Sorting algorithms/Quicksort

Sorting algorithms/Quicksort
You are encouraged to solve this task according to the task description, using any language you may know.

Sorting Algorithm
This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or:

O(n logn) sorts

Heap sort | Merge sort | Patience sort | Quick sort

O(n log²n) sorts
Shell Sort

O(n²) sorts
Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort

other sorts
Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort

This page uses content from Wikipedia. The original article was at Quicksort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

The task is to sort an array (or list) elements using the quicksort algorithm. The elements must have a strict weak order and the index of the array can be of any discrete type. For languages where this is not possible, sort an array of integers.

Quicksort, also known as partition-exchange sort, uses these steps.

1. Choose any element of the array to be the pivot.
2. Divide all other elements (except the pivot) into two partitions.
   • All elements less than the pivot must be in the first partition.
   • All elements greater than the pivot must be in the second partition.
3. Use recursion to sort both partitions.
4. Join the first sorted partition, the pivot, and the second sorted partition.

The best pivot creates partitions of equal length (or lengths differing by 1). The worst pivot creates an empty partition (for example, if the pivot is the first or last element of a sorted array). The runtime of Quicksort ranges from O(n log n) with the best pivots, to O(n²) with the worst pivots, where n is the number of elements in the array.

This is a simple quicksort algorithm, adapted from Wikipedia.

function quicksort(array)
    less, equal, greater := three empty arrays
    if length(array) > 1  
        pivot := select any element of array
        for each x in array
            if x < pivot then add x to less
            if x = pivot then add x to equal
            if x > pivot then add x to greater
        quicksort(less)
        quicksort(greater)
        array := concatenate(less, equal, greater)

A better quicksort algorithm works in place, by swapping elements within the array, to avoid the memory allocation of more arrays.

function quicksort(array)
    if length(array) > 1
        pivot := select any element of array
        left := first index of array
        right := last index of array
        while left ≤ right
            while array[left] < pivot
                left := left + 1
            while array[right] > pivot
                right := right - 1
            if left ≤ right
                swap array[left] with array[right]
                left := left + 1
                right := right - 1
        quicksort(array from first index to right)
        quicksort(array from left to last index)

Quicksort has a reputation as the fastest sort. Optimized variants of quicksort are common features of many languages and libraries. One often contrasts quicksort with merge sort, because both sorts have an average time of O(n log n).

"On average, mergesort does fewer comparisons than quicksort, so it may be better when complicated comparison routines are used. Mergesort also takes advantage of pre-existing order, so it would be favored for using sort() to merge several sorted arrays. On the other hand, quicksort is often faster for small arrays, and on arrays of a few distinct values, repeated many times." — http://perldoc.perl.org/sort.html

Quicksort is at one end of the spectrum of divide-and-conquer algorithms, with merge sort at the opposite end.

• Quicksort is a conquer-then-divide algorithm, which does most of the work during the partitioning and the recursive calls. The subsequent reassembly of the sorted partitions involves trivial effort.
• Merge sort is a divide-then-conquer algorithm. The partioning happens in a trivial way, by splitting the input array in half. Most of the work happens during the recursive calls and the merge phase.

With quicksort, every element in the first partition is less than or equal to every element in the second partition. Therefore, the merge phase of quicksort is so trivial that it needs no mention!

This task has not specified whether to allocate new arrays, or sort in place. This task also has not specified how to choose the pivot element. (Common ways to are to choose the first element, the middle element, or the median of three elements.) Thus there is a variety among the following implementations.

ACL2

<lang Lisp>(defun partition (p xs)

  (if (endp xs)
      (mv nil nil)
      (mv-let (less more)
              (partition p (rest xs))
         (if (< (first xs) p)
             (mv (cons (first xs) less) more)
             (mv less (cons (first xs) more))))))

(defun qsort (xs)

  (if (endp xs)
      nil
      (mv-let (less more)
              (partition (first xs) (rest xs))
         (append (qsort less)
                 (list (first xs))
                 (qsort more)))))</lang>

