5b859b7ad2e91de Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Wed, 5 Apr 2017 10:34:21 -0700
Subject: [PATCH 080/862] Revisions in README.markdown

I have revised your document to be simplified and concise.
---
 Array2D/README.markdown | 30 ++++++++++++++----------------
 1 file changed, 14 insertions(+), 16 deletions(-)

diff --git a/Array2D/README.markdown b/Array2D/README.markdown
index d67079691..88f25c99a 100644
--- a/Array2D/README.markdown
+++ b/Array2D/README.markdown
@@ -1,14 +1,14 @@
 # Array2D
 
-In C and Objective-C you can write the following line,
+In C and Objective-C, you can write the following line,
 
 	int cookies[9][7];
 	
-to make a 9x7 grid of cookies. This would create a two-dimensional array of 63 elements. To find the cookie at column 3, row 6, you'd write:
+to make a 9x7 grid of cookies. This creates a two-dimensional array of 63 elements. To find the cookie at column 3 and row 6, you can write:
 
 	myCookie = cookies[3][6];
 	
-Unfortunately, you can't write the above in Swift. To create a multi-dimensional array in Swift you'd have to do something like this:
+This statement is not acceptable in Swift. To create a multi-dimensional array in Swift, you can write:
 
 ```swift
 var cookies = [[Int]]()
@@ -21,19 +21,19 @@ for _ in 1...9 {
 }
 ```
 
-And then to find a cookie:
+Then, to find a cookie, you can write:
 
 ```swift
 let myCookie = cookies[3][6]
 ```
 
-Actually, you could create the array in a single line of code, like so:
+You can also create the array in a single line of code:
 
 ```swift
 var cookies = [[Int]](repeating: [Int](repeating: 0, count: 7), count: 9)
 ```
 
-but that's just ugly. To be fair, you can hide the ugliness in a helper function:
+This looks complicated, but can simplfy it in a helper function:
 
 ```swift
 func dim<T>(_ count: Int, _ value: T) -> [T] {
@@ -41,13 +41,13 @@ func dim<T>(_ count: Int, _ value: T) -> [T] {
 }
 ```
 
-And then creating the array looks like this:
+Then, you can create the array:
 
 ```swift
 var cookies = dim(9, dim(7, 0))
 ```
 
-Swift infers that the datatype of the array should be `Int` because you specified `0` as the default value of the array elements. To use a string instead, you'd write:
+Swift infers that the datatype of the array must be `Int` because you specified `0` as the default value of the array elements. To use a string instead, you can write:
 
 ```swift
 var cookies = dim(9, dim(7, "yum"))
@@ -59,9 +59,9 @@ The `dim()` function makes it easy to go into even more dimensions:
 var threeDimensions = dim(2, dim(3, dim(4, 0)))
 ```
 
-The downside of using multi-dimensional arrays in this fashion -- actually, multiple nested arrays -- is that it's easy to lose track of what dimension represents what.
+The downside of using multi-dimensional arrays or multiple nested arrays in this way is to lose track of what dimension represents what.
 
-So instead let's create our own type that acts like a 2-D array and that is more convenient to use. Here it is, short and sweet:
+Instead, you can create your own type that acts like a 2-D array which is more convenient to use:
 
 ```swift
 public struct Array2D<T> {
@@ -92,26 +92,24 @@ public struct Array2D<T> {
 
 `Array2D` is a generic type, so it can hold any kind of object, not just numbers.
 
-To create an instance of `Array2D` you'd write:
+To create an instance of `Array2D`, you can write:
 
 ```swift
 var cookies = Array2D(columns: 9, rows: 7, initialValue: 0)
 ```
 
-Thanks to the `subscript` function, you can do the following to retrieve an object from the array:
+By using the `subscript` function, you can retrieve an object from the array:
 
 ```swift
 let myCookie = cookies[column, row]
 ```
 
-Or change it:
+Or, you can change it:
 
 ```swift
 cookies[column, row] = newCookie
 ```
 
-Internally, `Array2D` uses a single one-dimensional array to store the data. The index of an object in that array is given by `(row x numberOfColumns) + column`. But as a user of `Array2D` you don't have to worry about that; you only have to think in terms of "column" and "row", and let `Array2D` figure out the details for you. That's the advantage of wrapping primitive types into a wrapper class or struct.
-
-And that's all there is to it.
+Internally, `Array2D` uses a single one-dimensional array to store the data. The index of an object in that array is given by `(row x numberOfColumns) + column`, but as a user of `Array2D`, you only need to think in terms of "column" and "row", and the details will be done by `Array2D`. This is the advantage of wrapping primitive types into a wrapper class or struct.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 777bf7b948e75d77bbac8cbba5dc40716c6b5d61 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 6 Apr 2017 16:34:58 +0300
Subject: [PATCH 081/862] Deleted unnecessary code and added comments

---
 .../Dijkstra.playground/Contents.swift        | 37 +++++++++++++------
 1 file changed, 26 insertions(+), 11 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index 8d600d577..13087a8f9 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -3,19 +3,15 @@
 import Foundation
 import UIKit
 
-open class ProductVertex: Vertex {}
-
 open class Vertex: Hashable, Equatable {
 
     open var identifier: String!
     open var neighbors: [(Vertex, Double)] = []
     open var pathLengthFromStart: Double = Double.infinity
     open var pathVerticesFromStart: [Vertex] = []
-//    open var point: CGPoint!
 
-    public init(identifier: String/*, point: CGPoint*/) {
+    public init(identifier: String) {
         self.identifier = identifier
-//        self.point = point
     }
 
     open var hashValue: Int {
@@ -77,7 +73,9 @@ public class Dijkstra {
 var _vertices: Set<Vertex> = Set()
 
 func createNotConnectedVertices() {
-    for i in 0..<15 {
+    //change this value to increase or decrease amount of vertices in the graph
+    let numberOfVerticesInGraph = 15
+    for i in 0..<numberOfVerticesInGraph {
         let vertex = Vertex(identifier: "\(i)")
         _vertices.insert(vertex)
     }
@@ -108,15 +106,32 @@ func randomVertex(except vertex: Vertex) -> Vertex {
     return newSet[index]
 }
 
+func randomVertex() -> Vertex {
+    let offset = Int(arc4random_uniform(UInt32(_vertices.count)))
+    let index = _vertices.index(_vertices.startIndex, offsetBy: offset)
+    return _vertices[index]
+}
+
+//initialize random graph
 createNotConnectedVertices()
 setupConnections()
+
+//initialize Dijkstra algorithm with graph vertices
 let dijkstra = Dijkstra(vertices: _vertices)
-let offset = Int(arc4random_uniform(UInt32(_vertices.count)))
-let index = _vertices.index(_vertices.startIndex, offsetBy: offset)
-let startVertex = _vertices[index]
+
+//decide which vertex will be the starting one
+let startVertex = randomVertex()
+
+//ask algorithm to find shortest paths from start vertex to all others
 dijkstra.findShortestPaths(from: startVertex)
+
+//printing results
 let destinationVertex = randomVertex(except: startVertex)
-destinationVertex.pathLengthFromStart
-destinationVertex.pathVerticesFromStart
+print(destinationVertex.pathLengthFromStart)
+var pathVerticesFromStartString: [String] = []
+for vertex in destinationVertex.pathVerticesFromStart {
+    pathVerticesFromStartString.append(vertex.identifier)
+}
+print(pathVerticesFromStartString.joined(separator: "->"))
 
 

From 11fdc6ca756b4d402e807a0f9b6063fd6f38dab1 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Thu, 6 Apr 2017 11:57:03 -0700
Subject: [PATCH 082/862] Revisions in README.markdown

I have revised your document to be more concise.
---
 Graph/README.markdown | 62 +++++++++++++++++++++----------------------
 1 file changed, 31 insertions(+), 31 deletions(-)

diff --git a/Graph/README.markdown b/Graph/README.markdown
index a2531e808..bc33b044a 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -1,26 +1,26 @@
 # Graph
 
-A graph is something that looks like this:
+A graph looks like the following picture:
 
 ![A graph](Images/Graph.png)
 
-In computer-science lingo, a graph is a set of *vertices* paired with a set of *edges*. The vertices are the round things and the edges are the lines between them. Edges connect a vertex to other vertices.
+In computer science, a graph is defined as a set of *vertices* paired with a set of *edges*. The vertices are represented by circles, and the edges are the lines between them. Edges connect a vertex to other vertices.
 
-> **Note:** Vertices are sometimes also called "nodes" and edges are also called "links".
+> **Note:** Vertices are sometimes called "nodes", and edges are called "links".
 
-For example, a graph can represent a social network. Each person is a vertex, and people who know each other are connected by edges. A somewhat historically inaccurate example:
+A graph can represent a social network. Each person is a vertex, and people who know each other are connected by edges. Here is a somewhat historically inaccurate example:
 
 ![Social network](Images/SocialNetwork.png)
 
-Graphs come in all kinds of shapes and sizes. The edges can have a *weight*, where a positive or negative numeric value is assigned to each edge. Consider an example of a graph representing airplane flights. Cities can be vertices, and flights can be edges. Then an edge weight could describe flight time or the price of a ticket.
+Graphs have various shapes and sizes. The edges can have a *weight*, where a positive or negative numeric value is assigned to each edge. Consider an example of a graph representing airplane flights. Cities can be vertices, and flights can be edges. Then, an edge weight could describe flight time or the price of a ticket.
 
 ![Airplane flights](Images/Flights.png)
 
 With this hypothetical airline, flying from San Francisco to Moscow is cheapest by going through New York.
 
-Edges can also be *directed*. So far the edges you've seen have been undirected, so if Ada knows Charles, then Charles also knows Ada. A directed edge, on the other hand, implies a one-way relationship. A directed edge from vertex X to vertex Y connects X to Y, but *not* Y to X.
+Edges can also be *directed*. In examples mentioned above, the edges are undirected. For instance, if Ada knows Charles, then Charles also knows Ada. A directed edge, on the other hand, implies a one-way relationship. A directed edge from vertex X to vertex Y connects X to Y, but *not* Y to X.
 
-Continuing from the flights example, a directed edge from San Francisco to Juneau in Alaska would indicate that there is a flight from San Francisco to Juneau, but not from Juneau to San Francisco (I suppose that means you're walking back).
+Continuing from the flights example, a directed edge from San Francisco to Juneau in Alaska indicates that there is a flight from San Francisco to Juneau, but not from Juneau to San Francisco (I suppose that means you're walking back).
 
 ![One-way flights](Images/FlightsDirected.png)
 
@@ -28,51 +28,51 @@ The following are also graphs:
 
 ![Tree and linked list](Images/TreeAndList.png)
 
-On the left is a [tree](../Tree/) structure, on the right a [linked list](../Linked%20List/). Both can be considered graphs, but in a simpler form. After all, they have vertices (nodes) and edges (links).
+On the left is a [tree](../Tree/) structure, on the right a [linked list](../Linked%20List/). They can be considered graphs but in a simpler form. They both have vertices (nodes) and edges (links).
 
-The very first graph I showed you contained *cycles*, where you can start off at a vertex, follow a path, and come back to the original vertex. A tree is a graph without such cycles.
+The first graph includes *cycles*, where you can start off at a vertex, follow a path, and come back to the original vertex. A tree is a graph without such cycles.
 
-Another very common type of graph is the *directed acyclic graph* or DAG:
+Another common type of graph is the *directed acyclic graph* or DAG:
 
 ![DAG](Images/DAG.png)
 
-Like a tree this does not have any cycles in it (no matter where you start, there is no path back to the starting vertex), but unlike a tree the edges are directional and the shape doesn't necessarily form a hierarchy.
+Like a tree, this graph does not have any cycles (no matter where you start, there is no path back to the starting vertex), but this graph has directional edges with the shape that does not necessarily form a hierarchy.
 
 ## Why use graphs?
 
-Maybe you're shrugging your shoulders and thinking, what's the big deal? Well, it turns out that graphs are an extremely useful data structure.
+Maybe you're shrugging your shoulders and thinking, what's the big deal? Well, it turns out that a graph is a useful data structure.
 
-If you have some programming problem where you can represent some of your data as vertices and some of it as edges between those vertices, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First%20Search/) or [depth-first search](../Depth-First%20Search) to find a solution.
+If you have a programming problem where you can represent your data as vertices and edges, then you can draw your problem as a graph and use well-known graph algorithms such as [breadth-first search](../Breadth-First%20Search/) or [depth-first search](../Depth-First%20Search) to find a solution.
 
-For example, let's say you have a list of tasks where some tasks have to wait on others before they can begin. You can model this using an acyclic directed graph:
+For example, suppose you have a list of tasks where some tasks have to wait on others before they can begin. You can model this using an acyclic directed graph:
 
 ![Tasks as a graph](Images/Tasks.png)
 
-Each vertex represents a task. Here, an edge between two vertices means that the source task must be completed before the destination task can start. So task C cannot start before B and D are finished, and B nor D can start before A is finished.
+Each vertex represents a task. An edge between two vertices means the source task must be completed before the destination task can start. As an example, task C cannot start before B and D are finished, and B nor D can start before A is finished.
 
 Now that the problem is expressed using a graph, you can use a depth-first search to perform a [topological sort](../Topological%20Sort/). This will put the tasks in an optimal order so that you minimize the time spent waiting for tasks to complete. (One possible order here is A, B, D, E, C, F, G, H, I, J, K.)
 
-Whenever you're faced with a tough programming problem, ask yourself, "how can I express this problem using a graph?" Graphs are all about representing relationships between your data. The trick is in how you define "relationship".
+Whenever you are faced with a tough programming problem, ask yourself, "how can I express this problem using a graph?" Graphs are all about representing relationships between your data. The trick is in how you define "relationships".
 
-If you're a musician you might appreciate this graph:
+If you are a musician you might appreciate this graph:
 
 ![Chord map](Images/ChordMap.png)
 
-The vertices are chords from the C major scale. The edges -- the relationships between the chords -- represent how [likely one chord is to follow another](http://mugglinworks.com/chordmaps/genmap.htm). This is a directed graph, so the direction of the arrows shows how you can go from one chord to the next. It's also a weighted graph, where the weight of the edges -- portrayed here by line thickness -- shows a strong relationship between two chords. As you can see, a G7-chord is very likely to be followed by a C chord, and much less likely by a Am chord.
+The vertices are chords from the C major scale. The edges -- the relationships between the chords -- represent how [likely one chord is to follow another](http://mugglinworks.com/chordmaps/genmap.htm). This is a directed graph, so the direction of the arrows shows how you can go from one chord to the next. It is also a weighted graph, where the weight of the edges -- portrayed here by line thickness -- shows a strong relationship between two chords. As you can see, a G7-chord is very likely to be followed by a C chord, and much less likely by a Am chord.
 
-You're probably already using graphs without even knowing it. Your data model is also a graph (from Apple's Core Data documentation):
+You are probably already using graphs without even knowing it. Your data model is also a graph (from Apple's Core Data documentation):
 
 ![Core Data model](https://developer.apple.com/library/ios/documentation/Cocoa/Conceptual/CoreDataVersioning/Art/recipe_version2.0.jpg)
 
-Another common graph that's used by programmers is the state machine, where edges depict the conditions for transitioning between states. Here is a state machine that models my cat:
+Another common graph used by programmers is the state machine, where edges depict the conditions for transitioning between states. Here is a state machine that models my cat:
 
 ![State machine](Images/StateMachine.png)
 
-Graphs are awesome. Facebook made a fortune from their social graph. If you're going to learn any data structure, it should be the graph and the vast collection of standard graph algorithms.
+Graphs are awesome. Facebook made a fortune from their social graph. If you are going to learn any data structure, you must choose the graph and the vast collection of standard graph algorithms.
 
 ## Vertices and edges, oh my!
 
-In theory, a graph is just a bunch of vertex objects and a bunch of edge objects. But how do you describe these in code?
+In theory, a graph is just a bunch of vertex and edge objects, but how do you describe this in code?
 
 There are two main strategies: adjacency list and adjacency matrix.
 
@@ -80,9 +80,9 @@ There are two main strategies: adjacency list and adjacency matrix.
 
 ![Adjacency list](Images/AdjacencyList.png)
 
-The adjacency list describes outgoing edges. A has an edge to B but B does not have an edge back to A, so A does not appear in B's adjacency list. Finding an edge or weight between two vertices can be expensive because there is no random access to edges–you must traverse the adjacency lists until it is found.
+The adjacency list describes outgoing edges. A has an edge to B, but B does not have an edge back to A, so A does not appear in B's adjacency list. Finding an edge or weight between two vertices can be expensive because there is no random access to edges. You must traverse the adjacency lists until it is found.
 
-**Adjacency Matrix.** In an adjacency matrix implementation, a matrix with rows and columns representing vertices stores a weight to indicate if vertices are connected, and by what weight. For example, if there is a directed edge of weight 5.6 from vertex A to vertex B, then the entry with row for vertex A, column for vertex B would have value 5.6:
+**Adjacency Matrix.** In an adjacency matrix implementation, a matrix with rows and columns representing vertices stores a weight to indicate if vertices are connected and by what weight. For example, if there is a directed edge of weight 5.6 from vertex A to vertex B, then the entry with row for vertex A and column for vertex B would have the value 5.6:
 
 ![Adjacency matrix](Images/AdjacencyMatrix.png)
 
@@ -103,7 +103,7 @@ Let *V* be the number of vertices in the graph, and *E* the number of edges.  Th
 
 In the case of a *sparse* graph, where each vertex is connected to only a handful of other vertices, an adjacency list is the best way to store the edges. If the graph is *dense*, where each vertex is connected to most of the other vertices, then a matrix is preferred.
 
-We'll show you sample implementations of both adjacency list and adjacency matrix.
+Here are sample implementations of both adjacency list and adjacency matrix:
 
 ## The code: edges and vertices
 
@@ -137,9 +137,9 @@ It stores arbitrary data with a generic type `T`, which is `Hashable` to enforce
 
 ## The code: graphs
 
-> **Note:** There are many, many ways to implement graphs. The code given here is just one possible implementation. You probably want to tailor the graph code to each individual problem you're trying to solve. For instance, your edges may not need a `weight` property, or you may not have the need to distinguish between directed and undirected edges.
+> **Note:** There are many ways to implement graphs. The code given here is just one possible implementation. You probably want to tailor the graph code to each individual problem you are trying to solve. For instance, your edges may not need a `weight` property, or you may not have the need to distinguish between directed and undirected edges.
 
-Here's an example of a very simple graph:
+Here is an example of a simple graph:
 
 ![Demo](Images/Demo1.png)
 
@@ -165,7 +165,7 @@ for graph in [AdjacencyMatrixGraph<Int>(), AdjacencyListGraph<Int>()] {
 }
 ```
 
-As mentioned earlier, to create an undirected edge you need to make two directed edges. If we wanted undirected graphs, we'd call this method instead, which takes care of that work for us:
+As mentioned earlier, to create an undirected edge you need to make two directed edges. For undirected graphs, we call the following method instead:
 
 ```swift
   graph.addUndirectedEdge(v1, to: v2, withWeight: 1.0)
@@ -198,7 +198,7 @@ private class EdgeList<T> where T: Equatable, T: Hashable {
 }
 ```
 
-They are implemented as a class as opposed to structs so we can modify them by reference, in place, like when adding an edge to a new vertex, where the source vertex already has an edge list:
+They are implemented as a class as opposed to structs, so we can modify them by reference, in place, like when adding an edge to a new vertex, where the source vertex already has an edge list:
 
 ```swift
 open override func createVertex(_ data: T) -> Vertex<T> {
@@ -231,7 +231,7 @@ where the general form `a -> [(b: w), ...]` means an edge exists from `a` to `b`
 
 ## The code: adjacency matrix
 
-We'll keep track of the adjacency matrix in a two-dimensional `[[Double?]]` array. An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight. If `adjacencyMatrix[i][j]` is not nil, then there is an edge from vertex `i` to vertex `j`.
+We will keep track of the adjacency matrix in a two-dimensional `[[Double?]]` array. An entry of `nil` indicates no edge, while any other value indicates an edge of the given weight. If `adjacencyMatrix[i][j]` is not nil, then there is an edge from vertex `i` to vertex `j`.
 
 To index into the matrix using vertices, we use the `index` property in `Vertex`, which is assigned when creating the vertex through the graph object. When creating a new vertex, the graph must resize the matrix:
 
@@ -277,6 +277,6 @@ Then the adjacency matrix looks like this:
 
 ## See also
 
-This article described what a graph is and how you can implement the basic data structure. But we have many more articles on practical uses for graphs, so check those out too!
+This article described what a graph is, and how you can implement the basic data structure. We have other articles on practical uses of graphs, so check those out too!
 
 *Written by Donald Pinckney and Matthijs Hollemans*

From 0a77b0685a7c26512377ba57ed02d2ee4644a880 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Thu, 6 Apr 2017 13:57:39 -0700
Subject: [PATCH 083/862] Revisions in README.markdown

I have revised your document to be more concise.
---
 Binary Search Tree/README.markdown | 138 ++++++++++++++---------------
 1 file changed, 69 insertions(+), 69 deletions(-)

diff --git a/Binary Search Tree/README.markdown b/Binary Search Tree/README.markdown
index b3b955c61..14ef931b9 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -2,7 +2,7 @@
 
 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.
 
-If you don't know what a tree is or what it is for, then [read this first](../Tree/).
+For more iformation about a tree, [read this first](../Tree/).
 
 ## "Always sorted" property
 
@@ -12,56 +12,56 @@ Here is an example of a valid binary search tree:
 
 Notice how each left child is smaller than its parent node, and each right child is greater than its parent node. This is the key feature of a binary search tree.
 
-For example, `2` is smaller than `7` so it goes on the left; `5` is greater than `2` so it goes on the right.
+For example, `2` is smaller than `7`, so it goes on the left; `5` is greater than `2`, so it goes on the right.
 
 ## Inserting new nodes
 
 When performing an insertion, we first compare the new value to the root node. If the new value is smaller, we take the *left* branch; if greater, we take the *right* branch. We work our way down the tree this way until we find an empty spot where we can insert the new value.
 
-Say we want to insert the new value `9`:
+Suppose we want to insert the new value `9`:
 
 - We start at the root of the tree (the node with the value `7`) and compare it to the new value `9`.
 - `9 > 7`, so we go down the right branch and repeat the same procedure but this time on node `10`.
 - Because `9 < 10`, we go down the left branch.
-- We've now arrived at a point where there are no more values to compare with. A new node for `9` is inserted at that location.
+- We now arrived at a point where there are no more values to compare with. A new node for `9` is inserted at that location.
 
-The tree now looks like this:
+Here is the tree after inserting the new value `9`:
 
 ![After adding 9](Images/Tree2.png)
 
-There is always only one possible place where the new element can be inserted in the tree. Finding this place is usually pretty quick. It takes **O(h)** time, where **h** is the height of the tree.
+There is only one possible place where the new element can be inserted in the tree. Finding this place is usually quick. It takes **O(h)** time, where **h** is the height of the tree.
 
 > **Note:** The *height* of a node is the number of steps it takes to go from that node to its lowest leaf. The height of the entire tree is the distance from the root to the lowest leaf. Many of the operations on a binary search tree are expressed in terms of the tree's height.
 
-By following this simple rule -- smaller values on the left, larger values on the right -- we keep the tree sorted in a way such that whenever we query it, we can quickly check if a value is in the tree.
+By following this simple rule -- smaller values on the left, larger values on the right -- we keep the tree sorted, so whenever we query it, we can check if a value is in the tree.
 
 ## Searching the tree
 
-To find a value in the tree, we essentially perform the same steps as with insertion:
+To find a value in the tree, we perform the same steps as with insertion:
 
 - If the value is less than the current node, then take the left branch.
 - If the value is greater than the current node, take the right branch.
-- And if the value is equal to the current node, we've found it!
+- If the value is equal to the current node, we've found it!
 
-Like most tree operations, this is performed recursively until either we find what we're looking for, or run out of nodes to look at.
+Like most tree operations, this is performed recursively until either we find what we are looking for or run out of nodes to look at.
 
-If we were looking for the value `5` in the example, it would go as follows:
+Here is an example for searching the value `5`:
 
 ![Searching the tree](Images/Searching.png)
 
-Thanks to the structure of the tree, searching is really fast. It runs in **O(h)** time. If you have a well-balanced tree with a million nodes, it only takes about 20 steps to find anything in this tree. (The idea is very similar to [binary search](../Binary%20Search) in an array.)
+Searching is fast using the structure of the tree. It runs in **O(h)** time. If you have a well-balanced tree with a million nodes, it only takes about 20 steps to find anything in this tree. (The idea is very similar to [binary search](../Binary%20Search) in an array.)
 
 ## Traversing the tree
 
-Sometimes you don't want to look at just a single node, but at all of them.
+Sometimes you need to look at all nodes rather than only one.
 
 There are three ways to traverse a binary tree:
 
-1. *In-order* (or *depth-first*): first look at the left child of a node, then at the node itself, and finally at its right child.
-2. *Pre-order*: first look at a node, then its left and right children.
+1. *In-order* (or *depth-first*): first look at the left child of a node then at the node itself and finally at its right child.
+2. *Pre-order*: first look at a node then its left and right children.
 3. *Post-order*: first look at the left and right children and process the node itself last.
 
-Once again, this happens recursively.
+Traversing the tree also happens recursively.
 
 If you traverse a binary search tree in-order, it looks at all the nodes as if they were sorted from low to high. For the example tree, it would print `1, 2, 5, 7, 9, 10`:
 
@@ -69,7 +69,7 @@ If you traverse a binary search tree in-order, it looks at all the nodes as if t
 
 ## Deleting nodes
 
-Removing nodes is also easy. After removing a node, we replace the node with either its biggest child on the left or its smallest child on the right. That way the tree is still sorted after the removal. In following example, 10 is removed and replaced with either 9 (Figure 2), or 11 (Figure 3).
+Removing nodes is easy. After removing a node, we replace the node with either its biggest child on the left or its smallest child on the right. That way the tree is still sorted after the removal. In the following example, 10 is removed and replaced with either 9 (Figure 2) or 11 (Figure 3).
 
 ![Deleting a node with two children](Images/DeleteTwoChildren.png)
 
@@ -80,9 +80,9 @@ Note the replacement needs to happen when the node has at least one child. If it
 
 ## The code (solution 1)
 
-So much for the theory. Let's see how we can implement a binary search tree in Swift. There are different approaches you can take. First, I'll show you how to make a class-based version but we'll also look at how to make one using enums.
+So much for the theory. Let's see how we can implement a binary search tree in Swift. There are different approaches you can take. First, I will show you how to make a class-based version, but we will also look at how to make one using enums.
 
-Here's a first stab at a `BinarySearchTree` class:
+Here is an example for a `BinarySearchTree` class:
 
 ```swift
 public class BinarySearchTree<T: Comparable> {
@@ -133,21 +133,21 @@ public class BinarySearchTree<T: Comparable> {
 }
 ```
 
-This class describes just a single node, not the entire tree. It's a generic type, so the node can store any kind of data. It also has references to its `left` and `right` child nodes and a `parent` node.
+This class describes just a single node not the entire tree. It is a generic type, so the node can store any kind of data. It also has references to its `left` and `right` child nodes and a `parent` node.
 
-Here's how you'd use it:
+Here is how you can use it:
 
 ```swift
 let tree = BinarySearchTree<Int>(value: 7)
 ```
 
-The `count` property determines how many nodes are in the subtree described by this node. This doesn't just count the node's immediate children but also their children and their children's children, and so on. If this particular object is the root node, then it counts how many nodes are in the entire tree. Initially, `count = 0`.
+The `count` property determines how many nodes are in the subtree described by this node. This does not just count the node's immediate children but also their children and their children's children, and so on. If this particular object is the root node, then it counts how many nodes are in the entire tree. Initially, `count = 0`.
 
-> **Note:** Because `left`, `right`, and `parent` are optionals, we can make good use of Swift's optional chaining (`?`) and nil-coalescing operators (`??`). You could also write this sort of thing with `if let` but that is less concise.
+> **Note:** Because `left`, `right`, and `parent` are optional, we can make good use of Swift's optional chaining (`?`) and nil-coalescing operators (`??`). You could also write this sort of thing with `if let`, but that is less concise.
 
 ### Inserting nodes
 
-A tree node by itself is pretty useless, so here is how you would add new nodes to the tree:
+A tree node by itself is useless, so here is how you would add new nodes to the tree:
 
 ```swift
   public func insert(value: T) {
@@ -173,9 +173,9 @@ Like so many other tree operations, insertion is easiest to implement with recur
 
 If there is no more left or right child to look at, we create a `BinarySearchTree` object for the new node and connect it to the tree by setting its `parent` property.
 
-> **Note:** Because the whole point of a binary search tree is to have smaller nodes on the left and larger ones on the right, you should always insert elements at the root, to make to sure this remains a valid binary tree!
+> **Note:** Because the whole point of a binary search tree is to have smaller nodes on the left and larger ones on the right, you should always insert elements at the root to make sure this remains a valid binary tree!
 
-To build the complete tree from the example you'd do:
+To build the complete tree from the example you can do:
 
 ```swift
 let tree = BinarySearchTree<Int>(value: 7)
@@ -186,7 +186,7 @@ tree.insert(9)
 tree.insert(1)
 ```
 
-> **Note:** For reasons that will become clear later, you should insert the numbers in a somewhat random order. If you insert them in sorted order, the tree won't have the right shape.
+> **Note:** For reasons that will become clear later, you should insert the numbers in a random order. If you insert them in a sorted order, the tree will not have the right shape.
 
 For convenience, let's add an init method that calls `insert()` for all the elements in an array:
 
@@ -210,7 +210,7 @@ The first value in the array becomes the root of the tree.
 
 ### Debug output
 
-When working with somewhat complicated data structures such as this, it's useful to have human-readable debug output.
+When working with complicated data structures, it is useful to have human-readable debug output.
 
 ```swift
 extension BinarySearchTree: CustomStringConvertible {
@@ -236,11 +236,11 @@ The root node is in the middle. With some imagination, you should see that this
 
 ![The tree](Images/Tree2.png)
 
-By the way, you may be wondering what happens when you insert duplicate items? We always insert those in the right branch. Try it out!
+You may be wondering what happens when you insert duplicate items? We always insert those in the right branch. Try it out!
 
 ### Searching
 
-What do we do now that we have some values in our tree? Search for them, of course! Being able to find items quickly is the entire purpose of a binary search tree. :-)
+What do we do now that we have some values in our tree? Search for them, of course! To find items quickly is the main purpose of a binary search tree. :-)
 
 Here is the implementation of `search()`:
 
@@ -258,11 +258,11 @@ Here is the implementation of `search()`:
 
 I hope the logic is clear: this starts at the current node (usually the root) and compares the values. If the search value is less than the node's value, we continue searching in the left branch; if the search value is greater, we dive into the right branch.
 
-Of course, if there are no more nodes to look at -- when `left` or `right` is nil -- then we return `nil` to indicate the search value is not in the tree.
+If there are no more nodes to look at -- when `left` or `right` is nil -- then we return `nil` to indicate the search value is not in the tree.
 
-> **Note:** In Swift that's very conveniently done with optional chaining; when you write `left?.search(value)` it automatically returns nil if `left` is nil. There's no need to explicitly check for this with an `if` statement.
+> **Note:** In Swift, that is conveniently done with optional chaining; when you write `left?.search(value)` it automatically returns nil if `left` is nil. There is no need to explicitly check for this with an `if` statement.
 
-Searching is a recursive process but you can also implement it with a simple loop instead:
+Searching is a recursive process, but you can also implement it with a simple loop instead:
 
 ```swift
   public func search(value: T) -> BinarySearchTree? {
@@ -280,9 +280,9 @@ Searching is a recursive process but you can also implement it with a simple loo
   }
 ```
 
-Verify for yourself that you understand that these two implementations are equivalent. Personally, I prefer to use iterative code over recursive code but your opinion may differ. ;-)
+Verify that you understand these two implementations are equivalent. Personally, I prefer to use iterative code over recursive code, but your opinion may differ. ;-)
 
-Here's how to test searching:
+Here is how to test searching:
 
 ```swift
 tree.search(5)
@@ -291,9 +291,9 @@ tree.search(7)
 tree.search(6)   // nil
 ```
 
-The first three lines all return the corresponding `BinaryTreeNode` object. The last line returns `nil` because there is no node with value `6`.
+The first three lines return the corresponding `BinaryTreeNode` object. The last line returns `nil` because there is no node with value `6`.
 
-> **Note:** If there are duplicate items in the tree, `search()` always returns the "highest" node. That makes sense, because we start searching from the root downwards.
+> **Note:** If there are duplicate items in the tree, `search()` returns the "highest" node. That makes sense, because we start searching from the root downwards.
 
 ### Traversal
 
@@ -319,9 +319,9 @@ Remember there are 3 different ways to look at all nodes in the tree? Here they
   }
 ```
 
-They all do pretty much the same thing but in different orders. Notice once again that all the work is done recursively. Thanks to Swift's optional chaining, the calls to `traverseInOrder()` etc are ignored when there is no left or right child.
+They all work the same but in different orders. Notice that all the work is done recursively. The Swift's optional chaining makes it clear that the calls to `traverseInOrder()` etc are ignored when there is no left or right child.
 
-To print out all the values from the tree sorted from low to high you can write:
+To print out all the values of the tree sorted from low to high you can write:
 
 ```swift
 tree.traverseInOrder { value in print(value) }
@@ -336,7 +336,7 @@ This prints the following:
 	9
 	10
 
-You can also add things like `map()` and `filter()` to the tree. For example, here's an implementation of map:
+You can also add things like `map()` and `filter()` to the tree. For example, here is an implementation of map:
 
 ```swift
 
@@ -365,11 +365,11 @@ This turns the contents of the tree back into a sorted array. Try it out in the
 tree.toArray()   // [1, 2, 5, 7, 9, 10]
 ```
 
-As an exercise for yourself, see if you can implement filter and reduce.
+As an exercise, see if you can implement filter and reduce.
 
 ### Deleting nodes
 
-We can make the code much more readable by defining some helper functions.
+We can make the code more readable by defining some helper functions.
 
 ```swift
   private func reconnectParentToNode(node: BinarySearchTree?) {
@@ -384,7 +384,7 @@ We can make the code much more readable by defining some helper functions.
   }
 ```
 
-Making changes to the tree involves changing a bunch of `parent` and `left` and `right` pointers. This function helps with that. It takes the parent of the current node -- that is `self` -- and connects it to another node. Usually that other node will be one of the children of `self`.
+Making changes to the tree involves changing a bunch of `parent` and `left` and `right` pointers. This function helps with this implementation. It takes the parent of the current node -- that is `self` -- and connects it to another node which will be one of the children of `self`.
 
 We also need a function that returns the minimum and maximum of a node:
 
@@ -407,7 +407,7 @@ We also need a function that returns the minimum and maximum of a node:
 
 ```
 
-The rest of the code is pretty self-explanatory:
+The rest of the code is self-explanatory:
 
 ```swift
   @discardableResult public func remove() -> BinarySearchTree? {
@@ -457,7 +457,7 @@ Recall that the height of a node is the distance to its lowest leaf. We can calc
 
 We look at the heights of the left and right branches and take the highest one. Again, this is a recursive procedure. Since this looks at all children of this node, performance is **O(n)**.
 
-> **Note:** Swift's null-coalescing operator is used as shorthand to deal with `left` or `right` pointers that are nil. You could write this with `if let` but this is a lot more concise.
+> **Note:** Swift's null-coalescing operator is used as shorthand to deal with `left` or `right` pointers that are nil. You could write this with `if let`, but this is more concise.
 
 Try it out:
 
@@ -479,7 +479,7 @@ You can also calculate the *depth* of a node, which is the distance to the root.
   }
 ```
 
-It steps upwards through the tree, following the `parent` pointers until we reach the root node (whose `parent` is nil). This takes **O(h)** time. Example:
+It steps upwards through the tree, following the `parent` pointers until we reach the root node (whose `parent` is nil). This takes **O(h)** time. Here is an example:
 
 ```swift
 if let node9 = tree.search(9) {
@@ -489,11 +489,11 @@ if let node9 = tree.search(9) {
 
 ### Predecessor and successor
 
-The binary search tree is always "sorted" but that doesn't mean that consecutive numbers are actually next to each other in the tree.
+The binary search tree is always "sorted" but that does not mean that consecutive numbers are actually next to each other in the tree.
 
 ![Example](Images/Tree2.png)
 
-Note that you can't find the number that comes before `7` by just looking at its left child node. The left child is `2`, not `5`. Likewise for the number that comes after `7`.
+Note that you cannot find the number that comes before `7` by just looking at its left child node. The left child is `2`, not `5`. Likewise for the number that comes after `7`.
 
 The `predecessor()` function returns the node whose value precedes the current value in sorted order:
 
@@ -512,11 +512,11 @@ The `predecessor()` function returns the node whose value precedes the current v
   }
 ```
 
-It's easy if we have a left subtree. In that case, the immediate predecessor is the maximum value in that subtree. You can verify in the above picture that `5` is indeed the maximum value in `7`'s left branch.
+It is easy if we have a left subtree. In that case, the immediate predecessor is the maximum value in that subtree. You can verify in the above picture that `5` is indeed the maximum value in `7`'s left branch.
 
-However, if there is no left subtree then we have to look at our parent nodes until we find a smaller value. So if we want to know what the predecessor is of node `9`, we keep going up until we find the first parent with a smaller value, which is `7`.
+If there is no left subtree, then we have to look at our parent nodes until we find a smaller value. If we want to know what the predecessor is of node `9`, we keep going up until we find the first parent with a smaller value, which is `7`.
 
-The code for `successor()` works the exact same way but mirrored:
+The code for `successor()` works the same way but mirrored:
 
 ```swift
   public func successor() -> BinarySearchTree<T>? {
@@ -535,11 +535,11 @@ The code for `successor()` works the exact same way but mirrored:
 
 Both these methods run in **O(h)** time.
 
-> **Note:** There is a cool variation called a ["threaded" binary tree](../Threaded%20Binary%20Tree) where "unused" left and right pointers are repurposed to make direct links between predecessor and successor nodes. Very clever!
+> **Note:** There is a variation called a ["threaded" binary tree](../Threaded%20Binary%20Tree) where "unused" left and right pointers are repurposed to make direct links between predecessor and successor nodes. Very clever!
 
 ### Is the search tree valid?
 
-If you were intent on sabotage you could turn the binary search tree into an invalid tree by calling `insert()` on a node that is not the root, like so:
+If you were intent on sabotage you could turn the binary search tree into an invalid tree by calling `insert()` on a node that is not the root. Here is an example:
 
 ```swift
 if let node1 = tree.search(1) {
@@ -547,7 +547,7 @@ if let node1 = tree.search(1) {
 }
 ```
 
-The value of the root node is `7`, so a node with value `100` is supposed to be in the tree's right branch. However, you're not inserting at the root but at a leaf node in the tree's left branch. So the new `100` node is in the wrong place in the tree!
+The value of the root node is `7`, so a node with value `100`must be in the tree's right branch. However, you are not inserting at the root but at a leaf node in the tree's left branch. So the new `100` node is in the wrong place in the tree!
 
 As a result, doing `tree.search(100)` gives nil.
 
@@ -562,7 +562,7 @@ You can check whether a tree is a valid binary search tree with the following me
   }
 ```
 
-This verifies that the left branch does indeed contain values that are less than the current node's value, and that the right branch only contains values that are larger.
+This verifies the left branch contains values that are less than the current node's value, and that the right branch only contains values that are larger.
 
 Call it as follows:
 
@@ -577,11 +577,11 @@ if let node1 = tree.search(1) {
 
 ## The code (solution 2)
 
-We've implemented the binary tree node as a class but you can also use an enum.
+We have implemented the binary tree node as a class, but you can also use an enum.
 
-The difference is reference semantics versus value semantics. Making a change to the class-based tree will update that same instance in memory. But the enum-based tree is immutable -- any insertions or deletions will give you an entirely new copy of the tree. Which one is best totally depends on what you want to use it for.
+The difference is reference semantics versus value semantics. Making a change to the class-based tree will update that same instance in memory, but the enum-based tree is immutable -- any insertions or deletions will give you an entirely new copy of the tree. Which one is best, totally depends on what you want to use it for.
 
-Here's how you'd make a binary search tree using an enum:
+Here is how you can make a binary search tree using an enum:
 
 ```swift
 public enum BinarySearchTree<T: Comparable> {
@@ -597,9 +597,9 @@ The enum has three cases:
 - `Leaf` for a leaf node that has no children.
 - `Node` for a node that has one or two children. This is marked `indirect` so that it can hold `BinarySearchTree` values. Without `indirect` you can't make recursive enums.
 
-> **Note:** The nodes in this binary tree don't have a reference to their parent node. It's not a major impediment but it will make certain operations slightly more cumbersome to implement.
+> **Note:** The nodes in this binary tree do not have a reference to their parent node. It is not a major impediment, but it will make certain operations more cumbersome to implement.
 
-As usual, we'll implement most functionality recursively. We'll treat each case of the enum slightly differently. For example, this is how you could calculate the number of nodes in the tree and the height of the tree:
+This implementation is recursive, and each case of the enum will be treated differently. For example, this is how you can calculate the number of nodes in the tree and the height of the tree:
 
 ```swift
   public var count: Int {
@@ -655,7 +655,7 @@ tree = tree.insert(9)
 tree = tree.insert(1)
 ```
 
-Notice that each time you insert something, you get back a completely new tree object. That's why you need to assign the result back to the `tree` variable.
+Notice that for each insertion, you get back a new tree object, so you need to assign the result back to the `tree` variable.
 
 Here is the all-important search function:
 
@@ -678,7 +678,7 @@ Here is the all-important search function:
   }
 ```
 
-As you can see, most of these functions have the same structure.
+Most of these functions have the same structure.
 
 Try it out in a playground:
 
@@ -688,7 +688,7 @@ tree.search(1)
 tree.search(11)   // nil
 ```
 
-To print the tree for debug purposes you can use this method:
+To print the tree for debug purposes, you can use this method:
 
 ```swift
 extension BinarySearchTree: CustomDebugStringConvertible {
@@ -703,21 +703,21 @@ extension BinarySearchTree: CustomDebugStringConvertible {
 }
 ```
 
-When you do `print(tree)` it will look something like this:
+When you do `print(tree)`, it will look like this:
 
 	((1 <- 2 -> 5) <- 7 -> (9 <- 10 -> .))
 
-The root node is in the middle; a dot means there is no child at that position.
+The root node is in the middle, and a dot means there is no child at that position.
 
 ## When the tree becomes unbalanced...
 
-A binary search tree is *balanced* when its left and right subtrees contain roughly the same number of nodes. In that case, the height of the tree is *log(n)*, where *n* is the number of nodes. That's the ideal situation.
+A binary search tree is *balanced* when its left and right subtrees contain the same number of nodes. In that case, the height of the tree is *log(n)*, where *n* is the number of nodes. That is the ideal situation.
 
-However, if one branch is significantly longer than the other, searching becomes very slow. We end up checking way more values than we'd ideally have to. In the worst case, the height of the tree can become *n*. Such a tree acts more like a [linked list](../Linked%20List/) than a binary search tree, with performance degrading to **O(n)**. Not good!
+If one branch is significantly longer than the other, searching becomes very slow. We end up checking more values than we need. In the worst case, the height of the tree can become *n*. Such a tree acts like a [linked list](../Linked%20List/) than a binary search tree, with performance degrading to **O(n)**. Not good!
 
-One way to make the binary search tree balanced is to insert the nodes in a totally random order. On average that should balance out the tree quite nicely. But it doesn't guarantee success, nor is it always practical.
+One way to make the binary search tree balanced is to insert the nodes in a totally random order. On average that should balance out the tree well, but it not guaranteed, nor is it always practical.
 
-The other solution is to use a *self-balancing* binary tree. This type of data structure adjusts the tree to keep it balanced after you insert or delete nodes. See [AVL tree](../AVL%20Tree) and [red-black tree](../Red-Black%20Tree) for examples.
+The other solution is to use a *self-balancing* binary tree. This type of data structure adjusts the tree to keep it balanced after you insert or delete nodes. To see examples, check [AVL tree](../AVL%20Tree) and [red-black tree](../Red-Black%20Tree).
 
 ## See also
 

From 499bd86cd7ffab858dac481735b532f1789c0ab9 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Thu, 6 Apr 2017 17:07:38 -0700
Subject: [PATCH 084/862] Revisions in README.markdown

I have revised your document to be more concise. Some words and phrases are removed or replaced due to redundancy.
---
 Queue/README.markdown | 52 +++++++++++++++++++++----------------------
 1 file changed, 26 insertions(+), 26 deletions(-)

diff --git a/Queue/README.markdown b/Queue/README.markdown
index 9efce66b9..8938e0cf1 100644
--- a/Queue/README.markdown
+++ b/Queue/README.markdown
@@ -2,11 +2,11 @@
 
 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 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.
+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.
 
-A queue gives you a FIFO or first-in, first-out order. The element you inserted first is also the first one to come out again. It's only fair! (A very similar data structure, the [stack](../Stack/), is LIFO or last-in first-out.)
+A queue gives you a FIFO or first-in, first-out order. The element you inserted first is the first one to come out. It is only fair! (A similar data structure, the [stack](../Stack/), is LIFO or last-in first-out.)
 
-For example, let's enqueue a number:
+Here is an example to enqueue a number:
 
 ```swift
 queue.enqueue(10)
@@ -38,11 +38,11 @@ queue.dequeue()
 
 This returns `3`, the next dequeue returns `57`, and so on. If the queue is empty, dequeuing returns `nil` or in some implementations it gives an error message.
 
-> **Note:** A queue is not always the best choice. If the order in which the items are added and removed from the list isn't important, you might as well use a [stack](../Stack/) instead of a queue. Stacks are simpler and faster.
+> **Note:** A queue is not always the best choice. If the order in which the items are added and removed from the list is not important, you can use a [stack](../Stack/) instead of a queue. Stacks are simpler and faster.
 
 ## The code
 
-Here is a very simplistic implementation of a queue in Swift. It's just a wrapper around an array that lets you enqueue, dequeue, and peek at the front-most item:
+Here is a simplistic implementation of a queue in Swift. It is a wrapper around an array to enqueue, dequeue, and peek at the front-most item:
 
 ```swift
 public struct Queue<T> {
@@ -74,11 +74,11 @@ public struct Queue<T> {
 }
 ```
 
-This queue works just fine but it is not optimal.
+This queue works well, but it is not optimal.
 
-Enqueuing is an **O(1)** operation because adding to the end of an array always takes the same amount of time, regardless of the size of the array. So that's great.
+Enqueuing is an **O(1)** operation because adding to the end of an array always takes the same amount of time regardless of the size of the array.
 
-You might be wondering why appending items to an array is **O(1)**, or a constant-time operation. That is so because an array in Swift always has some empty space at the end. If we do the following:
+You might be wondering why appending items to an array is **O(1)** or a constant-time operation. That is because an array in Swift always has some empty space at the end. If we do the following:
 
 ```swift
 var queue = Queue<String>()
@@ -95,13 +95,13 @@ where `xxx` is memory that is reserved but not filled in yet. Adding a new eleme
 
 	[ "Ada", "Steve", "Tim", "Grace", xxx, xxx ]
 
-This is simply matter of copying memory from one place to another, a constant-time operation.
+This results by copying memory from one place to another which is a constant-time operation.
 
-Of course, there are only a limited number of such unused spots at the end of the array. When the last `xxx` gets used and you want to add another item, the array needs to resize to make more room.
+There are only a limited number of unused spots at the end of the array. When the last `xxx` gets used, and you want to add another item, the array needs to resize to make more room.
 
-Resizing includes allocating new memory and copying all the existing data over to the new array. This is an **O(n)** process, so it's relatively slow. But since it happens only every so often, the time for appending a new element to the end of the array is still **O(1)** on average, or **O(1)** "amortized".
+Resizing includes allocating new memory and copying all the existing data over to the new array. This is an **O(n)** process which is relatively slow. Since it happens occasionally, the time for appending a new element to the end of the array is still **O(1)** on average or **O(1)** "amortized".
 
-The story for dequeueing is slightly different. To dequeue we remove the element from the *beginning* of the array, not the end. This is always an **O(n)** operation because it requires all remaining array elements to be shifted in memory.
+The story for dequeueing is different. To dequeue, we remove the element from the *beginning* of the array. This is always an **O(n)** operation because it requires all remaining array elements to be shifted in memory.
 
 In our example, dequeuing the first element `"Ada"` copies `"Steve"` in the place of `"Ada"`, `"Tim"` in the place of `"Steve"`, and `"Grace"` in the place of `"Tim"`:
 
@@ -112,13 +112,13 @@ In our example, dequeuing the first element `"Ada"` copies `"Steve"` in the plac
 	                /       /      /
 	 after   [ "Steve", "Tim", "Grace", xxx, xxx, xxx ]
  
-Moving all these elements in memory is always an **O(n)** operation. So with our simple implementation of a queue, enqueuing is efficient but dequeueing leaves something to be desired...
+Moving all these elements in memory is always an **O(n)** operation. So with our simple implementation of a queue, enqueuing is efficient, but dequeueing leaves something to be desired...
 
 ## A more efficient queue
 
-To make dequeuing more efficient, we can use the same trick of reserving some extra free space, but this time do it at the front of the array. We're going to have to write this code ourselves as the built-in Swift array doesn't support this out of the box.
+To make dequeuing efficient, we can also reserve some extra free space but this time at the front of the array. We must write this code ourselves because the built-in Swift array does not support it.
 
-The idea is as follows: whenever we dequeue an item, we don't shift the contents of the array to the front (slow) but mark the item's position in the array as empty (fast). After dequeuing `"Ada"`, the array is:
+The main idea is whenever we dequeue an item, we do not shift the contents of the array to the front (slow) but mark the item's position in the array as empty (fast). After dequeuing `"Ada"`, the array is:
 
 	[ xxx, "Steve", "Tim", "Grace", xxx, xxx ]
 
@@ -126,13 +126,13 @@ After dequeuing `"Steve"`, the array is:
 
 	[ xxx, xxx, "Tim", "Grace", xxx, xxx ]
 
-These empty spots at the front never get reused for anything, so they're wasting space. Every so often you can trim the array by moving the remaining elements to the front again:
+Because these empty spots at the front never get reused, you can periodically trim the array by moving the remaining elements to the front:
 
 	[ "Tim", "Grace", xxx, xxx, xxx, xxx ]
 
-This trimming procedure involves shifting memory so it's an **O(n)** operation. But because it only happens once in a while, dequeuing is now **O(1)** on average.
+This trimming procedure involves shifting memory which is an **O(n)** operation. Because this only happens once in a while, dequeuing is **O(1)** on average.
 
-Here is how you could implement this version of `Queue`:
+Here is how you can implement this version of `Queue`:
 
 ```swift
 public struct Queue<T> {
@@ -176,9 +176,9 @@ public struct Queue<T> {
 }
 ```
 
-The array now stores objects of type `T?` instead of just `T` because we need some way to mark array elements as being empty. The `head` variable is the index in the array of the front-most object.
+The array now stores objects of type `T?` instead of just `T` because we need to mark array elements as being empty. The `head` variable is the index in the array of the front-most object.
 
-Most of the new functionality sits in `dequeue()`. When we dequeue an item, we first set `array[head]` to `nil` to remove the object from the array. Then we increment `head` because now the next item has become the front one.
+Most of the new functionality sits in `dequeue()`. When we dequeue an item, we first set `array[head]` to `nil` to remove the object from the array. Then, we increment `head` because the next item has become the front one.
 
 We go from this:
 
@@ -190,9 +190,9 @@ to this:
 	[ xxx, "Steve", "Tim", "Grace", xxx, xxx ]
 	        head
 
-It's like some weird supermarket where the people in the checkout lane don't shuffle forward towards the cash register, but the cash register moves up the queue.
+It is like if in a supermarket the people in the checkout lane do not shuffle forward towards the cash register, but the cash register moves up the queue.
 
-Of course, if we never remove those empty spots at the front then the array will keep growing as we enqueue and dequeue elements. To periodically trim down the array, we do the following:
+If we never remove those empty spots at the front then the array will keep growing as we enqueue and dequeue elements. To periodically trim down the array, we do the following:
 
 ```swift
     let percentage = Double(head)/Double(array.count)
@@ -202,11 +202,11 @@ Of course, if we never remove those empty spots at the front then the array will
     }
 ```
 
-This calculates the percentage of empty spots at the beginning as a ratio of the total array size. If more than 25% of the array is unused, we chop off that wasted space. However, if the array is small we don't want to resize it all the time, so there must be at least 50 elements in the array before we try to trim it. 
+This calculates the percentage of empty spots at the beginning as a ratio of the total array size. If more than 25% of the array is unused, we chop off that wasted space. However, if the array is small we do not resize it all the time, so there must be at least 50 elements in the array before we try to trim it. 
 
 > **Note:** I just pulled these numbers out of thin air -- you may need to tweak them based on the behavior of your app in a production environment.
 
-To test this in a playground, do:
+To test this in a playground, do the following:
 
 ```swift
 var q = Queue<String>()
@@ -251,11 +251,11 @@ q.array             // [{Some "Grace"}]
 q.count             // 1
 ```
 
-The `nil` objects at the front have been removed and the array is no longer wasting space. This new version of `Queue` isn't much more complicated than the first one but dequeuing is now also an **O(1)** operation, just because we were a bit smarter about how we used the array.
+The `nil` objects at the front have been removed, and the array is no longer wasting space. This new version of `Queue` is not more complicated than the first one but dequeuing is now also an **O(1)** operation, just because we were aware about how we used the array.
 
 ## See also
 
-There are many other ways to create a queue. Alternative implementations use a [linked list](../Linked%20List/), a [circular buffer](../Ring%20Buffer/), or a [heap](../Heap/). 
+There are many ways to create a queue. Alternative implementations use a [linked list](../Linked%20List/), a [circular buffer](../Ring%20Buffer/), or a [heap](../Heap/). 
 
 Variations on this theme are [deque](../Deque/), a double-ended queue where you can enqueue and dequeue at both ends, and [priority queue](../Priority%20Queue/), a sorted queue where the "most important" item is always at the front.
 

From 0f4baf57b3485af6391de0bc06f626e8efc88c82 Mon Sep 17 00:00:00 2001
From: Parva9eh <berespectful9@gmail.com>
Date: Thu, 6 Apr 2017 17:38:53 -0700
Subject: [PATCH 085/862] Revisions in README.markdown

I have revised your document to be more concise.
---
 Selection Sort/README.markdown | 34 +++++++++++++++++-----------------
 1 file changed, 17 insertions(+), 17 deletions(-)

diff --git a/Selection Sort/README.markdown b/Selection Sort/README.markdown
index cb8ed59c2..daebc64f4 100644
--- a/Selection Sort/README.markdown	
+++ b/Selection Sort/README.markdown	
@@ -1,6 +1,6 @@
 # Selection Sort
 
-Goal: Sort an array from low to high (or high to low).
+Goal: To sort an array from low to high (or high to low).
 
 You are given an array of numbers and need to put them in the right order. The selection sort algorithm divides the array into two parts: the beginning of the array is sorted, while the rest of the array consists of the numbers that still remain to be sorted.
 
@@ -10,20 +10,20 @@ This is similar to [insertion sort](../Insertion%20Sort/), but the difference is
 
 It works as follows:
 
-- Find the lowest number in the array. You start at index 0, loop through all the numbers in the array, and keep track of what the lowest number is.
-- Swap the lowest number you've found with the number at index 0. Now the sorted portion consists of just the number at index 0.
+- Find the lowest number in the array. You must start at index 0, loop through all the numbers in the array, and keep track of what the lowest number is.
+- Swap the lowest number with the number at index 0. Now, the sorted portion consists of just the number at index 0.
 - Go to index 1.
 - Find the lowest number in the rest of the array. This time you start looking from index 1. Again you loop until the end of the array and keep track of the lowest number you come across.
-- Swap it with the number at index 1. Now the sorted portion contains two numbers and extends from index 0 to index 1.
+- Swap  the lowest number with the number at index 1. Now, the sorted portion contains two numbers and extends from index 0 to index 1.
 - Go to index 2.
-- 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 so on... until no numbers remain to be sorted.
+- 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's called a "selection" sort, because at every step you search through the rest of the array to select the next lowest number.
+It nis called a "selection" sort because at every step you search through the rest of the array to select the next lowest number.
 
 ## An example
 
-Let's say the numbers to sort are `[ 5, 8, 3, 4, 6 ]`. We also keep track of where the sorted portion of the array ends, denoted by the `|` symbol.
+Suppose the numbers to sort are `[ 5, 8, 3, 4, 6 ]`. We also keep track of where the sorted portion of the array ends, denoted by the `|` symbol.
 
 Initially, the sorted portion is empty:
 
@@ -43,7 +43,7 @@ Again, we look for the lowest number, starting from the `|` bar. We find `4` and
 	[ 3, 4 | 5, 8, 6 ]
 	     *      *
 
-With every step, the `|` bar moves one position to the right. We again look through the rest of the array and find `5` as the lowest number. There's no need to swap `5` with itself and we simply move forward:
+With every step, the `|` bar moves one position to the right. We again look through the rest of the array and find `5` as the lowest number. There is no need to swap `5` with itself, and we simply move forward:
 
 	[ 3, 4, 5 | 8, 6 ]
 	        *
@@ -52,7 +52,7 @@ This process repeats until the array is sorted. Note that everything to the left
 
 	[ 3, 4, 5, 6, 8 |]
 
-As you can see, selection sort is an *in-place* sort because everything happens in the same array; no additional memory is necessary. You can also implement this as a *stable* sort so that identical elements do not get swapped around relative to each other (note that the version given below isn't stable).
+The selection sort is an *in-place* sort because everything happens in the same array without using additional memory. You can also implement this as a *stable* sort so that identical elements do not get swapped around relative to each other (note that the version given below is not stable).
 
 ## The code
 
@@ -90,9 +90,9 @@ selectionSort(list)
 
 A step-by-step explanation of how the code works:
 
-1. If the array is empty or only contains a single element, then there's not much point to sorting it.
+1. If the array is empty or only contains a single element, then there is no need to sort.
 
-2. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly in Swift. Like Swift's own `sort()`, the `selectionSort()` function will return a sorted *copy* of the original array.
+2. Make a copy of the array. This is necessary because we cannot modify the contents of the `array` parameter directly in Swift. Like the Swift's `sort()` function, the `selectionSort()` function will return a sorted *copy* of the original array.
 
 3. There are two loops inside this function. The outer loop looks at each of the elements in the array in turn; this is what moves the `|` bar forward.
 
@@ -100,17 +100,17 @@ A step-by-step explanation of how the code works:
 
 5. Swap the lowest number with the current array index. The `if` check is necessary because you can't `swap()` an element with itself in Swift.
 
-In summary: For each element of the array, selection sort swaps positions with the lowest value from the rest of the array. As a result, the array gets sorted from the left to the right. (You can also do it right-to-left, in which case you always look for the largest number in the array. Give that a try!)
+In summary: For each element of the array, the selection sort swaps positions with the lowest value from the rest of the array. As a result, the array gets sorted from the left to the right. (You can also do it right-to-left, in which case you always look for the largest number in the array. Give that a try!)
 
-> **Note:** The outer loop ends at index `a.count - 2`. The very last element will automatically always be in the correct position because at that point there are no other smaller elements left.
+> **Note:** The outer loop ends at index `a.count - 2`. The very last element will automatically be in the correct position because at that point there are no other smaller elements left.
 
-The source file [SelectionSort.swift](SelectionSort.swift) has a version of this function that uses generics, so you can also use it to sort strings and other types.
+The source file [SelectionSort.swift](SelectionSort.swift) has a version of this function that uses generics, so you can also use it to sort strings and other data types.
 
 ## Performance
 
-Selection sort is easy to understand but it performs quite badly, **O(n^2)**. It's worse than [insertion sort](../Insertion%20Sort/) but better than [bubble sort](../Bubble%20Sort/). The killer is  finding the lowest element in the rest of the array. This takes up a lot of time, especially since the inner loop will be performed over and over.
+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 .
 
-[Heap sort](../Heap%20Sort/) uses the same principle as selection sort but has a really fast method for finding the minimum value in the rest of the array. Its performance is **O(n log n)**.
+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)**.
 
 ## See also
 

From 8d84f6fdb9996e0a8b84360fd54eeb9892965e04 Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Thu, 6 Apr 2017 22:25:17 -0400
Subject: [PATCH 086/862] Spelling 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 14ef931b9..80c2df7df 100644
--- a/Binary Search Tree/README.markdown	
+++ b/Binary Search Tree/README.markdown	
@@ -2,7 +2,7 @@
 
 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 iformation about a tree, [read this first](../Tree/).
+For more information about a tree, [read this first](../Tree/).
 
 ## "Always sorted" property
 

From 8080f271109d494eed485137392363bed2d462f4 Mon Sep 17 00:00:00 2001
From: Jacopo Mangiavacchi <Jacopo.Mangiavacchi@uk.ibm.com>
Date: Fri, 7 Apr 2017 19:18:26 +0200
Subject: [PATCH 087/862] Fix and optimizations

---
 .../Sources/MinimumCoinChange.swift           | 89 +++++++++++--------
 .../MinimumCoinChangeTests.swift              | 20 +++--
 2 files changed, 66 insertions(+), 43 deletions(-)

diff --git a/MinimumCoinChange/Sources/MinimumCoinChange.swift b/MinimumCoinChange/Sources/MinimumCoinChange.swift
index db7edecbe..c995063ab 100644
--- a/MinimumCoinChange/Sources/MinimumCoinChange.swift
+++ b/MinimumCoinChange/Sources/MinimumCoinChange.swift
@@ -1,5 +1,5 @@
 //
-//  Minimum Coin Change Problem 
+//  Minimum Coin Change Problem Playground
 //  Compare Greedy Algorithm and Dynamic Programming Algorithm in Swift
 //
 //  Created by Jacopo Mangiavacchi on 04/03/17.
@@ -7,70 +7,85 @@
 
 import Foundation
 
+public enum MinimumCoinChangeError: Error {
+    case noRestPossibleForTheGivenValue
+}
+
 public struct MinimumCoinChange {
-    private let sortedCoinSet: [Int]
-    private var cache: [Int : [Int]]
+    internal let sortedCoinSet: [Int]
     
     public init(coinSet: [Int]) {
         self.sortedCoinSet = coinSet.sorted(by: { $0 > $1} )
-        self.cache = [:]
     }
 
     //Greedy Algorithm
-    public func changeGreedy(_ value: Int) -> [Int] {
+    public func changeGreedy(_ value: Int) throws -> [Int] {
+        guard value > 0 else { return [] }
+
         var change:  [Int] = []
         var newValue = value
-        
+
         for coin in sortedCoinSet {
             while newValue - coin >= 0 {
                 change.append(coin)
                 newValue -= coin
             }
 
-            if newValue  == 0 {
+            if newValue == 0 {
                 break
             }
         }
         
+        if newValue > 0 { 
+            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue 
+        } 
+
         return change
     }
 
     //Dynamic Programming Algorithm
-    public mutating func changeDynamic(_ value: Int) -> [Int] {
-        if value <= 0 {
-            return []
-        }
+    public func changeDynamic(_ value: Int) throws -> [Int] {
+        guard value > 0 else { return [] }
         
-        if let cached = cache[value] {
-            return cached
-        }
-        
-        var change:  [Int] = []
-        
-        var potentialChangeArray: [[Int]] = []
-        
-        for coin in sortedCoinSet {
-            if value - coin >= 0 {
-                var potentialChange: [Int] = []
-                 potentialChange.append(coin)
-                let newPotentialValue = value - coin
+        var cache: [Int : [Int]] = [:]
 
-                if value  > 0 {
-                    potentialChange.append(contentsOf: changeDynamic(newPotentialValue))
-                }
+        func _changeDynamic(_ value: Int) -> [Int] {
+            guard value > 0 else { return [] }
 
-                //print("value: \(value) coin: \(coin) potentialChange: \(potentialChange)")
-                potentialChangeArray.append(potentialChange)
+            if let cached = cache[value] {
+                return cached
             }
+            
+            var change: [Int] = []
+            
+            var potentialChangeArray: [[Int]] = []
+            
+            for coin in sortedCoinSet {
+                if value - coin >= 0 {
+                    var potentialChange: [Int] = [coin]
+                    potentialChange.append(contentsOf: _changeDynamic(value - coin))
+                    potentialChangeArray.append(potentialChange)
+                }
+            }
+            
+            if potentialChangeArray.count > 0 {
+                let sortedPotentialChangeArray = potentialChangeArray.sorted(by: { $0.count < $1.count })
+                change = sortedPotentialChangeArray[0]
+            }
+            
+            if change.reduce(0, +) == value { 
+                cache[value] = change
+            } 
+
+            return change
         }
-        
-        if potentialChangeArray.count > 0 {
-            let sortedPotentialChangeArray = potentialChangeArray.sorted(by: { $0.count < $1.count })
-            change = sortedPotentialChangeArray[0]
-        }
-        
-        cache[value] = change
+
+        let change: [Int] = _changeDynamic(value)
+
+        if change.reduce(0, +) != value { 
+            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue 
+        } 
+
         return change
     }
 }
-
diff --git a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
index 86c9007ba..705113e92 100644
--- a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
+++ b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
@@ -3,16 +3,24 @@ import XCTest
 
 class MinimumCoinChangeTests: XCTestCase {
     func testExample() {
-        var mcc = MinimumCoinChange(coinSet: [1, 2, 5, 10, 20, 25])
+        let mcc = MinimumCoinChange(coinSet: [1, 2, 5, 10, 20, 25])
+        print("Coin set: \(mcc.sortedCoinSet)")
 
-        for i in 0..<100 {
-            let greedy = mcc.changeGreedy(i)
-            let dynamic = mcc.changeDynamic(i)
+        do {
+            for i in 0..<100 {
+                let greedy = try mcc.changeGreedy(i)
+                let dynamic = try mcc.changeDynamic(i)
 
-            if greedy.count != dynamic.count {
-                print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
+                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 = [

From 7abd8765deff7437e591730ea5c4cbf263ec9fc6 Mon Sep 17 00:00:00 2001
From: Ievgen Pavliuk <ievgen.pavliuk@virtual-solution.com>
Date: Sat, 8 Apr 2017 14:30:42 +0200
Subject: [PATCH 088/862] Fixed typo in AVL

---
 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 c8d8d4628..e7515d99f 100644
--- a/AVL Tree/README.markdown	
+++ b/AVL Tree/README.markdown	
@@ -48,7 +48,7 @@ Each tree node keeps track of its current balance factor in a variable. After in
 ![Rotation0](Images/RotationStep0.jpg)
 
 For the rotation we're using the terminology:
-* *Root* - the parent not of the subtrees that will be rotated;
+* *Root* - the parent node of the subtrees that will be rotated;
 * *Pivot* - the node that will become parent (basically will be on the *Root*'s position) after rotation;
 * *RotationSubtree* - subtree of the *Pivot* upon the side of rotation
 * *OppositeSubtree* - subtree of the *Pivot* opposite the side of rotation

From 3e62df6cff7e3408647b8da016ca4230fb2a191c Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Mon, 10 Apr 2017 11:18:34 +0200
Subject: [PATCH 089/862] Silenced warnings in print statements

---
 .../RedBlackTree.playground/Sources/RedBlackTree.swift    | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index 6f3b16b86..351f89a9d 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -638,11 +638,11 @@ extension RedBlackTree {
     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 \(node.key ?? nil) has red left child")
+            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 \(node.key ?? nil) has red right child")
+          print("Property-Error: Red node with key \(String(describing: node.key)) has red right child")
           return false
         }
       }
@@ -677,7 +677,7 @@ extension RedBlackTree {
       let addedHeight = node.color == .black ? 1 : 0
       return left + addedHeight
     } else {
-      print("Property-Error: Black height violated at node with key \(node.key ?? nil)")
+      print("Property-Error: Black height violated at node with key \(String(describing: node.key))")
       return -1
     }
   }
@@ -697,7 +697,7 @@ extension RBTreeNode: CustomDebugStringConvertible {
         s = "key: nil"
       }
       if let parent = parent {
-        s += ", parent: \(parent.key)"
+        s += ", parent: \(String(describing: parent.key))"
       }
       if let left = leftChild {
         s += ", left = [" + left.debugDescription + "]"

From 51d36815aaf49d23cc0630ed36459141acbdab9e Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Mon, 10 Apr 2017 15:38:52 -0400
Subject: [PATCH 090/862] Updated a comment about nested class declarations for
 Swift 3. Formatted the signature at the bottom

---
 Linked List/README.markdown | 24 ++++++++++++------------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/Linked List/README.markdown b/Linked List/README.markdown
index 1884aeb23..c5a752e13 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -79,18 +79,18 @@ public class LinkedList<T> {
   public typealias Node = LinkedListNode<T>
 
   private var head: Node?
-  
+
   public var isEmpty: Bool {
     return head == nil
   }
-  
+
   public var first: Node? {
     return head
   }
 }
 ```
 
-Ideally, I'd like to put the `LinkedListNode` class inside `LinkedList` but Swift currently doesn't allow generic types to have nested types. Instead we're using a typealias so inside `LinkedList` we can write the shorter `Node` instead of `LinkedListNode<T>`.
+Ideally, we would want a class name to be as descriptive as possible, yet, we don't want to type a long name every time we want to use the class, therefore, we're using a typealias so inside `LinkedList` we can write the shorter `Node` instead of `LinkedListNode<T>`.
 
 This linked list only has a `head` pointer, not a tail. Adding a tail pointer is left as an exercise for the reader. (I'll point out which functions would be different if we also had a tail pointer.)
 
@@ -267,7 +267,7 @@ Let's write a method that lets you insert a new node at any index in the list. F
 ```swift
   private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
     assert(index >= 0)
-    
+
     var i = index
     var next = head
     var prev: Node?
@@ -283,13 +283,13 @@ Let's write a method that lets you insert a new node at any index in the list. F
   }
 ```
 
-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. 
+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. 
+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
@@ -320,7 +320,7 @@ Now that we have this helper function, we can write the method for inserting nod
 ```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
@@ -364,20 +364,20 @@ What else do we need? Removing nodes, of course! First we'll do `removeAll()`, w
 
 If you had a tail pointer, you'd set it to `nil` here too.
 
-Next we'll add some functions that let you remove individual nodes. If you already have a reference to the node, then using `removeNode()` is the most optimal because you don't need to iterate through the list to find the node first. 
+Next we'll add some functions that let you remove individual nodes. If you already have a reference to the node, then using `removeNode()` is the most optimal because you don't need to iterate through the list to find the node first.
 
 ```swift
   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
@@ -412,7 +412,7 @@ If you don't have a reference to the node, you can use `removeLast()` or `remove
   }
 ```
 
-All these removal functions also return the value from the removed element. 
+All these removal functions also return the value from the removed element.
 
 ```swift
 list.removeLast()              // "World"
@@ -543,4 +543,4 @@ When performing operations on a linked list, you always need to be careful to up
 
 When processing lists, you can often use recursion: process the first element and then recursively call the function again on the rest of the list. You’re done when there is no next element. This is why linked lists are the foundation of functional programming languages such as LISP.
 
-*Written for Swift Algorithm Club by Matthijs Hollemans*
+*Originally written by Matthijs Hollemans for Ray Wenderlich's Swift Algorithm Club*

From a613ca599c03a98e588e32982d57097d5b388909 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Mon, 10 Apr 2017 16:39:50 -0400
Subject: [PATCH 091/862] Updated the Playground file with more comments and
 added an overloadded implementations of 'insert' & 'append' to accept a whole
 list as an argument

---
 .../LinkedList.playground/Contents.swift      | 96 +++++++++++++++----
 .../contents.xcplayground                     |  2 +-
 2 files changed, 81 insertions(+), 17 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index abbb90467..93ed4246d 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -1,30 +1,41 @@
-//: Playground - noun: a place where people can play
+//: # Linked Lists
 
-public class LinkedListNode<T> {
-  var value: T
-  var next: LinkedListNode?
-  weak var previous: LinkedListNode?
-  
-  public init(value: T) {
-    self.value = value
-  }
-}
+// For best results, don't forget to select "Show Rendered Markup" from XCode's "Editor" menu
 
+//: Linked List Class Declaration:
 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>
   
+  // 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? {
     if var node = head {
       while case let next? = node.next {
@@ -36,6 +47,7 @@ public final class LinkedList<T> {
     }
   }
   
+  // 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
@@ -49,6 +61,7 @@ public final class LinkedList<T> {
     }
   }
   
+  // Function to return the node at a specific index
   public func node(atIndex index: Int) -> Node? {
     if index >= 0 {
       var node = head
@@ -62,17 +75,20 @@ public final class LinkedList<T> {
     return nil
   }
   
+  // Subscript function to return the node at a specific index
   public subscript(index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
     return node!.value
   }
   
+  // Append a value
   public func append(_ value: T) {
     let newNode = Node(value: value)
     self.append(newNode)
   }
   
+  // Append a node without taking ownership (appends a copy)
   public func append(_ node: Node) {
     let newNode = LinkedListNode(value: node.value)
     if let lastNode = last {
@@ -83,6 +99,16 @@ public final class LinkedList<T> {
     }
   }
   
+  // Append a whole linked list without taking ownership (appends a copy)
+  public func append(_ list: LinkedList) {
+    var nodeToCopy = list.head
+    while let node = nodeToCopy {
+      self.append(node.value)
+      nodeToCopy = node.next
+    }
+  }
+  
+  // Private helper function to return the nodes (in a tuple) before and after a specific index
   private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
     assert(index >= 0)
     
@@ -100,11 +126,13 @@ public final class LinkedList<T> {
     return (prev, next)
   }
   
+  // Insert a value at a specific index
   public func insert(_ value: T, atIndex index: Int) {
     let newNode = Node(value: value)
     self.insert(newNode, atIndex: index)
   }
   
+  // Insert a node at a specific index without taking ownership (inserts a copy)
   public func insert(_ node: Node, atIndex index: Int) {
     let (prev, next) = nodesBeforeAndAfter(index: index)
     let newNode = LinkedListNode(value: node.value)
@@ -118,10 +146,33 @@ public final class LinkedList<T> {
     }
   }
   
+  // Insert a whole linked list at a specific index without taking ownership (inserts a copy)
+  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
+    }
+    prev?.next = next
+    next?.previous = prev
+  }
+  
+  // Function to remove all nodes from the list
   public func removeAll() {
     head = nil
   }
   
+  // Function to remove a specific node from the list and return its value
   @discardableResult public func remove(node: Node) -> T {
     let prev = node.previous
     let next = node.next
@@ -138,11 +189,13 @@ public final class LinkedList<T> {
     return node.value
   }
   
+  // Function to remove the last node in the list
   @discardableResult public func removeLast() -> T {
     assert(!isEmpty)
     return remove(node: last!)
   }
   
+  // Function to remove the node at a specific index from the list
   @discardableResult public func remove(atIndex index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
@@ -150,6 +203,7 @@ public final class LinkedList<T> {
   }
 }
 
+//: End of the base class declarations & beginning of extensions' declarations:
 extension LinkedList: CustomStringConvertible {
   public var description: String {
     var s = "["
@@ -218,6 +272,8 @@ extension LinkedList: ExpressibleByArrayLiteral {
   }
 }
 
+
+//: 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
@@ -247,10 +303,20 @@ list[0]     // "Hello"
 list[1]     // "World"
 //list[2]   // crash!
 
+let list2 = LinkedList<String>()
+list2.append("Goodbye")
+list2.append("World")
+list.append(list2)            // [Hello, World, Goodbye, World]
+list2.removeAll()             // [ ]
+list2.isEmpty                 // true
+list.removeLast()             // "World"
+list.remove(atIndex: 2)       // "Goodbye"
+
+
 list.insert("Swift", atIndex: 1)
-list[0]
-list[1]
-list[2]
+list[0]     // "Hello"
+list[1]     // "Swift"
+list[2]     // "World"
 print(list)
 
 list.reverse()   // [World, Swift, Hello]
@@ -262,9 +328,6 @@ m    // [8, 6, 5]
 let f = list.filter { s in s.characters.count > 5 }
 f    // [Universe, Swifty]
 
-//list.removeAll()
-//list.isEmpty
-
 list.remove(node: list.first!) // "Universe"
 list.count                     // 2
 list[0]                        // "Swifty"
@@ -286,3 +349,4 @@ let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
 listArrayLiteral2.count        // 3
 listArrayLiteral2[0]           // "Swift"
 listArrayLiteral2.removeLast()  // "Club"
+
diff --git a/Linked List/LinkedList.playground/contents.xcplayground b/Linked List/LinkedList.playground/contents.xcplayground
index 06828af92..3de2b51ba 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'>
+<playground version='5.0' target-platform='osx' display-mode='rendered'>
     <timeline fileName='timeline.xctimeline'/>
 </playground>
\ No newline at end of file

From 45ef5cc2e0fb0f340744812a43b0fa329b20f867 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Mon, 10 Apr 2017 16:57:12 -0400
Subject: [PATCH 092/862] Added 2 overloaded 'insert' & 'append' funcs that
 take a List as an argument to LinkedList.swift. Added 5 tests to
 LinkedListTests.swift to check the added 2 functions

---
 Linked List/LinkedList.swift            | 51 ++++++++++++++++-----
 Linked List/Tests/LinkedListTests.swift | 60 +++++++++++++++++++++++++
 2 files changed, 100 insertions(+), 11 deletions(-)

diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 55593cdc9..a7ef9bf5e 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -1,14 +1,15 @@
-public class LinkedListNode<T> {
-    var value: T
-    var next: LinkedListNode?
-    weak var previous: LinkedListNode?
+public final class LinkedList<T> {
     
-    public init(value: T) {
-        self.value = value
+    public class LinkedListNode<T> {
+        var value: T
+        var next: LinkedListNode?
+        weak var previous: LinkedListNode?
+        
+        public init(value: T) {
+            self.value = value
+        }
     }
-}
-
-public final class LinkedList<T> {
+  
     public typealias Node = LinkedListNode<T>
     
     fileprivate var head: Node?
@@ -72,7 +73,7 @@ public final class LinkedList<T> {
     }
     
     public func append(_ node: Node) {
-        let newNode = Node(value: node.value)
+        let newNode = LinkedListNode(value: node.value)
         if let lastNode = last {
             newNode.previous = lastNode
             lastNode.next = newNode
@@ -81,6 +82,14 @@ public final class LinkedList<T> {
         }
     }
     
+    public func append(_ list: LinkedList) {
+        var nodeToCopy = list.head
+        while let node = nodeToCopy {
+            self.append(node.value)
+            nodeToCopy = node.next
+        }
+    }
+    
     private func nodesBeforeAndAfter(index: Int) -> (Node?, Node?) {
         assert(index >= 0)
         
@@ -105,7 +114,7 @@ public final class LinkedList<T> {
     
     public func insert(_ node: Node, atIndex index: Int) {
         let (prev, next) = nodesBeforeAndAfter(index: index)
-        let newNode = Node(value: node.value)
+        let newNode = LinkedListNode(value: node.value)
         newNode.previous = prev
         newNode.next = next
         prev?.next = newNode
@@ -116,6 +125,26 @@ public final class LinkedList<T> {
         }
     }
     
+    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
+        }
+        prev?.next = next
+        next?.previous = prev
+    }
+    
     public func removeAll() {
         head = nil
     }
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index 6f58d9775..ea063cacb 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -165,7 +165,67 @@ class LinkedListTest: XCTestCase {
     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, 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)
+  }
 
+  func testInsertListAtFirstIndex() {
+    let list = buildList()
+    let list2 = LinkedList<Int>()
+    list2.append(99)
+    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)
+  }
+  
+  func testInsertListAtLastIndex() {
+    let list = buildList()
+    let list2 = LinkedList<Int>()
+    list2.append(99)
+    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)
+  }
+  
+  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(atIndex: 5)?.value, 5)
+    XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
+    XCTAssertEqual(list.node(atIndex: 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(atIndex: 0)?.value, 5)
+    XCTAssertEqual(list.node(atIndex: 1)?.value, 10)
+  }
+  
   func testRemoveAtIndexOnListWithOneElement() {
     let list = LinkedList<Int>()
     list.append(123)

From c74bec1667b6be79b6a8dd56dd09b9c0076c1ef7 Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Mon, 10 Apr 2017 19:24:50 -0400
Subject: [PATCH 093/862] Updated the xcode version in .travis.yml

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

diff --git a/.travis.yml b/.travis.yml
index b6ff6190c..d413140fc 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,5 +1,5 @@
 language: objective-c
-osx_image: xcode8
+osx_image: xcode8.3
 # sudo: false
 
 install:

From 84009ae732937157fd3f071b78430895968d500b Mon Sep 17 00:00:00 2001
From: Marwan Alani <marwan@alani.ca>
Date: Tue, 11 Apr 2017 19:33:40 -0400
Subject: [PATCH 094/862] Added proper annotation to the Linked List playground
 files

---
 .../LinkedList.playground/Contents.swift      | 82 ++++++++++++++-----
 1 file changed, 61 insertions(+), 21 deletions(-)

diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 93ed4246d..b86fbf0b4 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -5,7 +5,7 @@
 //: Linked List Class Declaration:
 public final class LinkedList<T> {
   
-  // Linked List's Node Class Declaration
+  /// Linked List's Node Class Declaration
   public class LinkedListNode<T> {
     var value: T
     var next: LinkedListNode?
@@ -16,26 +16,26 @@ public final class LinkedList<T> {
     }
   }
   
-  // Typealiasing the node class to increase readability of code
+  /// Typealiasing the node class to increase readability of code
   public typealias Node = LinkedListNode<T>
   
-  // The head of the Linked List
+  /// The head of the Linked List
   fileprivate var head: Node?
   
-  // Default initializer
+  /// Default initializer
   public init() {}
   
-  // Computed property to check if the linked list is empty
+  /// 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)
+  /// 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)
+  /// 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 {
@@ -47,7 +47,7 @@ public final class LinkedList<T> {
     }
   }
   
-  // Computed property to iterate through the linked list and return the total number of nodes
+  /// 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
@@ -61,7 +61,10 @@ public final class LinkedList<T> {
     }
   }
   
-  // Function to return the node at a specific index
+  /// 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
@@ -75,20 +78,26 @@ public final class LinkedList<T> {
     return nil
   }
   
-  // Subscript function to return the node at a specific index
+  /// 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(atIndex: index)
     assert(node != nil)
     return node!.value
   }
   
-  // Append a 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 node without taking ownership (appends a copy)
+  /// 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 = LinkedListNode(value: node.value)
     if let lastNode = last {
@@ -99,7 +108,9 @@ public final class LinkedList<T> {
     }
   }
   
-  // Append a whole linked list without taking ownership (appends a copy)
+  /// 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 {
@@ -108,7 +119,10 @@ public final class LinkedList<T> {
     }
   }
   
-  // Private helper function to return the nodes (in a tuple) before and after a specific index
+  /// 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)
     
@@ -126,13 +140,21 @@ public final class LinkedList<T> {
     return (prev, next)
   }
   
-  // Insert a value at a specific index
+  /// 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, atIndex index: Int) {
     let newNode = Node(value: value)
     self.insert(newNode, atIndex: index)
   }
   
-  // Insert a node at a specific index without taking ownership (inserts a copy)
+  /// 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(_ node: Node, atIndex index: Int) {
     let (prev, next) = nodesBeforeAndAfter(index: index)
     let newNode = LinkedListNode(value: node.value)
@@ -146,7 +168,11 @@ public final class LinkedList<T> {
     }
   }
   
-  // Insert a whole linked list at a specific index without taking ownership (inserts a copy)
+  /// 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, atIndex index: Int) {
     if list.isEmpty { return }
     var (prev, next) = nodesBeforeAndAfter(index: index)
@@ -167,12 +193,15 @@ public final class LinkedList<T> {
     next?.previous = prev
   }
   
-  // Function to remove all nodes from the list
+  /// Function to remove all nodes/value from the list
   public func removeAll() {
     head = nil
   }
   
-  // Function to remove a specific node from the list and return its value
+  /// 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
@@ -189,13 +218,18 @@ public final class LinkedList<T> {
     return node.value
   }
   
-  // Function to remove the last node in the list
+  /// 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 the node at a specific index from the list
+  /// 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(atIndex index: Int) -> T {
     let node = self.node(atIndex: index)
     assert(node != nil)
@@ -204,6 +238,8 @@ public final class LinkedList<T> {
 }
 
 //: 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 = "["
@@ -217,6 +253,7 @@ extension LinkedList: CustomStringConvertible {
   }
 }
 
+// MARK: - Extension to add a 'reverse' function to the list
 extension LinkedList {
   public func reverse() {
     var node = head
@@ -228,6 +265,7 @@ 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>()
@@ -252,6 +290,7 @@ extension LinkedList {
   }
 }
 
+// MARK: - Extension to enable initialization from an Array
 extension LinkedList {
   convenience init(array: Array<T>) {
     self.init()
@@ -262,6 +301,7 @@ extension LinkedList {
   }
 }
 
+// MARK: - Extension to enable initialization from an Array Literal
 extension LinkedList: ExpressibleByArrayLiteral {
   public convenience init(arrayLiteral elements: T...) {
     self.init()

From 621a28da46cebf8bcd003ef6e80afb7e63b01136 Mon Sep 17 00:00:00 2001
From: vincentngo <vincentn@vt.edu>
Date: Thu, 13 Apr 2017 21:07:51 -0400
Subject: [PATCH 095/862] Update README.markdown

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

diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index 958c3595a..bc9636195 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -103,7 +103,7 @@ it first hashes the key `"lastName"` to calculate the array index, which is 3. S
 
 Common ways to implement this chaining mechanism are to use a linked list or another array. Since the order of the items in the chain does not matter, you can think of it as a set instead of a list. (Now you can also imagine where the term "bucket" comes from; we just dump all the objects together into the bucket.)
 
