Add quicksort

Author: hollance

Quicksort/Images/Example.graffle

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+//: Playground - noun: a place where people can play
+
+import Foundation
+
+
+// *** Simple but inefficient version of quicksort ***
+
+func quicksort<T: Comparable>(a: [T]) -> [T] {
+  if a.count <= 1 {
+    return a
+  } else {
+    let pivot = a[a.count/2]
+    let less = a.filter { $0 < pivot }
+    let equal = a.filter { $0 == pivot }
+    let greater = a.filter { $0 > pivot }
+    
+    // Uncomment this following line to see in detail what the 
+    // pivot is in each step and how the subarrays are partitioned.
+    //print(pivot, less, equal, greater)
+    
+    return quicksort(less) + equal + quicksort(greater)
+  }
+}
+
+let list1 = [ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
+quicksort(list1)
+
+
+
+// *** Using Lomuto partitioning ***
+
+/*
+  Lomuto's partitioning algorithm.
+
+  The return value is the index of the pivot element in the new array. The left
+  partition is [low...p-1]; the right partition is [p+1...high], where p is the
+  return value.
+*/
+func partitionLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) -> Int {
+  let pivot = a[high]
+  
+  var i = low
+  for j in low..<high {
+    if a[j] <= pivot {
+      (a[i], a[j]) = (a[j], a[i])
+      i += 1
+    }
+  }
+  
+  (a[i], a[high]) = (a[high], a[i])
+  return i
+}
+
+var list2 = [ 10, 0, 3, 9, 2, 14, 26, 27, 1, 5, 8, -1, 8 ]
+partitionLomuto(&list2, low: 0, high: list2.count - 1)
+list2
+
+func quicksortLomuto<T: Comparable>(inout a: [T], low: Int, high: Int) {
+  if low < high {
+    let p = partitionLomuto(&a, low: low, high: high)
+    quicksortLomuto(&a, low: low, high: p - 1)
+    quicksortLomuto(&a, low: p + 1, high: high)
+  }
+}
+
+quicksortLomuto(&list2, low: 0, high: list2.count - 1)
+
+
+
+// *** Hoare partitioning ***
+
+/*
+  Hoare's partitioning scheme.
+
+  The return value is NOT necessarily the index of the pivot element in the
+  new array. Instead, the array is partitioned into [low...p] and [p+1...high],
+  where p is the return value. The pivot value is placed somewhere inside one
+  of the two partitions, but the algorithm doesn't tell you which one or where.
+*/
+func partitionHoare<T: Comparable>(inout a: [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 {
+      return j
+    }
+  }
+}
+
+var list3 = [ 8, 0, 3, 9, 2, 14, 10, 27, 1, 5, 8, -1, 26 ]
+partitionHoare(&list3, low: 0, high: list3.count - 1)
+list3
+
+func quicksortHoare<T: Comparable>(inout a: [T], low: Int, high: Int) {
+  if low < high {
+    let p = partitionHoare(&a, low: low, high: high)
+    quicksortHoare(&a, low: low, high: p)
+    quicksortHoare(&a, low: p + 1, high: high)
+  }
+}
+
+quicksortHoare(&list3, low: 0, high: list3.count - 1)
+
+
+
+// *** Randomized sorting ***
+
+/* Returns a random integer in the range min...max, inclusive. */
+public func random(min min: Int, max: Int) -> Int {
+  assert(min < max)
+  return min + Int(arc4random_uniform(UInt32(max - min + 1)))
+}
+
+func quicksortRandom<T: Comparable>(inout a: [T], low: Int, high: Int) {
+  if low < high {
+    let pivotIndex = random(min: low, max: high)
+    (a[pivotIndex], a[high]) = (a[high], a[pivotIndex])
+    
+    let p = partitionLomuto(&a, low: low, high: high)
+    quicksortRandom(&a, low: low, high: p - 1)
+    quicksortRandom(&a, low: p + 1, high: high)
+  }
+}
+
+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 ***
+
+/*
+  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])
+  }
+}
+
+/*
+  Dutch national flag partitioning.
+  Returns a tuple with the start and end index of the middle area.
+*/
+func partitionDutchFlag<T: Comparable>(inout a: [T], low: Int, high: Int, pivotIndex: Int) -> (Int, Int) {
+  let pivot = a[pivotIndex]
+  
+  var smaller = low
+  var equal = low
+  var larger = high
+  
+  while equal <= larger {
+    if a[equal] < pivot {
+      swap(&a, smaller, equal)
+      smaller += 1
+      equal += 1
+    } else if a[equal] == pivot {
+      equal += 1
+    } else {
+      swap(&a, equal, larger)
+      larger -= 1
+    }
+  }
+  return (smaller, larger)
+}
+
+var list5 = [ 10, 0, 3, 9, 2, 14, 8, 27, 1, 5, 8, -1, 26 ]
+partitionDutchFlag(&list5, low: 0, high: list5.count - 1, pivotIndex: 10)
+list5
+
+func quicksortDutchFlag<T: Comparable>(inout a: [T], low: Int, high: Int) {
+  if low < high {
+    let pivotIndex = random(min: low, max: high)
+    let (p, q) = partitionDutchFlag(&a, low: low, high: high, pivotIndex: pivotIndex)
+    quicksortDutchFlag(&a, low: low, high: p - 1)
+    quicksortDutchFlag(&a, low: q + 1, high: high)
+  }
+}
+
+quicksortDutchFlag(&list5, low: 0, high: list5.count - 1)

Quicksort/Images/Example.png

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+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='osx'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>

Quicksort/Quicksort.playground/Contents.swift

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+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>