Usage: <lang>> (qsort '(8 6 7 5 3 0 9)) (0 3 5 6 7 8 9)</lang>

ActionScript

Works with: ActionScript version 3

The functional programming way <lang actionscript>function quickSort (array:Array):Array {

   if (array.length <= 1)
       return array;

   var pivot:Number = array[Math.round(array.length / 2)];

   return quickSort(array.filter(function (x:Number, index:int, array:Array):Boolean { return x <  pivot; })).concat(
           array.filter(function (x:Number, index:int, array:Array):Boolean { return x == pivot; })).concat(
       quickSort(array.filter(function (x:Number, index:int, array:Array):Boolean { return x > pivot; })));

}</lang>

The faster way <lang actionscript>function quickSort (array:Array):Array {

   if (array.length <= 1)
       return array;

   var pivot:Number = array[Math.round(array.length / 2)];

   var less:Array = [];
   var equal:Array = [];
   var greater:Array = [];

   for each (var x:Number in array) {
       if (x < pivot)
           less.push(x);
       if (x == pivot)
           equal.push(x);
       if (x > pivot)
           greater.push(x);
   }

   return quickSort(less).concat(
           equal).concat(
           quickSort(greater));

}</lang>

Ada

This example is implemented as a generic procedure. The procedure specification is: <lang ada>----------------------------------------------------------------------- -- Generic Quicksort procedure

---

generic

   type Element_Type is private;
  type Index_Type is (<>);
  type Element_Array is array(Index_Type range <>) of Element_Type;
  with function "<" (Left, Right : Element_Type) return Boolean is <>; 
  with function ">" (Left, Right : Element_Type) return Boolean is <>;

procedure Sort(Item : in out Element_Array);</lang> The procedure body deals with any discrete index type, either an integer type or an enumerated type. <lang ada>----------------------------------------------------------------------- -- Generic Quicksort procedure

---

procedure Sort (Item : in out Element_Array) is

  procedure Swap(Left, Right : in out Element_Type) is
     Temp : Element_Type := Left;
  begin
     Left := Right;
     Right := Temp;
  end Swap;
          
  Pivot_Index : Index_Type;
  Pivot_Value : Element_Type;
  Right       : Index_Type := Item'Last;
  Left        : Index_Type := Item'First;
 

begin

  if Item'Length > 1 then
     Pivot_Index := Index_Type'Val((Index_Type'Pos(Item'Last) + 1 + 
                                   Index_Type'Pos(Item'First)) / 2);
     Pivot_Value := Item(Pivot_Index);

     Left  := Item'First;
     Right := Item'Last;
     loop
        while Left < Item'Last and then Item(Left) < Pivot_Value loop
           Left := Index_Type'Succ(Left);
        end loop;
        while Right > Item'First and then Item(Right) > Pivot_Value loop
           Right := Index_Type'Pred(Right);
        end loop;
        exit when Left >= Right;
        Swap(Item(Left), Item(Right));
        if Left < Item'Last and Right > Item'First then
           Left := Index_Type'Succ(Left);
           Right := Index_Type'Pred(Right);
        end if;
     end loop;
     if Right > Item'First then
        Sort(Item(Item'First..Index_Type'Pred(Right)));
     end if;
     if Left < Item'Last then
        Sort(Item(Left..Item'Last));
     end if;
  end if;

end Sort;</lang> An example of how this procedure may be used is: <lang ada>with Sort; with Ada.Text_Io; with Ada.Float_Text_IO; use Ada.Float_Text_IO;

procedure Sort_Test is

  type Days is (Mon, Tue, Wed, Thu, Fri, Sat, Sun);
  type Sales is array(Days range <>) of Float;
  procedure Sort_Days is new Sort(Float, Days, Sales);
  
  procedure Print(Item : Sales) is
  begin
     for I in Item'range loop
        Put(Item => Item(I), Fore => 5, Aft => 2, Exp => 0);
     end loop;
  end Print;
 
  Weekly_Sales : Sales := (Mon => 300.0, 
     Tue => 700.0, 
     Wed => 800.0, 
     Thu => 500.0, 
     Fri => 200.0, 
     Sat => 100.0, 
     Sun => 900.0);
 

begin

  Print(Weekly_Sales);
  Ada.Text_Io.New_Line(2);
  Sort_Days(Weekly_Sales);
  Print(Weekly_Sales);
 

end Sort_Test;</lang>

ALGOL 68

From: http://en.wikibooks.org/wiki/Algorithm_implementation/Sorting/Quicksort#ALGOL_68 <lang algol68>PROC partition =(REF [] DATA array, PROC (REF DATA, REF DATA) BOOL cmp)INT: (