-Chains should not become long becasuse the slow process of looking up items in the hash table. Ideally, we would have no chains at all, but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets using high-quality hash functions.
+Chains should not become long because the slow process of looking up items in the hash table. Ideally, we would have no chains at all, but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets using high-quality hash functions.
 
 > **Note:** An alternative to chaining is "open addressing". The idea is this: if an array index is already taken, we put the element in the next unused bucket. This approach has its own upsides and downsides.
 
@@ -127,7 +127,7 @@ public struct HashTable<Key: Hashable, Value> {
   }
 ```
 
-The `HashTable` is a generic container, and the two generic types are named `Key` (which must be `Hashable`) and `Value`. We also define two other types: `Element` is a key/value pair for useing in a chain, and `Bucket` is an array of such `Elements`.
+The `HashTable` is a generic container, and the two generic types are named `Key` (which must be `Hashable`) and `Value`. We also define two other types: `Element` is a key/value pair for using in a chain, and `Bucket` is an array of such `Elements`.
 
 The main array is named `buckets`. It has a fixed size, the so-called capacity, provided by the `init(capacity)` method. We are also keeping track of how many items have been added to the hash table using the `count` variable.
 

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 096/862] 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 097/862] 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 098/862] 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 099/862] 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 100/862] 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 101/862] 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 102/862] 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 103/862] 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 104/862] 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 105/862] 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 106/862] 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 107/862] 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 108/862] 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 42db9a9d9a823a5bd0f2acf5f629881265ba7a83 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:12:10 +0300
Subject: [PATCH 109/862] Removed extra screenshots

---
 Dijkstra Algorithm/README.md                  |   4 ----
 .../Screenshots/screenshot1.jpg               | Bin 214771 -> 224243 bytes
 .../Screenshots/screenshot2.jpg               | Bin 225916 -> 0 bytes
 .../Screenshots/screenshot3.jpg               | Bin 224243 -> 0 bytes
 4 files changed, 4 deletions(-)
 delete mode 100644 Dijkstra Algorithm/Screenshots/screenshot2.jpg
 delete mode 100644 Dijkstra Algorithm/Screenshots/screenshot3.jpg

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 872e9f851..10166a63f 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -17,7 +17,3 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 ## Screenshots
 
 <img src="Screenshots/screenshot1.jpg" height="400" />
-
-<img src="Screenshots/screenshot2.jpg" height="400" />
-
-<img src="Screenshots/screenshot3.jpg" height="400" />
diff --git a/Dijkstra Algorithm/Screenshots/screenshot1.jpg b/Dijkstra Algorithm/Screenshots/screenshot1.jpg
index 390bc658224310c7720678cffd68bf1654b5c045..e9f7a1207f315e8f5aa20c72f3264c65edafd3a8 100644
GIT binary patch
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From a6020a54187ff8f473b1bccae3229846b7716258 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:13:19 +0300
Subject: [PATCH 110/862] Credits to the bottom

---
 Dijkstra Algorithm/README.md | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 10166a63f..bf158def9 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,6 +1,4 @@
 # Dijkstra-algorithm
-WWDC 2017 Scholarship Project
-Created by [Taras Nikulin](https://github.com/crabman448)
 
 ## About
 Dijkstra's algorithm is used for finding shortest paths from start vertex in graph(with weighted vertices) to all other vertices. 
@@ -17,3 +15,7 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 ## Screenshots
 
 <img src="Screenshots/screenshot1.jpg" height="400" />
+
+## Credits
+WWDC 2017 Scholarship Project
+Created by [Taras Nikulin](https://github.com/crabman448)

From a76764eaa0907a8ec455f911af14a0ad27087a95 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:16:05 +0300
Subject: [PATCH 111/862] Moved Vertex and Dijkstra classes to sources

---
 .../Dijkstra.playground/Contents.swift        | 69 -------------------
 .../Sources/Dijkstra.swift                    | 40 +++++++++++
 .../Dijkstra.playground/Sources/Vertex.swift  | 29 ++++++++
 3 files changed, 69 insertions(+), 69 deletions(-)
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
 create mode 100644 Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index 13087a8f9..cd08e26fb 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -1,74 +1,5 @@
 //: Playground - noun: a place where people can play
-
 import Foundation
-import UIKit
-
-open class Vertex: Hashable, Equatable {
-
-    open var identifier: String!
-    open var neighbors: [(Vertex, Double)] = []
-    open var pathLengthFromStart: Double = Double.infinity
-    open var pathVerticesFromStart: [Vertex] = []
-
-    public init(identifier: String) {
-        self.identifier = identifier
-    }
-
-    open var hashValue: Int {
-        return self.identifier.hashValue
-    }
-
-    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
-        if lhs.hashValue == rhs.hashValue {
-            return true
-        }
-        return false
-    }
-
-    open func clearCache() {
-        self.pathLengthFromStart = Double.infinity
-        self.pathVerticesFromStart = []
-    }
-}
-
-public class Dijkstra {
-    private var totalVertices: Set<Vertex>
-
-    public init(vertices: Set<Vertex>) {
-        self.totalVertices = vertices
-    }
-
-    private func clearCache() {
-        self.totalVertices.forEach { $0.clearCache() }
-    }
-
-    public func findShortestPaths(from startVertex: Vertex) {
-        self.clearCache()
-        startVertex.pathLengthFromStart = 0
-        startVertex.pathVerticesFromStart.append(startVertex)
-        var currentVertex: Vertex! = startVertex
-        while currentVertex != nil {
-            totalVertices.remove(currentVertex)
-            let filteredNeighbors = currentVertex.neighbors.filter { totalVertices.contains($0.0) }
-            for neighbor in filteredNeighbors {
-                let neighborVertex = neighbor.0
-                let weight = neighbor.1
-
-                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
-                if theoreticNewWeight < neighborVertex.pathLengthFromStart {
-                    neighborVertex.pathLengthFromStart = theoreticNewWeight
-                    neighborVertex.pathVerticesFromStart = currentVertex.pathVerticesFromStart
-                    neighborVertex.pathVerticesFromStart.append(neighborVertex)
-                }
-            }
-            if totalVertices.isEmpty {
-                currentVertex = nil
-                break
-            }
-            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
-        }
-    }
-}
 
 var _vertices: Set<Vertex> = Set()
 
diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
new file mode 100644
index 000000000..0ae83589e
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
@@ -0,0 +1,40 @@
+import Foundation
+
+public class Dijkstra {
+    private var totalVertices: Set<Vertex>
+
+    public init(vertices: Set<Vertex>) {
+        self.totalVertices = vertices
+    }
+
+    private func clearCache() {
+        self.totalVertices.forEach { $0.clearCache() }
+    }
+
+    public func findShortestPaths(from startVertex: Vertex) {
+        self.clearCache()
+        startVertex.pathLengthFromStart = 0
+        startVertex.pathVerticesFromStart.append(startVertex)
+        var currentVertex: Vertex! = startVertex
+        while currentVertex != nil {
+            totalVertices.remove(currentVertex)
+            let filteredNeighbors = currentVertex.neighbors.filter { totalVertices.contains($0.0) }
+            for neighbor in filteredNeighbors {
+                let neighborVertex = neighbor.0
+                let weight = neighbor.1
+
+                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
+                if theoreticNewWeight < neighborVertex.pathLengthFromStart {
+                    neighborVertex.pathLengthFromStart = theoreticNewWeight
+                    neighborVertex.pathVerticesFromStart = currentVertex.pathVerticesFromStart
+                    neighborVertex.pathVerticesFromStart.append(neighborVertex)
+                }
+            }
+            if totalVertices.isEmpty {
+                currentVertex = nil
+                break
+            }
+            currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
+        }
+    }
+}
diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
new file mode 100644
index 000000000..035db2713
--- /dev/null
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -0,0 +1,29 @@
+import Foundation
+
+open class Vertex: Hashable, Equatable {
+
+    open var identifier: String!
+    open var neighbors: [(Vertex, Double)] = []
+    open var pathLengthFromStart: Double = Double.infinity
+    open var pathVerticesFromStart: [Vertex] = []
+
+    public init(identifier: String) {
+        self.identifier = identifier
+    }
+
+    open var hashValue: Int {
+        return self.identifier.hashValue
+    }
+
+    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
+        if lhs.hashValue == rhs.hashValue {
+            return true
+        }
+        return false
+    }
+
+    open func clearCache() {
+        self.pathLengthFromStart = Double.infinity
+        self.pathVerticesFromStart = []
+    }
+}

From 3bdb63de34cba4abcc581980c83da650bc8d3ba4 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:17:45 +0300
Subject: [PATCH 112/862] Hashable, Equatable to Extensions

---
 .../Dijkstra.playground/Sources/Vertex.swift     | 16 ++++++++++------
 1 file changed, 10 insertions(+), 6 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
index 035db2713..67ba3791e 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -1,6 +1,6 @@
 import Foundation
 
-open class Vertex: Hashable, Equatable {
+open class Vertex {
 
     open var identifier: String!
     open var neighbors: [(Vertex, Double)] = []
@@ -11,19 +11,23 @@ open class Vertex: Hashable, Equatable {
         self.identifier = identifier
     }
 
+    open func clearCache() {
+        self.pathLengthFromStart = Double.infinity
+        self.pathVerticesFromStart = []
+    }
+}
+
+extension Vertex: Hashable {
     open var hashValue: Int {
         return self.identifier.hashValue
     }
+}
 
+extension Vertex: Equatable {
     public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
         if lhs.hashValue == rhs.hashValue {
             return true
         }
         return false
     }
-
-    open func clearCache() {
-        self.pathLengthFromStart = Double.infinity
-        self.pathVerticesFromStart = []
-    }
 }

From b2c5674b0c7d818cf061309e1cb7988e808d294b Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:18:44 +0300
Subject: [PATCH 113/862] Removed simplicity unwrapped for initialized variable

---
 Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
index 67ba3791e..22c04a0e1 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -2,7 +2,7 @@ import Foundation
 
 open class Vertex {
 
-    open var identifier: String!
+    open var identifier: String
     open var neighbors: [(Vertex, Double)] = []
     open var pathLengthFromStart: Double = Double.infinity
     open var pathVerticesFromStart: [Vertex] = []

From f0d057b89058c10cfe749990d5bdc3c669696610 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:19:34 +0300
Subject: [PATCH 114/862] Removed unnecessary explicit typing

---
 Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
index 22c04a0e1..dcdc64691 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -4,7 +4,7 @@ open class Vertex {
 
     open var identifier: String
     open var neighbors: [(Vertex, Double)] = []
-    open var pathLengthFromStart: Double = Double.infinity
+    open var pathLengthFromStart = Double.infinity
     open var pathVerticesFromStart: [Vertex] = []
 
     public init(identifier: String) {

From d0c68887780424e343f6663391eb5d70998fe166 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:20:05 +0300
Subject: [PATCH 115/862] Refactor Equatable extension

---
 Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
index dcdc64691..89e66c68d 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -25,9 +25,6 @@ extension Vertex: Hashable {
 
 extension Vertex: Equatable {
     public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
-        if lhs.hashValue == rhs.hashValue {
-            return true
-        }
-        return false
+        return lhs.hashValue == rhs.hashValue
     }
 }

From 222e96d2f221c2f0549b5292be8b60adee93e1de Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:23:14 +0300
Subject: [PATCH 116/862] Made vertex optional

---
 .../Dijkstra.playground/Sources/Dijkstra.swift       | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
index 0ae83589e..f0a9386b4 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
@@ -15,18 +15,18 @@ public class Dijkstra {
         self.clearCache()
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
-        var currentVertex: Vertex! = startVertex
-        while currentVertex != nil {
-            totalVertices.remove(currentVertex)
-            let filteredNeighbors = currentVertex.neighbors.filter { totalVertices.contains($0.0) }
+        var currentVertex: Vertex? = startVertex
+        while let vertex = currentVertex {
+            totalVertices.remove(vertex)
+            let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
             for neighbor in filteredNeighbors {
                 let neighborVertex = neighbor.0
                 let weight = neighbor.1
 
-                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
+                let theoreticNewWeight = vertex.pathLengthFromStart + weight
                 if theoreticNewWeight < neighborVertex.pathLengthFromStart {
                     neighborVertex.pathLengthFromStart = theoreticNewWeight
-                    neighborVertex.pathVerticesFromStart = currentVertex.pathVerticesFromStart
+                    neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart.append(neighborVertex)
                 }
             }

From e2561032e31912df5dab472f7d63a3900d05ac70 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:26:57 +0300
Subject: [PATCH 117/862] Removed unnecessary self

---
 .../Dijkstra.playground/Sources/Dijkstra.swift              | 6 +++---
 Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift | 6 +++---
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
index f0a9386b4..f4cd8503a 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
@@ -4,15 +4,15 @@ public class Dijkstra {
     private var totalVertices: Set<Vertex>
 
     public init(vertices: Set<Vertex>) {
-        self.totalVertices = vertices
+        totalVertices = vertices
     }
 
     private func clearCache() {
-        self.totalVertices.forEach { $0.clearCache() }
+        totalVertices.forEach { $0.clearCache() }
     }
 
     public func findShortestPaths(from startVertex: Vertex) {
-        self.clearCache()
+        clearCache()
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
         var currentVertex: Vertex? = startVertex
diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift
index 89e66c68d..a3587e04e 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Vertex.swift	
@@ -12,14 +12,14 @@ open class Vertex {
     }
 
     open func clearCache() {
-        self.pathLengthFromStart = Double.infinity
-        self.pathVerticesFromStart = []
+        pathLengthFromStart = Double.infinity
+        pathVerticesFromStart = []
     }
 }
 
 extension Vertex: Hashable {
     open var hashValue: Int {
-        return self.identifier.hashValue
+        return identifier.hashValue
     }
 }
 

From 5060d788da63363809c93996aa9851751131e2d2 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:53:05 +0300
Subject: [PATCH 118/862] Removed self, unnecessary imports

---
 .../Sources/CustomUI/EdgeRepresentation.swift |  24 +-
 .../Sources/CustomUI/ErrorView.swift          |  23 +-
 .../Sources/CustomUI/MyShapeLayer.swift       |   1 -
 .../Sources/CustomUI/RoundedButton.swift      |   8 +-
 .../Sources/CustomUI/VertexView.swift         |  48 ++--
 .../Sources/Graph.swift                       |  84 +++---
 .../Sources/GraphView.swift                   |  62 ++--
 .../Sources/SimpleObjects/Vertex.swift        |  59 ++--
 .../Sources/Window.swift                      | 272 +++++++++---------
 9 files changed, 291 insertions(+), 290 deletions(-)

diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift
index 5ff656dab..d827d3924 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/EdgeRepresentation.swift	
@@ -1,6 +1,6 @@
 import UIKit
 
-public class EdgeRepresentation: Equatable {
+public class EdgeRepresentation {
     private var graphColors: GraphColors = GraphColors.sharedInstance
 
     public private(set)var label: UILabel!
@@ -67,7 +67,7 @@ public class EdgeRepresentation: Equatable {
 
         let label = UILabel(frame: CGRect(origin: circleOrigin, size: CGSize(width: arcDiameter, height: arcDiameter)))
         label.textAlignment = .center
-        label.backgroundColor = self.graphColors.defaultEdgeColor
+        label.backgroundColor = graphColors.defaultEdgeColor
         label.clipsToBounds = true
         label.adjustsFontSizeToFitWidth = true
         label.layer.cornerRadius = arcDiameter / 2
@@ -75,35 +75,35 @@ public class EdgeRepresentation: Equatable {
 
         let shapeLayer = MyShapeLayer()
         shapeLayer.path = path.cgPath
-        shapeLayer.strokeColor = self.graphColors.defaultEdgeColor.cgColor
+        shapeLayer.strokeColor = graphColors.defaultEdgeColor.cgColor
         shapeLayer.fillColor = UIColor.clear.cgColor
         shapeLayer.lineWidth = 2.0
         shapeLayer.startPoint = startPoint
         shapeLayer.endPoint = endPoint
         shapeLayer.actions = ["position" : NSNull(), "bounds" : NSNull(), "path" : NSNull()]
+
         self.layer = shapeLayer
         self.label = label
         self.label.text = "\(weight)"
     }
 
     public func setCheckingColor() {
-        self.layer.strokeColor = self.graphColors.checkingColor.cgColor
-        self.label.backgroundColor = self.graphColors.checkingColor
+        layer.strokeColor = graphColors.checkingColor.cgColor
+        label.backgroundColor = graphColors.checkingColor
     }
 
     public func setDefaultColor() {
-        self.layer.strokeColor = self.graphColors.defaultEdgeColor.cgColor
-        self.label.backgroundColor = self.graphColors.defaultEdgeColor
+        layer.strokeColor = graphColors.defaultEdgeColor.cgColor
+        label.backgroundColor = graphColors.defaultEdgeColor
     }
 
     public func setText(text: String) {
-        self.label.text = text
+        label.text = text
     }
+}
 
+extension EdgeRepresentation: Equatable {
     public static func ==(lhs: EdgeRepresentation, rhs: EdgeRepresentation) -> Bool {
-        if lhs.label.hashValue == rhs.label.hashValue && lhs.layer.hashValue == rhs.layer.hashValue {
-            return true
-        }
-        return false
+        return lhs.label.hashValue == rhs.label.hashValue && lhs.layer.hashValue == rhs.layer.hashValue
     }
 }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift
index 69874e5d7..a63655dd9 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/ErrorView.swift	
@@ -2,9 +2,10 @@ import UIKit
 
 public class ErrorView: UIView {
     private var label: UILabel!
+
     public override init(frame: CGRect) {
         super.init(frame: frame)
-        self.commonInit()
+        commonInit()
     }
 
     public required init?(coder aDecoder: NSCoder) {
@@ -12,19 +13,19 @@ public class ErrorView: UIView {
     }
 
     private func commonInit() {
-        self.backgroundColor = UIColor(red: 242/255, green: 156/255, blue: 84/255, alpha: 1)
-        self.layer.cornerRadius = 10
+        backgroundColor = UIColor(red: 242/255, green: 156/255, blue: 84/255, alpha: 1)
+        layer.cornerRadius = 10
 
-        let labelFrame = CGRect(x: 10, y: 10, width: self.frame.width - 20, height: self.frame.height - 20)
-        self.label = UILabel(frame: labelFrame)
-        self.label.numberOfLines = 0
-        self.label.adjustsFontSizeToFitWidth = true
-        self.label.textAlignment = .center
-        self.label.textColor = UIColor.white
-        self.addSubview(self.label)
+        let labelFrame = CGRect(x: 10, y: 10, width: frame.width - 20, height: frame.height - 20)
+        label = UILabel(frame: labelFrame)
+        label.numberOfLines = 0
+        label.adjustsFontSizeToFitWidth = true
+        label.textAlignment = .center
+        label.textColor = UIColor.white
+        addSubview(label)
     }
 
     public func setText(text: String) {
-        self.label.text = text
+        label.text = text
     }
 }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift
index 54147f5e1..33bf4a515 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/MyShapeLayer.swift	
@@ -1,4 +1,3 @@
-import Foundation
 import UIKit
 
 public class MyShapeLayer: CAShapeLayer {
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift
index 2647c4525..819fcfc5c 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/RoundedButton.swift	
@@ -5,7 +5,7 @@ public class RoundedButton: UIButton {
     
     public override init(frame: CGRect) {
         super.init(frame: frame)
-        self.commonInit()
+        commonInit()
     }
     
     public required init?(coder aDecoder: NSCoder) {
@@ -13,8 +13,8 @@ public class RoundedButton: UIButton {
     }
 
     private func commonInit() {
-        self.backgroundColor = self.graphColors.buttonsBackgroundColor
-        self.titleLabel?.adjustsFontSizeToFitWidth = true
-        self.layer.cornerRadius = 7
+        backgroundColor = graphColors.buttonsBackgroundColor
+        titleLabel?.adjustsFontSizeToFitWidth = true
+        layer.cornerRadius = 7
     }
 }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift
index 29c971411..e785e120b 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/CustomUI/VertexView.swift	
@@ -15,49 +15,49 @@ public class VertexView: UIButton {
         precondition(frame.height == frame.width)
         precondition(frame.height >= 30)
         super.init(frame: frame)
-        self.backgroundColor = self.graphColors.defaultVertexColor
-        self.layer.cornerRadius = frame.width / 2
-        self.clipsToBounds = true
-        self.setupIdLabel()
-        self.setupPathLengthFromStartLabel()
+        backgroundColor = graphColors.defaultVertexColor
+        layer.cornerRadius = frame.width / 2
+        clipsToBounds = true
+        setupIdLabel()
+        setupPathLengthFromStartLabel()
     }
 
     private func setupIdLabel() {
-        let x: CGFloat = self.frame.width * 0.2
+        let x: CGFloat = frame.width * 0.2
         let y: CGFloat = 0
-        let width: CGFloat = self.frame.width * 0.6
-        let height: CGFloat = self.frame.height / 2
+        let width: CGFloat = frame.width * 0.6
+        let height: CGFloat = frame.height / 2
         let idLabelFrame = CGRect(x: x, y: y, width: width, height: height)
 
-        self.idLabel = UILabel(frame: idLabelFrame)
-        self.idLabel.textAlignment = .center
-        self.idLabel.adjustsFontSizeToFitWidth = true
-        self.addSubview(self.idLabel)
+        idLabel = UILabel(frame: idLabelFrame)
+        idLabel.textAlignment = .center
+        idLabel.adjustsFontSizeToFitWidth = true
+        addSubview(idLabel)
     }
 
     private func setupPathLengthFromStartLabel() {
-        let x: CGFloat = self.frame.width * 0.2
-        let y: CGFloat = self.frame.height / 2
-        let width: CGFloat = self.frame.width * 0.6
-        let height: CGFloat = self.frame.height / 2
+        let x: CGFloat = frame.width * 0.2
+        let y: CGFloat = frame.height / 2
+        let width: CGFloat = frame.width * 0.6
+        let height: CGFloat = frame.height / 2
         let pathLengthLabelFrame = CGRect(x: x, y: y, width: width, height: height)
 
-        self.pathLengthLabel = UILabel(frame: pathLengthLabelFrame)
-        self.pathLengthLabel.textAlignment = .center
-        self.pathLengthLabel.adjustsFontSizeToFitWidth = true
-        self.addSubview(self.pathLengthLabel)
+        pathLengthLabel = UILabel(frame: pathLengthLabelFrame)
+        pathLengthLabel.textAlignment = .center
+        pathLengthLabel.adjustsFontSizeToFitWidth = true
+        addSubview(pathLengthLabel)
     }
 
     public func setIdLabel(text: String) {
-        self.idLabel.text = text
+        idLabel.text = text
     }
 
     public func setPathLengthLabel(text: String) {
-        self.pathLengthLabel.text = text
+        pathLengthLabel.text = text
     }
 
     public func setLabelsTextColor(color: UIColor) {
-        self.idLabel.textColor = color
-        self.pathLengthLabel.textColor = color
+        idLabel.textColor = color
+        pathLengthLabel.textColor = color
     }
 }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift
index 0b0b97b92..7c4a8e373 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
@@ -22,20 +22,20 @@ public class Graph {
     public var startVertex: Vertex!
     public var interactiveNeighborCheckAnimationDuration: Double = 1.8 {
         didSet {
-            self._interactiveOneSleepDuration = UInt32(self.interactiveNeighborCheckAnimationDuration * 1000000.0 / 3.0)
+            _interactiveOneSleepDuration = UInt32(interactiveNeighborCheckAnimationDuration * 1000000.0 / 3.0)
         }
     }
     private var _interactiveOneSleepDuration: UInt32 = 600000
 
     public var visualizationNeighborCheckAnimationDuration: Double = 2.25 {
         didSet {
-            self._visualizationOneSleepDuration = UInt32(self.visualizationNeighborCheckAnimationDuration * 1000000.0 / 3.0)
+            _visualizationOneSleepDuration = UInt32(visualizationNeighborCheckAnimationDuration * 1000000.0 / 3.0)
         }
     }
     private var _visualizationOneSleepDuration: UInt32 = 750000
 
     public var vertices: Set<Vertex> {
-        return self._vertices
+        return _vertices
     }
 
     public init(verticesCount: UInt) {
@@ -43,46 +43,46 @@ public class Graph {
     }
 
     public func removeGraph() {
-        self._vertices.removeAll()
-        self.startVertex = nil
+        _vertices.removeAll()
+        startVertex = nil
     }
 
     public func createNewGraph() {
-        guard self._vertices.isEmpty, self.startVertex == nil else {
+        guard _vertices.isEmpty, startVertex == nil else {
             assertionFailure("Clear graph before creating new one")
             return
         }
-        self.createNotConnectedVertices()
-        self.setupConnections()
-        let offset = Int(arc4random_uniform(UInt32(self._vertices.count)))
-        let index = self._vertices.index(self._vertices.startIndex, offsetBy: offset)
-        self.startVertex =  self._vertices[index]
-        self.setVertexLevels()
+        createNotConnectedVertices()
+        setupConnections()
+        let offset = Int(arc4random_uniform(UInt32(_vertices.count)))
+        let index = _vertices.index(_vertices.startIndex, offsetBy: offset)
+        startVertex =  _vertices[index]
+        setVertexLevels()
     }
     
     private func clearCache() {
-        self._vertices.forEach { $0.clearCache() }
+        _vertices.forEach { $0.clearCache() }
     }
 
     public func reset() {
-        for vertex in self._vertices {
+        for vertex in _vertices {
             vertex.clearCache()
         }
     }
 
     private func createNotConnectedVertices() {
-        for i in 0..<self.verticesCount {
+        for i in 0..<verticesCount {
             let vertex = Vertex(identifier: "\(i)")
-            self._vertices.insert(vertex)
+            _vertices.insert(vertex)
         }
     }
 
     private func setupConnections() {
-        for vertex in self._vertices {
+        for vertex in _vertices {
             let randomEdgesCount = arc4random_uniform(4) + 1
             for _ in 0..<randomEdgesCount {
                 let randomWeight = Double(arc4random_uniform(10))
-                let neighbor = self.randomVertex(except: vertex)
+                let neighbor = randomVertex(except: vertex)
                 let edge1 = Edge(vertex: neighbor, weight: randomWeight)
                 if vertex.edges.contains(where: { $0.neighbor == neighbor }) {
                     continue
@@ -95,7 +95,7 @@ public class Graph {
     }
 
     private func randomVertex(except vertex: Vertex) -> Vertex {
-        var newSet = self._vertices
+        var newSet = _vertices
         newSet.remove(vertex)
         let offset = Int(arc4random_uniform(UInt32(newSet.count)))
         let index = newSet.index(newSet.startIndex, offsetBy: offset)
@@ -103,8 +103,8 @@ public class Graph {
     }
 
     private func setVertexLevels() {
-        self._vertices.forEach { $0.clearLevelInfo() }
-        guard let startVertex = self.startVertex else {
+        _vertices.forEach { $0.clearLevelInfo() }
+        guard let startVertex = startVertex else {
             assertionFailure()
             return
         }
@@ -127,21 +127,21 @@ public class Graph {
     }
 
     public func findShortestPathsWithVisualization(completion: () -> Void) {
-        self.clearCache()
+        clearCache()
         startVertex.pathLengthFromStart = 0
-        startVertex.pathVerticesFromStart.append(self.startVertex)
-        var currentVertex: Vertex! = self.startVertex
+        startVertex.pathVerticesFromStart.append(startVertex)
+        var currentVertex: Vertex! = startVertex
 
-        var totalVertices = self._vertices
+        var totalVertices = _vertices
 
         breakableLoop: while currentVertex != nil {
             totalVertices.remove(currentVertex)
-            while self.pauseVisualization == true {
-                if self.stopVisualization == true {
+            while pauseVisualization == true {
+                if stopVisualization == true {
                     break breakableLoop
                 }
             }
-            if self.stopVisualization == true {
+            if stopVisualization == true {
                 break breakableLoop
             }
             DispatchQueue.main.async {
@@ -155,12 +155,12 @@ public class Graph {
                 let weight = edge.weight
                 let edgeRepresentation = edge.edgeRepresentation
 
-                while self.pauseVisualization == true {
-                    if self.stopVisualization == true {
+                while pauseVisualization == true {
+                    if stopVisualization == true {
                         break breakableLoop
                     }
                 }
-                if self.stopVisualization == true {
+                if stopVisualization == true {
                     break breakableLoop
                 }
                 DispatchQueue.main.async {
@@ -170,32 +170,32 @@ public class Graph {
                                                        edgePathLength: weight,
                                                        endVertexPathLength: neighbor.pathLengthFromStart)
                 }
-                usleep(self._visualizationOneSleepDuration)
+                usleep(_visualizationOneSleepDuration)
 
 
                 let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
 
                 if theoreticNewWeight < neighbor.pathLengthFromStart {
-                    while self.pauseVisualization == true {
-                        if self.stopVisualization == true {
+                    while pauseVisualization == true {
+                        if stopVisualization == true {
                             break breakableLoop
                         }
                     }
-                    if self.stopVisualization == true {
+                    if stopVisualization == true {
                         break breakableLoop
                     }
                     neighbor.pathLengthFromStart = theoreticNewWeight
                     neighbor.pathVerticesFromStart = currentVertex.pathVerticesFromStart
                     neighbor.pathVerticesFromStart.append(neighbor)
                 }
-                usleep(self._visualizationOneSleepDuration)
+                usleep(_visualizationOneSleepDuration)
 
                 DispatchQueue.main.async {
                     self.delegate?.didFinishCompare()
                     edge.edgeRepresentation?.setDefaultColor()
                     edge.neighbor.setDefaultColor()
                 }
-                usleep(self._visualizationOneSleepDuration)
+                usleep(_visualizationOneSleepDuration)
             }
             if totalVertices.isEmpty {
                 currentVertex = nil
@@ -203,7 +203,7 @@ public class Graph {
             }
             currentVertex = totalVertices.min { $0.pathLengthFromStart < $1.pathLengthFromStart }
         }
-        if self.stopVisualization == true {
+        if stopVisualization == true {
             DispatchQueue.main.async {
                 self.delegate?.didStop()
             }
@@ -294,10 +294,10 @@ public class Graph {
     }
 
     public func didTapVertex(vertex: Vertex) {
-        if self.nextVertices.contains(vertex) {
-            self.delegate?.willStartVertexNeighborsChecking()
-            self.state = .parsing
-            self.parseNeighborsFor(vertex: vertex) {
+        if nextVertices.contains(vertex) {
+            delegate?.willStartVertexNeighborsChecking()
+            state = .parsing
+            parseNeighborsFor(vertex: vertex) {
                 self.state = .interactiveVisualization
                 self.delegate?.didFinishVertexNeighborsChecking()
             }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift
index 49bc6853f..bdeab7669 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift	
@@ -7,7 +7,7 @@ public class GraphView: UIView {
 
     public override init(frame: CGRect) {
         super.init(frame: frame)
-        self.backgroundColor = self.graphColors.graphBackgroundColor
+        backgroundColor = graphColors.graphBackgroundColor
     }
     
     public required init?(coder aDecoder: NSCoder) {
@@ -20,13 +20,13 @@ public class GraphView: UIView {
     }
 
     public func removeGraph() {
-        for vertex in self.graph.vertices {
+        for vertex in graph.vertices {
             if let view = vertex.view {
                 view.removeFromSuperview()
                 vertex.view = nil
             }
         }
-        for vertex in self.graph.vertices {
+        for vertex in graph.vertices {
             for edge in vertex.edges {
                 if let edgeRepresentation = edge.edgeRepresentation {
                     edgeRepresentation.layer.removeFromSuperlayer()
@@ -38,41 +38,41 @@ public class GraphView: UIView {
     }
 
     public func createNewGraph() {
-        self.setupVertexViews()
-        self.setupEdgeRepresentations()
-        self.addGraph()
+        setupVertexViews()
+        setupEdgeRepresentations()
+        addGraph()
     }
 
     public func reset() {
-        for vertex in self.graph.vertices {
+        for vertex in graph.vertices {
             vertex.edges.forEach { $0.edgeRepresentation?.setDefaultColor() }
             vertex.setDefaultColor()
         }
     }
 
     private func addGraph() {
-        for vertex in self.graph.vertices {
+        for vertex in graph.vertices {
             for edge in vertex.edges {
                 if let edgeRepresentation = edge.edgeRepresentation {
-                    self.layer.addSublayer(edgeRepresentation.layer)
-                    self.addSubview(edgeRepresentation.label)
+                    layer.addSublayer(edgeRepresentation.layer)
+                    addSubview(edgeRepresentation.label)
                 }
             }
         }
-        for vertex in self.graph.vertices {
+        for vertex in graph.vertices {
             if let view = vertex.view {
-                self.addSubview(view)
+                addSubview(view)
             }
         }
     }
 
     private func setupVertexViews() {
         var level = 0
-        var buildViewQueue = [self.graph.startVertex!]
+        var buildViewQueue = [graph.startVertex!]
         let itemWidth: CGFloat = 40
         while !buildViewQueue.isEmpty {
             let levelItemsCount = CGFloat(buildViewQueue.count)
-            let xStep = (self.frame.width - levelItemsCount * itemWidth) / (levelItemsCount + 1)
+            let xStep = (frame.width - levelItemsCount * itemWidth) / (levelItemsCount + 1)
             var previousVertexMaxX: CGFloat = 0.0
             for vertex in buildViewQueue {
                 let x: CGFloat = previousVertexMaxX + xStep
@@ -84,12 +84,12 @@ public class GraphView: UIView {
                 vertexView.vertex = vertex
                 vertex.view?.setIdLabel(text: vertex.identifier)
                 vertex.view?.setPathLengthLabel(text: "\(vertex.pathLengthFromStart)")
-                vertex.view?.addTarget(self, action: #selector(self.didTapVertex(sender:)), for: .touchUpInside)
-                let panGesture = UIPanGestureRecognizer(target: self, action: #selector(self.handlePan(recognizer:)))
+                vertex.view?.addTarget(self, action: #selector(didTapVertex(sender:)), for: .touchUpInside)
+                let panGesture = UIPanGestureRecognizer(target: self, action: #selector(handlePan(recognizer:)))
                 vertex.view?.addGestureRecognizer(panGesture)
             }
             level += 1
-            buildViewQueue = self.graph.vertices.filter { $0.level == level }
+            buildViewQueue = graph.vertices.filter { $0.level == level }
         }
     }
 
@@ -100,8 +100,8 @@ public class GraphView: UIView {
         guard let vertexView = recognizer.view as? VertexView, let vertex = vertexView.vertex else {
             return
         }
-        if self.panningView != nil {
-            if self.panningView != vertexView {
+        if panningView != nil {
+            if panningView != vertexView {
                 return
             }
         }
@@ -122,39 +122,39 @@ public class GraphView: UIView {
                     }
                 }
             }
-            self.panningView = vertexView
+            panningView = vertexView
         case .changed:
-            if self.movingVertexOutputEdges.isEmpty && self.movingVertexInputEdges.isEmpty {
+            if movingVertexOutputEdges.isEmpty && movingVertexInputEdges.isEmpty {
                 return
             }
             let translation = recognizer.translation(in: self)
             if vertexView.frame.origin.x + translation.x <= 0
                 || vertexView.frame.origin.y + translation.y <= 0
-                || (vertexView.frame.origin.x + vertexView.frame.width + translation.x) >= self.frame.width
-                || (vertexView.frame.origin.y + vertexView.frame.height + translation.y) >= self.frame.height {
+                || (vertexView.frame.origin.x + vertexView.frame.width + translation.x) >= frame.width
+                || (vertexView.frame.origin.y + vertexView.frame.height + translation.y) >= frame.height {
                 break
             }
-            self.movingVertexInputEdges.forEach { edgeRepresentation in
+            movingVertexInputEdges.forEach { edgeRepresentation in
                 let originalLabelCenter = edgeRepresentation.label.center
                 edgeRepresentation.label.center = CGPoint(x: originalLabelCenter.x + translation.x * 0.625,
                                                           y: originalLabelCenter.y + translation.y * 0.625)
 
                 CATransaction.begin()
                 CATransaction.setValue(kCFBooleanTrue, forKey: kCATransactionDisableActions)
-                let newPath = self.path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: false)
+                let newPath = path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: false)
                 edgeRepresentation.layer.path = newPath
                 CATransaction.commit()
 
             }
 
-            self.movingVertexOutputEdges.forEach { edgeRepresentation in
+            movingVertexOutputEdges.forEach { edgeRepresentation in
                 let originalLabelCenter = edgeRepresentation.label.center
                 edgeRepresentation.label.center = CGPoint(x: originalLabelCenter.x + translation.x * 0.375,
                                                           y: originalLabelCenter.y + translation.y * 0.375)
 
                 CATransaction.begin()
                 CATransaction.setValue(kCFBooleanTrue, forKey: kCATransactionDisableActions)
-                let newPath = self.path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: true)
+                let newPath = path(fromEdgeRepresentation: edgeRepresentation, movingVertex: vertex, translation: translation, outPath: true)
                 edgeRepresentation.layer.path = newPath
                 CATransaction.commit()
             }
@@ -163,9 +163,9 @@ public class GraphView: UIView {
                                         y: vertexView.center.y + translation.y)
             recognizer.setTranslation(CGPoint.zero, in: self)
         case .ended:
-            self.movingVertexInputEdges = []
-            self.movingVertexOutputEdges = []
-            self.panningView = nil
+            movingVertexInputEdges = []
+            movingVertexOutputEdges = []
+            panningView = nil
         default:
             break
         }
@@ -223,7 +223,7 @@ public class GraphView: UIView {
     }
 
     private func setupEdgeRepresentations() {
-        var edgeQueue: [Vertex] = [self.graph.startVertex!]
+        var edgeQueue: [Vertex] = [graph.startVertex!]
 
         //BFS
         while !edgeQueue.isEmpty {
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift
index c9270b0df..f18ec3114 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/SimpleObjects/Vertex.swift	
@@ -1,10 +1,17 @@
 import UIKit
 
-public class Vertex: Hashable, Equatable {
+public class Vertex {
     private var graphColors: GraphColors = GraphColors.sharedInstance
 
+    public var view: VertexView?
+    
     public var identifier: String
     public var edges: [Edge] = []
+    public var pathVerticesFromStart: [Vertex] = []
+    public var level: Int = 0
+    public var levelChecked: Bool = false
+    public var haveAllEdges: Bool = false
+    public var visited: Bool = false
     public var pathLengthFromStart: Double = Double.infinity {
         didSet {
             DispatchQueue.main.async {
@@ -12,51 +19,45 @@ public class Vertex: Hashable, Equatable {
             }
         }
     }
-    public var pathVerticesFromStart: [Vertex] = []
-    public var level: Int = 0
-    public var levelChecked: Bool = false
-    public var haveAllEdges: Bool = false
-    public var visited: Bool = false
-
-    public var view: VertexView?
 
     public init(identifier: String) {
         self.identifier = identifier
     }
 
-    public var hashValue: Int {
-        return self.identifier.hashValue
-    }
-
-    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
-        if lhs.hashValue == rhs.hashValue {
-            return true
-        }
-        return false
-    }
-
     public func clearCache() {
-        self.pathLengthFromStart = Double.infinity
-        self.pathVerticesFromStart = []
-        self.visited = false
+        pathLengthFromStart = Double.infinity
+        pathVerticesFromStart = []
+        visited = false
     }
 
     public func clearLevelInfo() {
-        self.level = 0
-        self.levelChecked = false
+        level = 0
+        levelChecked = false
     }
 
     public func setVisitedColor() {
-        self.view?.backgroundColor = self.graphColors.visitedColor
-        self.view?.setLabelsTextColor(color: UIColor.white)
+        view?.backgroundColor = graphColors.visitedColor
+        view?.setLabelsTextColor(color: UIColor.white)
     }
 
     public func setCheckingPathColor() {
-        self.view?.backgroundColor = self.graphColors.checkingColor
+        view?.backgroundColor = graphColors.checkingColor
     }
 
     public func setDefaultColor() {
-        self.view?.backgroundColor = self.graphColors.defaultVertexColor
-        self.view?.setLabelsTextColor(color: UIColor.black)
+        view?.backgroundColor = graphColors.defaultVertexColor
+        view?.setLabelsTextColor(color: UIColor.black)
+    }
+}
+
+extension Vertex: Hashable {
+    public var hashValue: Int {
+        return identifier.hashValue
+    }
+}
+
+extension Vertex: Equatable {
+    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
+        return lhs.hashValue == rhs.hashValue
     }
 }
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift
index e8aabad27..054b804c9 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
@@ -30,7 +30,7 @@ public class Window: UIView, GraphDelegate {
     public override init(frame: CGRect) {
         super.init(frame: frame)
         self.frame = frame
-        self.backgroundColor = self.graphColors.mainWindowBackgroundColor
+        backgroundColor = graphColors.mainWindowBackgroundColor
     }
     
     public required init?(coder aDecoder: NSCoder) {
@@ -39,130 +39,130 @@ public class Window: UIView, GraphDelegate {
 
     public func configure(graph: Graph) {
         self.graph = graph
-        self.graph.createNewGraph()
-        self.graph.delegate = self
+        graph.createNewGraph()
+        graph.delegate = self
         let frame = CGRect(x: 10, y: 170, width: self.frame.width - 20, height: self.frame.height - 180)
-        self.graphView = GraphView(frame: frame)
-        self.graphView.layer.cornerRadius = 15
-
-        self.graphView.configure(graph: self.graph)
-        self.graphView.createNewGraph()
-        self.addSubview(self.graphView)
-
-        self.configureCreateGraphButton()
-        self.configureStartVisualizationButton()
-        self.configureStartInteractiveVisualizationButton()
-        self.configureStartButton()
-        self.configurePauseButton()
-        self.configureStopButton()
-        self.configureComparisonLabel()
-        self.configureActivityIndicator()
-
-        self.topView = UIView(frame: CGRect(x: 10, y: 10, width: self.frame.width - 20, height: 150))
-        self.topView.backgroundColor = self.graphColors.topViewBackgroundColor
-        self.topView.layer.cornerRadius = 15
-        self.addSubview(self.topView)
-
-        self.topView.addSubview(self.createGraphButton)
-        self.topView.addSubview(self.startVisualizationButton)
-        self.topView.addSubview(self.startInteractiveVisualizationButton)
-        self.topView.addSubview(self.startButton)
-        self.topView.addSubview(self.pauseButton)
-        self.topView.addSubview(self.stopButton)
-        self.topView.addSubview(self.comparisonLabel)
-        self.topView.addSubview(self.activityIndicator)
+        graphView = GraphView(frame: frame)
+        graphView.layer.cornerRadius = 15
+
+        graphView.configure(graph: graph)
+        graphView.createNewGraph()
+        addSubview(graphView)
+
+        configureCreateGraphButton()
+        configureStartVisualizationButton()
+        configureStartInteractiveVisualizationButton()
+        configureStartButton()
+        configurePauseButton()
+        configureStopButton()
+        configureComparisonLabel()
+        configureActivityIndicator()
+
+        topView = UIView(frame: CGRect(x: 10, y: 10, width: frame.width - 20, height: 150))
+        topView.backgroundColor = graphColors.topViewBackgroundColor
+        topView.layer.cornerRadius = 15
+        addSubview(topView)
+
+        topView.addSubview(createGraphButton)
+        topView.addSubview(startVisualizationButton)
+        topView.addSubview(startInteractiveVisualizationButton)
+        topView.addSubview(startButton)
+        topView.addSubview(pauseButton)
+        topView.addSubview(stopButton)
+        topView.addSubview(comparisonLabel)
+        topView.addSubview(activityIndicator)
     }
 
     private func configureCreateGraphButton() {
-        let frame = CGRect(x: self.center.x - 200, y: 12, width: 100, height: 34)
-        self.createGraphButton = RoundedButton(frame: frame)
-        self.createGraphButton.setTitle("New graph", for: .normal)
-        self.createGraphButton.addTarget(self, action: #selector(self.createGraphButtonTap), for: .touchUpInside)
+        let frame = CGRect(x: center.x - 200, y: 12, width: 100, height: 34)
+        createGraphButton = RoundedButton(frame: frame)
+        createGraphButton.setTitle("New graph", for: .normal)
+        createGraphButton.addTarget(self, action: #selector(createGraphButtonTap), for: .touchUpInside)
     }
 
     private func configureStartVisualizationButton() {
-        let frame = CGRect(x: self.center.x - 50, y: 12, width: 100, height: 34)
-        self.startVisualizationButton = RoundedButton(frame: frame)
-        self.startVisualizationButton.setTitle("Auto", for: .normal)
-        self.startVisualizationButton.addTarget(self, action: #selector(self.startVisualizationButtonDidTap), for: .touchUpInside)
+        let frame = CGRect(x: center.x - 50, y: 12, width: 100, height: 34)
+        startVisualizationButton = RoundedButton(frame: frame)
+        startVisualizationButton.setTitle("Auto", for: .normal)
+        startVisualizationButton.addTarget(self, action: #selector(startVisualizationButtonDidTap), for: .touchUpInside)
     }
 
     private func configureStartInteractiveVisualizationButton() {
-        let frame = CGRect(x: self.center.x + 100, y: 12, width: 100, height: 34)
-        self.startInteractiveVisualizationButton = RoundedButton(frame: frame)
-        self.startInteractiveVisualizationButton.setTitle("Interactive", for: .normal)
-        self.startInteractiveVisualizationButton.addTarget(self, action: #selector(self.startInteractiveVisualizationButtonDidTap), for: .touchUpInside)
+        let frame = CGRect(x: center.x + 100, y: 12, width: 100, height: 34)
+        startInteractiveVisualizationButton = RoundedButton(frame: frame)
+        startInteractiveVisualizationButton.setTitle("Interactive", for: .normal)
+        startInteractiveVisualizationButton.addTarget(self, action: #selector(startInteractiveVisualizationButtonDidTap), for: .touchUpInside)
     }
 
     private func configureStartButton() {
-        let frame = CGRect(x: self.center.x - 65, y: 56, width: 30, height: 30)
-        self.startButton = UIButton(frame: frame)
+        let frame = CGRect(x: center.x - 65, y: 56, width: 30, height: 30)
+        startButton = UIButton(frame: frame)
         let playImage = UIImage(named: "Start.png")
-        self.startButton.setImage(playImage, for: .normal)
-        self.startButton.isEnabled = false
-        self.startButton.addTarget(self, action: #selector(self.didTapStartButton), for: .touchUpInside)
+        startButton.setImage(playImage, for: .normal)
+        startButton.isEnabled = false
+        startButton.addTarget(self, action: #selector(didTapStartButton), for: .touchUpInside)
     }
 
     private func configurePauseButton() {
-        let frame = CGRect(x: self.center.x - 15, y: 56, width: 30, height: 30)
-        self.pauseButton = UIButton(frame: frame)
+        let frame = CGRect(x: center.x - 15, y: 56, width: 30, height: 30)
+        pauseButton = UIButton(frame: frame)
         let pauseImage = UIImage(named: "Pause.png")
-        self.pauseButton.setImage(pauseImage, for: .normal)
-        self.pauseButton.isEnabled = false
-        self.pauseButton.addTarget(self, action: #selector(self.didTapPauseButton), for: .touchUpInside)
+        pauseButton.setImage(pauseImage, for: .normal)
+        pauseButton.isEnabled = false
+        pauseButton.addTarget(self, action: #selector(didTapPauseButton), for: .touchUpInside)
     }
 
     private func configureStopButton() {
-        let frame = CGRect(x: self.center.x + 35, y: 56, width: 30, height: 30)
-        self.stopButton = UIButton(frame: frame)
+        let frame = CGRect(x: center.x + 35, y: 56, width: 30, height: 30)
+        stopButton = UIButton(frame: frame)
         let stopImage = UIImage(named: "Stop.png")
-        self.stopButton.setImage(stopImage, for: .normal)
-        self.stopButton.isEnabled = false
-        self.stopButton.addTarget(self, action: #selector(self.didTapStopButton), for: .touchUpInside)
+        stopButton.setImage(stopImage, for: .normal)
+        stopButton.isEnabled = false
+        stopButton.addTarget(self, action: #selector(didTapStopButton), for: .touchUpInside)
     }
 
     private func configureComparisonLabel() {
         let size = CGSize(width: 250, height: 42)
-        let origin = CGPoint(x: self.center.x - 125, y: 96)
+        let origin = CGPoint(x: center.x - 125, y: 96)
         let frame = CGRect(origin: origin, size: size)
-        self.comparisonLabel = UILabel(frame: frame)
-        self.comparisonLabel.textAlignment = .center
-        self.comparisonLabel.text = "Have fun!"
+        comparisonLabel = UILabel(frame: frame)
+        comparisonLabel.textAlignment = .center
+        comparisonLabel.text = "Have fun!"
     }
 
     private func configureActivityIndicator() {
         let size = CGSize(width: 50, height: 42)
-        let origin = CGPoint(x: self.center.x - 25, y: 100)
+        let origin = CGPoint(x: center.x - 25, y: 100)
         let activityIndicatorFrame = CGRect(origin: origin, size: size)
-        self.activityIndicator = UIActivityIndicatorView(frame: activityIndicatorFrame)
-        self.activityIndicator.activityIndicatorViewStyle = .whiteLarge
+        activityIndicator = UIActivityIndicatorView(frame: activityIndicatorFrame)
+        activityIndicator.activityIndicatorViewStyle = .whiteLarge
     }
 
     @objc private func createGraphButtonTap() {
-        self.comparisonLabel.text = ""
-        self.graphView.removeGraph()
-        self.graph.removeGraph()
-        self.graph.createNewGraph()
-        self.graphView.createNewGraph()
-        self.graph.state = .initial
+        comparisonLabel.text = ""
+        graphView.removeGraph()
+        graph.removeGraph()
+        graph.createNewGraph()
+        graphView.createNewGraph()
+        graph.state = .initial
     }
 
     @objc private func startVisualizationButtonDidTap() {
-        self.comparisonLabel.text = ""
-        self.pauseButton.isEnabled = true
-        self.stopButton.isEnabled = true
-        self.createGraphButton.isEnabled = false
-        self.startVisualizationButton.isEnabled = false
-        self.startInteractiveVisualizationButton.isEnabled = false
-        self.createGraphButton.alpha = 0.5
-        self.startVisualizationButton.alpha = 0.5
-        self.startInteractiveVisualizationButton.alpha = 0.5
-
-        if self.graph.state == .completed {
-            self.graphView.reset()
-            self.graph.reset()
+        comparisonLabel.text = ""
+        pauseButton.isEnabled = true
+        stopButton.isEnabled = true
+        createGraphButton.isEnabled = false
+        startVisualizationButton.isEnabled = false
+        startInteractiveVisualizationButton.isEnabled = false
+        createGraphButton.alpha = 0.5
+        startVisualizationButton.alpha = 0.5
+        startInteractiveVisualizationButton.alpha = 0.5
+
+        if graph.state == .completed {
+            graphView.reset()
+            graph.reset()
         }
-        self.graph.state = .autoVisualization
+        graph.state = .autoVisualization
         DispatchQueue.global(qos: .background).async {
             self.graph.findShortestPathsWithVisualization {
                 self.graph.state = .completed
@@ -184,25 +184,25 @@ public class Window: UIView, GraphDelegate {
     }
 
     @objc private func startInteractiveVisualizationButtonDidTap() {
-        self.comparisonLabel.text = ""
-        self.pauseButton.isEnabled = true
-        self.stopButton.isEnabled = true
-        self.createGraphButton.isEnabled = false
-        self.startVisualizationButton.isEnabled = false
-        self.startInteractiveVisualizationButton.isEnabled = false
-        self.createGraphButton.alpha = 0.5
-        self.startVisualizationButton.alpha = 0.5
-        self.startInteractiveVisualizationButton.alpha = 0.5
-
-        if self.graph.state == .completed {
-            self.graphView.reset()
-            self.graph.reset()
+        comparisonLabel.text = ""
+        pauseButton.isEnabled = true
+        stopButton.isEnabled = true
+        createGraphButton.isEnabled = false
+        startVisualizationButton.isEnabled = false
+        startInteractiveVisualizationButton.isEnabled = false
+        createGraphButton.alpha = 0.5
+        startVisualizationButton.alpha = 0.5
+        startInteractiveVisualizationButton.alpha = 0.5
+
+        if graph.state == .completed {
+            graphView.reset()
+            graph.reset()
         }
         
-        self.graph.startVertex.pathLengthFromStart = 0
-        self.graph.startVertex.pathVerticesFromStart.append(self.graph.startVertex)
-        self.graph.state = .parsing
-        self.graph.parseNeighborsFor(vertex: self.graph.startVertex) {
+        graph.startVertex.pathLengthFromStart = 0
+        graph.startVertex.pathVerticesFromStart.append(graph.startVertex)
+        graph.state = .parsing
+        graph.parseNeighborsFor(vertex: graph.startVertex) {
             self.graph.state = .interactiveVisualization
             DispatchQueue.main.async {
                 self.comparisonLabel.text = "Pick next vertex"
@@ -211,43 +211,43 @@ public class Window: UIView, GraphDelegate {
     }
 
     @objc private func didTapStartButton() {
-        self.startButton.isEnabled = false
-        self.pauseButton.isEnabled = true
+        startButton.isEnabled = false
+        pauseButton.isEnabled = true
         DispatchQueue.global(qos: .utility).async {
             self.graph.pauseVisualization = false
         }
     }
 
     @objc private func didTapPauseButton() {
-        self.startButton.isEnabled = true
-        self.pauseButton.isEnabled = false
+        startButton.isEnabled = true
+        pauseButton.isEnabled = false
         DispatchQueue.global(qos: .utility).async {
             self.graph.pauseVisualization = true
         }
     }
 
     @objc private func didTapStopButton() {
-        self.startButton.isEnabled = false
-        self.pauseButton.isEnabled = false
-        self.comparisonLabel.text = ""
-        self.activityIndicator.startAnimating()
-        if self.graph.state == .parsing || self.graph.state == .autoVisualization {
-            self.graph.stopVisualization = true
-        } else if self.graph.state == .interactiveVisualization {
-            self.didStop()
+        startButton.isEnabled = false
+        pauseButton.isEnabled = false
+        comparisonLabel.text = ""
+        activityIndicator.startAnimating()
+        if graph.state == .parsing || graph.state == .autoVisualization {
+            graph.stopVisualization = true
+        } else if graph.state == .interactiveVisualization {
+            didStop()
         }
     }
 
     private func setButtonsToInitialState() {
-        self.createGraphButton.isEnabled = true
-        self.startVisualizationButton.isEnabled = true
-        self.startInteractiveVisualizationButton.isEnabled = true
-        self.startButton.isEnabled = false
-        self.pauseButton.isEnabled = false
-        self.stopButton.isEnabled = false
-        self.createGraphButton.alpha = 1
-        self.startVisualizationButton.alpha = 1
-        self.startInteractiveVisualizationButton.alpha = 1
+        createGraphButton.isEnabled = true
+        startVisualizationButton.isEnabled = true
+        startInteractiveVisualizationButton.isEnabled = true
+        startButton.isEnabled = false
+        pauseButton.isEnabled = false
+        stopButton.isEnabled = false
+        createGraphButton.alpha = 1
+        startVisualizationButton.alpha = 1
+        startInteractiveVisualizationButton.alpha = 1
     }
 
     private func showError(error: String) {
@@ -268,14 +268,14 @@ public class Window: UIView, GraphDelegate {
 
     // MARK: GraphDelegate
     public func didCompleteGraphParsing() {
-        self.graph.state = .completed
-        self.setButtonsToInitialState()
-        self.comparisonLabel.text = "Completed!"
+        graph.state = .completed
+        setButtonsToInitialState()
+        comparisonLabel.text = "Completed!"
     }
 
     public func didTapWrongVertex() {
-        if !self.subviews.contains { $0 is ErrorView } {
-            self.showError(error: "You have picked wrong next vertex")
+        if !subviews.contains { $0 is ErrorView } {
+            showError(error: "You have picked wrong next vertex")
         }
     }
 
@@ -296,13 +296,13 @@ public class Window: UIView, GraphDelegate {
     }
 
     public func didStop() {
-        self.graph.state = .initial
-        self.graph.stopVisualization = false
-        self.graph.pauseVisualization = false
-        self.graphView.reset()
-        self.graph.reset()
-        self.setButtonsToInitialState()
-        self.activityIndicator.stopAnimating()
+        graph.state = .initial
+        graph.stopVisualization = false
+        graph.pauseVisualization = false
+        graphView.reset()
+        graph.reset()
+        setButtonsToInitialState()
+        activityIndicator.stopAnimating()
     }
 
     public func willStartVertexNeighborsChecking() {

From 900b7caf229697f5666627bd7cdc34c6f1143702 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 12:56:12 +0300
Subject: [PATCH 119/862] Replaced with optional

---
 .../Sources/Graph.swift                        | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift
index 7c4a8e373..8bf2452cc 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
@@ -130,12 +130,12 @@ public class Graph {
         clearCache()
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
-        var currentVertex: Vertex! = startVertex
+        var currentVertex: Vertex? = startVertex
 
         var totalVertices = _vertices
 
-        breakableLoop: while currentVertex != nil {
-            totalVertices.remove(currentVertex)
+        breakableLoop: while let vertex = currentVertex {
+            totalVertices.remove(vertex)
             while pauseVisualization == true {
                 if stopVisualization == true {
                     break breakableLoop
@@ -145,11 +145,11 @@ public class Graph {
                 break breakableLoop
             }
             DispatchQueue.main.async {
-                currentVertex.setVisitedColor()
+                vertex.setVisitedColor()
             }
             usleep(750000)
-            currentVertex.visited = true
-            let filteredEdges = currentVertex.edges.filter { !$0.neighbor.visited }
+            vertex.visited = true
+            let filteredEdges = vertex.edges.filter { !$0.neighbor.visited }
             for edge in filteredEdges {
                 let neighbor = edge.neighbor
                 let weight = edge.weight
@@ -166,14 +166,14 @@ public class Graph {
                 DispatchQueue.main.async {
                     edgeRepresentation?.setCheckingColor()
                     neighbor.setCheckingPathColor()
-                    self.delegate?.willCompareVertices(startVertexPathLength: currentVertex.pathLengthFromStart,
+                    self.delegate?.willCompareVertices(startVertexPathLength: vertex.pathLengthFromStart,
                                                        edgePathLength: weight,
                                                        endVertexPathLength: neighbor.pathLengthFromStart)
                 }
                 usleep(_visualizationOneSleepDuration)
 
 
-                let theoreticNewWeight = currentVertex.pathLengthFromStart + weight
+                let theoreticNewWeight = vertex.pathLengthFromStart + weight
 
                 if theoreticNewWeight < neighbor.pathLengthFromStart {
                     while pauseVisualization == true {
@@ -185,7 +185,7 @@ public class Graph {
                         break breakableLoop
                     }
                     neighbor.pathLengthFromStart = theoreticNewWeight
-                    neighbor.pathVerticesFromStart = currentVertex.pathVerticesFromStart
+                    neighbor.pathVerticesFromStart = vertex.pathVerticesFromStart
                     neighbor.pathVerticesFromStart.append(neighbor)
                 }
                 usleep(_visualizationOneSleepDuration)

From 2a1a2a1a7bbdf738b8643d49775ccf7895d476b6 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 13:27:18 +0300
Subject: [PATCH 120/862] Refactored a bit

---
 .../Sources/Graph.swift                       | 14 ++++++++------
 .../Sources/GraphView.swift                   | 12 +++++-------
 .../Sources/Window.swift                      | 19 +++++++++++--------
 3 files changed, 24 insertions(+), 21 deletions(-)

diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift
index 8bf2452cc..447b3dbe1 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Graph.swift	
@@ -10,16 +10,14 @@ public enum GraphState {
 }
 
 public class Graph {
-    private init() { }
-
-    private var verticesCount: UInt!
+    private var verticesCount: UInt
     private var _vertices: Set<Vertex> = Set()
     public weak var delegate: GraphDelegate?
     public var nextVertices: [Vertex] = []
     public var state: GraphState = .initial
-    public var pauseVisualization: Bool = false
-    public var stopVisualization: Bool = false
-    public var startVertex: Vertex!
+    public var pauseVisualization = false
+    public var stopVisualization = false
+    public var startVertex: Vertex?
     public var interactiveNeighborCheckAnimationDuration: Double = 1.8 {
         didSet {
             _interactiveOneSleepDuration = UInt32(interactiveNeighborCheckAnimationDuration * 1000000.0 / 3.0)
@@ -127,6 +125,10 @@ public class Graph {
     }
 
     public func findShortestPathsWithVisualization(completion: () -> Void) {
+        guard let startVertex = self.startVertex else {
+            assertionFailure("start vertex is nil")
+            return
+        }
         clearCache()
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift
index bdeab7669..ec4f74705 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/GraphView.swift	
@@ -1,13 +1,15 @@
 import UIKit
 
 public class GraphView: UIView {
-    private var graph: Graph!
+    private var graph: Graph
     private var panningView: VertexView? = nil
-    private var graphColors: GraphColors = GraphColors.sharedInstance
+    private var graphColors = GraphColors.sharedInstance
 
-    public override init(frame: CGRect) {
+    public init(frame: CGRect, graph: Graph) {
+        self.graph = graph
         super.init(frame: frame)
         backgroundColor = graphColors.graphBackgroundColor
+        layer.cornerRadius = 15
     }
     
     public required init?(coder aDecoder: NSCoder) {
@@ -15,10 +17,6 @@ public class GraphView: UIView {
     
     }
 
-    public func configure(graph: Graph) {
-        self.graph = graph
-    }
-
     public func removeGraph() {
         for vertex in graph.vertices {
             if let view = vertex.view {
diff --git a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift
index 054b804c9..73c512e6b 100644
--- a/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
+++ b/Dijkstra Algorithm/VisualizedDijkstra.playground/Sources/Window.swift	
@@ -25,7 +25,7 @@ public class Window: UIView, GraphDelegate {
     private var activityIndicator: UIActivityIndicatorView!
     private var graph: Graph!
     private var numberOfVertices: UInt!
-    private var graphColors: GraphColors = GraphColors.sharedInstance
+    private var graphColors = GraphColors.sharedInstance
 
     public override init(frame: CGRect) {
         super.init(frame: frame)
@@ -42,10 +42,9 @@ public class Window: UIView, GraphDelegate {
         graph.createNewGraph()
         graph.delegate = self
         let frame = CGRect(x: 10, y: 170, width: self.frame.width - 20, height: self.frame.height - 180)
-        graphView = GraphView(frame: frame)
-        graphView.layer.cornerRadius = 15
+        graphView = GraphView(frame: frame, graph: graph)
+        
 
-        graphView.configure(graph: graph)
         graphView.createNewGraph()
         addSubview(graphView)
 
@@ -198,11 +197,15 @@ public class Window: UIView, GraphDelegate {
             graphView.reset()
             graph.reset()
         }
-        
-        graph.startVertex.pathLengthFromStart = 0
-        graph.startVertex.pathVerticesFromStart.append(graph.startVertex)
+
+        guard let startVertex = graph.startVertex else {
+            assertionFailure("startVertex is nil")
+            return
+        }
+        startVertex.pathLengthFromStart = 0
+        startVertex.pathVerticesFromStart.append(startVertex)
         graph.state = .parsing
-        graph.parseNeighborsFor(vertex: graph.startVertex) {
+        graph.parseNeighborsFor(vertex: startVertex) {
             self.graph.state = .interactiveVisualization
             DispatchQueue.main.async {
                 self.comparisonLabel.text = "Pick next vertex"

From 846101720981de86abf8fe8f372715fa50f12dcb Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:02:43 +0300
Subject: [PATCH 121/862] Updated description

---
 Dijkstra Algorithm/README.md | 38 ++++++++++++++++++++++++++----------
 1 file changed, 28 insertions(+), 10 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index bf158def9..2bbf74b87 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,21 +1,39 @@
 # Dijkstra-algorithm
 
-## About
-Dijkstra's algorithm is used for finding shortest paths from start vertex in graph(with weighted vertices) to all other vertices. 
-More algorithm's description can be found in playground or on wikipedia:
-[Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
-
-To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
-
-If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
+## About this repository
+This repository contains to playgrounds:
+* To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
+* If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
 ## Demo video
 Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Screenshots
-
 <img src="Screenshots/screenshot1.jpg" height="400" />
 
+## Dijkstra's algorithm explanation
+
+Wikipedia's explanation:
+Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.
+
+1. Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes.
+2. Set the initial node as current. Mark all other nodes unvisited. Create a set of all the unvisited nodes called the unvisited set.
+3. For the current node, consider all of its unvisited neighbors and calculate their tentative distances. Compare the newly calculated tentative distance to the current assigned value and assign the smaller one. For example, if the current node A is marked with a distance of 6, and the edge connecting it with a neighbor B has length 2, then the distance to B (through A) will be 6 + 2 = 8. If B was previously marked with a distance greater than 8 then change it to 8. Otherwise, keep the current value.
+4. When we are done considering all of the neighbors of the current node, mark the current node as visited and remove it from the unvisited set. A visited node will never be checked again.
+5. If the destination node has been marked visited (when planning a route between two specific nodes) or if the smallest tentative distance among the nodes in the unvisited set is infinity (when planning a complete traversal; occurs when there is no connection between the initial node and remaining unvisited nodes), then stop. The algorithm has finished.
+6. Otherwise, select the unvisited node that is marked with the smallest tentative distance, set it as the new "current node", and go back to step 3.
+
+Explanation, that can be found in the **VisualizedDijkstra.playground**
+Algorithm's flow:
+First of all, this program randomly decides which vertex will be the start one, then the program assigns a zero value to the start vertex path length from the start.
+
+Then the algorithm repeats following cycle until all vertices are marked as visited.
+Cycle:
+1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
+2. The algorithm marks picked vertex as visited.
+3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
+When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
+
 ## Credits
-WWDC 2017 Scholarship Project
+WWDC 2017 Scholarship Project  
 Created by [Taras Nikulin](https://github.com/crabman448)

From f7793cc6b6692000e4fd878afce62fd67d5b5f00 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:38:47 +0300
Subject: [PATCH 122/862] Added gif

---
 Dijkstra Algorithm/Images/Dijkstra_Animation.gif | Bin 0 -> 8561 bytes
 .../{Screenshots => Images}/screenshot1.jpg      | Bin
 Dijkstra Algorithm/README.md                     |   8 +++++++-
 3 files changed, 7 insertions(+), 1 deletion(-)
 create mode 100644 Dijkstra Algorithm/Images/Dijkstra_Animation.gif
 rename Dijkstra Algorithm/{Screenshots => Images}/screenshot1.jpg (100%)

diff --git a/Dijkstra Algorithm/Images/Dijkstra_Animation.gif b/Dijkstra Algorithm/Images/Dijkstra_Animation.gif
new file mode 100644
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diff --git a/Dijkstra Algorithm/Screenshots/screenshot1.jpg b/Dijkstra Algorithm/Images/screenshot1.jpg
similarity index 100%
rename from Dijkstra Algorithm/Screenshots/screenshot1.jpg
rename to Dijkstra Algorithm/Images/screenshot1.jpg
diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 2bbf74b87..0ac4bc17e 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -9,10 +9,12 @@ This repository contains to playgrounds:
 Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Screenshots
-<img src="Screenshots/screenshot1.jpg" height="400" />
+<img src="Images/screenshot1.jpg" height="400" />
 
 ## Dijkstra's algorithm explanation
 
+<img src="Images/Dijkstra_Animation.gif" height="250" />
+
 Wikipedia's explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.
 
@@ -34,6 +36,10 @@ Cycle:
 3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
 When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
 
+## Usage
+
+
+
 ## Credits
 WWDC 2017 Scholarship Project  
 Created by [Taras Nikulin](https://github.com/crabman448)

From 3f6be33a1750d6f9122ca8ab38b70c3a9e4d123b Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:40:34 +0300
Subject: [PATCH 123/862] Added link

---
 Dijkstra Algorithm/README.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 0ac4bc17e..b2606f0f9 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -13,7 +13,8 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Dijkstra's algorithm explanation
 
-<img src="Images/Dijkstra_Animation.gif" height="250" />
+GIF from Wikipedia
+<img src="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#/media/File:Dijkstra_Animation.gif" height="250" />
 
 Wikipedia's explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.

From a153067e60fcd90d8a8b6448fbc5d9e0c5753076 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:41:35 +0300
Subject: [PATCH 124/862] Updated link

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

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index b2606f0f9..cf939c7cc 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -14,7 +14,7 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 ## Dijkstra's algorithm explanation
 
 GIF from Wikipedia
-<img src="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#/media/File:Dijkstra_Animation.gif" height="250" />
+<img src="https://commons.wikimedia.org/wiki/File:Dijkstra_Animation.gif#/media/File:Dijkstra_Animation.gif" height="250" />
 
 Wikipedia's explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.

From b59ffa53930e3021a22bee31923965a12f7031a3 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:42:10 +0300
Subject: [PATCH 125/862] Revert "Updated link"

This reverts commit a153067e60fcd90d8a8b6448fbc5d9e0c5753076.
---
 Dijkstra Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index cf939c7cc..b2606f0f9 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -14,7 +14,7 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 ## Dijkstra's algorithm explanation
 
 GIF from Wikipedia
-<img src="https://commons.wikimedia.org/wiki/File:Dijkstra_Animation.gif#/media/File:Dijkstra_Animation.gif" height="250" />
+<img src="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#/media/File:Dijkstra_Animation.gif" height="250" />
 
 Wikipedia's explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.

From ef13b5076e1741023c6d014e32266044d8d63d7b Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:42:40 +0300
Subject: [PATCH 126/862] Revert "Added link"

This reverts commit 3f6be33a1750d6f9122ca8ab38b70c3a9e4d123b.
---
 Dijkstra Algorithm/README.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index b2606f0f9..0ac4bc17e 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -13,8 +13,7 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Dijkstra's algorithm explanation
 
-GIF from Wikipedia
-<img src="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#/media/File:Dijkstra_Animation.gif" height="250" />
+<img src="Images/Dijkstra_Animation.gif" height="250" />
 
 Wikipedia's explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.

From aea01e8b68d7fefd06ccae2d3afeb253a43abba0 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Mon, 17 Apr 2017 14:44:39 +0300
Subject: [PATCH 127/862] Added link to Wikipedia

This reverts commit a153067e60fcd90d8a8b6448fbc5d9e0c5753076.
---
 Dijkstra Algorithm/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 0ac4bc17e..325bab40f 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -15,7 +15,7 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 <img src="Images/Dijkstra_Animation.gif" height="250" />
 
-Wikipedia's explanation:
+[Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)'s explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.
 
 1. Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes.

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 128/862] 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
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+3;14.16;2.51;2.48;20;91;1.68;.7;.44;1.24;9.7;.62;1.71;660
+3;13.71;5.65;2.45;20.5;95;1.68;.61;.52;1.06;7.7;.64;1.74;740
+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 129/862] 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 d9e36fa2800c2c67e07df17048424903ab5a7eb6 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 18 Apr 2017 13:43:41 +0200
Subject: [PATCH 130/862] Missing word

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

diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 69e105c87..7058096d0 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -1,6 +1,6 @@
 # Huffman Coding
 
-The idea: To encode objects that occur with a smaller number of bits than objects that occur less frequently.
+The idea: To encode objects that occur often with a smaller number of bits than objects that occur less frequently.
 
 Although any type of objects can be encoded with this scheme, it is common to compress a stream of bytes. Suppose you have the following text, where each character is one byte:
 

From 6c7e9de65cb84da86bb0a5de554f5d13fa6412e6 Mon Sep 17 00:00:00 2001
From: Matthijs Hollemans <mail@hollance.com>
Date: Tue, 18 Apr 2017 13:45:16 +0200
Subject: [PATCH 131/862] Fix alignment

---
 Huffman Coding/README.markdown | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/Huffman Coding/README.markdown b/Huffman Coding/README.markdown
index 7058096d0..d1181d215 100644
--- a/Huffman Coding/README.markdown	
+++ b/Huffman Coding/README.markdown	
@@ -9,13 +9,13 @@ Although any type of objects can be encoded with this scheme, it is common to co
 If you count how often each byte appears, you can see some bytes occur more than others:
 
 	space: 5                  u: 1
-	    o: 5	              h: 1
-	    s: 4	              d: 1
-	    m: 3	              a: 1
-	    w: 3	              y: 1
-	    c: 2	              p: 1
-	    r: 2	              e: 1
-	    n: 2	              i: 1
+	    o: 5                  h: 1
+	    s: 4                  d: 1
+	    m: 3                  a: 1
+	    w: 3                  y: 1
+	    c: 2                  p: 1
+	    r: 2                  e: 1
+	    n: 2                  i: 1
 
 We can assign bit strings to each of these bytes. The more common a byte is, the fewer bits we assign to it. We might get something like this:
 
@@ -23,10 +23,10 @@ We can assign bit strings to each of these bytes. The more common a byte is, the
 	    o: 5    000	          h: 1    10001
 	    s: 4    101	          d: 1    11010
 	    m: 3    111	          a: 1    11011
-	    w: 3    0010	      y: 1    01111
-	    c: 2    0011	      p: 1    11000
-	    r: 2    1001	      e: 1    01110
-	    n: 2    0110	      i: 1    10000
+	    w: 3    0010          y: 1    01111
+	    c: 2    0011          p: 1    11000
+	    r: 2    1001          e: 1    01110
+	    n: 2    0110          i: 1    10000
 
 Now if we replace the original bytes with these bit strings, the compressed output becomes:
 

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 132/862] 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
new file mode 100644
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diff --git a/Naive Bayes Classifier/images/code_example.png b/Naive Bayes Classifier/images/code_example.png
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HcmV?d00001


From 149515f17494f0a9c790fbfa84dca3e6b926887e Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 19 Apr 2017 16:44:55 +0300
Subject: [PATCH 133/862] Replaced _vertices with vertices

---
 .../Dijkstra.playground/Contents.swift          | 17 +++++++++--------
 1 file changed, 9 insertions(+), 8 deletions(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index cd08e26fb..1c12245bd 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -1,19 +1,19 @@
 //: Playground - noun: a place where people can play
 import Foundation
 
-var _vertices: Set<Vertex> = Set()
+var vertices: Set<Vertex> = Set()
 
 func createNotConnectedVertices() {
     //change this value to increase or decrease amount of vertices in the graph
     let numberOfVerticesInGraph = 15
     for i in 0..<numberOfVerticesInGraph {
         let vertex = Vertex(identifier: "\(i)")
-        _vertices.insert(vertex)
+        vertices.insert(vertex)
     }
 }
 
 func setupConnections() {
-    for vertex in _vertices {
+    for vertex in vertices {
         let randomEdgesCount = arc4random_uniform(4) + 1
         for _ in 0..<randomEdgesCount {
             let randomWeight = Double(arc4random_uniform(10))
@@ -30,7 +30,7 @@ func setupConnections() {
 }
 
 func randomVertex(except vertex: Vertex) -> Vertex {
-    var newSet = _vertices
+    var newSet = vertices
     newSet.remove(vertex)
     let offset = Int(arc4random_uniform(UInt32(newSet.count)))
     let index = newSet.index(newSet.startIndex, offsetBy: offset)
@@ -38,9 +38,9 @@ func randomVertex(except vertex: Vertex) -> Vertex {
 }
 
 func randomVertex() -> Vertex {
-    let offset = Int(arc4random_uniform(UInt32(_vertices.count)))
-    let index = _vertices.index(_vertices.startIndex, offsetBy: offset)
-    return _vertices[index]
+    let offset = Int(arc4random_uniform(UInt32(vertices.count)))
+    let index = vertices.index(vertices.startIndex, offsetBy: offset)
+    return vertices[index]
 }
 
 //initialize random graph
@@ -48,7 +48,7 @@ createNotConnectedVertices()
 setupConnections()
 
 //initialize Dijkstra algorithm with graph vertices
-let dijkstra = Dijkstra(vertices: _vertices)
+let dijkstra = Dijkstra(vertices: vertices)
 
 //decide which vertex will be the starting one
 let startVertex = randomVertex()
@@ -63,6 +63,7 @@ var pathVerticesFromStartString: [String] = []
 for vertex in destinationVertex.pathVerticesFromStart {
     pathVerticesFromStartString.append(vertex.identifier)
 }
+
 print(pathVerticesFromStartString.joined(separator: "->"))
 
 

From 93aad5ea36a1f09d62c8c877675877097e9b29fc Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 03:39:21 -0700
Subject: [PATCH 134/862] Added templates for the repository.

---
 .github/CONTRIBUTING.md          |  0
 .github/ISSUE_TEMPLATE.md        | 19 +++++++++++++++++++
 .github/PULL_REQUEST_TEMPLATE.md |  0
 3 files changed, 19 insertions(+)
 create mode 100644 .github/CONTRIBUTING.md
 create mode 100644 .github/ISSUE_TEMPLATE.md
 create mode 100644 .github/PULL_REQUEST_TEMPLATE.md

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
new file mode 100644
index 000000000..e69de29bb
diff --git a/.github/ISSUE_TEMPLATE.md b/.github/ISSUE_TEMPLATE.md
new file mode 100644
index 000000000..27a857ef5
--- /dev/null
+++ b/.github/ISSUE_TEMPLATE.md
@@ -0,0 +1,19 @@
+### Category
+
+- [ ] Bug
+- [ ] Feature Request
+- [ ] Question
+
+### Brief Intro
+
+> Describe this issue below in 1 sentence.
+
+### More Details
+
+> If necessary, start off with the code snippet. Put the code in between ``` to format them into code blocks.
+
+[INSERT CODE HERE]
+
+> Describe the problem in more detail.
+
+[INSERT DETAILS HERE]
\ No newline at end of file
diff --git a/.github/PULL_REQUEST_TEMPLATE.md b/.github/PULL_REQUEST_TEMPLATE.md
new file mode 100644
index 000000000..e69de29bb

From 5128bfa4dca199beeda930dacf0623d7f6e0e926 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:32:41 -0700
Subject: [PATCH 135/862] Updated contribution guidelines.

---
 .github/CONTRIBUTING.md | 57 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index e69de29bb..a1393a2e0 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -0,0 +1,57 @@
+# Contributing Guidelines
+
+Want to help out with the Swift Algorithm Club? Great! While we don't have strict templates on the format of each contribution, we do have a few guidelines that should be kept in mind:
+
+**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. 
+
+**API Design Guidelines**
+
+A good contribution abides to the [Swift API Guidelines](https://swift.org/documentation/api-design-guidelines/). We review the pull requests with this in mind.
+
+**Swift Language Guidelines**
+
+We follow the following Swift [style guide](https://github.com/raywenderlich/swift-style-guide). 
+
+### Contribution Categories
+
+### Refinement
+
+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. 
+
+### New Contributions
+
+Before writing about something new, you should do 2 things:
+
+1. Check the main page for existing implementations
+2. Check the [pull requests](https://github.com/raywenderlich/swift-algorithm-club/pulls) for "claimed" topics. More info on that below. 
+
+If what you have in mind is a new addition, please follow this process when submitting your contribution:
+
+1. Create a pull request to "claim" an algorithm or data structure. This is to avoid having multiple people working on the same thing.
+2. Use this [style guide](https://github.com/raywenderlich/swift-style-guide) for writing code (more or less).
+3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](Quicksort/) to get an idea.
+4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. 
+5. Add a playground and/or unit tests.
+
+For the unit tests:
+
+- Add the unit test project to `.travis.yml` so they will be run on [Travis-CI](https://travis-ci.org/raywenderlich/swift-algorithm-club). Add a line to `.travis.yml` like this:
+
+```
+- xctool test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests
+```
+
+- Configure the Test project's scheme to run on Travis-CI:
+    - Open **Product -> Scheme -> Manage Schemes...**
+    - Uncheck **Autocreate schemes**
+    - Check **Shared**
+
+![Screenshot of scheme settings](Images/scheme-settings-for-travis.png)
+
+## Want to chat?
+
+This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/raywenderlich/swift-algorithm-club/issues) and we'll talk!
\ No newline at end of file

From 1e149dc959731e16eb303396293e1e719f86d2ef Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:33:33 -0700
Subject: [PATCH 136/862] Fixed broken link.

---
 .github/CONTRIBUTING.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index a1393a2e0..fe8a23278 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -50,7 +50,7 @@ For the unit tests:
     - Uncheck **Autocreate schemes**
     - Check **Shared**
 
-![Screenshot of scheme settings](Images/scheme-settings-for-travis.png)
+![Screenshot of scheme settings](../Images/scheme-settings-for-travis.png)
 
 ## Want to chat?
 

From 1620a9cb811ecac68528c8f330f45762ec1beb6a Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:34:11 -0700
Subject: [PATCH 137/862] Fixes another broken link in the readme.

---
 .github/CONTRIBUTING.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index fe8a23278..5b6f5d4dd 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -33,7 +33,7 @@ If what you have in mind is a new addition, please follow this process when subm
 
 1. Create a pull request to "claim" an algorithm or data structure. This is to avoid having multiple people working on the same thing.
 2. Use this [style guide](https://github.com/raywenderlich/swift-style-guide) for writing code (more or less).
-3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](Quicksort/) to get an idea.
+3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](../Quicksort/) to get an idea.
 4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. 
 5. Add a playground and/or unit tests.
 

From d83263cd7e2dcd13e7e2e8ad7c9f624fab337a00 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:43:55 -0700
Subject: [PATCH 138/862] Updated issue and pr template.

---
 .github/ISSUE_TEMPLATE.md        | 10 ++--------
 .github/PULL_REQUEST_TEMPLATE.md | 11 +++++++++++
 2 files changed, 13 insertions(+), 8 deletions(-)

diff --git a/.github/ISSUE_TEMPLATE.md b/.github/ISSUE_TEMPLATE.md
index 27a857ef5..416641261 100644
--- a/.github/ISSUE_TEMPLATE.md
+++ b/.github/ISSUE_TEMPLATE.md
@@ -6,14 +6,8 @@
 
 ### Brief Intro
 
-> Describe this issue below in 1 sentence.
+<!-- 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.
-
-[INSERT CODE HERE]
-
-> Describe the problem in more detail.
-
-[INSERT DETAILS HERE]
\ 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.-->
\ No newline at end of file
diff --git a/.github/PULL_REQUEST_TEMPLATE.md b/.github/PULL_REQUEST_TEMPLATE.md
index e69de29bb..c52564721 100644
--- a/.github/PULL_REQUEST_TEMPLATE.md
+++ b/.github/PULL_REQUEST_TEMPLATE.md
@@ -0,0 +1,11 @@
+<!-- Thanks for contributing to the SAC! Before you submit your pull request, please make sure to check the following boxes by putting an x in the [ ] -->
+
+### Checklist
+
+- [ ] I've looked at the [contribution guidelines](https://github.com/raywenderlich/swift-algorithm-club/blob/master/.github/CONTRIBUTING.md).
+- [ ] This pull request is complete and ready for review.
+
+### Description
+
+<!-- In a short paragraph, describe the PR --> 
+

From bb6c29fee3cf3549c56cf5fb351bf01b15301177 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:45:44 -0700
Subject: [PATCH 139/862] Fixes formatting.

---
 .github/CONTRIBUTING.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index 5b6f5d4dd..2b08e2633 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -14,7 +14,7 @@ A good contribution abides to the [Swift API Guidelines](https://swift.org/docum
 
 We follow the following Swift [style guide](https://github.com/raywenderlich/swift-style-guide). 
 
-### Contribution Categories
+## Contribution Categories
 
 ### Refinement
 

From aadae31ed56f8317eae20e94196b2c242994d1fb Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:54:06 -0700
Subject: [PATCH 140/862] Updated readme with links to updated/new
 contributions.

---
 README.markdown | 19 +++++++------------
 1 file changed, 7 insertions(+), 12 deletions(-)

diff --git a/README.markdown b/README.markdown
index 29fc9d748..e0983f22e 100644
--- a/README.markdown
+++ b/README.markdown
@@ -8,9 +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 8.2** and **Swift 3**. We'll keep this updated with the latest version of Swift.
-
-This is a work in progress. More algorithms will be added soon. :-)
+Most code is compatible with **Xcode 8.3** and **Swift 3**. We'll keep this updated with the latest version of Swift.
 
 :heart_eyes: **Suggestions and contributions are welcome!** :heart_eyes:
 
@@ -24,9 +22,7 @@ This is a work in progress. More algorithms will be added soon. :-)
 
 [Algorithm design techniques](Algorithm%20Design.markdown). How do you create your own algorithms?
 
-[How to contribute](How%20to%20Contribute.markdown). Report an issue to leave feedback, or submit a pull request.
-
-[Under construction](Under%20Construction.markdown). Algorithms that are under construction.
+[How to contribute](https://github.com/raywenderlich/swift-algorithm-club/blob/master/.github/CONTRIBUTING.md). Report an issue to leave feedback, or submit a pull request.
 
 ## Where to start?
 
@@ -56,7 +52,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 
 - [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.
-- Knuth-Morris-Pratt
+- [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.
 - [Z-Algorithm](Z-Algorithm/). Finds all instances of a pattern in a String, and returns the indexes of where the pattern starts within the String.
@@ -103,7 +99,6 @@ Bad sorting algorithms (don't use these!):
 - [Greatest Common Divisor (GCD)](GCD/). Special bonus: the least common multiple.
 - [Permutations and Combinations](Combinatorics/). Get your combinatorics on!
 - [Shunting Yard Algorithm](Shunting%20Yard/). Convert infix expressions to postfix.
-- Statistics
 - [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.
@@ -112,7 +107,7 @@ Bad sorting algorithms (don't use these!):
 
 - [k-Means Clustering](K-Means/). Unsupervised classifier that partitions data into *k* clusters.
 - k-Nearest Neighbors
-- [Linear Regression](Linear%20Regression/)
+- [Linear Regression](Linear%20Regression/). A technique for creating a model of the relationship between two (or more) variable quantities.
 - Logistic Regression
 - Neural Networks
 - PageRank
@@ -153,9 +148,9 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Tree](Tree/). A general-purpose tree structure.
 - [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 Tree](Red-Black%20Tree/). A self balancing binary search tree.
 - Splay Tree
-- Threaded Binary Tree
+- [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
 - [Heap](Heap/). A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
@@ -226,7 +221,7 @@ Other algorithm repositories:
 
 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 [Ross O'brien](https://www.raywenderlich.com/u/narrativium).
 
 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](How%20to%20Contribute.markdown)? :]
 

From 2ce23ca2b1059050be7c87cf45df184dd5090008 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Thu, 20 Apr 2017 04:55:50 -0700
Subject: [PATCH 141/862] Removed old contribution guidelines.

---
 How to Contribute.markdown | 55 --------------------------------------
 1 file changed, 55 deletions(-)
 delete mode 100644 How to Contribute.markdown

diff --git a/How to Contribute.markdown b/How to Contribute.markdown
deleted file mode 100644
index 1235f07ff..000000000
--- a/How to Contribute.markdown	
+++ /dev/null
@@ -1,55 +0,0 @@
-# How to contribute
-
-Want to help out with the Swift Algorithm Club? Great!
-
-## What sort of things can you contribute?
-
-Take a look at the [list](README.markdown). Any algorithms or data structures that don't have a link yet are up for grabs.
-
-Algorithms in the [Under construction](Under%20Construction.markdown) area are being worked on. Suggestions and feedback is welcome!
-
-New algorithms and data structures are always welcome (even if they aren't on the list).
-
-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.
-
-Unit tests. Fixes for typos. No contribution is too small. :-)
-
-## Please follow this process
-
-To keep this a high quality repo, please follow this process when submitting your contribution:
-
-1. Create a pull request to "claim" an algorithm or data structure. Just so multiple people don't work on the same thing.
-2. Use this [style guide](https://github.com/raywenderlich/swift-style-guide) for writing code (more or less).
-3. Write an explanation of how the algorithm works. Include **plenty of examples** for readers to follow along. Pictures are good. Take a look at [the explanation of quicksort](Quicksort/) to get an idea.
-4. Include your name in the explanation, something like *Written by Your Name* at the end of the document. 
-5. Add a playground and/or unit tests.
-6. Run [SwiftLint](https://github.com/realm/SwiftLint)  
-  - [Install](https://github.com/realm/SwiftLint#installation)
-  - Open terminal and run the `swiftlint` command:
-
-```
-cd path/to/swift-algorithm-club
-swiftlint
-```
-
-
-Just so you know, I will probably edit your text and code for grammar etc, just to ensure a certain level of polish.
-
-For the unit tests:
-
-- Add the unit test project to `.travis.yml` so they will be run on [Travis-CI](https://travis-ci.org/raywenderlich/swift-algorithm-club). Add a line to `.travis.yml` like this:
-
-```
-- xctool test -project ./Algorithm/Tests/Tests.xcodeproj -scheme Tests
-```
-
-- Configure the Test project's scheme to run on Travis-CI:
-    - Open **Product -> Scheme -> Manage Schemes...**
-    - Uncheck **Autocreate schemes**
-    - Check **Shared**
-
-![Screenshot of scheme settings](Images/scheme-settings-for-travis.png)
-
-## Want to chat?
-
-This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/raywenderlich/swift-algorithm-club/issues) and we'll talk!

From 37de447879960291131d97aecb3d56c89da77429 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:07:29 +0300
Subject: [PATCH 142/862] Updating

---
 Dijkstra Algorithm/README.md | 61 +++++++++++++++++++++++++++++++-----
 1 file changed, 53 insertions(+), 8 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 325bab40f..7ec9d352e 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,19 +1,59 @@
 # Dijkstra-algorithm
 
-## About this repository
+This algorithm was invented in 1956 by Edsger W. Dijkstra. 
+
+This algorithm can be used, when you have one source vertex and want to find the shortest paths to all other vertices in the graph.
+
+The best example is road network. If you wnat to find the shortest path from your house to your job, then it is time for the Dijkstra's algorithm.
+
+I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
+So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
+When the algorithm starts to work initial graph looks like this:
+[image1.png all are non visited]
+Graph's array contains 5 vertices [A, B, C, D, E].
+Let's assume, that edge weight it is path length in kilometers between vertices.
+A vertex has neighbors: B(path from A: 5.0), C(path from A: 0.0), D(path from A: 0.0)
+And because algorithm has done nothing, then all vertices' path length from source vertex values are infinity (think about infinity as "I don't know, how long will it takes to get this vertex from source one")
+Finally we have to set source vertex path length from source vertex to 0.
+
+Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
+
+|                           |  A  |  B  |  C  |  D  |  E  |
+| ------------------------- | --- | --- | --- | --- | --- |
+| Visited                   |  F  |  F  |  F  |  F  |  F  |
+| Path Length From Start    | inf | inf | inf | inf | inf |
+| Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
+
+But before we will go through all process side by side let me explain how algorithm works.
+The algorithm repeats following cycle until all vertices are marked as visited.
+Cycle:
+1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
+2. The algorithm marks picked vertex as visited.
+3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
+When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
+
+Okay, let's start!
+From now we will keep array which contains non visited vertices. Here they are:
+var nonVisitedVertices = [A, B, C, D, E]
+Let's follow the algorithm and pick the first vertex, which neighbors we want to check.
+Imagine that we have function, that returns vertex with smallest path length from start.
+var checkingVertex = nonVisitedVertices.smallestPathLengthFromStartVertex()
+Then we set this vertex as visited 
+checkingVertex.visited = true
+[image2.jpg visited first]
+Then we check all of its neighbors. 
+If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
+[image3.jpg visited first with checked neighbors]
+
+
+
 This repository contains to playgrounds:
 * To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
 * If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
-## Demo video
-Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
-
-## Screenshots
-<img src="Images/screenshot1.jpg" height="400" />
-
 ## Dijkstra's algorithm explanation
 
-<img src="Images/Dijkstra_Animation.gif" height="250" />
+
 
 [Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)'s explanation:
 Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.
@@ -37,8 +77,13 @@ Cycle:
 When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
 
 ## Usage
+This algorithm is popular in routing. For example, biggest Russian IT company Yandex uses it in [Яндекс.Карты](https://yandex.ru/company/technologies/routes/)
 
+## Demo video
+Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
+## VisualizedDijkstra.playground Screenshots
+<img src="Images/screenshot1.jpg" height="400" />
 
 ## Credits
 WWDC 2017 Scholarship Project  

From f24ecc22436be2b71f6c840464d6826ddf9e258c Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:30:59 +0300
Subject: [PATCH 143/862] Still updating

---
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 Dijkstra Algorithm/Images/image2.png | Bin 0 -> 63758 bytes
 Dijkstra Algorithm/Images/image3.png | Bin 0 -> 65232 bytes
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 Dijkstra Algorithm/Images/image5.png | Bin 0 -> 66333 bytes
 Dijkstra Algorithm/Images/image6.png | Bin 0 -> 67070 bytes
 Dijkstra Algorithm/Images/image7.png | Bin 0 -> 66716 bytes
 Dijkstra Algorithm/README.md         |  66 +++++++++++++++++++++------
 8 files changed, 52 insertions(+), 14 deletions(-)
 create mode 100644 Dijkstra Algorithm/Images/image1.png
 create mode 100644 Dijkstra Algorithm/Images/image2.png
 create mode 100644 Dijkstra Algorithm/Images/image3.png
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diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 7ec9d352e..9a48bbeb3 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -9,7 +9,15 @@ The best example is road network. If you wnat to find the shortest path from you
 I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
 So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
 When the algorithm starts to work initial graph looks like this:
-[image1.png all are non visited]
+[image1.png]
+
+The table below will represent graph state
+|                           |  A  |  B  |  C  |  D  |  E  |
+| ------------------------- | --- | --- | --- | --- | --- |
+| Visited                   |  F  |  F  |  F  |  F  |  F  |
+| Path Length From Start    | inf | inf | inf | inf | inf |
+| Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
+
 Graph's array contains 5 vertices [A, B, C, D, E].
 Let's assume, that edge weight it is path length in kilometers between vertices.
 A vertex has neighbors: B(path from A: 5.0), C(path from A: 0.0), D(path from A: 0.0)
@@ -18,12 +26,6 @@ Finally we have to set source vertex path length from source vertex to 0.
 
 Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
 
-|                           |  A  |  B  |  C  |  D  |  E  |
-| ------------------------- | --- | --- | --- | --- | --- |
-| Visited                   |  F  |  F  |  F  |  F  |  F  |
-| Path Length From Start    | inf | inf | inf | inf | inf |
-| Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
-
 But before we will go through all process side by side let me explain how algorithm works.
 The algorithm repeats following cycle until all vertices are marked as visited.
 Cycle:
@@ -39,13 +41,52 @@ Let's follow the algorithm and pick the first vertex, which neighbors we want to
 Imagine that we have function, that returns vertex with smallest path length from start.
 var checkingVertex = nonVisitedVertices.smallestPathLengthFromStartVertex()
 Then we set this vertex as visited 
+
+|                           |  A  |  B  |  C  |  D  |  E  |
+| ------------------------- | --- | --- | --- | --- | --- |
+| Visited                   |  T  |  F  |  F  |  F  |  F  |
+| Path Length From Start    |  0  | inf | inf | inf | inf |
+| Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
+
 checkingVertex.visited = true
-[image2.jpg visited first]
+[image2.jpg]
 Then we check all of its neighbors. 
 If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
-[image3.jpg visited first with checked neighbors]
-
-
+[image3.jpg]
+
+|                           |     A      |     B      |     C      |     D      |     E      |
+| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+| Visited                   |     T      |     F      |     F      |     F      |     F      |
+| Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
+| Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
+
+[image4.jpg]
+|                           |     A      |     B      |     C      |     D      |     E      |
+| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+| Visited                   |     T      |     F      |     F      |     T      |     F      |
+| Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
+| Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
+
+[image5.jpg]
+|                           |     A      |     B      |     C      |     D      |     E      |
+| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+| Visited                   |     T      |     F      |     F      |     T      |     T      |
+| Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
+| Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
+
+[image6.jpg]
+|                           |     A      |     B      |     C      |     D      |     E      |
+| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+| Visited                   |     T      |     T      |     F      |     T      |     T      |
+| Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
+| Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
+
+[image7.jpg]
+|                           |     A      |     B      |     C      |     D      |     E      |
+| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+| Visited                   |     T      |     T      |     T      |     T      |     T      |
+| Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
+| Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
 This repository contains to playgrounds:
 * To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
@@ -82,9 +123,6 @@ This algorithm is popular in routing. For example, biggest Russian IT company Ya
 ## Demo video
 Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
-## VisualizedDijkstra.playground Screenshots
-<img src="Images/screenshot1.jpg" height="400" />
-
 ## Credits
 WWDC 2017 Scholarship Project  
 Created by [Taras Nikulin](https://github.com/crabman448)

From fb4c63bc92ac909159528e2e1c3f16d99eb9665a Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:32:05 +0300
Subject: [PATCH 144/862] Tables fix

---
 Dijkstra Algorithm/README.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 9a48bbeb3..132f4e5bd 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -12,6 +12,7 @@ When the algorithm starts to work initial graph looks like this:
 [image1.png]
 
 The table below will represent graph state
+
 |                           |  A  |  B  |  C  |  D  |  E  |
 | ------------------------- | --- | --- | --- | --- | --- |
 | Visited                   |  F  |  F  |  F  |  F  |  F  |
@@ -61,6 +62,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
 [image4.jpg]
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 | ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
 | Visited                   |     T      |     F      |     F      |     T      |     F      |
@@ -68,6 +70,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
 [image5.jpg]
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 | ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
 | Visited                   |     T      |     F      |     F      |     T      |     T      |
@@ -75,6 +78,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
 [image6.jpg]
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 | ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
 | Visited                   |     T      |     T      |     F      |     T      |     T      |
@@ -82,6 +86,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
 [image7.jpg]
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 | ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
 | Visited                   |     T      |     T      |     T      |     T      |     T      |

From cce96e2694e71e473f30817a535a97a6d59591f3 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:34:16 +0300
Subject: [PATCH 145/862] Updating

---
 Dijkstra Algorithm/README.md | 28 ++++++++++++++--------------
 1 file changed, 14 insertions(+), 14 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 132f4e5bd..cb0683e5d 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -9,12 +9,12 @@ The best example is road network. If you wnat to find the shortest path from you
 I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
 So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
 When the algorithm starts to work initial graph looks like this:
-[image1.png]
+[images/image1.png]
 
 The table below will represent graph state
 
 |                           |  A  |  B  |  C  |  D  |  E  |
-| ------------------------- | --- | --- | --- | --- | --- |
+|:------------------------- |:---:|:---:|:---:|:---:|:---:|
 | Visited                   |  F  |  F  |  F  |  F  |  F  |
 | Path Length From Start    | inf | inf | inf | inf | inf |
 | Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
@@ -44,51 +44,51 @@ var checkingVertex = nonVisitedVertices.smallestPathLengthFromStartVertex()
 Then we set this vertex as visited 
 
 |                           |  A  |  B  |  C  |  D  |  E  |
-| ------------------------- | --- | --- | --- | --- | --- |
+|:------------------------- |:---:|:---:|:---:|:---:|:---:|
 | Visited                   |  T  |  F  |  F  |  F  |  F  |
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
 checkingVertex.visited = true
-[image2.jpg]
+[images/image2.jpg]
 Then we check all of its neighbors. 
 If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
-[image3.jpg]
+[images/image3.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
-| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+|:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     F      |     F      |     F      |     F      |
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
-[image4.jpg]
+[images/image4.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
-| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+|:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     F      |     F      |     T      |     F      |
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
-[image5.jpg]
+[images/image5.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
-| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+|:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     F      |     F      |     T      |     T      |
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
-[image6.jpg]
+[images/image6.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
-| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+|:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     T      |     F      |     T      |     T      |
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-[image7.jpg]
+[images/image7.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
-| ------------------------- | ---------- | ---------- | ---------- | ---------- | ---------- |
+|:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     T      |     T      |     T      |     T      |
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |

From 142ff2e866c89259c576b03b025b500e655cf028 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:35:00 +0300
Subject: [PATCH 146/862] Fix folder references

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

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index cb0683e5d..677c97447 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -9,7 +9,7 @@ The best example is road network. If you wnat to find the shortest path from you
 I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
 So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
 When the algorithm starts to work initial graph looks like this:
-[images/image1.png]
+[Images/image1.png]
 
 The table below will represent graph state
 
@@ -50,10 +50,10 @@ Then we set this vertex as visited
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
 checkingVertex.visited = true
-[images/image2.jpg]
+[Images/image2.jpg]
 Then we check all of its neighbors. 
 If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
-[images/image3.jpg]
+[Images/image3.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -61,7 +61,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
-[images/image4.jpg]
+[Images/image4.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -69,7 +69,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
-[images/image5.jpg]
+[Images/image5.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -77,7 +77,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
-[images/image6.jpg]
+[Images/image6.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -85,7 +85,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-[images/image7.jpg]
+[Images/image7.jpg]
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|

From 8e0d77ff9f99812bb8de307b66f1d211ef4ea785 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:37:15 +0300
Subject: [PATCH 147/862] Images

---
 Dijkstra Algorithm/README.md | 18 +++++++++++-------
 1 file changed, 11 insertions(+), 7 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 677c97447..490b4de1d 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -9,7 +9,8 @@ The best example is road network. If you wnat to find the shortest path from you
 I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
 So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
 When the algorithm starts to work initial graph looks like this:
-[Images/image1.png]
+
+<img src="Images/image1.png" height="250" />
 
 The table below will represent graph state
 
@@ -50,10 +51,13 @@ Then we set this vertex as visited
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
 checkingVertex.visited = true
-[Images/image2.jpg]
+
+<img src="Images/image2.png" height="250" />
+
 Then we check all of its neighbors. 
 If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
-[Images/image3.jpg]
+
+<img src="Images/image3.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -61,7 +65,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
-[Images/image4.jpg]
+<img src="Images/image4.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -69,7 +73,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
-[Images/image5.jpg]
+<img src="Images/image5.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -77,7 +81,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
-[Images/image6.jpg]
+<img src="Images/image6.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
@@ -85,7 +89,7 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-[Images/image7.jpg]
+<img src="Images/image7.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|

From 37550365f6db8b980cfe1792a3122efe24a1ed91 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:55:29 +0300
Subject: [PATCH 148/862] Still improving description

---
 Dijkstra Algorithm/README.md | 73 ++++++++++++++++++++++++++----------
 1 file changed, 54 insertions(+), 19 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 490b4de1d..5541276fc 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,4 +1,4 @@
-# Dijkstra-algorithm
+# Dijkstra's algorithm
 
 This algorithm was invented in 1956 by Edsger W. Dijkstra. 
 
@@ -6,13 +6,17 @@ This algorithm can be used, when you have one source vertex and want to find the
 
 The best example is road network. If you wnat to find the shortest path from your house to your job, then it is time for the Dijkstra's algorithm.
 
-I have a gif example, which will show you how algorithm works. If this is not enough, then you can play with my **VisualizedDijkstra.playground**.
-So let's image, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
+I have created **VisualizedDijkstra.playground** to help you to understand, how this algorithm works. Besides, I have described below step by step how does it works.
+
+So let's imagine, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
+
+> Initialization
+
 When the algorithm starts to work initial graph looks like this:
 
 <img src="Images/image1.png" height="250" />
 
-The table below will represent graph state
+The table below represents graph state:
 
 |                           |  A  |  B  |  C  |  D  |  E  |
 |:------------------------- |:---:|:---:|:---:|:---:|:---:|
@@ -20,11 +24,17 @@ The table below will represent graph state
 | Path Length From Start    | inf | inf | inf | inf | inf |
 | Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
 
-Graph's array contains 5 vertices [A, B, C, D, E].
-Let's assume, that edge weight it is path length in kilometers between vertices.
-A vertex has neighbors: B(path from A: 5.0), C(path from A: 0.0), D(path from A: 0.0)
-And because algorithm has done nothing, then all vertices' path length from source vertex values are infinity (think about infinity as "I don't know, how long will it takes to get this vertex from source one")
-Finally we have to set source vertex path length from source vertex to 0.
+_inf is equal infinity, which basically means, that algorithm doesn't know how far away is this vertex from start one._
+_F states for False_
+_T states for True_
+
+To initialize out graph we have to set source vertex path length from source vertex to 0.
+
+|                           |  A  |  B  |  C  |  D  |  E  |
+|:------------------------- |:---:|:---:|:---:|:---:|:---:|
+| Visited                   |  F  |  F  |  F  |  F  |  F  |
+| Path Length From Start    |  0  | inf | inf | inf | inf |
+| Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
 
 Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
 
@@ -37,12 +47,15 @@ Cycle:
 When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
 
 Okay, let's start!
-From now we will keep array which contains non visited vertices. Here they are:
-var nonVisitedVertices = [A, B, C, D, E]
-Let's follow the algorithm and pick the first vertex, which neighbors we want to check.
-Imagine that we have function, that returns vertex with smallest path length from start.
-var checkingVertex = nonVisitedVertices.smallestPathLengthFromStartVertex()
-Then we set this vertex as visited 
+Let's follow the algorithm's cycle and pick the first vertex, which neighbors we want to check.
+All our vertices are not visited, but there is only one have the smallest path length from start - A. This vertex is th first one, which neighbors we will check.
+First of all, set this vertex as visited 
+
+A.visited = true
+
+<img src="Images/image2.png" height="250" />
+
+After this step graph has this state:
 
 |                           |  A  |  B  |  C  |  D  |  E  |
 |:------------------------- |:---:|:---:|:---:|:---:|:---:|
@@ -50,21 +63,35 @@ Then we set this vertex as visited
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
-checkingVertex.visited = true
-
-<img src="Images/image2.png" height="250" />
+> Step 1
 
 Then we check all of its neighbors. 
-If neighbor's path length from start is bigger than checking vertex path length from start + edge weigth, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
+If checking vertex path length from start + edge weigth is smaller than neighbor's path length from start, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
+
+for clarity:
+```swift
+if (A.pathLengthFromStart + AB.weight) < B.pathLengthFromStart {
+    B.pathLengthFromStart = A.pathLengthFromStart + AB.weight
+    B.pathVerticesFromStart = A.pathVerticesFromStart
+    B.pathVerticesFromStart.append(B)
+}
+```
+And now our graph looks like this one:
 
 <img src="Images/image3.png" height="250" />
 
+And its state is here:
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     F      |     F      |     F      |     F      |
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
+> Step 2
+
+From now we repeat all actions again and fill our table with new info! 
+
 <img src="Images/image4.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
@@ -73,6 +100,8 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
+> Step 3
+
 <img src="Images/image5.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
@@ -81,6 +110,8 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
+> Step 4
+
 <img src="Images/image6.png" height="250" />
 
 |                           |     A      |     B      |     C      |     D      |     E      |
@@ -89,8 +120,12 @@ If neighbor's path length from start is bigger than checking vertex path length
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
+> Step 5
+
 <img src="Images/image7.png" height="250" />
 
+> Step 6
+
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     T      |     T      |     T      |     T      |

From 5e5e7a93188b79ee6693b19fd03d387635b87dbf Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:57:33 +0300
Subject: [PATCH 149/862] Description

---
 Dijkstra Algorithm/README.md | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 5541276fc..206507b7b 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -63,7 +63,7 @@ After this step graph has this state:
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
-> Step 1
+## Step 1
 
 Then we check all of its neighbors. 
 If checking vertex path length from start + edge weigth is smaller than neighbor's path length from start, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
@@ -88,7 +88,7 @@ And its state is here:
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
-> Step 2
+## Step 2
 
 From now we repeat all actions again and fill our table with new info! 
 
@@ -100,7 +100,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
-> Step 3
+## Step 3
 
 <img src="Images/image5.png" height="250" />
 
@@ -110,7 +110,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
-> Step 4
+## Step 4
 
 <img src="Images/image6.png" height="250" />
 
@@ -120,23 +120,23 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-> Step 5
+## Step 5
 
 <img src="Images/image7.png" height="250" />
 
-> Step 6
-
 |                           |     A      |     B      |     C      |     D      |     E      |
 |:------------------------- |:----------:|:----------:|:----------:|:----------:|:----------:|
 | Visited                   |     T      |     T      |     T      |     T      |     T      |
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
+## About
+
 This repository contains to playgrounds:
 * To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
 * If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
-## Dijkstra's algorithm explanation
+
 
 
 

From 2e7c34c8d59c003dffe5f51a5f035a8c9b1141ba Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 15:58:50 +0300
Subject: [PATCH 150/862] Probably final updates

---
 Dijkstra Algorithm/README.md | 34 ++++------------------------------
 1 file changed, 4 insertions(+), 30 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 206507b7b..e73f95393 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -10,7 +10,7 @@ I have created **VisualizedDijkstra.playground** to help you to understand, how
 
 So let's imagine, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
 
-> Initialization
+## Initialization
 
 When the algorithm starts to work initial graph looks like this:
 
@@ -130,43 +130,17 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-## About
+## About this repository
 
 This repository contains to playgrounds:
 * To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
 * If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
-
-
-
-
-[Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)'s explanation:
-Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.
-
-1. Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes.
-2. Set the initial node as current. Mark all other nodes unvisited. Create a set of all the unvisited nodes called the unvisited set.
-3. For the current node, consider all of its unvisited neighbors and calculate their tentative distances. Compare the newly calculated tentative distance to the current assigned value and assign the smaller one. For example, if the current node A is marked with a distance of 6, and the edge connecting it with a neighbor B has length 2, then the distance to B (through A) will be 6 + 2 = 8. If B was previously marked with a distance greater than 8 then change it to 8. Otherwise, keep the current value.
-4. When we are done considering all of the neighbors of the current node, mark the current node as visited and remove it from the unvisited set. A visited node will never be checked again.
-5. If the destination node has been marked visited (when planning a route between two specific nodes) or if the smallest tentative distance among the nodes in the unvisited set is infinity (when planning a complete traversal; occurs when there is no connection between the initial node and remaining unvisited nodes), then stop. The algorithm has finished.
-6. Otherwise, select the unvisited node that is marked with the smallest tentative distance, set it as the new "current node", and go back to step 3.
-
-Explanation, that can be found in the **VisualizedDijkstra.playground**
-Algorithm's flow:
-First of all, this program randomly decides which vertex will be the start one, then the program assigns a zero value to the start vertex path length from the start.
-
-Then the algorithm repeats following cycle until all vertices are marked as visited.
-Cycle:
-1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
-2. The algorithm marks picked vertex as visited.
-3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
-When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
-
-## Usage
-This algorithm is popular in routing. For example, biggest Russian IT company Yandex uses it in [Яндекс.Карты](https://yandex.ru/company/technologies/routes/)
-
 ## Demo video
+
 Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Credits
+
 WWDC 2017 Scholarship Project  
 Created by [Taras Nikulin](https://github.com/crabman448)

From dd9e998e4482ff9665e3964829569a0c5489daf4 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 16:01:01 +0300
Subject: [PATCH 151/862] Added reference to wikipedia

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

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index e73f95393..76cc4ca1d 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,6 +1,6 @@
 # Dijkstra's algorithm
 
-This algorithm was invented in 1956 by Edsger W. Dijkstra. 
+This [algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) was invented in 1956 by Edsger W. Dijkstra. 
 
 This algorithm can be used, when you have one source vertex and want to find the shortest paths to all other vertices in the graph.
 

From e2282045c04aeab0ff7eeb2c1df8edc33c92c76c Mon Sep 17 00:00:00 2001
From: Taras <crabman448@gmail.com>
Date: Thu, 20 Apr 2017 16:07:33 +0300
Subject: [PATCH 152/862] Update README.md

---
 Dijkstra Algorithm/README.md | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 76cc4ca1d..61b47e97f 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -24,9 +24,11 @@ The table below represents graph state:
 | Path Length From Start    | inf | inf | inf | inf | inf |
 | Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
 
-_inf is equal infinity, which basically means, that algorithm doesn't know how far away is this vertex from start one._
-_F states for False_
-_T states for True_
+>inf is equal infinity, which basically means, that algorithm doesn't know how far away is this vertex from start one.
+
+>F states for False
+
+>T states for True
 
 To initialize out graph we have to set source vertex path length from source vertex to 0.
 

From b95331012e6fa880928b38a7606384e6b7a0db9a Mon Sep 17 00:00:00 2001
From: Taras <crabman448@gmail.com>
Date: Thu, 20 Apr 2017 16:09:14 +0300
Subject: [PATCH 153/862] Update README.md

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

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 61b47e97f..9999e224e 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -30,13 +30,13 @@ The table below represents graph state:
 
 >T states for True
 
-To initialize out graph we have to set source vertex path length from source vertex to 0.
+To initialize out graph we have to set source vertex path length from source vertex to 0, and append itself to path vertices ffrom start.
 
 |                           |  A  |  B  |  C  |  D  |  E  |
 |:------------------------- |:---:|:---:|:---:|:---:|:---:|
 | Visited                   |  F  |  F  |  F  |  F  |  F  |
 | Path Length From Start    |  0  | inf | inf | inf | inf |
-| Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
+| Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
 Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
 

From a44f84ecad941273df7472ef1c7de7aa93b1d1c8 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Thu, 20 Apr 2017 16:26:33 +0300
Subject: [PATCH 154/862] Removed unnecessary images

---
 .../Images/Dijkstra_Animation.gif              | Bin 8561 -> 0 bytes
 Dijkstra Algorithm/Images/screenshot1.jpg      | Bin 224243 -> 0 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 Dijkstra Algorithm/Images/Dijkstra_Animation.gif
 delete mode 100644 Dijkstra Algorithm/Images/screenshot1.jpg

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From 3395c01c00c80554be30f91310f2878d7faedcce Mon Sep 17 00:00:00 2001
From: darrellhz <zh0521@gmail.com>
Date: Fri, 21 Apr 2017 16:04:19 +0900
Subject: [PATCH 155/862] Update README.markdown

updated to Swift 3 syntax
---
 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 c5a752e13..c03023c42 100644
--- a/Linked List/README.markdown	
+++ b/Linked List/README.markdown	
@@ -364,7 +364,7 @@ What else do we need? Removing nodes, of course! First we'll do `removeAll()`, w
 
 If you had a tail pointer, you'd set it to `nil` here too.
 
-Next we'll add some functions that let you remove individual nodes. If you already have a reference to the node, then using `removeNode()` is the most optimal because you don't need to iterate through the list to find the node first.
+Next we'll add some functions that let you remove individual nodes. If you already have a reference to the node, then using `remove()` is the most optimal because you don't need to iterate through the list to find the node first.
 
 ```swift
   public func remove(node: Node) -> T {

From b66e31825d9025916d9617073830f50284ebd488 Mon Sep 17 00:00:00 2001
From: Jacopo <jmangia@kywix.com>
Date: Fri, 21 Apr 2017 19:25:23 +0100
Subject: [PATCH 156/862] Filters the potential change arrays for only the ones
 which add up to the exact value

---
 MinimumCoinChange/Sources/MinimumCoinChange.swift | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/MinimumCoinChange/Sources/MinimumCoinChange.swift b/MinimumCoinChange/Sources/MinimumCoinChange.swift
index c995063ab..8b0da80ac 100644
--- a/MinimumCoinChange/Sources/MinimumCoinChange.swift
+++ b/MinimumCoinChange/Sources/MinimumCoinChange.swift
@@ -64,7 +64,10 @@ public struct MinimumCoinChange {
                 if value - coin >= 0 {
                     var potentialChange: [Int] = [coin]
                     potentialChange.append(contentsOf: _changeDynamic(value - coin))
-                    potentialChangeArray.append(potentialChange)
+
+                    if potentialChange.reduce(0, +) == value { 
+                        potentialChangeArray.append(potentialChange)
+                    } 
                 }
             }
             

From d5c9d179f63767cfad7dda48faad914f808ca68b Mon Sep 17 00:00:00 2001
From: Jacopo <jmangia@kywix.com>
Date: Fri, 21 Apr 2017 19:38:45 +0100
Subject: [PATCH 157/862] Optimisation: removed double check if the winner
 change is valid

---
 MinimumCoinChange/Sources/MinimumCoinChange.swift | 11 +++--------
 1 file changed, 3 insertions(+), 8 deletions(-)

diff --git a/MinimumCoinChange/Sources/MinimumCoinChange.swift b/MinimumCoinChange/Sources/MinimumCoinChange.swift
index 8b0da80ac..55629d020 100644
--- a/MinimumCoinChange/Sources/MinimumCoinChange.swift
+++ b/MinimumCoinChange/Sources/MinimumCoinChange.swift
@@ -56,8 +56,6 @@ public struct MinimumCoinChange {
                 return cached
             }
             
-            var change: [Int] = []
-            
             var potentialChangeArray: [[Int]] = []
             
             for coin in sortedCoinSet {
@@ -73,14 +71,11 @@ public struct MinimumCoinChange {
             
             if potentialChangeArray.count > 0 {
                 let sortedPotentialChangeArray = potentialChangeArray.sorted(by: { $0.count < $1.count })
-                change = sortedPotentialChangeArray[0]
+                cache[value] = sortedPotentialChangeArray[0]
+                return sortedPotentialChangeArray[0]
             }
             
-            if change.reduce(0, +) == value { 
-                cache[value] = change
-            } 
-
-            return change
+            return []
         }
 
         let change: [Int] = _changeDynamic(value)

From 2ff26a1365cce2d47e7cf8cc341eadf3134cfdac Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Fri, 21 Apr 2017 23:07:00 -0700
Subject: [PATCH 158/862] prettify some syntax around optionals

---
 AVL Tree/AVLTree.swift | 28 +++++-----------------------
 1 file changed, 5 insertions(+), 23 deletions(-)

diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index cfcf114c0..4feb691e4 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -99,17 +99,11 @@ open class AVLTree<Key: Comparable, Payload> {
 
 extension TreeNode {
   public func minimum() -> TreeNode? {
-    if let leftChild = self.leftChild {
-      return leftChild.minimum()
-    }
-    return self
+    return leftChild?.minimum() ?? self
   }
 
   public func maximum() -> TreeNode? {
-    if let rightChild = self.rightChild {
-      return rightChild.maximum()
-    }
-    return self
+    return rightChild?.maximum() ?? self
   }
 }
 
@@ -120,11 +114,7 @@ extension AVLTree {
   }
 
   public func search(input: Key) -> Payload? {
-    if let result = search(key: input, node: root) {
-      return result.payload
-    } else {
-      return nil
-    }
+    return search(key: input, node: root)?.payload
   }
 
   fileprivate func search(key: Key, node: Node?) -> Node? {
@@ -385,11 +375,7 @@ extension TreeNode: CustomDebugStringConvertible {
 
 extension AVLTree: CustomDebugStringConvertible {
   public var debugDescription: String {
-    if let root = root {
-      return root.debugDescription
-    } else {
-      return "[]"
-    }
+    return root?.debugDescription ?? "[]"
   }
 }
 
@@ -409,10 +395,6 @@ extension TreeNode: CustomStringConvertible {
 
 extension AVLTree: CustomStringConvertible {
   public var description: String {
-    if let root = root {
-      return root.description
-    } else {
-      return "[]"
-    }
+    return root?.description ?? "[]"
   }
 }

From 7ecbb716fb9bd16f5f89bd491edc1fe81d3c85be Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Fri, 21 Apr 2017 23:15:30 -0700
Subject: [PATCH 159/862] prettify some syntax around optionals

---
 .../AVLTree.playground/Sources/AVLTree.swift  | 28 ++++---------------
 1 file changed, 5 insertions(+), 23 deletions(-)

diff --git a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift
index b4b97f0d6..56ba81608 100644
--- a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
+++ b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
@@ -99,17 +99,11 @@ open class AVLTree<Key: Comparable, Payload> {
 
 extension TreeNode {
   public func minimum() -> TreeNode? {
-    if let leftChild = self.leftChild {
-      return leftChild.minimum()
-    }
-    return self
+    return leftChild?.minimum() ?? self
   }
 
   public func maximum() -> TreeNode? {
-    if let rightChild = self.rightChild {
-      return rightChild.maximum()
-    }
-    return self
+    return rightChild?.maximum() ?? self
   }
 }
 
@@ -120,11 +114,7 @@ extension AVLTree {
   }
 
   public func search(input: Key) -> Payload? {
-    if let result = search(key: input, node: root) {
-      return result.payload
-    } else {
-      return nil
-    }
+    return search(key: input, node: root)?.payload
   }
 
   fileprivate func search(key: Key, node: Node?) -> Node? {
@@ -385,11 +375,7 @@ extension TreeNode: CustomDebugStringConvertible {
 
 extension AVLTree: CustomDebugStringConvertible {
   public var debugDescription: String {
-    if let root = root {
-      return root.debugDescription
-    } else {
-      return "[]"
-    }
+    return root?.debugDescription ?? "[]"
   }
 }
 
@@ -409,10 +395,6 @@ extension TreeNode: CustomStringConvertible {
 
 extension AVLTree: CustomStringConvertible {
   public var description: String {
-    if let root = root {
-      return root.description
-    } else {
-      return "[]"
-    }
+    return root?.description ?? "[]"
   }
 }

From 3d48ed411d872b5b3f03c114e6b1c074bb4293e8 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Sun, 23 Apr 2017 23:36:55 +0300
Subject: [PATCH 160/862] Credits

---
 Dijkstra Algorithm/README.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 9999e224e..086e60c55 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -144,5 +144,4 @@ Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
 ## Credits
 
-WWDC 2017 Scholarship Project  
-Created by [Taras Nikulin](https://github.com/crabman448)
+WWDC 2017 Scholarship Project (Rejected) created by [Taras Nikulin](https://github.com/crabman448)

From 83f7a32ccf0a2fe4b6223305bf89a7724b666a65 Mon Sep 17 00:00:00 2001
From: Antonio081014 <antonio081014@antonio081014.com>
Date: Mon, 24 Apr 2017 11:23:09 -0700
Subject: [PATCH 161/862] Add variety implementation with complexity analysis.

---
 Union-Find/README.markdown                    | 63 ++++++++++----
 .../UnionFind.playground/Contents.swift       | 82 ++++---------------
 .../Sources/UnionFindQuickFind.swift          | 50 +++++++++++
 .../Sources/UnionFindQuickUnion.swift         | 51 ++++++++++++
 .../Sources/UnionFindWeightedQuickFind.swift  | 59 +++++++++++++
 .../Sources/UnionFindWeightedQuickUnion.swift | 56 +++++++++++++
 ...indWeightedQuickUnionPathCompression.swift | 53 ++++++++++++
 .../UnionFind.playground/timeline.xctimeline  |  6 --
 Union-Find/UnionFind.swift                    | 59 -------------
 9 files changed, 330 insertions(+), 149 deletions(-)
 create mode 100644 Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
 create mode 100644 Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
 create mode 100644 Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
 create mode 100644 Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
 create mode 100644 Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
 delete mode 100644 Union-Find/UnionFind.playground/timeline.xctimeline
 delete mode 100644 Union-Find/UnionFind.swift

diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index 5102f6b89..03e082507 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -23,7 +23,8 @@ The most common application of this data structure is keeping track of the conne
 
 ## Implementation
 
-Union-Find can be implemented in many ways but we'll look at the most efficient.
+Union-Find can be implemented in many ways but we'll look at an efficient and easy to understand implementation: Weighted Quick Union.
+> __PS: Variety implementation of Union-Find has been included in playground.__
 
 ```swift
 public struct UnionFind<T: Hashable> {
@@ -141,24 +142,24 @@ public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool
 
 Since this calls `setOf()` it also optimizes the tree.
 
-## Union
+## Union (Weighted)
 
 The final operation is **Union**, which combines two sets into one larger set.
 
 ```swift
-public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-  if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {  // 1
-    if firstSet != secondSet {               // 2
-      if size[firstSet] < size[secondSet] {  // 3
-        parent[firstSet] = secondSet         // 4
-        size[secondSet] += size[firstSet]    // 5
-      } else {
-        parent[secondSet] = firstSet
-        size[firstSet] += size[secondSet]
-      }
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) { // 1
+            if firstSet != secondSet {                // 2
+                if size[firstSet] < size[secondSet] { // 3
+                    parent[firstSet] = secondSet      // 4
+                    size[secondSet] += size[firstSet] // 5
+                } else {
+                    parent[secondSet] = firstSet
+                    size[firstSet] += size[secondSet]
+                }
+            }
+        }
     }
-  }
-}
 ```
 
 Here is how it works:
@@ -167,7 +168,7 @@ Here is how it works:
 
 2. Check that the sets are not equal because if they are it makes no sense to union them.
 
-3. This is where the size optimization comes in. We want to keep the trees as shallow as possible so we always attach the smaller tree to the root of the larger tree. To determine which is the smaller tree we compare trees by their sizes.
+3. This is where the size optimization comes in (Weighting). We want to keep the trees as shallow as possible so we always attach the smaller tree to the root of the larger tree. To determine which is the smaller tree we compare trees by their sizes.
 
 4. Here we attach the smaller tree to the root of the larger tree.
 
@@ -185,10 +186,40 @@ Note that, because we call `setOf()` at the start of the method, the larger tree
 
 Union with optimizations also takes almost **O(1)** time.
 
+## Path Compression
+```swift
+private mutating func setByIndex(_ index: Int) -> Int {
+    if index != parent[index] {
+        // Updating parent index while looking up the index of parent.
+        parent[index] = setByIndex(parent[index])
+    }
+    return parent[index]
+}
+```
+Path Compression helps keep trees very flat, thus find operation could take __ALMOST__ in __O(1)__
+
+## Complexity Summary of Variety Implementation
+
+##### To process N objects
+| Data Structure | Union | Find |
+|---|---|---|
+|Quick Find|N|1|
+|Quick Union|Tree height|Tree height|
+|Weighted Quick Union|lgN|lgN|
+|Weighted Quick Union + Path Compression| very close, but not O(1)| very close, but not O(1) |
+
+##### To process M union commands on N objects
+| Algorithm | Worst-case time|
+|---|---|
+|Quick Find| M N |
+|Quick Union| M N |
+|Weighted Quick Union| N + M lgN |
+|Weighted Quick Union + Path Compression| (M + N) lgN |
+
 ## See also
 
 See the playground for more examples of how to use this handy data structure.
 
 [Union-Find at Wikipedia](https://en.wikipedia.org/wiki/Disjoint-set_data_structure)
 
-*Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*
+*Written for Swift Algorithm Club by [Artur Antonov](https://github.com/goingreen)*, *modified by [Yi Ding](https://github.com/antonio081014).*
\ No newline at end of file
diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 09649b938..9ad5215b3 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -1,73 +1,19 @@
 //: Playground - noun: a place where people can play
 
-public struct UnionFind<T: Hashable> {
-  private var index = [T: Int]()
-  private var parent = [Int]()
-  private var size = [Int]()
-
-  public mutating func addSetWith(_ element: T) {
-    index[element] = parent.count
-    parent.append(parent.count)
-    size.append(1)
-  }
-
-  private mutating func setByIndex(_ index: Int) -> Int {
-    if parent[index] == index {
-      return index
-    } else {
-      parent[index] = setByIndex(parent[index])
-      return parent[index]
-    }
-  }
-
-  public mutating func setOf(_ element: T) -> Int? {
-    if let indexOfElement = index[element] {
-      return setByIndex(indexOfElement)
-    } else {
-      return nil
-    }
-  }
-
-  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-      if firstSet != secondSet {
-        if size[firstSet] < size[secondSet] {
-          parent[firstSet] = secondSet
-          size[secondSet] += size[firstSet]
-        } else {
-          parent[secondSet] = firstSet
-          size[firstSet] += size[secondSet]
-        }
-      }
-    }
-  }
-
-  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-      return firstSet == secondSet
-    } else {
-      return false
-    }
-  }
-}
-
-
-
-
-var dsu = UnionFind<Int>()
+var dsu = UnionFindQuickUnion<Int>()
 
 for i in 1...10 {
-  dsu.addSetWith(i)
+    dsu.addSetWith(i)
 }
 // now our dsu contains 10 independent sets
 
 // let's divide our numbers into two sets by divisibility by 2
 for i in 3...10 {
-  if i % 2 == 0 {
-    dsu.unionSetsContaining(2, and: i)
-  } else {
-    dsu.unionSetsContaining(1, and: i)
-  }
+    if i % 2 == 0 {
+        dsu.unionSetsContaining(2, and: i)
+    } else {
+        dsu.unionSetsContaining(1, and: i)
+    }
 }
 
 // check our division
@@ -88,7 +34,7 @@ print(dsu.inSameSet(3, and: 6))
 
 
 
-var dsuForStrings = UnionFind<String>()
+var dsuForStrings = UnionFindQuickUnion<String>()
 let words = ["all", "border", "boy", "afternoon", "amazing", "awesome", "best"]
 
 dsuForStrings.addSetWith("a")
@@ -96,12 +42,12 @@ dsuForStrings.addSetWith("b")
 
 // In that example we divide strings by its first letter
 for word in words {
-  dsuForStrings.addSetWith(word)
-  if word.hasPrefix("a") {
-    dsuForStrings.unionSetsContaining("a", and: word)
-  } else if word.hasPrefix("b") {
-    dsuForStrings.unionSetsContaining("b", and: word)
-  }
+    dsuForStrings.addSetWith(word)
+    if word.hasPrefix("a") {
+        dsuForStrings.unionSetsContaining("a", and: word)
+    } else if word.hasPrefix("b") {
+        dsuForStrings.unionSetsContaining("b", and: word)
+    }
 }
 
 print(dsuForStrings.inSameSet("a", and: "all"))
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
new file mode 100644
index 000000000..25d7f5b5d
--- /dev/null
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
@@ -0,0 +1,50 @@
+import Foundation
+
+/// Quick-find algorithm may take ~MN steps
+/// to process M union commands on N objects
+public struct UnionFindQuickFind<T: Hashable> {
+    private var index = [T: Int]()
+    private var parent = [Int]()
+    private var size = [Int]()
+    
+    public init() {}
+    
+    public mutating func addSetWith(_ element: T) {
+        index[element] = parent.count
+        parent.append(parent.count)
+        size.append(1)
+    }
+    
+    private mutating func setByIndex(_ index: Int) -> Int {
+        return parent[index]
+    }
+    
+    public mutating func setOf(_ element: T) -> Int? {
+        if let indexOfElement = index[element] {
+            return setByIndex(indexOfElement)
+        } else {
+            return nil
+        }
+    }
+    
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            if firstSet != secondSet {
+                for index in 0..<parent.count {
+                    if parent[index] == firstSet {
+                        parent[index] = secondSet
+                    }
+                }
+                size[secondSet] += size[firstSet]
+            }
+        }
+    }
+    
+    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            return firstSet == secondSet
+        } else {
+            return false
+        }
+    }
+}
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
new file mode 100644
index 000000000..4c848e61d
--- /dev/null
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
@@ -0,0 +1,51 @@
+import Foundation
+
+/// Quick-Union algorithm may take ~MN steps
+/// to process M union commands on N objects
+public struct UnionFindQuickUnion<T: Hashable> {
+    private var index = [T: Int]()
+    private var parent = [Int]()
+    private var size = [Int]()
+    
+    public init() {}
+    
+    public mutating func addSetWith(_ element: T) {
+        index[element] = parent.count
+        parent.append(parent.count)
+        size.append(1)
+    }
+    
+    private mutating func setByIndex(_ index: Int) -> Int {
+        if parent[index] == index {
+            return index
+        } else {
+            parent[index] = setByIndex(parent[index])
+            return parent[index]
+        }
+    }
+    
+    public mutating func setOf(_ element: T) -> Int? {
+        if let indexOfElement = index[element] {
+            return setByIndex(indexOfElement)
+        } else {
+            return nil
+        }
+    }
+    
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            if firstSet != secondSet {
+                parent[firstSet] = secondSet
+                size[secondSet] += size[firstSet]
+            }
+        }
+    }
+    
+    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            return firstSet == secondSet
+        } else {
+            return false
+        }
+    }
+}
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
new file mode 100644
index 000000000..02bec94a8
--- /dev/null
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
@@ -0,0 +1,59 @@
+import Foundation
+
+/// Quick-find algorithm may take ~MN steps
+/// to process M union commands on N objects
+public struct UnionFindWeightedQuickFind<T: Hashable> {
+    private var index = [T: Int]()
+    private var parent = [Int]()
+    private var size = [Int]()
+    
+    public init() {}
+    
+    public mutating func addSetWith(_ element: T) {
+        index[element] = parent.count
+        parent.append(parent.count)
+        size.append(1)
+    }
+    
+    private mutating func setByIndex(_ index: Int) -> Int {
+        return parent[index]
+    }
+    
+    public mutating func setOf(_ element: T) -> Int? {
+        if let indexOfElement = index[element] {
+            return setByIndex(indexOfElement)
+        } else {
+            return nil
+        }
+    }
+    
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            if firstSet != secondSet {
+                if size[firstSet] < size[secondSet] {
+                    for index in 0..<parent.count {
+                        if parent[index] == firstSet {
+                            parent[index] = secondSet
+                        }
+                    }
+                    size[secondSet] += size[firstSet]
+                } else {
+                    for index in 0..<parent.count {
+                        if parent[index] == secondSet {
+                            parent[index] = firstSet
+                        }
+                    }
+                    size[firstSet] += size[secondSet]
+                }
+            }
+        }
+    }
+    
+    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            return firstSet == secondSet
+        } else {
+            return false
+        }
+    }
+}
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
new file mode 100644
index 000000000..b3ac7445e
--- /dev/null
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
@@ -0,0 +1,56 @@
+import Foundation
+
+public struct UnionFindWeightedQuickUnion<T: Hashable> {
+    private var index = [T: Int]()
+    private var parent = [Int]()
+    private var size = [Int]()
+    
+    public init() {}
+    
+    public mutating func addSetWith(_ element: T) {
+        index[element] = parent.count
+        parent.append(parent.count)
+        size.append(1)
+    }
+    
+    private mutating func setByIndex(_ index: Int) -> Int {
+        if parent[index] == index {
+            return index
+        } else {
+            parent[index] = setByIndex(parent[index])
+            return parent[index]
+        }
+    }
+    
+    public mutating func setOf(_ element: T) -> Int? {
+        if let indexOfElement = index[element] {
+            return setByIndex(indexOfElement)
+        } else {
+            return nil
+        }
+    }
+    
+    /// Weighted, by comparing set size.
+    /// Merge small set into the large one.
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            if firstSet != secondSet {
+                if size[firstSet] < size[secondSet] {
+                    parent[firstSet] = secondSet
+                    size[secondSet] += size[firstSet]
+                } else {
+                    parent[secondSet] = firstSet
+                    size[firstSet] += size[secondSet]
+                }
+            }
+        }
+    }
+    
+    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            return firstSet == secondSet
+        } else {
+            return false
+        }
+    }
+}
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
new file mode 100644
index 000000000..892f46a3c
--- /dev/null
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
@@ -0,0 +1,53 @@
+import Foundation
+
+public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
+    private var index = [T: Int]()
+    private var parent = [Int]()
+    private var size = [Int]()
+    
+    public init() {}
+    
+    public mutating func addSetWith(_ element: T) {
+        index[element] = parent.count
+        parent.append(parent.count)
+        size.append(1)
+    }
+    
+    /// Path Compression.
+    private mutating func setByIndex(_ index: Int) -> Int {
+        if index != parent[index] {
+            parent[index] = setByIndex(parent[index])
+        }
+        return parent[index]
+    }
+    
+    public mutating func setOf(_ element: T) -> Int? {
+        if let indexOfElement = index[element] {
+            return setByIndex(indexOfElement)
+        } else {
+            return nil
+        }
+    }
+    
+    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            if firstSet != secondSet {
+                if size[firstSet] < size[secondSet] {
+                    parent[firstSet] = secondSet
+                    size[secondSet] += size[firstSet]
+                } else {
+                    parent[secondSet] = firstSet
+                    size[firstSet] += size[secondSet]
+                }
+            }
+        }
+    }
+    
+    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+            return firstSet == secondSet
+        } else {
+            return false
+        }
+    }
+}
diff --git a/Union-Find/UnionFind.playground/timeline.xctimeline b/Union-Find/UnionFind.playground/timeline.xctimeline
deleted file mode 100644
index bf468afec..000000000
--- a/Union-Find/UnionFind.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/Union-Find/UnionFind.swift b/Union-Find/UnionFind.swift
deleted file mode 100644
index 506cdc1fe..000000000
--- a/Union-Find/UnionFind.swift
+++ /dev/null
@@ -1,59 +0,0 @@
-/*
-  Union-Find Data Structure
-
-  Performance:
-    adding new set is almost O(1)
-    finding set of element is almost O(1)
-    union sets is almost O(1)
-*/
-
-public struct UnionFind<T: Hashable> {
-  private var index = [T: Int]()
-  private var parent = [Int]()
-  private var size = [Int]()
-
-  public mutating func addSetWith(_ element: T) {
-    index[element] = parent.count
-    parent.append(parent.count)
-    size.append(1)
-  }
-
-  private mutating func setByIndex(_ index: Int) -> Int {
-    if parent[index] == index {
-      return index
-    } else {
-      parent[index] = setByIndex(parent[index])
-      return parent[index]
-    }
-  }
-
-  public mutating func setOf(_ element: T) -> Int? {
-    if let indexOfElement = index[element] {
-      return setByIndex(indexOfElement)
-    } else {
-      return nil
-    }
-  }
-
-  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-      if firstSet != secondSet {
-        if size[firstSet] < size[secondSet] {
-          parent[firstSet] = secondSet
-          size[secondSet] += size[firstSet]
-        } else {
-          parent[secondSet] = firstSet
-          size[firstSet] += size[secondSet]
-        }
-      }
-    }
-  }
-
-  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-      return firstSet == secondSet
-    } else {
-      return false
-    }
-  }
-}

From 0de6055763a91902d3a52ef4857930aec6dbd0d7 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Tue, 25 Apr 2017 17:36:09 +0300
Subject: [PATCH 162/862] Added code description

---
 Dijkstra Algorithm/README.md | 138 +++++++++++++++++++++++++++++++++++
 1 file changed, 138 insertions(+)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 086e60c55..a72843e69 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -132,6 +132,144 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
+
+## Code implementation 
+First of all, lets create class, that will describe any Vertex in the graph.
+It is pretty simple
+```swift
+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 use cases, 
+	//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
+	//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
+    open var neighbors: [(Vertex, Double)] = []
+	
+	//As it was mentioned in 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 algorithm execution.
+    open var pathLengthFromStart = Double.infinity
+	
+	//This array containt vertices, which we need to go through to reach this vertex from starting one
+	//As with path length from start, we will change this array during algorithm execution.
+    open var pathVerticesFromStart: [Vertex] = []
+
+    public init(identifier: String) {
+        self.identifier = identifier
+    }
+
+	//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
+	//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
+    open func clearCache() {
+        pathLengthFromStart = Double.infinity
+        pathVerticesFromStart = []
+    }
+}
+```
+
+Because every vertex should be unique it is usefull to make them Hashable and according Equatable. We use identifier for this purposes.
+```swift
+extension Vertex: Hashable {
+    open var hashValue: Int {
+        return identifier.hashValue
+    }
+}
+
+extension Vertex: Equatable {
+    public static func ==(lhs: Vertex, rhs: Vertex) -> Bool {
+        return lhs.hashValue == rhs.hashValue
+    }
+}
+```
+
+We've created a base for our algorithm. Now let's create a house :)
+Dijkstra's realization is really straightforward.
+```swift
+public class Dijkstra {
+	//It 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>
+
+    public init(vertices: Set<Vertex>) {
+        totalVertices = vertices
+    }
+
+	//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 shortes path from startVertex, 
+		//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
+		//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 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 {
+			
+			//Nex 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)
+			
+			//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
+            let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
+			
+			//Let's iterate through them
+            for neighbor in filteredNeighbors {
+				//These variable are more representative, than neighbor.0 or neighbor.1
+                let neighborVertex = neighbor.0
+                let weight = neighbor.1
+				
+				//Here we calculate new weight, that we can offer to neighbor. 
+                let theoreticNewWeight = vertex.pathLengthFromStart + weight
+				
+				//If it is smaller than neighbor's current pathLengthFromStart
+				//Then we perform this code
+                if theoreticNewWeight < neighborVertex.pathLengthFromStart {
+					
+					//set new pathLengthFromStart
+                    neighborVertex.pathLengthFromStart = theoreticNewWeight
+					
+					//set new pathVerticesFromStart
+                    neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
+					
+					//append current vertex to neighbor's pathVerticesFromStart
+                    neighborVertex.pathVerticesFromStart.append(neighborVertex)
+                }
+            }
+			
+			//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 }
+        }
+    }
+}
+```
+
+That's all! Now you can check this algorithm in the playground. On the main page there is a code for creating random graph.
+
+Also there is a **VisualizedDijkstra.playground**. Use it to figure out algorithm flow in real (slowed :)) time.  
+
 ## About this repository
 
 This repository contains to playgrounds:

From aac4f8fbf24f6996b70ea5c1f792ba7b81cd9e98 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Tue, 25 Apr 2017 17:54:34 +0300
Subject: [PATCH 163/862] Fixed code comments

---
 Dijkstra Algorithm/README.md | 76 ++++++++++++++++++------------------
 1 file changed, 38 insertions(+), 38 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index a72843e69..2b6bc3875 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -139,28 +139,28 @@ It is pretty simple
 ```swift
 open class Vertex {
 
-	//Every vertex should be unique, that's why we set up identifier
+//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 use cases, 
-	//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
-	//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
+//For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
+//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
+//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
     open var neighbors: [(Vertex, Double)] = []
 	
-	//As it was mentioned in 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 algorithm execution.
+//As it was mentioned in 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 algorithm execution.
     open var pathLengthFromStart = Double.infinity
 	
-	//This array containt vertices, which we need to go through to reach this vertex from starting one
-	//As with path length from start, we will change this array during algorithm execution.
+//This array containt vertices, which we need to go through to reach this vertex from starting one
+//As with path length from start, we will change this array during algorithm execution.
     open var pathVerticesFromStart: [Vertex] = []
 
     public init(identifier: String) {
         self.identifier = identifier
     }
 
-	//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
-	//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
+//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
+//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
     open func clearCache() {
         pathLengthFromStart = Double.infinity
         pathVerticesFromStart = []
@@ -187,79 +187,79 @@ We've created a base for our algorithm. Now let's create a house :)
 Dijkstra's realization is really straightforward.
 ```swift
 public class Dijkstra {
-	//It 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.
+//It 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>
 
     public init(vertices: Set<Vertex>) {
         totalVertices = vertices
     }
 
-	//Remember clearCache function in the Vertex class implementation? 
-	//This is just a wrapper that cleans cache for all stored vertices.
+//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 shortes path from startVertex, 
-		//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
-		//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
+//Before we start searching shortes path from startVertex, 
+//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
+//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 empty pathVerticesFromStart array.
+//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
 		
-		//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
+//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.
+//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 {
 			
-			//Nex 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"*
+//Nex 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)
 			
-			//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
+//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
             let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
 			
-			//Let's iterate through them
+//Let's iterate through them
             for neighbor in filteredNeighbors {
-				//These variable are more representative, than neighbor.0 or neighbor.1
+//These variable are more representative, than neighbor.0 or neighbor.1
                 let neighborVertex = neighbor.0
                 let weight = neighbor.1
 				
-				//Here we calculate new weight, that we can offer to neighbor. 
+//Here we calculate new weight, that we can offer to neighbor. 
                 let theoreticNewWeight = vertex.pathLengthFromStart + weight
 				
-				//If it is smaller than neighbor's current pathLengthFromStart
-				//Then we perform this code
+//If it is smaller than neighbor's current pathLengthFromStart
+//Then we perform this code
                 if theoreticNewWeight < neighborVertex.pathLengthFromStart {
 					
-					//set new pathLengthFromStart
+//set new pathLengthFromStart
                     neighborVertex.pathLengthFromStart = theoreticNewWeight
 					
-					//set new pathVerticesFromStart
+//set new pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
 					
-					//append current vertex to neighbor's pathVerticesFromStart
+//append current vertex to neighbor's pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart.append(neighborVertex)
                 }
             }
 			
-			//If totalVertices is empty, i.e. all vertices are visited
-			//Than break the loop
+//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.
+//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 edbccd3b4fee79fe55ce2d741833dbef431bf466 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Tue, 25 Apr 2017 17:57:12 +0300
Subject: [PATCH 164/862] Fixed comments again

---
 Dijkstra Algorithm/README.md | 76 ++++++++++++++++++------------------
 1 file changed, 38 insertions(+), 38 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 2b6bc3875..a8ed3c827 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -139,28 +139,28 @@ It is pretty simple
 ```swift
 open class Vertex {
 
-//Every vertex should be unique, that's why we set up identifier
+	//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 use cases, 
-//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
-//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
+	//For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
+	//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
+	//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
     open var neighbors: [(Vertex, Double)] = []
 	
-//As it was mentioned in 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 algorithm execution.
+	//As it was mentioned in 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 algorithm execution.
     open var pathLengthFromStart = Double.infinity
 	
-//This array containt vertices, which we need to go through to reach this vertex from starting one
-//As with path length from start, we will change this array during algorithm execution.
+	//This array containt vertices, which we need to go through to reach this vertex from starting one
+	//As with path length from start, we will change this array during algorithm execution.
     open var pathVerticesFromStart: [Vertex] = []
 
     public init(identifier: String) {
         self.identifier = identifier
     }
 
-//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
-//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
+	//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
+	//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
     open func clearCache() {
         pathLengthFromStart = Double.infinity
         pathVerticesFromStart = []
@@ -187,79 +187,79 @@ We've created a base for our algorithm. Now let's create a house :)
 Dijkstra's realization is really straightforward.
 ```swift
 public class Dijkstra {
-//It 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.
+	//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>
 
     public init(vertices: Set<Vertex>) {
         totalVertices = vertices
     }
 
-//Remember clearCache function in the Vertex class implementation? 
-//This is just a wrapper that cleans cache for all stored vertices.
+	//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 shortes path from startVertex, 
-//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
-//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
+		//Before we start searching shortes path from startVertex, 
+		//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
+		//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 empty pathVerticesFromStart array.
+		//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
 		
-//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
+		//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.
+		//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 {
 			
-//Nex 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"*
+			//Nex 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)
 			
-//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
+			//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
             let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
 			
-//Let's iterate through them
+			//Let's iterate through them
             for neighbor in filteredNeighbors {
-//These variable are more representative, than neighbor.0 or neighbor.1
+				//These variable are more representative, than neighbor.0 or neighbor.1
                 let neighborVertex = neighbor.0
                 let weight = neighbor.1
 				
-//Here we calculate new weight, that we can offer to neighbor. 
+				//Here we calculate new weight, that we can offer to neighbor. 
                 let theoreticNewWeight = vertex.pathLengthFromStart + weight
 				
-//If it is smaller than neighbor's current pathLengthFromStart
-//Then we perform this code
+				//If it is smaller than neighbor's current pathLengthFromStart
+				//Then we perform this code
                 if theoreticNewWeight < neighborVertex.pathLengthFromStart {
 					
-//set new pathLengthFromStart
+					//set new pathLengthFromStart
                     neighborVertex.pathLengthFromStart = theoreticNewWeight
 					
-//set new pathVerticesFromStart
+					//set new pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
 					
-//append current vertex to neighbor's pathVerticesFromStart
+					//append current vertex to neighbor's pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart.append(neighborVertex)
                 }
             }
 			
-//If totalVertices is empty, i.e. all vertices are visited
-//Than break the loop
+			//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.
+			//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 b6c5b820be7506bbbfec04b230bbedcda1b6f5d0 Mon Sep 17 00:00:00 2001
From: Taras <crabman448@gmail.com>
Date: Tue, 25 Apr 2017 18:02:52 +0300
Subject: [PATCH 165/862] Update README.md

---
 Dijkstra Algorithm/README.md | 80 ++++++++++++++++++------------------
 1 file changed, 40 insertions(+), 40 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index a8ed3c827..f8ac37cf0 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -139,28 +139,28 @@ It is pretty simple
 ```swift
 open class Vertex {
 
-	//Every vertex should be unique, that's why we set up identifier
+    //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 use cases, 
-	//when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
-	//Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
+    //For dijkstra every vertex in the graph should be connected with at least one other vertex. But there can be some use cases, 
+    //when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
+    //Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
     open var neighbors: [(Vertex, Double)] = []
 	
-	//As it was mentioned in 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 algorithm execution.
+    //As it was mentioned in 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 algorithm execution.
     open var pathLengthFromStart = Double.infinity
-	
-	//This array containt vertices, which we need to go through to reach this vertex from starting one
-	//As with path length from start, we will change this array during algorithm execution.
+
+    //This array containt vertices, which we need to go through to reach this vertex from starting one
+    //As with path length from start, we will change this array during algorithm execution.
     open var pathVerticesFromStart: [Vertex] = []
 