 INT begin:=LWB array;
 INT end:=UPB array;
 WHILE begin < end DO
    WHILE begin < end DO
     IF cmp(array[begin], array[end]) THEN
       DATA tmp=array[begin];
       array[begin]:=array[end];
       array[end]:=tmp;
       GO TO break while decr end
     FI;
     end -:= 1
   OD;
   break while decr end: SKIP;
    WHILE begin < end DO
     IF cmp(array[begin], array[end]) THEN
       DATA tmp=array[begin];
        array[begin]:=array[end];
       array[end]:=tmp;
       GO TO break while incr begin
     FI;
     begin +:= 1
    OD;
    break while incr begin: SKIP
 OD;
 begin

);

PROC qsort=(REF [] DATA array, PROC (REF DATA, REF DATA) BOOL cmp)VOID: (

 IF LWB array < UPB array THEN
   INT i := partition(array, cmp);
   PAR ( # remove PAR for single threaded sort #
     qsort(array[:i-1], cmp),
     qsort(array[i+1:], cmp)
   )
 FI

);

MODE DATA = INT; PROC cmp=(REF DATA a,b)BOOL: a>b;

main:(

 []DATA const l=(5,4,3,2,1);
 [UPB const l]DATA l:=const l;
 qsort(l,cmp);
 printf(($g(3)$,l))

)</lang>

APL

Works with: Dyalog APL

Translation of: J

<lang apl> qsort ← {1≥⍴⍵:⍵⋄e←⍵[?⍴⍵]⋄ (∇(⍵<e)/⍵) , ((⍵=e)/⍵) , ∇(⍵>e)/⍵}

     qsort 1 3 5 7 9 8 6 4 2

1 2 3 4 5 6 7 8 9</lang>

Of course, in real APL applications, one would use ⍋ to sort (which will pick a sorting algorithm suited to the argument).

AWK

<lang awk>

1. the following qsort implementation extracted from:
3. ftp://ftp.armory.com/pub/lib/awk/qsort
5. Copyleft GPLv2 John DuBois
7. @(#) qsort 1.2.1 2005-10-21
8. 1990 john h. dubois iii (john@armory.com)
10. qsortArbIndByValue(): Sort an array according to the values of its elements.
12. Input variables:
14. Arr[] is an array of values with arbitrary (associative) indices.
16. Output variables:
18. k[] is returned with numeric indices 1..n. The values assigned to these
19. indices are the indices of Arr[], ordered so that if Arr[] is stepped
20. through in the order Arr[k[1]] .. Arr[k[n]], it will be stepped through in
21. order of the values of its elements.
23. Return value: The number of elements in the arrays (n).
25. NOTES:
27. Full example for accessing results:
29. foolist["second"] = 2;
30. foolist["zero"] = 0;
31. foolist["third"] = 3;
32. foolist["first"] = 1;
34. outlist[1] = 0;
35. n = qsortArbIndByValue(foolist, outlist)
37. for (i = 1; i <= n; i++) {
38. printf("item at %s has value %d\n", outlist[i], foolist[outlist[i]]);
39. }
40. delete outlist;

function qsortArbIndByValue(Arr, k,

                           ArrInd, ElNum)

{

       ElNum = 0;
       for (ArrInd in Arr) {
               k[++ElNum] = ArrInd;
       }
       qsortSegment(Arr, k, 1, ElNum);
       return ElNum;

}

2. qsortSegment(): Sort a segment of an array.
4. Input variables:
6. Arr[] contains data with arbitrary indices.
8. k[] has indices 1..nelem, with the indices of Arr[] as values.
10. Output variables:
12. k[] is modified by this function. The elements of Arr[] that are pointed to
13. by k[start..end] are sorted, with the values of elements of k[] swapped
14. so that when this function returns, Arr[k[start..end]] will be in order.
16. Return value: None.