     public init(identifier: String) {
         self.identifier = identifier
     }
 
-	//This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
-	//When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
+    //This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
+    //When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
     open func clearCache() {
         pathLengthFromStart = Double.infinity
         pathVerticesFromStart = []
@@ -187,79 +187,79 @@ We've created a base for our algorithm. Now let's create a house :)
 Dijkstra's realization is really straightforward.
 ```swift
 public class Dijkstra {
-	//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.
+    //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>
 
     public init(vertices: Set<Vertex>) {
         totalVertices = vertices
     }
 
-	//Remember clearCache function in the Vertex class implementation? 
-	//This is just a wrapper that cleans cache for all stored vertices.
+    //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 shortes path from startVertex, 
-		//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
-		//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
+	//Before we start searching shortes path from startVertex, 
+	//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
+	//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 empty pathVerticesFromStart array.
+	//Now all our vertices have Double.infinity pathLengthFromStart and empty pathVerticesFromStart array.
 		
-		//The next step in the algorithm is to set startVertex pathLengthFromStart and pathVerticesFromStart
+	//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.
+	//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 {
-			
-			//Nex 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"*
+    			
+    	    //Nex 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)
 			
-			//filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
+	    //filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
             let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
 			
-			//Let's iterate through them
+	    //Let's iterate through them
             for neighbor in filteredNeighbors {
-				//These variable are more representative, than neighbor.0 or neighbor.1
+		//These variable are more representative, than neighbor.0 or neighbor.1
                 let neighborVertex = neighbor.0
                 let weight = neighbor.1
 				
-				//Here we calculate new weight, that we can offer to neighbor. 
+		//Here we calculate new weight, that we can offer to neighbor. 
                 let theoreticNewWeight = vertex.pathLengthFromStart + weight
 				
-				//If it is smaller than neighbor's current pathLengthFromStart
-				//Then we perform this code
+		//If it is smaller than neighbor's current pathLengthFromStart
+		//Then we perform this code
                 if theoreticNewWeight < neighborVertex.pathLengthFromStart {
 					
-					//set new pathLengthFromStart
+		    //set new pathLengthFromStart
                     neighborVertex.pathLengthFromStart = theoreticNewWeight
 					
-					//set new pathVerticesFromStart
+		    //set new pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
 					
-					//append current vertex to neighbor's pathVerticesFromStart
+		    //append current vertex to neighbor's pathVerticesFromStart
                     neighborVertex.pathVerticesFromStart.append(neighborVertex)
                 }
             }
 			
-			//If totalVertices is empty, i.e. all vertices are visited
-			//Than break the loop
+	    //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.
+	    //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 9575a6745caa33bc5d864d6e406682af2f5f9515 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Tue, 25 Apr 2017 18:22:00 +0300
Subject: [PATCH 166/862] Added some comments to playground

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

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift
index 1c12245bd..7c7f1a4b0 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Contents.swift	
@@ -14,13 +14,18 @@ func createNotConnectedVertices() {
 
 func setupConnections() {
     for vertex in vertices {
+        //the amount of edges each vertex can have
         let randomEdgesCount = arc4random_uniform(4) + 1
         for _ in 0..<randomEdgesCount {
+            //randomize weight value from 0 to 9
             let randomWeight = Double(arc4random_uniform(10))
             let neighborVertex = randomVertex(except: vertex)
+
+            //we need this check to set only one connection between two equal pairs of vertices
             if vertex.neighbors.contains(where: { $0.0 == neighborVertex }) {
                 continue
             }
+            //creating neighbors and setting them
             let neighbor1 = (neighborVertex, randomWeight)
             let neighbor2 = (vertex, randomWeight)
             vertex.neighbors.append(neighbor1)
@@ -53,9 +58,15 @@ let dijkstra = Dijkstra(vertices: vertices)
 //decide which vertex will be the starting one
 let startVertex = randomVertex()
 
+let startTime = Date()
+
 //ask algorithm to find shortest paths from start vertex to all others
 dijkstra.findShortestPaths(from: startVertex)
 
+let endTime = Date()
+
+print("calculation time is = \((endTime.timeIntervalSince(startTime))) sec")
+
 //printing results
 let destinationVertex = randomVertex(except: startVertex)
 print(destinationVertex.pathLengthFromStart)

From 9a8467fa24c780c3f4b2404989fa7a6616ea0946 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 26 Apr 2017 10:31:44 +0300
Subject: [PATCH 167/862] Final edits

---
 Dijkstra Algorithm/README.md | 16 +++++++++-------
 1 file changed, 9 insertions(+), 7 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index f8ac37cf0..db1726b1f 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -2,13 +2,13 @@
 
 This [algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) was invented in 1956 by Edsger W. Dijkstra. 
 
-This algorithm can be used, when you have one source vertex and want to find the shortest paths to all other vertices in the graph.
+It can be used, when you have one source vertex and want to find the shortest paths to all other vertices in the graph.
 
 The best example is road network. If you wnat to find the shortest path from your house to your job, then it is time for the Dijkstra's algorithm.
 
-I have created **VisualizedDijkstra.playground** to help you to understand, how this algorithm works. Besides, I have described below step by step how does it works.
+I have created **VisualizedDijkstra.playground** to improve your understanding of the algorithm's flow. Besides, below is step by step algorithm's description.
 
-So let's imagine, that your house is "A" vertex and your job is "B" vertex. And you are lucky, you have graph with all possible routes.
+Let's imagine, 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 graph, that connects your house with all these stores. So, you know what to do :)
 
 ## Initialization
 
@@ -30,7 +30,7 @@ The table below represents graph state:
 
 >T states for True
 
-To initialize out graph we have to set source vertex path length from source vertex to 0, and append itself to path vertices ffrom start.
+To initialize our graph we have to set source vertex path length from source vertex to 0, and append itself to path vertices from start.
 
 |                           |  A  |  B  |  C  |  D  |  E  |
 |:------------------------- |:---:|:---:|:---:|:---:|:---:|
@@ -40,7 +40,7 @@ To initialize out graph we have to set source vertex path length from source ver
 
 Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
 
-But before we will go through all process side by side let me explain how algorithm works.
+But before we will go through all process side by side read this explanation.
 The algorithm repeats following cycle until all vertices are marked as visited.
 Cycle:
 1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
@@ -50,7 +50,7 @@ When all vertices are marked as visited, the algorithm's job is done. Now, you c
 
 Okay, let's start!
 Let's follow the algorithm's cycle and pick the first vertex, which neighbors we want to check.
-All our vertices are not visited, but there is only one have the smallest path length from start - A. This vertex is th first one, which neighbors we will check.
+All our vertices are not visited, but there is only one has the smallest path length from start - A. This vertex is the first one, which neighbors we will check.
 First of all, set this vertex as visited 
 
 A.visited = true
@@ -268,7 +268,9 @@ public class Dijkstra {
 
 That's all! Now you can check this algorithm in the playground. On the main page there is a code for creating random graph.
 
-Also there is a **VisualizedDijkstra.playground**. Use it to figure out algorithm flow in real (slowed :)) time.  
+Also there is a **VisualizedDijkstra.playground**. Use it to figure out algorithm's flow in real (slowed :)) time.
+
+It is up to you how to implement some specific parts of algorithm, you can use Array instead of Set, add _visited_ property to Vertex or you can create some local totalVertices Array/Set inside _func findShortestPaths(from startVertex: Vertex)_ to keep totalVertices Array/Set unchanged. This is a general explanation with one possible implementation :)
 
 ## About this repository
 

From d79a076ea901657161392a4fc3b53b0e2df65cdd Mon Sep 17 00:00:00 2001
From: Lucy Jeong <yureka5345@gmail.com>
Date: Thu, 27 Apr 2017 11:31:57 +0900
Subject: [PATCH 168/862] Update README.markdown

changed enumerate() -> enumerated()
---
 Hash Table/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index bc9636195..8f1eaaf70 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -202,7 +202,7 @@ The code to insert a new element or update an existing element lives in `updateV
     let index = self.index(forKey: key)
     
     // Do we already have this key in the bucket?
-    for (i, element) in buckets[index].enumerate() {
+    for (i, element) in buckets[index].enumerated() {
       if element.key == key {
         let oldValue = element.value
         buckets[index][i].value = value

From 03393a86a3864221ff1f0b7137eefb619bf19698 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 06:17:13 +0500
Subject: [PATCH 169/862] Fix "found unknown escape character" while trying to
 run swiftlint 0.18.1

Also update the smiley face regex check to have a space before the colon so that it doesn't match: fatalError("init(coder:) has not been implemented")
---
 .swiftlint.yml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.swiftlint.yml b/.swiftlint.yml
index 1434bf637..6cb714110 100644
--- a/.swiftlint.yml
+++ b/.swiftlint.yml
@@ -17,8 +17,8 @@ disabled_rules:
 custom_rules:
   smiley_face:
     name: "Smiley Face"
-    regex: "(\:\))"
-    match_kinds: 
+    regex: '( :\))'
+    match_kinds:
       - comment
       - string
     message: "A closing parenthesis smiley :) creates a half-hearted smile, and thus is not preferred. Use :]"

From 018ddaccfc0276ac8740c093731b92aeae122a9d Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:42:15 +0500
Subject: [PATCH 170/862] [swiftlint] Fix: MARK comment should be in valid
 format.

---
 .../TST.playground/Sources/TernarySearchTree.swift            | 4 ++--
 Ternary Search Tree/TernarySearchTree.swift                   | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
index fed8f9710..21b8f0dc3 100644
--- a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
@@ -15,7 +15,7 @@ public class TernarySearchTree<Element> {
 
     public init() {}
 
-    //MARK: - Insertion
+    // MARK: - Insertion
 
     public func insert(data: Element, withKey key: String) -> Bool {
         return insert(node: &root, withData: data, andKey: key, atIndex: 0)
@@ -59,7 +59,7 @@ public class TernarySearchTree<Element> {
     }
 
 
-    //MARK: - Finding
+    // MARK: - Finding
 
 
     public func find(key: String) -> Element? {
diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index 2e2ca2917..0fa6d9634 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -23,7 +23,7 @@ public class TernarySearchTree<Element> {
      */
     public init() {}
 
-    //MARK: - Insertion
+    // MARK: - Insertion
 
     /**
     Public insertion method.
@@ -85,7 +85,7 @@ public class TernarySearchTree<Element> {
     }
 
 
-    //MARK: - Finding
+    // MARK: - Finding
 
     /**
     Public find method.

From 29c5952fadf80e8ac3f0c717d7d7ae08620b0dcb Mon Sep 17 00:00:00 2001
From: Felipe Naranjo <fenaranjo42@gmail.com>
Date: Fri, 28 Apr 2017 10:57:48 -0400
Subject: [PATCH 171/862] Update README.markdown

Though "indexes" is grammatically correct, the word "indices" is used in Apple documentation.
---
 Union-Find/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index 5102f6b89..68698f39e 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -119,7 +119,7 @@ Here's illustration of what I mean. Let's say the tree looks like this:
 
 ![BeforeFind](Images/BeforeFind.png)
 
-We call `setOf(4)`. To find the root node we have to first go to node `2` and then to node `7`. (The indexes of the elements are marked in red.)
+We call `setOf(4)`. To find the root node we have to first go to node `2` and then to node `7`. (The indices of the elements are marked in red.)
 
 During the call to `setOf(4)`, the tree is reorganized to look like this:
 

From 137c36051dff6a1e3965dad4959ad0a742fc01b4 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:46:49 +0500
Subject: [PATCH 172/862] [swiftlint] Fix: Else and catch should be on the same
 line

warning: Statement Position Violation: Else and catch should be on the same line, one space after the previous declaration.
---
 DiningPhilosophers/Sources/main.swift | 3 +--
 Skip-List/SkipList.swift              | 3 +--
 2 files changed, 2 insertions(+), 4 deletions(-)

diff --git a/DiningPhilosophers/Sources/main.swift b/DiningPhilosophers/Sources/main.swift
index 285402d53..338a9074d 100755
--- a/DiningPhilosophers/Sources/main.swift
+++ b/DiningPhilosophers/Sources/main.swift
@@ -22,8 +22,7 @@ struct ForkPair {
         if leftIndex > rightIndex {
             leftFork = ForkPair.forksSemaphore[leftIndex]
             rightFork = ForkPair.forksSemaphore[rightIndex]
-        }
-        else {
+        } else {
             leftFork = ForkPair.forksSemaphore[rightIndex]
             rightFork = ForkPair.forksSemaphore[leftIndex]
         }
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 5fc61bf8e..c5fe2b821 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -118,8 +118,7 @@ extension SkipList {
           if value.key == key {
             isFound = true
             break
-          }
-          else {
+          } else {
             if key < value.key! {
               currentNode = node.down
             } else {

From c3a05c6bfe865554261fbb0b641651f7dcfffff4 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:49:54 +0500
Subject: [PATCH 173/862] [swiftlint] Fix: trailing_semicolon

warning: Trailing Semicolon Violation: Lines should not have trailing semicolons.
---
 Trie/Trie/TrieTests/TrieTests.swift | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index a75c35c62..50a30a552 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -175,21 +175,21 @@ class TrieTests: XCTestCase {
         trie.insert(word: "another")
         trie.insert(word: "exam")
         let wordsAll = trie.findWordsWithPrefix(prefix: "")
-        XCTAssertEqual(wordsAll.sorted(), ["another", "exam", "test"]);
+        XCTAssertEqual(wordsAll.sorted(), ["another", "exam", "test"])
         let words = trie.findWordsWithPrefix(prefix: "ex")
-        XCTAssertEqual(words, ["exam"]);
+        XCTAssertEqual(words, ["exam"])
         trie.insert(word: "examination")
         let words2 = trie.findWordsWithPrefix(prefix: "exam")
-        XCTAssertEqual(words2, ["exam", "examination"]);
+        XCTAssertEqual(words2, ["exam", "examination"])
         let noWords = trie.findWordsWithPrefix(prefix: "tee")
-        XCTAssertEqual(noWords, []);
+        XCTAssertEqual(noWords, [])
         let unicodeWord = "😬😎"
         trie.insert(word: unicodeWord)
         let wordsUnicode = trie.findWordsWithPrefix(prefix: "😬")
-        XCTAssertEqual(wordsUnicode, [unicodeWord]);
+        XCTAssertEqual(wordsUnicode, [unicodeWord])
         trie.insert(word: "Team")
         let wordsUpperCase = trie.findWordsWithPrefix(prefix: "Te")
-        XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"]);
+        XCTAssertEqual(wordsUpperCase.sorted(), ["team", "test"])
 
     }
 }

From 4eb7ac1975dfbd2f3d9059d649af3ab6f90d97a2 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:52:12 +0500
Subject: [PATCH 174/862] [swiftlint] Fix control_statement  (i.e. parens
 around if statement)

warning: Control Statement Violation: if,for,while,do statements shouldn't wrap their conditionals in parentheses.
---
 Rootish Array Stack/Tests/RootishArrayStackTests.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
index f73857d0f..9ffc4ebb9 100755
--- a/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -4,7 +4,7 @@ fileprivate extension RootishArrayStack {
 	func equal(toArray array: Array<Int>) -> Bool{
 		for index in 0..<count {
 			guard let integerElement = self[index] as? Int else { return false }
-			if (array[index] != integerElement) {
+			if array[index] != integerElement {
 				return false
 			}
 		}

From 821bee3e76fa3520b38f12fc6c4147a3dba8d371 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:53:16 +0500
Subject: [PATCH 175/862] [swiftlint] Fix redundant_optional_initialization
 (i.e. don't need "= nil")

warning: Redundant Optional Initialization Violation: Initializing an optional variable with nil is redundant.
---
 Graph/Graph/AdjacencyListGraph.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index e5e9fc2db..edb754c97 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -12,7 +12,7 @@ import Foundation
 private class EdgeList<T> where T: Equatable, T: Hashable {
 
   var vertex: Vertex<T>
-  var edges: [Edge<T>]? = nil
+  var edges: [Edge<T>]?
 
   init(vertex: Vertex<T>) {
     self.vertex = vertex

From 55eba6e7d86e468b1cb0f114c25f5439cf2d4702 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:55:51 +0500
Subject: [PATCH 176/862] [swiftlint] Fix: closure_parameter_position

warning: Closure Parameter Position Violation: Closure parameters should be on the same line as opening brace.
---
 B-Tree/BTree.playground/Contents.swift                    | 3 +--
 Shunting Yard/ShuntingYard.playground/Sources/Stack.swift | 3 +--
 Skip-List/SkipList.swift                                  | 7 +++----
 Stack/Stack.swift                                         | 3 +--
 4 files changed, 6 insertions(+), 10 deletions(-)

diff --git a/B-Tree/BTree.playground/Contents.swift b/B-Tree/BTree.playground/Contents.swift
index 8238fe5a5..710ace701 100644
--- a/B-Tree/BTree.playground/Contents.swift
+++ b/B-Tree/BTree.playground/Contents.swift
@@ -14,8 +14,7 @@ bTree[3]
 
 bTree.remove(2)
 
-bTree.traverseKeysInOrder {
-  key in
+bTree.traverseKeysInOrder { key in
   print(key)
 }
 
diff --git a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift
index a67bb9d64..27286fdbd 100644
--- a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
@@ -31,8 +31,7 @@ public struct Stack<T> {
 extension Stack: Sequence {
     public func makeIterator() -> AnyIterator<T> {
         var curr = self
-        return AnyIterator {
-            _ -> T? in
+        return AnyIterator { _ -> T? in
             return curr.pop()
         }
     }
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index c5fe2b821..1418656f3 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -52,10 +52,9 @@ public struct Stack<T> {
 extension Stack: Sequence {
   public func makeIterator() -> AnyIterator<T> {
     var curr = self
-    return AnyIterator {
-             _ -> T? in
-             return curr.pop()
-      }
+    return AnyIterator { _ -> T? in
+      return curr.pop()
+    }
   }
 }
 
diff --git a/Stack/Stack.swift b/Stack/Stack.swift
index 974d5a443..c3f42ea44 100644
--- a/Stack/Stack.swift
+++ b/Stack/Stack.swift
@@ -30,8 +30,7 @@ public struct Stack<T> {
 extension Stack: Sequence {
     public func makeIterator() -> AnyIterator<T> {
         var curr = self
-        return AnyIterator {
-            _ -> T? in
+        return AnyIterator { _ -> T? in
             return curr.pop()
         }
     }

From 6c3dcd4be40058e09875d4bcd3f6086e021380e4 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:57:19 +0500
Subject: [PATCH 177/862] [swiftlint] Fix: leading_whitespace

warning: Leading Whitespace Violation: File shouldn't start with whitespace.
---
 HaversineDistance/HaversineDistance.playground/Contents.swift   | 1 -
 QuadTree/QuadTree.playground/Contents.swift                     | 1 -
 QuadTree/QuadTree.playground/Sources/QuadTree.swift             | 1 -
 Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift | 1 -
 4 files changed, 4 deletions(-)

diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index f46d7c394..a6effb7b0 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -1,4 +1,3 @@
-
 import UIKit
 
 func haversineDinstance(la1: Double, lo1: Double, la2: Double, lo2: Double, radius: Double = 6367444.7) -> Double {
diff --git a/QuadTree/QuadTree.playground/Contents.swift b/QuadTree/QuadTree.playground/Contents.swift
index 41e73147f..ad8ee31f8 100644
--- a/QuadTree/QuadTree.playground/Contents.swift
+++ b/QuadTree/QuadTree.playground/Contents.swift
@@ -1,4 +1,3 @@
-
 import Foundation
 
 let tree = QuadTree(rect: Rect(origin: Point(0, 0), size: Size(xLength: 10, yLength: 10)))
diff --git a/QuadTree/QuadTree.playground/Sources/QuadTree.swift b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
index 65c55d49e..14d0dbba7 100644
--- a/QuadTree/QuadTree.playground/Sources/QuadTree.swift
+++ b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
@@ -1,4 +1,3 @@
-
 public struct Point {
   let x: Double
   let y: Double
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
index 1735798d5..b0f440809 100644
--- a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -1,4 +1,3 @@
-
 private enum RBTColor {
     case red
     case black

From 932b453d5b0ce1b5ad058323bed79728f92dfd52 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 09:58:51 +0500
Subject: [PATCH 178/862] [swiftlint] Fix rule: trailing_newline

warning: Trailing Newline Violation: Files should have a single trailing newline.
---
 B-Tree/Tests/Tests/BTreeNodeTests.swift                         | 1 -
 Comb Sort/Comb Sort.playground/Contents.swift                   | 2 --
 Convex Hull/Convex Hull/AppDelegate.swift                       | 1 -
 Fixed Size Array/FixedSizeArray.playground/Contents.swift       | 1 -
 Insertion Sort/InsertionSort.playground/Contents.swift          | 2 +-
 Linked List/LinkedList.playground/Contents.swift                | 1 -
 .../MRPrimality.playground/Contents.swift                       | 2 +-
 Run-Length Encoding/RLE.playground/Contents.swift               | 2 +-
 Trie/Trie/Trie/AppDelegate.swift                                | 1 -
 Trie/Trie/Trie/ViewController.swift                             | 1 -
 10 files changed, 3 insertions(+), 11 deletions(-)

diff --git a/B-Tree/Tests/Tests/BTreeNodeTests.swift b/B-Tree/Tests/Tests/BTreeNodeTests.swift
index da6ebe9f6..fd3ba10e8 100644
--- a/B-Tree/Tests/Tests/BTreeNodeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeNodeTests.swift
@@ -51,4 +51,3 @@ class BTreeNodeTests: XCTestCase {
     XCTAssertEqual(root.children!.count, 2)
   }
 }
-
diff --git a/Comb Sort/Comb Sort.playground/Contents.swift b/Comb Sort/Comb Sort.playground/Contents.swift
index d6add44f5..40176be9f 100644
--- a/Comb Sort/Comb Sort.playground/Contents.swift	
+++ b/Comb Sort/Comb Sort.playground/Contents.swift	
@@ -16,5 +16,3 @@ while i < 1000 {
   i += 1
 }
 combSort(bigArray)
-
-
diff --git a/Convex Hull/Convex Hull/AppDelegate.swift b/Convex Hull/Convex Hull/AppDelegate.swift
index 1901083a8..4f8496cd5 100644
--- a/Convex Hull/Convex Hull/AppDelegate.swift	
+++ b/Convex Hull/Convex Hull/AppDelegate.swift	
@@ -54,4 +54,3 @@ class AppDelegate: UIResponder, UIApplicationDelegate {
 
 
 }
-
diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
index f1bc63315..4bc5d66df 100644
--- a/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -53,4 +53,3 @@ array.append(2)
 array[1]
 array.removeAt(index: 0)
 array.removeAll()
-
diff --git a/Insertion Sort/InsertionSort.playground/Contents.swift b/Insertion Sort/InsertionSort.playground/Contents.swift
index b25916b23..df1822b8f 100644
--- a/Insertion Sort/InsertionSort.playground/Contents.swift	
+++ b/Insertion Sort/InsertionSort.playground/Contents.swift	
@@ -16,4 +16,4 @@ func insertionSort<T>(_ array: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
 
 let list = [ 10, -1, 3, 9, 2, 27, 8, 5, 1, 3, 0, 26 ]
 insertionSort(list, <)
-insertionSort(list, >)
\ No newline at end of file
+insertionSort(list, >)
diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index b86fbf0b4..10677935a 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -389,4 +389,3 @@ let listArrayLiteral2: LinkedList = ["Swift", "Algorithm", "Club"]
 listArrayLiteral2.count        // 3
 listArrayLiteral2[0]           // "Swift"
 listArrayLiteral2.removeLast()  // "Club"
-
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift
index 8d97dc409..98032bd59 100644
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Contents.swift	
@@ -21,4 +21,4 @@ mrPrimalityTest(178426363)
 mrPrimalityTest(32415187747)
 
 // With iteration
-mrPrimalityTest(32416190071, iteration: 10)
\ No newline at end of file
+mrPrimalityTest(32416190071, iteration: 10)
diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
index 62b4ef437..11e177d0d 100644
--- a/Run-Length Encoding/RLE.playground/Contents.swift	
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -113,4 +113,4 @@ func runTests() -> Bool {
     return result
 }
 
-runTests()
\ No newline at end of file
+runTests()
diff --git a/Trie/Trie/Trie/AppDelegate.swift b/Trie/Trie/Trie/AppDelegate.swift
index 4da9dc345..b2b4c0c5f 100644
--- a/Trie/Trie/Trie/AppDelegate.swift
+++ b/Trie/Trie/Trie/AppDelegate.swift
@@ -23,4 +23,3 @@ class AppDelegate: NSObject, NSApplicationDelegate {
 
 
 }
-
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
index b2e9d9105..e24a812cb 100644
--- a/Trie/Trie/Trie/ViewController.swift
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -24,4 +24,3 @@ class ViewController: NSViewController {
 
 
 }
-

From a025c0cc27b3fa4b8bfa2255f59eceb8447ad9b3 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 10:00:27 +0500
Subject: [PATCH 179/862] [swiftlint] Fix rule: opening_brace

warning: Opening Brace Spacing Violation: Opening braces should be preceded by a single space and on the same line as the declaration.
---
 .../BruteForceStringSearch.playground/Contents.swift        | 2 +-
 Brute-Force String Search/BruteForceStringSearch.swift      | 2 +-
 .../KaratsubaMultiplication.playground/Contents.swift       | 6 +++---
 .../Red-Black Tree 2.playground/Sources/RBTree.swift        | 2 +-
 Rootish Array Stack/Tests/RootishArrayStackTests.swift      | 2 +-
 Shell Sort/ShellSortExample.swift                           | 2 +-
 Skip-List/SkipList.swift                                    | 2 +-
 .../Sources/Number.swift                                    | 2 +-
 8 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
index 61064c698..00ac6da97 100644
--- a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
@@ -6,7 +6,7 @@ extension String {
     for i in self.characters.indices {
       var j = i
       var found = true
-      for p in pattern.characters.indices{
+      for p in pattern.characters.indices {
         if j == self.characters.endIndex || self[j] != pattern[p] {
           found = false
           break
diff --git a/Brute-Force String Search/BruteForceStringSearch.swift b/Brute-Force String Search/BruteForceStringSearch.swift
index 03a2dff13..016292304 100644
--- a/Brute-Force String Search/BruteForceStringSearch.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.swift	
@@ -6,7 +6,7 @@ extension String {
     for i in self.characters.indices {
         var j = i
         var found = true
-        for p in pattern.characters.indices{
+        for p in pattern.characters.indices {
             if j == self.characters.endIndex || self[j] != pattern[p] {
                 found = false
                 break
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index bde8fd9f9..3ac29301a 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -15,8 +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).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)
 
@@ -30,7 +30,7 @@ func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
     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))
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
index b0f440809..0038494d3 100644
--- a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -22,7 +22,7 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
             // If the value is encapsulated by double pipes it is double black (This should not occur in a verified RBTree)
             if self.isRed {
                 nodeValue = "(\(self.value!))"
-            } else if self.isBlack{
+            } else if self.isBlack {
                 nodeValue = "|\(self.value!)|"
             } else {
                 nodeValue = "||\(self.value!)||"
diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
index 9ffc4ebb9..f0aaa8bca 100755
--- a/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -1,7 +1,7 @@
 import XCTest
 
 fileprivate extension RootishArrayStack {
-	func equal(toArray array: Array<Int>) -> Bool{
+	func equal(toArray array: Array<Int>) -> Bool {
 		for index in 0..<count {
 			guard let integerElement = self[index] as? Int else { return false }
 			if array[index] != integerElement {
diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index 9174b935b..aaf58cf4d 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -22,7 +22,7 @@ public func shellSort(_ list : inout [Int]) {
             
             guard sublistCount == 1 && index > 0 else { continue }
             
-            while list[index - 1] > list[index] && index - 1 > 0  {
+            while list[index - 1] > list[index] && index - 1 > 0 {
                 swap(&list[index - 1], &list[index])
                 index -= 1
             }
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 1418656f3..52de1412e 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -283,7 +283,7 @@ extension SkipList {
 
 extension SkipList {
   
-  public func get(key:Key) -> Payload?{
+  public func get(key:Key) -> Payload? {
     return search(key: key)
   }
 }
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift
index 7da1eee60..69afe76e4 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
@@ -37,7 +37,7 @@ extension Array where Element: Number {
   public func dot(_ b: Array<Element>) -> Element {
     let a = self
     assert(a.count == b.count, "Can only take the dot product of arrays of the same length!")
-    let c = a.indices.map{ a[$0] * b[$0] }
+    let c = a.indices.map { a[$0] * b[$0] }
     return c.reduce(Element.zero, { $0 + $1 })
   }
 }

From 44adf5a8f6ac5e14ca74b761fbdd01083100ccf8 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 10:01:33 +0500
Subject: [PATCH 180/862] [swiftlint] Fix rule:
 empty_parentheses_with_trailing_closure

warning: Empty Parentheses with Trailing Closure Violation: When using trailing closures, empty parentheses should be avoided after the method call.
---
 All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift    | 2 +-
 Bloom Filter/BloomFilter.playground/Contents.swift        | 4 ++--
 Bloom Filter/BloomFilter.swift                            | 4 ++--
 Graph/Graph/AdjacencyListGraph.swift                      | 2 +-
 Graph/Graph/AdjacencyMatrixGraph.swift                    | 2 +-
 .../SSSP/BellmanFord.swift                                | 4 ++--
 Trie/Trie/TrieTests/TrieTests.swift                       | 8 ++++----
 7 files changed, 13 insertions(+), 13 deletions(-)

diff --git a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift
index b1a870f2a..7bc78f326 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/FloydWarshall.swift	
@@ -175,7 +175,7 @@ public struct FloydWarshallResult<T>: APSPResult where T: Hashable {
   public func path(fromVertex from: Vertex<T>, toVertex to: Vertex<T>, inGraph graph: AbstractGraph<T>) -> [T]? {
 
     if let path = recursePathFrom(fromVertex: from, toVertex: to, path: [ to ], inGraph: graph) {
-      let pathValues = path.map() { vertex in
+      let pathValues = path.map { vertex in
         vertex.data
       }
       return pathValues
diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index d5e7d2dc6..06022c9b3 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -10,7 +10,7 @@ public class BloomFilter<T> {
   }
 
   private func computeHashes(_ value: T) -> [Int] {
-    return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
+    return hashFunctions.map { hashFunc in abs(hashFunc(value) % array.count) }
   }
 
   public func insert(_ element: T) {
@@ -29,7 +29,7 @@ public class BloomFilter<T> {
     let hashValues = computeHashes(value)
 
     // Map hashes to indices in the Bloom Filter
-    let results = hashValues.map() { hashValue in array[hashValue] }
+    let results = hashValues.map { hashValue in array[hashValue] }
 
     // All values must be 'true' for the query to return true
 
diff --git a/Bloom Filter/BloomFilter.swift b/Bloom Filter/BloomFilter.swift
index 03b5333f1..56c3be328 100644
--- a/Bloom Filter/BloomFilter.swift	
+++ b/Bloom Filter/BloomFilter.swift	
@@ -8,7 +8,7 @@ public class BloomFilter<T> {
   }
 
   private func computeHashes(_ value: T) -> [Int] {
-    return hashFunctions.map() { hashFunc in abs(hashFunc(value) % array.count) }
+    return hashFunctions.map { hashFunc in abs(hashFunc(value) % array.count) }
   }
 
   public func insert(_ element: T) {
@@ -27,7 +27,7 @@ public class BloomFilter<T> {
     let hashValues = computeHashes(value)
 
     // Map hashes to indices in the Bloom Filter
-    let results = hashValues.map() { hashValue in array[hashValue] }
+    let results = hashValues.map { hashValue in array[hashValue] }
 
     // All values must be 'true' for the query to return true
 
diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index edb754c97..3d86c78f7 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -64,7 +64,7 @@ open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashab
 
   open override func createVertex(_ data: T) -> Vertex<T> {
     // check if the vertex already exists
-    let matchingVertices = vertices.filter() { vertex in
+    let matchingVertices = vertices.filter { vertex in
       return vertex.data == data
     }
 
diff --git a/Graph/Graph/AdjacencyMatrixGraph.swift b/Graph/Graph/AdjacencyMatrixGraph.swift
index 8f357bc8c..a9b43fb6d 100644
--- a/Graph/Graph/AdjacencyMatrixGraph.swift
+++ b/Graph/Graph/AdjacencyMatrixGraph.swift
@@ -46,7 +46,7 @@ open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Equatable, T: Hash
   // Performance: possibly O(n^2) because of the resizing of the matrix.
   open override func createVertex(_ data: T) -> Vertex<T> {
     // check if the vertex already exists
-    let matchingVertices = vertices.filter() { vertex in
+    let matchingVertices = vertices.filter { vertex in
       return vertex.data == data
     }
 
diff --git a/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift b/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift
index 5b6670806..41be9759b 100644
--- a/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift	
+++ b/Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift	
@@ -41,7 +41,7 @@ extension BellmanFord: SSSPAlgorithm {
 
     for _ in 0 ..< vertices.count - 1 {
       var weightsUpdated = false
-      edges.forEach() { edge in
+      edges.forEach { edge in
         let weight = edge.weight!
         let relaxedDistance = weights[edge.from.index] + weight
         let nextVertexIdx = edge.to.index
@@ -116,7 +116,7 @@ extension BellmanFordResult: SSSPResult {
       return nil
     }
 
-    return path.map() { vertex in
+    return path.map { vertex in
       return vertex.data
     }
   }
diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index 50a30a552..960b65791 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -101,7 +101,7 @@ class TrieTests: XCTestCase {
 
     /// Tests the performance of the insert method.
     func testInsertPerformance() {
-        self.measure() {
+        self.measure {
             let trie = Trie()
             for word in self.wordArray! {
                 trie.insert(word: word)
@@ -114,7 +114,7 @@ class TrieTests: XCTestCase {
     /// Tests the performance of the insert method when the words are already
     /// present.
     func testInsertAgainPerformance() {
-        self.measure() {
+        self.measure {
             for word in self.wordArray! {
                 self.trie.insert(word: word)
             }
@@ -123,7 +123,7 @@ class TrieTests: XCTestCase {
 
     /// Tests the performance of the contains method.
     func testContainsPerformance() {
-        self.measure() {
+        self.measure {
             for word in self.wordArray! {
                 XCTAssertTrue(self.trie.contains(word: word))
             }
@@ -136,7 +136,7 @@ class TrieTests: XCTestCase {
         for word in self.wordArray! {
             self.trie.remove(word: word)
         }
-        self.measure() {
+        self.measure {
             self.insertWordsIntoTrie()
             for word in self.wordArray! {
                 self.trie.remove(word: word)

From 71c0e32fbc9794289199c3a8bbe0e1719a9b2ece Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Fri, 28 Apr 2017 10:05:34 +0500
Subject: [PATCH 181/862] [swiftlint] Fix rule: colon (i.e. should be next to
 identifier)

warning: Colon Violation: Colons should be next to the identifier when specifying a type and next to the key in dictionary literals.
---
 .../BucketSort.playground/Sources/BucketSort.swift        | 2 +-
 Bucket Sort/BucketSort.swift                              | 2 +-
 Convex Hull/Convex Hull/View.swift                        | 2 +-
 Deque/Deque-Optimized.swift                               | 2 +-
 Linked List/LinkedList.playground/Contents.swift          | 2 +-
 Linked List/LinkedList.swift                              | 2 +-
 .../Red-Black Tree 2.playground/Sources/RBTree.swift      | 8 ++++----
 Skip-List/SkipList.swift                                  | 2 +-
 Topological Sort/Graph.swift                              | 4 ++--
 .../Topological Sort.playground/Sources/Graph.swift       | 4 ++--
 .../Sources/TopologicalSort1.swift                        | 2 +-
 Topological Sort/TopologicalSort1.swift                   | 2 +-
 12 files changed, 17 insertions(+), 17 deletions(-)

diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
index e510e51b4..08962c0e1 100644
--- a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -122,7 +122,7 @@ public struct InsertionSorter: Sorter {
 // MARK: Bucket
 //////////////////////////////////////
 
-public struct Bucket<T:Sortable> {
+public struct Bucket<T: Sortable> {
   var elements: [T]
   let capacity: Int
 
diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index ef72c67dc..ff36b372a 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -173,7 +173,7 @@ public struct InsertionSorter: Sorter {
 // MARK: Bucket
 //////////////////////////////////////
 
-public struct Bucket<T:Sortable> {
+public struct Bucket<T: Sortable> {
     var elements: [T]
     let capacity: Int
 
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index 2d7157e6f..f9f9f6ef4 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -150,7 +150,7 @@ class View: UIView {
         let context = UIGraphicsGetCurrentContext()
         
         // Draw hull
-        let lineWidth:CGFloat = 2.0
+        let lineWidth: CGFloat = 2.0
         
         context!.setFillColor(UIColor.black.cgColor)
         context!.setLineWidth(lineWidth)
diff --git a/Deque/Deque-Optimized.swift b/Deque/Deque-Optimized.swift
index f565458c7..4eea01f1a 100644
--- a/Deque/Deque-Optimized.swift
+++ b/Deque/Deque-Optimized.swift
@@ -7,7 +7,7 @@ public struct Deque<T> {
   private var array: [T?]
   private var head: Int
   private var capacity: Int
-  private let originalCapacity:Int
+  private let originalCapacity: Int
 
   public init(_ capacity: Int = 10) {
     self.capacity = max(capacity, 1)
diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 10677935a..08e14ef70 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -177,7 +177,7 @@ public final class LinkedList<T> {
     if list.isEmpty { return }
     var (prev, next) = nodesBeforeAndAfter(index: index)
     var nodeToCopy = list.head
-    var newNode:Node?
+    var newNode: Node?
     while let node = nodeToCopy {
       newNode = Node(value: node.value)
       newNode?.previous = prev
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index a7ef9bf5e..783e650e8 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -129,7 +129,7 @@ public final class LinkedList<T> {
         if list.isEmpty { return }
         var (prev, next) = nodesBeforeAndAfter(index: index)
         var nodeToCopy = list.head
-        var newNode:Node?
+        var newNode: Node?
         while let node = nodeToCopy {
             newNode = Node(value: node.value)
             newNode?.previous = prev
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
index 0038494d3..42a68237e 100644
--- a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -7,9 +7,9 @@ private enum RBTColor {
 public class RBTNode<T: Comparable>: CustomStringConvertible {
     fileprivate var color: RBTColor = .red
     public var value: T! = nil
-    public var right:  RBTNode<T>!
-    public var left:  RBTNode<T>!
-    public var parent:  RBTNode<T>!
+    public var right: RBTNode<T>!
+    public var left: RBTNode<T>!
+    public var parent: RBTNode<T>!
     
     public var description: String {
         if self.value == nil {
@@ -435,7 +435,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
     private func property3() {
         let bDepth = blackDepth(root: self.root)
         
-        let leaves:[RBTNode<T>] = getLeaves(n: self.root)
+        let leaves: [RBTNode<T>] = getLeaves(n: self.root)
         
         for leaflet in leaves {
             var leaf = leaflet
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 52de1412e..14b5a4076 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -283,7 +283,7 @@ extension SkipList {
 
 extension SkipList {
   
-  public func get(key:Key) -> Payload? {
+  public func get(key: Key) -> Payload? {
     return search(key: key)
   }
 }
diff --git a/Topological Sort/Graph.swift b/Topological Sort/Graph.swift
index 1e1be6919..5032ba1d1 100644
--- a/Topological Sort/Graph.swift	
+++ b/Topological Sort/Graph.swift	
@@ -4,7 +4,7 @@ public class Graph: CustomStringConvertible {
   private(set) public var adjacencyLists: [Node : [Node]]
 
   public init() {
-    adjacencyLists = [Node : [Node]]()
+    adjacencyLists = [Node: [Node]]()
   }
 
   public func addNode(_ value: Node) -> Node {
@@ -35,7 +35,7 @@ extension Graph {
   typealias InDegree = Int
 
   func calculateInDegreeOfNodes() -> [Node : InDegree] {
-    var inDegrees = [Node : InDegree]()
+    var inDegrees = [Node: InDegree]()
 
     for (node, _) in adjacencyLists {
       inDegrees[node] = 0
diff --git a/Topological Sort/Topological Sort.playground/Sources/Graph.swift b/Topological Sort/Topological Sort.playground/Sources/Graph.swift
index 1e1be6919..5032ba1d1 100644
--- a/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/Graph.swift	
@@ -4,7 +4,7 @@ public class Graph: CustomStringConvertible {
   private(set) public var adjacencyLists: [Node : [Node]]
 
   public init() {
-    adjacencyLists = [Node : [Node]]()
+    adjacencyLists = [Node: [Node]]()
   }
 
   public func addNode(_ value: Node) -> Node {
@@ -35,7 +35,7 @@ extension Graph {
   typealias InDegree = Int
 
   func calculateInDegreeOfNodes() -> [Node : InDegree] {
-    var inDegrees = [Node : InDegree]()
+    var inDegrees = [Node: InDegree]()
 
     for (node, _) in adjacencyLists {
       inDegrees[node] = 0
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift
index 0f9566f6a..4d3717fe6 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
@@ -23,7 +23,7 @@ extension Graph {
       return node
     })
 
-    var visited = [Node : Bool]()
+    var visited = [Node: Bool]()
     for (node, _) in adjacencyLists {
       visited[node] = false
     }
diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
index 0f9566f6a..4d3717fe6 100644
--- a/Topological Sort/TopologicalSort1.swift	
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -23,7 +23,7 @@ extension Graph {
       return node
     })
 
-    var visited = [Node : Bool]()
+    var visited = [Node: Bool]()
     for (node, _) in adjacencyLists {
       visited[node] = false
     }

From c4fdd035df77487756eee2389d18c89f9dc652cd Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sat, 29 Apr 2017 00:52:39 -0700
Subject: [PATCH 182/862] switch removeFirst to dropFirst

we don't need a mutable copy of `array` to alter it, instead we can just drop the first element
---
 Select Minimum Maximum/Maximum.swift | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/Select Minimum Maximum/Maximum.swift b/Select Minimum Maximum/Maximum.swift
index 991a0544e..c999504fb 100644
--- a/Select Minimum Maximum/Maximum.swift	
+++ b/Select Minimum Maximum/Maximum.swift	
@@ -3,13 +3,12 @@
  */
 
 func maximum<T: Comparable>(_ array: [T]) -> T? {
-    var array = array
     guard !array.isEmpty else {
         return nil
     }
 
-    var maximum = array.removeFirst()
-    for element in array {
+    var maximum = array.first!
+    for element in array.dropFirst() {
         maximum = element > maximum ? element : maximum
     }
     return maximum

From 5e7fc5487f833fd96852d21d7f856c300956a62b Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sat, 29 Apr 2017 00:56:51 -0700
Subject: [PATCH 183/862] switch removeFirst to dropFirst

we don't need to alter a mutable copy of `array`, instead we can just drop the first element.
---
 Select Minimum Maximum/Minimum.swift | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/Select Minimum Maximum/Minimum.swift b/Select Minimum Maximum/Minimum.swift
index 90dfbd54b..88a562170 100644
--- a/Select Minimum Maximum/Minimum.swift	
+++ b/Select Minimum Maximum/Minimum.swift	
@@ -3,13 +3,12 @@
  */
 
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-    var array = array
     guard !array.isEmpty else {
         return nil
     }
 
-    var minimum = array.removeFirst()
-    for element in array {
+    var minimum = array.first!
+    for element in array.dropFirst() {
         minimum = element < minimum ? element : minimum
     }
     return minimum

From e15e1330417dcbe2222d2606a35dd5462eac6b2c Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sat, 29 Apr 2017 18:14:37 -0700
Subject: [PATCH 184/862] switch from removeFirst to stride for pairing

We don't need to alter a local copy of `array` to generate each pair, instead use stride(from:to:by).  In my simple [tests](https://gist.github.com/TheIronBorn/cc0507b36fddad291aa34674eb52ad8f), this can be up to an order of magnitude faster.
---
 Select Minimum Maximum/MinimumMaximumPairs.swift | 13 +++++--------
 1 file changed, 5 insertions(+), 8 deletions(-)

diff --git a/Select Minimum Maximum/MinimumMaximumPairs.swift b/Select Minimum Maximum/MinimumMaximumPairs.swift
index b7deb570a..2c7b5bb5f 100644
--- a/Select Minimum Maximum/MinimumMaximumPairs.swift	
+++ b/Select Minimum Maximum/MinimumMaximumPairs.swift	
@@ -3,7 +3,6 @@
  */
 
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-    var array = array
     guard !array.isEmpty else {
         return nil
     }
@@ -11,13 +10,11 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
     var minimum = array.first!
     var maximum = array.first!
 
+    // if 'array' has an odd number of items, let 'minimum' or 'maximum' deal with the leftover
     let hasOddNumberOfItems = array.count % 2 != 0
-    if hasOddNumberOfItems {
-        array.removeFirst()
-    }
-
-    while !array.isEmpty {
-        let pair = (array.removeFirst(), array.removeFirst())
+    let start = hasOddNumberOfItems ? 1 : 0
+    for i in stride(from: start, to: array.count, by: 2) {
+        let pair = (array[i], array[i+1])
 
         if pair.0 > pair.1 {
             if pair.0 > maximum {
@@ -35,6 +32,6 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
             }
         }
     }
-    
+
     return (minimum, maximum)
 }

From b8d668d3883f79754aa83f5944a3e3d97e13d3a6 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sat, 29 Apr 2017 18:19:43 -0700
Subject: [PATCH 185/862] update to match source

---
 Select Minimum Maximum/README.markdown | 20 ++++++++------------
 1 file changed, 8 insertions(+), 12 deletions(-)

diff --git a/Select Minimum Maximum/README.markdown b/Select Minimum Maximum/README.markdown
index fa0f8fed8..3c29b5764 100644
--- a/Select Minimum Maximum/README.markdown	
+++ b/Select Minimum Maximum/README.markdown	
@@ -24,26 +24,24 @@ Here is a simple implementation in Swift:
 
 ```swift
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
 
-  var minimum = array.removeFirst()
-  for element in array {
+  var minimum = array.first!
+  for element in array.dropFirst() {
     minimum = element < minimum ? element : minimum
   }
   return minimum
 }
 
 func maximum<T: Comparable>(_ array: [T]) -> T? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
 
-  var maximum = array.removeFirst()
-  for element in array {
+  var maximum = array.first!
+  for element in array.dropFirst() {
     maximum = element > maximum ? element : maximum
   }
   return maximum
@@ -99,7 +97,6 @@ Here is a simple implementation in Swift:
 
 ```swift
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
@@ -107,13 +104,12 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
   var minimum = array.first!
   var maximum = array.first!
 
+  // if 'array' has an odd number of items, let 'minimum' or 'maximum' deal with the leftover
   let hasOddNumberOfItems = array.count % 2 != 0
-  if hasOddNumberOfItems {
-    array.removeFirst()
-  }
+  let start = hasOddNumberOfItems ? 1 : 0
+  for i in stride(from: start, to: array.count, by: 2) {
+    let pair = (array[i], array[i+1])
 
-  while !array.isEmpty {
-    let pair = (array.removeFirst(), array.removeFirst())
     if pair.0 > pair.1 {
       if pair.0 > maximum {
         maximum = pair.0

From 5ddf933c48da612a9489c77b095496b0c80c1b66 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sat, 29 Apr 2017 18:21:35 -0700
Subject: [PATCH 186/862] update to match source

---
 .../Contents.swift                            | 33 ++++++++-----------
 1 file changed, 14 insertions(+), 19 deletions(-)

diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift
index 182060805..427ccdb9e 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
+++ b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
@@ -1,12 +1,11 @@
 // Compare each item to find minimum
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
-  
-  var minimum = array.removeFirst()
-  for element in array {
+
+  var minimum = array.first!
+  for element in array.dropFirst() {
     minimum = element < minimum ? element : minimum
   }
   return minimum
@@ -14,13 +13,12 @@ func minimum<T: Comparable>(_ array: [T]) -> T? {
 
 // Compare each item to find maximum
 func maximum<T: Comparable>(_ array: [T]) -> T? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
-  
-  var maximum = array.removeFirst()
-  for element in array {
+
+  var maximum = array.first!
+  for element in array.dropFirst() {
     maximum = element > maximum ? element : maximum
   }
   return maximum
@@ -28,22 +26,19 @@ func maximum<T: Comparable>(_ array: [T]) -> T? {
 
 // Compare in pairs to find minimum and maximum
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-  var array = array
   guard !array.isEmpty else {
     return nil
   }
-  
+
   var minimum = array.first!
   var maximum = array.first!
-  
+
+  // if 'array' has an odd number of items, let 'minimum' or 'maximum' deal with the leftover
   let hasOddNumberOfItems = array.count % 2 != 0
-  if hasOddNumberOfItems {
-    array.removeFirst()
-  }
-  
-  while !array.isEmpty {
-    let pair = (array.removeFirst(), array.removeFirst())
-    
+  let start = hasOddNumberOfItems ? 1 : 0
+  for i in stride(from: start, to: array.count, by: 2) {
+    let pair = (array[i], array[i+1])
+
     if pair.0 > pair.1 {
       if pair.0 > maximum {
         maximum = pair.0
@@ -60,7 +55,7 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
       }
     }
   }
-  
+
   return (minimum, maximum)
 }
 

From 3f156498b0cb043f103eef22216f2e4e9df6edd6 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 1 May 2017 01:03:09 +0500
Subject: [PATCH 187/862] Fix alignment by adding an additional tab

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

diff --git a/Tree/README.markdown b/Tree/README.markdown
index 440d9c9a4..566864a8f 100644
--- a/Tree/README.markdown
+++ b/Tree/README.markdown
@@ -153,7 +153,7 @@ tree.search("bubbly")   // nil
 
 It's also possible to describe a tree using nothing more than an array. The indices in the array then create the links between the different nodes. For example, if we have:
 
-	0 = beverage	5 = cocoa		9  = green
+	0 = beverage		5 = cocoa		9  = green
 	1 = hot			6 = soda		10 = chai
 	2 = cold		7 = milk		11 = ginger ale
 	3 = tea			8 = black		12 = bitter lemon

From 32457ce5aca5bcdee4acc1f8d6f6c0c6a075daba Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 1 May 2017 02:03:34 +0500
Subject: [PATCH 188/862] Fix misindented return statement

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

diff --git a/Trie/ReadMe.md b/Trie/ReadMe.md
index 7caa927a7..356f6887e 100644
--- a/Trie/ReadMe.md
+++ b/Trie/ReadMe.md
@@ -46,7 +46,7 @@ func contains(word: String) -> Bool {
 	if currentIndex == characters.count && currentNode.isTerminating {
 	  return true
 	} else {
-		return false
+	  return false
 	}
 }
 ```

From 09f2c8fb8564bd956beb1a067b6ad21255bad97c Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 1 May 2017 05:25:13 +0500
Subject: [PATCH 189/862] [swiftlint] Fix rule: force_cast (Force casts should
 be avoided)

---
 Trie/Trie/TrieTests/TrieTests.swift | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Trie/Trie/TrieTests/TrieTests.swift b/Trie/Trie/TrieTests/TrieTests.swift
index 960b65791..b69c5666e 100644
--- a/Trie/Trie/TrieTests/TrieTests.swift
+++ b/Trie/Trie/TrieTests/TrieTests.swift
@@ -164,8 +164,8 @@ class TrieTests: XCTestCase {
         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)
+        let trieCopy = NSKeyedUnarchiver.unarchiveObject(withFile: filePath) as? Trie
+        XCTAssertEqual(trieCopy?.count, trie.count)
 
     }
 

From b1319ce90d5288e20ee02b56390c61895d1d7765 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:23:06 +0500
Subject: [PATCH 190/862] [swiftlint] Fix violation: unused_closure_parameter

warning: Unused Closure Parameter Violation: Unused parameters in a closure should be replaced with _.
---
 B-Tree/Tests/Tests/BTreeTests.swift                             | 2 +-
 .../Topological Sort.playground/Sources/TopologicalSort1.swift  | 2 +-
 .../Topological Sort.playground/Sources/TopologicalSort2.swift  | 2 +-
 Topological Sort/TopologicalSort1.swift                         | 2 +-
 Topological Sort/TopologicalSort2.swift                         | 2 +-
 5 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/B-Tree/Tests/Tests/BTreeTests.swift b/B-Tree/Tests/Tests/BTreeTests.swift
index c8db17fa3..f2dac7511 100644
--- a/B-Tree/Tests/Tests/BTreeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeTests.swift
@@ -31,7 +31,7 @@ class BTreeTests: XCTestCase {
   }
   
   func testInorderTraversalOfEmptyTree() {
-    bTree.traverseKeysInOrder { i in
+    bTree.traverseKeysInOrder { _ in
       XCTFail("Inorder travelsal fail.")
     }
   }
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift
index 4d3717fe6..2ad9b51a0 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort1.swift	
@@ -19,7 +19,7 @@ extension Graph {
 
     let startNodes = calculateInDegreeOfNodes().filter({ _, indegree in
       return indegree == 0
-    }).map({ node, indegree in
+    }).map({ node, _ in
       return node
     })
 
diff --git a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift
index f4c1cdd6f..589801d33 100644
--- a/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift	
+++ b/Topological Sort/Topological Sort.playground/Sources/TopologicalSort2.swift	
@@ -8,7 +8,7 @@ extension Graph {
     // topologically sorted list.
     var leaders = nodes.filter({ _, indegree in
       return indegree == 0
-    }).map({ node, indegree in
+    }).map({ node, _ in
       return node
     })
 
diff --git a/Topological Sort/TopologicalSort1.swift b/Topological Sort/TopologicalSort1.swift
index 4d3717fe6..2ad9b51a0 100644
--- a/Topological Sort/TopologicalSort1.swift	
+++ b/Topological Sort/TopologicalSort1.swift	
@@ -19,7 +19,7 @@ extension Graph {
 
     let startNodes = calculateInDegreeOfNodes().filter({ _, indegree in
       return indegree == 0
-    }).map({ node, indegree in
+    }).map({ node, _ in
       return node
     })
 
diff --git a/Topological Sort/TopologicalSort2.swift b/Topological Sort/TopologicalSort2.swift
index f4c1cdd6f..589801d33 100644
--- a/Topological Sort/TopologicalSort2.swift	
+++ b/Topological Sort/TopologicalSort2.swift	
@@ -8,7 +8,7 @@ extension Graph {
     // topologically sorted list.
     var leaders = nodes.filter({ _, indegree in
       return indegree == 0
-    }).map({ node, indegree in
+    }).map({ node, _ in
       return node
     })
 

From 9107542b7753210cef8eaf982373db377f6a8a62 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:25:35 +0500
Subject: [PATCH 191/862] [swiftlint] Fix violation: redundant_discardable_let

warning: Redundant Discardable Let Violation: Prefer `_ = foo()` over `let _ = foo()` when discarding a result from a function.
---
 Breadth-First Search/Tests/Graph.swift | 2 +-
 Palindromes/Test/Test/Test.swift       | 6 +++---
 Treap/TreapCollectionType.swift        | 2 +-
 3 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/Breadth-First Search/Tests/Graph.swift b/Breadth-First Search/Tests/Graph.swift
index 5e0837160..a8c34b3f6 100644
--- a/Breadth-First Search/Tests/Graph.swift	
+++ b/Breadth-First Search/Tests/Graph.swift	
@@ -86,7 +86,7 @@ public class Graph: CustomStringConvertible, Equatable {
     let duplicated = Graph()
 
     for node in nodes {
-      let _ = duplicated.addNode(node.label)
+      _ = duplicated.addNode(node.label)
     }
 
     for node in nodes {
diff --git a/Palindromes/Test/Test/Test.swift b/Palindromes/Test/Test/Test.swift
index e86a40cfb..1dd79ea97 100644
--- a/Palindromes/Test/Test/Test.swift
+++ b/Palindromes/Test/Test/Test.swift
@@ -29,9 +29,9 @@ class PalindromeTests: XCTestCase {
         // This is an example of a performance test case.
         self.measure {
             // Put the code you want to measure the time of here.
-            let _ = isPalindrome("abbcbba")
-            let _ = isPalindrome("asdkfaksjdfasjkdfhaslkjdfakjsdfhakljsdhflkjasdfhkasdjhfklajsdfhkljasdf")
-            let _ = isPalindrome("abababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababa")
+            _ = isPalindrome("abbcbba")
+            _ = isPalindrome("asdkfaksjdfasjkdfhaslkjdfakjsdfhakljsdhflkjasdfhkasdjhfklajsdfhkljasdf")
+            _ = isPalindrome("abababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababa")
         }
     }
     
diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
index de40464d1..9f7f81905 100644
--- a/Treap/TreapCollectionType.swift
+++ b/Treap/TreapCollectionType.swift
@@ -50,7 +50,7 @@ extension Treap: MutableCollection {
     
     mutating set {
       guard let value = newValue else {
-        let _ = try? self.delete(key: key)
+        _ = try? self.delete(key: key)
         return
       }
       

From c67a277487e3611ad51b0c88855540d3f56f58bb Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:34:24 +0500
Subject: [PATCH 192/862] [swiftlint] Fix violation: operator_whitespace

warning: Operator Function Whitespace Violation: Operators should be surrounded by a single whitespace when defining them.

Apple has also used spacing in The Swift Programming Language book
https://developer.apple.com/library/content/documentation/Swift/Conceptual/Swift_Programming_Language/AdvancedOperators.html#//apple_ref/doc/uid/TP40014097-CH27-ID42
---
 QuadTree/Tests/Tests/Tests.swift                            | 2 +-
 .../Sources/Matrix.swift                                    | 2 +-
 .../Sources/Number.swift                                    | 6 +++---
 Treap/TreapCollectionType.swift                             | 2 +-
 4 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/QuadTree/Tests/Tests/Tests.swift b/QuadTree/Tests/Tests/Tests.swift
index b7bcda4e6..b408c4f7e 100644
--- a/QuadTree/Tests/Tests/Tests.swift
+++ b/QuadTree/Tests/Tests/Tests.swift
@@ -12,7 +12,7 @@ extension Point: Equatable {
 
 }
 
-public func ==(lhs: Point, rhs: Point) -> Bool {
+public func == (lhs: Point, rhs: Point) -> Bool {
   return lhs.x == rhs.x && lhs.y == rhs.y
 }
 
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index c13b3eeee..ccfa58b09 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -19,7 +19,7 @@ public struct Matrix<T: Number> {
   public struct Size: Equatable {
     let rows: Int, columns: Int
     
-    public static func ==(lhs: Size, rhs: Size) -> Bool {
+    public static func == (lhs: Size, rhs: Size) -> Bool {
       return lhs.columns == rhs.columns && lhs.rows == rhs.rows
     }
   }
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift
index 69afe76e4..d53ef75bd 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Number.swift	
@@ -13,12 +13,12 @@ public protocol Number: Multipliable, Addable {
 }
 
 public protocol Addable {
-  static func +(lhs: Self, rhs: Self) -> Self
-  static func -(lhs: Self, rhs: Self) -> Self
+  static func + (lhs: Self, rhs: Self) -> Self
+  static func - (lhs: Self, rhs: Self) -> Self
 }
 
 public protocol Multipliable {
-  static func *(lhs: Self, rhs: Self) -> Self
+  static func * (lhs: Self, rhs: Self) -> Self
 }
 
 extension Int: Number {
diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
index 9f7f81905..7292c5f0a 100644
--- a/Treap/TreapCollectionType.swift
+++ b/Treap/TreapCollectionType.swift
@@ -85,7 +85,7 @@ extension Treap: MutableCollection {
 
 public struct TreapIndex<Key: Comparable>: Comparable {
   
-  public static func <(lhs: TreapIndex<Key>, rhs: TreapIndex<Key>) -> Bool {
+  public static func < (lhs: TreapIndex<Key>, rhs: TreapIndex<Key>) -> Bool {
     return lhs.keyIndex < rhs.keyIndex
   }
   

From 18c7b435cec0eafb657f28f7c80345d8a7aa513a Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:41:07 +0500
Subject: [PATCH 193/862] [swiftlint] Fix violation: Colons should be next to
 the identifier

warning: Colon Violation: Colons should be next to the identifier when specifying a type and next to the key in dictionary literals.
---
 Bucket Sort/BucketSort.swift |  4 ++--
 Skip-List/SkipList.swift     | 12 ++++++------
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index ff36b372a..5845819f2 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -23,7 +23,7 @@
 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 {
+fileprivate func < <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
   switch (lhs, rhs) {
   case let (l?, r?):
     return l < r
@@ -36,7 +36,7 @@ fileprivate func < <T : Comparable>(lhs: T?, rhs: T?) -> Bool {
 
 // 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 {
+fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
   switch (lhs, rhs) {
   case let (l?, r?):
     return l >= r
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index 14b5a4076..e844f9959 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -71,10 +71,10 @@ private func coinFlip() -> Bool {
 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?
+  var data: Payload?  
+  fileprivate var key: Key?
+  var next: Node?
+  var down: Node?
   
   public init(key: Key, data: Payload) {
     self.key  = key
@@ -102,8 +102,8 @@ open class SkipList<Key: Comparable, Payload> {
 extension SkipList {
   
   func findNode(key: Key) -> Node? {
-    var currentNode : Node? = head
-    var isFound     : Bool  = false
+    var currentNode: Node? = head
+    var isFound: Bool = false
 
     while !isFound {
       if let node = currentNode {

From e3a4494138ca4776aab23bed0428b3e4063395ca Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:47:57 +0500
Subject: [PATCH 194/862] [swiftlint] Fix violation: Computed properties should
 avoid using get

Rule: implicit_getter
warning: Implicit Getter Violation: Computed read-only properties should avoid using the get keyword.
---
 Graph/Graph/AdjacencyListGraph.swift   | 58 ++++++++++++--------------
 Graph/Graph/AdjacencyMatrixGraph.swift | 44 +++++++++----------
 Graph/Graph/Edge.swift                 | 19 ++++-----
 Graph/Graph/Graph.swift                | 12 ++----
 Graph/Graph/Vertex.swift               |  8 +---
 Treap/Treap.swift                      | 31 ++++++--------
 Treap/TreapMergeSplit.swift            |  4 +-
 7 files changed, 71 insertions(+), 105 deletions(-)

diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index 3d86c78f7..57fd75fed 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -37,29 +37,25 @@ open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashab
   }
 
   open override var vertices: [Vertex<T>] {
-    get {
-      var vertices = [Vertex<T>]()
-      for edgeList in adjacencyList {
-        vertices.append(edgeList.vertex)
-      }
-      return vertices
+    var vertices = [Vertex<T>]()
+    for edgeList in adjacencyList {
+      vertices.append(edgeList.vertex)
     }
+    return vertices
   }
 
   open override var edges: [Edge<T>] {
-    get {
-      var allEdges = Set<Edge<T>>()
-      for edgeList in adjacencyList {
-        guard let edges = edgeList.edges else {
-          continue
-        }
+    var allEdges = Set<Edge<T>>()
+    for edgeList in adjacencyList {
+      guard let edges = edgeList.edges else {
+        continue
+      }
 
-        for edge in edges {
-          allEdges.insert(edge)
-        }
+      for edge in edges {
+        allEdges.insert(edge)
       }
-      return Array(allEdges)
     }
+    return Array(allEdges)
   }
 
   open override func createVertex(_ data: T) -> Vertex<T> {
@@ -114,27 +110,25 @@ open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashab
   }
 
   open override var description: String {
-    get {
-      var rows = [String]()
-      for edgeList in adjacencyList {
+    var rows = [String]()
+    for edgeList in adjacencyList {
 
-        guard let edges = edgeList.edges else {
-          continue
-        }
+      guard let edges = edgeList.edges else {
+        continue
+      }
 
-        var row = [String]()
-        for edge in edges {
-          var value = "\(edge.to.data)"
-          if edge.weight != nil {
-            value = "(\(value): \(edge.weight!))"
-          }
-          row.append(value)
+      var row = [String]()
+      for edge in edges {
+        var value = "\(edge.to.data)"
+        if edge.weight != nil {
+          value = "(\(value): \(edge.weight!))"
         }
-
-        rows.append("\(edgeList.vertex.data) -> [\(row.joined(separator: ", "))]")
+        row.append(value)
       }
 
-      return rows.joined(separator: "\n")
+      rows.append("\(edgeList.vertex.data) -> [\(row.joined(separator: ", "))]")
     }
+
+    return rows.joined(separator: "\n")
   }
 }
diff --git a/Graph/Graph/AdjacencyMatrixGraph.swift b/Graph/Graph/AdjacencyMatrixGraph.swift
index a9b43fb6d..1b12790d8 100644
--- a/Graph/Graph/AdjacencyMatrixGraph.swift
+++ b/Graph/Graph/AdjacencyMatrixGraph.swift
@@ -23,23 +23,19 @@ open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Equatable, T: Hash
   }
 
   open override var vertices: [Vertex<T>] {
-    get {
-      return _vertices
-    }
+    return _vertices
   }
 
   open override var edges: [Edge<T>] {
-    get {
-      var edges = [Edge<T>]()
-      for row in 0 ..< adjacencyMatrix.count {
-        for column in 0 ..< adjacencyMatrix.count {
-          if let weight = adjacencyMatrix[row][column] {
-            edges.append(Edge(from: vertices[row], to: vertices[column], weight: weight))
-          }
+    var edges = [Edge<T>]()
+    for row in 0 ..< adjacencyMatrix.count {
+      for column in 0 ..< adjacencyMatrix.count {
+        if let weight = adjacencyMatrix[row][column] {
+          edges.append(Edge(from: vertices[row], to: vertices[column], weight: weight))
         }
       }
-      return edges
     }
+    return edges
   }
 
   // Adds a new vertex to the matrix.
@@ -96,23 +92,21 @@ open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Equatable, T: Hash
   }
 
   open override var description: String {
-    get {
-      var grid = [String]()
-      let n = self.adjacencyMatrix.count
-      for i in 0..<n {
-        var row = ""
-        for j in 0..<n {
-          if let value = self.adjacencyMatrix[i][j] {
-            let number = NSString(format: "%.1f", value)
-            row += "\(value >= 0 ? " " : "")\(number) "
-          } else {
-            row += "  ø  "
-          }
+    var grid = [String]()
+    let n = self.adjacencyMatrix.count
+    for i in 0..<n {
+      var row = ""
+      for j in 0..<n {
+        if let value = self.adjacencyMatrix[i][j] {
+          let number = NSString(format: "%.1f", value)
+          row += "\(value >= 0 ? " " : "")\(number) "
+        } else {
+          row += "  ø  "
         }
-        grid.append(row)
       }
-      return (grid as NSArray).componentsJoined(by: "\n")
+      grid.append(row)
     }
+    return (grid as NSArray).componentsJoined(by: "\n")
   }
 
 }
diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index 03518da83..28ef91834 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -19,12 +19,10 @@ public struct Edge<T>: Equatable where T: Equatable, T: Hashable {
 extension Edge: CustomStringConvertible {
 
   public var description: String {
-    get {
-      guard let unwrappedWeight = weight else {
-        return "\(from.description) -> \(to.description)"
-      }
-      return "\(from.description) -(\(unwrappedWeight))-> \(to.description)"
+    guard let unwrappedWeight = weight else {
+      return "\(from.description) -> \(to.description)"
     }
+    return "\(from.description) -(\(unwrappedWeight))-> \(to.description)"
   }
 
 }
@@ -32,15 +30,12 @@ extension Edge: CustomStringConvertible {
 extension Edge: Hashable {
 
   public var hashValue: Int {
-    get {
-      var string = "\(from.description)\(to.description)"
-      if weight != nil {
-        string.append("\(weight!)")
-      }
-      return string.hashValue
+    var string = "\(from.description)\(to.description)"
+    if weight != nil {
+      string.append("\(weight!)")
     }
+    return string.hashValue
   }
-
 }
 
 public func == <T>(lhs: Edge<T>, rhs: Edge<T>) -> Bool {
diff --git a/Graph/Graph/Graph.swift b/Graph/Graph/Graph.swift
index 2ad91608b..13d6802b9 100644
--- a/Graph/Graph/Graph.swift
+++ b/Graph/Graph/Graph.swift
@@ -21,21 +21,15 @@ open class AbstractGraph<T>: CustomStringConvertible where T: Equatable, T: Hash
   }
 
   open var description: String {
-    get {
-      fatalError("abstract property accessed")
-    }
+    fatalError("abstract property accessed")
   }
 
   open var vertices: [Vertex<T>] {
-    get {
-      fatalError("abstract property accessed")
-    }
+    fatalError("abstract property accessed")
   }
 
   open var edges: [Edge<T>] {
-    get {
-      fatalError("abstract property accessed")
-    }
+    fatalError("abstract property accessed")
   }
 
   // Adds a new vertex to the matrix.
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index 43cabcd1f..42a7dad7b 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -17,9 +17,7 @@ public struct Vertex<T>: Equatable where T: Equatable, T: Hashable {
 extension Vertex: CustomStringConvertible {
 
   public var description: String {
-    get {
-      return "\(index): \(data)"
-    }
+    return "\(index): \(data)"
   }
 
 }
@@ -27,9 +25,7 @@ extension Vertex: CustomStringConvertible {
 extension Vertex: Hashable {
 
   public var hashValue: Int {
-    get {
-      return "\(data)\(index)".hashValue
-    }
+    return "\(data)\(index)".hashValue
   }
 
 }
diff --git a/Treap/Treap.swift b/Treap/Treap.swift
index 478f248df..6e80abfb2 100644
--- a/Treap/Treap.swift
+++ b/Treap/Treap.swift
@@ -63,27 +63,22 @@ public indirect enum Treap<Key: Comparable, Element> {
   }
   
   public var depth: Int {
-    get {
-      switch self {
-      case .empty:
-        return 0
-      case let .node(_, _, _, left, .empty):
-        return 1 + left.depth
-      case let .node(_, _, _, .empty, right):
-        return 1 + right.depth
-      case let .node(_, _, _, left, right):
-        let leftDepth = left.depth
-        let rightDepth = right.depth
-        return 1 + leftDepth > rightDepth ? leftDepth : rightDepth
-      }
-      
+    switch self {
+    case .empty:
+      return 0
+    case let .node(_, _, _, left, .empty):
+      return 1 + left.depth
+    case let .node(_, _, _, .empty, right):
+      return 1 + right.depth
+    case let .node(_, _, _, left, right):
+      let leftDepth = left.depth
+      let rightDepth = right.depth
+      return 1 + leftDepth > rightDepth ? leftDepth : rightDepth
     }
   }
-  
+
   public var count: Int {
-    get {
-      return Treap.countHelper(self)
-    }
+    return Treap.countHelper(self)
   }
   
   fileprivate static func countHelper(_ treap: Treap<Key, Element>) -> Int {
diff --git a/Treap/TreapMergeSplit.swift b/Treap/TreapMergeSplit.swift
index 660bd4932..34cfec3d2 100644
--- a/Treap/TreapMergeSplit.swift
+++ b/Treap/TreapMergeSplit.swift
@@ -94,9 +94,7 @@ internal func merge<Key: Comparable, Element>(_ left: Treap<Key, Element>, right
 
 extension Treap: CustomStringConvertible {
   public var description: String {
-    get {
-      return Treap.descHelper(self, indent: 0)
-    }
+    return Treap.descHelper(self, indent: 0)
   }
   
   fileprivate static func descHelper(_ treap: Treap<Key, Element>, indent: Int) -> String {

From 9af41f20ed8318739bd4f1d582a6789fe650e9b5 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:49:49 +0500
Subject: [PATCH 195/862] [swiftlint] Fix violation: trailing_whitespace

---
 Array2D/Array2D.playground/Contents.swift     |   4 +-
 Array2D/Array2D.swift                         |   4 +-
 B-Tree/BTree.playground/Sources/BTree.swift   | 108 +++++++-------
 B-Tree/BTree.swift                            | 108 +++++++-------
 B-Tree/Tests/Tests/BTreeNodeTests.swift       |  18 +--
 B-Tree/Tests/Tests/BTreeTests.swift           | 112 +++++++-------
 .../Contents.swift                            |   2 +-
 .../Sources/Comb Sort.swift                   |   4 +-
 Comb Sort/Comb Sort.swift                     |   4 +-
 Comb Sort/Tests/CombSortTests.swift           |   2 +-
 Convex Hull/Convex Hull/AppDelegate.swift     |   8 +-
 Convex Hull/Convex Hull/View.swift            |  80 +++++-----
 .../FixedSizeArray.playground/Contents.swift  |  10 +-
 Graph/Graph.playground/Contents.swift         |   2 +-
 .../HashSet.playground/Sources/HashSet.swift  |  16 +-
 .../Sources/HashTable.swift                   |  28 ++--
 .../Contents.swift                            |  10 +-
 Heap/Heap.swift                               |   4 +-
 Heap/Tests/HeapTests.swift                    |   4 +-
 Huffman Coding/Huffman.swift                  |  34 ++---
 Huffman Coding/NSData+Bits.swift              |   8 +-
 .../Contents.swift                            |  16 +-
 .../KaratsubaMultiplication.swift             |  12 +-
 Knuth-Morris-Pratt/KnuthMorrisPratt.swift     |  26 ++--
 .../LinkedList.playground/Contents.swift      |  62 ++++----
 Linked List/LinkedList.swift                  |  62 ++++----
 Linked List/Tests/LinkedListTests.swift       |  18 +--
 .../Sources/MRPrimality.swift                 |  28 ++--
 Miller-Rabin Primality Test/MRPrimality.swift |  28 ++--
 .../Contents.swift                            |   8 +-
 .../OrderedArray.playground/Contents.swift    |   2 +-
 .../Palindromes.playground/Contents.swift     |   8 +-
 Palindromes/Palindromes.swift                 |   8 +-
 Palindromes/Test/Palindromes.swift            |   8 +-
 Palindromes/Test/Test/Test.swift              |  18 +--
 .../Sources/QuadTree.swift                    |  88 +++++------
 QuadTree/Tests/Tests/Tests.swift              |  34 ++---
 .../Sources/radixSort.swift                   |  18 +--
 Radix Sort/RadixSortExample.swift             |  12 +-
 Radix Sort/radixSort.swift                    |  18 +--
 .../Contents.swift                            |   2 +-
 .../Sources/RBTree.swift                      | 138 +++++++++---------
 .../RLE.playground/Contents.swift             |  14 +-
 .../RLE.playground/Sources/RLE.swift          |  12 +-
 .../SegmentTree.playground/Contents.swift     |  18 +--
 Segment Tree/SegmentTree.swift                |  16 +-
 .../MinimumMaximumPairs.swift                 |   2 +-
 .../Contents.swift                            |  14 +-
 Shell Sort/ShellSortExample.swift             |  10 +-
 Shortest Path (Unweighted)/Tests/Graph.swift  |  32 ++--
 .../ShuntingYard.playground/Contents.swift    |  52 +++----
 .../Sources/Stack.swift                       |  14 +-
 Shunting Yard/ShuntingYard.swift              |  52 +++----
 Skip-List/SkipList.swift                      |  84 +++++------
 .../Sources/Matrix.swift                      |  88 +++++------
 .../TST.playground/Sources/Utils.swift        |   8 +-
 .../Tests/TernarySearchTreeTests.swift        |  18 +--
 Ternary Search Tree/Utils.swift               |   8 +-
 .../Sources/ThreadedBinaryTree.swift          |  52 +++----
 Treap/Treap.swift                             |  18 +--
 Treap/Treap/TreapTests/TreapTests.swift       |  12 +-
 Treap/TreapCollectionType.swift               |  34 ++---
 Treap/TreapMergeSplit.swift                   |  14 +-
 Trie/Trie/Trie/Trie.swift                     |  16 +-
 Trie/Trie/TrieUITests/TrieUITests.swift       |  12 +-
 Z-Algorithm/ZAlgorithm.swift                  |  22 +--
 .../ZetaAlgorithm.playground/Contents.swift   |  34 ++---
 Z-Algorithm/ZetaAlgorithm.swift               |  12 +-
 68 files changed, 926 insertions(+), 926 deletions(-)

diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index d088c99af..1a6a439bd 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -7,13 +7,13 @@ public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
   fileprivate var array: [T]
-  
+
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
     array = .init(repeating: initialValue, count: rows*columns)
   }
-  
+
   public subscript(column: Int, row: Int) -> T {
     get {
       precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
diff --git a/Array2D/Array2D.swift b/Array2D/Array2D.swift
index df4822916..caff8373c 100644
--- a/Array2D/Array2D.swift
+++ b/Array2D/Array2D.swift
@@ -7,13 +7,13 @@ public struct Array2D<T> {
   public let columns: Int
   public let rows: Int
   fileprivate var array: [T]
-  
+
   public init(columns: Int, rows: Int, initialValue: T) {
     self.columns = columns
     self.rows = rows
     array = .init(repeating: initialValue, count: rows*columns)
   }
-  
+
   public subscript(column: Int, row: Int) -> T {
     get {
       precondition(column < columns, "Column \(column) Index is out of range. Array<T>(columns: \(columns), rows:\(rows))")
diff --git a/B-Tree/BTree.playground/Sources/BTree.swift b/B-Tree/BTree.playground/Sources/BTree.swift
index 52cda4e43..2693eb308 100644
--- a/B-Tree/BTree.playground/Sources/BTree.swift
+++ b/B-Tree/BTree.playground/Sources/BTree.swift
@@ -33,23 +33,23 @@ class BTreeNode<Key: Comparable, Value> {
    * The tree that owns the node.
    */
   unowned var owner: BTree<Key, Value>
-  
+
   fileprivate var keys = [Key]()
   fileprivate var values = [Value]()
   var children: [BTreeNode]?
-  
+
   var isLeaf: Bool {
     return children == nil
   }
-  
+
   var numberOfKeys: Int {
     return keys.count
   }
-  
+
   init(owner: BTree<Key, Value>) {
     self.owner = owner
   }
-  
+
   convenience init(owner: BTree<Key, Value>, keys: [Key],
                    values: [Value], children: [BTreeNode]? = nil) {
     self.init(owner: owner)
@@ -62,7 +62,7 @@ class BTreeNode<Key: Comparable, Value> {
 // MARK: BTreeNode extesnion: Searching
 
 extension BTreeNode {
-  
+
   /**
    *  Returns the value for a given `key`, returns nil if the `key` is not found.
    *  
@@ -71,11 +71,11 @@ extension BTreeNode {
    */
   func value(for key: Key) -> Value? {
     var index = keys.startIndex
-    
+
     while (index + 1) < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if key == keys[index] {
       return values[index]
     } else if key < keys[index] {
@@ -89,7 +89,7 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Travelsals
 
 extension BTreeNode {
-  
+
   /**
    *  Traverses the keys in order, executes `process` for every key.
    * 
@@ -101,7 +101,7 @@ extension BTreeNode {
       children?[i].traverseKeysInOrder(process)
       process(keys[i])
     }
-    
+
     children?.last?.traverseKeysInOrder(process)
   }
 }
@@ -109,7 +109,7 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Insertion
 
 extension BTreeNode {
-  
+
   /**
    *  Inserts `value` for `key` to the node, or to one if its descendants.
    *  
@@ -119,16 +119,16 @@ extension BTreeNode {
    */
   func insert(_ value: Value, for key: Key) {
     var index = keys.startIndex
-    
+
     while index < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if index < keys.endIndex && keys[index] == key {
       values[index] = value
       return
     }
-    
+
     if isLeaf {
       keys.insert(key, at: index)
       values.insert(value, at: index)
@@ -140,7 +140,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Splits `child` at `index`.
    *  The key-value pair at `index` gets moved up to the parent node,
@@ -156,7 +156,7 @@ extension BTreeNode {
     values.insert(child.values[middleIndex], at: index)
     child.keys.remove(at: middleIndex)
     child.values.remove(at: middleIndex)
-    
+
     let rightSibling = BTreeNode(
       owner: owner,
       keys: Array(child.keys[child.keys.indices.suffix(from: middleIndex)]),
@@ -164,9 +164,9 @@ extension BTreeNode {
     )
     child.keys.removeSubrange(child.keys.indices.suffix(from: middleIndex))
     child.values.removeSubrange(child.values.indices.suffix(from: middleIndex))
-    
+
     children!.insert(rightSibling, at: (index + 1))
-    
+
     if child.children != nil {
       rightSibling.children = Array(
         child.children![child.children!.indices.suffix(from: (middleIndex + 1))]
@@ -198,7 +198,7 @@ extension BTreeNode {
       return children!.last!.inorderPredecessor
     }
   }
-  
+
   /**
    *  Removes `key` and the value associated with it from the node
    *  or one of its descendants.
@@ -208,11 +208,11 @@ extension BTreeNode {
    */
   func remove(_ key: Key) {
     var index = keys.startIndex
-    
+
     while (index + 1) < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if keys[index] == key {
       if isLeaf {
         keys.remove(at: index)
@@ -229,7 +229,7 @@ extension BTreeNode {
       }
     } else if key < keys[index] {
       // We should go to left child...
-      
+
       if let leftChild = children?[index] {
         leftChild.remove(key)
         if leftChild.numberOfKeys < owner.order {
@@ -240,7 +240,7 @@ extension BTreeNode {
       }
     } else {
       // We should go to right child...
-      
+
       if let rightChild = children?[(index + 1)] {
         rightChild.remove(key)
         if rightChild.numberOfKeys < owner.order {
@@ -251,7 +251,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Fixes `childWithTooFewKeys` by either moving a key to it from 
    *  one of its neighbouring nodes, or by merging.
@@ -264,7 +264,7 @@ extension BTreeNode {
    *    - index: the index of the child to be fixed in the current node
    */
   private func fix(childWithTooFewKeys child: BTreeNode, atIndex index: Int) {
-    
+
     if (index - 1) >= 0 && children![(index - 1)].numberOfKeys > owner.order {
       move(keyAtIndex: (index - 1), to: child, from: children![(index - 1)], at: .left)
     } else if (index + 1) < children!.count && children![(index + 1)].numberOfKeys > owner.order {
@@ -275,7 +275,7 @@ extension BTreeNode {
       merge(child: child, atIndex: index, to: .right)
     }
   }
-  
+
   /**
    *  Moves the key at the specified `index` from `node` to
    *  the `targetNode` at `position`
@@ -301,7 +301,7 @@ extension BTreeNode {
                                     at: targetNode.children!.startIndex)
         node.children!.removeLast()
       }
-      
+
     case .right:
       targetNode.keys.insert(keys[index], at: targetNode.keys.endIndex)
       targetNode.values.insert(values[index], at: targetNode.values.endIndex)
@@ -316,7 +316,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Merges `child` at `position` to the node at the `position`.
    *  
@@ -329,33 +329,33 @@ extension BTreeNode {
     switch position {
     case .left:
       // We can merge to the left sibling
-      
+
       children![(index - 1)].keys = children![(index - 1)].keys +
         [keys[(index - 1)]] + child.keys
-      
+
       children![(index - 1)].values = children![(index - 1)].values +
         [values[(index - 1)]] + child.values
-      
+
       keys.remove(at: (index - 1))
       values.remove(at: (index - 1))
-      
+
       if !child.isLeaf {
         children![(index - 1)].children =
           children![(index - 1)].children! + child.children!
       }
-      
+
     case .right:
       // We should merge to the right sibling
-      
+
       children![(index + 1)].keys = child.keys + [keys[index]] +
         children![(index + 1)].keys
-      
+
       children![(index + 1)].values = child.values + [values[index]] +
         children![(index + 1)].values
-      
+
       keys.remove(at: index)
       values.remove(at: index)
-      
+
       if !child.isLeaf {
         children![(index + 1)].children =
           child.children! + children![(index + 1)].children!
@@ -374,18 +374,18 @@ extension BTreeNode {
    */
   var inorderArrayFromKeys: [Key] {
     var array = [Key] ()
-    
+
     for i in 0..<numberOfKeys {
       if let returnedArray = children?[i].inorderArrayFromKeys {
         array += returnedArray
       }
       array += [keys[i]]
     }
-    
+
     if let returnedArray = children?.last?.inorderArrayFromKeys {
       array += returnedArray
     }
-    
+
     return array
   }
 }
@@ -398,13 +398,13 @@ extension BTreeNode: CustomStringConvertible {
    */
   var description: String {
     var str = "\(keys)"
-    
+
     if !isLeaf {
       for child in children! {
         str += child.description
       }
     }
-    
+
     return str
   }
 }
@@ -419,14 +419,14 @@ public class BTree<Key: Comparable, Value> {
    *  except the root node which is allowed to contain less keys than the value of order.
    */
   public let order: Int
-  
+
   /**
    *  The root node of the tree
    */
   var rootNode: BTreeNode<Key, Value>!
-  
+
   fileprivate(set) public var numberOfKeys = 0
-  
+
   /**
    *  Designated initializer for the tree
    *
@@ -484,7 +484,7 @@ extension BTree {
     guard rootNode.numberOfKeys > 0 else {
       return nil
     }
-    
+
     return rootNode.value(for: key)
   }
 }
@@ -501,12 +501,12 @@ extension BTree {
    */
   public func insert(_ value: Value, for key: Key) {
     rootNode.insert(value, for: key)
-    
+
     if rootNode.numberOfKeys > order * 2 {
       splitRoot()
     }
   }
-  
+
   /**
    *  Splits the root node of the tree.
    *  
@@ -515,7 +515,7 @@ extension BTree {
    */
   private func splitRoot() {
     let middleIndexOfOldRoot = rootNode.numberOfKeys / 2
-    
+
     let newRoot = BTreeNode<Key, Value>(
       owner: self,
       keys: [rootNode.keys[middleIndexOfOldRoot]],
@@ -524,7 +524,7 @@ extension BTree {
     )
     rootNode.keys.remove(at: middleIndexOfOldRoot)
     rootNode.values.remove(at: middleIndexOfOldRoot)
-    
+
     let newRightChild = BTreeNode<Key, Value>(
       owner: self,
       keys: Array(rootNode.keys[rootNode.keys.indices.suffix(from: middleIndexOfOldRoot)]),
@@ -532,7 +532,7 @@ extension BTree {
     )
     rootNode.keys.removeSubrange(rootNode.keys.indices.suffix(from: middleIndexOfOldRoot))
     rootNode.values.removeSubrange(rootNode.values.indices.suffix(from: middleIndexOfOldRoot))
-    
+
     if rootNode.children != nil {
       newRightChild.children = Array(
         rootNode.children![rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))]
@@ -541,7 +541,7 @@ extension BTree {
         rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))
       )
     }
-    
+
     newRoot.children!.append(newRightChild)
     rootNode = newRoot
   }
@@ -560,9 +560,9 @@ extension BTree {
     guard rootNode.numberOfKeys > 0 else {
       return
     }
-    
+
     rootNode.remove(key)
-    
+
     if rootNode.numberOfKeys == 0 && !rootNode.isLeaf {
       rootNode = rootNode.children!.first!
     }
diff --git a/B-Tree/BTree.swift b/B-Tree/BTree.swift
index 52cda4e43..2693eb308 100644
--- a/B-Tree/BTree.swift
+++ b/B-Tree/BTree.swift
@@ -33,23 +33,23 @@ class BTreeNode<Key: Comparable, Value> {
    * The tree that owns the node.
    */
   unowned var owner: BTree<Key, Value>
-  
+
   fileprivate var keys = [Key]()
   fileprivate var values = [Value]()
   var children: [BTreeNode]?
-  
+
   var isLeaf: Bool {
     return children == nil
   }
-  
+
   var numberOfKeys: Int {
     return keys.count
   }
-  
+
   init(owner: BTree<Key, Value>) {
     self.owner = owner
   }
-  
+
   convenience init(owner: BTree<Key, Value>, keys: [Key],
                    values: [Value], children: [BTreeNode]? = nil) {
     self.init(owner: owner)
@@ -62,7 +62,7 @@ class BTreeNode<Key: Comparable, Value> {
 // MARK: BTreeNode extesnion: Searching
 
 extension BTreeNode {
-  
+
   /**
    *  Returns the value for a given `key`, returns nil if the `key` is not found.
    *  
@@ -71,11 +71,11 @@ extension BTreeNode {
    */
   func value(for key: Key) -> Value? {
     var index = keys.startIndex
-    
+
     while (index + 1) < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if key == keys[index] {
       return values[index]
     } else if key < keys[index] {
@@ -89,7 +89,7 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Travelsals
 
 extension BTreeNode {
-  
+
   /**
    *  Traverses the keys in order, executes `process` for every key.
    * 
@@ -101,7 +101,7 @@ extension BTreeNode {
       children?[i].traverseKeysInOrder(process)
       process(keys[i])
     }
-    
+
     children?.last?.traverseKeysInOrder(process)
   }
 }
@@ -109,7 +109,7 @@ extension BTreeNode {
 // MARK: BTreeNode extension: Insertion
 
 extension BTreeNode {
-  
+
   /**
    *  Inserts `value` for `key` to the node, or to one if its descendants.
    *  
@@ -119,16 +119,16 @@ extension BTreeNode {
    */
   func insert(_ value: Value, for key: Key) {
     var index = keys.startIndex
-    
+
     while index < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if index < keys.endIndex && keys[index] == key {
       values[index] = value
       return
     }
-    
+
     if isLeaf {
       keys.insert(key, at: index)
       values.insert(value, at: index)
@@ -140,7 +140,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Splits `child` at `index`.
    *  The key-value pair at `index` gets moved up to the parent node,
@@ -156,7 +156,7 @@ extension BTreeNode {
     values.insert(child.values[middleIndex], at: index)
     child.keys.remove(at: middleIndex)
     child.values.remove(at: middleIndex)
-    
+
     let rightSibling = BTreeNode(
       owner: owner,
       keys: Array(child.keys[child.keys.indices.suffix(from: middleIndex)]),
@@ -164,9 +164,9 @@ extension BTreeNode {
     )
     child.keys.removeSubrange(child.keys.indices.suffix(from: middleIndex))
     child.values.removeSubrange(child.values.indices.suffix(from: middleIndex))
-    
+
     children!.insert(rightSibling, at: (index + 1))
-    
+
     if child.children != nil {
       rightSibling.children = Array(
         child.children![child.children!.indices.suffix(from: (middleIndex + 1))]
@@ -198,7 +198,7 @@ extension BTreeNode {
       return children!.last!.inorderPredecessor
     }
   }
-  
+
   /**
    *  Removes `key` and the value associated with it from the node
    *  or one of its descendants.
@@ -208,11 +208,11 @@ extension BTreeNode {
    */
   func remove(_ key: Key) {
     var index = keys.startIndex
-    
+
     while (index + 1) < keys.endIndex && keys[index] < key {
       index = (index + 1)
     }
-    
+
     if keys[index] == key {
       if isLeaf {
         keys.remove(at: index)
@@ -229,7 +229,7 @@ extension BTreeNode {
       }
     } else if key < keys[index] {
       // We should go to left child...
-      
+
       if let leftChild = children?[index] {
         leftChild.remove(key)
         if leftChild.numberOfKeys < owner.order {
@@ -240,7 +240,7 @@ extension BTreeNode {
       }
     } else {
       // We should go to right child...
-      
+
       if let rightChild = children?[(index + 1)] {
         rightChild.remove(key)
         if rightChild.numberOfKeys < owner.order {
@@ -251,7 +251,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Fixes `childWithTooFewKeys` by either moving a key to it from 
    *  one of its neighbouring nodes, or by merging.
@@ -264,7 +264,7 @@ extension BTreeNode {
    *    - index: the index of the child to be fixed in the current node
    */
   private func fix(childWithTooFewKeys child: BTreeNode, atIndex index: Int) {
-    
+
     if (index - 1) >= 0 && children![(index - 1)].numberOfKeys > owner.order {
       move(keyAtIndex: (index - 1), to: child, from: children![(index - 1)], at: .left)
     } else if (index + 1) < children!.count && children![(index + 1)].numberOfKeys > owner.order {
@@ -275,7 +275,7 @@ extension BTreeNode {
       merge(child: child, atIndex: index, to: .right)
     }
   }
-  
+
   /**
    *  Moves the key at the specified `index` from `node` to
    *  the `targetNode` at `position`
@@ -301,7 +301,7 @@ extension BTreeNode {
                                     at: targetNode.children!.startIndex)
         node.children!.removeLast()
       }
-      
+
     case .right:
       targetNode.keys.insert(keys[index], at: targetNode.keys.endIndex)
       targetNode.values.insert(values[index], at: targetNode.values.endIndex)
@@ -316,7 +316,7 @@ extension BTreeNode {
       }
     }
   }
-  
+
   /**
    *  Merges `child` at `position` to the node at the `position`.
    *  
@@ -329,33 +329,33 @@ extension BTreeNode {
     switch position {
     case .left:
       // We can merge to the left sibling
-      
+
       children![(index - 1)].keys = children![(index - 1)].keys +
         [keys[(index - 1)]] + child.keys
-      
+
       children![(index - 1)].values = children![(index - 1)].values +
         [values[(index - 1)]] + child.values
-      
+
       keys.remove(at: (index - 1))
       values.remove(at: (index - 1))
-      
+
       if !child.isLeaf {
         children![(index - 1)].children =
           children![(index - 1)].children! + child.children!
       }
-      
+
     case .right:
       // We should merge to the right sibling
-      
+
       children![(index + 1)].keys = child.keys + [keys[index]] +
         children![(index + 1)].keys
-      
+
       children![(index + 1)].values = child.values + [values[index]] +
         children![(index + 1)].values
-      
+
       keys.remove(at: index)
       values.remove(at: index)
-      
+
       if !child.isLeaf {
         children![(index + 1)].children =
           child.children! + children![(index + 1)].children!
@@ -374,18 +374,18 @@ extension BTreeNode {
    */
   var inorderArrayFromKeys: [Key] {
     var array = [Key] ()
-    
+
     for i in 0..<numberOfKeys {
       if let returnedArray = children?[i].inorderArrayFromKeys {
         array += returnedArray
       }
       array += [keys[i]]
     }
-    
+
     if let returnedArray = children?.last?.inorderArrayFromKeys {
       array += returnedArray
     }
-    
+
     return array
   }
 }
@@ -398,13 +398,13 @@ extension BTreeNode: CustomStringConvertible {
    */
   var description: String {
     var str = "\(keys)"
-    
+
     if !isLeaf {
       for child in children! {
         str += child.description
       }
     }
-    
+
     return str
   }
 }
@@ -419,14 +419,14 @@ public class BTree<Key: Comparable, Value> {
    *  except the root node which is allowed to contain less keys than the value of order.
    */
   public let order: Int
-  
+
   /**
    *  The root node of the tree
    */
   var rootNode: BTreeNode<Key, Value>!
-  
+
   fileprivate(set) public var numberOfKeys = 0
-  
+
   /**
    *  Designated initializer for the tree
    *
@@ -484,7 +484,7 @@ extension BTree {
     guard rootNode.numberOfKeys > 0 else {
       return nil
     }
-    
+
     return rootNode.value(for: key)
   }
 }
@@ -501,12 +501,12 @@ extension BTree {
    */
   public func insert(_ value: Value, for key: Key) {
     rootNode.insert(value, for: key)
-    
+
     if rootNode.numberOfKeys > order * 2 {
       splitRoot()
     }
   }
-  
+
   /**
    *  Splits the root node of the tree.
    *  
@@ -515,7 +515,7 @@ extension BTree {
    */
   private func splitRoot() {
     let middleIndexOfOldRoot = rootNode.numberOfKeys / 2
-    
+
     let newRoot = BTreeNode<Key, Value>(
       owner: self,
       keys: [rootNode.keys[middleIndexOfOldRoot]],
@@ -524,7 +524,7 @@ extension BTree {
     )
     rootNode.keys.remove(at: middleIndexOfOldRoot)
     rootNode.values.remove(at: middleIndexOfOldRoot)
-    
+
     let newRightChild = BTreeNode<Key, Value>(
       owner: self,
       keys: Array(rootNode.keys[rootNode.keys.indices.suffix(from: middleIndexOfOldRoot)]),
@@ -532,7 +532,7 @@ extension BTree {
     )
     rootNode.keys.removeSubrange(rootNode.keys.indices.suffix(from: middleIndexOfOldRoot))
     rootNode.values.removeSubrange(rootNode.values.indices.suffix(from: middleIndexOfOldRoot))
-    
+
     if rootNode.children != nil {
       newRightChild.children = Array(
         rootNode.children![rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))]
@@ -541,7 +541,7 @@ extension BTree {
         rootNode.children!.indices.suffix(from: (middleIndexOfOldRoot + 1))
       )
     }
-    
+
     newRoot.children!.append(newRightChild)
     rootNode = newRoot
   }
@@ -560,9 +560,9 @@ extension BTree {
     guard rootNode.numberOfKeys > 0 else {
       return
     }
-    
+
     rootNode.remove(key)
-    
+
     if rootNode.numberOfKeys == 0 && !rootNode.isLeaf {
       rootNode = rootNode.children!.first!
     }
diff --git a/B-Tree/Tests/Tests/BTreeNodeTests.swift b/B-Tree/Tests/Tests/BTreeNodeTests.swift
index fd3ba10e8..8eff926b5 100644
--- a/B-Tree/Tests/Tests/BTreeNodeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeNodeTests.swift
@@ -9,44 +9,44 @@
 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)
   }
diff --git a/B-Tree/Tests/Tests/BTreeTests.swift b/B-Tree/Tests/Tests/BTreeTests.swift
index f2dac7511..1e94bfd7d 100644
--- a/B-Tree/Tests/Tests/BTreeTests.swift
+++ b/B-Tree/Tests/Tests/BTreeTests.swift
@@ -10,201 +10,201 @@ import XCTest
 
 class BTreeTests: XCTestCase {
   var bTree: BTree<Int, Int>!
-  
+
   override func setUp() {
     super.setUp()
     bTree = BTree<Int, Int>(order: 3)!
   }
-  
+
   // MARK: - Tests on empty tree
-  
+
   func testOrder() {
     XCTAssertEqual(bTree.order, 3)
   }
-  
+
   func testRootNode() {
     XCTAssertNotNil(bTree.rootNode)
   }
-  
+
   func testNumberOfNodesOnEmptyTree() {
     XCTAssertEqual(bTree.numberOfKeys, 0)
   }
-  
+
   func testInorderTraversalOfEmptyTree() {
     bTree.traverseKeysInOrder { _ in
       XCTFail("Inorder travelsal fail.")
     }
   }
-  
+
   func testSubscriptOnEmptyTree() {
     XCTAssertEqual(bTree[1], nil)
   }
-  
+
   func testSearchEmptyTree() {
     XCTAssertEqual(bTree.value(for: 1), nil)
   }
-  
+
   func testInsertToEmptyTree() {
     bTree.insert(1, for: 1)
-    
+
     XCTAssertEqual(bTree[1]!, 1)
   }
-  
+
   func testRemoveFromEmptyTree() {
     bTree.remove(1)
     XCTAssertEqual(bTree.description, "[]")
   }
-  
+
   func testInorderArrayFromEmptyTree() {
     XCTAssertEqual(bTree.inorderArrayFromKeys, [Int]())
   }
-  
+
   func testDescriptionOfEmptyTree() {
     XCTAssertEqual(bTree.description, "[]")
   }
-  
+
   // MARK: - Travelsal
-  
+
   func testInorderTravelsal() {
     for i in 1...20 {
       bTree.insert(i, for: i)
     }
-    
+
     var j = 1
-    
+
     bTree.traverseKeysInOrder { i in
       XCTAssertEqual(i, j)
       j += 1
     }
   }
-  
+
   // MARK: - Searching
-  
+
   func testSearchForMaximum() {
     for i in 1...20 {
       bTree.insert(i, for: i)
     }
-    
+
     XCTAssertEqual(bTree.value(for: 20)!, 20)
   }
-  
+
   func testSearchForMinimum() {
     for i in 1...20 {
       bTree.insert(i, for: i)
     }
-    
+
     XCTAssertEqual(bTree.value(for: 1)!, 1)
   }
-  
+
   // MARK: - Insertion
-  
+
   func testInsertion() {
     bTree.insertKeysUpTo(20)
-    
+
     XCTAssertEqual(bTree.numberOfKeys, 20)
-    
+
     for i in 1...20 {
       XCTAssertNotNil(bTree[i])
     }
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
   }
-  
+
   // MARK: - Removal
-  
+
   func testRemoveMaximum() {
     for i in 1...20 {
       bTree.insert(i, for: i)
     }
-    
+
     bTree.remove(20)
-    
+
     XCTAssertNil(bTree[20])
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
   }
-  
+
   func testRemoveMinimum() {
     bTree.insertKeysUpTo(20)
-    
+
     bTree.remove(1)
-    
+
     XCTAssertNil(bTree[1])
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
   }
-  
+
   func testRemoveSome() {
     bTree.insertKeysUpTo(20)
-    
+
     bTree.remove(6)
     bTree.remove(9)
-    
+
     XCTAssertNil(bTree[6])
     XCTAssertNil(bTree[9])
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
   }
-  
+
   func testRemoveSomeFrom2ndOrder() {
     bTree = BTree<Int, Int>(order: 2)!
     bTree.insertKeysUpTo(20)
-    
+
     bTree.remove(6)
     bTree.remove(9)
-    
+
     XCTAssertNil(bTree[6])
     XCTAssertNil(bTree[9])
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
   }
-  
+
   func testRemoveAll() {
     bTree.insertKeysUpTo(20)
-    
+
     XCTAssertEqual(bTree.numberOfKeys, 20)
-    
+
     for i in (1...20).reversed() {
       bTree.remove(i)
     }
-    
+
     do {
       try bTree.checkBalance()
     } catch {
       XCTFail("BTree is not balanced")
     }
-    
+
     XCTAssertEqual(bTree.numberOfKeys, 0)
   }
-  
+
   // MARK: - InorderArray
-  
+
 	func testInorderArray() {
     bTree.insertKeysUpTo(20)
-		
+
 		let returnedArray = bTree.inorderArrayFromKeys
 		let targetArray = Array<Int>(1...20)
-		
+
 		XCTAssertEqual(returnedArray, targetArray)
 	}
 }
@@ -221,7 +221,7 @@ extension BTreeNode {
     } else if !root && numberOfKeys < owner.order {
       throw BTreeError.tooFewNodes
     }
-    
+
     if !isLeaf {
       for child in children! {
         try child.checkBalance(isRoot: false)
@@ -234,14 +234,14 @@ extension BTree where Key: SignedInteger, Value: SignedInteger {
   func insertKeysUpTo(_ to: Int) {
     var k: Key = 1
     var v: Value = 1
-    
+
     for _ in 1...to {
       insert(v, for: k)
       k = k + 1
       v = v + 1
     }
   }
-  
+
   func checkBalance() throws {
     try rootNode.checkBalance(isRoot: true)
   }
diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
index 00ac6da97..b9f2b1432 100644
--- a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
@@ -2,7 +2,7 @@
 
 extension String {
   func indexOf(_ pattern: String) -> String.Index? {
-    
+
     for i in self.characters.indices {
       var j = i
       var found = true
diff --git a/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift b/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift
index b6e85fa2b..f7c4eec61 100644
--- a/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift	
+++ b/Comb Sort/Comb Sort.playground/Sources/Comb Sort.swift	
@@ -11,13 +11,13 @@ 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] {
diff --git a/Comb Sort/Comb Sort.swift b/Comb Sort/Comb Sort.swift
index b6e85fa2b..f7c4eec61 100644
--- a/Comb Sort/Comb Sort.swift	
+++ b/Comb Sort/Comb Sort.swift	
@@ -11,13 +11,13 @@ 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] {
diff --git a/Comb Sort/Tests/CombSortTests.swift b/Comb Sort/Tests/CombSortTests.swift
index 1bcc67fd0..b9287f84a 100644
--- a/Comb Sort/Tests/CombSortTests.swift	
+++ b/Comb Sort/Tests/CombSortTests.swift	
@@ -16,7 +16,7 @@ class CombSortTests: XCTestCase {
         super.setUp()
         sequence = [2, 32, 9, -1, 89, 101, 55, -10, -12, 67]
     }
-    
+
     override func tearDown() {
         super.tearDown()
     }
diff --git a/Convex Hull/Convex Hull/AppDelegate.swift b/Convex Hull/Convex Hull/AppDelegate.swift
index 4f8496cd5..bfe15e1a7 100644
--- a/Convex Hull/Convex Hull/AppDelegate.swift	
+++ b/Convex Hull/Convex Hull/AppDelegate.swift	
@@ -17,16 +17,16 @@ class AppDelegate: UIResponder, UIApplicationDelegate {
     func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplicationLaunchOptionsKey: Any]?) -> Bool {
 
         let screenBounds = UIScreen.main.bounds
-        
+
         window = UIWindow(frame: screenBounds)
-        
+
         let viewController = UIViewController()
         viewController.view = View(frame: (window?.frame)!)
         viewController.view.backgroundColor = .white
-        
+
         window?.rootViewController = viewController
         window?.makeKeyAndVisible()
-        
+
         return true
     }
 
diff --git a/Convex Hull/Convex Hull/View.swift b/Convex Hull/Convex Hull/View.swift
index f9f9f6ef4..2f2c3e046 100644
--- a/Convex Hull/Convex Hull/View.swift	
+++ b/Convex Hull/Convex Hull/View.swift	
@@ -9,24 +9,24 @@
 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")
     }
-    
+
     func generatePoints() {
         for _ in 0..<MAX_POINTS {
             let offset: CGFloat = 50
@@ -35,101 +35,101 @@ class View: UIView {
             let point = CGPoint(x: xrand, y: yrand)
             points.append(point)
         }
-        
+
         points.sort { (a: CGPoint, b: CGPoint) -> Bool in
             return a.x < b.x
         }
     }
-    
+
     func quickHull(points: [CGPoint]) {
         var pts = points
-                
+
         // 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()
-        
+
         // 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 p2 to p1
         var s2 = [CGPoint]()
-        
+
         // 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.
-            
+
             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)
     }
-    
+
     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
         }
-        
+
         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
             if dist > maxDist { // if distance is larger than current maxDist remember new point p
                 maxDist = dist
                 maxPoint = p
             }
         }
-        
+
         convexHull.insert(maxPoint, at: convexHull.index(of: p1)! + 1) // insert point with max distance from line in the convexHull after p1
-        
+
         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 p1 to maxPoint
         var s1 = [CGPoint]()
-        
+
         // points to the right of oriented line from maxPoint to p2
         var s2 = [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)
-        
+
         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
-            
+
             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
 
@@ -139,34 +139,34 @@ class View: UIView {
                 s2.append(p)
             }
         }
-        
+
         // find new hull points
         findHull(s1, p1, maxPoint)
         findHull(s2, maxPoint, p2)
     }
 
     override func draw(_ rect: CGRect) {
-        
+
         let context = UIGraphicsGetCurrentContext()
-        
+
         // Draw hull
         let lineWidth: CGFloat = 2.0
-        
+
         context!.setFillColor(UIColor.black.cgColor)
         context!.setLineWidth(lineWidth)
         context!.setStrokeColor(UIColor.red.cgColor)
         context!.setFillColor(UIColor.black.cgColor)
-        
+
         let firstPoint = convexHull.first!
         context!.move(to: firstPoint)
-        
+
         for p in convexHull.dropFirst() {
             context!.addLine(to: p)
         }
         context!.addLine(to: firstPoint)
-        
+
         context!.strokePath()
-        
+
         // Draw points
         for p in points {
             let radius: CGFloat = 5
diff --git a/Fixed Size Array/FixedSizeArray.playground/Contents.swift b/Fixed Size Array/FixedSizeArray.playground/Contents.swift
index 4bc5d66df..8ef545e45 100644
--- a/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
+++ b/Fixed Size Array/FixedSizeArray.playground/Contents.swift	
@@ -10,25 +10,25 @@ struct FixedSizeArray<T> {
   private var defaultValue: T
   private var array: [T]
   private (set) var count = 0
-  
+
   init(maxSize: Int, defaultValue: T) {
     self.maxSize = maxSize
     self.defaultValue = defaultValue
     self.array = [T](repeating: defaultValue, count: maxSize)
   }
-  
+
   subscript(index: Int) -> T {
     assert(index >= 0)
     assert(index < count)
     return array[index]
   }
-  
+
   mutating func append(_ newElement: T) {
     assert(count < maxSize)
     array[count] = newElement
     count += 1
   }
-  
+
   mutating func removeAt(index: Int) -> T {
     assert(index >= 0)
     assert(index < count)
@@ -38,7 +38,7 @@ struct FixedSizeArray<T> {
     array[count] = defaultValue
     return result
   }
-  
+
   mutating func removeAll() {
     for i in 0..<count {
       array[i] = defaultValue
diff --git a/Graph/Graph.playground/Contents.swift b/Graph/Graph.playground/Contents.swift
index 77de8484b..fde396e64 100644
--- a/Graph/Graph.playground/Contents.swift
+++ b/Graph/Graph.playground/Contents.swift
@@ -1,7 +1,7 @@
 import Graph
 
 for graph in [AdjacencyMatrixGraph<Int>(), AdjacencyListGraph<Int>()] {
-    
+
   let v1 = graph.createVertex(1)
   let v2 = graph.createVertex(2)
   let v3 = graph.createVertex(3)
diff --git a/Hash Set/HashSet.playground/Sources/HashSet.swift b/Hash Set/HashSet.playground/Sources/HashSet.swift
index c3365110b..3ccaa94ea 100644
--- a/Hash Set/HashSet.playground/Sources/HashSet.swift	
+++ b/Hash Set/HashSet.playground/Sources/HashSet.swift	
@@ -2,31 +2,31 @@
 
 public struct HashSet<T: Hashable> {
     fileprivate var dictionary = Dictionary<T, Bool>()
-    
+
     public init() {
-        
+
     }
-    
+
     public mutating func insert(_ element: T) {
         dictionary[element] = true
     }
-    
+
     public mutating func remove(_ element: T) {
         dictionary[element] = nil
     }
-    
+
     public func contains(_ element: T) -> Bool {
         return dictionary[element] != nil
     }
-    
+
     public func allElements() -> [T] {
         return Array(dictionary.keys)
     }
-    
+
     public var count: Int {
         return dictionary.count
     }
-    
+
     public var isEmpty: Bool {
         return dictionary.isEmpty
     }
diff --git a/Hash Table/HashTable.playground/Sources/HashTable.swift b/Hash Table/HashTable.playground/Sources/HashTable.swift
index 947737c32..2383b8192 100644
--- a/Hash Table/HashTable.playground/Sources/HashTable.swift	
+++ b/Hash Table/HashTable.playground/Sources/HashTable.swift	
@@ -34,19 +34,19 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
     private typealias Element = (key: Key, value: Value)
     private typealias Bucket = [Element]
     private var buckets: [Bucket]
-    
+
     /// The number of key-value pairs in the hash table.
     private(set) public var count = 0
-    
+
     /// 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 {
@@ -57,7 +57,7 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         }
         return str
     }
-    
+
     /**
      Create a hash table with the given capacity.
      */
@@ -65,7 +65,7 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         assert(capacity > 0)
         buckets = Array<Bucket>(repeatElement([], count: capacity))
     }
-    
+
     /**
      Accesses the value associated with
      the given key for reading and writing.
@@ -82,7 +82,7 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
             }
         }
     }
-    
+
     /**
      Returns the value for the given key.
      */
@@ -95,14 +95,14 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         }
         return nil  // key not in hash table
     }
-    
+
     /**
      Updates the value stored in the hash table for the given key,
      or adds a new key-value pair if the key does not exist.
      */
     @discardableResult public mutating func updateValue(_ value: Value, forKey key: Key) -> Value? {
         let index = self.index(forKey: key)
-        
+
         // Do we already have this key in the bucket?
         for (i, element) in buckets[index].enumerated() {
             if element.key == key {
@@ -111,20 +111,20 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
                 return oldValue
             }
         }
-        
+
         // This key isn't in the bucket yet; add it to the chain.
         buckets[index].append((key: key, value: value))
         count += 1
         return nil
     }
-    
+
     /**
      Removes the given key and its
      associated value from the hash table.
      */
     @discardableResult public mutating func removeValue(forKey key: Key) -> Value? {
         let index = self.index(forKey: key)
-        
+
         // Find the element in the bucket's chain and remove it.
         for (i, element) in buckets[index].enumerated() {
             if element.key == key {
@@ -135,7 +135,7 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         }
         return nil  // key not in hash table
     }
-    
+
     /**
      Removes all key-value pairs from the hash table.
      */
@@ -143,7 +143,7 @@ public struct HashTable<Key: Hashable, Value>: CustomStringConvertible {
         buckets = Array<Bucket>(repeatElement([], count: buckets.count))
         count = 0
     }
-    
+
     /**
      Returns the given key's array index.
      */
diff --git a/HaversineDistance/HaversineDistance.playground/Contents.swift b/HaversineDistance/HaversineDistance.playground/Contents.swift
index a6effb7b0..449fa366d 100644
--- a/HaversineDistance/HaversineDistance.playground/Contents.swift
+++ b/HaversineDistance/HaversineDistance.playground/Contents.swift
@@ -1,25 +1,25 @@
 import UIKit
 
 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))
 }
 
diff --git a/Heap/Heap.swift b/Heap/Heap.swift
index fa30df362..80b40c65f 100644
--- a/Heap/Heap.swift
+++ b/Heap/Heap.swift
@@ -113,7 +113,7 @@ public struct Heap<T> {
    */
   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)
@@ -144,7 +144,7 @@ public struct Heap<T> {
    */
   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])
diff --git a/Heap/Tests/HeapTests.swift b/Heap/Tests/HeapTests.swift
index 0e6c504f3..cac934406 100644
--- a/Heap/Tests/HeapTests.swift
+++ b/Heap/Tests/HeapTests.swift
@@ -201,7 +201,7 @@ class HeapTests: XCTestCase {
     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))
@@ -314,7 +314,7 @@ class HeapTests: XCTestCase {
     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))
diff --git a/Huffman Coding/Huffman.swift b/Huffman Coding/Huffman.swift
index 7e2961a2f..cad80327d 100644
--- a/Huffman Coding/Huffman.swift	
+++ b/Huffman Coding/Huffman.swift	
@@ -13,7 +13,7 @@ public class Huffman {
     /* Tree nodes don't use pointers to refer to each other, but simple integer
      indices. That allows us to use structs for the nodes. */
     typealias NodeIndex = Int
-    
+
     /* A node in the compression tree. Leaf nodes represent the actual bytes that
      are present in the input data. The count of an intermediary node is the sum
      of the counts of all nodes below it. The root node's count is the number of
@@ -25,15 +25,15 @@ public class Huffman {
         var left: NodeIndex = -1
         var right: NodeIndex = -1
     }
-    
+
     /* The tree structure. The first 256 entries are for the leaf nodes (not all
      of those may be used, depending on the input). We add additional nodes as
      we build the tree. */
     var tree = [Node](repeating: Node(), count: 256)
-    
+
     /* This is the last node we add to the tree. */
     var root: NodeIndex = -1
-    
+
     /* The frequency table describes how often a byte occurs in the input data.
      You need it to decompress the Huffman-encoded data. The frequency table
      should be serialized along with the compressed data. */
@@ -41,7 +41,7 @@ public class Huffman {
         var byte: UInt8 = 0
         var count = 0
     }
-    
+
     public init() { }
 }
 
@@ -59,7 +59,7 @@ extension Huffman {
             ptr = ptr.successor()
         }
     }
-    
+
     /* Takes a frequency table and rebuilds the tree. This is the first step of
      decompression. */
     fileprivate func restoreTree(fromTable frequencyTable: [Freq]) {
@@ -70,7 +70,7 @@ extension Huffman {
         }
         buildTree()
     }
-    
+
     /* Returns the frequency table. This is the first 256 nodes from the tree but
      only those that are actually used, without the parent/left/right pointers.
      You would serialize this along with the compressed file. */
@@ -91,13 +91,13 @@ extension Huffman {
         for node in tree where node.count > 0 {
             queue.enqueue(node)
         }
-        
+
         while queue.count > 1 {
             // Find the two nodes with the smallest frequencies that do not have
             // a parent node yet.
             let node1 = queue.dequeue()!
             let node2 = queue.dequeue()!
-            
+
             // Create a new intermediate node.
             var parentNode = Node()
             parentNode.count = node1.count + node2.count
@@ -105,15 +105,15 @@ extension Huffman {
             parentNode.right = node2.index
             parentNode.index = tree.count
             tree.append(parentNode)
-            
+
             // Link the two nodes into their new parent node.
             tree[node1.index].parent = parentNode.index
             tree[node2.index].parent = parentNode.index
-            
+
             // Put the intermediate node back into the queue.
             queue.enqueue(parentNode)
         }
-        
+
         // The final remaining node in the queue becomes the root of the tree.
         let rootNode = queue.dequeue()!
         root = rootNode.index
@@ -125,7 +125,7 @@ extension Huffman {
     public func compressData(data: NSData) -> NSData {
         countByteFrequency(inData: data)
         buildTree()
-        
+
         let writer = BitWriter()
         var ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
         for _ in 0..<data.length {
@@ -137,7 +137,7 @@ extension Huffman {
         writer.flush()
         return writer.data
     }
-    
+
     /* Recursively walks the tree from a leaf node up to the root, and then back
      again. If a child is the right node, we emit a 0 bit; if it's the left node,
      we emit a 1 bit. */
@@ -159,11 +159,11 @@ extension Huffman {
     /* Takes a Huffman-compressed NSData object and outputs the uncompressed data. */
     public func decompressData(data: NSData, frequencyTable: [Freq]) -> NSData {
         restoreTree(fromTable: frequencyTable)
-        
+
         let reader = BitReader(data: data)
         let outData = NSMutableData()
         let byteCount = tree[root].count
-        
+
         var i = 0
         while i < byteCount {
             var b = findLeafNode(reader: reader, nodeIndex: root)
@@ -172,7 +172,7 @@ extension Huffman {
         }
         return outData
     }
-    
+
     /* Walks the tree from the root down to the leaf node. At every node, read the
      next bit and use that to determine whether to step to the left or right.
      When we get to the leaf node, we simply return its index, which is equal to
diff --git a/Huffman Coding/NSData+Bits.swift b/Huffman Coding/NSData+Bits.swift
index 4ae3c5c6d..1f5333296 100644
--- a/Huffman Coding/NSData+Bits.swift	
+++ b/Huffman Coding/NSData+Bits.swift	
@@ -5,7 +5,7 @@ public class BitWriter {
     public var data = NSMutableData()
     var outByte: UInt8 = 0
     var outCount = 0
-    
+
     public func writeBit(bit: Bool) {
         if outCount == 8 {
             data.append(&outByte, length: 1)
@@ -14,7 +14,7 @@ public class BitWriter {
         outByte = (outByte << 1) | (bit ? 1 : 0)
         outCount += 1
     }
-    
+
     public func flush() {
         if outCount > 0 {
             if outCount < 8 {
@@ -31,11 +31,11 @@ public class BitReader {
     var ptr: UnsafePointer<UInt8>
     var inByte: UInt8 = 0
     var inCount = 8
-    
+
     public init(data: NSData) {
         ptr = data.bytes.assumingMemoryBound(to: UInt8.self)
     }
-    
+
     public func readBit() -> Bool {
         if inCount == 8 {
             inByte = ptr.pointee    // load the next byte
diff --git a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift
index 3ac29301a..2d327fbac 100644
--- a/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
+++ b/Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift	
@@ -17,7 +17,7 @@ func ^^ (radix: Int, power: Int) -> Int {
 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 {
@@ -29,7 +29,7 @@ func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> Int {
     }
     product[i + num2Array.count] += carry
   }
-  
+
   return Int(product.reversed().map { String($0) }.reduce("", +))!
 }
 
@@ -37,24 +37,24 @@ func multiply(_ num1: Int, by num2: Int, base: Int = 10) -> 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 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 fb20a667d..0f0e8ed12 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
 }
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
index 46a88c134..45d9812b7 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.swift
@@ -9,54 +9,54 @@
 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
         }
diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 08e14ef70..9ee4cc4c4 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -4,37 +4,37 @@
 
 //: Linked List Class Declaration:
 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>
-  
+
   /// 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? {
     if var node = head {
@@ -46,7 +46,7 @@ public final class LinkedList<T> {
       return nil
     }
   }
-  
+
   /// Computed property to iterate through the linked list and return the total number of nodes
   public var count: Int {
     if var node = head {
@@ -60,7 +60,7 @@ public final class LinkedList<T> {
       return 0
     }
   }
-  
+
   /// 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
@@ -77,7 +77,7 @@ public final class LinkedList<T> {
     }
     return nil
   }
-  
+
   /// Subscript function to return the node at a specific index
   ///
   /// - Parameter index: Integer value of the requested value's index
@@ -86,7 +86,7 @@ public final class LinkedList<T> {
     assert(node != nil)
     return node!.value
   }
-  
+
   /// Append a value to the end of the list
   ///
   /// - Parameter value: The data value to be appended
@@ -94,7 +94,7 @@ public final class LinkedList<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
@@ -107,7 +107,7 @@ 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.
@@ -118,28 +118,28 @@ public final class LinkedList<T> {
       nodeToCopy = node.next
     }
   }
-  
+
   /// 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:
@@ -149,7 +149,7 @@ public final class LinkedList<T> {
     let newNode = Node(value: value)
     self.insert(newNode, atIndex: index)
   }
-  
+
   /// Insert a copy of a node at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameters:
@@ -162,12 +162,12 @@ public final class LinkedList<T> {
     newNode.next = next
     prev?.next = newNode
     next?.previous = newNode
-    
+
     if prev == nil {
       head = newNode
     }
   }
-  
+
   /// Insert a copy of a LinkedList at a specific index. Crashes if index is out of bounds (0...self.count)
   ///
   /// - Parameters:
@@ -192,12 +192,12 @@ public final class LinkedList<T> {
     prev?.next = next
     next?.previous = prev
   }
-  
+
   /// 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
@@ -205,19 +205,19 @@ public final class LinkedList<T> {
   @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.
@@ -225,7 +225,7 @@ public final class LinkedList<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
@@ -276,7 +276,7 @@ extension LinkedList {
     }
     return result
   }
-  
+
   public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
     let result = LinkedList<T>()
     var node = head
@@ -294,7 +294,7 @@ extension LinkedList {
 extension LinkedList {
   convenience init(array: Array<T>) {
     self.init()
-    
+
     for element in array {
       self.append(element)
     }
@@ -305,7 +305,7 @@ extension LinkedList {
 extension LinkedList: ExpressibleByArrayLiteral {
   public convenience init(arrayLiteral elements: T...) {
     self.init()
-    
+
     for element in elements {
       self.append(element)
     }
diff --git a/Linked List/LinkedList.swift b/Linked List/LinkedList.swift
index 783e650e8..94e978c07 100755
--- a/Linked List/LinkedList.swift	
+++ b/Linked List/LinkedList.swift	
@@ -1,29 +1,29 @@
 public final class LinkedList<T> {
-    
+
     public class LinkedListNode<T> {
         var value: T
         var next: LinkedListNode?
         weak var previous: LinkedListNode?
-        
+
         public init(value: T) {
             self.value = value
         }
     }
-  
+
     public typealias Node = LinkedListNode<T>
-    
+
     fileprivate var head: Node?
-    
+
     public init() {}
-    
+
     public var isEmpty: Bool {
         return head == nil
     }
-    
+
     public var first: Node? {
         return head
     }
-    
+
     public var last: Node? {
         if var node = head {
             while case let next? = node.next {
@@ -34,7 +34,7 @@ public final class LinkedList<T> {
             return nil
         }
     }
-    
+
     public var count: Int {
         if var node = head {
             var c = 1
@@ -47,7 +47,7 @@ public final class LinkedList<T> {
             return 0
         }
     }
-    
+
     public func node(atIndex index: Int) -> Node? {
         if index >= 0 {
             var node = head
@@ -60,18 +60,18 @@ public final class LinkedList<T> {
         }
         return nil
     }
-    
+
     public subscript(index: Int) -> T {
         let node = self.node(atIndex: index)
         assert(node != nil)
         return node!.value
     }
-    
+
     public func append(_ value: T) {
         let newNode = Node(value: value)
         self.append(newNode)
     }
-    
+
     public func append(_ node: Node) {
         let newNode = LinkedListNode(value: node.value)
         if let lastNode = last {
@@ -81,7 +81,7 @@ public final class LinkedList<T> {
             head = newNode
         }
     }
-    
+
     public func append(_ list: LinkedList) {
         var nodeToCopy = list.head
         while let node = nodeToCopy {
@@ -89,29 +89,29 @@ public final class LinkedList<T> {
             nodeToCopy = node.next
         }
     }
-    
+
     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)
@@ -119,12 +119,12 @@ public final class LinkedList<T> {
         newNode.next = next
         prev?.next = newNode
         next?.previous = newNode
-        
+
         if prev == nil {
             head = newNode
         }
     }
-    
+
     public func insert(_ list: LinkedList, atIndex index: Int) {
         if list.isEmpty { return }
         var (prev, next) = nodesBeforeAndAfter(index: index)
@@ -144,32 +144,32 @@ public final class LinkedList<T> {
         prev?.next = next
         next?.previous = prev
     }
-    
+
     public func removeAll() {
         head = nil
     }
-    
+
     @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
     }
-    
+
     @discardableResult public func removeLast() -> T {
         assert(!isEmpty)
         return remove(node: last!)
     }
-    
+
     @discardableResult public func remove(atIndex index: Int) -> T {
         let node = self.node(atIndex: index)
         assert(node != nil)
@@ -211,7 +211,7 @@ extension LinkedList {
         }
         return result
     }
-    
+
     public func filter(predicate: (T) -> Bool) -> LinkedList<T> {
         let result = LinkedList<T>()
         var node = head
@@ -228,7 +228,7 @@ extension LinkedList {
 extension LinkedList {
     convenience init(array: Array<T>) {
         self.init()
-        
+
         for element in array {
             self.append(element)
         }
@@ -238,7 +238,7 @@ extension LinkedList {
 extension LinkedList: ExpressibleByArrayLiteral {
   public convenience init(arrayLiteral elements: T...) {
     self.init()
-    
+
     for element in elements {
       self.append(element)
     }
diff --git a/Linked List/Tests/LinkedListTests.swift b/Linked List/Tests/LinkedListTests.swift
index ea063cacb..7fd31c2c7 100755
--- a/Linked List/Tests/LinkedListTests.swift	
+++ b/Linked List/Tests/LinkedListTests.swift	
@@ -165,7 +165,7 @@ class LinkedListTest: XCTestCase {
     XCTAssertTrue(prev!.next === node)
     XCTAssertTrue(next!.previous === node)
   }
-  
+
   func testInsertListAtIndex() {
     let list = buildList()
     let list2 = LinkedList<Int>()
@@ -190,7 +190,7 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(list.node(atIndex: 1)?.value, 102)
     XCTAssertEqual(list.node(atIndex: 2)?.value, 8)
   }
-  
+
   func testInsertListAtLastIndex() {
     let list = buildList()
     let list2 = LinkedList<Int>()
@@ -202,7 +202,7 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
     XCTAssertEqual(list.node(atIndex: 7)?.value, 102)
   }
-  
+
   func testAppendList() {
     let list = buildList()
     let list2 = LinkedList<Int>()
@@ -214,7 +214,7 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(list.node(atIndex: 6)?.value, 99)
     XCTAssertEqual(list.node(atIndex: 7)?.value, 102)
   }
-  
+
   func testAppendListToEmptyList() {
     let list = LinkedList<Int>()
     let list2 = LinkedList<Int>()
@@ -225,7 +225,7 @@ class LinkedListTest: XCTestCase {
     XCTAssertEqual(list.node(atIndex: 0)?.value, 5)
     XCTAssertEqual(list.node(atIndex: 1)?.value, 10)
   }
-  
+
   func testRemoveAtIndexOnListWithOneElement() {
     let list = LinkedList<Int>()
     list.append(123)
@@ -308,10 +308,10 @@ class LinkedListTest: XCTestCase {
     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)
@@ -319,10 +319,10 @@ class LinkedListTest: XCTestCase {
     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)
diff --git a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift
index 9dca23996..ee2ace8b9 100644
--- a/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.playground/Sources/MRPrimality.swift	
@@ -23,38 +23,38 @@ import Foundation
  */
 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
 }
 
@@ -71,17 +71,17 @@ public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
  */
 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
 }
 
@@ -100,12 +100,12 @@ 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.swift b/Miller-Rabin Primality Test/MRPrimality.swift
index 9dca23996..ee2ace8b9 100644
--- a/Miller-Rabin Primality Test/MRPrimality.swift	
+++ b/Miller-Rabin Primality Test/MRPrimality.swift	
@@ -23,38 +23,38 @@ import Foundation
  */
 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
 }
 
@@ -71,17 +71,17 @@ public func mrPrimalityTest(_ n: UInt64, iteration k: Int = 1) -> Bool {
  */
 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
 }
 
@@ -100,12 +100,12 @@ 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/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift
index d651ddf2e..238afeb9b 100755
--- a/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
+++ b/Minimum Edit Distance/MinimumEditDistance.playground/Contents.swift	
@@ -1,21 +1,21 @@
 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() {
diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index 1a0320a65..5ca0d7d31 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -49,7 +49,7 @@ public struct OrderedArray<T: Comparable> {
   private func findInsertionPoint(_ newElement: T) -> Int {
     var startIndex = 0
     var endIndex = array.count
-    
+
     while startIndex < endIndex {
         let midIndex = startIndex + (endIndex - startIndex) / 2
         if array[midIndex] == newElement {
diff --git a/Palindromes/Palindromes.playground/Contents.swift b/Palindromes/Palindromes.playground/Contents.swift
index e8562a367..b9e857dd0 100644
--- a/Palindromes/Palindromes.playground/Contents.swift
+++ b/Palindromes/Palindromes.playground/Contents.swift
@@ -10,7 +10,7 @@ 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)
     }
@@ -28,14 +28,14 @@ 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.swift b/Palindromes/Palindromes.swift
index 2760137ca..9ddd04c80 100644
--- a/Palindromes/Palindromes.swift
+++ b/Palindromes/Palindromes.swift
@@ -3,7 +3,7 @@ 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)
     }
@@ -14,13 +14,13 @@ 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/Palindromes.swift b/Palindromes/Test/Palindromes.swift
index 2760137ca..9ddd04c80 100644
--- a/Palindromes/Test/Palindromes.swift
+++ b/Palindromes/Test/Palindromes.swift
@@ -3,7 +3,7 @@ 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)
     }
@@ -14,13 +14,13 @@ 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/Test.swift b/Palindromes/Test/Test/Test.swift
index 1dd79ea97..ddf970300 100644
--- a/Palindromes/Test/Test/Test.swift
+++ b/Palindromes/Test/Test/Test.swift
@@ -9,22 +9,22 @@
 import XCTest
 
 class PalindromeTests: XCTestCase {
-    
+
     override func setUp() {
         super.setUp()
         // Put setup code here. This method is called before the invocation of each test method in the class.
     }
-    
+
     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() {
         // This is an example of a functional test case.
         // Use XCTAssert and related functions to verify your tests produce the correct results.
     }
-    
+
     func testPerformanceExample() {
         // This is an example of a performance test case.
         self.measure {
@@ -34,12 +34,12 @@ class PalindromeTests: XCTestCase {
             _ = isPalindrome("abababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababa")
         }
     }
-    
+
     func testPalindromeWord() {
         XCTAssertTrue(isPalindrome("abbcbba"))
         XCTAssertTrue(isPalindrome("racecar"))
     }
-    
+
     func testPalindromeSentence() {
         XCTAssertTrue(isPalindrome("A man, a plan, a canal, Panama!"))
         XCTAssertTrue(isPalindrome("Madam, I'm Adam"))
@@ -47,17 +47,17 @@ class PalindromeTests: XCTestCase {
         XCTAssertTrue(isPalindrome("In girum imus nocte et consumimur igni"))
         XCTAssertTrue(isPalindrome("Never odd or even"))
     }
-    
+
     func testPalindromeNumber() {
         XCTAssertTrue(isPalindrome("5885"))
         XCTAssertTrue(isPalindrome("5 8 8 5"))
         XCTAssertTrue(isPalindrome("58 85"))
     }
-    
+
     func testSpecialCharacters() {
         XCTAssertTrue(isPalindrome("৯৯"))
     }
-    
+
     func testNonPalindromes() {
         XCTAssertFalse(isPalindrome("\\\\"))
         XCTAssertFalse(isPalindrome("desserts"))
diff --git a/QuadTree/QuadTree.playground/Sources/QuadTree.swift b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
index 14d0dbba7..7fd459e97 100644
--- a/QuadTree/QuadTree.playground/Sources/QuadTree.swift
+++ b/QuadTree/QuadTree.playground/Sources/QuadTree.swift
@@ -1,7 +1,7 @@
 public struct Point {
   let x: Double
   let y: Double
-  
+
   public init(_ x: Double, _ y: Double) {
     self.x = x
     self.y = y
@@ -17,18 +17,18 @@ extension Point: CustomStringConvertible {
 public struct Size: CustomStringConvertible {
   var xLength: Double
   var yLength: Double
-  
+
   public init(xLength: Double, yLength: Double) {
     precondition(xLength >= 0, "xLength can not be negative")
     precondition(yLength >= 0, "yLength can not be negative")
     self.xLength = xLength
     self.yLength = yLength
   }
-  
+
   var half: Size {
     return Size(xLength: xLength / 2, yLength: yLength / 2)
   }
-  
+
   public var description: String {
     return "Size(\(xLength), \(yLength))"
   }
@@ -38,49 +38,49 @@ public struct Rect {
   // left top vertice
   var origin: Point
   var size: Size
-  
+
   public init(origin: Point, size: Size) {
     self.origin = origin
     self.size = size
   }
-  
+
   var minX: Double {
     return origin.x
   }
-  
+
   var minY: Double {
     return origin.y
   }
-  
+
   var maxX: Double {
     return origin.x + size.xLength
   }
-  
+
   var maxY: Double {
     return origin.y + size.yLength
   }
-  
+
   func containts(point: Point) -> Bool {
     return (minX <= point.x && point.x <= maxX) &&
       (minY <= point.y && point.y <= maxY)
   }
-  
+
   var leftTopRect: Rect {
     return Rect(origin: origin, size: size.half)
   }
-  
+
   var leftBottomRect: Rect {
     return Rect(origin: Point(origin.x, origin.y + size.half.yLength), size: size.half)
   }
-  
+
   var rightTopRect: Rect {
     return Rect(origin: Point(origin.x + size.half.xLength, origin.y), size: size.half)
   }
-  
+
   var rightBottomRect: Rect {
     return Rect(origin: Point(origin.x + size.half.xLength, origin.y + size.half.yLength), size: size.half)
   }
-  
+
   func intersects(rect: Rect) -> Bool {
 
     func lineSegmentsIntersect(lStart: Double, lEnd: Double, rStart: Double, rEnd: Double) -> Bool {
@@ -91,7 +91,7 @@ public struct Rect {
     if !lineSegmentsIntersect(lStart: minX, lEnd: maxX, rStart: rect.minX, rEnd: rect.maxX) {
       return false
     }
-    
+
     // vertical
     return lineSegmentsIntersect(lStart: minY, lEnd: maxY, rStart: rect.minY, rEnd: rect.maxY)
   }
@@ -109,37 +109,37 @@ protocol PointsContainer {
 }
 
 class QuadTreeNode {
-  
+
   enum NodeType {
     case leaf
     case `internal`(children: Children)
   }
-  
+
   struct Children: Sequence {
     let leftTop: QuadTreeNode
     let leftBottom: QuadTreeNode
     let rightTop: QuadTreeNode
     let rightBottom: QuadTreeNode
-    
+
     init(parentNode: QuadTreeNode) {
       leftTop = QuadTreeNode(rect: parentNode.rect.leftTopRect)
       leftBottom = QuadTreeNode(rect: parentNode.rect.leftBottomRect)
       rightTop = QuadTreeNode(rect: parentNode.rect.rightTopRect)
       rightBottom = QuadTreeNode(rect: parentNode.rect.rightBottomRect)
     }
-    
+
     struct ChildrenIterator: IteratorProtocol {
       private var index = 0
       private let children: Children
-      
+
       init(children: Children) {
         self.children = children
       }
-      
+
       mutating func next() -> QuadTreeNode? {
-        
+
         defer { index += 1 }
-        
+
         switch index {
         case 0: return children.leftTop
         case 1: return children.leftBottom
@@ -149,26 +149,26 @@ class QuadTreeNode {
         }
       }
     }
-    
+
     public func makeIterator() -> ChildrenIterator {
       return ChildrenIterator(children: self)
     }
   }
-  
+
   var points: [Point] = []
   let rect: Rect
   var type: NodeType = .leaf
-  
+
   static let maxPointCapacity = 3
-  
+
   init(rect: Rect) {
     self.rect = rect
   }
-  
+
   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"
@@ -185,13 +185,13 @@ class QuadTreeNode {
 }
 
 extension QuadTreeNode: PointsContainer {
-  
+
   @discardableResult
   func add(point: Point) -> Bool {
     if !rect.containts(point: point) {
       return false
     }
-    
+
     switch type {
     case .internal(let children):
       // pass the point to one of the children
@@ -200,7 +200,7 @@ extension QuadTreeNode: PointsContainer {
           return true
         }
       }
-      
+
       fatalError("rect.containts evaluted to true, but none of the children added the point")
     case .leaf:
       points.append(point)
@@ -211,7 +211,7 @@ extension QuadTreeNode: PointsContainer {
     }
     return true
   }
-  
+
   private func subdivide() {
     switch type {
     case .leaf:
@@ -220,25 +220,25 @@ extension QuadTreeNode: PointsContainer {
       preconditionFailure("Calling subdivide on an internal node")
     }
   }
-  
+
   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) {
         result.append(point)
       }
     }
-    
+
     switch type {
     case .leaf:
       break
@@ -248,7 +248,7 @@ extension QuadTreeNode: PointsContainer {
         result.append(contentsOf: childNode.points(inRect: rect))
       }
     }
-    
+
     return result
   }
 }
@@ -265,18 +265,18 @@ extension QuadTreeNode: CustomStringConvertible {
 }
 
 public class QuadTree: PointsContainer {
-  
+
   let root: QuadTreeNode
-  
+
   public init(rect: Rect) {
     self.root = QuadTreeNode(rect: rect)
   }
-  
+
   @discardableResult
   public func add(point: Point) -> Bool {
     return root.add(point: point)
   }
-  
+
   public func points(inRect rect: Rect) -> [Point] {
     return root.points(inRect: rect)
   }
diff --git a/QuadTree/Tests/Tests/Tests.swift b/QuadTree/Tests/Tests/Tests.swift
index b408c4f7e..9bd8ad28f 100644
--- a/QuadTree/Tests/Tests/Tests.swift
+++ b/QuadTree/Tests/Tests/Tests.swift
@@ -17,68 +17,68 @@ public func == (lhs: Point, rhs: Point) -> Bool {
 }
 
 class Tests: XCTestCase {
-  
+
   func testRectContains() {
     let rect = Rect(origin: Point(0, 0), size: Size(xLength: 3, yLength: 3))
-    
+
     XCTAssertTrue(rect.containts(point: Point(1, 1)))
     XCTAssertTrue(rect.containts(point: Point(0, 0)))
     XCTAssertTrue(rect.containts(point: Point(0, 3)))
     XCTAssertTrue(rect.containts(point: Point(3, 3)))
-    
+
     XCTAssertFalse(rect.containts(point: Point(-1, 1)))
     XCTAssertFalse(rect.containts(point: Point(-0.1, 0.1)))
     XCTAssertFalse(rect.containts(point: Point(0, 3.1)))
     XCTAssertFalse(rect.containts(point: Point(-4, 1)))
   }
-  
+
   func testIntersects() {
     let rect = Rect(origin: Point(0, 0), size: Size(xLength: 5, yLength: 5))
     let rect2 = Rect(origin: Point(1, 1), size: Size(xLength: 1, yLength: 1))
     XCTAssertTrue(rect.intersects(rect: rect2))
-    
+
     let rect3 = Rect(origin: Point(1, 0), size: Size(xLength: 1, yLength: 10))
     let rect4 = Rect(origin: Point(0, 1), size: Size(xLength: 10, yLength: 1))
     XCTAssertTrue(rect3.intersects(rect: rect4))
-    
+
     let rect5 = Rect(origin: Point(0, 0), size: Size(xLength: 4, yLength: 4))
     let rect6 = Rect(origin: Point(2, 2), size: Size(xLength: 4, yLength: 4))
     XCTAssertTrue(rect5.intersects(rect: rect6))
-    
+
     let rect7 = Rect(origin: Point(0, 0), size: Size(xLength: 4, yLength: 4))
     let rect8 = Rect(origin: Point(4, 4), size: Size(xLength: 1, yLength: 1))
     XCTAssertTrue(rect7.intersects(rect: rect8))
-    
+
     let rect9 = Rect(origin: Point(-1, -1), size: Size(xLength: 0.5, yLength: 0.5))
     let rect10 = Rect(origin: Point(0, 0), size: Size(xLength: 1, yLength: 1))
     XCTAssertFalse(rect9.intersects(rect: rect10))
-    
+
     let rect11 = Rect(origin: Point(0, 0), size: Size(xLength: 2, yLength: 1))
     let rect12 = Rect(origin: Point(3, 0), size: Size(xLength: 1, yLength: 1))
     XCTAssertFalse(rect11.intersects(rect: rect12))
   }
-  
+
   func testQuadTree() {
     let rect = Rect(origin: Point(0, 0), size: Size(xLength: 5, yLength: 5))
     let qt = QuadTree(rect: rect)
-    
+
     XCTAssertTrue(qt.points(inRect: rect) == [Point]())
-    
+
     XCTAssertFalse(qt.add(point: Point(-0.1, 0.1)))
-    
+
     XCTAssertTrue(qt.points(inRect: rect) == [Point]())
-    
+
     XCTAssertTrue(qt.add(point: Point(1, 1)))
     XCTAssertTrue(qt.add(point: Point(3, 3)))
     XCTAssertTrue(qt.add(point: Point(4, 4)))
     XCTAssertTrue(qt.add(point: Point(0.5, 0.5)))
-    
+
     XCTAssertFalse(qt.add(point: Point(5.5, 0)))
     XCTAssertFalse(qt.add(point: Point(5.5, 1)))
     XCTAssertFalse(qt.add(point: Point(5.5, 2)))
-    
+
     XCTAssertTrue(qt.add(point: Point(1.5, 1.5)))
-    
+
     let rect2 = Rect(origin: Point(0, 0), size: Size(xLength: 2, yLength: 2))
     XCTAssertTrue(qt.points(inRect: rect2) == [Point(1, 1), Point(0.5, 0.5), Point(1.5, 1.5)])
   }
diff --git a/Radix Sort/RadixSort.playground/Sources/radixSort.swift b/Radix Sort/RadixSort.playground/Sources/radixSort.swift
index 136ede4fd..81c2479e8 100644
--- a/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
+++ b/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
@@ -11,18 +11,18 @@ public func radixSort(_ array: inout [Int] ) {
   var done = false
   var index: Int
   var digit = 1  //Which digit are we on?
-  
-  
+
+
   while !done {  //While our  sorting is not completed
     done = true  //Assume it is done for now
-    
+
     var buckets: [[Int]] = []  //Our sorting subroutine is bucket sort, so let us predefine our buckets
-    
+
     for _ in 1...radix {
       buckets.append([])
     }
-    
-    
+
+
     for number in array {
       index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
@@ -30,9 +30,9 @@ public func radixSort(_ array: inout [Int] ) {
         done = false
       }
     }
-    
+
     var i = 0
-    
+
     for j in 0..<radix {
       let bucket = buckets[j]
       for number in bucket {
@@ -40,7 +40,7 @@ public func radixSort(_ array: inout [Int] ) {
         i += 1
       }
     }
-    
+
     digit *= radix  //Move to the next digit
   }
 }
diff --git a/Radix Sort/RadixSortExample.swift b/Radix Sort/RadixSortExample.swift
index 7d9461c5c..f64dcfeb9 100644
--- a/Radix Sort/RadixSortExample.swift	
+++ b/Radix Sort/RadixSortExample.swift	
@@ -9,21 +9,21 @@
 import Foundation
 
 func radixSort1(_ arr: inout [Int]) {
-   
+
     var temp = [[Int]](repeating: [], count: 10)
-    
+
     for num in arr { temp[num % 10].append(num) }
-    
+
     for i in 1...Int(arr.max()!.description.characters.count) {
-        
+
         for index in 0..<temp.count {
-           
+
             for num in temp[index] {
                 temp[index].remove(at: temp[index].index(of: num)!)
                 temp[(num / Int(pow(10, Double(i)))) % 10].append(num)
             }
         }
     }
-    
+
     arr = temp[0]
 }
diff --git a/Radix Sort/radixSort.swift b/Radix Sort/radixSort.swift
index 24d4155d7..9e48093ef 100644
--- a/Radix Sort/radixSort.swift	
+++ b/Radix Sort/radixSort.swift	
@@ -11,18 +11,18 @@ func radixSort(_ array: inout [Int] ) {
   var done = false
   var index: Int
   var digit = 1  //Which digit are we on?
-  
-  
+
+
   while !done {  //While our  sorting is not completed
     done = true  //Assume it is done for now
-    
+
     var buckets: [[Int]] = []  //Our sorting subroutine is bucket sort, so let us predefine our buckets
-    
+
     for _ in 1...radix {
       buckets.append([])
     }
-    
-    
+
+
     for number in array {
       index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
@@ -30,9 +30,9 @@ func radixSort(_ array: inout [Int] ) {
         done = false
       }
     }
-    
+
     var i = 0
-    
+
     for j in 0..<radix {
       let bucket = buckets[j]
       for number in bucket {
@@ -40,7 +40,7 @@ func radixSort(_ array: inout [Int] ) {
         i += 1
       }
     }
-    
+
     digit *= radix  //Move to the next digit
   }
 }
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift b/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift
index d55c153d5..791ae822a 100644
--- a/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift	
+++ b/Red-Black Tree/Red-Black Tree 2.playground/Contents.swift	
@@ -10,7 +10,7 @@ for _ in 0..<1000 {
     tree.insert(value)
 }
 tree.verify()
- 
+
 for _ in 0..<1000 {
     let rand = arc4random_uniform(UInt32(values.count))
     let index = Int(rand)
diff --git a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift
index 42a68237e..97bb52422 100644
--- a/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
+++ b/Red-Black Tree/Red-Black Tree 2.playground/Sources/RBTree.swift	
@@ -10,13 +10,13 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
     public var right: RBTNode<T>!
     public var left: RBTNode<T>!
     public var parent: RBTNode<T>!
-    
+
     public var description: String {
         if self.value == nil {
             return "null"
         } else {
             var nodeValue: String
-            
+
             // If the value is encapsulated by parentheses it is red
             // If the value is encapsulated by pipes it is black
             // If the value is encapsulated by double pipes it is double black (This should not occur in a verified RBTree)
@@ -27,33 +27,33 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
             } else {
                 nodeValue = "||\(self.value!)||"
             }
-            
+
             return "(\(self.left.description)<-\(nodeValue)->\(self.right.description))"
         }
     }
-    
+
     init(tree: RBTree<T>) {
         right = tree.nullLeaf
         left = tree.nullLeaf
         parent = tree.nullLeaf
     }
-    
+
     init() {
         //This method is here to support the creation of a nullLeaf
     }
-    
+
     public var isLeftChild: Bool {
         return self.parent.left === self
     }
-    
+
     public var isRightChild: Bool {
         return self.parent.right === self
     }
-    
+
     public var grandparent: RBTNode<T> {
         return parent.parent
     }
-    
+
     public var sibling: RBTNode<T> {
         if isLeftChild {
             return self.parent.right
@@ -61,19 +61,19 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
             return self.parent.left
         }
     }
-    
+
     public var uncle: RBTNode<T> {
         return parent.sibling
     }
-    
+
     fileprivate var isRed: Bool {
         return color == .red
     }
-    
+
     fileprivate var isBlack: Bool {
         return color == .black
     }
-    
+
     fileprivate var isDoubleBlack: Bool {
         return color == .doubleBlack
     }
@@ -82,70 +82,70 @@ public class RBTNode<T: Comparable>: CustomStringConvertible {
 public class RBTree<T: Comparable>: CustomStringConvertible {
     public var root: RBTNode<T>
     fileprivate let nullLeaf: RBTNode<T>
-    
+
     public var description: String {
         return root.description
     }
-    
+
     public init() {
         nullLeaf = RBTNode<T>()
         nullLeaf.color = .black
         root = nullLeaf
     }
-    
+
     public convenience init(withValue value: T) {
         self.init()
         insert(value)
     }
-    
+
     public convenience init(withArray array: [T]) {
         self.init()
         insert(array)
     }
-    
+
     public func insert(_ value: T) {
         let newNode = RBTNode<T>(tree: self)
         newNode.value = value
         insertNode(n: newNode)
     }
-    
+
     public func insert(_ values: [T]) {
         for value in values {
             print(value)
             insert(value)
         }
     }
-    
+
     public func delete(_ value: T) {
         let nodeToDelete = find(value)
         if nodeToDelete !== nullLeaf {
             deleteNode(n: nodeToDelete)
         }
     }
-    
+
     public func find(_ value: T) -> RBTNode<T> {
         let foundNode = findNode(rootNode: root, value: value)
         return foundNode
     }
-    
+
     public func minimum(n: RBTNode<T>) -> RBTNode<T> {
         var min = n
         if n.left !== nullLeaf {
             min = minimum(n: n.left)
         }
-        
+
         return min
     }
-    
+
     public func maximum(n: RBTNode<T>) -> RBTNode<T> {
         var max = n
         if n.right !== nullLeaf {
             max = maximum(n: n.right)
         }
-        
+
         return max
     }
-    
+
     public func verify() {
         if self.root === nullLeaf {
             print("The tree is empty")
@@ -155,7 +155,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
         property2(n: self.root)
         property3()
     }
-    
+
     private func findNode(rootNode: RBTNode<T>, value: T) -> RBTNode<T> {
         var nextNode = rootNode
         if rootNode !== nullLeaf && value != rootNode.value {
@@ -165,15 +165,15 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
                 nextNode = findNode(rootNode: rootNode.right, value: value)
             }
         }
-        
+
         return nextNode
     }
-    
+
     private func insertNode(n: RBTNode<T>) {
         BSTInsertNode(n: n, parent: root)
         insertCase1(n: n)
     }
-    
+
     private func BSTInsertNode(n: RBTNode<T>, parent: RBTNode<T>) {
         if parent === nullLeaf {
             self.root = n
@@ -193,7 +193,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             }
         }
     }
-    
+
     // if node is root change color to black, else move on
     private func insertCase1(n: RBTNode<T>) {
         if n === root {
@@ -202,14 +202,14 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             insertCase2(n: n)
         }
     }
-    
+
     // if parent of node is not black, and node is not root move on
     private func insertCase2(n: RBTNode<T>) {
         if !n.parent.isBlack {
             insertCase3(n: n)
         }
     }
-    
+
     // if uncle is red do stuff otherwise move to 4
     private func insertCase3(n: RBTNode<T>) {
         if n.uncle.isRed { // node must have grandparent as children of root have a black parent
@@ -224,14 +224,14 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             insertCase4(n: n)
         }
     }
-    
+
     // parent is red, grandparent is black, uncle is black
     // There are 4 cases left:
     // - left left
     // - left right
     // - right right
     // - right left
-    
+
     // the cases "left right" and "right left" can be rotated into the other two
     // so if either of the two is detected we apply a rotation and then move on to
     // deal with the final two cases, if neither is detected we move on to those cases anyway
@@ -246,28 +246,28 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             insertCase5(n: n)
         }
     }
-    
+
     private func insertCase5(n: RBTNode<T>) {
         // swap color of parent and grandparent
         // parent is red grandparent is black
         n.parent.color = .black
         n.grandparent.color = .red
-        
+
         if n.isLeftChild { // left left case
             rightRotate(n: n.grandparent)
         } else { // right right case
             leftRotate(n: n.grandparent)
         }
     }
-    
+
     private func deleteNode(n: RBTNode<T>) {
         var toDel = n
-        
+
         if toDel.left === nullLeaf && toDel.right === nullLeaf && toDel.parent === nullLeaf {
             self.root = nullLeaf
             return
         }
-        
+
         if toDel.left === nullLeaf && toDel.right === nullLeaf && toDel.isRed {
             if toDel.isLeftChild {
                 toDel.parent.left = nullLeaf
@@ -276,38 +276,38 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             }
             return
         }
-        
+
         if toDel.left !== nullLeaf && toDel.right !== nullLeaf {
             let pred = maximum(n: toDel.left)
             toDel.value = pred.value
             toDel = pred
         }
-        
+
         // from here toDel has at most 1 non nullLeaf child
-        
+
         var child: RBTNode<T>
         if toDel.left !== nullLeaf {
             child = toDel.left
         } else {
             child = toDel.right
         }
-        
+
         if toDel.isRed || child.isRed {
             child.color = .black
-            
+
             if toDel.isLeftChild {
                 toDel.parent.left = child
             } else {
                 toDel.parent.right = child
             }
-            
+
             if child !== nullLeaf {
                 child.parent = toDel.parent
             }
         } else { // both toDel and child are black
-            
+
             var sibling = toDel.sibling
-            
+
             if toDel.isLeftChild {
                 toDel.parent.left = child
             } else {
@@ -317,10 +317,10 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
                 child.parent = toDel.parent
             }
             child.color = .doubleBlack
-            
+
             while child.isDoubleBlack || (child.parent !== nullLeaf && child.parent != nil) {
                 if sibling.isBlack {
-                    
+
                     var leftRedChild: RBTNode<T>! = nil
                     if sibling.left.isRed {
                         leftRedChild = sibling.left
@@ -329,7 +329,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
                     if sibling.right.isRed {
                         rightRedChild = sibling.right
                     }
-                    
+
                     if leftRedChild != nil || rightRedChild != nil { // at least one of sibling's children are red
                         child.color = .black
                         if sibling.isLeftChild {
@@ -389,7 +389,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
                     }
                 } else { // sibling is red
                     sibling.color = .black
-                    
+
                     if sibling.isLeftChild { // left case
                         rightRotate(n: sibling.parent)
                         sibling = sibling.right.left
@@ -400,7 +400,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
                         sibling.parent.color = .red
                     }
                 }
-                
+
                 // sibling check is here for when child is a nullLeaf and thus does not have a parent.
                 // child is here as sibling can become nil when child is the root
                 if (sibling.parent === nullLeaf) || (child !== nullLeaf && child.parent === nullLeaf) {
@@ -409,14 +409,14 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             }
         }
     }
-    
+
     private func property1() {
-        
+
         if self.root.isRed {
             print("Root is not black")
         }
     }
-    
+
     private func property2(n: RBTNode<T>) {
         if n === nullLeaf {
             return
@@ -431,48 +431,48 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
         property2(n: n.left)
         property2(n: n.right)
     }
-    
+
     private func property3() {
         let bDepth = blackDepth(root: self.root)
-        
+
         let leaves: [RBTNode<T>] = getLeaves(n: self.root)
-        
+
         for leaflet in leaves {
             var leaf = leaflet
             var i = 0
-            
+
             while leaf !== nullLeaf {
                 if leaf.isBlack {
                     i = i + 1
                 }
                 leaf = leaf.parent
             }
-            
+
             if i != bDepth {
                 print("black depth: \(bDepth), is not equal (depth: \(i)) for leaf with value: \(leaflet.value)")
             }
         }
-        
+
     }
-    
+
     private func getLeaves(n: RBTNode<T>) -> [RBTNode<T>] {
         var leaves = [RBTNode<T>]()
-        
+
         if n !== nullLeaf {
             if n.left === nullLeaf && n.right === nullLeaf {
                 leaves.append(n)
             } else {
                 let leftLeaves = getLeaves(n: n.left)
                 let rightLeaves = getLeaves(n: n.right)
-                
+
                 leaves.append(contentsOf: leftLeaves)
                 leaves.append(contentsOf: rightLeaves)
             }
         }
-        
+
         return leaves
     }
-    
+
     private func blackDepth(root: RBTNode<T>) -> Int {
         if root === nullLeaf {
             return 0
@@ -481,7 +481,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
             return returnValue + (max(blackDepth(root: root.left), blackDepth(root: root.right)))
         }
     }
-    
+
     private func leftRotate(n: RBTNode<T>) {
         let newRoot = n.right!
         n.right = newRoot.left!
@@ -499,7 +499,7 @@ public class RBTree<T: Comparable>: CustomStringConvertible {
         newRoot.left = n
         n.parent = newRoot
     }
-    
+
     private func rightRotate(n: RBTNode<T>) {
         let newRoot = n.left!
         n.left = newRoot.right!
diff --git a/Run-Length Encoding/RLE.playground/Contents.swift b/Run-Length Encoding/RLE.playground/Contents.swift
index 11e177d0d..26f7dca48 100644
--- a/Run-Length Encoding/RLE.playground/Contents.swift	
+++ b/Run-Length Encoding/RLE.playground/Contents.swift	
@@ -12,16 +12,16 @@ originalString == restoredString
 
 func encodeAndDecode(_ bytes: [UInt8]) -> Bool {
     var bytes = bytes
-    
+
     var data1 = Data(bytes: &bytes, count: bytes.count)
     print("data1 is \(data1.count) bytes")
-    
+
     var rleData = data1.compressRLE()
     print("encoded data is \(rleData.count) bytes")
-    
+
     var data2 = rleData.decompressRLE()
     print("data2 is \(data2.count) bytes")
-    
+
     return data1 == data2
 }
 
@@ -66,10 +66,10 @@ func testBufferWithoutSpans() -> Bool {
 
 func testBufferWithSpans(_ spanSize: Int) -> Bool {
     print("span size \(spanSize)")
-    
+
     let length = spanSize * 32
     var bytes: [UInt8] = Array<UInt8>(repeating: 0, count: length)
-    
+
     for t in stride(from: 0, to: length, by: spanSize) {
         for i in 0..<spanSize {
             bytes[t + i] = UInt8(t % 256)
@@ -109,7 +109,7 @@ func runTests() -> Bool {
     for bool in tests {
         result = result && bool
     }
-    
+
     return result
 }
 
diff --git a/Run-Length Encoding/RLE.playground/Sources/RLE.swift b/Run-Length Encoding/RLE.playground/Sources/RLE.swift
index 5707e3d9d..0bb6fa00d 100644
--- a/Run-Length Encoding/RLE.playground/Sources/RLE.swift	
+++ b/Run-Length Encoding/RLE.playground/Sources/RLE.swift	
@@ -13,7 +13,7 @@ extension Data {
                 var count = 0
                 var byte = ptr.pointee
                 var next = byte
-                
+
                 // Is the next byte the same? Keep reading until we find a different
                 // value, or we reach the end of the data, or the run is 64 bytes.
                 while next == byte && ptr < end && count < 64 {
@@ -21,7 +21,7 @@ extension Data {
                     next = ptr.pointee
                     count += 1
                 }
-                
+
                 if count > 1 || byte >= 192 {       // byte run of up to 64 repeats
                     var size = 191 + UInt8(count)
                     data.append(&size, count: 1)
@@ -33,7 +33,7 @@ extension Data {
         }
         return data
     }
-    
+
     /*
      Converts a run-length encoded NSData back to the original.
      */
@@ -42,20 +42,20 @@ extension Data {
         self.withUnsafeBytes { (uPtr: UnsafePointer<UInt8>) in
             var ptr = uPtr
             let end = ptr + count
-            
+
             while ptr < end {
                 // Read the next byte. This is either a single value less than 192,
                 // or the start of a byte run.
                 var byte = ptr.pointee
                 ptr = ptr.advanced(by: 1)
-                
+
                 if byte < 192 {                     // single value
                     data.append(&byte, count: 1)
                 } else if ptr < end {               // byte run
                     // Read the actual data value.
                     var value = ptr.pointee
                     ptr = ptr.advanced(by: 1)
-                    
+
                     // And write it out repeatedly.
                     for _ in 0 ..< byte - 191 {
                         data.append(&value, count: 1)
diff --git a/Segment Tree/SegmentTree.playground/Contents.swift b/Segment Tree/SegmentTree.playground/Contents.swift
index 5bba56cc0..08474aee2 100644
--- a/Segment Tree/SegmentTree.playground/Contents.swift	
+++ b/Segment Tree/SegmentTree.playground/Contents.swift	
@@ -1,19 +1,19 @@
 //: Playground - noun: a place where people can play
 
 public class SegmentTree<T> {
-	
+
 	private var value: T
 	private var function: (T, T) -> T
 	private var leftBound: Int
 	private var rightBound: Int
 	private var leftChild: SegmentTree<T>?
 	private var rightChild: SegmentTree<T>?
-	
+
 	public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
 		self.leftBound = leftBound
 		self.rightBound = rightBound
 		self.function = function
-		
+
 		if leftBound == rightBound {
 			value = array[leftBound]
 		} else {
@@ -23,19 +23,19 @@ public class SegmentTree<T> {
 			value = function(leftChild!.value, rightChild!.value)
 		}
 	}
-	
+
 	public convenience init(array: [T], function: @escaping (T, T) -> T) {
 		self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
 	}
-	
+
 	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") }
-		
+
 		if leftChild.rightBound < leftBound {
 			return rightChild.query(leftBound: leftBound, rightBound: rightBound)
 		} else if rightChild.leftBound > rightBound {
@@ -46,7 +46,7 @@ public class SegmentTree<T> {
 			return function(leftResult, rightResult)
 		}
 	}
-	
+
 	public func replaceItem(at index: Int, withItem item: T) {
 		if leftBound == rightBound {
 			value = item
@@ -83,7 +83,7 @@ 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
diff --git a/Segment Tree/SegmentTree.swift b/Segment Tree/SegmentTree.swift
index a3ec8b1bf..6f4edd306 100644
--- a/Segment Tree/SegmentTree.swift	
+++ b/Segment Tree/SegmentTree.swift	
@@ -8,19 +8,19 @@
 */
 
 public class SegmentTree<T> {
-	
+
 	private var value: T
 	private var function: (T, T) -> T
 	private var leftBound: Int
 	private var rightBound: Int
 	private var leftChild: SegmentTree<T>?
 	private var rightChild: SegmentTree<T>?
-	
+
 	public init(array: [T], leftBound: Int, rightBound: Int, function: @escaping (T, T) -> T) {
 		self.leftBound = leftBound
 		self.rightBound = rightBound
 		self.function = function
-		
+
 		if leftBound == rightBound {
 			value = array[leftBound]
 		} else {
@@ -30,19 +30,19 @@ public class SegmentTree<T> {
 			value = function(leftChild!.value, rightChild!.value)
 		}
 	}
-	
+
 	public convenience init(array: [T], function: @escaping (T, T) -> T) {
 		self.init(array: array, leftBound: 0, rightBound: array.count-1, function: function)
 	}
-	
+
 	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") }
-		
+
 		if leftChild.rightBound < leftBound {
 			return rightChild.query(leftBound: leftBound, rightBound: rightBound)
 		} else if rightChild.leftBound > rightBound {
@@ -53,7 +53,7 @@ public class SegmentTree<T> {
 			return function(leftResult, rightResult)
 		}
 	}
-	
+
 	public func replaceItem(at index: Int, withItem item: T) {
 		if leftBound == rightBound {
 			value = item
diff --git a/Select Minimum Maximum/MinimumMaximumPairs.swift b/Select Minimum Maximum/MinimumMaximumPairs.swift
index b7deb570a..81942b303 100644
--- a/Select Minimum Maximum/MinimumMaximumPairs.swift	
+++ b/Select Minimum Maximum/MinimumMaximumPairs.swift	
@@ -35,6 +35,6 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
             }
         }
     }
-    
+
     return (minimum, maximum)
 }
diff --git a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift
index 182060805..dbf3a7468 100644
--- a/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
+++ b/Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift	
@@ -4,7 +4,7 @@ func minimum<T: Comparable>(_ array: [T]) -> T? {
   guard !array.isEmpty else {
     return nil
   }
-  
+
   var minimum = array.removeFirst()
   for element in array {
     minimum = element < minimum ? element : minimum
@@ -18,7 +18,7 @@ func maximum<T: Comparable>(_ array: [T]) -> T? {
   guard !array.isEmpty else {
     return nil
   }
-  
+
   var maximum = array.removeFirst()
   for element in array {
     maximum = element > maximum ? element : maximum
@@ -32,18 +32,18 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
   guard !array.isEmpty else {
     return nil
   }
-  
+
   var minimum = array.first!
   var maximum = array.first!
-  
+
   let hasOddNumberOfItems = array.count % 2 != 0
   if hasOddNumberOfItems {
     array.removeFirst()
   }
-  
+
   while !array.isEmpty {
     let pair = (array.removeFirst(), array.removeFirst())
-    
+
     if pair.0 > pair.1 {
       if pair.0 > maximum {
         maximum = pair.0
@@ -60,7 +60,7 @@ func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
       }
     }
   }
-  
+
   return (minimum, maximum)
 }
 
diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index aaf58cf4d..e9cee7543 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -10,18 +10,18 @@ import Foundation
 
 public func shellSort(_ list : inout [Int]) {
     var sublistCount = list.count / 2
-    
+
     while sublistCount > 0 {
         for var 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 }
-            
+
             while list[index - 1] > list[index] && index - 1 > 0 {
                 swap(&list[index - 1], &list[index])
                 index -= 1
diff --git a/Shortest Path (Unweighted)/Tests/Graph.swift b/Shortest Path (Unweighted)/Tests/Graph.swift
index 8322ba0a9..4d2e59eab 100644
--- a/Shortest Path (Unweighted)/Tests/Graph.swift	
+++ b/Shortest Path (Unweighted)/Tests/Graph.swift	
@@ -2,7 +2,7 @@
 
 open class Edge: Equatable {
     open var neighbor: Node
-    
+
     public init(neighbor: Node) {
         self.neighbor = neighbor
     }
@@ -17,28 +17,28 @@ public func == (lhs: Edge, rhs: Edge) -> Bool {
 
 open class Node: CustomStringConvertible, Equatable {
     open var neighbors: [Edge]
-    
+
     open fileprivate(set) var label: String
     open var distance: Int?
     open var visited: Bool
-    
+
     public init(label: String) {
         self.label = label
         neighbors = []
         visited = false
     }
-    
+
     open var description: String {
         if let distance = distance {
             return "Node(label: \(label), distance: \(distance))"
         }
         return "Node(label: \(label), distance: infinity)"
     }
-    
+
     open var hasDistance: Bool {
         return distance != nil
     }
-    
+
     open func remove(_ edge: Edge) {
         neighbors.remove(at: neighbors.index { $0 === edge }!)
     }
@@ -52,25 +52,25 @@ public func == (lhs: Node, rhs: Node) -> Bool {
 
 open class Graph: CustomStringConvertible, Equatable {
     open fileprivate(set) var nodes: [Node]
-    
+
     public init() {
         self.nodes = []
     }
-    
+
     open func addNode(label: String) -> Node {
         let node = Node(label: label)
         nodes.append(node)
         return node
     }
-    
+
     open func addEdge(_ source: Node, neighbor: Node) {
         let edge = Edge(neighbor: neighbor)
         source.neighbors.append(edge)
     }
-    
+
     open var description: String {
         var description = ""
-        
+
         for node in nodes {
             if !node.neighbors.isEmpty {
                 description += "[node: \(node.label) edges: \(node.neighbors.map { $0.neighbor.label})]"
@@ -78,18 +78,18 @@ open class Graph: CustomStringConvertible, Equatable {
         }
         return description
     }
-    
+
     open func findNodeWithLabel(label: String) -> Node {
         return nodes.filter { $0.label == label }.first!
     }
-    
+
     open func duplicate() -> Graph {
         let duplicated = Graph()
-        
+
         for node in nodes {
             duplicated.addNode(label: node.label)
         }
-        
+
         for node in nodes {
             for edge in node.neighbors {
                 let source = duplicated.findNodeWithLabel(label: node.label)
@@ -97,7 +97,7 @@ open class Graph: CustomStringConvertible, Equatable {
                 duplicated.addEdge(source, neighbor: neighbour)
             }
         }
-        
+
         return duplicated
     }
 }
diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index fa9f5745b..bd4d15515 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -12,7 +12,7 @@ public enum OperatorType: CustomStringConvertible {
   case multiply
   case percent
   case exponent
-  
+
   public var description: String {
     switch self {
     case .add:
@@ -36,7 +36,7 @@ public enum TokenType: CustomStringConvertible {
   case closeBracket
   case Operator(OperatorToken)
   case operand(Double)
-  
+
   public var description: String {
     switch self {
     case .openBracket:
@@ -53,11 +53,11 @@ public enum TokenType: CustomStringConvertible {
 
 public struct OperatorToken: CustomStringConvertible {
   let operatorType: OperatorType
-  
+
   init(operatorType: OperatorType) {
     self.operatorType = operatorType
   }
-  
+
   var precedence: Int {
     switch operatorType {
     case .add, .subtract:
@@ -68,7 +68,7 @@ public struct OperatorToken: CustomStringConvertible {
       return 10
     }
   }
-  
+
   var associativity: OperatorAssociativity {
     switch operatorType {
     case .add, .subtract, .divide, .multiply, .percent:
@@ -77,7 +77,7 @@ public struct OperatorToken: CustomStringConvertible {
       return .rightAssociative
     }
   }
-  
+
   public var description: String {
     return operatorType.description
   }
@@ -93,19 +93,19 @@ func < (left: OperatorToken, right: OperatorToken) -> Bool {
 
 public struct Token: CustomStringConvertible {
   let tokenType: TokenType
-  
+
   init(tokenType: TokenType) {
     self.tokenType = tokenType
   }
-  
+
   init(operand: Double) {
     tokenType = .operand(operand)
   }
-  
+
   init(operatorType: OperatorType) {
     tokenType = .Operator(OperatorToken(operatorType: operatorType))
   }
-  
+
   var isOpenBracket: Bool {
     switch tokenType {
     case .openBracket:
@@ -114,7 +114,7 @@ public struct Token: CustomStringConvertible {
       return false
     }
   }
-  
+
   var isOperator: Bool {
     switch tokenType {
     case .Operator(_):
@@ -123,7 +123,7 @@ public struct Token: CustomStringConvertible {
       return false
     }
   }
-  
+
   var operatorToken: OperatorToken? {
     switch tokenType {
     case .Operator(let operatorToken):
@@ -132,7 +132,7 @@ public struct Token: CustomStringConvertible {
       return nil
     }
   }
-  
+
   public var description: String {
     return tokenType.description
   }
@@ -140,27 +140,27 @@ public struct Token: CustomStringConvertible {
 
 public class InfixExpressionBuilder {
   private var expression = [Token]()
-  
+
   public func addOperator(_ operatorType: OperatorType) -> InfixExpressionBuilder {
     expression.append(Token(operatorType: operatorType))
     return self
   }
-  
+
   public func addOperand(_ operand: Double) -> InfixExpressionBuilder {
     expression.append(Token(operand: operand))
     return self
   }
-  
+
   public func addOpenBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .openBracket))
     return self
   }
-  
+
   public func addCloseBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .closeBracket))
     return self
   }
-  
+
   public func build() -> [Token] {
     // Maybe do some validation here
     return expression
@@ -169,29 +169,29 @@ public class InfixExpressionBuilder {
 
 // This returns the result of the shunting yard algorithm
 public func reversePolishNotation(_ expression: [Token]) -> String {
-  
+
   var tokenStack = Stack<Token>()
   var reversePolishNotation = [Token]()
-  
+
   for token in expression {
     switch token.tokenType {
     case .operand(_):
       reversePolishNotation.append(token)
-      
+
     case .openBracket:
       tokenStack.push(token)
-      
+
     case .closeBracket:
       while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
         reversePolishNotation.append(tempToken)
       }
-      
+
     case .Operator(let operatorToken):
       for tempToken in tokenStack.makeIterator() {
         if !tempToken.isOperator {
           break
         }
-        
+
         if let tempOperatorToken = tempToken.operatorToken {
           if operatorToken.associativity == .leftAssociative && operatorToken <= tempOperatorToken
             || operatorToken.associativity == .rightAssociative && operatorToken < tempOperatorToken {
@@ -204,11 +204,11 @@ public func reversePolishNotation(_ expression: [Token]) -> String {
       tokenStack.push(token)
     }
   }
-  
+
   while tokenStack.count > 0 {
     reversePolishNotation.append(tokenStack.pop()!)
   }
-  
+
   return reversePolishNotation.map({token in token.description}).joined(separator: " ")
 }
 
diff --git a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift
index 27286fdbd..c54c5a600 100644
--- a/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Sources/Stack.swift	
@@ -2,27 +2,27 @@ 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
     }
diff --git a/Shunting Yard/ShuntingYard.swift b/Shunting Yard/ShuntingYard.swift
index 97a72249d..201264650 100644
--- a/Shunting Yard/ShuntingYard.swift	
+++ b/Shunting Yard/ShuntingYard.swift	
@@ -18,7 +18,7 @@ public enum OperatorType: CustomStringConvertible {
   case multiply
   case percent
   case exponent
-  
+
   public var description: String {
     switch self {
     case .add:
@@ -42,7 +42,7 @@ public enum TokenType: CustomStringConvertible {
   case closeBracket
   case Operator(OperatorToken)
   case operand(Double)
-  
+
   public var description: String {
     switch self {
     case .openBracket:
@@ -59,11 +59,11 @@ public enum TokenType: CustomStringConvertible {
 
 public struct OperatorToken: CustomStringConvertible {
   let operatorType: OperatorType
-  
+
   init(operatorType: OperatorType) {
     self.operatorType = operatorType
   }
-  
+
   var precedence: Int {
     switch operatorType {
     case .add, .subtract:
@@ -74,7 +74,7 @@ public struct OperatorToken: CustomStringConvertible {
       return 10
     }
   }
-  
+
   var associativity: OperatorAssociativity {
     switch operatorType {
     case .add, .subtract, .divide, .multiply, .percent:
@@ -83,7 +83,7 @@ public struct OperatorToken: CustomStringConvertible {
       return .rightAssociative
     }
   }
-  
+
   public var description: String {
     return operatorType.description
   }
@@ -99,19 +99,19 @@ func < (left: OperatorToken, right: OperatorToken) -> Bool {
 
 public struct Token: CustomStringConvertible {
   let tokenType: TokenType
-  
+
   init(tokenType: TokenType) {
     self.tokenType = tokenType
   }
-  
+
   init(operand: Double) {
     tokenType = .operand(operand)
   }
-  
+
   init(operatorType: OperatorType) {
     tokenType = .Operator(OperatorToken(operatorType: operatorType))
   }
-  
+
   var isOpenBracket: Bool {
     switch tokenType {
     case .openBracket:
@@ -120,7 +120,7 @@ public struct Token: CustomStringConvertible {
       return false
     }
   }
-  
+
   var isOperator: Bool {
     switch tokenType {
     case .Operator(_):
@@ -129,7 +129,7 @@ public struct Token: CustomStringConvertible {
       return false
     }
   }
-  
+
   var operatorToken: OperatorToken? {
     switch tokenType {
     case .Operator(let operatorToken):
@@ -138,7 +138,7 @@ public struct Token: CustomStringConvertible {
       return nil
     }
   }
-  
+
   public var description: String {
     return tokenType.description
   }
@@ -146,27 +146,27 @@ public struct Token: CustomStringConvertible {
 
 public class InfixExpressionBuilder {
   private var expression = [Token]()
-  
+
   public func addOperator(_ operatorType: OperatorType) -> InfixExpressionBuilder {
     expression.append(Token(operatorType: operatorType))
     return self
   }
-  
+
   public func addOperand(_ operand: Double) -> InfixExpressionBuilder {
     expression.append(Token(operand: operand))
     return self
   }
-  
+
   public func addOpenBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .openBracket))
     return self
   }
-  
+
   public func addCloseBracket() -> InfixExpressionBuilder {
     expression.append(Token(tokenType: .closeBracket))
     return self
   }
-  
+
   public func build() -> [Token] {
     // Maybe do some validation here
     return expression
@@ -175,29 +175,29 @@ public class InfixExpressionBuilder {
 
 // This returns the result of the shunting yard algorithm
 public func reversePolishNotation(_ expression: [Token]) -> String {
-  
+
   var tokenStack = Stack<Token>()
   var reversePolishNotation = [Token]()
-  
+
   for token in expression {
     switch token.tokenType {
     case .operand(_):
       reversePolishNotation.append(token)
-      
+
     case .openBracket:
       tokenStack.push(token)
-      
+
     case .closeBracket:
       while tokenStack.count > 0, let tempToken = tokenStack.pop(), !tempToken.isOpenBracket {
         reversePolishNotation.append(tempToken)
       }
-      
+
     case .Operator(let operatorToken):
       for tempToken in tokenStack.makeIterator() {
         if !tempToken.isOperator {
           break
         }
-        
+
         if let tempOperatorToken = tempToken.operatorToken {
           if operatorToken.associativity == .leftAssociative && operatorToken <= tempOperatorToken
             || operatorToken.associativity == .rightAssociative && operatorToken < tempOperatorToken {
@@ -210,10 +210,10 @@ public func reversePolishNotation(_ expression: [Token]) -> String {
       tokenStack.push(token)
     }
   }
-  
+
   while tokenStack.count > 0 {
     reversePolishNotation.append(tokenStack.pop()!)
   }
-  
+
   return reversePolishNotation.map({token in token.description}).joined(separator: " ")
 }
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index e844f9959..cd832eef9 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -70,29 +70,29 @@ private func coinFlip() -> Bool {
 
 public class DataNode<Key: Comparable, Payload> {
   public typealias Node = DataNode<Key, Payload>
-  
-  var data: 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() {}
-  
+
 }
 
 
@@ -100,18 +100,18 @@ open class SkipList<Key: Comparable, Payload> {
 // 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          
+
+          currentNode = node.down
         case .some(let value) where value.key != nil:
 
           if value.key == key {
@@ -122,14 +122,14 @@ extension SkipList {
               currentNode = node.down
             } else {
               currentNode = node.next
-            }            
+            }
           }
-          
+
         default:
           continue
         }
-        
-      } else { 
+
+      } else {
         break
       }
     }
@@ -139,7 +139,7 @@ extension SkipList {
     } else {
       return nil
     }
-    
+
   }
 
   func search(key: Key) -> Payload? {
@@ -147,9 +147,9 @@ extension SkipList {
       return nil
     }
 
-    return node.next!.data    
-  }    
-  
+    return node.next!.data
+  }
+
 }
 
 
@@ -157,12 +157,12 @@ extension SkipList {
 // 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)    
+  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() {
@@ -174,7 +174,7 @@ extension SkipList {
       head           = newHead
       currentTopNode = node
     }
-    
+
   }
 
 
@@ -191,13 +191,13 @@ extension SkipList {
         } else {
           currentNode = nextNode
         }
-        
+
       } else {
         stack.push(currentNode!)
-        currentNode = currentNode!.down           
+        currentNode = currentNode!.down
       }
-      
-    }       
+
+    }
 
     let itemAtLayer    = stack.pop()
     var node           = Node(key: key, data: data)
@@ -208,24 +208,24 @@ extension SkipList {
     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 {        
+
+      } else {
         let nextNode  = stack.pop()
-        
+
         node           = Node(key: key, data: data)
         node.down      = currentTopNode
         node.next      = nextNode!.next
         nextNode!.next = node
         currentTopNode = node
       }
-    }     
+    }
   }
 
 
@@ -233,7 +233,7 @@ extension SkipList {
     if head != nil {
       if let node = findNode(key: key) {
         // replace, in case of key already exists. 
-        var currentNode = node.next        
+        var currentNode = node.next
         while currentNode != nil && currentNode!.key == key {
           currentNode!.data = data
           currentNode       = currentNode!.down
@@ -241,12 +241,12 @@ extension SkipList {
       } else {
         insertItem(key: key, data: data)
       }
-      
+
     } else {
       bootstrapBaseLayer(key: key, data: data)
     }
   }
-  
+
 }
 