function qsortSegment(Arr, k, start, end,

                     left, right, sepval, tmp, tmpe, tmps)

{

       if ((end - start) < 1) {        # 0 or 1 elements
               return;
       }
       # handle two-element case explicitly for a tiny speedup
       if ((end - start) == 1) {
               if (Arr[tmps = k[start]] > Arr[tmpe = k[end]]) {
                       k[start] = tmpe;
                       k[end] = tmps;
               }
               return;
       }
       # Make sure comparisons act on these as numbers
       left = start + 0;
       right = end + 0;
       sepval = Arr[k[int((left + right) / 2)]];
       # Make every element <= sepval be to the left of every element > sepval
       while (left < right) {
               while (Arr[k[left]] < sepval) {
                       left++;
               }
               while (Arr[k[right]] > sepval) {
                       right--;
               }
               if (left < right) {
                       tmp = k[left];
                       k[left++] = k[right];
                       k[right--] = tmp;
               }
       }
       if (left == right)
               if (Arr[k[left]] < sepval) {
                       left++;
               } else {
                       right--;
               }
       if (start < right) {
               qsortSegment(Arr, k, start, right);
       }
       if (left < end) {
               qsortSegment(Arr, k, left, end);
       }

} </lang>

AutoHotkey

translated from python example <lang AutoHotkey>MsgBox % quicksort("8,4,9,2,1")

quicksort(list) {

 StringSplit, list, list, `,
 If (list0 <= 1)
   Return list
 pivot := list1
 Loop, Parse, list, `,
 {
   If (A_LoopField < pivot)
     less = %less%,%A_LoopField%
   Else If (A_LoopField > pivot)
     more = %more%,%A_LoopField%
   Else
     pivotlist = %pivotlist%,%A_LoopField%
 }
 StringTrimLeft, less, less, 1
 StringTrimLeft, more, more, 1
 StringTrimLeft, pivotList, pivotList, 1
 less := quicksort(less)
 more := quicksort(more)
 Return less . pivotList . more

}</lang>

BASIC

Works with: FreeBASIC

Works with: PowerBASIC for DOS

Works with: QB64

Works with: QBasic

This is specifically for INTEGERs, but can be modified for any data type by changing arr()'s type.

<lang qbasic>DECLARE SUB quicksort (arr() AS INTEGER, leftN AS INTEGER, rightN AS INTEGER)

DIM q(99) AS INTEGER DIM n AS INTEGER

RANDOMIZE TIMER

FOR n = 0 TO 99

   q(n) = INT(RND * 9999)

NEXT

OPEN "output.txt" FOR OUTPUT AS 1

   FOR n = 0 TO 99
       PRINT #1, q(n),
   NEXT
   PRINT #1,
   quicksort q(), 0, 99
   FOR n = 0 TO 99
       PRINT #1, q(n),
   NEXT

CLOSE

SUB quicksort (arr() AS INTEGER, leftN AS INTEGER, rightN AS INTEGER)

   DIM pivot AS INTEGER, leftNIdx AS INTEGER, rightNIdx AS INTEGER
   leftNIdx = leftN
   rightNIdx = rightN
   IF (rightN - leftN) > 0 THEN
       pivot = (leftN + rightN) / 2
       WHILE (leftNIdx <= pivot) AND (rightNIdx >= pivot)
           WHILE (arr(leftNIdx) < arr(pivot)) AND (leftNIdx <= pivot)
               leftNIdx = leftNIdx + 1
           WEND
           WHILE (arr(rightNIdx) > arr(pivot)) AND (rightNIdx >= pivot)
               rightNIdx = rightNIdx - 1
           WEND
           SWAP arr(leftNIdx), arr(rightNIdx)
           leftNIdx = leftNIdx + 1
           rightNIdx = rightNIdx - 1
           IF (leftNIdx - 1) = pivot THEN
               rightNIdx = rightNIdx + 1
               pivot = rightNIdx
           ELSEIF (rightNIdx + 1) = pivot THEN
               leftNIdx = leftNIdx - 1
               pivot = leftNIdx
           END IF
       WEND
       quicksort arr(), leftN, pivot - 1
       quicksort arr(), pivot + 1, rightN
   END IF