 
@@ -257,32 +257,32 @@ extension SkipList {
     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/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index ccfa58b09..324e906ee 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -9,53 +9,53 @@
 import Foundation
 
 public struct Matrix<T: Number> {
-  
+
   // MARK: - Martix Objects
-  
+
   public enum Index {
     case row, column
   }
-  
+
   public struct Size: Equatable {
     let rows: Int, columns: Int
-    
+
     public static func == (lhs: Size, rhs: Size) -> Bool {
       return lhs.columns == rhs.columns && lhs.rows == rhs.rows
     }
   }
-  
+
   // MARK: - Variables
-  
+
   let rows: Int, columns: Int
   let size: Size
-  
+
   var grid: [T]
-  
+
   var isSquare: Bool {
     return rows == columns
   }
-  
+
   // MARK: - Init
-  
+
   public init(rows: Int, columns: Int, initialValue: T = T.zero) {
     self.rows = rows
     self.columns = columns
     self.size = Size(rows: rows, columns: columns)
     self.grid = Array(repeating: initialValue, count: rows * columns)
   }
-  
+
   public init(size: Int, initialValue: T = T.zero) {
     self.init(rows: size, columns: size, initialValue: initialValue)
   }
-  
+
   // MARK: - Private Functions
-  
+
   fileprivate func indexIsValid(row: Int, column: Int) -> Bool {
     return row >= 0 && row < rows && column >= 0 && column < columns
   }
-  
+
   // MARK: - Subscript
-  
+
   public subscript(row: Int, column: Int) -> T {
     get {
       assert(indexIsValid(row: row, column: column), "Index out of range")
@@ -65,7 +65,7 @@ public struct Matrix<T: Number> {
       grid[(row * columns) + column] = newValue
     }
   }
-  
+
   public subscript(type: Matrix.Index, value: Int) -> [T] {
     get {
       switch type {
@@ -95,24 +95,24 @@ public struct Matrix<T: Number> {
       }
     }
   }
-  
+
   // MARK: - Public Functions
-  
+
   public func row(for columnIndex: Int) -> [T] {
     assert(indexIsValid(row: columnIndex, column: 0), "Index out of range")
     return Array(grid[(columnIndex * columns)..<(columnIndex * columns) + columns])
   }
-  
+
   public func column(for rowIndex: Int) -> [T] {
     assert(indexIsValid(row: 0, column: rowIndex), "Index out of range")
-    
+
     let column = (0..<rows).map { (currentRow) -> T in
       let currentColumnIndex = currentRow * columns + rowIndex
       return grid[currentColumnIndex]
     }
     return column
   }
-  
+
   public func forEach(_ body: (Int, Int) throws -> Void) rethrows {
     for row in 0..<rows {
       for column in 0..<columns {
@@ -128,15 +128,15 @@ extension Matrix {
   public func matrixMultiply(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
+
     var C = Matrix<T>(rows: A.rows, columns: B.columns)
-    
+
     for i in 0..<A.rows {
       for j in 0..<B.columns {
         C[i, j] = A[.row, i].dot(B[.column, j])
       }
     }
-    
+
     return C
   }
 }
@@ -147,21 +147,21 @@ extension Matrix {
   public func strassenMatrixMultiply(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.columns == B.rows, "Two matricies can only be matrix mulitiplied if one has dimensions mxn & the other has dimensions nxp where m, n, p are in R")
-    
+
     let n = max(A.rows, A.columns, B.rows, B.columns)
     let m = nextPowerOfTwo(after: n)
-    
+
     var APrep = Matrix(size: m)
     var BPrep = Matrix(size: m)
-    
+
     A.forEach { (i, j) in
       APrep[i,j] = A[i,j]
     }
-    
+
     B.forEach { (i, j) in
       BPrep[i,j] = B[i,j]
     }
-    
+
     let CPrep = APrep.strassenR(by: BPrep)
     var C = Matrix(rows: A.rows, columns: B.columns)
     for i in 0..<A.rows {
@@ -169,25 +169,25 @@ extension Matrix {
         C[i,j] = CPrep[i,j]
       }
     }
-    
+
     return C
   }
-  
+
   private func strassenR(by B: Matrix<T>) -> Matrix<T> {
     let A = self
     assert(A.isSquare && B.isSquare, "This function requires square matricies!")
     guard A.rows > 1 && B.rows > 1 else { return A * B }
-    
+
     let n    = A.rows
     let nBy2 = n / 2
-    
+
     /*
     Assume submatricies are allocated as follows
     
      matrix A = |a b|,    matrix B = |e f|
                 |c d|                |g h|
     */
-    
+
     var a = Matrix(size: nBy2)
     var b = Matrix(size: nBy2)
     var c = Matrix(size: nBy2)
@@ -196,7 +196,7 @@ extension Matrix {
     var f = Matrix(size: nBy2)
     var g = Matrix(size: nBy2)
     var h = Matrix(size: nBy2)
-    
+
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
         a[i,j] = A[i,j]
@@ -209,7 +209,7 @@ extension Matrix {
         h[i,j] = B[i+nBy2, j+nBy2]
       }
     }
-    
+
     let p1 = a.strassenR(by: f-h)       // a * (f - h)
     let p2 = (a+b).strassenR(by: h)     // (a + b) * h
     let p3 = (c+d).strassenR(by: e)     // (c + d) * e
@@ -217,12 +217,12 @@ extension Matrix {
     let p5 = (a+d).strassenR(by: e+h)   // (a + d) * (e + h)
     let p6 = (b-d).strassenR(by: g+h)   // (b - d) * (g + h)
     let p7 = (a-c).strassenR(by: e+f)   // (a - c) * (e + f)
-    
+
     let c11 = p5 + p4 - p2 + p6         // p5 + p4 - p2 + p6
     let c12 = p1 + p2                   // p1 + p2
     let c21 = p3 + p4                   // p3 + p4
     let c22 = p1 + p5 - p3 - p7         // p1 + p5 - p3 - p7
-    
+
     var C = Matrix(size: n)
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
@@ -232,10 +232,10 @@ extension Matrix {
         C[i+nBy2, j+nBy2] = c22[i,j]
       }
     }
-    
+
     return C
   }
-  
+
   private func nextPowerOfTwo(after n: Int) -> Int {
     return Int(pow(2, ceil(log2(Double(n)))))
   }
@@ -248,7 +248,7 @@ extension Matrix: Addable {
     assert(lhs.size == rhs.size, "To term-by-term add matricies they need to be the same size!")
     let rows = lhs.rows
     let columns = lhs.columns
-    
+
     var newMatrix = Matrix<T>(rows: rows, columns: columns)
     for row in 0..<rows {
       for column in 0..<columns {
@@ -257,12 +257,12 @@ extension Matrix: Addable {
     }
     return newMatrix
   }
-  
+
   public static func -<T: Number>(lhs: Matrix<T>, rhs: Matrix<T>) -> Matrix<T> {
     assert(lhs.size == rhs.size, "To term-by-term subtract matricies they need to be the same size!")
     let rows = lhs.rows
     let columns = lhs.columns
-    
+
     var newMatrix = Matrix<T>(rows: rows, columns: columns)
     for row in 0..<rows {
       for column in 0..<columns {
@@ -278,7 +278,7 @@ extension Matrix: Multipliable {
     assert(lhs.size == rhs.size, "To term-by-term multiply matricies they need to be the same size!")
     let rows = lhs.rows
     let columns = lhs.columns
-    
+
     var newMatrix = Matrix<T>(rows: rows, columns: columns)
     for row in 0..<rows {
       for column in 0..<columns {
diff --git a/Ternary Search Tree/TST.playground/Sources/Utils.swift b/Ternary Search Tree/TST.playground/Sources/Utils.swift
index cabfe1b68..97f09fdd2 100644
--- a/Ternary Search Tree/TST.playground/Sources/Utils.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/Utils.swift	
@@ -9,22 +9,22 @@
 import Foundation
 
 public struct Utils {
-    
+
     public static let shared = Utils()
-    
+
     let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
     //Random string generator from:
     //http://stackoverflow.com/questions/26845307/generate-random-alphanumeric-string-in-swift/26845710
     public func randomAlphaNumericString(withLength length: Int) -> String {
         let allowedCharsCount = UInt32(allowedChars.characters.count)
         var randomString = ""
-        
+
         for _ in (0..<length) {
             let randomNum = Int(arc4random_uniform(allowedCharsCount))
             let newCharacter = allowedChars[allowedChars.index(allowedChars.startIndex, offsetBy: randomNum)]
             randomString += String(newCharacter)
         }
-        
+
         return randomString
     }
 }
diff --git a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift
index 40739c888..dfbbae9ca 100644
--- a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
+++ b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
@@ -9,19 +9,19 @@
 import XCTest
 
 class TernarySearchTreeTests: XCTestCase {
-    
+
 
     let testCount = 30
-    
+
     func testCanFindStringInTree() {
         var testStrings: [(key: String, data: String)] = []
         let treeOfStrings = TernarySearchTree<String>()
 
         for _ in (1...testCount) {
             var randomLength = Int(arc4random_uniform(10))
-            
+
             var key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
-            
+
             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))
@@ -29,20 +29,20 @@ class TernarySearchTreeTests: XCTestCase {
             }
             let data = Utils.shared.randomAlphaNumericString(withLength: randomLength)
             //    print("Key: \(key) Data: \(data)")
-            
+
             if key != "" && data != "" {
                 testStrings.append((key, data))
                 treeOfStrings.insert(data: data, withKey: key)
             }
         }
-        
+
         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>()
@@ -55,13 +55,13 @@ class TernarySearchTreeTests: XCTestCase {
                 randomLength = Int(arc4random_uniform(10))
                 key = Utils.shared.randomAlphaNumericString(withLength: randomLength)
             }
-            
+
             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)
diff --git a/Ternary Search Tree/Utils.swift b/Ternary Search Tree/Utils.swift
index cabfe1b68..97f09fdd2 100644
--- a/Ternary Search Tree/Utils.swift	
+++ b/Ternary Search Tree/Utils.swift	
@@ -9,22 +9,22 @@
 import Foundation
 
 public struct Utils {
-    
+
     public static let shared = Utils()
-    
+
     let allowedChars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
     //Random string generator from:
     //http://stackoverflow.com/questions/26845307/generate-random-alphanumeric-string-in-swift/26845710
     public func randomAlphaNumericString(withLength length: Int) -> String {
         let allowedCharsCount = UInt32(allowedChars.characters.count)
         var randomString = ""
-        
+
         for _ in (0..<length) {
             let randomNum = Int(arc4random_uniform(allowedCharsCount))
             let newCharacter = allowedChars[allowedChars.index(allowedChars.startIndex, offsetBy: randomNum)]
             randomString += String(newCharacter)
         }
-        
+
         return randomString
     }
 }
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift
index 6f438c0cf..c85f56a68 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Sources/ThreadedBinaryTree.swift	
@@ -82,7 +82,7 @@ extension ThreadedBinaryTree {
   public func insert(_ value: T) {
     insert(value, parent: self)
   }
-    
+
   fileprivate func insert(_ value: T, parent: ThreadedBinaryTree) {
     if value < self.value {
       if let left = left {
@@ -123,13 +123,13 @@ extension ThreadedBinaryTree {
   @discardableResult public func remove(_ value: T) -> ThreadedBinaryTree? {
     return search(value)?.remove()
   }
-    
+
   /*
   Deletes "this" node from the tree.
   */
   public func remove() -> ThreadedBinaryTree? {
     let replacement: ThreadedBinaryTree?
-        
+
     if let left = left {
       if let right = right {
         replacement = removeNodeWithTwoChildren(left, right)
@@ -155,33 +155,33 @@ extension ThreadedBinaryTree {
         parent?.rightThread = rightThread
       }
     }
-        
+
     reconnectParentToNode(replacement)
-        
+
     // The current node is no longer part of the tree, so clean it up.
     parent = nil
     left = nil
     right = nil
     leftThread = nil
     rightThread = nil
-        
+
     return replacement
   }
-    
+
   private func removeNodeWithTwoChildren(_ left: ThreadedBinaryTree, _ right: ThreadedBinaryTree) -> ThreadedBinaryTree {
     // 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.
@@ -191,11 +191,11 @@ extension ThreadedBinaryTree {
     } else {
       successor.right = nil
     }
-        
+
     // And finally, connect the successor node to our parent.
     return successor
   }
-    
+
   private func reconnectParentToNode(_ node: ThreadedBinaryTree?) {
     if let parent = parent {
       if isLeftChild {
@@ -228,7 +228,7 @@ extension ThreadedBinaryTree {
     }
     return nil
   }
-    
+
   /*
   // Recursive version of search
   // Educational but undesirable due to the overhead cost of recursion
@@ -242,11 +242,11 @@ extension ThreadedBinaryTree {
     }
   }
   */
-    
+
   public func contains(value: T) -> Bool {
     return search(value) != nil
   }
-    
+
   /*
   Returns the leftmost descendent. O(h) time.
   */
@@ -257,7 +257,7 @@ extension ThreadedBinaryTree {
     }
     return node
   }
-    
+
   /*
   Returns the rightmost descendent. O(h) time.
   */
@@ -268,7 +268,7 @@ extension ThreadedBinaryTree {
     }
     return node
   }
-    
+
   /*
   Calculates the depth of this node, i.e. the distance to the root.
   Takes O(h) time.
@@ -282,7 +282,7 @@ extension ThreadedBinaryTree {
     }
     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).
@@ -294,7 +294,7 @@ extension ThreadedBinaryTree {
       return 1 + max(left?.height() ?? 0, right?.height() ?? 0)
     }
   }
-    
+
   /*
   Finds the node whose value precedes our value in sorted order.
   */
@@ -305,7 +305,7 @@ extension ThreadedBinaryTree {
       return leftThread
     }
   }
-    
+
   /*
   Finds the node whose value succeeds our value in sorted order.
   */
@@ -333,7 +333,7 @@ extension ThreadedBinaryTree {
       }
     }
   }
-    
+
   public func traverseInOrderBackward(_ visit: (T) -> Void) {
     var n: ThreadedBinaryTree
     n = maximum()
@@ -346,19 +346,19 @@ extension ThreadedBinaryTree {
       }
     }
   }
-    
+
   public func traversePreOrder(_ visit: (T) -> Void) {
     visit(value)
     left?.traversePreOrder(visit)
     right?.traversePreOrder(visit)
   }
-    
+
   public func traversePostOrder(_ visit: (T) -> Void) {
     left?.traversePostOrder(visit)
     right?.traversePostOrder(visit)
     visit(value)
   }
-    
+
   /*
   Performs an in-order traversal and collects the results in an array.
   */
@@ -390,7 +390,7 @@ extension ThreadedBinaryTree {
     let rightBST = right?.isBST(minValue: value, maxValue: maxValue) ?? true
     return leftBST && rightBST
   }
-    
+
   /*
   Is this binary tree properly threaded?
   Either left or leftThread (but not both) must be nil (likewise for right).
@@ -452,7 +452,7 @@ extension ThreadedBinaryTree: CustomDebugStringConvertible {
     }
     return s
   }
-    
+
   public func toArray() -> [T] {
     return map { $0 }
   }
diff --git a/Treap/Treap.swift b/Treap/Treap.swift
index 6e80abfb2..7038e843e 100644
--- a/Treap/Treap.swift
+++ b/Treap/Treap.swift
@@ -27,11 +27,11 @@ import Foundation
 public indirect enum Treap<Key: Comparable, Element> {
   case empty
   case node(key: Key, val: Element, p: Int, left: Treap, right: Treap)
-  
+
   public init() {
     self = .empty
   }
-  
+
   internal func get(_ key: Key) -> Element? {
     switch self {
     case .empty:
@@ -46,7 +46,7 @@ public indirect enum Treap<Key: Comparable, Element> {
       return nil
     }
   }
-  
+
   public func contains(_ key: Key) -> Bool {
     switch self {
     case .empty:
@@ -61,7 +61,7 @@ public indirect enum Treap<Key: Comparable, Element> {
       return false
     }
   }
-  
+
   public var depth: Int {
     switch self {
     case .empty:
@@ -80,12 +80,12 @@ public indirect enum Treap<Key: Comparable, Element> {
   public var count: Int {
     return Treap.countHelper(self)
   }
-  
+
   fileprivate static func countHelper(_ treap: Treap<Key, Element>) -> Int {
     if case let .node(_, _, _, left, right) = treap {
       return countHelper(left) + 1 + countHelper(right)
     }
-    
+
     return 0
   }
 }
@@ -121,7 +121,7 @@ public extension Treap {
       return .empty
     }
   }
-  
+
   fileprivate func insertAndBalance(_ nodeKey: Key, _ nodeVal: Element, _ nodeP: Int, _ left: Treap,
                                     _ right: Treap, _ key: Key, _ val: Element, _ p: Int) -> Treap {
     let newChild: Treap<Key, Element>
@@ -141,14 +141,14 @@ public extension Treap {
       newNode = .empty
       return newNode
     }
-    
+
     if case let .node(_, _, newChildP, _, _) = newChild , newChildP < nodeP {
       return rotate(newNode)
     } else {
       return newNode
     }
   }
-  
+
   internal func delete(key: Key) throws -> Treap {
     switch self {
     case .empty:
diff --git a/Treap/Treap/TreapTests/TreapTests.swift b/Treap/Treap/TreapTests/TreapTests.swift
index f349e6ab8..d4fc4cfdb 100644
--- a/Treap/Treap/TreapTests/TreapTests.swift
+++ b/Treap/Treap/TreapTests/TreapTests.swift
@@ -27,17 +27,17 @@ THE SOFTWARE.*/
 import XCTest
 
 class TreapTests: XCTestCase {
-  
+
   override func setUp() {
     super.setUp()
     // Put setup code here. This method is called before the invocation of each test method in the class.
   }
-  
+
   override func tearDown() {
     // Put teardown code here. This method is called after the invocation of each test method in the class.
     super.tearDown()
   }
-  
+
   func testSanity() {
     var treap = Treap<Int, String>.empty
     treap = treap.set(key: 5, val: "a").set(key: 7, val: "b")
@@ -51,7 +51,7 @@ class TreapTests: XCTestCase {
     XCTAssert(!treap.contains(5))
     XCTAssert(treap.contains(7))
   }
-  
+
   func testFairlyBalanced() {
     var treap = Treap<Int, Int?>.empty
     for i in 0..<1000 {
@@ -60,7 +60,7 @@ class TreapTests: XCTestCase {
     let depth = treap.depth
     XCTAssert(depth < 30, "treap.depth was \(depth)")
   }
-  
+
   func testFairlyBalancedCollection() {
     var treap = Treap<Int, Int?>()
     for i in 0..<1000 {
@@ -69,5 +69,5 @@ class TreapTests: XCTestCase {
     let depth = treap.depth
     XCTAssert(depth > 0 && depth < 30)
   }
-  
+
 }
diff --git a/Treap/TreapCollectionType.swift b/Treap/TreapCollectionType.swift
index 7292c5f0a..eeee065fe 100644
--- a/Treap/TreapCollectionType.swift
+++ b/Treap/TreapCollectionType.swift
@@ -25,52 +25,52 @@ THE SOFTWARE.*/
 import Foundation
 
 extension Treap: MutableCollection {
-  
+
   public typealias Index = TreapIndex<Key>
-  
+
   public subscript(index: TreapIndex<Key>) -> Element {
     get {
       guard let result = self.get(index.keys[index.keyIndex]) else {
         fatalError("Invalid index!")
       }
-      
+
       return result
     }
-    
+
     mutating set {
       let key = index.keys[index.keyIndex]
       self = self.set(key: key, val: newValue)
     }
   }
-  
+
   public subscript(key: Key) -> Element? {
     get {
       return self.get(key)
     }
-    
+
     mutating set {
       guard let value = newValue else {
         _ = try? self.delete(key: key)
         return
       }
-      
+
       self = self.set(key: key, val: value)
     }
   }
-  
+
   public var startIndex: TreapIndex<Key> {
     return TreapIndex<Key>(keys: keys, keyIndex: 0)
   }
-  
+
   public var endIndex: TreapIndex<Key> {
     let keys = self.keys
     return TreapIndex<Key>(keys: keys, keyIndex: keys.count)
   }
-  
+
   public func index(after i: TreapIndex<Key>) -> TreapIndex<Key> {
     return i.successor()
   }
-  
+
   fileprivate var keys: [Key] {
     var results: [Key] = []
     if case let .node(key, _, _, left, right) = self {
@@ -78,28 +78,28 @@ extension Treap: MutableCollection {
       results.append(key)
       results.append(contentsOf: right.keys)
     }
-    
+
     return results
   }
 }
 
 public struct TreapIndex<Key: Comparable>: Comparable {
-  
+
   public static func < (lhs: TreapIndex<Key>, rhs: TreapIndex<Key>) -> Bool {
     return lhs.keyIndex < rhs.keyIndex
   }
-  
+
   fileprivate let keys: [Key]
   fileprivate let keyIndex: Int
-  
+
   public func successor() -> TreapIndex {
     return TreapIndex(keys: keys, keyIndex: keyIndex + 1)
   }
-  
+
   public func predecessor() -> TreapIndex {
     return TreapIndex(keys: keys, keyIndex: keyIndex - 1)
   }
-  
+
   fileprivate init(keys: [Key] = [], keyIndex: Int = 0) {
     self.keys = keys
     self.keyIndex = keyIndex
diff --git a/Treap/TreapMergeSplit.swift b/Treap/TreapMergeSplit.swift
index 34cfec3d2..62d18d16f 100644
--- a/Treap/TreapMergeSplit.swift
+++ b/Treap/TreapMergeSplit.swift
@@ -37,7 +37,7 @@ public extension Treap {
     } else {
       fatalError("No values in treap")
     }
-    
+
     switch self {
     case .node:
       if case let .node(_, _, _, left, right) = current.set(key: key, val: val, p: -1) {
@@ -49,7 +49,7 @@ public extension Treap {
       return (left: .empty, right: .empty)
     }
   }
-  
+
   internal var leastKey: Key? {
     switch self {
     case .empty:
@@ -60,7 +60,7 @@ public extension Treap {
       return left.leastKey
     }
   }
-  
+
   internal var mostKey: Key? {
     switch self {
     case .empty:
@@ -79,7 +79,7 @@ internal func merge<Key: Comparable, Element>(_ left: Treap<Key, Element>, right
     return right
   case (_, .empty):
     return left
-    
+
   case let (.node(leftKey, leftVal, leftP, leftLeft, leftRight), .node(rightKey, rightVal, rightP, rightLeft, rightRight)):
     if leftP < rightP {
       return .node(key: leftKey, val: leftVal, p: leftP, left: leftLeft, right: merge(leftRight, right: right))
@@ -96,16 +96,16 @@ extension Treap: CustomStringConvertible {
   public var description: String {
     return Treap.descHelper(self, indent: 0)
   }
-  
+
   fileprivate static func descHelper(_ treap: Treap<Key, Element>, indent: Int) -> String {
     if case let .node(key, value, priority, left, right) = treap {
       var result = ""
       let tabs = String(repeating: "\t", count: indent)
-      
+
       result += descHelper(left, indent: indent + 1)
       result += "\n" + tabs + "\(key), \(value), \(priority)\n"
       result += descHelper(right, indent: indent + 1)
-      
+
       return result
     } else {
       return ""
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index 4321479c3..7ff9638d7 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -18,8 +18,8 @@ class TrieNode<T: Hashable> {
   var isLeaf: Bool {
     return children.count == 0
   }
-  
-  
+
+
   /// Initializes a node.
   ///
   /// - Parameters:
@@ -29,7 +29,7 @@ class TrieNode<T: Hashable> {
     self.value = value
     self.parentNode = parentNode
   }
-  
+
   /// Adds a child node to self.  If the child is already present,
   /// do nothing.
   ///
@@ -92,7 +92,7 @@ class Trie: NSObject, NSCoding {
 
 // MARK: - Adds methods: insert, remove, contains
 extension Trie {
-  
+
   /// Inserts a word into the trie.  If the word is already present,
   /// there is no change.
   ///
@@ -117,7 +117,7 @@ extension Trie {
     wordCount += 1
     currentNode.isTerminating = true
   }
-  
+
   /// Determines whether a word is in the trie.
   ///
   /// - Parameter word: the word to check for
@@ -168,7 +168,7 @@ extension Trie {
     return nil
 
   }
-  
+
   /// Deletes a word from the trie by starting with the last letter
   /// and moving back, deleting nodes until either a non-leaf or a
   /// terminating node is found.
@@ -187,7 +187,7 @@ extension Trie {
       }
     }
   }
-  
+
   /// Removes a word from the trie.  If the word is not present or
   /// it is empty, just ignore it.  If the last node is a leaf,
   /// delete that node and higher nodes that are leaves until a
@@ -210,7 +210,7 @@ extension Trie {
     }
     wordCount -= 1
   }
-  
+
   /// Returns an array of words in a subtrie of the trie
   ///
   /// - Parameters:
diff --git a/Trie/Trie/TrieUITests/TrieUITests.swift b/Trie/Trie/TrieUITests/TrieUITests.swift
index f3da2a67f..acb3b1756 100644
--- a/Trie/Trie/TrieUITests/TrieUITests.swift
+++ b/Trie/Trie/TrieUITests/TrieUITests.swift
@@ -9,12 +9,12 @@
 import XCTest
 
 class TrieUITests: XCTestCase {
-        
+
     override func setUp() {
         super.setUp()
-        
+
         // 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.
@@ -22,15 +22,15 @@ class TrieUITests: XCTestCase {
 
         // 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()
     }
-    
+
     func testExample() {
         // Use recording to get started writing UI tests.
         // Use XCTAssert and related functions to verify your tests produce the correct results.
     }
-    
+
 }
diff --git a/Z-Algorithm/ZAlgorithm.swift b/Z-Algorithm/ZAlgorithm.swift
index 9bef69687..969a3599b 100644
--- a/Z-Algorithm/ZAlgorithm.swift
+++ b/Z-Algorithm/ZAlgorithm.swift
@@ -9,34 +9,34 @@
 import Foundation
 
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-  
+
   let pattern = Array(ptrn.characters)
   let patternLength = pattern.count
-  
+
   guard patternLength > 0 else {
     return nil
   }
-  
+
   var zeta = [Int](repeating: 0, count: patternLength)
-  
+
   var left = 0
   var right = 0
   var k_1 = 0
   var betaLength = 0
   var textIndex = 0
   var patternIndex = 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
@@ -44,18 +44,18 @@ func ZetaAlgorithm(ptrn: 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
         }
-        
+
         zeta[k] = patternIndex - k
         left = k
         right = patternIndex - 1
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
index 395122af0..44faf6790 100644
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -2,34 +2,34 @@
 
 
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
-  
+
   let pattern = Array(ptrn.characters)
   let patternLength = pattern.count
-  
+
   guard patternLength > 0 else {
     return nil
   }
-  
+
   var zeta = [Int](repeating: 0, count: patternLength)
-  
+
   var left = 0
   var right = 0
   var k_1 = 0
   var betaLength = 0
   var textIndex = 0
   var patternIndex = 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
@@ -37,18 +37,18 @@ func ZetaAlgorithm(ptrn: 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
         }
-        
+
         zeta[k] = patternIndex - k
         left = k
         right = patternIndex - 1
@@ -60,28 +60,28 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
 
 
 extension String {
-  
+
   func indexesOf(pattern: String) -> [Int]? {
     let patternLength = pattern.characters.count
     let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
-    
+
     guard zeta != nil else {
       return nil
     }
-    
+
     var indexes: [Int] = []
-    
+
     /* Scan the zeta array to find matched patterns */
     for i in 0 ..< zeta!.count {
       if zeta![i] == patternLength {
         indexes.append(i - patternLength - 1)
       }
     }
-    
+
     guard !indexes.isEmpty else {
       return nil
     }
-    
+
     return indexes
   }
 }
diff --git a/Z-Algorithm/ZetaAlgorithm.swift b/Z-Algorithm/ZetaAlgorithm.swift
index c35703272..e60c1617f 100644
--- a/Z-Algorithm/ZetaAlgorithm.swift
+++ b/Z-Algorithm/ZetaAlgorithm.swift
@@ -9,28 +9,28 @@
 import Foundation
 
 extension String {
-  
+
   func indexesOf(pattern: String) -> [Int]? {
     let patternLength = pattern.characters.count
     let zeta = ZetaAlgorithm(ptrn: pattern + "💲" + self)
-    
+
     guard zeta != nil else {
       return nil
     }
-    
+
     var indexes: [Int] = [Int]()
-    
+
     /* Scan the zeta array to find matched patterns */
     for i in 0 ..< zeta!.count {
       if zeta![i] == patternLength {
         indexes.append(i - patternLength - 1)
       }
     }
-    
+
     guard !indexes.isEmpty else {
       return nil
     }
-    
+
     return indexes
   }
 }

From b718f04b4be46ebe9d82cc1d18264d92b12be0a9 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Thu, 4 May 2017 03:53:31 +0500
Subject: [PATCH 196/862] Fix violation: unused_optional_binding

warning: Unused Optional Binding Violation: Prefer `!= nil` over `let _ =` ()
---
 Graph/Graph/AdjacencyListGraph.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index 57fd75fed..b58ef6417 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -78,7 +78,7 @@ open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashab
     // works
     let edge = Edge(from: from, to: to, weight: weight)
     let edgeList = adjacencyList[from.index]
-    if let _ = edgeList.edges {
+    if edgeList.edges != nil {
         edgeList.addEdge(edge)
     } else {
         edgeList.edges = [edge]

From 9a363c7082c2acbc6984864b67ac6c20ac911cdb Mon Sep 17 00:00:00 2001
From: Xiangxin <xiangxinsg@gmail.com>
Date: Fri, 17 Mar 2017 00:19:36 +0800
Subject: [PATCH 197/862] Minimum Spanning Tree (Kruskal's and Prim's)

---
 Minimum Spanning Tree/Images/kruskal.png      | Bin 0 -> 22083 bytes
 Minimum Spanning Tree/Images/prim.png         | Bin 0 -> 19053 bytes
 Minimum Spanning Tree/Kruskal.swift           |  31 +++
 .../Contents.swift                            |  93 +++++++
 .../Resources/mst.png                         | Bin 0 -> 19209 bytes
 .../Sources/Graph.swift                       |  55 +++++
 .../Sources/Heap.swift                        | 227 ++++++++++++++++++
 .../Sources/PriorityQueue.swift               |  58 +++++
 .../Sources/UnionFind.swift                   |  61 +++++
 .../contents.xcplayground                     |   4 +
 Minimum Spanning Tree/Prim.swift              |  45 ++++
 Minimum Spanning Tree/README.markdown         | 102 ++++++++
 README.markdown                               |   1 +
 .../contents.xcworkspacedata                  |  26 ++
 14 files changed, 703 insertions(+)
 create mode 100644 Minimum Spanning Tree/Images/kruskal.png
 create mode 100644 Minimum Spanning Tree/Images/prim.png
 create mode 100644 Minimum Spanning Tree/Kruskal.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Resources/mst.png
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/PriorityQueue.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/UnionFind.swift
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground
 create mode 100644 Minimum Spanning Tree/Prim.swift
 create mode 100644 Minimum Spanning Tree/README.markdown

diff --git a/Minimum Spanning Tree/Images/kruskal.png b/Minimum Spanning Tree/Images/kruskal.png
new file mode 100644
index 0000000000000000000000000000000000000000..5172f180fda8dff8666a4a38f08e675311c515dd
GIT binary patch
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diff --git a/Minimum Spanning Tree/Kruskal.swift b/Minimum Spanning Tree/Kruskal.swift
new file mode 100644
index 000000000..bebd32602
--- /dev/null
+++ b/Minimum Spanning Tree/Kruskal.swift	
@@ -0,0 +1,31 @@
+//
+//  Kruskal.swift
+//  
+//
+//  Created by xiang xin on 16/3/17.
+//
+//
+
+
+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
+    if !unionFind.inSameSet(v1, and: v2) {
+      cost += edge.weight
+      tree.addEdge(edge)
+      unionFind.unionSetsContaining(v1, and: v2)
+    }
+  }
+
+  return (cost: cost, tree: tree)
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift
new file mode 100644
index 000000000..99b5e859f
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
@@ -0,0 +1,93 @@
+/**
+ The following code demonstrates getting MST of the graph below by both
+ 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)
+  }
+
+  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>()
+
+  if graph.vertices.isEmpty {
+    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: graph.vertices.first!, 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)
+}
+
+/*:
+ ![Graph](mst.png)
+ */
+
+var graph = Graph<Int>()
+graph.addEdge(vertex1: 1, vertex2: 2, weight: 6)
+graph.addEdge(vertex1: 1, vertex2: 3, weight: 1)
+graph.addEdge(vertex1: 1, vertex2: 4, weight: 5)
+graph.addEdge(vertex1: 2, vertex2: 3, weight: 5)
+graph.addEdge(vertex1: 2, vertex2: 5, weight: 3)
+graph.addEdge(vertex1: 3, vertex2: 4, weight: 5)
+graph.addEdge(vertex1: 3, vertex2: 5, weight: 6)
+graph.addEdge(vertex1: 3, vertex2: 6, weight: 4)
+graph.addEdge(vertex1: 4, vertex2: 6, weight: 2)
+graph.addEdge(vertex1: 5, vertex2: 6, weight: 6)
+
+print("===== Kruskal's =====")
+let result1 = minimumSpanningTreeKruskal(graph: graph)
+print("Minimum spanning tree total weight: \(result1.cost)")
+print("Minimum spanning tree:")
+print(result1.tree)
+
+print("===== Prim's =====")
+let result2 = minimumSpanningTreePrim(graph: graph)
+print("Minimum spanning tree total weight: \(result2.cost)")
+print("Minimum spanning tree:")
+print(result2.tree)
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Resources/mst.png b/Minimum Spanning Tree/MinimumSpanningTree.playground/Resources/mst.png
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diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
new file mode 100644
index 000000000..0ae996646
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -0,0 +1,55 @@
+
+// Undirected edge
+public struct Edge<T>: CustomStringConvertible {
+  public let vertex1: T
+  public let vertex2: T
+  public let weight: Int
+
+  public var description: String {
+    return "[\(vertex1)-\(vertex2), \(weight)]"
+  }
+}
+
+
+// Undirected weighted graph
+public struct Graph<T: Hashable>: CustomStringConvertible {
+
+  public private(set) var edgeList: [Edge<T>]
+  public private(set) var vertices: Set<T>
+  public private(set) var adjList: [T: [(vertex: T, weight: Int)]]
+
+  public init() {
+    edgeList = [Edge<T>]()
+    vertices = Set<T>()
+    adjList = [T: [(vertex: T, weight: Int)]]()
+  }
+
+  public var description: String {
+    var description = ""
+    for edge in edgeList {
+      description += edge.description + "\n"
+    }
+    return description
+  }
+
+  public mutating func addEdge(vertex1 v1: T, vertex2 v2: T, weight w: Int) {
+    edgeList.append(Edge(vertex1: v1, vertex2: v2, weight: w))
+    vertices.insert(v1)
+    vertices.insert(v2)
+    if adjList[v1] == nil {
+      adjList[v1] = [(vertex: v2, weight: w)]
+    } else {
+      adjList[v1]!.append((vertex: v2, weight: w))
+    }
+
+    if adjList[v2] == nil {
+      adjList[v2] = [(vertex: v1, weight: w)]
+    } else {
+      adjList[v2]!.append((vertex: v1, weight: w))
+    }
+  }
+
+  public mutating func addEdge(_ edge: Edge<T>) {
+    addEdge(vertex1: edge.vertex1, vertex2: edge.vertex2, weight: edge.weight)
+  }
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift
new file mode 100644
index 000000000..fa30df362
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift	
@@ -0,0 +1,227 @@
+//
+//  Heap.swift
+//  Written for the Swift Algorithm Club by Kevin Randrup and Matthijs Hollemans
+//
+
+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
+    }
+  }
+}
+
+// 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
+  }
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/PriorityQueue.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/PriorityQueue.swift
new file mode 100644
index 000000000..92f7b6d3f
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/PriorityQueue.swift	
@@ -0,0 +1,58 @@
+/*
+  Priority Queue, a queue where the most "important" items are at the front of
+  the queue.
+
+  The heap is a natural data structure for a priority queue, so this object
+  simply wraps the Heap struct.
+
+  All operations are O(lg n).
+
+  Just like a heap can be a max-heap or min-heap, the queue can be a max-priority
+  queue (largest element first) or a min-priority queue (smallest element first).
+*/
+public struct PriorityQueue<T> {
+  fileprivate var heap: Heap<T>
+
+  /*
+    To create a max-priority queue, supply a > sort function. For a min-priority
+    queue, use <.
+  */
+  public init(sort: @escaping (T, T) -> Bool) {
+    heap = Heap(sort: sort)
+  }
+
+  public var isEmpty: Bool {
+    return heap.isEmpty
+  }
+
+  public var count: Int {
+    return heap.count
+  }
+
+  public func peek() -> T? {
+    return heap.peek()
+  }
+
+  public mutating func enqueue(_ element: T) {
+    heap.insert(element)
+  }
+
+  public mutating func dequeue() -> T? {
+    return heap.remove()
+  }
+
+  /*
+    Allows you to change the priority of an element. In a max-priority queue,
+    the new priority should be larger than the old one; in a min-priority queue
+    it should be smaller.
+  */
+  public mutating func changePriority(index i: Int, value: T) {
+    return heap.replace(index: i, value: value)
+  }
+}
+
+extension PriorityQueue where T: Equatable {
+  public func index(of element: T) -> Int? {
+    return heap.index(of: element)
+  }
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/UnionFind.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/UnionFind.swift
new file mode 100644
index 000000000..29ea0a373
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/UnionFind.swift	
@@ -0,0 +1,61 @@
+/*
+ Union-Find Data Structure
+
+ Performance:
+ adding new set is almost O(1)
+ finding set of element is almost O(1)
+ union sets is almost O(1)
+ */
+
+public struct UnionFind<T: Hashable> {
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+
+  public init() {}
+
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+
+  private mutating func setByIndex(_ index: Int) -> Int {
+    if parent[index] == index {
+      return index
+    } else {
+      parent[index] = setByIndex(parent[index])
+      return parent[index]
+    }
+  }
+
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
+    }
+  }
+
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        if size[firstSet] < size[secondSet] {
+          parent[firstSet] = secondSet
+          size[secondSet] += size[firstSet]
+        } else {
+          parent[secondSet] = firstSet
+          size[firstSet] += size[secondSet]
+        }
+      }
+    }
+  }
+
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
+    }
+  }
+}
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground b/Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground
new file mode 100644
index 000000000..89da2d470
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/contents.xcplayground	
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' display-mode='rendered'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>
\ No newline at end of file
diff --git a/Minimum Spanning Tree/Prim.swift b/Minimum Spanning Tree/Prim.swift
new file mode 100644
index 000000000..89c26cff0
--- /dev/null
+++ b/Minimum Spanning Tree/Prim.swift	
@@ -0,0 +1,45 @@
+//
+//  Prim.swift
+//  
+//
+//  Created by xiang xin on 16/3/17.
+//
+//
+
+func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>) {
+  var cost: Int = 0
+  var tree = Graph<T>()
+
+  if graph.vertices.isEmpty {
+    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: graph.vertices.first!, 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)
+}
diff --git a/Minimum Spanning Tree/README.markdown b/Minimum Spanning Tree/README.markdown
new file mode 100644
index 000000000..c47713701
--- /dev/null
+++ b/Minimum Spanning Tree/README.markdown	
@@ -0,0 +1,102 @@
+# Minimum Spanning Tree (Weighted Graph)
+
+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.
+
+### Kruskal's Algorithm
+Sort the edges base on weight. Greedily select the smallest one each time and add into the MST as long as it doesn't form a cycle.
+Kruskal's algoritm uses [Union Find](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Union-Find) data structure to check whether any additional edge causes a cycle. The logic is to put all connected vertices into the same set (in Union Find's concept). If the two vertices from a new edge do not belong to the same set, then it's safe to add that edge into the MST.
+
+The following graph demonstrates the steps:
+
+![Graph](Images/kruskal.png)
+
+Preparation
+```swift
+// Initialize the values to be returned and Union Find data structure.
+var cost: Int = 0
+var tree = Graph<T>()
+var unionFind = UnionFind<T>()
+for vertex in graph.vertices {
+
+// Initially all vertices are disconnected.
+// Each of them belongs to it's individual set.
+  unionFind.addSetWith(vertex)
+}
+```
+
+Sort the edges
+```swift
+let sortedEdgeListByWeight = graph.edgeList.sorted(by: { $0.weight < $1.weight })
+```
+
+Take one edge at a time and try to insert it into the MST. 
+```swift
+for edge in sortedEdgeListByWeight {
+  let v1 = edge.vertex1
+  let v2 = edge.vertex2 
+  
+  // Same set means the two vertices of this edge were already connected in the MST.
+  // Adding this one will cause a cycle.
+  if !unionFind.inSameSet(v1, and: v2) {
+    // Add the edge into the MST and update the final cost.
+    cost += edge.weight
+    tree.addEdge(edge)
+    
+    // Put the two vertices into the same set.
+    unionFind.unionSetsContaining(v1, and: v2)
+  }
+}
+```
+### Prim's Algorithm
+Prim's algorithm doesn't pre-sort all edges. Instead, it uses a [Priority Queue](https://github.com/raywenderlich/swift-algorithm-club/tree/master/Priority%20Queue) to maintain a running sorted next-possile vertices.
+Starting from one vertex, loop through all unvisited neighbours and enqueue a pair of values for each neighbour - the vertex and the weight of edge connecting current vertex to the neighbour. Each time it greedily select the top of the priority queue (the one with least weight value) and add the edge into the final MST if the enqueued neighbour hasn't been already visited.
+
+The following graph demonstrates the steps:
+
+![Graph](Images/prim.png)
+
+Preparation
+```swift
+// Initialize the values to be returned and Priority Queue data structure.
+var cost: Int = 0
+var tree = Graph<T>()
+var visited = Set<T>()
+
+// In addition to the (neighbour vertex, weight) pair, parent is added for the purpose of printing out the MST later.
+// parent is basically current vertex. aka. the previous vertex before neigbour vertex gets visited.
+var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(sort: { $0.weight < $1.weight })
+```
+
+Start from any vertex
+```swift
+priorityQueue.enqueue((vertex: graph.vertices.first!, weight: 0, parent: nil))
+```
+
+```swift
+// Take from the top of the priority queue ensures getting the least weight edge.
+while let head = priorityQueue.dequeue() {
+  let vertex = head.vertex
+  if visited.contains(vertex) {
+    continue
+  }
+
+  // If the vertex hasn't been visited before, its edge (parent-vertex) is selected for MST.
+  visited.insert(vertex)
+  cost += head.weight
+  if let prev = head.parent { // The first vertex doesn't have a parent.
+    tree.addEdge(vertex1: prev, vertex2: vertex, weight: head.weight)
+  }
+
+  // Add all unvisted neighbours into the priority queue.
+  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))
+      }
+    }
+  }
+}
+```
diff --git a/README.markdown b/README.markdown
index e0983f22e..579ca0b4e 100644
--- a/README.markdown
+++ b/README.markdown
@@ -178,6 +178,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - [Shortest Path](Shortest%20Path%20%28Unweighted%29/) on an unweighted tree
 - [Single-Source Shortest Paths](Single-Source%20Shortest%20Paths%20(Weighted)/)
 - [Minimum Spanning Tree](Minimum%20Spanning%20Tree%20%28Unweighted%29/) on an unweighted tree
+- [Minimum Spanning Tree](Minimum%20Spanning%20Tree/)
 - [All-Pairs Shortest Paths](All-Pairs%20Shortest%20Paths/)
 
 ## Puzzles
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index b2ffce836..c89ac0dfe 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1267,6 +1267,32 @@
          location = "group:README.markdown">
       </FileRef>
    </Group>
+   <Group
+      location = "group:Minimum Spanning Tree"
+      name = "Minimum Spanning Tree">
+      <FileRef
+         location = "group:Kruskal.swift">
+      </FileRef>
+      <FileRef
+         location = "group:Prim.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:kruskal.png">
+         </FileRef>
+         <FileRef
+            location = "group:prim.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:MinimumSpanningTree.playground">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Minimum Spanning Tree (Unweighted)"
       name = "Minimum Spanning Tree (Unweighted)">

From 6bc50e5f9a966738b8331d68de8ed421067d4f4e Mon Sep 17 00:00:00 2001
From: Xiangxin <xiangxinsg@gmail.com>
Date: Tue, 25 Apr 2017 15:29:45 +0800
Subject: [PATCH 198/862] Address comments and refactor

---
 .../MinimumSpanningTree.playground/Contents.swift   |  4 ++--
 .../Sources/Graph.swift                             | 13 +++++++------
 .../playground.xcworkspace/contents.xcworkspacedata |  7 +++++++
 Minimum Spanning Tree/Prim.swift                    |  5 +++--
 4 files changed, 19 insertions(+), 10 deletions(-)
 create mode 100644 Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata

diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift
index 99b5e859f..2981d30ea 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Contents.swift	
@@ -30,7 +30,7 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
   var cost: Int = 0
   var tree = Graph<T>()
 
-  if graph.vertices.isEmpty {
+  guard let start = graph.vertices.first else {
     return (cost: cost, tree: tree)
   }
 
@@ -38,7 +38,7 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
   var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
     sort: { $0.weight < $1.weight })
 
-  priorityQueue.enqueue((vertex: graph.vertices.first!, weight: 0, parent: nil))
+  priorityQueue.enqueue((vertex: start, weight: 0, parent: nil))
   while let head = priorityQueue.dequeue() {
     let vertex = head.vertex
     if visited.contains(vertex) {
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
index 0ae996646..a2f243202 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -36,16 +36,17 @@ public struct Graph<T: Hashable>: CustomStringConvertible {
     edgeList.append(Edge(vertex1: v1, vertex2: v2, weight: w))
     vertices.insert(v1)
     vertices.insert(v2)
-    if adjList[v1] == nil {
-      adjList[v1] = [(vertex: v2, weight: w)]
+
+    if let _ = adjList[v1] {
+      adjList[v1]?.append((vertex: v2, weight: w))
     } else {
-      adjList[v1]!.append((vertex: v2, weight: w))
+      adjList[v1] = [(vertex: v2, weight: w)]
     }
 
-    if adjList[v2] == nil {
-      adjList[v2] = [(vertex: v1, weight: w)]
+    if let _ = adjList[v2] {
+      adjList[v2]?.append((vertex: v1, weight: w))
     } else {
-      adjList[v2]!.append((vertex: v1, weight: w))
+      adjList[v2] = [(vertex: v1, weight: w)]
     }
   }
 
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata b/Minimum Spanning Tree/MinimumSpanningTree.playground/playground.xcworkspace/contents.xcworkspacedata
new file mode 100644
index 000000000..919434a62
--- /dev/null
+++ b/Minimum Spanning Tree/MinimumSpanningTree.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/Minimum Spanning Tree/Prim.swift b/Minimum Spanning Tree/Prim.swift
index 89c26cff0..d975fc430 100644
--- a/Minimum Spanning Tree/Prim.swift	
+++ b/Minimum Spanning Tree/Prim.swift	
@@ -10,7 +10,7 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
   var cost: Int = 0
   var tree = Graph<T>()
 
-  if graph.vertices.isEmpty {
+  guard let start = graph.vertices.first else {
     return (cost: cost, tree: tree)
   }
 
@@ -18,7 +18,7 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
   var priorityQueue = PriorityQueue<(vertex: T, weight: Int, parent: T?)>(
     sort: { $0.weight < $1.weight })
 
-  priorityQueue.enqueue((vertex: graph.vertices.first!, weight: 0, parent: nil))
+  priorityQueue.enqueue((vertex: start, weight: 0, parent: nil))
   while let head = priorityQueue.dequeue() {
     let vertex = head.vertex
     if visited.contains(vertex) {
@@ -43,3 +43,4 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
 
   return (cost: cost, tree: tree)
 }
+

From ea777fb3bc861e4818c414a97eb72fb8b9e3b644 Mon Sep 17 00:00:00 2001
From: Xiangxin <xiangxinsg@gmail.com>
Date: Sat, 6 May 2017 13:08:41 +0800
Subject: [PATCH 199/862] refactor

---
 .../Sources/Graph.swift                            | 14 ++++----------
 1 file changed, 4 insertions(+), 10 deletions(-)

diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
index a2f243202..5e74e14cb 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -37,17 +37,11 @@ public struct Graph<T: Hashable>: CustomStringConvertible {
     vertices.insert(v1)
     vertices.insert(v2)
 
-    if let _ = adjList[v1] {
-      adjList[v1]?.append((vertex: v2, weight: w))
-    } else {
-      adjList[v1] = [(vertex: v2, weight: w)]
-    }
+    adjList[v1] = adjList[v1] ?? []
+    adjList[v1]?.append((vertex: v2, weight: w))
 
-    if let _ = adjList[v2] {
-      adjList[v2]?.append((vertex: v1, weight: w))
-    } else {
-      adjList[v2] = [(vertex: v1, weight: w)]
-    }
+    adjList[v2] = adjList[v2] ?? []
+    adjList[v2]?.append((vertex: v1, weight: w))
   }
 
   public mutating func addEdge(_ edge: Edge<T>) {

From 12fac48235b369612be3a96b807e4e4ba2ad237c Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 7 May 2017 04:45:19 -0700
Subject: [PATCH 200/862] Fixed spacing, and fixes some English.

---
 .../UnionFind.playground/Contents.swift       | 24 ++---
 .../Sources/UnionFindQuickFind.swift          | 80 ++++++++--------
 .../Sources/UnionFindQuickUnion.swift         | 82 ++++++++--------
 .../Sources/UnionFindWeightedQuickFind.swift  | 94 +++++++++----------
 .../Sources/UnionFindWeightedQuickUnion.swift | 92 +++++++++---------
 ...indWeightedQuickUnionPathCompression.swift | 86 ++++++++---------
 6 files changed, 229 insertions(+), 229 deletions(-)

diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 9ad5215b3..0a50d1ba6 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -3,17 +3,17 @@
 var dsu = UnionFindQuickUnion<Int>()
 
 for i in 1...10 {
-    dsu.addSetWith(i)
+  dsu.addSetWith(i)
 }
 // now our dsu contains 10 independent sets
 
 // let's divide our numbers into two sets by divisibility by 2
 for i in 3...10 {
-    if i % 2 == 0 {
-        dsu.unionSetsContaining(2, and: i)
-    } else {
-        dsu.unionSetsContaining(1, and: i)
-    }
+  if i % 2 == 0 {
+    dsu.unionSetsContaining(2, and: i)
+  } else {
+    dsu.unionSetsContaining(1, and: i)
+  }
 }
 
 // check our division
@@ -42,12 +42,12 @@ dsuForStrings.addSetWith("b")
 
 // In that example we divide strings by its first letter
 for word in words {
-    dsuForStrings.addSetWith(word)
-    if word.hasPrefix("a") {
-        dsuForStrings.unionSetsContaining("a", and: word)
-    } else if word.hasPrefix("b") {
-        dsuForStrings.unionSetsContaining("b", and: word)
-    }
+  dsuForStrings.addSetWith(word)
+  if word.hasPrefix("a") {
+    dsuForStrings.unionSetsContaining("a", and: word)
+  } else if word.hasPrefix("b") {
+    dsuForStrings.unionSetsContaining("b", and: word)
+  }
 }
 
 print(dsuForStrings.inSameSet("a", and: "all"))
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
index 25d7f5b5d..33e81832d 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
@@ -3,48 +3,48 @@ import Foundation
 /// Quick-find algorithm may take ~MN steps
 /// to process M union commands on N objects
 public struct UnionFindQuickFind<T: Hashable> {
-    private var index = [T: Int]()
-    private var parent = [Int]()
-    private var size = [Int]()
-    
-    public init() {}
-    
-    public mutating func addSetWith(_ element: T) {
-        index[element] = parent.count
-        parent.append(parent.count)
-        size.append(1)
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  public init() {}
+  
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  private mutating func setByIndex(_ index: Int) -> Int {
+    return parent[index]
+  }
+  
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
     }
-    
-    private mutating func setByIndex(_ index: Int) -> Int {
-        return parent[index]
-    }
-    
-    public mutating func setOf(_ element: T) -> Int? {
-        if let indexOfElement = index[element] {
-            return setByIndex(indexOfElement)
-        } else {
-            return nil
-        }
-    }
-    
-    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            if firstSet != secondSet {
-                for index in 0..<parent.count {
-                    if parent[index] == firstSet {
-                        parent[index] = secondSet
-                    }
-                }
-                size[secondSet] += size[firstSet]
-            }
+  }
+  
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        for index in 0..<parent.count {
+          if parent[index] == firstSet {
+            parent[index] = secondSet
+          }
         }
+        size[secondSet] += size[firstSet]
+      }
     }
-    
-    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            return firstSet == secondSet
-        } else {
-            return false
-        }
+  }
+  
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
     }
+  }
 }
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
index 4c848e61d..9bff31616 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
@@ -3,49 +3,49 @@ import Foundation
 /// Quick-Union algorithm may take ~MN steps
 /// to process M union commands on N objects
 public struct UnionFindQuickUnion<T: Hashable> {
-    private var index = [T: Int]()
-    private var parent = [Int]()
-    private var size = [Int]()
-    
-    public init() {}
-    
-    public mutating func addSetWith(_ element: T) {
-        index[element] = parent.count
-        parent.append(parent.count)
-        size.append(1)
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  public init() {}
+  
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  private mutating func setByIndex(_ index: Int) -> Int {
+    if parent[index] == index {
+      return index
+    } else {
+      parent[index] = setByIndex(parent[index])
+      return parent[index]
     }
-    
-    private mutating func setByIndex(_ index: Int) -> Int {
-        if parent[index] == index {
-            return index
-        } else {
-            parent[index] = setByIndex(parent[index])
-            return parent[index]
-        }
+  }
+  
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
     }
-    
-    public mutating func setOf(_ element: T) -> Int? {
-        if let indexOfElement = index[element] {
-            return setByIndex(indexOfElement)
-        } else {
-            return nil
-        }
+  }
+  
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        parent[firstSet] = secondSet
+        size[secondSet] += size[firstSet]
+      }
     }
-    
-    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            if firstSet != secondSet {
-                parent[firstSet] = secondSet
-                size[secondSet] += size[firstSet]
-            }
-        }
-    }
-    
-    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            return firstSet == secondSet
-        } else {
-            return false
-        }
+  }
+  
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
     }
+  }
 }
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
index 02bec94a8..c89f2a457 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
@@ -3,57 +3,57 @@ import Foundation
 /// Quick-find algorithm may take ~MN steps
 /// to process M union commands on N objects
 public struct UnionFindWeightedQuickFind<T: Hashable> {
-    private var index = [T: Int]()
-    private var parent = [Int]()
-    private var size = [Int]()
-    
-    public init() {}
-    
-    public mutating func addSetWith(_ element: T) {
-        index[element] = parent.count
-        parent.append(parent.count)
-        size.append(1)
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  public init() {}
+  
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  private mutating func setByIndex(_ index: Int) -> Int {
+    return parent[index]
+  }
+  
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
     }
-    
-    private mutating func setByIndex(_ index: Int) -> Int {
-        return parent[index]
-    }
-    
-    public mutating func setOf(_ element: T) -> Int? {
-        if let indexOfElement = index[element] {
-            return setByIndex(indexOfElement)
+  }
+  
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        if size[firstSet] < size[secondSet] {
+          for index in 0..<parent.count {
+            if parent[index] == firstSet {
+              parent[index] = secondSet
+            }
+          }
+          size[secondSet] += size[firstSet]
         } else {
-            return nil
-        }
-    }
-    
-    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            if firstSet != secondSet {
-                if size[firstSet] < size[secondSet] {
-                    for index in 0..<parent.count {
-                        if parent[index] == firstSet {
-                            parent[index] = secondSet
-                        }
-                    }
-                    size[secondSet] += size[firstSet]
-                } else {
-                    for index in 0..<parent.count {
-                        if parent[index] == secondSet {
-                            parent[index] = firstSet
-                        }
-                    }
-                    size[firstSet] += size[secondSet]
-                }
+          for index in 0..<parent.count {
+            if parent[index] == secondSet {
+              parent[index] = firstSet
             }
+          }
+          size[firstSet] += size[secondSet]
         }
+      }
     }
-    
-    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            return firstSet == secondSet
-        } else {
-            return false
-        }
+  }
+  
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
     }
+  }
 }
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
index b3ac7445e..cd33007bc 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
@@ -1,56 +1,56 @@
 import Foundation
 
 public struct UnionFindWeightedQuickUnion<T: Hashable> {
-    private var index = [T: Int]()
-    private var parent = [Int]()
-    private var size = [Int]()
-    
-    public init() {}
-    
-    public mutating func addSetWith(_ element: T) {
-        index[element] = parent.count
-        parent.append(parent.count)
-        size.append(1)
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  public init() {}
+  
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  private mutating func setByIndex(_ index: Int) -> Int {
+    if parent[index] == index {
+      return index
+    } else {
+      parent[index] = setByIndex(parent[index])
+      return parent[index]
     }
-    
-    private mutating func setByIndex(_ index: Int) -> Int {
-        if parent[index] == index {
-            return index
-        } else {
-            parent[index] = setByIndex(parent[index])
-            return parent[index]
-        }
+  }
+  
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
     }
-    
-    public mutating func setOf(_ element: T) -> Int? {
-        if let indexOfElement = index[element] {
-            return setByIndex(indexOfElement)
+  }
+  
+  /// Weighted, by comparing set size.
+  /// Merge small set into the large one.
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        if size[firstSet] < size[secondSet] {
+          parent[firstSet] = secondSet
+          size[secondSet] += size[firstSet]
         } else {
-            return nil
-        }
-    }
-    
-    /// Weighted, by comparing set size.
-    /// Merge small set into the large one.
-    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            if firstSet != secondSet {
-                if size[firstSet] < size[secondSet] {
-                    parent[firstSet] = secondSet
-                    size[secondSet] += size[firstSet]
-                } else {
-                    parent[secondSet] = firstSet
-                    size[firstSet] += size[secondSet]
-                }
-            }
+          parent[secondSet] = firstSet
+          size[firstSet] += size[secondSet]
         }
+      }
     }
-    
-    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            return firstSet == secondSet
-        } else {
-            return false
-        }
+  }
+  
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
     }
+  }
 }
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
index 892f46a3c..7eb8fe209 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
@@ -1,53 +1,53 @@
 import Foundation
 
 public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
-    private var index = [T: Int]()
-    private var parent = [Int]()
-    private var size = [Int]()
-    
-    public init() {}
-    
-    public mutating func addSetWith(_ element: T) {
-        index[element] = parent.count
-        parent.append(parent.count)
-        size.append(1)
+  private var index = [T: Int]()
+  private var parent = [Int]()
+  private var size = [Int]()
+  
+  public init() {}
+  
+  public mutating func addSetWith(_ element: T) {
+    index[element] = parent.count
+    parent.append(parent.count)
+    size.append(1)
+  }
+  
+  /// Path Compression.
+  private mutating func setByIndex(_ index: Int) -> Int {
+    if index != parent[index] {
+      parent[index] = setByIndex(parent[index])
     }
-    
-    /// Path Compression.
-    private mutating func setByIndex(_ index: Int) -> Int {
-        if index != parent[index] {
-            parent[index] = setByIndex(parent[index])
-        }
-        return parent[index]
+    return parent[index]
+  }
+  
+  public mutating func setOf(_ element: T) -> Int? {
+    if let indexOfElement = index[element] {
+      return setByIndex(indexOfElement)
+    } else {
+      return nil
     }
-    
-    public mutating func setOf(_ element: T) -> Int? {
-        if let indexOfElement = index[element] {
-            return setByIndex(indexOfElement)
+  }
+  
+  public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      if firstSet != secondSet {
+        if size[firstSet] < size[secondSet] {
+          parent[firstSet] = secondSet
+          size[secondSet] += size[firstSet]
         } else {
-            return nil
-        }
-    }
-    
-    public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            if firstSet != secondSet {
-                if size[firstSet] < size[secondSet] {
-                    parent[firstSet] = secondSet
-                    size[secondSet] += size[firstSet]
-                } else {
-                    parent[secondSet] = firstSet
-                    size[firstSet] += size[secondSet]
-                }
-            }
+          parent[secondSet] = firstSet
+          size[firstSet] += size[secondSet]
         }
+      }
     }
-    
-    public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
-        if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
-            return firstSet == secondSet
-        } else {
-            return false
-        }
+  }
+  
+  public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
+    if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
+      return firstSet == secondSet
+    } else {
+      return false
     }
+  }
 }

From e560f60fc35889fefba95389ea53c6d02a9e22e9 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 8 May 2017 01:09:02 +0500
Subject: [PATCH 201/862] Fix a few typos in DiningPhilosophers Readme

an -> a
dinining -> dining
"no needs" -> "no need"
---
 DiningPhilosophers/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index 0bf4f28ce..bc622e559 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -22,12 +22,12 @@ Eating is not limited by the remaining amounts of spaghetti or stomach space; an
 
 The problem is how to design a discipline of behavior (a concurrent algorithm) such that no philosopher will starve; i.e., each can forever continue to alternate between eating and thinking, assuming that no philosopher can know when others may want to eat or think.
 
-This is an illustration of an dinining table:
+This is an illustration of a dining table:
 
 ![Dining Philosophers table](https://upload.wikimedia.org/wikipedia/commons/7/7b/An_illustration_of_the_dining_philosophers_problem.png)
 
 # Solution
-There are different solutions for this classic algorithm, and this Swift implementation is based on the Chandy/Misra solution. This implementation allows agents to contend for an arbitrary number of resources in a completely distributed scenario with no needs for a central authority to control the locking and serialization of resources. 
+There are different solutions for this classic algorithm, and this Swift implementation is based on the Chandy/Misra solution. This implementation allows agents to contend for an arbitrary number of resources in a completely distributed scenario with no need for a central authority to control the locking and serialization of resources. 
 
 However, this solution violates the requirement that "the philosophers do not speak to each other" (due to the request messages).
 

From 297b0d4679fbd8607edb5b59b87d273962354e84 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 8 May 2017 01:26:16 +0500
Subject: [PATCH 202/862] Fix minor grammar typo

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

diff --git a/Graph/README.markdown b/Graph/README.markdown
index bc33b044a..d3c8b89e5 100644
--- a/Graph/README.markdown
+++ b/Graph/README.markdown
@@ -143,7 +143,7 @@ Here is an example of a simple graph:
 
 ![Demo](Images/Demo1.png)
 
-We can represent it as an adjacency matrix or adjacency list. The classes implementing those concept both inherit a common API from `AbstractGraph`, so they can be created in an identical fashion, with different optimized data structures behind the scenes.
+We can represent it as an adjacency matrix or adjacency list. The classes implementing those concepts both inherit a common API from `AbstractGraph`, so they can be created in an identical fashion, with different optimized data structures behind the scenes.
 
 Let's create some directed, weighted graphs, using each representation, to store the example:
 

From 24d5adeba873dc184e2fc28dcaf942b15c60b95e Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Mon, 8 May 2017 01:32:34 +0500
Subject: [PATCH 203/862] Fix broken links by replacing spaces with %20

---
 Heap/README.markdown | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Heap/README.markdown b/Heap/README.markdown
index 7beea4f34..a3b0038ab 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -1,11 +1,11 @@
 # Heap
 
-A heap is a [binary tree](../Binary Tree/) 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.
+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:
 
-- To build [priority queues](../Priority Queue/).
-- To support [heap sorts](../Heap Sort/).
+- To build [priority queues](../Priority%20Queue/).
+- To support [heap sorts](../Heap%20Sort/).
 - To compute the minimum (or maximum) element of a collection quickly.
 - To impress your non-programmer friends.
 
@@ -21,7 +21,7 @@ An example:
 
 This is a max-heap because every parent node is greater than its children. `(10)` is greater than `(7)` and `(2)`. `(7)` is greater than `(5)` and `(1)`.
 
-As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. The heap property is useful because heaps are often used as a [priority queue](../Priority Queue/)to access the "most important" element quickly.
+As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. The heap property is useful because heaps are often used as a [priority queue](../Priority%20Queue/)to access the "most important" element quickly.
 
 > **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.
 
@@ -30,11 +30,11 @@ As a result of this heap property, a max-heap always stores its largest item at
 A heap is not a replacement for a binary search tree, and there are similarities and differnces between them. Here are some main differences:
 
 
-**Order of the nodes.** In a [binary search tree (BST)](../Binary Search Tree/), 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.
+**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.
 
 **Memory.** Traditional trees take up more memory than just the data they store. You need to allocate additional storage for the node objects and pointers to the left/right child nodes. A heap only uses a plain array for storage and uses no pointers.
 
-**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 Tree/) or [red-black tree](../Red-Black Tree/), 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.
+**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. 
 
@@ -112,7 +112,7 @@ Is this a valid heap? The answer is yes! A sorted array from low-to-high is a va
 
 The heap property holds for each node because a parent is always smaller than its children. (Verify for yourself that an array sorted from high-to-low is always a valid max-heap.)
 
-> **Note:** But not every min-heap is necessarily a sorted array! It only works one way. To turn a heap back into a sorted array, you need to use [heap sort](../Heap Sort/).
+> **Note:** But not every min-heap is necessarily a sorted array! It only works one way. To turn a heap back into a sorted array, you need to use [heap sort](../Heap%20Sort/).
 
 ## More math!
 
@@ -162,7 +162,7 @@ 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 Sort/). 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 lg 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)**.
 
@@ -289,7 +289,7 @@ Here, `elements` is the heap's own array. We walk backwards through this array,
 
 Heaps are not made for fast searches, but if you want to remove an arbitrary element using `removeAtIndex()` or change the value of an element with `replace()`, then you need to obtain the index of that element. Searching is one way to do this, but it is slow.
 
-In a [binary search tree](../Binary Search Tree/), depending on the order of the nodes, a fast search can be guaranteed. Since a heap orders its nodes differently, a binary search will not work, and you need to check every node in the tree.
+In a [binary search tree](../Binary%20Search%20Tree/), depending on the order of the nodes, a fast search can be guaranteed. Since a heap orders its nodes differently, a binary search will not work, and you need to check every node in the tree.
 
 Let's take our example heap again:
 

From 1eb61c97a7949a0088834759bd9b1f40d884a9e9 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 8 May 2017 05:16:23 -0700
Subject: [PATCH 204/862] Improves the wording for a few sentences.

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

diff --git a/Union-Find/README.markdown b/Union-Find/README.markdown
index dfec7dbe6..a268f1d70 100644
--- a/Union-Find/README.markdown
+++ b/Union-Find/README.markdown
@@ -9,7 +9,7 @@ What do we mean by this? For example, the Union-Find data structure could be kee
 	[ g, d, c ]
 	[ i, j ]
 
-These sets are disjoint because they have no members in common.
+These sets are **disjoint** because they have no members in common.
 
 Union-Find supports three basic operations:
 
@@ -24,7 +24,7 @@ The most common application of this data structure is keeping track of the conne
 ## Implementation
 
 Union-Find can be implemented in many ways but we'll look at an efficient and easy to understand implementation: Weighted Quick Union.
-> __PS: Variety implementation of Union-Find has been included in playground.__
+> __PS: Multiple implementations of Union-Find has been included in playground.__
 
 ```swift
 public struct UnionFind<T: Hashable> {
@@ -198,7 +198,7 @@ private mutating func setByIndex(_ index: Int) -> Int {
 ```
 Path Compression helps keep trees very flat, thus find operation could take __ALMOST__ in __O(1)__
 
-## Complexity Summary of Variety Implementation
+## Complexity Summary
 
 ##### To process N objects
 | Data Structure | Union | Find |

From a087b19f146e32ac731fac5c4c989b1eff3c7401 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Mon, 8 May 2017 05:17:49 -0700
Subject: [PATCH 205/862] Fixes spelling.

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

diff --git a/DiningPhilosophers/README.md b/DiningPhilosophers/README.md
index 0bf4f28ce..e4db0d7e0 100755
--- a/DiningPhilosophers/README.md
+++ b/DiningPhilosophers/README.md
@@ -10,7 +10,7 @@ In computer science, the dining philosophers problem is often used in the concur
 
 It was originally formulated in 1965 by Edsger Dijkstra as a student exam exercise, presented in terms of computers competing for access to tape drive peripherals. Soon after, Tony Hoare gave the problem its present formulation.
 
-This Swift implementation is based on the Chandy/Misra solution, and it uses the GCD Dispatch and Semaphone on the Swift cross platform.
+This Swift implementation is based on the Chandy/Misra solution, and it uses the GCD Dispatch and Semaphores on the Swift cross platform.
 
 # Problem statement
 

From 988e354fed9122acb0b7b7ec8098b0a29c374070 Mon Sep 17 00:00:00 2001
From: Mike <perryao@users.noreply.github.com>
Date: Mon, 8 May 2017 18:54:43 -0400
Subject: [PATCH 206/862] Formatted headers in readme

Github seems to require spaces between "#" and headings .
---
 Radix Sort/ReadMe.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Radix Sort/ReadMe.md b/Radix Sort/ReadMe.md
index 5bdb931ca..ceb4459d7 100644
--- a/Radix Sort/ReadMe.md	
+++ b/Radix Sort/ReadMe.md	
@@ -2,19 +2,19 @@
 
 Radix sort is a sorting algorithm that takes as input an array of integers and uses a sorting subroutine( that is often another efficient sorting algorith) to sort the integers by their radix, or rather their digit.  Counting Sort, and Bucket Sort are often times used as the subroutine for Radix Sort.
 
-##Example
+## Example
 
 * Input Array: [170, 45, 75, 90, 802, 24, 2, 66]
 * Output Array (Sorted):  [2, 24, 45, 66, 75, 90, 170, 802]
 
-###Step 1:
+### Step 1:
 The first step in this algorithm is to define the digit or rather the "base" or radix that we will use to sort.
 For this example we will let radix = 10, since the integers we are working with in the example are of base 10.
 
-###Step 2:
+### Step 2:
 The next step is to simply iterate n times (where n is the number of digits in the largest integer in the input array), and upon each iteration perform a sorting subroutine on the current digit in question.
 
-###Algorithm in Action
+### Algorithm in Action
 
 Let's take a look at our example input array.
 

From 90730ade45d11947529e51acf15e09f1ef622596 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Tue, 16 May 2017 09:56:13 -0700
Subject: [PATCH 207/862] Fixes #464.

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

diff --git a/Threaded Binary Tree/README.markdown b/Threaded Binary Tree/README.markdown
index 8a1c518f1..f631b86f9 100644
--- a/Threaded Binary Tree/README.markdown	
+++ b/Threaded Binary Tree/README.markdown	
@@ -267,9 +267,9 @@ something simple, like removing **7**, which has no children:
 Before we can just throw **7** away, we have to perform some clean-up.  In this
 case, because **7** is a `right` child and has no children itself, we can
 simply set the `rightThread` of **7**'s `parent`(**5**) to **7**'s (now
-outdated) `rightThread`.  Then we can just set **7**'s `parent`, `left`,
+outdated) `rightThread`. Then we can just set **7**'s `parent`, `left`,
 `right`, `leftThread`, and `rightThread` to `nil`, effectively removing it from
-the tree.
+the tree. We also set the parent's `rightChild` to `nil`, which completes the deletion of this right child. 
 
 Let's try something a little harder.  Say we remove **5** from the tree:
 

From cde6f854865d19c4cefb187894a4da09a0be4fee Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Wed, 17 May 2017 05:16:52 +0500
Subject: [PATCH 208/862] Fix a few typos in Heap/README

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

diff --git a/Heap/README.markdown b/Heap/README.markdown
index a3b0038ab..bb7a785a5 100644
--- a/Heap/README.markdown
+++ b/Heap/README.markdown
@@ -21,7 +21,7 @@ An example:
 
 This is a max-heap because every parent node is greater than its children. `(10)` is greater than `(7)` and `(2)`. `(7)` is greater than `(5)` and `(1)`.
 
-As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. The heap property is useful because heaps are often used as a [priority queue](../Priority%20Queue/)to access the "most important" element quickly.
+As a result of this heap property, a max-heap always stores its largest item at the root of the tree. For a min-heap, the root is always the smallest item in the tree. The heap property is useful because heaps are often used as a [priority queue](../Priority%20Queue/) to access the "most important" element quickly.
 
 > **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.
 
@@ -124,7 +124,7 @@ This heap has height 3, so it has 4 levels:
 
 ![Large heap](Images/LargeHeap.png)
 
-A heap with *n* nodes has height *h = floor(log_2(n))*. This is because we always fill up the lowest level completely before we add a new level. The example has 15 nodes, so the height is `floor(log_2(15)) = floor(3.91) = 3`.
+A heap with *n* nodes has height *h = floor(log2(n))*. This is because we always fill up the lowest level completely before we add a new level. The example has 15 nodes, so the height is `floor(log2(15)) = floor(3.91) = 3`.
 
 If the lowest level is completely full, then that level contains *2^h* nodes. The rest of the tree above it contains *2^h - 1* nodes. Fill in the numbers from the example: the lowest level has 8 nodes, which indeed is `2^3 = 8`. The first three levels contain a total of 7 nodes, i.e. `2^3 - 1 = 8 - 1 = 7`.
 
@@ -303,7 +303,7 @@ Let's say we want to see if the heap contains the value `8` (it doesn't). We sta
 
 Despite this small optimization, searching is still an **O(n)** operation.
 
-> **Note:** There is away to turn lookups into a **O(1)** operation by keeping an additional dictionary that maps node values to indices. This may be worth doing if you often need to call `replace()` to change the "priority" of objects in a [priority queue](../Priority%20Queue/) that's built on a heap.
+> **Note:** There is a way to turn lookups into a **O(1)** operation by keeping an additional dictionary that maps node values to indices. This may be worth doing if you often need to call `replace()` to change the "priority" of objects in a [priority queue](../Priority%20Queue/) that's built on a heap.
 
 ## The code
 

From c014bd9a0823d6206fa18e915f6e4f01d5852beb Mon Sep 17 00:00:00 2001
From: Artur <gitkid@icloud.com>
Date: Wed, 17 May 2017 03:19:47 +0300
Subject: [PATCH 209/862] remove "countingSort" func throws

if you received empty array, just return empty array
---
 Counting Sort/CountingSort.swift | 10 ++--------
 1 file changed, 2 insertions(+), 8 deletions(-)

diff --git a/Counting Sort/CountingSort.swift b/Counting Sort/CountingSort.swift
index abece0213..725a634a4 100644
--- a/Counting Sort/CountingSort.swift	
+++ b/Counting Sort/CountingSort.swift	
@@ -6,14 +6,8 @@
 //  Copyright © 2016 Ali Hafizji. All rights reserved.
 //
 
-enum CountingSortError: Error {
-  case arrayEmpty
-}
-
-func countingSort(_ array: [Int]) throws -> [Int] {
-  guard array.count > 0 else {
-    throw CountingSortError.arrayEmpty
-  }
+func countingSort(_ array: [Int])-> [Int] {
+  guard array.count > 0 else {return []}
 
   // Step 1
   // Create an array to store the count of each element

From d705414bbcf2eb62232d5c456befc193e397b208 Mon Sep 17 00:00:00 2001
From: Jawwad Ahmad <jawwad.f.ahmad@gmail.com>
Date: Wed, 17 May 2017 05:20:54 +0500
Subject: [PATCH 210/862] Update displayed code to use 2 space indentation

---
 Heap Sort/README.markdown | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Heap Sort/README.markdown b/Heap Sort/README.markdown
index 7fdd8d2ca..a45dad6f9 100644
--- a/Heap Sort/README.markdown	
+++ b/Heap Sort/README.markdown	
@@ -48,13 +48,13 @@ Here's how you can implement heap sort in Swift:
 
 ```swift
 extension Heap {
-    public mutating func sort() -> [T] {
-        for i in stride(from: (elements.count - 1), through: 1, by: -1) {
-            swap(&elements[0], &elements[i])
-            shiftDown(0, heapSize: i)
-        }
-    return elements
+  public mutating func sort() -> [T] {
+    for i in stride(from: (elements.count - 1), through: 1, by: -1) {
+      swap(&elements[0], &elements[i])
+      shiftDown(0, heapSize: i)
     }
+    return elements
+  }
 }
 ```
 
@@ -71,9 +71,9 @@ We can write a handy helper function for that:
 
 ```swift
 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)
-    return h.sort()
+  let reverseOrder = { i1, i2 in sort(i2, i1) }
+  var h = Heap(array: a, sort: reverseOrder)
+  return h.sort()
 }
 ```
 

From e311ee9b88a16d9dfaeacc7f2e7ea7825169fe8b Mon Sep 17 00:00:00 2001
From: Tobias Helmrich <helmrich@users.noreply.github.com>
Date: Thu, 18 May 2017 21:52:38 +0900
Subject: [PATCH 211/862] Fix typos and markdown formatting

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

diff --git a/Linear Regression/README.markdown b/Linear Regression/README.markdown
index 1a1a1eb8b..29ac2e321 100644
--- a/Linear Regression/README.markdown	
+++ b/Linear Regression/README.markdown	
@@ -75,7 +75,7 @@ for n 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 minimse 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 proprotional 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.
 
@@ -98,7 +98,7 @@ Here is the same data shown as a graph. Each of the blue lines on the graph repr
 
 After 18,000 iterations it looks as if the line is getting closer to what we would expect (just by looking) to be the correct line of best fit. Also, each additional 2,000 iterations has less and less effect on the final result - the values of the intercept and the slope are converging on the correct values.
 
-##A closed form solution
+## A closed form solution
 
 There is another way we can calculate the line of best fit, without having to do multiple iterations. We can solve the equations describing the least squares minimisation and just work out the intercept and slope directly. 
 
@@ -139,7 +139,7 @@ This function takes as arguments two arrays of Doubles, and returns a function w
 Using this line, we would predict a price for our 4 year old car of £6952.
 
 
-##Summary
+## Summary
 We've seen two different ways to implement a simple linear regression in Swift. An obvious question is: why bother with the iterative approach at all? 
 
 Well, the line we've found doesn't fit the data perfectly. For one thing, the graph includes some negative values at high car ages! Possibly we would have to pay someone to tow away a very old car... but really these negative values just show that we have not modelled the real life situation very accurately. The relationship between the car age and the car price is not linear but instead is some other function. We also know that a car's price is not just related to its age but also other factors such as the make, model and engine size of the car. We would need to use additional variables to describe these other factors. 

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 212/862] 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 213/862] 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 214/862] 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
new file mode 100644
index 0000000000000000000000000000000000000000..af2c6ee9d06b7e35afcd6a88b5c2767fce07d838
GIT binary patch
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diff --git a/Splay Tree/Images /examplezig.svg b/Splay Tree/Images /examplezig.svg
new file mode 100644
index 000000000..800ef1886
--- /dev/null
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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 215/862] 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
 Splay Tree/{Images  => Images}/examplezigzig1.png | Bin
 Splay Tree/{Images  => Images}/examplezigzig2.png | Bin
 Splay Tree/{Images  => Images}/examplezigzig3.png | Bin
 Splay Tree/{Images  => Images}/zig.png            | Bin
 Splay Tree/{Images  => Images}/zigzag1.png        | Bin
 Splay Tree/{Images  => Images}/zigzag2.png        | Bin
 Splay Tree/{Images  => Images}/zigzig1.png        | Bin
 Splay Tree/{Images  => Images}/zigzig2.png        | Bin
 15 files changed, 0 insertions(+), 0 deletions(-)
 rename Splay Tree/{Images  => Images}/example1-1.png (100%)
 rename Splay Tree/{Images  => Images}/example1-2.png (100%)
 rename Splay Tree/{Images  => Images}/example1-3.png (100%)
 rename Splay Tree/{Images  => Images}/examplezig.svg (100%)
 rename Splay Tree/{Images  => Images}/examplezig1.png (100%)
 rename Splay Tree/{Images  => Images}/examplezig2.png (100%)
 rename Splay Tree/{Images  => Images}/examplezigzig.svg (100%)
 rename Splay Tree/{Images  => Images}/examplezigzig1.png (100%)
 rename Splay Tree/{Images  => Images}/examplezigzig2.png (100%)
 rename Splay Tree/{Images  => Images}/examplezigzig3.png (100%)
 rename Splay Tree/{Images  => Images}/zig.png (100%)
 rename Splay Tree/{Images  => Images}/zigzag1.png (100%)
 rename Splay Tree/{Images  => Images}/zigzag2.png (100%)
 rename Splay Tree/{Images  => Images}/zigzig1.png (100%)
 rename Splay Tree/{Images  => Images}/zigzig2.png (100%)

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
diff --git a/Splay Tree/Images /example1-3.png b/Splay Tree/Images/example1-3.png
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
diff --git a/Splay Tree/Images /examplezig2.png b/Splay Tree/Images/examplezig2.png
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
diff --git a/Splay Tree/Images /examplezigzig1.png b/Splay Tree/Images/examplezigzig1.png
similarity index 100%
rename from Splay Tree/Images /examplezigzig1.png
rename to Splay Tree/Images/examplezigzig1.png
diff --git a/Splay Tree/Images /examplezigzig2.png b/Splay Tree/Images/examplezigzig2.png
similarity index 100%
rename from Splay Tree/Images /examplezigzig2.png
rename to Splay Tree/Images/examplezigzig2.png
diff --git a/Splay Tree/Images /examplezigzig3.png b/Splay Tree/Images/examplezigzig3.png
similarity index 100%
rename from Splay Tree/Images /examplezigzig3.png
rename to Splay Tree/Images/examplezigzig3.png
diff --git a/Splay Tree/Images /zig.png b/Splay Tree/Images/zig.png
similarity index 100%
rename from Splay Tree/Images /zig.png
rename to Splay Tree/Images/zig.png
diff --git a/Splay Tree/Images /zigzag1.png b/Splay Tree/Images/zigzag1.png
similarity index 100%
rename from Splay Tree/Images /zigzag1.png
rename to Splay Tree/Images/zigzag1.png
diff --git a/Splay Tree/Images /zigzag2.png b/Splay Tree/Images/zigzag2.png
similarity index 100%
rename from Splay Tree/Images /zigzag2.png
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 216/862] 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 217/862] 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 0a813ba0f16865323529e7de03ff9cb69eea378d Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 24 May 2017 16:05:34 +0300
Subject: [PATCH 218/862] Code improvements

---
 Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift
index f4cd8503a..9c5961c71 100644
--- a/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
+++ b/Dijkstra Algorithm/Dijkstra.playground/Sources/Dijkstra.swift	
@@ -13,11 +13,12 @@ public class Dijkstra {
 
     public func findShortestPaths(from startVertex: Vertex) {
         clearCache()
+        var currentVertices = self.totalVertices
         startVertex.pathLengthFromStart = 0
         startVertex.pathVerticesFromStart.append(startVertex)
         var currentVertex: Vertex? = startVertex
         while let vertex = currentVertex {
-            totalVertices.remove(vertex)
+            currentVertices.remove(vertex)
             let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
             for neighbor in filteredNeighbors {
                 let neighborVertex = neighbor.0

From 35db21bb212b56ab13a1ecf67b251727ca3718a9 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 24 May 2017 17:54:49 +0300
Subject: [PATCH 219/862] Updated description

---
 Dijkstra Algorithm/Images/DirectedGraph.png   | Bin 0 -> 68702 bytes
 Dijkstra Algorithm/Images/Vertices.png        | Bin 0 -> 35896 bytes
 .../Images/WeightedDirectedGraph.png          | Bin 0 -> 70820 bytes
 .../Images/WeightedDirectedGraphFinal.png     | Bin 0 -> 76503 bytes
 .../Images/WeightedUndirectedGraph.png        | Bin 0 -> 78079 bytes
 Dijkstra Algorithm/README.md                  |  56 +++++++++++++-----
 6 files changed, 42 insertions(+), 14 deletions(-)
 create mode 100644 Dijkstra Algorithm/Images/DirectedGraph.png
 create mode 100644 Dijkstra Algorithm/Images/Vertices.png
 create mode 100644 Dijkstra Algorithm/Images/WeightedDirectedGraph.png
 create mode 100644 Dijkstra Algorithm/Images/WeightedDirectedGraphFinal.png
 create mode 100644 Dijkstra Algorithm/Images/WeightedUndirectedGraph.png

diff --git a/Dijkstra Algorithm/Images/DirectedGraph.png b/Dijkstra Algorithm/Images/DirectedGraph.png
new file mode 100644
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diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index db1726b1f..ddce51525 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,13 +1,50 @@
+#Weighted graph general cocepts
+
+Every weighted graph should contain: 
+1. Vertices/Nodes (I will use "vertex" in this readme).
+
+<img src="Images/Vertices.png" height="250" />
+
+2. Edges connecting vertices. Let's add some edges to our graph. For simplicity let's create directed graph for now. Directed means, that edge have a direction, i.e. vertex, where it starts and vertex, where it ends. But remember VERY IMPORTANT thing:
+    * All undirected graphs can be viewed as a directed graph.
+    * A directed graph is undirected if and only if every edge is paired with an edge going in the opposite direction.
+
+<img src="Images/DirectedGraph.png" height="250" />
+
+3. Weights for every edge. 
+
+<img src="Images/WeightedDirectedGraph.png" height="250" />
+
+Final result. 
+Directed weighted graph:
+
+<img src="Images/WeightedDirectedGraphFinal.png" height="250" />
+
+Undirected weighted graph:
+
+<img src="Images/WeightedUndirectedGraph.png" height="250" />
+
+And once again: An undireceted graph - it is a directed graph with every edge paired with an edge going in the opposite direction. This statement is clear on the image above.
+
+Great! Now we are familiar with general concepts about graphs.
+
 # Dijkstra's algorithm
+This [algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) was invented in 1956 by Edsger W. Dijkstra.
 
-This [algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) was invented in 1956 by Edsger W. Dijkstra. 
+It can be used, when you have one source vertex and want to find the shortest paths to ALL other vertices in the graph.
 
-It can be used, when you have one source vertex and want to find the shortest paths to all other vertices in the graph.
+The best example is road network. If you wnat to find the shortest path from your house to your job, or if you want to find the closest store to your house, then it is time for the Dijkstra's algorithm.
 
-The best example is road network. If you wnat to find the shortest path from your house to your job, then it is time for the Dijkstra's algorithm.
+The algorithm repeats following cycle until all vertices are marked as visited.
+Cycle:
+1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
+2. The algorithm marks picked vertex as visited.
+3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
+When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
 
-I have created **VisualizedDijkstra.playground** to improve your understanding of the algorithm's flow. Besides, below is step by step algorithm's description.
+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 
 Let's imagine, 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 graph, that connects your house with all these stores. So, you know what to do :)
 
 ## Initialization
@@ -38,17 +75,8 @@ To initialize our graph we have to set source vertex path length from source ver
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
-Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm.
-
-But before we will go through all process side by side read this explanation.
-The algorithm repeats following cycle until all vertices are marked as visited.
-Cycle:
-1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
-2. The algorithm marks picked vertex as visited.
-3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
-When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
+Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm, let's start!
 
-Okay, let's start!
 Let's follow the algorithm's cycle and pick the first vertex, which neighbors we want to check.
 All our vertices are not visited, but there is only one has the smallest path length from start - A. This vertex is the first one, which neighbors we will check.
 First of all, set this vertex as visited 

From e9017365a47a93a977dc0f26c42045d6fccd4b76 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 24 May 2017 18:01:53 +0300
Subject: [PATCH 220/862] Fix

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

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index ddce51525..5cf312acc 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,4 +1,4 @@
-#Weighted graph general cocepts
+# Weighted graph general cocepts
 
 Every weighted graph should contain: 
 1. Vertices/Nodes (I will use "vertex" in this readme).

From b1a50b492373dba7490e603975f9bec8e98c4725 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 24 May 2017 18:04:09 +0300
Subject: [PATCH 221/862] fix

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

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 5cf312acc..a9a898d80 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -44,7 +44,7 @@ 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 
+# Example 
 Let's imagine, 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 graph, that connects your house with all these stores. So, you know what to do :)
 
 ## Initialization

From bb8b2a7d480b6e9f3d5eeee87eaf4a7e01e2ba36 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman@yandex-team.ru>
Date: Wed, 24 May 2017 18:07:47 +0300
Subject: [PATCH 222/862] Fixes

---
 Dijkstra Algorithm/README.md | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index a9a898d80..7afc34094 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -44,10 +44,10 @@ 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 
+## Example 
 Let's imagine, 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 graph, that connects your house with all these stores. So, you know what to do :)
 
-## Initialization
+### Initialization
 
 When the algorithm starts to work initial graph looks like this:
 
@@ -93,7 +93,7 @@ After this step graph has this state:
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
-## Step 1
+### Step 1
 
 Then we check all of its neighbors. 
 If checking vertex path length from start + edge weigth is smaller than neighbor's path length from start, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
@@ -118,7 +118,7 @@ And its state is here:
 | Path Length From Start    |     0      |     3      |    inf     |     1      |    inf     |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   |    [ ]     |
 
-## Step 2
+### Step 2
 
 From now we repeat all actions again and fill our table with new info! 
 
@@ -130,7 +130,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |    inf     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |    [ ]     |   [A, D]   | [A, D, E]  |
 
-## Step 3
+### Step 3
 
 <img src="Images/image5.png" height="250" />
 
@@ -140,7 +140,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     11     |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |[A, D, E, C]|   [A, D]   | [A, D, E ] |
 
-## Step 4
+### Step 4
 
 <img src="Images/image6.png" height="250" />
 
@@ -150,7 +150,7 @@ From now we repeat all actions again and fill our table with new info!
 | Path Length From Start    |     0      |     3      |     8      |     1      |     2      |
 | Path Vertices From Start  |    [A]     |   [A, B]   |   [A, B, C]|   [A, D]   | [A, D, E ] |
 
-## Step 5
+### Step 5
 
 <img src="Images/image7.png" height="250" />
 
@@ -300,16 +300,16 @@ Also there is a **VisualizedDijkstra.playground**. Use it to figure out algorith
 
 It is up to you how to implement some specific parts of algorithm, you can use Array instead of Set, add _visited_ property to Vertex or you can create some local totalVertices Array/Set inside _func findShortestPaths(from startVertex: Vertex)_ to keep totalVertices Array/Set unchanged. This is a general explanation with one possible implementation :)
 
-## About this repository
+# About this repository
 
 This repository contains to playgrounds:
 * To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
 * If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
-## Demo video
+# Demo video
 
 Click the link: [YouTube](https://youtu.be/PPESI7et0cQ)
 
-## Credits
+# Credits
 
 WWDC 2017 Scholarship Project (Rejected) created by [Taras Nikulin](https://github.com/crabman448)

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 223/862] 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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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 224/862] 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 83745f236a3084a6fff50c1b12def18ffbdc7707 Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Thu, 25 May 2017 21:46:56 +0200
Subject: [PATCH 225/862] Fix workspace structure

---
 .../contents.xcworkspacedata                  | 760 ++++++++++++++----
 1 file changed, 602 insertions(+), 158 deletions(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index c89ac0dfe..8ba66e153 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1,50 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Workspace
    version = "1.0">
-   <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:How to Contribute.markdown">
-   </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:Miller-Rabin Primality Test"
-      name = "Miller-Rabin Primality Test">
-      <Group
-         location = "container:Miller-Rabin Primality Test/Images"
-         name = "Images">
-         <FileRef
-            location = "group:img_pseudo.png">
-         </FileRef>
-      </Group>
-      <FileRef
-         location = "group:MRPrimality.playground">
-      </FileRef>
-      <FileRef
-         location = "group:MRPrimality.swift">
-      </FileRef>
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-   </Group>
    <Group
       location = "group:All-Pairs Shortest Paths"
       name = "All-Pairs Shortest Paths">
@@ -193,6 +149,18 @@
          <FileRef
             location = "group:Height.png">
          </FileRef>
+         <FileRef
+            location = "group:RotationStep0.jpg">
+         </FileRef>
+         <FileRef
+            location = "group:RotationStep1.jpg">
+         </FileRef>
+         <FileRef
+            location = "group:RotationStep2.jpg">
+         </FileRef>
+         <FileRef
+            location = "group:RotationStep3.jpg">
+         </FileRef>
          <FileRef
             location = "group:Unbalanced.graffle">
          </FileRef>
@@ -220,6 +188,58 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:B-Tree"
+      name = "B-Tree">
+      <FileRef
+         location = "group:BTree.playground">
+      </FileRef>
+      <FileRef
+         location = "group:BTree.swift">
+      </FileRef>
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:BTree20.png">
+         </FileRef>
+         <FileRef
+            location = "group:InsertionSplit.png">
+         </FileRef>
+         <FileRef
+            location = "group:MergingNodes.png">
+         </FileRef>
+         <FileRef
+            location = "group:MovingKey.png">
+         </FileRef>
+         <FileRef
+            location = "group:Node.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <Group
+            location = "group:Tests"
+            name = "Tests">
+            <FileRef
+               location = "group:BTreeNodeTests.swift">
+            </FileRef>
+            <FileRef
+               location = "group:BTreeTests.swift">
+            </FileRef>
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "group:Binary Search"
       name = "Binary Search">
@@ -441,6 +461,22 @@
       <FileRef
          location = "group:README.markdown">
       </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:BoyerMooreHorspoolTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:BoyerMooreTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
    </Group>
    <Group
       location = "group:Breadth-First Search"
@@ -546,6 +582,32 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Comb Sort"
+      name = "Comb Sort">
+      <FileRef
+         location = "group:Comb Sort.playground">
+      </FileRef>
+      <FileRef
+         location = "group:Comb Sort.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:CombSortTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "group:Combinatorics"
       name = "Combinatorics">
@@ -553,10 +615,48 @@
          location = "group:Combinatorics.playground">
       </FileRef>
       <FileRef
-         location = "group:Combinatorics.swift">
+         location = "group:README.markdown">
+      </FileRef>
+   </Group>
+   <Group
+      location = "group:Convex Hull"
+      name = "Convex Hull">
+      <Group
+         location = "group:Convex Hull"
+         name = "Convex Hull">
+         <FileRef
+            location = "group:AppDelegate.swift">
+         </FileRef>
+         <Group
+            location = "group:Assets.xcassets"
+            name = "Assets.xcassets">
+            <Group
+               location = "group:AppIcon.appiconset"
+               name = "AppIcon.appiconset">
+               <FileRef
+                  location = "group:Contents.json">
+               </FileRef>
+            </Group>
+         </Group>
+         <Group
+            location = "group:Base.lproj"
+            name = "Base.lproj">
+            <FileRef
+               location = "group:LaunchScreen.storyboard">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:View.swift">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:Convex Hull.xcodeproj">
       </FileRef>
       <FileRef
-         location = "group:README.markdown">
+         location = "group:README.md">
       </FileRef>
    </Group>
    <Group
@@ -662,11 +762,34 @@
          location = "group:README.markdown">
       </FileRef>
    </Group>
+   <Group
+      location = "group:DiningPhilosophers"
+      name = "DiningPhilosophers">
+      <FileRef
+         location = "group:DiningPhilosophers.xcodeproj">
+      </FileRef>
+      <FileRef
+         location = "group:LICENSE">
+      </FileRef>
+      <FileRef
+         location = "group:Package.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <Group
+         location = "group:Sources"
+         name = "Sources">
+         <FileRef
+            location = "group:main.swift">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "group:Fixed Size Array"
       name = "Fixed Size Array">
       <FileRef
-         location = "group:FixedSizeArray.swift">
+         location = "group:FixedSizeArray.playground">
       </FileRef>
       <Group
          location = "group:Images"
@@ -889,6 +1012,16 @@
          location = "group:README.markdown">
       </FileRef>
    </Group>
+   <Group
+      location = "group:HaversineDistance"
+      name = "HaversineDistance">
+      <FileRef
+         location = "group:HaversineDistance.playground">
+      </FileRef>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Heap"
       name = "Heap">
@@ -1033,13 +1166,6 @@
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       </Group>
    </Group>
-   <Group
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-      name = "Slow Sort">
-      <FileRef
-         location = "group:Slow Sort/SlowSort.swift">
-      </FileRef>
-   </Group>
    <Group
       location = "group:Huffman Coding"
       name = "Huffman Coding">
@@ -1162,6 +1288,32 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Karatsuba Multiplication"
+      name = "Karatsuba Multiplication">
+      <FileRef
+         location = "group:KaratsubaMultiplication.playground">
+      </FileRef>
+      <FileRef
+         location = "group:KaratsubaMultiplication.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+   </Group>
+   <Group
+      location = "group:Knuth-Morris-Pratt"
+      name = "Knuth-Morris-Pratt">
+      <FileRef
+         location = "group:KnuthMorrisPratt.playground">
+      </FileRef>
+      <FileRef
+         location = "group:KnuthMorrisPratt.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Kth Largest Element"
       name = "Kth Largest Element">
@@ -1175,6 +1327,29 @@
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       </FileRef>
    </Group>
+   <Group
+      location = "group:Linear Regression"
+      name = "Linear Regression">
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:graph1.png">
+         </FileRef>
+         <FileRef
+            location = "group:graph2.png">
+         </FileRef>
+         <FileRef
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+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:LinearRegression.playground">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Linear Search"
       name = "Linear Search">
@@ -1258,27 +1433,38 @@
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    </Group>
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-      name = "Minimum Edit Distance">
+      location = "group:Miller-Rabin Primality Test"
+      name = "Miller-Rabin Primality Test">
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:img_pseudo.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:MRPrimality.playground">
+      </FileRef>
       <FileRef
-         location = "group:MinimumEditDistance.swift">
+         location = "group:MRPrimality.swift">
       </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>
    </Group>
    <Group
-      location = "group:Minimum Spanning Tree"
-      name = "Minimum Spanning Tree">
-      <FileRef
-         location = "group:Kruskal.swift">
-      </FileRef>
+      location = "group:Minimum Edit Distance"
+      name = "Minimum Edit Distance">
       <FileRef
-         location = "group:Prim.swift">
+         location = "group:MinimumEditDistance.playground">
       </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>
+   </Group>
+   <Group
+      location = "group:Minimum Spanning Tree"
+      name = "Minimum Spanning Tree">
       <Group
          location = "group:Images"
          name = "Images">
@@ -1289,9 +1475,18 @@
             location = "group:prim.png">
          </FileRef>
       </Group>
+      <FileRef
+         location = "group:Kruskal.swift">
+      </FileRef>
       <FileRef
          location = "group:MinimumSpanningTree.playground">
       </FileRef>
+      <FileRef
+         location = "group:Prim.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
    </Group>
    <Group
       location = "group:Minimum Spanning Tree (Unweighted)"
@@ -1347,6 +1542,43 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:MinimumCoinChange"
+      name = "MinimumCoinChange">
+      <FileRef
+         location = "group:eurocoins.gif">
+      </FileRef>
+      <FileRef
+         location = "group:LICENSE">
+      </FileRef>
+      <FileRef
+         location = "group:Package.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <Group
+         location = "group:Sources"
+         name = "Sources">
+         <FileRef
+            location = "group:MinimumCoinChange.swift">
+         </FileRef>
+      </Group>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:LinuxMain.swift">
+         </FileRef>
+         <Group
+            location = "group:MinimumCoinChangeTests"
+            name = "MinimumCoinChangeTests">
+            <FileRef
+               location = "group:MinimumCoinChangeTests.swift">
+            </FileRef>
+         </Group>
+      </Group>
+   </Group>
    <Group
       location = "group:Monty Hall Problem"
       name = "Monty Hall Problem">
@@ -1384,13 +1616,46 @@
       </FileRef>
    </Group>
    <Group
-      location = "group:Priority Queue"
-      name = "Priority Queue">
+      location = "group:Palindromes"
+      name = "Palindromes">
       <FileRef
-         location = "group:PriorityQueue.swift">
+         location = "group:Palindromes.playground">
       </FileRef>
       <FileRef
-         location = "group:README.markdown">
+         location = "group:Palindromes.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <Group
+         location = "group:Test"
+         name = "Test">
+         <FileRef
+            location = "group:Palindromes.swift">
+         </FileRef>
+         <Group
+            location = "group:Test"
+            name = "Test">
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:Test.swift">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Test.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
+   <Group
+      location = "group:Priority Queue"
+      name = "Priority Queue">
+      <FileRef
+         location = "group:PriorityQueue.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
       </FileRef>
       <Group
          location = "group:Tests"
@@ -1406,6 +1671,40 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:QuadTree"
+      name = "QuadTree">
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:quadtree.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:QuadTree.playground">
+      </FileRef>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <Group
+            location = "group:Tests"
+            name = "Tests">
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:Tests.swift">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
+   </Group>
    <Group
       location = "group:Queue"
       name = "Queue">
@@ -1474,15 +1773,47 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Rabin-Karp"
+      name = "Rabin-Karp">
+      <FileRef
+         location = "group:Rabin-Karp.playground">
+      </FileRef>
+      <FileRef
+         location = "group:rabin-karp.swift">
+      </FileRef>
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Radix Sort"
       name = "Radix Sort">
+      <FileRef
+         location = "group:RadixSort.playground">
+      </FileRef>
       <FileRef
          location = "group:radixSort.swift">
       </FileRef>
+      <FileRef
+         location = "group:RadixSortExample.swift">
+      </FileRef>
       <FileRef
          location = "group:ReadMe.md">
       </FileRef>
+      <Group
+         location = "group:Tests"
+         name = "Tests">
+         <FileRef
+            location = "group:Info.plist">
+         </FileRef>
+         <FileRef
+            location = "group:RadixSortTests.swift">
+         </FileRef>
+         <FileRef
+            location = "group:Tests.xcodeproj">
+         </FileRef>
+      </Group>
    </Group>
    <Group
       location = "group:Radix Tree"
@@ -1507,21 +1838,11 @@
    <Group
       location = "group:Red-Black Tree"
       name = "Red-Black Tree">
-      <Group
-         location = "group:files"
-         name = "files">
-         <FileRef
-            location = "group:fig1.png">
-         </FileRef>
-         <FileRef
-            location = "group:fig2.png">
-         </FileRef>
-      </Group>
       <FileRef
-         location = "group:RBTree.swift">
+         location = "group:README.markdown">
       </FileRef>
       <FileRef
-         location = "group:README.md">
+         location = "group:Red-Black Tree 2.playground">
       </FileRef>
    </Group>
    <Group
@@ -1537,32 +1858,6 @@
          location = "group:RingBuffer.swift">
       </FileRef>
    </Group>
-   <Group
-      location = "group:Run-Length Encoding"
-      name = "Run-Length Encoding">
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-      <FileRef
-         location = "group:RLE.playground">
-      </FileRef>
-      <FileRef
-         location = "group:RLE.swift">
-      </FileRef>
-      <Group
-         location = "group:Tests"
-         name = "Tests">
-         <FileRef
-            location = "group:Info.plist">
-         </FileRef>
-         <FileRef
-            location = "group:RLETests.swift">
-         </FileRef>
-         <FileRef
-            location = "group:Tests.xcodeproj">
-         </FileRef>
-      </Group>
-   </Group>
    <Group
       location = "group:Rootish Array Stack"
       name = "Rootish Array Stack">
@@ -1579,6 +1874,15 @@
             location = "group:RootishArrayStackIntro.png">
          </FileRef>
       </Group>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <FileRef
+         location = "group:RootishArrayStack.playground">
+      </FileRef>
+      <FileRef
+         location = "group:RootishArrayStack.swift">
+      </FileRef>
       <Group
          location = "group:Tests"
          name = "Tests">
@@ -1586,23 +1890,24 @@
             location = "group:Info.plist">
          </FileRef>
          <FileRef
-            location = "group:RootishArrayStackTests.swift">
+            location = "group:RootishArrayStack.swift">
          </FileRef>
          <FileRef
-            location = "group:RootishArrayStack.swift">
+            location = "group:RootishArrayStackTests.swift">
          </FileRef>
          <FileRef
             location = "group:Tests.xcodeproj">
          </FileRef>
       </Group>
+   </Group>
+   <Group
+      location = "group:Run-Length Encoding"
+      name = "Run-Length Encoding">
       <FileRef
-         location = "group:README.md">
-      </FileRef>
-      <FileRef
-         location = "group:RootishArrayStack.swift">
+         location = "group:README.markdown">
       </FileRef>
       <FileRef
-         location = "group:RootishArrayStack.playground">
+         location = "group:RLE.playground">
       </FileRef>
    </Group>
    <Group
@@ -1718,16 +2023,16 @@
       </Group>
    </Group>
    <Group
-      location = "container:"
+      location = "group:Set Cover (Unweighted)"
       name = "Set Cover (Unweighted)">
       <FileRef
-         location = "group:Set Cover (Unweighted)/README.markdown">
+         location = "group:README.markdown">
       </FileRef>
       <FileRef
-         location = "group:Set Cover (Unweighted)/SetCover.playground">
+         location = "group:SetCover.playground">
       </FileRef>
       <FileRef
-         location = "group:Set Cover (Unweighted)/SetCover.swift">
+         location = "group:SetCover.swift">
       </FileRef>
    </Group>
    <Group
@@ -1739,6 +2044,9 @@
       <FileRef
          location = "group:shellsort.swift">
       </FileRef>
+      <FileRef
+         location = "group:ShellSortExample.swift">
+      </FileRef>
       <Group
          location = "group:Tests"
          name = "Tests">
@@ -1873,6 +2181,72 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Skip-List"
+      name = "Skip-List">
+      <Group
+         location = "group:Images"
+         name = "Images">
+         <FileRef
+            location = "group:Insert1.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert10.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert11.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert12.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert2.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert3.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert4.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert5.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert6.png">
+         </FileRef>
+         <FileRef
+            location = "group:insert7.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert8.png">
+         </FileRef>
+         <FileRef
+            location = "group:Insert9.png">
+         </FileRef>
+         <FileRef
+            location = "group:Intro.png">
+         </FileRef>
+         <FileRef
+            location = "group:Search1.png">
+         </FileRef>
+      </Group>
+      <FileRef
+         location = "group:README.md">
+      </FileRef>
+      <FileRef
+         location = "group:SkipList.swift">
+      </FileRef>
+   </Group>
+   <Group
+      location = "group:Slow Sort"
+      name = "Slow Sort">
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:SlowSort.swift">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Stack"
       name = "Stack">
@@ -1899,31 +2273,47 @@
          </FileRef>
       </Group>
    </Group>
+   <Group
+      location = "group:Strassen Matrix Multiplication"
+      name = "Strassen Matrix Multiplication">
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:StrassensMatrixMultiplication.playground">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Ternary Search Tree"
       name = "Ternary Search Tree">
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:TernarySearchTree.swift">
+      </FileRef>
       <Group
-         location = "container:Ternary Search Tree/Tests"
+         location = "group:Tests"
          name = "Tests">
          <FileRef
             location = "group:Info.plist">
          </FileRef>
+         <FileRef
+            location = "group:TernarySearchTreeTests.swift">
+         </FileRef>
          <FileRef
             location = "group:Tests.xcodeproj">
          </FileRef>
       </Group>
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-      <FileRef
-         location = "group:TernarySearchTree.swift">
-      </FileRef>
       <FileRef
          location = "group:TST.playground">
       </FileRef>
       <FileRef
          location = "group:TSTNode.swift">
       </FileRef>
+      <FileRef
+         location = "group:Utils.swift">
+      </FileRef>
    </Group>
    <Group
       location = "group:Threaded Binary Tree"
@@ -1966,10 +2356,7 @@
          location = "group:README.markdown">
       </FileRef>
       <FileRef
-         location = "group:ThreadedBinaryTree.swift">
-      </FileRef>
-      <FileRef
-         location = "group:ThreadedBinaryTreeTests.swift">
+         location = "group:ThreadedBinaryTree.playground">
       </FileRef>
    </Group>
    <Group
@@ -2056,27 +2443,6 @@
          <Group
             location = "group:Treap"
             name = "Treap">
-            <FileRef
-               location = "group:AppDelegate.swift">
-            </FileRef>
-            <Group
-               location = "group:Assets.xcassets"
-               name = "Assets.xcassets">
-               <Group
-                  location = "group:AppIcon.appiconset"
-                  name = "AppIcon.appiconset">
-                  <FileRef
-                     location = "group:Contents.json">
-                  </FileRef>
-               </Group>
-            </Group>
-            <Group
-               location = "group:Base.lproj"
-               name = "Base.lproj">
-               <FileRef
-                  location = "group:MainMenu.xib">
-               </FileRef>
-            </Group>
             <FileRef
                location = "group:Info.plist">
             </FileRef>
@@ -2149,12 +2515,83 @@
    <Group
       location = "group:Trie"
       name = "Trie">
+      <Group
+         location = "group:images"
+         name = "images">
+         <FileRef
+            location = "group:trie.png">
+         </FileRef>
+      </Group>
       <FileRef
          location = "group:ReadMe.md">
       </FileRef>
-      <FileRef
-         location = "group:trie.swift">
-      </FileRef>
+      <Group
+         location = "group:Trie"
+         name = "Trie">
+         <Group
+            location = "group:Trie"
+            name = "Trie">
+            <FileRef
+               location = "group:AppDelegate.swift">
+            </FileRef>
+            <Group
+               location = "group:Assets.xcassets"
+               name = "Assets.xcassets">
+               <Group
+                  location = "group:AppIcon.appiconset"
+                  name = "AppIcon.appiconset">
+                  <FileRef
+                     location = "group:Contents.json">
+                  </FileRef>
+               </Group>
+            </Group>
+            <Group
+               location = "group:Base.lproj"
+               name = "Base.lproj">
+               <FileRef
+                  location = "group:Main.storyboard">
+               </FileRef>
+            </Group>
+            <FileRef
+               location = "group:dictionary.txt">
+            </FileRef>
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:ReadMe.md">
+            </FileRef>
+            <FileRef
+               location = "group:Trie.swift">
+            </FileRef>
+            <FileRef
+               location = "group:ViewController.swift">
+            </FileRef>
+         </Group>
+         <FileRef
+            location = "group:Trie.xcodeproj">
+         </FileRef>
+         <Group
+            location = "group:TrieTests"
+            name = "TrieTests">
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:TrieTests.swift">
+            </FileRef>
+         </Group>
+         <Group
+            location = "group:TrieUITests"
+            name = "TrieUITests">
+            <FileRef
+               location = "group:Info.plist">
+            </FileRef>
+            <FileRef
+               location = "group:TrieUITests.swift">
+            </FileRef>
+         </Group>
+      </Group>
    </Group>
    <Group
       location = "group:Two-Sum Problem"
@@ -2168,9 +2605,6 @@
          <FileRef
             location = "group:2Sum.playground">
          </FileRef>
-         <FileRef
-            location = "group:2Sum.swift">
-         </FileRef>
       </Group>
       <Group
          location = "group:Solution 2"
@@ -2178,9 +2612,6 @@
          <FileRef
             location = "group:2Sum.playground">
          </FileRef>
-         <FileRef
-            location = "group:2Sum.swift">
-         </FileRef>
       </Group>
    </Group>
    <Group
@@ -2208,8 +2639,21 @@
       <FileRef
          location = "group:UnionFind.playground">
       </FileRef>
+   </Group>
+   <Group
+      location = "group:Z-Algorithm"
+      name = "Z-Algorithm">
+      <FileRef
+         location = "group:README.markdown">
+      </FileRef>
+      <FileRef
+         location = "group:ZAlgorithm.swift">
+      </FileRef>
+      <FileRef
+         location = "group:ZetaAlgorithm.playground">
+      </FileRef>
       <FileRef
-         location = "group:UnionFind.swift">
+         location = "group:ZetaAlgorithm.swift">
       </FileRef>
    </Group>
 </Workspace>

From 613a420c92c2dc330506af0e3fdf8dbc5cac0ff4 Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Thu, 25 May 2017 21:52:55 +0200
Subject: [PATCH 226/862] Swiftlint autocorrect

---
 .../AVLTree.playground/Sources/AVLTree.swift  |  5 ++-
 AVL Tree/AVLTree.swift                        |  5 ++-
 AVL Tree/Tests/TreeNodeTests.swift            |  1 -
 .../APSP/APSP/Helpers.swift                   |  1 -
 Array2D/Array2D.playground/Contents.swift     |  1 -
 .../BinaryTree.playground/Contents.swift      |  4 ---
 Bit Set/BitSet.playground/Contents.swift      |  9 -----
 .../BloomFilter.playground/Contents.swift     |  4 ---
 Bloom Filter/Tests/BloomFilterTests.swift     |  1 -
 .../Contents.swift                            |  6 ----
 .../Contents.swift                            |  3 --
 .../Contents.swift                            |  2 --
 .../Sources/BucketSort.swift                  |  2 --
 Bucket Sort/BucketSort.swift                  |  3 --
 Bucket Sort/Tests/Tests.swift                 |  1 -
 .../Combinatorics.playground/Contents.swift   | 12 -------
 Convex Hull/Convex Hull/AppDelegate.swift     |  2 --
 .../Contents.swift                            |  2 --
 .../CountingSort.playground/Contents.swift    |  1 -
 .../Contents.swift                            |  2 --
 DiningPhilosophers/Sources/main.swift         |  4 ---
 Graph/Graph/AdjacencyListGraph.swift          |  3 --
 .../Contents.swift                            |  1 -
 .../kthLargest.playground/Contents.swift      |  4 ---
 Kth Largest Element/kthLargest.swift          |  1 -
 .../Contents.swift                            |  2 +-
 .../LinkedList.playground/Contents.swift      |  2 --
 .../MergeSort.playground/Contents.swift       |  2 --
 .../Contents.swift                            |  2 --
 Minimum Spanning Tree/Kruskal.swift           |  1 -
 .../Sources/Graph.swift                       |  2 --
 .../Sources/Heap.swift                        |  4 +--
 Minimum Spanning Tree/Prim.swift              |  1 -
 .../Sources/MinimumCoinChange.swift           | 34 +++++++++----------
 .../MinimumCoinChangeTests.swift              |  3 +-
 .../OrderedArray.playground/Contents.swift    |  2 --
 Queue/Queue.playground/Contents.swift         |  3 --
 Quicksort/Quicksort.playground/Contents.swift |  9 -----
 .../Sources/radixSort.swift                   |  2 --
 Radix Sort/radixSort.swift                    |  3 --
 .../Contents.swift                            |  2 --
 .../Tests/RootishArrayStackTests.swift        |  1 -
 .../SegmentTree.playground/Contents.swift     |  6 ----
 .../Contents.swift                            |  3 --
 .../Contents.swift                            |  2 --
 Shortest Path (Unweighted)/Tests/Graph.swift  |  1 -
 Shuffle/Shuffle.playground/Contents.swift     |  4 ---
 .../ShuntingYard.playground/Contents.swift    |  1 -
 Skip-List/SkipList.swift                      | 15 +-------
 Slow Sort/SlowSort.swift                      | 11 +++---
 .../Contents.swift                            |  1 -
 .../Sources/Matrix.swift                      | 30 ++++++++--------
 .../TST.playground/Sources/TSTNode.swift      |  1 -
 .../Sources/TernarySearchTree.swift           |  3 --
 Ternary Search Tree/TernarySearchTree.swift   |  1 -
 .../Tests/TernarySearchTreeTests.swift        |  1 -
 .../Contents.swift                            |  5 ---
 .../Contents.swift                            |  2 --
 Treap/Treap.swift                             |  2 +-
 Tree/Tree.playground/Contents.swift           |  3 --
 Trie/Trie/Trie/AppDelegate.swift              |  3 --
 Trie/Trie/Trie/Trie.swift                     |  3 --
 Trie/Trie/Trie/ViewController.swift           |  1 -
 .../UnionFind.playground/Contents.swift       |  4 ---
 .../Sources/UnionFindQuickFind.swift          | 12 +++----
 .../Sources/UnionFindQuickUnion.swift         | 12 +++----
 .../Sources/UnionFindWeightedQuickFind.swift  | 12 +++----
 .../Sources/UnionFindWeightedQuickUnion.swift | 12 +++----
 ...indWeightedQuickUnionPathCompression.swift | 12 +++----
 .../ZetaAlgorithm.playground/Contents.swift   |  2 --
 70 files changed, 77 insertions(+), 243 deletions(-)

diff --git a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift
index 56ba81608..9f8695a83 100644
--- a/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
+++ b/AVL Tree/AVLTree.playground/Sources/AVLTree.swift	
@@ -341,11 +341,11 @@ extension AVLTree {
       }
     } else {
       // Handle stem cases
-      if let replacement = node.leftChild?.maximum() , replacement !== node {
+      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 {
+      } else if let replacement = node.rightChild?.minimum(), replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
         delete(node: replacement)
@@ -354,7 +354,6 @@ extension AVLTree {
   }
 }
 
-
 // MARK: - Debugging
 
 extension TreeNode: CustomDebugStringConvertible {
diff --git a/AVL Tree/AVLTree.swift b/AVL Tree/AVLTree.swift
index 4feb691e4..52ea082ce 100644
--- a/AVL Tree/AVLTree.swift	
+++ b/AVL Tree/AVLTree.swift	
@@ -341,11 +341,11 @@ extension AVLTree {
       }
     } else {
       // Handle stem cases
-      if let replacement = node.leftChild?.maximum() , replacement !== node {
+      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 {
+      } else if let replacement = node.rightChild?.minimum(), replacement !== node {
         node.key = replacement.key
         node.payload = replacement.payload
         delete(node: replacement)
@@ -354,7 +354,6 @@ extension AVLTree {
   }
 }
 
-
 // MARK: - Debugging
 
 extension TreeNode: CustomDebugStringConvertible {
diff --git a/AVL Tree/Tests/TreeNodeTests.swift b/AVL Tree/Tests/TreeNodeTests.swift
index 88b314e41..cac7e549b 100644
--- a/AVL Tree/Tests/TreeNodeTests.swift	
+++ b/AVL Tree/Tests/TreeNodeTests.swift	
@@ -27,7 +27,6 @@ class TreeNodeTests: XCTestCase {
         super.tearDown()
     }
 
-
     func testSingleNodeCreationNOPayload() {
         let treeNode = TreeNode<String, String>(key: "Building")
         XCTAssertNil(treeNode.payload, "Payload for this case should be nil")
diff --git a/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift b/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift
index 3812b3f58..f590a6e50 100644
--- a/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift	
+++ b/All-Pairs Shortest Paths/APSP/APSP/Helpers.swift	
@@ -7,7 +7,6 @@
 
 import Foundation
 
-
 /**
  Print a matrix, optionally specifying only the cells to display with the triplet (i, j, k) -> matrix[i][j], matrix[i][k], matrix[k][j]
  */
diff --git a/Array2D/Array2D.playground/Contents.swift b/Array2D/Array2D.playground/Contents.swift
index 1a6a439bd..d31d77540 100644
--- a/Array2D/Array2D.playground/Contents.swift
+++ b/Array2D/Array2D.playground/Contents.swift
@@ -28,7 +28,6 @@ public struct Array2D<T> {
   }
 }
 
-
 // initialization
 var matrix = Array2D(columns: 3, rows: 5, initialValue: 0)
 
diff --git a/Binary Tree/BinaryTree.playground/Contents.swift b/Binary Tree/BinaryTree.playground/Contents.swift
index aa084e44d..b0bff577a 100644
--- a/Binary Tree/BinaryTree.playground/Contents.swift	
+++ b/Binary Tree/BinaryTree.playground/Contents.swift	
@@ -25,8 +25,6 @@ extension BinaryTree: CustomStringConvertible {
   }
 }
 
-
-
 // leaf nodes
 let node5 = BinaryTree.node(.empty, "5", .empty)
 let nodeA = BinaryTree.node(.empty, "a", .empty)
@@ -50,8 +48,6 @@ let tree = BinaryTree.node(timesLeft, "+", timesRight)
 print(tree)
 tree.count  // 12
 
-
-
 extension BinaryTree {
   public func traverseInOrder(process: (T) -> Void) {
     if case let .node(left, value, right) = self {
diff --git a/Bit Set/BitSet.playground/Contents.swift b/Bit Set/BitSet.playground/Contents.swift
index 77d371420..d11b36e8c 100644
--- a/Bit Set/BitSet.playground/Contents.swift	
+++ b/Bit Set/BitSet.playground/Contents.swift	
@@ -29,9 +29,6 @@ print(bits)
 
 print("")
 
-
-
-
 // Bitwise operations
 
 var a = BitSet(size: 4)
@@ -69,9 +66,6 @@ print(~c)  // 0101110000000000000000000000000000000000000000000000000000000000
 (~b).cardinality  // 5
 (~c).cardinality  // 4
 
-
-
-
 var z = BitSet(size: 66)
 z.all0()        // true
 z.all1()        // false
@@ -93,8 +87,5 @@ z.all1()        // true
 z[65] = false
 z.all1()        // false
 
-
-
-
 //var bigBits = BitSet(size: 10000)
 //print(bigBits)
diff --git a/Bloom Filter/BloomFilter.playground/Contents.swift b/Bloom Filter/BloomFilter.playground/Contents.swift
index 06022c9b3..3dac76e8e 100644
--- a/Bloom Filter/BloomFilter.playground/Contents.swift	
+++ b/Bloom Filter/BloomFilter.playground/Contents.swift	
@@ -47,8 +47,6 @@ public class BloomFilter<T> {
   }
 }
 
-
-
 /* Two hash functions, adapted from http://www.cse.yorku.ca/~oz/hash.html */
 
 func djb2(x: String) -> Int {
@@ -67,8 +65,6 @@ func sdbm(x: String) -> Int {
   return Int(hash)
 }
 
-
-
 /* A simple test */
 
 let bloom = BloomFilter<String>(size: 17, hashFunctions: [djb2, sdbm])
diff --git a/Bloom Filter/Tests/BloomFilterTests.swift b/Bloom Filter/Tests/BloomFilterTests.swift
index 82bf4fb8f..55db71f3f 100644
--- a/Bloom Filter/Tests/BloomFilterTests.swift	
+++ b/Bloom Filter/Tests/BloomFilterTests.swift	
@@ -23,7 +23,6 @@ func sdbm(_ x: String) -> Int {
   return Int(hash)
 }
 
-
 class BloomFilterTests: XCTestCase {
 
   func testSingleHashFunction() {
diff --git a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift
index 1bc678ccc..d6204abec 100644
--- a/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
+++ b/Bounded Priority Queue/BoundedPriorityQueue.playground/Contents.swift	
@@ -15,8 +15,6 @@ func < (m1: Message, m2: Message) -> Bool {
   return m1.priority < m2.priority
 }
 
-
-
 let queue = BoundedPriorityQueue<Message>(maxElements: 5)
 queue.count
 
@@ -48,8 +46,6 @@ print(queue)
 // At this point, the queue is:
 // <world:150, swift:110, hello:100, there:99, is:30, >
 
-
-
 // Try to insert an item with a really low priority. This should not get added.
 queue.enqueue(Message(name: "very", priority: -1))
 queue.count    // 5
@@ -70,8 +66,6 @@ queue.count
 queue.peek()
 print(queue)
 
-
-
 // Test dequeuing
 queue.dequeue()
 queue.count
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 0fb98e1c8..675be2203 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	
@@ -19,8 +19,6 @@ func breadthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   return nodesExplored
 }
 
-
-
 let graph = Graph()
 
 let nodeA = graph.addNode("a")
@@ -42,6 +40,5 @@ graph.addEdge(nodeE, neighbor: nodeH)
 graph.addEdge(nodeE, neighbor: nodeF)
 graph.addEdge(nodeF, neighbor: nodeG)
 
-
 let nodesExplored = breadthFirstSearch(graph, source: nodeA)
 print(nodesExplored)
diff --git a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift
index b9f2b1432..fcee59a7b 100644
--- a/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
+++ b/Brute-Force String Search/BruteForceStringSearch.playground/Contents.swift	
@@ -22,8 +22,6 @@ extension String {
   }
 }
 
-
-
 // A few simple tests
 
 let s = "Hello, World"
diff --git a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift
index 08962c0e1..f16db3e67 100644
--- a/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.playground/Sources/BucketSort.swift	
@@ -26,7 +26,6 @@ import Foundation
 // MARK: Main algorithm
 //////////////////////////////////////
 
-
 public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sorter: Sorter, buckets: inout [Bucket<T>]) -> [T] {
   for elem in elements {
     distributor.distribute(element: elem, buckets: &buckets)
@@ -45,7 +44,6 @@ public func bucketSort<T: Sortable>(elements: [T], distributor: Distributor, sor
 // MARK: Distributor
 //////////////////////////////////////
 
-
 public protocol Distributor {
   func distribute<T: Sortable>(element: T, buckets: inout [Bucket<T>])
 }
diff --git a/Bucket Sort/BucketSort.swift b/Bucket Sort/BucketSort.swift
index 5845819f2..f2aeaae99 100644
--- a/Bucket Sort/BucketSort.swift	
+++ b/Bucket Sort/BucketSort.swift	
@@ -45,12 +45,10 @@ fileprivate func >= <T: Comparable>(lhs: T?, rhs: T?) -> Bool {
   }
 }
 
-
 //////////////////////////////////////
 // MARK: Main algorithm
 //////////////////////////////////////
 
-
 /**
     Performs bucket sort algorithm on the given input elements.
     [Bucket Sort Algorithm Reference](https://en.wikipedia.org/wiki/Bucket_sort)
@@ -96,7 +94,6 @@ private func enoughSpaceInBuckets<T: Sortable>(_ buckets: [Bucket<T>], elements:
 // MARK: Distributor
 //////////////////////////////////////
 
-
 public protocol Distributor {
     func distribute<T: Sortable>(_ element: T, buckets: inout [Bucket<T>])
 }
diff --git a/Bucket Sort/Tests/Tests.swift b/Bucket Sort/Tests/Tests.swift
index b50789ed0..1a06c92b5 100644
--- a/Bucket Sort/Tests/Tests.swift	
+++ b/Bucket Sort/Tests/Tests.swift	
@@ -86,7 +86,6 @@ class TestTests: XCTestCase {
     }
 }
 
-
 //////////////////////////////////////
 // MARK: Extensions
 //////////////////////////////////////
diff --git a/Combinatorics/Combinatorics.playground/Contents.swift b/Combinatorics/Combinatorics.playground/Contents.swift
index 94951810f..9fbcc1c58 100644
--- a/Combinatorics/Combinatorics.playground/Contents.swift
+++ b/Combinatorics/Combinatorics.playground/Contents.swift
@@ -14,8 +14,6 @@ func factorial(_ n: Int) -> Int {
 factorial(5)
 factorial(20)
 
-
-
 /*
  Calculates P(n, k), the number of permutations of n distinct symbols
  in groups of size k.
@@ -34,8 +32,6 @@ permutations(5, 3)
 permutations(50, 6)
 permutations(9, 4)
 
-
-
 /*
  Prints out all the permutations of the given array.
  Original algorithm by Niklaus Wirth.
@@ -63,8 +59,6 @@ let xyz = [ "x", "y", "z" ]
 print("\nPermutations of \(xyz):")
 permuteWirth(xyz, 2)
 
-
-
 /*
  Prints out all the permutations of an n-element collection.
 
@@ -97,8 +91,6 @@ let numbers = [0, 0, 0, 0]  // must be all zeros
 var pos = -1
 permuteSedgewick(numbers, 0, &pos)
 
-
-
 /*
  Calculates C(n, k), or "n-choose-k", i.e. how many different selections
  of size k out of a total number of distinct elements (n) you can make.
@@ -115,8 +107,6 @@ for i in 1...20 {
     print("\(20)-choose-\(i) = \(combinations(20, choose: i))")
 }
 
-
-
 /*
  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
  k things out of n possibilities.
@@ -134,8 +124,6 @@ func quickBinomialCoefficient(_ n: Int, choose k: Int) -> Int {
 quickBinomialCoefficient(8, choose: 2)
 quickBinomialCoefficient(30, choose: 15)
 
-
-
 /* Supporting code because Swift doesn't have a built-in 2D array. */
 struct Array2D<T> {
   let columns: Int
diff --git a/Convex Hull/Convex Hull/AppDelegate.swift b/Convex Hull/Convex Hull/AppDelegate.swift
index bfe15e1a7..9bc61ff96 100644
--- a/Convex Hull/Convex Hull/AppDelegate.swift	
+++ b/Convex Hull/Convex Hull/AppDelegate.swift	
@@ -13,7 +13,6 @@ class AppDelegate: UIResponder, UIApplicationDelegate {
 
     var window: UIWindow?
 
-
     func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplicationLaunchOptionsKey: Any]?) -> Bool {
 
         let screenBounds = UIScreen.main.bounds
@@ -52,5 +51,4 @@ class AppDelegate: UIResponder, UIApplicationDelegate {
         // Called when the application is about to terminate. Save data if appropriate. See also applicationDidEnterBackground:.
     }
 
-
 }
diff --git a/Count Occurrences/CountOccurrences.playground/Contents.swift b/Count Occurrences/CountOccurrences.playground/Contents.swift
index cbb43c868..b4392d501 100644
--- a/Count Occurrences/CountOccurrences.playground/Contents.swift	
+++ b/Count Occurrences/CountOccurrences.playground/Contents.swift	
@@ -32,13 +32,11 @@ func countOccurrencesOfKey(_ key: Int, inArray a: [Int]) -> Int {
   return rightBoundary() - leftBoundary()
 }
 
-
 // Simple test
 
 let a = [ 0, 1, 1, 3, 3, 3, 3, 6, 8, 10, 11, 11 ]
 countOccurrencesOfKey(3, inArray: a)
 
-
 // Test with arrays of random size and contents (see debug output)
 
 import Foundation
diff --git a/Counting Sort/CountingSort.playground/Contents.swift b/Counting Sort/CountingSort.playground/Contents.swift
index 1d84f8132..dc375512a 100644
--- a/Counting Sort/CountingSort.playground/Contents.swift	
+++ b/Counting Sort/CountingSort.playground/Contents.swift	
@@ -37,5 +37,4 @@ func countingSort(array: [Int]) throws -> [Int] {
   return sortedArray
 }
 
-
 try countingSort(array: [10, 9, 8, 7, 1, 2, 7, 3])
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 b1d8494d6..1e32b4bbf 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	
@@ -10,8 +10,6 @@ func depthFirstSearch(_ graph: Graph, source: Node) -> [String] {
   return nodesExplored
 }
 
-
-
 let graph = Graph()
 
 let nodeA = graph.addNode("a")
diff --git a/DiningPhilosophers/Sources/main.swift b/DiningPhilosophers/Sources/main.swift
index 338a9074d..32c3af979 100755
--- a/DiningPhilosophers/Sources/main.swift
+++ b/DiningPhilosophers/Sources/main.swift
@@ -6,7 +6,6 @@
 //
 //
 
-
 import Dispatch
 
 let numberOfPhilosophers = 4
@@ -41,7 +40,6 @@ struct ForkPair {
     }
 }
 
-
 struct Philosophers {
     let forkPair: ForkPair
     let philosopherIndex: Int
@@ -75,7 +73,6 @@ struct Philosophers {
     }
 }
 
-
 // Layout of the table (P = philosopher, f = fork) for 4 Philosophers
 //          P0
 //       f3    f0
@@ -99,6 +96,5 @@ for semaphore in ForkPair.forksSemaphore {
     semaphore.signal()
 }
 
-
 //Wait forever
 globalSem.wait()
diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index b58ef6417..4a84129df 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -7,8 +7,6 @@
 
 import Foundation
 
-
-
 private class EdgeList<T> where T: Equatable, T: Hashable {
 
   var vertex: Vertex<T>
@@ -90,7 +88,6 @@ open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashab
     addDirectedEdge(vertices.1, to: vertices.0, withWeight: weight)
   }
 
-
   open override func weightFrom(_ sourceVertex: Vertex<T>, to destinationVertex: Vertex<T>) -> Double? {
     guard let edges = adjacencyList[sourceVertex.index].edges else {
       return nil
diff --git a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
index 35fb27ff8..a27726648 100644
--- a/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
+++ b/Knuth-Morris-Pratt/KnuthMorrisPratt.playground/Contents.swift
@@ -1,6 +1,5 @@
 //: Playground - noun: a place where people can play
 
-
 func ZetaAlgorithm(ptnr: String) -> [Int]? {
 
     let pattern = Array(ptnr.characters)
diff --git a/Kth Largest Element/kthLargest.playground/Contents.swift b/Kth Largest Element/kthLargest.playground/Contents.swift
index 9fba2b483..3e186760c 100644
--- a/Kth Largest Element/kthLargest.playground/Contents.swift	
+++ b/Kth Largest Element/kthLargest.playground/Contents.swift	
@@ -22,9 +22,6 @@ kthLargest(a, 6)
 kthLargest(a, 7)
 kthLargest(a, 8)
 
-
-
-
 import Foundation
 
 /* Returns a random integer in the range min...max, inclusive. */
@@ -84,7 +81,6 @@ public func randomizedSelect<T: Comparable>(_ array: [T], order k: Int) -> T {
   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.swift
index 1f90b096f..16f6caf0c 100644
--- a/Kth Largest Element/kthLargest.swift	
+++ b/Kth Largest Element/kthLargest.swift	
@@ -14,7 +14,6 @@ func kthLargest(a: [Int], k: Int) -> Int? {
   }
 }
 
-
 // MARK: - Randomized selection
 
 /* Returns a random integer in the range min...max, inclusive. */
diff --git a/Linear Regression/LinearRegression.playground/Contents.swift b/Linear Regression/LinearRegression.playground/Contents.swift
index 8b579b3c1..8faf2b738 100644
--- a/Linear Regression/LinearRegression.playground/Contents.swift	
+++ b/Linear Regression/LinearRegression.playground/Contents.swift	
@@ -34,7 +34,7 @@ func average(_ input: [Double]) -> Double {
 }
 
 func multiply(_ a: [Double], _ b: [Double]) -> [Double] {
-    return zip(a,b).map(*)
+    return zip(a, b).map(*)
 }
 
 func linearRegression(_ xs: [Double], _ ys: [Double]) -> (Double) -> Double {
diff --git a/Linked List/LinkedList.playground/Contents.swift b/Linked List/LinkedList.playground/Contents.swift
index 9ee4cc4c4..c7cd6265d 100644
--- a/Linked List/LinkedList.playground/Contents.swift	
+++ b/Linked List/LinkedList.playground/Contents.swift	
@@ -312,7 +312,6 @@ extension LinkedList: ExpressibleByArrayLiteral {
   }
 }
 
-
 //: Ok, now that the declarations are done, let's see our Linked List in action:
 let list = LinkedList<String>()
 list.isEmpty                  // true
@@ -352,7 +351,6 @@ list2.isEmpty                 // true
 list.removeLast()             // "World"
 list.remove(atIndex: 2)       // "Goodbye"
 
-
 list.insert("Swift", atIndex: 1)
 list[0]     // "Hello"
 list[1]     // "Swift"
diff --git a/Merge Sort/MergeSort.playground/Contents.swift b/Merge Sort/MergeSort.playground/Contents.swift
index 137dd19e2..f5a1dbbcf 100644
--- a/Merge Sort/MergeSort.playground/Contents.swift	
+++ b/Merge Sort/MergeSort.playground/Contents.swift	
@@ -49,8 +49,6 @@ let sortedArray = mergeSort(array)
 let array2 = ["Tom", "Harry", "Ron", "Chandler", "Monica"]
 let sortedArray2 = mergeSort(array2)
 
-
-
 /* Bottom-up iterative version */
 
 func mergeSortBottomUp<T>(_ a: [T], _ isOrderedBefore: (T, T) -> Bool) -> [T] {
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 86fe27df8..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	
@@ -21,12 +21,10 @@ func breadthFirstSearchMinimumSpanningTree(_ graph: Graph, source: Node) -> Grap
   return minimumSpanningTree
 }
 
-
 /*:
 ![Graph](Minimum_Spanning_Tree.png)
 */
 
-
 let graph = Graph()
 
 let nodeA = graph.addNode("a")
diff --git a/Minimum Spanning Tree/Kruskal.swift b/Minimum Spanning Tree/Kruskal.swift
index bebd32602..5e6fc5fd2 100644
--- a/Minimum Spanning Tree/Kruskal.swift	
+++ b/Minimum Spanning Tree/Kruskal.swift	
@@ -6,7 +6,6 @@
 //
 //
 
-
 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/Sources/Graph.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift
index 5e74e14cb..f6e4d4fc1 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Graph.swift	
@@ -1,4 +1,3 @@
-
 // Undirected edge
 public struct Edge<T>: CustomStringConvertible {
   public let vertex1: T
@@ -10,7 +9,6 @@ public struct Edge<T>: CustomStringConvertible {
   }
 }
 
-
 // Undirected weighted graph
 public struct Graph<T: Hashable>: CustomStringConvertible {
 
diff --git a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift
index fa30df362..80b40c65f 100644
--- a/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift	
+++ b/Minimum Spanning Tree/MinimumSpanningTree.playground/Sources/Heap.swift	
@@ -113,7 +113,7 @@ public struct Heap<T> {
    */
   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)
@@ -144,7 +144,7 @@ public struct Heap<T> {
    */
   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])
diff --git a/Minimum Spanning Tree/Prim.swift b/Minimum Spanning Tree/Prim.swift
index d975fc430..d65d53f29 100644
--- a/Minimum Spanning Tree/Prim.swift	
+++ b/Minimum Spanning Tree/Prim.swift	
@@ -43,4 +43,3 @@ func minimumSpanningTreePrim<T>(graph: Graph<T>) -> (cost: Int, tree: Graph<T>)
 
   return (cost: cost, tree: tree)
 }
-
diff --git a/MinimumCoinChange/Sources/MinimumCoinChange.swift b/MinimumCoinChange/Sources/MinimumCoinChange.swift
index 55629d020..c83708dee 100644
--- a/MinimumCoinChange/Sources/MinimumCoinChange.swift
+++ b/MinimumCoinChange/Sources/MinimumCoinChange.swift
@@ -13,16 +13,16 @@ public enum MinimumCoinChangeError: Error {
 
 public struct MinimumCoinChange {
     internal let sortedCoinSet: [Int]
-    
+
     public init(coinSet: [Int]) {
-        self.sortedCoinSet = coinSet.sorted(by: { $0 > $1} )
+        self.sortedCoinSet = coinSet.sorted(by: { $0 > $1})
     }
 
     //Greedy Algorithm
     public func changeGreedy(_ value: Int) throws -> [Int] {
         guard value > 0 else { return [] }
 
-        var change:  [Int] = []
+        var change: [Int] = []
         var newValue = value
 
         for coin in sortedCoinSet {
@@ -35,10 +35,10 @@ public struct MinimumCoinChange {
                 break
             }
         }
-        
-        if newValue > 0 { 
-            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue 
-        } 
+
+        if newValue > 0 {
+            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue
+        }
 
         return change
     }
@@ -46,7 +46,7 @@ public struct MinimumCoinChange {
     //Dynamic Programming Algorithm
     public func changeDynamic(_ value: Int) throws -> [Int] {
         guard value > 0 else { return [] }
-        
+
         var cache: [Int : [Int]] = [:]
 
         func _changeDynamic(_ value: Int) -> [Int] {
@@ -55,34 +55,34 @@ public struct MinimumCoinChange {
             if let cached = cache[value] {
                 return cached
             }
-            
+
             var potentialChangeArray: [[Int]] = []
-            
+
             for coin in sortedCoinSet {
                 if value - coin >= 0 {
                     var potentialChange: [Int] = [coin]
                     potentialChange.append(contentsOf: _changeDynamic(value - coin))
 
-                    if potentialChange.reduce(0, +) == value { 
+                    if potentialChange.reduce(0, +) == value {
                         potentialChangeArray.append(potentialChange)
-                    } 
+                    }
                 }
             }
-            
+
             if potentialChangeArray.count > 0 {
                 let sortedPotentialChangeArray = potentialChangeArray.sorted(by: { $0.count < $1.count })
                 cache[value] = sortedPotentialChangeArray[0]
                 return sortedPotentialChangeArray[0]
             }
-            
+
             return []
         }
 
         let change: [Int] = _changeDynamic(value)
 
-        if change.reduce(0, +) != value { 
-            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue 
-        } 
+        if change.reduce(0, +) != value {
+            throw MinimumCoinChangeError.noRestPossibleForTheGivenValue
+        }
 
         return change
     }
diff --git a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
index 705113e92..7c106eeb9 100644
--- a/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
+++ b/MinimumCoinChange/Tests/MinimumCoinChangeTests/MinimumCoinChangeTests.swift
@@ -17,8 +17,7 @@ class MinimumCoinChangeTests: XCTestCase {
                     print("\(i): greedy = \(greedy) dynamic = \(dynamic)")
                 }
             }
-        }
-        catch {
+        } catch {
             XCTFail("Test Failed: impossible to change with the given coin set")
         }
     }
diff --git a/Ordered Array/OrderedArray.playground/Contents.swift b/Ordered Array/OrderedArray.playground/Contents.swift
index 5ca0d7d31..4fe199f28 100644
--- a/Ordered Array/OrderedArray.playground/Contents.swift	
+++ b/Ordered Array/OrderedArray.playground/Contents.swift	
@@ -70,8 +70,6 @@ extension OrderedArray: CustomStringConvertible {
   }
 }
 
-
-
 var a = OrderedArray<Int>(array: [5, 1, 3, 9, 7, -1])
 a              // [-1, 1, 3, 5, 7, 9]
 
diff --git a/Queue/Queue.playground/Contents.swift b/Queue/Queue.playground/Contents.swift
index a90fa647e..08327783f 100644
--- a/Queue/Queue.playground/Contents.swift
+++ b/Queue/Queue.playground/Contents.swift
@@ -39,9 +39,6 @@ public struct Queue<T> {
   }
 }
 
-
-
-
 // Create a queue and put some elements on it already.
 var queueOfNames = Queue(array: ["Carl", "Lisa", "Stephanie", "Jeff", "Wade"])
 
diff --git a/Quicksort/Quicksort.playground/Contents.swift b/Quicksort/Quicksort.playground/Contents.swift
index da02b69ce..972d0b5e1 100644
--- a/Quicksort/Quicksort.playground/Contents.swift
+++ b/Quicksort/Quicksort.playground/Contents.swift
@@ -2,7 +2,6 @@
 
 import Foundation
 
-
 // *** Simple but inefficient version of quicksort ***
 
 func quicksort<T: Comparable>(_ a: [T]) -> [T] {
@@ -23,8 +22,6 @@ func quicksort<T: Comparable>(_ a: [T]) -> [T] {
 let list1 = [ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
 quicksort(list1)
 
-
-
 // *** Using Lomuto partitioning ***
 
 /*
@@ -63,8 +60,6 @@ func quicksortLomuto<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
 
 quicksortLomuto(&list2, low: 0, high: list2.count - 1)
 
-
-
 // *** Hoare partitioning ***
 
 /*
@@ -106,8 +101,6 @@ func quicksortHoare<T: Comparable>(_ a: inout [T], low: Int, high: Int) {
 
 quicksortHoare(&list3, low: 0, high: list3.count - 1)
 
-
-
 // *** Randomized sorting ***
 
 /* Returns a random integer in the range min...max, inclusive. */
@@ -131,8 +124,6 @@ var list4 = [ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
 quicksortRandom(&list4, low: 0, high: list4.count - 1)
 list4
 
-
-
 // *** Dutch national flag partioning ***
 
 /*
diff --git a/Radix Sort/RadixSort.playground/Sources/radixSort.swift b/Radix Sort/RadixSort.playground/Sources/radixSort.swift
index 81c2479e8..424d33fb9 100644
--- a/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
+++ b/Radix Sort/RadixSort.playground/Sources/radixSort.swift	
@@ -12,7 +12,6 @@ public func radixSort(_ array: inout [Int] ) {
   var index: Int
   var digit = 1  //Which digit are we on?
 
-
   while !done {  //While our  sorting is not completed
     done = true  //Assume it is done for now
 
@@ -22,7 +21,6 @@ public func radixSort(_ array: inout [Int] ) {
       buckets.append([])
     }
 
-
     for number in array {
       index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
diff --git a/Radix Sort/radixSort.swift b/Radix Sort/radixSort.swift
index 9e48093ef..302ea6056 100644
--- a/Radix Sort/radixSort.swift	
+++ b/Radix Sort/radixSort.swift	
@@ -4,7 +4,6 @@
 
 */
 
-
 // NOTE: This implementation does not handle negative numbers
 func radixSort(_ array: inout [Int] ) {
   let radix = 10  //Here we define our radix to be 10
@@ -12,7 +11,6 @@ func radixSort(_ array: inout [Int] ) {
   var index: Int
   var digit = 1  //Which digit are we on?
 
-
   while !done {  //While our  sorting is not completed
     done = true  //Assume it is done for now
 
@@ -22,7 +20,6 @@ func radixSort(_ array: inout [Int] ) {
       buckets.append([])
     }
 
-
     for number in array {
       index = number / digit  //Which bucket will we access?
       buckets[index % radix].append(number)
diff --git a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift
index 68ec0a53e..8b630528d 100644
--- a/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
+++ b/Rootish Array Stack/RootishArrayStack.playground/Contents.swift	
@@ -177,14 +177,12 @@ list[0]       // "Hello"
 list[1]       // "World"
 //list[2]     // crash!
 
-
 list.memoryDescription
 //	{
 //		[Optional("Hello")]
 //		[Optional("World"), nil]
 //	}
 
-
 list.insert(element: "Swift", atIndex: 1)
 list.isEmpty  // false
 list.first    // "Hello"
diff --git a/Rootish Array Stack/Tests/RootishArrayStackTests.swift b/Rootish Array Stack/Tests/RootishArrayStackTests.swift
index f0aaa8bca..9d5972a41 100755
--- a/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
+++ b/Rootish Array Stack/Tests/RootishArrayStackTests.swift	
@@ -170,7 +170,6 @@ class RootishArrayStackTests: XCTestCase {
 		XCTAssertTrue(list.equal(toArray: array))
 	}
 
-
 	func testRemoveMiddle() {
 		var array = [0, 1, 2, 3]
 		var list = buildList(withNumbers: array)
diff --git a/Segment Tree/SegmentTree.playground/Contents.swift b/Segment Tree/SegmentTree.playground/Contents.swift
index 08474aee2..3a758981f 100644
--- a/Segment Tree/SegmentTree.playground/Contents.swift	
+++ b/Segment Tree/SegmentTree.playground/Contents.swift	
@@ -61,9 +61,6 @@ public class SegmentTree<T> {
 	}
 }
 
-
-
-
 let array = [1, 2, 3, 4]
 
 let sumSegmentTree = SegmentTree(array: array, function: +)
@@ -77,7 +74,6 @@ sumSegmentTree.replaceItem(at: 0, withItem: 2) //our array now is [2, 2, 3, 4]
 print(sumSegmentTree.query(leftBound: 0, rightBound: 0)) // 2 = 2
 print(sumSegmentTree.query(leftBound: 0, rightBound: 1)) // 2 + 2 = 4
 
-
 //you can use any associative function (i.e (a+b)+c == a+(b+c)) as function for segment tree
 func gcd(_ m: Int, _ n: Int) -> Int {
 	var a = 0
@@ -105,7 +101,6 @@ gcdSegmentTree.replaceItem(at: 3, withItem: 10) //gcdArray now is [2, 4, 6, 10,
 
 print(gcdSegmentTree.query(leftBound: 3, rightBound: 4)) // gcd(10, 5) = 5
 
-
 //example of segment tree which finds minimum on given range
 let minArray = [2, 4, 1, 5, 3]
 
@@ -118,7 +113,6 @@ minSegmentTree.replaceItem(at: 2, withItem: 10) // minArray now is [2, 4, 10, 5,
 
 print(minSegmentTree.query(leftBound: 0, rightBound: 4)) // min(2, 4, 10, 5, 3) = 2
 
-
 //type of elements in array can be any type which has some associative function
 let stringArray = ["a", "b", "c", "A", "B", "C"]
 
diff --git a/Selection Sampling/SelectionSampling.playground/Contents.swift b/Selection Sampling/SelectionSampling.playground/Contents.swift
index df1bb2e32..4a2484162 100644
--- a/Selection Sampling/SelectionSampling.playground/Contents.swift	
+++ b/Selection Sampling/SelectionSampling.playground/Contents.swift	
@@ -44,7 +44,6 @@ func select<T>(from a: [T], count requested: Int) -> [T] {
   return b
 }
 
-
 let poem = [
   "there", "once", "was", "a", "man", "from", "nantucket",
   "who", "kept", "all", "of", "his", "cash", "in", "a", "bucket",
@@ -57,8 +56,6 @@ let output = select(from: poem, count: 10)
 print(output)
 output.count
 
-
-
 // Use this to verify that all input elements have the same probability
 // of being chosen. The "counts" dictionary should have a roughly equal
 // count for each input element.
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 2380ebb69..9f2eda4f3 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	
@@ -19,8 +19,6 @@ func breadthFirstSearchShortestPath(graph: Graph, source: Node) -> Graph {
   return shortestPathGraph
 }
 
-
-
 let graph = Graph()
 
 let nodeA = graph.addNode(label: "a")
diff --git a/Shortest Path (Unweighted)/Tests/Graph.swift b/Shortest Path (Unweighted)/Tests/Graph.swift
index 4d2e59eab..cce697344 100644
--- a/Shortest Path (Unweighted)/Tests/Graph.swift	
+++ b/Shortest Path (Unweighted)/Tests/Graph.swift	
@@ -12,7 +12,6 @@ public func == (lhs: Edge, rhs: Edge) -> Bool {
     return lhs.neighbor == rhs.neighbor
 }
 
-
 // MARK: - Node
 
 open class Node: CustomStringConvertible, Equatable {
diff --git a/Shuffle/Shuffle.playground/Contents.swift b/Shuffle/Shuffle.playground/Contents.swift
index e6d4f000d..704a94e7d 100644
--- a/Shuffle/Shuffle.playground/Contents.swift
+++ b/Shuffle/Shuffle.playground/Contents.swift
@@ -7,8 +7,6 @@ public func random(_ n: Int) -> Int {
   return Int(arc4random_uniform(UInt32(n)))
 }
 
-
-
 /* Fisher-Yates / Knuth shuffle */
 extension Array {
   public mutating func shuffle() {
@@ -26,8 +24,6 @@ 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)
diff --git a/Shunting Yard/ShuntingYard.playground/Contents.swift b/Shunting Yard/ShuntingYard.playground/Contents.swift
index bd4d15515..38431f5e2 100644
--- a/Shunting Yard/ShuntingYard.playground/Contents.swift	
+++ b/Shunting Yard/ShuntingYard.playground/Contents.swift	
@@ -212,7 +212,6 @@ public func reversePolishNotation(_ expression: [Token]) -> String {
   return reversePolishNotation.map({token in token.description}).joined(separator: " ")
 }
 
-
 // Simple demo
 
 let expr = InfixExpressionBuilder()
diff --git a/Skip-List/SkipList.swift b/Skip-List/SkipList.swift
index cd832eef9..43173f236 100644
--- a/Skip-List/SkipList.swift
+++ b/Skip-List/SkipList.swift
@@ -20,10 +20,8 @@
 // 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] = []
@@ -58,7 +56,6 @@ extension Stack: Sequence {
   }
 }
 
-
 private func coinFlip() -> Bool {
   #if os(Linux)
       return random() % 2 == 0
@@ -67,7 +64,6 @@ private func coinFlip() -> Bool {
   #endif
 }
 
-
 public class DataNode<Key: Comparable, Payload> {
   public typealias Node = DataNode<Key, Payload>
 
@@ -81,11 +77,10 @@ public class DataNode<Key: Comparable, Payload> {
     self.data = data
   }
 
-  public init(asHead head: Bool){}
+  public init(asHead head: Bool) {}
 
 }
 
-
 open class SkipList<Key: Comparable, Payload> {
   public typealias Node = DataNode<Key, Payload>
 
@@ -95,8 +90,6 @@ open class SkipList<Key: Comparable, Payload> {
 
 }
 
-
-
 // MARK: - Search lanes for a node with a given key
 
 extension SkipList {
@@ -152,8 +145,6 @@ extension SkipList {
 
 }
 
-
-
 // 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 {
@@ -177,7 +168,6 @@ extension SkipList {
 
   }
 
-
   private func insertItem(key: Key, data: Payload) {
     var stack              = Stack<Node>()
     var currentNode: Node? = head
@@ -228,7 +218,6 @@ extension SkipList {
     }
   }
 
-
   func insert(key: Key, data: Payload) {
     if head != nil {
       if let node = findNode(key: key) {
@@ -249,7 +238,6 @@ extension SkipList {
 
 }
 
-
 // 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 {
@@ -278,7 +266,6 @@ extension SkipList {
   }
 }
 
-
 // MARK: - Get associated payload from a node with a given key.
 
 extension SkipList {
diff --git a/Slow Sort/SlowSort.swift b/Slow Sort/SlowSort.swift
index c21a77fd8..6396e8b38 100644
--- a/Slow Sort/SlowSort.swift	
+++ b/Slow Sort/SlowSort.swift	
@@ -6,23 +6,22 @@
 //
 //
 
-var numberList = [1,12,9,17,13,12]
+var numberList = [1, 12, 9, 17, 13, 12]
 
 public func slowsort(_ i: Int, _ j: Int) {
     if i>=j {
         return
     }
     let m = (i+j)/2
-    slowsort(i,m)
-    slowsort(m+1,j)
+    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)
+    slowsort(i, j-1)
 }
 
-
-slowsort(0,numberList.count-1)
+slowsort(0, numberList.count-1)
 print(numberList)
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift
index 9e11cb6a1..6b9314557 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Contents.swift	
@@ -11,7 +11,6 @@ print(B)
 B[.column, 0] = [3, 2, -1, 2]
 B[.column, 1] = [4, 1, 2, 7]
 
-
 let C = A.matrixMultiply(by: B)
 let D = A.strassenMatrixMultiply(by: B)
 let E = B.matrixMultiply(by: A)
diff --git a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift
index 324e906ee..da4b95a78 100644
--- a/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
+++ b/Strassen Matrix Multiplication/StrassensMatrixMultiplication.playground/Sources/Matrix.swift	
@@ -155,18 +155,18 @@ extension Matrix {
     var BPrep = Matrix(size: m)
 
     A.forEach { (i, j) in
-      APrep[i,j] = A[i,j]
+      APrep[i, j] = A[i, j]
     }
 
     B.forEach { (i, j) in
-      BPrep[i,j] = B[i,j]
+      BPrep[i, j] = B[i, j]
     }
 
     let CPrep = APrep.strassenR(by: BPrep)
     var C = Matrix(rows: A.rows, columns: B.columns)
     for i in 0..<A.rows {
       for j in 0..<B.columns {
-        C[i,j] = CPrep[i,j]
+        C[i, j] = CPrep[i, j]
       }
     }
 
@@ -199,14 +199,14 @@ extension Matrix {
 
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
-        a[i,j] = A[i,j]
-        b[i,j] = A[i, j+nBy2]
-        c[i,j] = A[i+nBy2, j]
-        d[i,j] = A[i+nBy2, j+nBy2]
-        e[i,j] = B[i,j]
-        f[i,j] = B[i, j+nBy2]
-        g[i,j] = B[i+nBy2, j]
-        h[i,j] = B[i+nBy2, j+nBy2]
+        a[i, j] = A[i, j]
+        b[i, j] = A[i, j+nBy2]
+        c[i, j] = A[i+nBy2, j]
+        d[i, j] = A[i+nBy2, j+nBy2]
+        e[i, j] = B[i, j]
+        f[i, j] = B[i, j+nBy2]
+        g[i, j] = B[i+nBy2, j]
+        h[i, j] = B[i+nBy2, j+nBy2]
       }
     }
 
@@ -226,10 +226,10 @@ extension Matrix {
     var C = Matrix(size: n)
     for i in 0..<nBy2 {
       for j in 0..<nBy2 {
-        C[i, j]           = c11[i,j]
-        C[i, j+nBy2]      = c12[i,j]
-        C[i+nBy2, j]      = c21[i,j]
-        C[i+nBy2, j+nBy2] = c22[i,j]
+        C[i, j]           = c11[i, j]
+        C[i, j+nBy2]      = c12[i, j]
+        C[i+nBy2, j]      = c21[i, j]
+        C[i+nBy2, j+nBy2] = c22[i, j]
       }
     }
 
diff --git a/Ternary Search Tree/TST.playground/Sources/TSTNode.swift b/Ternary Search Tree/TST.playground/Sources/TSTNode.swift
index efdfd4299..7fea88d1d 100644
--- a/Ternary Search Tree/TST.playground/Sources/TSTNode.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TSTNode.swift	
@@ -17,7 +17,6 @@ class TSTNode<Element> {
     //Children
     var left: TSTNode?, right: TSTNode?, middle: TSTNode?
 
-
     init(key: Character, data: Element?) {
         self.key = key
         self.data = data
diff --git a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift
index 21b8f0dc3..9c4c860d8 100644
--- a/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TST.playground/Sources/TernarySearchTree.swift	
@@ -8,7 +8,6 @@
 
 import Foundation
 
-
 public class TernarySearchTree<Element> {
 
     var root: TSTNode<Element>?
@@ -58,10 +57,8 @@ public class TernarySearchTree<Element> {
         }
     }
 
-
     // MARK: - Finding
 
-
     public func find(key: String) -> Element? {
         return find(node: root, withKey: key, atIndex: 0)
     }
diff --git a/Ternary Search Tree/TernarySearchTree.swift b/Ternary Search Tree/TernarySearchTree.swift
index 0fa6d9634..761c75b6f 100644
--- a/Ternary Search Tree/TernarySearchTree.swift	
+++ b/Ternary Search Tree/TernarySearchTree.swift	
@@ -84,7 +84,6 @@ public class TernarySearchTree<Element> {
         }
     }
 
-
     // MARK: - Finding
 
     /**
diff --git a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift
index dfbbae9ca..4a1816412 100644
--- a/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
+++ b/Ternary Search Tree/Tests/TernarySearchTreeTests.swift	
@@ -10,7 +10,6 @@ import XCTest
 
 class TernarySearchTreeTests: XCTestCase {
 
-
     let testCount = 30
 
     func testCanFindStringInTree() {
diff --git a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift
index e4b527664..ece1966e0 100644
--- a/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
+++ b/Threaded Binary Tree/ThreadedBinaryTree.playground/Contents.swift	
@@ -1,6 +1,5 @@
 //: Playground - noun: a place where people can play
 
-
 // Simple little debug function to make testing output pretty
 func check(_ tree: ThreadedBinaryTree<Int>?) {
   if let tree = tree {
@@ -28,12 +27,10 @@ func check(_ tree: ThreadedBinaryTree<Int>?) {
     }
 }
 
-
 print("\nTree with Single Node")
 let emptyTree = ThreadedBinaryTree<Int>(value: 1)
 check(emptyTree)
 
-
 print("\nFull Balanced Binary Tree with 7 Nodes")
 let fullTree = ThreadedBinaryTree<Int>(value: 4)
 fullTree.insert(2)
@@ -44,7 +41,6 @@ fullTree.insert(3)
 fullTree.insert(7)
 check(fullTree)
 
-
 print("\n\nBase Binary Tree with 5 Nodes")
 let tree = ThreadedBinaryTree<Int>(array: [9, 5, 12, 2, 7])
 check(tree)
@@ -81,5 +77,4 @@ print("\nRemove 12")
 newRoot?.remove(12)
 check(newRoot)
 
-
 print("\n\nDone with Tests!\n")
diff --git a/Topological Sort/Topological Sort.playground/Contents.swift b/Topological Sort/Topological Sort.playground/Contents.swift
index d0ebe550d..8f78c388a 100644
--- a/Topological Sort/Topological Sort.playground/Contents.swift	
+++ b/Topological Sort/Topological Sort.playground/Contents.swift	
@@ -23,8 +23,6 @@ graph.addEdge(fromNode: node11, toNode: node9)
 graph.addEdge(fromNode: node11, toNode: node10)
 graph.addEdge(fromNode: node8, toNode: node9)
 
-
-
 // using depth-first search
 graph.topologicalSort()
 
diff --git a/Treap/Treap.swift b/Treap/Treap.swift
index 7038e843e..d6cee2e70 100644
--- a/Treap/Treap.swift
+++ b/Treap/Treap.swift
@@ -142,7 +142,7 @@ public extension Treap {
       return newNode
     }
 
-    if case let .node(_, _, newChildP, _, _) = newChild , newChildP < nodeP {
+    if case let .node(_, _, newChildP, _, _) = newChild, newChildP < nodeP {
       return rotate(newNode)
     } else {
       return newNode
diff --git a/Tree/Tree.playground/Contents.swift b/Tree/Tree.playground/Contents.swift
index 77e8fd22e..d59b7eedb 100644
--- a/Tree/Tree.playground/Contents.swift
+++ b/Tree/Tree.playground/Contents.swift
@@ -26,9 +26,6 @@ extension TreeNode: CustomStringConvertible {
   }
 }
 
-
-
-
 let tree = TreeNode<String>(value: "beverages")
 
 let hotNode = TreeNode<String>(value: "hot")
diff --git a/Trie/Trie/Trie/AppDelegate.swift b/Trie/Trie/Trie/AppDelegate.swift
index b2b4c0c5f..b2c46695b 100644
--- a/Trie/Trie/Trie/AppDelegate.swift
+++ b/Trie/Trie/Trie/AppDelegate.swift
@@ -11,8 +11,6 @@ import Cocoa
 @NSApplicationMain
 class AppDelegate: NSObject, NSApplicationDelegate {
 
-
-
     func applicationDidFinishLaunching(_ aNotification: Notification) {
         // Insert code here to initialize your application
     }
@@ -21,5 +19,4 @@ class AppDelegate: NSObject, NSApplicationDelegate {
         // Insert code here to tear down your application
     }
 
-
 }
diff --git a/Trie/Trie/Trie/Trie.swift b/Trie/Trie/Trie/Trie.swift
index 7ff9638d7..856384fff 100644
--- a/Trie/Trie/Trie/Trie.swift
+++ b/Trie/Trie/Trie/Trie.swift
@@ -8,7 +8,6 @@
 
 import Foundation
 
-
 /// A node in the trie
 class TrieNode<T: Hashable> {
   var value: T?
@@ -19,7 +18,6 @@ class TrieNode<T: Hashable> {
     return children.count == 0
   }
 
-
   /// Initializes a node.
   ///
   /// - Parameters:
@@ -136,7 +134,6 @@ extension Trie {
     return currentNode.isTerminating
   }
 
-
   /// Attempts to walk to the last node of a word.  The
   /// search will fail if the word is not present. Doesn't
   /// check if the node is terminating
diff --git a/Trie/Trie/Trie/ViewController.swift b/Trie/Trie/Trie/ViewController.swift
index e24a812cb..928b01f4c 100644
--- a/Trie/Trie/Trie/ViewController.swift
+++ b/Trie/Trie/Trie/ViewController.swift
@@ -22,5 +22,4 @@ class ViewController: NSViewController {
         }
     }
 
-
 }
diff --git a/Union-Find/UnionFind.playground/Contents.swift b/Union-Find/UnionFind.playground/Contents.swift
index 0a50d1ba6..b1f7fb4e1 100644
--- a/Union-Find/UnionFind.playground/Contents.swift
+++ b/Union-Find/UnionFind.playground/Contents.swift
@@ -22,18 +22,14 @@ print(dsu.inSameSet(4, and: 6))
 print(dsu.inSameSet(6, and: 8))
 print(dsu.inSameSet(8, and: 10))
 
-
 print(dsu.inSameSet(1, and: 3))
 print(dsu.inSameSet(3, and: 5))
 print(dsu.inSameSet(5, and: 7))
 print(dsu.inSameSet(7, and: 9))
 
-
 print(dsu.inSameSet(7, and: 4))
 print(dsu.inSameSet(3, and: 6))
 
-
-
 var dsuForStrings = UnionFindQuickUnion<String>()
 let words = ["all", "border", "boy", "afternoon", "amazing", "awesome", "best"]
 
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
index 33e81832d..2cd048de6 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickFind.swift
@@ -6,19 +6,19 @@ public struct UnionFindQuickFind<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public init() {}
-  
+
   public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   private mutating func setByIndex(_ index: Int) -> Int {
     return parent[index]
   }
-  
+
   public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -26,7 +26,7 @@ public struct UnionFindQuickFind<T: Hashable> {
       return nil
     }
   }
-  
+
   public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       if firstSet != secondSet {
@@ -39,7 +39,7 @@ public struct UnionFindQuickFind<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
index 9bff31616..2be8875eb 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindQuickUnion.swift
@@ -6,15 +6,15 @@ public struct UnionFindQuickUnion<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public init() {}
-  
+
   public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   private mutating func setByIndex(_ index: Int) -> Int {
     if parent[index] == index {
       return index
@@ -23,7 +23,7 @@ public struct UnionFindQuickUnion<T: Hashable> {
       return parent[index]
     }
   }
-  
+
   public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -31,7 +31,7 @@ public struct UnionFindQuickUnion<T: Hashable> {
       return nil
     }
   }
-  
+
   public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       if firstSet != secondSet {
@@ -40,7 +40,7 @@ public struct UnionFindQuickUnion<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
index c89f2a457..49a526fe3 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickFind.swift
@@ -6,19 +6,19 @@ public struct UnionFindWeightedQuickFind<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public init() {}
-  
+
   public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   private mutating func setByIndex(_ index: Int) -> Int {
     return parent[index]
   }
-  
+
   public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -26,7 +26,7 @@ public struct UnionFindWeightedQuickFind<T: Hashable> {
       return nil
     }
   }
-  
+
   public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       if firstSet != secondSet {
@@ -48,7 +48,7 @@ public struct UnionFindWeightedQuickFind<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
index cd33007bc..70217422f 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnion.swift
@@ -4,15 +4,15 @@ public struct UnionFindWeightedQuickUnion<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public init() {}
-  
+
   public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   private mutating func setByIndex(_ index: Int) -> Int {
     if parent[index] == index {
       return index
@@ -21,7 +21,7 @@ public struct UnionFindWeightedQuickUnion<T: Hashable> {
       return parent[index]
     }
   }
-  
+
   public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -29,7 +29,7 @@ public struct UnionFindWeightedQuickUnion<T: Hashable> {
       return nil
     }
   }
-  
+
   /// Weighted, by comparing set size.
   /// Merge small set into the large one.
   public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
@@ -45,7 +45,7 @@ public struct UnionFindWeightedQuickUnion<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
diff --git a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
index 7eb8fe209..1c0bacd82 100644
--- a/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
+++ b/Union-Find/UnionFind.playground/Sources/UnionFindWeightedQuickUnionPathCompression.swift
@@ -4,15 +4,15 @@ public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
   private var index = [T: Int]()
   private var parent = [Int]()
   private var size = [Int]()
-  
+
   public init() {}
-  
+
   public mutating func addSetWith(_ element: T) {
     index[element] = parent.count
     parent.append(parent.count)
     size.append(1)
   }
-  
+
   /// Path Compression.
   private mutating func setByIndex(_ index: Int) -> Int {
     if index != parent[index] {
@@ -20,7 +20,7 @@ public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
     }
     return parent[index]
   }
-  
+
   public mutating func setOf(_ element: T) -> Int? {
     if let indexOfElement = index[element] {
       return setByIndex(indexOfElement)
@@ -28,7 +28,7 @@ public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
       return nil
     }
   }
-  
+
   public mutating func unionSetsContaining(_ firstElement: T, and secondElement: T) {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       if firstSet != secondSet {
@@ -42,7 +42,7 @@ public struct UnionFindWeightedQuickUnionPathCompression<T: Hashable> {
       }
     }
   }
-  
+
   public mutating func inSameSet(_ firstElement: T, and secondElement: T) -> Bool {
     if let firstSet = setOf(firstElement), let secondSet = setOf(secondElement) {
       return firstSet == secondSet
diff --git a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
index 44faf6790..b1d49eec7 100644
--- a/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
+++ b/Z-Algorithm/ZetaAlgorithm.playground/Contents.swift
@@ -1,6 +1,5 @@
 //: Playground - noun: a place where people can play
 
-
 func ZetaAlgorithm(ptrn: String) -> [Int]? {
 
   let pattern = Array(ptrn.characters)
@@ -58,7 +57,6 @@ func ZetaAlgorithm(ptrn: String) -> [Int]? {
   return zeta
 }
 
-
 extension String {
 
   func indexesOf(pattern: String) -> [Int]? {

From af2f370111a2b58bddcd6aed09d2edad1e5442ad Mon Sep 17 00:00:00 2001
From: ph1ps <gabriel.phi@gmx.at>
Date: Thu, 25 May 2017 22:28:45 +0200
Subject: [PATCH 227/862] Remove images group from workspace

---
 .../contents.xcworkspacedata                           | 10 ----------
 1 file changed, 10 deletions(-)

diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index 8ba66e153..aa4529a48 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1213,16 +1213,6 @@
          location = "group:README.markdown">
       </FileRef>
    </Group>
-   <Group
-      location = "group:Images"
-      name = "Images">
-      <FileRef
-         location = "group:scheme-settings-for-travis.png">
-      </FileRef>
-      <FileRef
-         location = "group:SwiftAlgorithm-410-transp.png">
-      </FileRef>
-   </Group>
    <Group
       location = "group:Insertion Sort"
       name = "Insertion Sort">

From 5765dbf6448b15382e5c68cb1c2750c5b800a07d Mon Sep 17 00:00:00 2001
From: andmeics <396783795@qq.com>
Date: Sun, 28 May 2017 15:32:40 +0800
Subject: [PATCH 228/862] Remove "How to Contribute.markdown" from Workspace

Remove "How to Contribute.markdown" from Workspace,because file is not exist.
---
 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 c89ac0dfe..a9c348d09 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -13,9 +13,6 @@
    <FileRef
       location = "group:Big-O Notation.markdown">
    </FileRef>
-   <FileRef
-      location = "group:How to Contribute.markdown">
-   </FileRef>
    <FileRef
       location = "group:Under Construction.markdown">
    </FileRef>

From c848c7e05c32362dc09384ee27c4f6ef1af7043f Mon Sep 17 00:00:00 2001
From: andmeics <396783795@qq.com>
Date: Sun, 28 May 2017 15:49:33 +0800
Subject: [PATCH 229/862] Add "CONTRIBUTING.md" file to Workspacedata

---
 .github/CONTRIBUTING.md                                   | 2 +-
 swift-algorithm-club.xcworkspace/contents.xcworkspacedata | 3 +++
 2 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index 2b08e2633..3bd5a1a91 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -54,4 +54,4 @@ For the unit tests:
 
 ## Want to chat?
 
-This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/raywenderlich/swift-algorithm-club/issues) and we'll talk!
\ No newline at end of file
+This isn't just a repo with a bunch of code... If you want to learn more about how an algorithm works or want to discuss better ways of solving problems, then open a [Github issue](https://github.com/raywenderlich/swift-algorithm-club/issues) and we'll talk!
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index a9c348d09..d4b6645a9 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -13,6 +13,9 @@
    <FileRef
       location = "group:Big-O Notation.markdown">
    </FileRef>
+   <FileRef
+      location = "group:.github/CONTRIBUTING.md">
+   </FileRef>
    <FileRef
       location = "group:Under Construction.markdown">
    </FileRef>

From 919a5fe9a59564463720626a85938c3fdab9ecab Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Tue, 30 May 2017 16:09:04 -0700
Subject: [PATCH 230/862] Update README.markdown

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

diff --git a/README.markdown b/README.markdown
index 579ca0b4e..f4f10ef96 100644
--- a/README.markdown
+++ b/README.markdown
@@ -224,7 +224,7 @@ 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 [Ross O'brien](https://www.raywenderlich.com/u/narrativium).
 
-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](How%20to%20Contribute.markdown)? :]
+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)? :]
 
 ## License
 

From 5d378d52c6d455aae8f1c310dd6074fc7d084a7f Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlauKL@users.noreply.github.com>
Date: Wed, 31 May 2017 15:30:09 -0700
Subject: [PATCH 231/862] Update README.markdown

Addresses #477
---
 README.markdown | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/README.markdown b/README.markdown
index f4f10ef96..e81fe7932 100644
--- a/README.markdown
+++ b/README.markdown
@@ -93,6 +93,9 @@ Bad sorting algorithms (don't use these!):
 
 - [Shuffle](Shuffle/). Randomly rearranges the contents of an array.
 - [Comb Sort](Comb%20Sort/). An improve upon the Bubble Sort algorithm.
+- [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.
 
 ### Mathematics
 
@@ -157,6 +160,7 @@ Most of the time using just the built-in `Array`, `Dictionary`, and `Set` types
 - 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.
 
 ### Hashing
 

From 9bea75e527e666765a331737058317b4855953a6 Mon Sep 17 00:00:00 2001
From: Tobias Helmrich <me@tobias-helmrich.de>
Date: Sat, 3 Jun 2017 20:38:37 +0900
Subject: [PATCH 232/862] Fix minor typo

---
 Convex Hull/README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Convex Hull/README.md b/Convex Hull/README.md
index b73f66176..2e1fbe6a3 100644
--- a/Convex Hull/README.md	
+++ b/Convex Hull/README.md	
@@ -2,12 +2,12 @@
 
 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 dimention. This implementation however covers points on a plane. It essentially calculates the lines between points which together contain all points.
+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.
 
 ## 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.
+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:
 
 `findHull(points: [CGPoint], p1: CGPoint, p2: CGPoint)`

From 4e8614b84895240b6d7ae693ba07496a45df80de Mon Sep 17 00:00:00 2001
From: Tobias Helmrich <me@tobias-helmrich.de>
Date: Sat, 3 Jun 2017 20:51:47 +0900
Subject: [PATCH 233/862] Fix minor typo

---
 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 f8bd1c084..bf17d93bd 100644
--- a/Selection Sampling/README.markdown	
+++ b/Selection Sampling/README.markdown	
@@ -151,7 +151,7 @@ The random number is 0.346. The formula gives:
 	
 Just a tiny bit too high. We skip `"e"`. Only two candidates left...
 
-Note that now literally we're dealing with a toin coss: if the random number is less than 0.5 we select `"f"` and we're done. If it's greater than 0.5, we go on to the final element. Let's say we get 0.583:
+Note that now literally we're dealing with a coin toss: if the random number is less than 0.5 we select `"f"` and we're done. If it's greater than 0.5, we go on to the final element. Let's say we get 0.583:
 
 	2 * 0.583 = 1.166
 

From 519683761400c43236c29d1c39bac9cf313887da Mon Sep 17 00:00:00 2001
From: Ute Schiehlen <ute.schiehlen@tum.de>
Date: Sat, 3 Jun 2017 16:36:08 +0200
Subject: [PATCH 234/862] Incorporated reviews. changed isNullLeaf variable to
 a computed property

---
 .../RedBlackTree.playground/Contents.swift    | 14 +++-
 .../Sources/RedBlackTree.swift                | 65 +++++++++----------
 2 files changed, 43 insertions(+), 36 deletions(-)

diff --git a/Red-Black Tree/RedBlackTree.playground/Contents.swift b/Red-Black Tree/RedBlackTree.playground/Contents.swift
index 5b19f9bd1..50d61167d 100644
--- a/Red-Black Tree/RedBlackTree.playground/Contents.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Contents.swift	
@@ -6,17 +6,25 @@ let redBlackTree = RedBlackTree<Double>()
 
 let randomMax = Double(0x10000000)
 var values = [Double]()
-for _ in 0..<1000 {
+for i in 0..<1000 {
   let value = Double(arc4random()) / randomMax
   values.append(value)
   redBlackTree.insert(key: value)
+  
+  if i % 100 == 0 {
+    redBlackTree.verify()
+  }
 }
 redBlackTree.verify()
 
-for _ in 0..<1000 {
+for i in 0..<1000 {
   let rand = arc4random_uniform(UInt32(values.count))
   let index = Int(rand)
   let value = values.remove(at: index)
   redBlackTree.delete(key: value)
+  
+  if i % 100 == 0 {
+    redBlackTree.verify()
+  }
 }
-redBlackTree.verify()
+redBlackTree.verify()
\ No newline at end of file
diff --git a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift
index 351f89a9d..59633031d 100644
--- a/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
+++ b/Red-Black Tree/RedBlackTree.playground/Sources/RedBlackTree.swift	
@@ -32,17 +32,16 @@ private enum RotationDirection {
 
 // MARK: - RBNode
 
-public class RBTreeNode<Key: Comparable>: Equatable {
-  public typealias RBNode = RBTreeNode<Key>
+public class RBTreeNode<T: Comparable>: Equatable {
+  public typealias RBNode = RBTreeNode<T>
   
   fileprivate var color: RBTreeColor = .black
-  fileprivate var key: Key?
-  fileprivate var isNullLeaf = true
+  fileprivate var key: T?
   var leftChild: RBNode?
   var rightChild: RBNode?
   fileprivate weak var parent: RBNode?
   
-  public init(key: Key?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
+  public init(key: T?, leftChild: RBNode?, rightChild: RBNode?, parent: RBNode?) {
     self.key = key
     self.leftChild = leftChild
     self.rightChild = rightChild
@@ -52,16 +51,14 @@ public class RBTreeNode<Key: Comparable>: Equatable {
     self.rightChild?.parent = self
   }
   
-  public convenience init(key: Key?) {
+  public convenience init(key: T?) {
     self.init(key: key, leftChild: RBNode(), rightChild: RBNode(), parent: RBNode())
-    self.isNullLeaf = false
   }
   
   // For initialising the nullLeaf
   public convenience init() {
     self.init(key: nil, leftChild: nil, rightChild: nil, parent: nil)
     self.color = .black
-    self.isNullLeaf = true
   }
   
   var isRoot: Bool {
@@ -72,7 +69,11 @@ public class RBTreeNode<Key: Comparable>: Equatable {
     return rightChild == nil && leftChild == nil
   }
   
-  var isLeftCild: Bool {
+  var isNullLeaf: Bool {
+    return key == nil && isLeaf && color == .black
+  }
+  
+  var isLeftChild: Bool {
     return parent?.leftChild === self
   }
   
@@ -85,7 +86,7 @@ public class RBTreeNode<Key: Comparable>: Equatable {
   }
   
   var sibling: RBNode? {
-    if isLeftCild {
+    if isLeftChild {
       return parent?.rightChild
     } else {
       return parent?.leftChild
@@ -99,8 +100,8 @@ public class RBTreeNode<Key: Comparable>: Equatable {
 
 // MARK: - RedBlackTree
 
-public class RedBlackTree<Key: Comparable> {
-  public typealias RBNode = RBTreeNode<Key>
+public class RedBlackTree<T: Comparable> {
+  public typealias RBNode = RBTreeNode<T>
   
   fileprivate(set) var root: RBNode
   fileprivate(set) var size = 0
@@ -180,14 +181,14 @@ extension RedBlackTree {
   /*
    * Returns the node with the given key |input| if existing
    */
-  public func search(input: Key) -> RBNode? {
+  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: Key, node: RBNode?) -> RBNode? {
+  fileprivate func search(key: T, node: RBNode?) -> RBNode? {
     // If node nil -> key not found
     guard let node = node else {
       return nil
@@ -215,23 +216,21 @@ extension RedBlackTree {
   /*
    * Returns the minimum key value of the whole tree
    */
-  public func minValue() -> Key? {
-    if let minNode = root.minimum() {
-       return minNode.key
-    } else {
+  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() -> Key? {
-      if let maxNode = root.maximum() {
-        return maxNode.key
-      } else {
-        return nil
+  public func maxValue() -> T? {
+    guard let maxNode = root.maximum() else {
+      return nil
     }
+    return maxNode.key
   }
 }
 
@@ -244,7 +243,7 @@ extension RedBlackTree {
    * 2. Fix red-black properties
    * Runntime: O(log n)
    */
-  public func insert(key: Key) {
+  public func insert(key: T) {
     if root.isNullLeaf {
       root = RBNode(key: key)
     } else {
@@ -332,10 +331,10 @@ extension RedBlackTree {
         else {
           var zNew = z
           // Case 2.a: z right child -> rotate
-          if parentZ.isLeftCild && z.isRightChild {
+          if parentZ.isLeftChild && z.isRightChild {
             zNew = parentZ
             leftRotate(node: zNew)
-          } else if parentZ.isRightChild && z.isLeftCild {
+          } else if parentZ.isRightChild && z.isLeftChild {
             zNew = parentZ
             rightRotate(node: zNew)
           }
@@ -343,7 +342,7 @@ extension RedBlackTree {
           zNew.parent?.color = .black
           if let grandparentZnew = zNew.grandparent {
             grandparentZnew.color = .red
-            if z.isLeftCild {
+            if z.isLeftChild {
               rightRotate(node: grandparentZnew)
             } else {
               leftRotate(node: grandparentZnew)
@@ -365,7 +364,7 @@ extension RedBlackTree {
    * 2. Fix red-black properties
    * Runntime: O(log n)
    */
-  public func delete(key: Key) {
+  public func delete(key: T) {
     if size == 1 {
       root = nullLeaf
       size -= 1
@@ -408,7 +407,7 @@ extension RedBlackTree {
       if parentY.isNullLeaf {
         root = nodeX
       } else {
-        if nodeY.isLeftCild {
+        if nodeY.isLeftChild {
           parentY.leftChild = nodeX
         } else {
           parentY.rightChild = nodeX
@@ -450,7 +449,7 @@ extension RedBlackTree {
         if let parentX = x.parent {
           parentX.color = .red
           // Rotation
-          if x.isLeftCild {
+          if x.isLeftChild {
             leftRotate(node: parentX)
           } else {
             rightRotate(node: parentX)
@@ -472,7 +471,7 @@ extension RedBlackTree {
         // We have a valid red-black-tree
       } else {
         // Case 3: a. Sibling black with one black child to the right
-        if x.isLeftCild && sibling.rightChild?.color == .black {
+        if x.isLeftChild && sibling.rightChild?.color == .black {
           // Recolor
           sibling.leftChild?.color = .black
           sibling.color = .red
@@ -501,7 +500,7 @@ extension RedBlackTree {
           sibling.color = parentX.color
           parentX.color = .black
           // a. x left and sibling with red right child
-          if x.isLeftCild {
+          if x.isLeftChild {
             sibling.rightChild?.color = .black
             // Rotate
             leftRotate(node: parentX)
@@ -581,7 +580,7 @@ extension RedBlackTree {
       if let node = nodeY {
         root = node
       }
-    } else if x.isLeftCild {
+    } else if x.isLeftChild {
       x.parent?.leftChild = nodeY
     } else if x.isRightChild {
       x.parent?.rightChild = nodeY

From ded16b8eea2a9243f8a948aaf5da806aa81cbc2b Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:47:29 -0700
Subject: [PATCH 235/862] implement gaurded array first

---
 Select Minimum Maximum/Maximum.swift | 9 +++------
 1 file changed, 3 insertions(+), 6 deletions(-)

diff --git a/Select Minimum Maximum/Maximum.swift b/Select Minimum Maximum/Maximum.swift
index c999504fb..20c7d7c62 100644
--- a/Select Minimum Maximum/Maximum.swift	
+++ b/Select Minimum Maximum/Maximum.swift	
@@ -2,12 +2,9 @@
  Finds the maximum value in an array in O(n) time.
  */
 
-func maximum<T: Comparable>(_ array: [T]) -> T? {
-    guard !array.isEmpty else {
-        return nil
-    }
-
-    var maximum = array.first!
+func maximum1<T: Comparable>(_ array: [T]) -> T? {
+    guard var maximum = array.first else { return nil }
+    
     for element in array.dropFirst() {
         maximum = element > maximum ? element : maximum
     }

From 8e85522d34ce09f49430e9e7ee37465c52c2cbd2 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:48:29 -0700
Subject: [PATCH 236/862] Update Maximum.swift

---
 Select Minimum Maximum/Maximum.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Select Minimum Maximum/Maximum.swift b/Select Minimum Maximum/Maximum.swift
index 20c7d7c62..82b76fd73 100644
--- a/Select Minimum Maximum/Maximum.swift	
+++ b/Select Minimum Maximum/Maximum.swift	
@@ -2,7 +2,7 @@
  Finds the maximum value in an array in O(n) time.
  */
 
-func maximum1<T: Comparable>(_ array: [T]) -> T? {
+func maximum<T: Comparable>(_ array: [T]) -> T? {
     guard var maximum = array.first else { return nil }
     
     for element in array.dropFirst() {

From 183815a72d83885fea57fb6fa8e316c6f43f5257 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:50:01 -0700
Subject: [PATCH 237/862] implement guarded array first

---
 Select Minimum Maximum/Minimum.swift | 7 ++-----
 1 file changed, 2 insertions(+), 5 deletions(-)

diff --git a/Select Minimum Maximum/Minimum.swift b/Select Minimum Maximum/Minimum.swift
index 88a562170..891a69142 100644
--- a/Select Minimum Maximum/Minimum.swift	
+++ b/Select Minimum Maximum/Minimum.swift	
@@ -3,11 +3,8 @@
  */
 
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-    guard !array.isEmpty else {
-        return nil
-    }
-
-    var minimum = array.first!
+    guard minimum = array.first else { return nil }
+ 
     for element in array.dropFirst() {
         minimum = element < minimum ? element : minimum
     }

From 87bde229ad8b63a1711552085ca0eb5cd6252a82 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:50:15 -0700
Subject: [PATCH 238/862] Update Minimum.swift

---
 Select Minimum Maximum/Minimum.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Select Minimum Maximum/Minimum.swift b/Select Minimum Maximum/Minimum.swift
index 891a69142..75ecfc3b1 100644
--- a/Select Minimum Maximum/Minimum.swift	
+++ b/Select Minimum Maximum/Minimum.swift	
@@ -3,7 +3,7 @@
  */
 
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-    guard minimum = array.first else { return nil }
+    guard var minimum = array.first else { return nil }
  
     for element in array.dropFirst() {
         minimum = element < minimum ? element : minimum

From 5aef7034c482327a1a4c3a02e0474609ed6ffb2f Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:54:36 -0700
Subject: [PATCH 239/862] implement guarded array.first

---
 Select Minimum Maximum/MinimumMaximumPairs.swift | 11 +++--------
 1 file changed, 3 insertions(+), 8 deletions(-)

diff --git a/Select Minimum Maximum/MinimumMaximumPairs.swift b/Select Minimum Maximum/MinimumMaximumPairs.swift
index 2c7b5bb5f..a19b037d1 100644
--- a/Select Minimum Maximum/MinimumMaximumPairs.swift	
+++ b/Select Minimum Maximum/MinimumMaximumPairs.swift	
@@ -3,16 +3,11 @@
  */
 
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-    guard !array.isEmpty else {
-        return nil
-    }
-
-    var minimum = array.first!
-    var maximum = array.first!
+    guard var minimum = array.first else { return nil }
+    var maximum = minimum
 
     // if 'array' has an odd number of items, let 'minimum' or 'maximum' deal with the leftover
-    let hasOddNumberOfItems = array.count % 2 != 0
-    let start = hasOddNumberOfItems ? 1 : 0
+    let start = array.count % 2 // 1 if odd, skipping the first element
     for i in stride(from: start, to: array.count, by: 2) {
         let pair = (array[i], array[i+1])
 

From a76ac65096e664e44a53c5c3fff6e11eca314ed1 Mon Sep 17 00:00:00 2001
From: TheIronBorn <TheIronBorn@users.noreply.github.com>
Date: Sun, 4 Jun 2017 08:58:10 -0700
Subject: [PATCH 240/862] implement guarded array first

---
 Select Minimum Maximum/README.markdown | 17 ++++++-----------
 1 file changed, 6 insertions(+), 11 deletions(-)

diff --git a/Select Minimum Maximum/README.markdown b/Select Minimum Maximum/README.markdown
index 3c29b5764..c55272c63 100644
--- a/Select Minimum Maximum/README.markdown	
+++ b/Select Minimum Maximum/README.markdown	
@@ -24,11 +24,10 @@ Here is a simple implementation in Swift:
 
 ```swift
 func minimum<T: Comparable>(_ array: [T]) -> T? {
-  guard !array.isEmpty else {
+  guard var minimum = array.first else {
     return nil
   }
 
-  var minimum = array.first!
   for element in array.dropFirst() {
     minimum = element < minimum ? element : minimum
   }
@@ -36,11 +35,10 @@ func minimum<T: Comparable>(_ array: [T]) -> T? {
 }
 
 func maximum<T: Comparable>(_ array: [T]) -> T? {
-  guard !array.isEmpty else {
+  guard var maximum = array.first else {
     return nil
   }
 
-  var maximum = array.first!
   for element in array.dropFirst() {
     maximum = element > maximum ? element : maximum
   }
@@ -66,7 +64,7 @@ array.minElement()   // This will return 3
 array.maxElement()   // This will return 9
 ```
 
-```
+```swift
 let array = [ 8, 3, 9, 4, 6 ]
 //swift3
 array.min()   // This will return 3
@@ -97,16 +95,13 @@ Here is a simple implementation in Swift:
 
 ```swift
 func minimumMaximum<T: Comparable>(_ array: [T]) -> (minimum: T, maximum: T)? {
-  guard !array.isEmpty else {
+  guard var minimum = array.first else {
     return nil
   }
-
-  var minimum = array.first!
-  var maximum = array.first!
+  var maximum = minimum
 
   // if 'array' has an odd number of items, let 'minimum' or 'maximum' deal with the leftover
-  let hasOddNumberOfItems = array.count % 2 != 0
-  let start = hasOddNumberOfItems ? 1 : 0
+  let start = array.count % 2 // 1 if odd, skipping the first element
   for i in stride(from: start, to: array.count, by: 2) {
     let pair = (array[i], array[i+1])
 

From b2b88c03bd3944ef01d71ddc31bff9ae603e2bf7 Mon Sep 17 00:00:00 2001
From: Hassan Ahmed Khan <hassandotahmed@gmail.com>
Date: Fri, 9 Jun 2017 11:20:45 +0500
Subject: [PATCH 241/862] Divide and Conquer

Added description for Divide and Conquer section.
---
 Algorithm Design.markdown | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/Algorithm Design.markdown b/Algorithm Design.markdown
index 23f8ad70e..5d89cb05a 100644
--- a/Algorithm Design.markdown	
+++ b/Algorithm Design.markdown	
@@ -18,6 +18,13 @@ And if you only work with small datasets, then a brute force approach may actual
 
 ### Divide and conquer
 
-A big problem is often just a whole bunch of much smaller problems.
+>"When you change the way you look at things, the things you look at change."</br>
+>Max Planck, Quantum theorist and Nobel Prize Winner
 
-[More to come here]
+Divide and conquer is a way of dealing with a large problem by breaking it down into bits and pieces and working your way up towards the solution.
+
+Instead of seeing the whole problem as a single, huge and complex task you divide the problem in relatively smaller problems that are easier to understand and deal with.
+
+You solve smaller problems and aggregate the solution until you are left with the solution only. At each step the problem at hand shrinks and the solution gets mature until you have the final correct solution.
+
+Solving the smaller task and applying the same solution repetitively ( or often times recursively) to other chunks give you the result in less time.

From 1bc6990fe584080dcca0249bdb05d8a7c56907cd Mon Sep 17 00:00:00 2001
From: Darragh <Darraghk500@yahoo.ie>
Date: Sat, 10 Jun 2017 15:49:46 +0100
Subject: [PATCH 242/862] Create ShellSortExample.swift

Inner while loop was slightly incorrect - for example try array [64, 20, 50, 33, 72, 10, 23, -1, 4,-2,-3] with previous version.
---
 Shell Sort/ShellSortExample.swift | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Shell Sort/ShellSortExample.swift b/Shell Sort/ShellSortExample.swift
index e9cee7543..df0842770 100644
--- a/Shell Sort/ShellSortExample.swift	
+++ b/Shell Sort/ShellSortExample.swift	
@@ -22,7 +22,7 @@ public func shellSort(_ list : inout [Int]) {
 
             guard sublistCount == 1 && index > 0 else { continue }
 
-            while list[index - 1] > list[index] && index - 1 > 0 {
+            while index > 0 && list[index - 1] > list[index] {
                 swap(&list[index - 1], &list[index])
                 index -= 1
             }

From 5428e53eee961acc2d2dc7c0af0d6ef6a431f6e1 Mon Sep 17 00:00:00 2001
From: Taras Nikulin <crabman448@gmail.com>
Date: Mon, 12 Jun 2017 05:29:06 +0300
Subject: [PATCH 243/862] Language fixes

---
 Dijkstra Algorithm/README.md | 114 +++++++++++++++++------------------
 1 file changed, 57 insertions(+), 57 deletions(-)

diff --git a/Dijkstra Algorithm/README.md b/Dijkstra Algorithm/README.md
index 7afc34094..5f8a0ce07 100644
--- a/Dijkstra Algorithm/README.md	
+++ b/Dijkstra Algorithm/README.md	
@@ -1,11 +1,11 @@
-# Weighted graph general cocepts
+# Weighted graph general concepts
 
 Every weighted graph should contain: 
 1. Vertices/Nodes (I will use "vertex" in this readme).
 
 <img src="Images/Vertices.png" height="250" />
 
-2. Edges connecting vertices. Let's add some edges to our graph. For simplicity let's create directed graph for now. Directed means, that edge have a direction, i.e. vertex, where it starts and vertex, where it ends. But remember VERY IMPORTANT thing:
+2. Edges connecting vertices. Let's add some edges to our graph. For simplicity let's create directed graph for now. Directed means that edge has a direction, i.e. vertex, where it starts and vertex, where it ends. But remember a VERY IMPORTANT thing:
     * All undirected graphs can be viewed as a directed graph.
     * A directed graph is undirected if and only if every edge is paired with an edge going in the opposite direction.
 
@@ -24,30 +24,30 @@ Undirected weighted graph:
 
 <img src="Images/WeightedUndirectedGraph.png" height="250" />
 
-And once again: An undireceted graph - it is a directed graph with every edge paired with an edge going in the opposite direction. This statement is clear on the image above.
+And once again: An undirected graph it is a directed graph with every edge paired with an edge going in the opposite direction. This statement is clear on the image above.
 
 Great! Now we are familiar with general concepts about graphs.
 
-# Dijkstra's algorithm
+# The Dijkstra's algorithm
 This [algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) was invented in 1956 by Edsger W. Dijkstra.
 
-It can be used, when you have one source vertex and want to find the shortest paths to ALL other vertices in the graph.
+It can be used when you have one source vertex and want to find the shortest paths to ALL other vertices in the graph.
 
-The best example is road network. If you wnat to find the shortest path from your house to your job, or if you want to find the closest store to your house, then it is time for the Dijkstra's algorithm.
+The best example is a road network. If you want to find the shortest path from your house to your job or if you want to find the closest store to your house then it is time for the Dijkstra's algorithm.
 
 The algorithm repeats following cycle until all vertices are marked as visited.
 Cycle:
-1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value, then algorithm picks any of them)
+1. From the non-visited vertices the algorithm picks a vertex with the shortest path length from the start (if there are more than one vertex with the same shortest path value then algorithm picks any of them)
 2. The algorithm marks picked vertex as visited.
-3. The algorithm check all of its neighbors. If the current vertex path length from the start plus an edge weight to a neighbor less than the neighbor current path length from the start, than it assigns new path length from the start to the neihgbor.
+3. The algorithm checks all of its neighbours. If the current vertex path length from the start plus an edge weight to a neighbour less than the neighbour current path length from the start than it assigns new path length from the start to the neighbour.
 When all vertices are marked as visited, the algorithm's job is done. Now, you can see the shortest path from the start for every vertex by pressing the one you are interested in.
 
 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 
-Let's imagine, 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 graph, that connects your house with all these stores. So, you know what to do :)
+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 :)
 
-### Initialization
+### Initialisation
 
 When the algorithm starts to work initial graph looks like this:
 
@@ -61,13 +61,13 @@ The table below represents graph state:
 | Path Length From Start    | inf | inf | inf | inf | inf |
 | Path Vertices From Start  | [ ] | [ ] | [ ] | [ ] | [ ] |
 
->inf is equal infinity, which basically means, that algorithm doesn't know how far away is this vertex from start one.
+>inf is equal infinity which basically means that algorithm doesn't know how far away is this vertex from start one.
 
 >F states for False
 
 >T states for True
 
-To initialize our graph we have to set source vertex path length from source vertex to 0, and append itself to path vertices from start.
+To initialize our graph we have to set source vertex path length from source vertex to 0 and append itself to path vertices from start.
 
 |                           |  A  |  B  |  C  |  D  |  E  |
 |:------------------------- |:---:|:---:|:---:|:---:|:---:|
@@ -75,11 +75,11 @@ To initialize our graph we have to set source vertex path length from source ver
 | Path Length From Start    |  0  | inf | inf | inf | inf |
 | Path Vertices From Start  | [A] | [ ] | [ ] | [ ] | [ ] |
 
-Great, now our graph is initialized and we can pass it to the Dijkstra's algorithm, let's start!
+Great, now our graph is initialised and we can pass it to the Dijkstra's algorithm, let's start!
 
-Let's follow the algorithm's cycle and pick the first vertex, which neighbors we want to check.
-All our vertices are not visited, but there is only one has the smallest path length from start - A. This vertex is the first one, which neighbors we will check.
-First of all, set this vertex as visited 
+Let's follow the algorithm's cycle and pick the first vertex which neighbours we want to check.
+All our vertices are not visited but there is only one has the smallest path length from start. It is A. This vertex is the first one which neighbors we will check.
+First of all, set this vertex as visited.
 
 A.visited = true
 
@@ -95,8 +95,8 @@ After this step graph has this state:
 
 ### Step 1
 
-Then we check all of its neighbors. 
-If checking vertex path length from start + edge weigth is smaller than neighbor's path length from start, then we set neighbor's path length from start new value and append to its pathVerticesFromStart array new vertex: checkingVertex. Repeat this action for every vertex.
+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:
 ```swift
@@ -162,25 +162,25 @@ From now we repeat all actions again and fill our table with new info!
 
 
 ## Code implementation 
-First of all, lets create class, that will describe any Vertex in the graph.
+First of all, let’s create class that will describe any Vertex in the graph.
 It is pretty simple
 ```swift
 open class Vertex {
 
-    //Every vertex should be unique, that's why we set up identifier
+    //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 use cases, 
-    //when you firstly initialize all vertices without neighbors. And then on next interation set up thei neighbors. So, initially neighbors is an empty array.
-    //Array contains tuples (Vertex, Double). Vertex is a neighbor and Double is as edge weight to that neighbor.
-    open var neighbors: [(Vertex, Double)] = []
+    //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 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 algorithm execution.
+    //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
 
-    //This array containt vertices, which we need to go through to reach this vertex from starting one
-    //As with path length from start, we will change this array during algorithm execution.
+    //This array contains vertices which we need to go through to reach this vertex from starting one
+    //As with path length from start, we will change this array during the algorithm execution.
     open var pathVerticesFromStart: [Vertex] = []
 
     public init(identifier: String) {
@@ -188,7 +188,7 @@ open class Vertex {
     }
 
     //This function let us use the same array of vertices again and again to calculate paths with different starting vertex.
-    //When we will need to set new starting vertex andd recalculate paths, then we will simply clear graph vertices' cashes.
+    //When we will need to set new starting vertex and recalculate paths then we will simply clear graph vertices' cashes.
     open func clearCache() {
         pathLengthFromStart = Double.infinity
         pathVerticesFromStart = []
@@ -196,7 +196,7 @@ open class Vertex {
 }
 ```
 
-Because every vertex should be unique it is usefull to make them Hashable and according Equatable. We use identifier for this purposes.
+As every vertex should be unique it is useful to make them Hashable and according Equatable. We use an identifier for this purposes.
 ```swift
 extension Vertex: Hashable {
     open var hashValue: Int {
@@ -212,11 +212,11 @@ extension Vertex: Equatable {
 ```
 
 We've created a base for our algorithm. Now let's create a house :)
-Dijkstra's realization is really straightforward.
+Dijkstra's realisation is really straightforward.
 ```swift
 public class Dijkstra {
     //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.
+    //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>
 
     public init(vertices: Set<Vertex>) {
@@ -230,52 +230,52 @@ public class Dijkstra {
     }
 
     public func findShortestPaths(from startVertex: Vertex) {
-	//Before we start searching shortes path from startVertex, 
-	//we need to clear vertices cache just to be sure, that out graph is as clean as a baby.
+	//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. 
-	//So whenever you change vertex outside of this class, it will affect this vertex inside totalVertices Set
+	//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 empty pathVerticesFromStart array.
+	//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.
+	//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 {
     			
-    	    //Nex line of code is an implementation of setting vertex as visited.
+    	    //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)
 			
-	    //filteredNeighbors is and arrray, that contains current vertex neighbors, which aren't yet visited
-            let filteredNeighbors = vertex.neighbors.filter { totalVertices.contains($0.0) }
+	    //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 neighbor in filteredNeighbors {
-		//These variable are more representative, than neighbor.0 or neighbor.1
-                let neighborVertex = neighbor.0
-                let weight = neighbor.1
+            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 neighbor. 
+		//Here we calculate new weight, that we can offer to neighbour. 
                 let theoreticNewWeight = vertex.pathLengthFromStart + weight
 				
-		//If it is smaller than neighbor's current pathLengthFromStart
+		//If it is smaller than neighbour's current pathLengthFromStart
 		//Then we perform this code
-                if theoreticNewWeight < neighborVertex.pathLengthFromStart {
+                if theoreticNewWeight < neighbourVertex.pathLengthFromStart {
 					
 		    //set new pathLengthFromStart
-                    neighborVertex.pathLengthFromStart = theoreticNewWeight
+                    neighbourVertex.pathLengthFromStart = theoreticNewWeight
 					
 		    //set new pathVerticesFromStart
-                    neighborVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
+                    neighbourVertex.pathVerticesFromStart = vertex.pathVerticesFromStart
 					
-		    //append current vertex to neighbor's pathVerticesFromStart
-                    neighborVertex.pathVerticesFromStart.append(neighborVertex)
+		    //append current vertex to neighbour's pathVerticesFromStart
+                    neighbourVertex.pathVerticesFromStart.append(neighbourVertex)
                 }
             }
 			
@@ -294,17 +294,17 @@ public class Dijkstra {
 }
 ```
 
-That's all! Now you can check this algorithm in the playground. On the main page there is a code for creating random graph.
+That's all! Now you can check this algorithm in the playground. On the main page there is a code for creating a random graph.
 
-Also there is a **VisualizedDijkstra.playground**. Use it to figure out algorithm's flow in real (slowed :)) time.
+Also there is a **VisualizedDijkstra.playground**. Use it to figure out the algorithm's flow in real (slowed :)) time.
 
-It is up to you how to implement some specific parts of algorithm, you can use Array instead of Set, add _visited_ property to Vertex or you can create some local totalVertices Array/Set inside _func findShortestPaths(from startVertex: Vertex)_ to keep totalVertices Array/Set unchanged. This is a general explanation with one possible implementation :)
+It is up to you how to implement some specific parts of the algorithm, you can use Array instead of Set, add _visited_ property to Vertex or you can create some local totalVertices Array/Set inside _func findShortestPaths(from startVertex: Vertex)_ to keep totalVertices Array/Set unchanged. This is a general explanation with one possible implementation :)
 
 # About this repository
 
-This repository contains to playgrounds:
-* To understand how does this algorithm works, I have created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover there are play/pause/stop buttons.
-* If you need only realization of the algorithm without visualization then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
+This repository contains two playgrounds:
+* To understand how does this algorithm works, I created **VisualizedDijkstra.playground.** It works in auto and interactive modes. Moreover, there are play/pause/stop buttons.
+* If you need only realisation of the algorithm without visualisation then run **Dijkstra.playground.** It contains necessary classes and couple functions to create random graph for algorithm testing.
 
 # Demo video
 

From 8c34127f87850c2e1b378310c5a9c0a3a69c10f4 Mon Sep 17 00:00:00 2001
From: Ravi <imrvshah@gmail.com>
Date: Wed, 21 Jun 2017 21:27:51 -0500
Subject: [PATCH 244/862] Updated project settings to Swift4

---
 Graph/Graph.xcodeproj/project.pbxproj         | 22 +++++++++++++++----
 .../xcshareddata/xcschemes/Graph.xcscheme     |  2 +-
 .../xcschemes/GraphTests.xcscheme             |  2 +-
 3 files changed, 20 insertions(+), 6 deletions(-)

diff --git a/Graph/Graph.xcodeproj/project.pbxproj b/Graph/Graph.xcodeproj/project.pbxproj
index ba07c3c26..4822d80bb 100644
--- a/Graph/Graph.xcodeproj/project.pbxproj
+++ b/Graph/Graph.xcodeproj/project.pbxproj
@@ -158,12 +158,12 @@
 			isa = PBXProject;
 			attributes = {
 				LastSwiftUpdateCheck = 0730;
-				LastUpgradeCheck = 0800;
+				LastUpgradeCheck = 0900;
 				ORGANIZATIONNAME = "Swift Algorithm Club";
 				TargetAttributes = {
 					49BFA2FC1CDF886B00522D66 = {
 						CreatedOnToolsVersion = 7.3;
-						LastSwiftMigration = 0820;
+						LastSwiftMigration = 0900;
 					};
 					49BFA3061CDF886B00522D66 = {
 						CreatedOnToolsVersion = 7.3;
@@ -247,14 +247,20 @@
 				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;
@@ -297,14 +303,20 @@
 				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;
@@ -349,7 +361,8 @@
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
 				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Debug;
 		};
@@ -370,7 +383,8 @@
 				PRODUCT_BUNDLE_IDENTIFIER = "com.swift-algorithm-club.Graph";
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
-				SWIFT_VERSION = 3.0;
+				SWIFT_SWIFT3_OBJC_INFERENCE = Off;
+				SWIFT_VERSION = 4.0;
 			};
 			name = Release;
 		};
diff --git a/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme b/Graph/Graph.xcodeproj/xcshareddata/xcschemes/Graph.xcscheme
index c4750d846..a12d85dad 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 = "0800"
+   LastUpgradeVersion = "0900"
    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 42c83c5ad..28df1be50 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 = "0800"
+   LastUpgradeVersion = "0900"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"

From b9ef916383a476f053fdc88fb2c86d04a6d7a2c8 Mon Sep 17 00:00:00 2001
From: Ravi <imrvshah@gmail.com>
Date: Wed, 21 Jun 2017 21:31:47 -0500
Subject: [PATCH 245/862] Fixed some warnings related to Redundant conformance

---
 Graph/Graph/AdjacencyListGraph.swift   | 4 ++--
 Graph/Graph/AdjacencyMatrixGraph.swift | 2 +-
 Graph/Graph/Edge.swift                 | 2 +-
 Graph/Graph/Graph.swift                | 2 +-
 Graph/Graph/Vertex.swift               | 4 ++--
 5 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/Graph/Graph/AdjacencyListGraph.swift b/Graph/Graph/AdjacencyListGraph.swift
index 4a84129df..a24e732e7 100644
--- a/Graph/Graph/AdjacencyListGraph.swift
+++ b/Graph/Graph/AdjacencyListGraph.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-private class EdgeList<T> where T: Equatable, T: Hashable {
+private class EdgeList<T> where T: Hashable {
 
   var vertex: Vertex<T>
   var edges: [Edge<T>]?
@@ -22,7 +22,7 @@ private class EdgeList<T> where T: Equatable, T: Hashable {
 
 }
 
-open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashable {
+open class AdjacencyListGraph<T>: AbstractGraph<T> where T: Hashable {
 
   fileprivate var adjacencyList: [EdgeList<T>] = []
 
diff --git a/Graph/Graph/AdjacencyMatrixGraph.swift b/Graph/Graph/AdjacencyMatrixGraph.swift
index 1b12790d8..4d3ae9731 100644
--- a/Graph/Graph/AdjacencyMatrixGraph.swift
+++ b/Graph/Graph/AdjacencyMatrixGraph.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Equatable, T: Hashable {
+open class AdjacencyMatrixGraph<T>: AbstractGraph<T> where T: Hashable {
 
   // If adjacencyMatrix[i][j] is not nil, then there is an edge from
   // vertex i to vertex j.
diff --git a/Graph/Graph/Edge.swift b/Graph/Graph/Edge.swift
index 28ef91834..ac5ed6a25 100644
--- a/Graph/Graph/Edge.swift
+++ b/Graph/Graph/Edge.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-public struct Edge<T>: Equatable where T: Equatable, T: Hashable {
+public struct Edge<T>: Equatable where T: Hashable {
 
   public let from: Vertex<T>
   public let to: Vertex<T>
diff --git a/Graph/Graph/Graph.swift b/Graph/Graph/Graph.swift
index 13d6802b9..ddae4eddd 100644
--- a/Graph/Graph/Graph.swift
+++ b/Graph/Graph/Graph.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-open class AbstractGraph<T>: CustomStringConvertible where T: Equatable, T: Hashable {
+open class AbstractGraph<T>: CustomStringConvertible where T: Hashable {
 
   public required init() {}
 
diff --git a/Graph/Graph/Vertex.swift b/Graph/Graph/Vertex.swift
index 42a7dad7b..758a367bb 100644
--- a/Graph/Graph/Vertex.swift
+++ b/Graph/Graph/Vertex.swift
@@ -7,7 +7,7 @@
 
 import Foundation
 
-public struct Vertex<T>: Equatable where T: Equatable, T: Hashable {
+public struct Vertex<T>: Equatable where T: Hashable {
 
   public var data: T
   public let index: Int
@@ -30,7 +30,7 @@ extension Vertex: Hashable {
 
 }
 
-public func ==<T: Equatable>(lhs: Vertex<T>, rhs: Vertex<T>) -> Bool {
+public func ==<T>(lhs: Vertex<T>, rhs: Vertex<T>) -> Bool {
   guard lhs.index == rhs.index else {
     return false
   }

From 89b337def3b3af1dea8a5d6223346dade373bb94 Mon Sep 17 00:00:00 2001
From: remlostime <remlostime@gmail.com>
Date: Sat, 24 Jun 2017 09:06:34 -0700
Subject: [PATCH 246/862] Ordered Set - Apple Version

https://developer.apple.com/documentation/foundation/nsmutableorderedset

In this repo, the ordered set is actually not the right apple library ordered set. So, I write the one exactly the same as Apple one.
---
 .../AppleOrderedSet.playground/Contents.swift | 13 ++++
 .../Sources/AppleOrderedSet.swift             | 72 +++++++++++++++++++
 .../contents.xcplayground                     |  4 ++
 Ordered Set/AppleOrderedSet.swift             | 72 +++++++++++++++++++
 .../contents.xcworkspacedata                  |  6 ++
 5 files changed, 167 insertions(+)
 create mode 100644 Ordered Set/AppleOrderedSet.playground/Contents.swift
 create mode 100644 Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift
 create mode 100644 Ordered Set/AppleOrderedSet.playground/contents.xcplayground
 create mode 100644 Ordered Set/AppleOrderedSet.swift

diff --git a/Ordered Set/AppleOrderedSet.playground/Contents.swift b/Ordered Set/AppleOrderedSet.playground/Contents.swift
new file mode 100644
index 000000000..4388c664b
--- /dev/null
+++ b/Ordered Set/AppleOrderedSet.playground/Contents.swift	
@@ -0,0 +1,13 @@
+let s = AppleOrderedSet<Int>()
+
+s.add(1)
+s.add(2)
+s.add(-1)
+s.add(0)
+s.insert(4, at: 3)
+
+s.set(-1, at: 0)
+s.remove(-1)
+
+print(s.object(at: 1))
+
diff --git a/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift
new file mode 100644
index 000000000..3ff19cb8d
--- /dev/null
+++ b/Ordered Set/AppleOrderedSet.playground/Sources/AppleOrderedSet.swift	
@@ -0,0 +1,72 @@
+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
+        }
+    }
+}
diff --git a/Ordered Set/AppleOrderedSet.playground/contents.xcplayground b/Ordered Set/AppleOrderedSet.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/Ordered Set/AppleOrderedSet.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/Ordered Set/AppleOrderedSet.swift b/Ordered Set/AppleOrderedSet.swift
new file mode 100644
index 000000000..3ff19cb8d
--- /dev/null
+++ b/Ordered Set/AppleOrderedSet.swift	
@@ -0,0 +1,72 @@
+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
+        }
+    }
+}
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index ebc2fb33b..59852e045 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -1645,6 +1645,12 @@
       <FileRef
          location = "group:OrderedSet.swift">
       </FileRef>
+      <FileRef
+         location = "group:AppleOrderedSet.swift">
+      </FileRef>
+      <FileRef
+         location = "group:AppleOrderedSet.playground">
+      </FileRef>
       <FileRef
          location = "group:README.markdown">
       </FileRef>

From 88e76dbb4e8fab288c683fc74505ab7c5b39f436 Mon Sep 17 00:00:00 2001
From: Brian Young <bdy-github@hiddentower.com>
Date: Sun, 9 Jul 2017 22:32:11 -0700
Subject: [PATCH 247/862] Add links to SortedArray Type

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

diff --git a/Ordered Array/README.markdown b/Ordered Array/README.markdown
index 974a42cae..c40e5eff5 100644
--- a/Ordered Array/README.markdown	
+++ b/Ordered Array/README.markdown	
@@ -110,4 +110,6 @@ The big difference with a regular binary search is that this doesn't return `nil
 
 Note that using binary search doesn't change the worst-case running time complexity of `insert()`. The binary search itself takes only **O(log n)** time, but inserting a new object in the middle of an array still involves shifting all remaining elements in memory. So overall, the time complexity is still **O(n)**. But in practice this new version definitely is a lot faster, especially on large arrays.
 
+A more complete and production ready [SortedArray](https://github.com/ole/SortedArray) is avalible from [Ole Begemann](https://github.com/ole). The [accompanying article](https://oleb.net/blog/2017/02/sorted-array/) explains to advantages and tradeoffs.
+
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From 6ee39fea58b47e0797401f81ee86c099bfc6fe57 Mon Sep 17 00:00:00 2001
From: Brian Young <bdy-github@hiddentower.com>
Date: Sun, 9 Jul 2017 22:33:19 -0700
Subject: [PATCH 248/862] typo fix

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

diff --git a/Ordered Array/README.markdown b/Ordered Array/README.markdown
index c40e5eff5..42c9880a3 100644
--- a/Ordered Array/README.markdown	
+++ b/Ordered Array/README.markdown	
@@ -110,6 +110,6 @@ The big difference with a regular binary search is that this doesn't return `nil
 
 Note that using binary search doesn't change the worst-case running time complexity of `insert()`. The binary search itself takes only **O(log n)** time, but inserting a new object in the middle of an array still involves shifting all remaining elements in memory. So overall, the time complexity is still **O(n)**. But in practice this new version definitely is a lot faster, especially on large arrays.
 
-A more complete and production ready [SortedArray](https://github.com/ole/SortedArray) is avalible from [Ole Begemann](https://github.com/ole). The [accompanying article](https://oleb.net/blog/2017/02/sorted-array/) explains to advantages and tradeoffs.
+A more complete and production ready [SortedArray](https://github.com/ole/SortedArray) is avalible from [Ole Begemann](https://github.com/ole). The [accompanying article](https://oleb.net/blog/2017/02/sorted-array/) explains the advantages and tradeoffs.
 
 *Written for Swift Algorithm Club by Matthijs Hollemans*

From df1440e2a74d37d7674efbd83c68fbcf9b680b95 Mon Sep 17 00:00:00 2001
From: Mayur <jhonmathews@gmail.com>
Date: Fri, 14 Jul 2017 11:39:18 +0530
Subject: [PATCH 249/862] Updated README for clarity

There was a typo in the line that has been changed. The sentence itself has been altered slightly to accommodate the fix for the typo and maintain clarity.
---
 Hash Table/README.markdown | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Hash Table/README.markdown b/Hash Table/README.markdown
index 8f1eaaf70..9c4065a51 100644
--- a/Hash Table/README.markdown	
+++ b/Hash Table/README.markdown	
@@ -103,7 +103,7 @@ it first hashes the key `"lastName"` to calculate the array index, which is 3. S
 
 Common ways to implement this chaining mechanism are to use a linked list or another array. Since the order of the items in the chain does not matter, you can think of it as a set instead of a list. (Now you can also imagine where the term "bucket" comes from; we just dump all the objects together into the bucket.)
 
-Chains should not become long because the slow process of looking up items in the hash table. Ideally, we would have no chains at all, but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets using high-quality hash functions.
+Chains should not become long because looking up items in the hash table would become a slow process. Ideally, we would have no chains at all, but in practice it is impossible to avoid collisions. You can improve the odds by giving the hash table enough buckets using high-quality hash functions.
 
 > **Note:** An alternative to chaining is "open addressing". The idea is this: if an array index is already taken, we put the element in the next unused bucket. This approach has its own upsides and downsides.
 

From 4fc84eeecfc2238791e338dd8537745b39656791 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvinlau@Kelvins-MacBook-Pro.local>
Date: Sat, 15 Jul 2017 17:34:25 -0700
Subject: [PATCH 250/862] Adds reference to the Apple version of the ordered
 set.

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

diff --git a/Ordered Set/README.markdown b/Ordered Set/README.markdown
index 1c0d5a8ac..bc5003a61 100644
--- a/Ordered Set/README.markdown	
+++ b/Ordered Set/README.markdown	
@@ -329,4 +329,9 @@ The right side did not contain the item, so we look at the left side:
 
 Finally, we've found `Player 2`, and return index 3.
 
+## See Also
+
+[Apple Ordered Set](AppleOrderedSet.playground)
+@remlostime added an Apple version of `OrderedSet`
+
 *Written By Zain Humayun*

From 5616f825c10be7bc0b81b538e7679fafab5d0f4f Mon Sep 17 00:00:00 2001
From: ck <remlostime@gmail.com>
Date: Mon, 17 Jul 2017 09:14:40 -0700
Subject: [PATCH 251/862] LRU Cache

Implement a simple LRU Cache algorithm.
---
 LRU Cache/LRUCache.playground/Contents.swift  |  10 +
 .../Sources/LRUCache.swift                    |  59 +++++
 .../Sources/LinkedList.swift                  | 246 ++++++++++++++++++
 .../LRUCache.playground/contents.xcplayground |   4 +
 LRU Cache/LRUCache.swift                      |  59 +++++
 LRU Cache/Readme.md                           |  50 ++++
 .../contents.xcworkspacedata                  |  13 +
 7 files changed, 441 insertions(+)
 create mode 100644 LRU Cache/LRUCache.playground/Contents.swift
 create mode 100644 LRU Cache/LRUCache.playground/Sources/LRUCache.swift
 create mode 100755 LRU Cache/LRUCache.playground/Sources/LinkedList.swift
 create mode 100644 LRU Cache/LRUCache.playground/contents.xcplayground
 create mode 100644 LRU Cache/LRUCache.swift
 create mode 100644 LRU Cache/Readme.md

diff --git a/LRU Cache/LRUCache.playground/Contents.swift b/LRU Cache/LRUCache.playground/Contents.swift
new file mode 100644
index 000000000..35dcc5d59
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/Contents.swift	
@@ -0,0 +1,10 @@
+let cache = LRUCache<String>(2)
+cache.set("a", val: 1)
+cache.set("b", val: 2)
+cache.get("a") // returns 1
+cache.set("c", val: 3) // evicts key "b"
+cache.get("b") // returns nil (not found)
+cache.set("d", val: 4) // evicts key "a"
+cache.get("a") // returns nil (not found)
+cache.get("c") // returns 3
+cache.get("d") // returns 4
diff --git a/LRU Cache/LRUCache.playground/Sources/LRUCache.swift b/LRU Cache/LRUCache.playground/Sources/LRUCache.swift
new file mode 100644
index 000000000..3b9ca1139
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/Sources/LRUCache.swift	
@@ -0,0 +1,59 @@
+//
+//  LRUCache.swift
+//  
+//
+//  Created by Kai Chen on 16/07/2017.
+//
+//
+
+import Foundation
+
+public class LRUCache<KeyType: Hashable> {
+    private let maxSize: Int
+    private var cache: [KeyType: Any] = [:]
+    private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
+    private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
+
+    public init(_ maxSize: Int) {
+        self.maxSize = maxSize
+    }
+
+    public func get(_ key: KeyType) -> Any? {
+        guard let val = cache[key] else {
+            return nil
+        }
+
+        remove(key)
+        insert(key, val: val)
+
+        return val
+    }
+
+    public func set(_ key: KeyType, val: Any) {
+        if cache[key] != nil {
+            remove(key)
+        } else if priority.count >= maxSize, let keyToRemove = priority.last?.value {
+            remove(keyToRemove)
+        }
+
+        insert(key, val: val)
+    }
+
+    private func remove(_ key: KeyType) {
+        cache.removeValue(forKey: key)
+        guard let node = key2node[key] else {
+            return
+        }
+        priority.remove(node: node)
+        key2node.removeValue(forKey: key)
+    }
+
+    private func insert(_ key: KeyType, val: Any) {
+        cache[key] = val
+        priority.insert(key, atIndex: 0)
+        guard let first = priority.first else {
+            return
+        }
+        key2node[key] = first
+    }
+}
diff --git a/LRU Cache/LRUCache.playground/Sources/LinkedList.swift b/LRU Cache/LRUCache.playground/Sources/LinkedList.swift
new file mode 100755
index 000000000..94e978c07
--- /dev/null
+++ b/LRU Cache/LRUCache.playground/Sources/LinkedList.swift	
@@ -0,0 +1,246 @@
+public final class LinkedList<T> {
+
+    public class LinkedListNode<T> {
+        var value: T
+        var next: LinkedListNode?
+        weak var previous: LinkedListNode?
+
+        public init(value: T) {
+            self.value = value
+        }
+    }
+
+    public typealias Node = LinkedListNode<T>
+
+    fileprivate var head: Node?
+
+    public init() {}
+
+    public var isEmpty: Bool {
+        return head == nil
+    }
+
+    public var first: Node? {
+        return head
+    }
+
+    public var last: Node? {
+        if var node = head {
+            while case let next? = node.next {
+                node = next
+            }
+            return node
+        } else {
+            return nil
+        }
+    }
+
+    public var count: Int {
+        if var node = head {
+            var c = 1
+            while case let next? = node.next {
+                node = next
+                c += 1
+            }
+            return c
+        } 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
+            }
+        }
+        return nil
+    }
+
+    public subscript(index: Int) -> T {
+        let node = self.node(atIndex: index)
+        assert(node != nil)
+        return node!.value
+    }
+
+    public func append(_ value: T) {
+        let newNode = Node(value: value)
+        self.append(newNode)
+    }
+
+    public func append(_ node: Node) {
+        let newNode = LinkedListNode(value: node.value)
+        if let lastNode = last {
+            newNode.previous = lastNode
+            lastNode.next = newNode
+        } else {
+            head = newNode
+        }
+    }
+
+    public func append(_ list: LinkedList) {
+        var nodeToCopy = list.head
+        while let node = nodeToCopy {
+            self.append(node.value)
+            nodeToCopy = node.next
+        }
+    }
+
+    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 {
+            head = 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
+        }
+        prev?.next = next
+        next?.previous = prev
+    }
+
+    public func removeAll() {
+        head = nil
+    }
+
+    @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
+    }
+
+    @discardableResult public func removeLast() -> T {
+        assert(!isEmpty)
+        return remove(node: last!)
+    }
+
+    @discardableResult public func remove(atIndex index: Int) -> T {
+        let node = self.node(atIndex: index)
+        assert(node != nil)
+        return remove(node: node!)
+    }
+}
+
+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 += ", " }
+        }
+        return s + "]"
+    }
+}
+
+extension LinkedList {
+    public func reverse() {
+        var node = head
+        while let currentNode = node {
+            node = currentNode.next
+            swap(&currentNode.next, &currentNode.previous)
+            head = currentNode
+        }
+    }
+}
+
+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
+        }
+        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
+        }
+        return result
+    }
+}
+
+extension LinkedList {
+    convenience init(array: Array<T>) {
+        self.init()
+
+        for element in array {
+            self.append(element)
+        }
+    }
+}
+
+extension LinkedList: ExpressibleByArrayLiteral {
+  public convenience init(arrayLiteral elements: T...) {
+    self.init()
+
+    for element in elements {
+      self.append(element)
+    }
+  }
+}
diff --git a/LRU Cache/LRUCache.playground/contents.xcplayground b/LRU Cache/LRUCache.playground/contents.xcplayground
new file mode 100644
index 000000000..5da2641c9
--- /dev/null
+++ b/LRU Cache/LRUCache.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/LRU Cache/LRUCache.swift b/LRU Cache/LRUCache.swift
new file mode 100644
index 000000000..4bfb3eabc
--- /dev/null
+++ b/LRU Cache/LRUCache.swift	
@@ -0,0 +1,59 @@
+//
+//  LRUCache.swift
+//
+//
+//  Created by Kai Chen on 16/07/2017.
+//
+//
+
+import Foundation
+
+public class LRUCache<KeyType: Hashable> {
+    private let maxSize: Int
+    private var cache: [KeyType: Any] = [:]
+    private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
+    private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
+
+    public init(_ maxSize: Int) {
+        self.maxSize = maxSize
+    }
+
+    public func get(_ key: KeyType) -> Any? {
+        guard let val = cache[key] else {
+            return nil
+        }
+
+        remove(key)
+        insert(key, val: val)
+
+        return val
+    }
+
+    public func set(_ key: KeyType, val: Any) {
+        if cache[key] != nil {
+            remove(key)
+        } else if priority.count >= maxSize, let keyToRemove = priority.last?.value {
+            remove(keyToRemove)
+        }
+
+        insert(key, val: val)
+    }
+
+    private func remove(_ key: KeyType) {
+        cache.removeValue(forKey: key)
+        guard let node = key2node[key] else {
+            return
+        }
+        priority.remove(node: node)
+        key2node.removeValue(forKey: key)
+    }
+
+    private func insert(_ key: KeyType, val: Any) {
+        cache[key] = val
+        priority.insert(key, atIndex: 0)
+        guard let first = priority.first else {
+            return
+        }
+        key2node[key] = first
+    }
+}
diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
new file mode 100644
index 000000000..c9a5de7a4
--- /dev/null
+++ b/LRU Cache/Readme.md	
@@ -0,0 +1,50 @@
+# LRU Cache
+
+[Least Recently Used][1] (LRU) is a popular algorithm in cache design. Here, we will try to write this algorithm ourselves.
+It should support the 2 operations: `get(key)` and `set(key, value)`.
+
+## Solution
+The key point in this algorithm is how to  maintain a priority queue when we do `get` and `set`.  Let’s say we have `priority` list, the priority is ranked from high to low. So, head has the highest priority and tail has the lowest priority. 
+
+There will be 2 key operations related to this queue. 
+* Remove element
+* Insert element
+
+Each time we access an element, either `set` or `get` we need to insert the element in the head of priority list. The `insert` operation will be look like this.
+
+```swift
+private func insert(_ key: KeyType, val: Any) {
+	cache[key] = val
+	priority.insert(key, atIndex: 0)
+	guard let first = priority.first else {
+		return
+	}
+	key2node[key]() = first
+}
+```
+
+Each time, when we `set`, the cache size maybe already full. In this case, we need to `remove` the lowest priority node. The operation is like this.
+
+```swift
+private func remove(_ key: KeyType) {
+	cache.removeValue(key)
+	guard let node = key2node[key] else {
+		return
+	}
+	priority.remove(node)
+	key2node.removeValue(key)
+}
+```
+
+
+Other hard part in this problem is usually find the element in the list will cost `O(n)` time. So, that's the bottleneck for `set` and `get` . It could slow down the whole cache alorightm. Is there a way to reduce this time complexity? The key idea here is to find a way to look up the element in the list fast. So, how about record the element position in the list. Then each time we just ask this record data structe to give us the element position in the list. So, that will be `O(1)` time, right? Aha, you got it. Which kind of data structe will have `O(1)` time? It's hash table. So, we use hash table to maintain the node's position. Here is the code.
+
+```swift
+private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
+private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
+```
+
+
+
+
+[1]:	https://en.wikipedia.org/wiki/Cache_replacement_policies#LRU
diff --git a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
index ebc2fb33b..d92007304 100644
--- a/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
+++ b/swift-algorithm-club.xcworkspace/contents.xcworkspacedata
@@ -25,6 +25,19 @@
    <FileRef
       location = "group:Why Algorithms.markdown">
    </FileRef>
+   <Group
+      location = "container:"
+      name = "LRU Cache">
+      <FileRef
+         location = "group:LRU Cache/LRUCache.playground">
+      </FileRef>
+      <FileRef
+         location = "group:LRU Cache/LRUCache.swift">
+      </FileRef>
+      <FileRef
+         location = "group:LRU Cache/Readme.md">
+      </FileRef>
+   </Group>
    <Group
       location = "group:Miller-Rabin Primality Test"
       name = "Miller-Rabin Primality Test">

From 955bae283ab5d385f5bb62009b9af70aab301689 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 12:34:12 -0700
Subject: [PATCH 252/862] Fixes indentation of code to 2 spaces

---
 LRU Cache/LRUCache.swift | 86 ++++++++++++++++++++--------------------
 1 file changed, 43 insertions(+), 43 deletions(-)

diff --git a/LRU Cache/LRUCache.swift b/LRU Cache/LRUCache.swift
index 4bfb3eabc..4d15599de 100644
--- a/LRU Cache/LRUCache.swift	
+++ b/LRU Cache/LRUCache.swift	
@@ -9,51 +9,51 @@
 import Foundation
 
 public class LRUCache<KeyType: Hashable> {
-    private let maxSize: Int
-    private var cache: [KeyType: Any] = [:]
-    private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
-    private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
-
-    public init(_ maxSize: Int) {
-        self.maxSize = maxSize
+  private let maxSize: Int
+  private var cache: [KeyType: Any] = [:]
+  private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
+  private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
+  
+  public init(_ maxSize: Int) {
+    self.maxSize = maxSize
+  }
+  
+  public func get(_ key: KeyType) -> Any? {
+    guard let val = cache[key] else {
+      return nil
     }
-
-    public func get(_ key: KeyType) -> Any? {
-        guard let val = cache[key] else {
-            return nil
-        }
-
-        remove(key)
-        insert(key, val: val)
-
-        return val
+    
+    remove(key)
+    insert(key, val: val)
+    
+    return val
+  }
+  
+  public func set(_ key: KeyType, val: Any) {
+    if cache[key] != nil {
+      remove(key)
+    } else if priority.count >= maxSize, let keyToRemove = priority.last?.value {
+      remove(keyToRemove)
     }
-
-    public func set(_ key: KeyType, val: Any) {
-        if cache[key] != nil {
-            remove(key)
-        } else if priority.count >= maxSize, let keyToRemove = priority.last?.value {
-            remove(keyToRemove)
-        }
-
-        insert(key, val: val)
-    }
-
-    private func remove(_ key: KeyType) {
-        cache.removeValue(forKey: key)
-        guard let node = key2node[key] else {
-            return
-        }
-        priority.remove(node: node)
-        key2node.removeValue(forKey: key)
+    
+    insert(key, val: val)
+  }
+  
+  private func remove(_ key: KeyType) {
+    cache.removeValue(forKey: key)
+    guard let node = key2node[key] else {
+      return
     }
-
-    private func insert(_ key: KeyType, val: Any) {
-        cache[key] = val
-        priority.insert(key, atIndex: 0)
-        guard let first = priority.first else {
-            return
-        }
-        key2node[key] = first
+    priority.remove(node: node)
+    key2node.removeValue(forKey: key)
+  }
+  
+  private func insert(_ key: KeyType, val: Any) {
+    cache[key] = val
+    priority.insert(key, atIndex: 0)
+    guard let first = priority.first else {
+      return
     }
+    key2node[key] = first
+  }
 }

From 2cbed848bbeff4fe595658b532bb7e075af4cce3 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 12:38:11 -0700
Subject: [PATCH 253/862] Refactors some of the readme files.

---
 LRU Cache/Readme.md | 15 +++++++--------
 1 file changed, 7 insertions(+), 8 deletions(-)

diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
index c9a5de7a4..8c51cb6dc 100644
--- a/LRU Cache/Readme.md	
+++ b/LRU Cache/Readme.md	
@@ -1,14 +1,13 @@
 # LRU Cache
 
-[Least Recently Used][1] (LRU) is a popular algorithm in cache design. Here, we will try to write this algorithm ourselves.
-It should support the 2 operations: `get(key)` and `set(key, value)`.
+Caches are used to hold objects in memory. A caches size is finite; If the system doesn't have enough memory, the cache must be purged or the program will crash. [Least Recently Used][1] (LRU) is a popular algorithm in cache design. The idea is simple: In low memory situations, the oldest used member of the cache will be purged. A *priority queue* is used to enforce this behavior.
 
-## Solution
-The key point in this algorithm is how to  maintain a priority queue when we do `get` and `set`.  Let’s say we have `priority` list, the priority is ranked from high to low. So, head has the highest priority and tail has the lowest priority. 
+## The priority queue
 
-There will be 2 key operations related to this queue. 
-* Remove element
-* Insert element
+The key to the LRU cache is the priority queue. For simplicity, you'll model the queue using a linked list. All interactions with the LRU cache should respect this queue; Calling `get` and `set` should update the priority queue to reflect the most recently accessed element.
+
+
+### Operations
 
 Each time we access an element, either `set` or `get` we need to insert the element in the head of priority list. The `insert` operation will be look like this.
 
@@ -19,7 +18,7 @@ private func insert(_ key: KeyType, val: Any) {
 	guard let first = priority.first else {
 		return
 	}
-	key2node[key]() = first
+	key2node[key] = first
 }
 ```
 

From 87cae58bdc594217ca87c1e8b761bac74c5a7344 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 12:38:53 -0700
Subject: [PATCH 254/862] Added credits

---
 LRU Cache/Readme.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
index 8c51cb6dc..ada2c9f9a 100644
--- a/LRU Cache/Readme.md	
+++ b/LRU Cache/Readme.md	
@@ -43,7 +43,7 @@ private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
 private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
 ```
 
-
+*Written for the Swift Algorithm Club by Kai Chen, with additions by Kelvin Lau*
 
 
 [1]:	https://en.wikipedia.org/wiki/Cache_replacement_policies#LRU

From 6c36ae77085b71932900cdc89bacbfcd2219e542 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 12:46:12 -0700
Subject: [PATCH 255/862] Updates wording for performance considerations
 paragraph.

---
 LRU Cache/Readme.md | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
index ada2c9f9a..a268a667a 100644
--- a/LRU Cache/Readme.md	
+++ b/LRU Cache/Readme.md	
@@ -35,11 +35,13 @@ private func remove(_ key: KeyType) {
 }
 ```
 
+### Optimizing Performance
 
-Other hard part in this problem is usually find the element in the list will cost `O(n)` time. So, that's the bottleneck for `set` and `get` . It could slow down the whole cache alorightm. Is there a way to reduce this time complexity? The key idea here is to find a way to look up the element in the list fast. So, how about record the element position in the list. Then each time we just ask this record data structe to give us the element position in the list. So, that will be `O(1)` time, right? Aha, you got it. Which kind of data structe will have `O(1)` time? It's hash table. So, we use hash table to maintain the node's position. Here is the code.
+Removing elements from the priority queue is a frequent operation for the LRU cache. Since priority queue is modelled using a linked list, this is an expensive operation that costs `O(n)` time. This is the bottleneck for both the `set` and `get` methods.
 
-```swift
-private var priority: LinkedList<KeyType> = LinkedList<KeyType>()
+To help alleviate this problem, a hash table is used to store the references of each node:
+
+```
 private var key2node: [KeyType: LinkedList<KeyType>.LinkedListNode<KeyType>] = [:]
 ```
 

From 1de41865df6c9887c54b78bb35ede5847511f543 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 12:50:19 -0700
Subject: [PATCH 256/862] Refactors more of the readme.

---
 LRU Cache/Readme.md | 14 ++++++++++----
 1 file changed, 10 insertions(+), 4 deletions(-)

diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
index a268a667a..580fed0d8 100644
--- a/LRU Cache/Readme.md	
+++ b/LRU Cache/Readme.md	
@@ -1,15 +1,19 @@
 # LRU Cache
 
-Caches are used to hold objects in memory. A caches size is finite; If the system doesn't have enough memory, the cache must be purged or the program will crash. [Least Recently Used][1] (LRU) is a popular algorithm in cache design. The idea is simple: In low memory situations, the oldest used member of the cache will be purged. A *priority queue* is used to enforce this behavior.
+Caches are used to hold objects in memory. A caches size is finite; If the system doesn't have enough memory, the cache must be purged or the program will crash. [Least Recently Used][1] (LRU) is a popular algorithm in cache design.
+
+In this implementation of the LRU Cache, a size is declared during instantiation, and any insertions that go beyond the size will purge the least recently used element of the cache. A *priority queue* is used to enforce this behavior.
 
 ## The priority queue
 
 The key to the LRU cache is the priority queue. For simplicity, you'll model the queue using a linked list. All interactions with the LRU cache should respect this queue; Calling `get` and `set` should update the priority queue to reflect the most recently accessed element.
 
+### Interesting tidbits
+
 
-### Operations
+#### Adding values
 
-Each time we access an element, either `set` or `get` we need to insert the element in the head of priority list. The `insert` operation will be look like this.
+Each time we access an element, either `set` or `get` we need to insert the element in the head of priority list. We use a helper method to handle this procedure:
 
 ```swift
 private func insert(_ key: KeyType, val: Any) {
@@ -22,7 +26,9 @@ private func insert(_ key: KeyType, val: Any) {
 }
 ```
 
-Each time, when we `set`, the cache size maybe already full. In this case, we need to `remove` the lowest priority node. The operation is like this.
+#### Purging the cache
+
+When the cahce is full, a purge must take place starting with the least recently used element. In this case, we need to `remove` the lowest priority node. The operation is like this:
 
 ```swift
 private func remove(_ key: KeyType) {

From e7a0002ed4c1e653bdfb2d4673fabd30a1cf2505 Mon Sep 17 00:00:00 2001
From: Kelvin Lau <kelvin.kl.lau@gmail.com>
Date: Sun, 23 Jul 2017 13:00:58 -0700
Subject: [PATCH 257/862] Fixes a spelling mistake.

---
 LRU Cache/Readme.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/LRU Cache/Readme.md b/LRU Cache/Readme.md
index 580fed0d8..8e2941991 100644
--- a/LRU Cache/Readme.md	
+++ b/LRU Cache/Readme.md	
@@ -28,7 +28,7 @@ private func insert(_ key: KeyType, val: Any) {
 
 #### Purging the cache
 
-When the cahce is full, a purge must take place starting with the least recently used element. In this case, we need to `remove` the lowest priority node. The operation is like this:
+When the cache is full, a purge must take place starting with the least recently used element. In this case, we need to `remove` the lowest priority node. The operation is like this:
 
 ```swift
 private func remove(_ key: KeyType) {

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 258/862] 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 259/862] 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 260/862] 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 261/862] 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 262/862] 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 263/862] 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 264/862] 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 265/862] 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 266/862] 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 267/862] 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 268/862] 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 269/862] 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 270/862] [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 271/862] [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 272/862] [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 273/862] [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 274/862] [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 275/862] [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 276/862] [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 277/862] [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 278/862] [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 279/862] [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 280/862] 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 281/862] 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 282/862] [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 283/862] [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 284/862] [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 285/862] [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 286/862] [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 287/862] [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 288/862] [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 289/862] [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 290/862] 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 291/862] 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 292/862] 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 293/862] 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 294/862] 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 295/862] 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 296/862] 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 297/862] 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 298/862] 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 299/862] 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 300/862] [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 301/862] [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 302/862] [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 303/862] 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 304/862] 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 305/862] 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 306/862] 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 307/862] 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 308/862] [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 309/862] [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 310/862] [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 311/862] [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 312/862] [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 313/862] [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 314/862] [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 315/862] [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 316/862] 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 317/862] 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 318/862] 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 319/862] [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 320/862] [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 321/862] 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 322/862] 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 323/862] 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 324/862] 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 325/862] 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 326/862] 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 327/862] 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 328/862] 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 329/862] 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 330/862] 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 331/862] 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 332/862] 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 333/862] [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 334/862] [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 335/862] [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 336/862] [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 337/862] [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 338/862] [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 339/862] [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 340/862] [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 341/862] 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 342/862] 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 343/862] [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 344/862] 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 345/862] 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 */; };
+		7B80C3FE1C77A65E003CECC7 /* HashedHeapTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 7B80C3FD1C77A65E003CECC7 /* HashedHeapTests.swift */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXFileReference section */
+		7B2BBC801C779D720067B71D /* Hashed Heap Tests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "Hashed Heap Tests.xctest"; sourceTree = BUILT_PRODUCTS_DIR; };
+		7B2BBC941C779E7B0067B71D /* Info.plist */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = SOURCE_ROOT; };
+		7B80C3FB1C77A658003CECC7 /* HashedHeap.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; name = HashedHeap.swift; path = ../HashedHeap.swift; sourceTree = SOURCE_ROOT; };
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+/* End PBXFileReference section */
+
+/* Begin PBXFrameworksBuildPhase section */
+		7B2BBC7D1C779D720067B71D /* Frameworks */ = {
+			isa = PBXFrameworksBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC831C779D720067B71D /* Tests */,
+				7B2BBC721C779D710067B71D /* Products */,
+			);
+			sourceTree = "<group>";
+		};
+		7B2BBC721C779D710067B71D /* Products */ = {
+			isa = PBXGroup;
+			children = (
+				7B2BBC801C779D720067B71D /* Hashed Heap Tests.xctest */,
+			);
+			name = Products;
+			sourceTree = "<group>";
+		};
+		7B2BBC831C779D720067B71D /* Tests */ = {
+			isa = PBXGroup;
+			children = (
+				7B80C3FB1C77A658003CECC7 /* HashedHeap.swift */,
+				7B80C3FD1C77A65E003CECC7 /* HashedHeapTests.swift */,
+				7B2BBC941C779E7B0067B71D /* Info.plist */,
+			);
+			name = Tests;
+			sourceTree = "<group>";
+		};
+/* End PBXGroup section */
+
+/* Begin PBXNativeTarget section */
+		7B2BBC7F1C779D720067B71D /* Hashed Heap Tests */ = {
+			isa = PBXNativeTarget;
+			buildConfigurationList = 7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "Hashed Heap Tests" */;
+			buildPhases = (
+				7B2BBC7C1C779D720067B71D /* Sources */,
+				7B2BBC7D1C779D720067B71D /* Frameworks */,
+				7B2BBC7E1C779D720067B71D /* Resources */,
+			);
+			buildRules = (
+			);
+			dependencies = (
+			);
+			name = "Hashed Heap Tests";
+			productName = TestsTests;
+			productReference = 7B2BBC801C779D720067B71D /* Hashed Heap Tests.xctest */;
+			productType = "com.apple.product-type.bundle.unit-test";
+		};
+/* End PBXNativeTarget section */
+
+/* Begin PBXProject section */
+		7B2BBC691C779D710067B71D /* Project object */ = {
+			isa = PBXProject;
+			attributes = {
+				LastSwiftUpdateCheck = 0720;
+				LastUpgradeCheck = 0800;
+				ORGANIZATIONNAME = "Swift Algorithm Club";
+				TargetAttributes = {
+					7B2BBC7F1C779D720067B71D = {
+						CreatedOnToolsVersion = 7.2;
+						LastSwiftMigration = 0820;
+					};
+				};
+			};
+			buildConfigurationList = 7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Hashed Heap Tests" */;
+			compatibilityVersion = "Xcode 3.2";
+			developmentRegion = English;
+			hasScannedForEncodings = 0;
+			knownRegions = (
+				en,
+				Base,
+			);
+			mainGroup = 7B2BBC681C779D710067B71D;
+			productRefGroup = 7B2BBC721C779D710067B71D /* Products */;
+			projectDirPath = "";
+			projectRoot = "";
+			targets = (
+				7B2BBC7F1C779D720067B71D /* Hashed Heap Tests */,
+			);
+		};
+/* End PBXProject section */
+
+/* Begin PBXResourcesBuildPhase section */
+		7B2BBC7E1C779D720067B71D /* Resources */ = {
+			isa = PBXResourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXResourcesBuildPhase section */
+
+/* Begin PBXSourcesBuildPhase section */
+		7B2BBC7C1C779D720067B71D /* Sources */ = {
+			isa = PBXSourcesBuildPhase;
+			buildActionMask = 2147483647;
+			files = (
+				7B80C3FE1C77A65E003CECC7 /* HashedHeapTests.swift in Sources */,
+				7B80C3FC1C77A658003CECC7 /* HashedHeap.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
+/* End PBXSourcesBuildPhase section */
+
+/* Begin XCBuildConfiguration section */
+		7B2BBC871C779D720067B71D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				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_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 = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				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_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 = 10.11;
+				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;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 3.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "Hashed Heap Tests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				7B2BBC871C779D720067B71D /* Debug */,
+				7B2BBC881C779D720067B71D /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			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>
+      </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/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 346/862] [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
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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 347/862] 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 348/862] 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 349/862] 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 350/862] 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 351/862] 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 352/862] 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 353/862] 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 354/862] 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 355/862] 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 356/862] 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 357/862] 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 358/862] 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 359/862] 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 360/862] 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 361/862] 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 362/862] 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 363/862] 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 364/862] 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 365/862] 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 366/862] 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 367/862] 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 368/862] 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 369/862] 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 370/862] [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 371/862] [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 372/862] 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 373/862] 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 374/862] 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 375/862] [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 376/862] [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 377/862] [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 378/862] [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 379/862] [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 380/862] [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 381/862] [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 382/862] [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 383/862] [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 384/862] [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 385/862] [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 386/862] [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 387/862] [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 388/862] 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 389/862] [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 390/862] 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 391/862] 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 392/862] 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 393/862] 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 394/862] 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 395/862] 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 396/862] 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 397/862] 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 398/862] 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 399/862] 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 400/862] 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 401/862] 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 402/862] 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
index 0000000000000000000000000000000000000000..283bcca5d0a356323acf277f4266ae08c4eb09fd
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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 403/862] [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 404/862] [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 405/862] 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 406/862] 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 407/862] 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 408/862] 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 409/862] 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 410/862] 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 411/862] 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 412/862] 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 413/862] 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 414/862] 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 415/862] 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 416/862] 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 417/862] 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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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 418/862] 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 419/862] 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 420/862] 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
new file mode 100644
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literal 0
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 421/862] 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 422/862] 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 423/862] 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 424/862] 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 425/862] 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 426/862] 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 427/862] 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 428/862] 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 429/862] 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 430/862] 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 431/862] 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 432/862] 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 433/862] 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 434/862] 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 435/862] 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 436/862] 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 437/862] 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 438/862] 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 439/862] 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 440/862] 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 441/862] 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 442/862] 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 443/862] 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 444/862] 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 445/862] 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 446/862] 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 447/862] 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 448/862] 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 449/862] 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 450/862] 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 451/862] 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 452/862] 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 453/862] 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 454/862] 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 455/862] 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 456/862] 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 457/862] 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 458/862] 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 459/862] 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 460/862] 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 461/862] =?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 462/862] 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 463/862] 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 464/862] 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 465/862] 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 466/862] 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 467/862] 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 468/862] 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 469/862] 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 470/862] 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 471/862] 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 472/862] 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 473/862] 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 474/862] 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 475/862] 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 476/862] 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 477/862] 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 478/862] 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 479/862] 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 480/862] 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 481/862] 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 482/862] 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 483/862] 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 484/862] 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 485/862] 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 486/862] 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 487/862] 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 488/862] 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 489/862] 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 490/862] 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 491/862] 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 492/862] 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 493/862] 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 494/862] 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 495/862] 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 496/862] 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 497/862] 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 498/862] 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 499/862] 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 500/862] 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 501/862] 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 502/862] 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 503/862] 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 504/862] 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 */; };
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+		8EA8A3BC1F9F7B7100FD8BC0 /* Line2D.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Line2D.swift; sourceTree = "<group>"; };
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+		8EF612471F9E00E000267358 /* main.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = main.swift; sourceTree = "<group>"; };
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+
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+		8EF612411F9E00E000267358 /* Frameworks */ = {
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+			);
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+/* End PBXFrameworksBuildPhase section */
+
+/* Begin PBXGroup section */
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+				8EA8A3BA1F9F7B6300FD8BC0 /* Point2D.swift */,
+				8EA8A3BC1F9F7B7100FD8BC0 /* Line2D.swift */,
+			);
+			path = 2D;
+			sourceTree = "<group>";
+		};
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+			isa = PBXGroup;
+			children = (
+				8EF612461F9E00E000267358 /* Points Lines Planes */,
+				8EF612451F9E00E000267358 /* Products */,
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+				8EF612441F9E00E000267358 /* Points Lines Planes */,
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+				8EA8A3C21F9F7C9000FD8BC0 /* 2D */,
+			);
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+
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+			buildConfigurationList = 8EF6123F1F9E00DF00267358 /* Build configuration list for PBXProject "Points Lines Planes" */;
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+				8EA8A3BD1F9F7B7100FD8BC0 /* Line2D.swift in Sources */,
+			);
+			runOnlyForDeploymentPostprocessing = 0;
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+				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_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 = "Mac Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = dwarf;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_TESTABILITY = YES;
+				GCC_C_LANGUAGE_STANDARD = gnu11;
+				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 = 10.13;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_ACTIVE_COMPILATION_CONDITIONS = DEBUG;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+			};
+			name = Debug;
+		};
+		8EF6124A1F9E00E000267358 /* 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_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_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_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 = "Mac Developer";
+				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;
+				MACOSX_DEPLOYMENT_TARGET = 10.13;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule";
+			};
+			name = Release;
+		};
+		8EF6124C1F9E00E000267358 /* Debug */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CODE_SIGN_STYLE = Automatic;
+				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 4.0;
+			};
+			name = Debug;
+		};
+		8EF6124D1F9E00E000267358 /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				CODE_SIGN_STYLE = Automatic;
+				DEVELOPMENT_TEAM = 7C4LVS3ZVC;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_VERSION = 4.0;
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		8EF6123F1F9E00DF00267358 /* Build configuration list for PBXProject "Points Lines Planes" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				8EF612491F9E00E000267358 /* Debug */,
+				8EF6124A1F9E00E000267358 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		8EF6124B1F9E00E000267358 /* Build configuration list for PBXNativeTarget "Points Lines Planes" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				8EF6124C1F9E00E000267358 /* Debug */,
+				8EF6124D1F9E00E000267358 /* Release */,
+			);
+			defaultConfigurationIsVisible = 0;
+			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 505/862] 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 506/862] 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 507/862] 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 508/862] 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 509/862] 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 510/862] 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 511/862] 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 512/862] 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 513/862] 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 514/862] 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 515/862] 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 516/862] 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 = {
+
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+		};
+/* End PBXFrameworksBuildPhase section */
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+		7B2BBC681C779D710067B71D = {
+			isa = PBXGroup;
+			children = (
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+				7B2BBC721C779D710067B71D /* Products */,
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+			files = (
+			);
+			runOnlyForDeploymentPostprocessing = 0;
+		};
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+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
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+				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;
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+				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 = 10.11;
+				MTL_ENABLE_DEBUG_INFO = YES;
+				ONLY_ACTIVE_ARCH = YES;
+				SDKROOT = macosx;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+			};
+			name = Debug;
+		};
+		7B2BBC881C779D720067B71D /* Release */ = {
+			isa = XCBuildConfiguration;
+			buildSettings = {
+				ALWAYS_SEARCH_USER_PATHS = NO;
+				CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x";
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+				CLANG_WARN_BLOCK_CAPTURE_AUTORELEASING = YES;
+				CLANG_WARN_BOOL_CONVERSION = YES;
+				CLANG_WARN_COMMA = YES;
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+				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;
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+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
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+				CLANG_WARN_STRICT_PROTOTYPES = YES;
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+				CLANG_WARN_UNREACHABLE_CODE = YES;
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+				GCC_WARN_UNUSED_FUNCTION = YES;
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+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = macosx;
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+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+			};
+			name = Release;
+		};
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+			buildSettings = {
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+				PRODUCT_BUNDLE_IDENTIFIER = swift.algorithm.club.Tests;
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+				SWIFT_VERSION = 4.0;
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+			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;
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+				SWIFT_SWIFT3_OBJC_INFERENCE = Default;
+				SWIFT_VERSION = 4.0;
+			};
+			name = Release;
+		};
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+
+/* Begin XCConfigurationList section */
+		7B2BBC6C1C779D710067B71D /* Build configuration list for PBXProject "AStarTests" */ = {
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+		};
+		7B2BBC8C1C779D720067B71D /* Build configuration list for PBXNativeTarget "AStarTests" */ = {
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+				7B2BBC8E1C779D720067B71D /* Release */,
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+			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 517/862] 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 518/862] 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
index 0000000000000000000000000000000000000000..c0a4b1cc8fd31a372f6843f858703950a0adee4a
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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
new file mode 100644
index 0000000000000000000000000000000000000000..10b4300f406be65ffb0e356666ed5ce965b5ca32
GIT binary patch
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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
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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
index 0000000000000000000000000000000000000000..40a7008da206816baa056fa95d9f69c5b6db89ad
GIT binary patch
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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
new file mode 100644
index 0000000000000000000000000000000000000000..9e7baef2622aaea8538f6f4fcfce9fc732f5403d
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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 519/862] 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 520/862] 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 521/862] 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 522/862] 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 523/862] 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 524/862] 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 525/862] 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 526/862] 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 527/862] 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 528/862] 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 529/862] 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 530/862] 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 531/862] 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 532/862] 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 533/862] 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 534/862] [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 535/862] 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 536/862] 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 537/862] 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 538/862] 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 539/862] 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 540/862] 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 541/862] 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 542/862] 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 543/862] - 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 544/862] 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 545/862] 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 546/862] 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 547/862] 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 548/862] 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 549/862] 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 550/862] 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 551/862] 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 552/862] 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 553/862] 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 554/862] 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 555/862] 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 556/862] 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 557/862] 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 558/862] 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 559/862] 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 560/862] 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 561/862] 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 562/862] 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 563/862] 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 564/862] 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 565/862] 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 566/862] :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 567/862] :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 568/862] :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 569/862] :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 570/862] :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 571/862] 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 572/862] 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 573/862] 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 574/862] 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 575/862] 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 576/862] 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 577/862] 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 578/862] 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 579/862] 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 580/862] 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 581/862] 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 582/862] 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 583/862] 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 584/862] 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
new file mode 100644
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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 585/862] 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 586/862] 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 587/862] 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 588/862] 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 589/862] 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 590/862] 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 591/862] 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 592/862] 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 593/862] 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 594/862] 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 595/862] 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 596/862] 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 597/862] 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 598/862] 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 599/862] 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 600/862] [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 601/862] 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 602/862] 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 603/862] 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 604/862] 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 605/862] 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 606/862] 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 607/862] 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 608/862] 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 609/862] 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 610/862] 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 611/862] 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 612/862] 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 613/862] [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 614/862] 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 615/862] 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 616/862] 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 617/862] 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 618/862] 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 619/862] 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 620/862] 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 621/862] 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 622/862] 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 623/862] 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 624/862] 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 625/862] 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 626/862] [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 627/862] [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 628/862] [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 629/862] 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 630/862] [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 631/862] 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 632/862] 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 633/862] 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 634/862] 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 635/862] 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 636/862] 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 637/862] 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 638/862] 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 639/862] 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 640/862] 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 641/862] [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 642/862] [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 643/862] [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 644/862] [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 645/862] [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 646/862] [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 647/862] [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 648/862] [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 649/862] 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 650/862] 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 651/862] 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 652/862] 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 653/862] 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 654/862] [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 655/862] [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 656/862] [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 657/862] 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 658/862] 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 659/862] [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 660/862] [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 661/862] [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 */; };
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+				GCC_NO_COMMON_BLOCKS = YES;
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+				GCC_PREPROCESSOR_DEFINITIONS = (
+					"DEBUG=1",
+					"$(inherited)",
+				);
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+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				INFOPLIST_FILE = Tests/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/../Frameworks",
+					"@loader_path/../Frameworks",
+				);
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+			};
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+		};
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+				CLANG_WARN_COMMA = YES;
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+				CLANG_WARN_EMPTY_BODY = YES;
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+				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 662/862] [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 663/862] [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 664/862] 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 665/862] 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 666/862] 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 667/862] [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 668/862] 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 669/862] 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 670/862] 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 671/862] 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 672/862] 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 673/862] 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 674/862] 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 675/862] 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 676/862] 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 677/862] 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 678/862] 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 679/862] 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 680/862] 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 681/862] 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 682/862] 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 683/862] 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 684/862] 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 685/862] 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 686/862] 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 687/862] 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 688/862] 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 689/862] 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 690/862] 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 691/862] [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 692/862] 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 693/862] 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 694/862] 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
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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 695/862] 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 696/862] 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 697/862] 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 698/862] 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 699/862] 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 700/862] 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 701/862] 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 702/862] 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 703/862] 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 704/862] 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 705/862] 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 706/862] 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 707/862] 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 708/862] 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 709/862] 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 710/862] [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 711/862] 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 712/862] [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 713/862] [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 714/862] 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 715/862] 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 716/862] 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 717/862] 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 718/862] 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 719/862] 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 720/862] 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 721/862] 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 722/862] 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 723/862] 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 724/862] 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 725/862] 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 726/862] 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 727/862] 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 728/862] 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 729/862] 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 730/862] 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 731/862] 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 732/862] 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 733/862] 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 734/862] 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 735/862] 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 736/862] 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 737/862] 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 738/862] 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 739/862] 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 740/862] 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 741/862] 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 742/862] 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 743/862] 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 744/862] 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 745/862] 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 746/862] 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 747/862] 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
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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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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
zZ}#D4fq$h!)7Ew3rR#O!P(-io3<tXsiP{HroYl4@Ts8h=Fd1r>$Ik7Vr$+Us66*tv
zk>u?)+oewHlFhWl$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
z-zMwvl6`VRDB<zfH#YkH8)MqWy&FTW%v6QG<vSb<&175&&h?tJP}JU6g+9#`Is6+$
zAG}P^U=9BuN(BFmNr!fam8hd*PKM>$kV~$oNfYlQ=}>)Jx@twF{+AI?)Ks_NU$WYg
WO2$%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 748/862] 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 749/862] 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 750/862] 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 751/862] 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 752/862] [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 753/862] [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 754/862] [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 755/862] [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 756/862] 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 757/862] 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 758/862] 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 759/862] 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 760/862] [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 761/862] 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 762/862] 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 763/862] 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 764/862] 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 765/862] 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 766/862] 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 767/862] 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 768/862] 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 769/862] 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 770/862] 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 771/862] 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 772/862] 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 773/862] 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 774/862] 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 775/862] 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 776/862] 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 777/862] 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 778/862] 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 779/862] [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 780/862] 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 781/862] 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 782/862] 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 783/862] 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 784/862] 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 785/862] 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 786/862] 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 787/862] 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 788/862] 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 789/862] 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 790/862] 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 791/862] 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 792/862] 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 793/862] 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 794/862] 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 795/862] 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 796/862] 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 797/862] 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 798/862] 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 799/862] 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 800/862] 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 801/862] 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 802/862] 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 803/862] 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 804/862] 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 805/862] 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 806/862] 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 807/862] 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 808/862] 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 809/862] 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 810/862] 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 811/862] 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 812/862] 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 813/862] 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 814/862] 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>
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-         location = "group:/Users/a14757/Documents/Commiter/swift-algorithm-club/Myers Difference Algorithm/MyersDifferenceAlgorithm.swift">
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-         location = "group:MyersDifferenceAlgorithm.playground">
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-         name = "Images">
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-            location = "group:Graph.png">
-         </FileRef>
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-            location = "group:GraphResult.png">
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-         <FileRef
-            location = "group:InvalidSort.png">
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-            location = "group:TopologicalSort.graffle">
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-         </FileRef>
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-            location = "group:Tests.xcodeproj">
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-         <FileRef
-            location = "group:TopologicalSortTests.swift">
-         </FileRef>
-      </Group>
-      <FileRef
-         location = "group:Topological Sort.playground">
-      </FileRef>
-      <FileRef
-         location = "group:TopologicalSort1.swift">
-      </FileRef>
-      <FileRef
-         location = "group:TopologicalSort2.swift">
-      </FileRef>
-      <FileRef
-         location = "group:TopologicalSort3.swift">
-      </FileRef>
-   </Group>
-   <Group
-      location = "group:Treap"
-      name = "Treap">
-      <Group
-         location = "group:Treap"
-         name = "Treap">
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-            location = "group:Treap"
-            name = "Treap">
-            <FileRef
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-            </FileRef>
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-            </FileRef>
-            <FileRef
-               location = "group:TreapTests.swift">
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-         location = "group:Treap.swift">
-      </FileRef>
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-      </FileRef>
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-         location = "group:TreapMergeSplit.swift">
-      </FileRef>
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-      location = "group:Tree"
-      name = "Tree">
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-         location = "group:Images"
-         name = "Images">
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-            location = "group:Cycles.graffle">
-         </FileRef>
-         <FileRef
-            location = "group:Cycles.png">
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-      </FileRef>
-      <FileRef
-         location = "group:Tree.playground">
-      </FileRef>
-      <FileRef
-         location = "group:Tree.swift">
-      </FileRef>
-   </Group>
-   <Group
-      location = "group:Trie"
-      name = "Trie">
-      <Group
-         location = "group:images"
-         name = "images">
-         <FileRef
-            location = "group:trie.png">
-         </FileRef>
-      </Group>
-      <FileRef
-         location = "group:ReadMe.md">
-      </FileRef>
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-         location = "group:Trie"
-         name = "Trie">
-         <Group
-            location = "group:Trie"
-            name = "Trie">
-            <FileRef
-               location = "group:AppDelegate.swift">
-            </FileRef>
-            <Group
-               location = "group:Assets.xcassets"
-               name = "Assets.xcassets">
-               <Group
-                  location = "group:AppIcon.appiconset"
-                  name = "AppIcon.appiconset">
-                  <FileRef
-                     location = "group:Contents.json">
-                  </FileRef>
-               </Group>
-            </Group>
-            <Group
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-               name = "Base.lproj">
-               <FileRef
-                  location = "group:Main.storyboard">
-               </FileRef>
-            </Group>
-            <FileRef
-               location = "group:dictionary.txt">
-            </FileRef>
-            <FileRef
-               location = "group:Info.plist">
-            </FileRef>
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-               location = "group:ReadMe.md">
-            </FileRef>
-            <FileRef
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-            </FileRef>
-            <FileRef
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-         </Group>
-         <FileRef
-            location = "group:Trie.xcodeproj">
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-         <Group
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-            name = "TrieTests">
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-               location = "group:Info.plist">
-            </FileRef>
-            <FileRef
-               location = "group:TrieTests.swift">
-            </FileRef>
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-            name = "TrieUITests">
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-               location = "group:Info.plist">
-            </FileRef>
-            <FileRef
-               location = "group:TrieUITests.swift">
-            </FileRef>
-         </Group>
-      </Group>
-   </Group>
-   <Group
-      location = "group:Two-Sum Problem"
-      name = "Two-Sum Problem">
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-      <Group
-         location = "group:Solution 1"
-         name = "Solution 1">
-         <FileRef
-            location = "group:2Sum.playground">
-         </FileRef>
-      </Group>
-      <Group
-         location = "group:Solution 2"
-         name = "Solution 2">
-         <FileRef
-            location = "group:2Sum.playground">
-         </FileRef>
-      </Group>
-   </Group>
-   <Group
-      location = "group:Union-Find"
-      name = "Union-Find">
-      <Group
-         location = "group:Images"
-         name = "Images">
-         <FileRef
-            location = "group:AfterFind.png">
-         </FileRef>
-         <FileRef
-            location = "group:AfterUnion.png">
-         </FileRef>
-         <FileRef
-            location = "group:BeforeFind.png">
-         </FileRef>
-         <FileRef
-            location = "group:BeforeUnion.png">
-         </FileRef>
-      </Group>
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-      <FileRef
-         location = "group:UnionFind.playground">
-      </FileRef>
-   </Group>
-   <Group
-      location = "group:Z-Algorithm"
-      name = "Z-Algorithm">
-      <FileRef
-         location = "group:README.markdown">
-      </FileRef>
-      <FileRef
-         location = "group:ZAlgorithm.swift">
-      </FileRef>
-      <FileRef
-         location = "group:ZetaAlgorithm.playground">
-      </FileRef>
-      <FileRef
-         location = "group:ZetaAlgorithm.swift">
-      </FileRef>
-   </Group>
-</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 815/862] 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 816/862] 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 817/862] 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 818/862] 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 819/862] 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 820/862] 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 821/862] 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 822/862] 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 823/862] 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 824/862] 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 825/862] 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 826/862] 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 827/862] 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 828/862] 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 829/862] 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 830/862] 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 831/862] 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 832/862] 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 833/862] 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 834/862] 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 835/862] 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 836/862] 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 837/862] 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 838/862] 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 839/862] 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 840/862] 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 841/862] 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 842/862] 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 843/862] 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 844/862] 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 845/862] 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 846/862] 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 847/862] 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 848/862] 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 849/862] 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 850/862] 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 851/862] 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 852/862] 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 853/862] 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 854/862] 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 855/862] 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 856/862] 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 857/862] 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 858/862] 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 859/862] 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 860/862] 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 861/862] #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 862/862] 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])