END SUB</lang>

BBC BASIC

<lang bbcbasic> DIM test(9)

     test() = 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
     PROCquicksort(test(), 0, 10)
     FOR i% = 0 TO 9
       PRINT test(i%) ;
     NEXT
     PRINT
     END
     
     DEF PROCquicksort(a(), s%, n%)
     LOCAL l%, p, r%, t%
     IF n% < 2 THEN ENDPROC
     t% = s% + n% - 1
     l% = s%
     r% = t%
     p = a((l% + r%) DIV 2)
     REPEAT
       WHILE a(l%) < p l% += 1 : ENDWHILE
       WHILE a(r%) > p r% -= 1 : ENDWHILE
       IF l% <= r% THEN
         SWAP a(l%), a(r%)
         l% += 1
         r% -= 1
       ENDIF
     UNTIL l% > r%
     IF s% < r% PROCquicksort(a(), s%, r% - s% + 1)
     IF l% < t% PROCquicksort(a(), l%, t% - l% + 1 )
     ENDPROC</lang>

Output:

       -31         0         1         2         2         4        65        83        99       782

BCPL

<lang BCPL>// This can be run using Cintcode BCPL freely available from www.cl.cam.ac.uk/users/mr10.

GET "libhdr.h"

LET quicksort(v, n) BE qsort(v+1, v+n)

AND qsort(l, r) BE { WHILE l+8<r DO

 { LET midpt = (l+r)/2
   // Select a good(ish) median value.
   LET val   = middle(!l, !midpt, !r)
   LET i = partition(val, l, r)
   // Only use recursion on the smaller partition.
   TEST i>midpt THEN { qsort(i, r);   r := i-1 }
                ELSE { qsort(l, i-1); l := i   }
 }

 FOR p = l+1 TO r DO  // Now perform insertion sort.
  FOR q = p-1 TO l BY -1 TEST q!0<=q!1 THEN BREAK
                                       ELSE { LET t = q!0
                                              q!0 := q!1
                                              q!1 := t
                                            }

}

AND middle(a, b, c) = a b<c -> b,

                                   a<c -> c,
                                          a,
                            b<c -> a<c -> a,
                                          c,
                                   b

AND partition(median, p, q) = VALOF { LET t = ?

 WHILE !p < median DO p := p+1
 WHILE !q > median DO q := q-1
 IF p>=q RESULTIS p
 t  := !p
 !p := !q
 !q := t
 p, q := p+1, q-1

} REPEAT

LET start() = VALOF {

 LET v = VEC 1000
 FOR i = 1 TO 1000 DO v!i := randno(1_000_000)
 quicksort(v, 1000)
 FOR i = 1 TO 1000 DO
 { IF i MOD 10 = 0 DO newline()
   writef(" %i6", v!i)
 }
 newline()

}</lang>

C

<lang c> void quick_sort (int *a, int n) {

   if (n < 2)
       return;
   int p = a[n / 2];
   int *l = a;
   int *r = a + n - 1;
   while (l <= r) {
       if (*l < p) {
           l++;
           continue;
       }
       if (*r > p) {
           r--;
           continue; // we need to check the condition (l <= r) every time we change the value of l or r
       }
       int t = *l;
       *l++ = *r;
       *r-- = t;
   }
   quick_sort(a, r - a + 1);
   quick_sort(l, a + n - l);

}

int main () {

   int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
   int n = sizeof a / sizeof a[0];
   quick_sort(a, n);
   return 0;

} </lang>

C++

The following implements quicksort with a median-of-three pivot. As idiomatic in C++, the argument last is a one-past-end iterator. Note that this code takes advantage of std::partition, which is O(n). Also note that it needs a random-access iterator for efficient calculation of the median-of-three pivot (more exactly, for O(1) calculation of the iterator mid). <lang cpp>#include <iterator>

1. include <algorithm> // for std::partition
2. include <functional> // for std::less

// helper function for median of three template<typename T>

T median(T t1, T t2, T t3)

{

 if (t1 < t2)
 {
   if (t2 < t3)
     return t2;
   else if (t1 < t3)
     return t3;
   else
     return t1;
 }
 else
 {
   if (t1 < t3)
     return t1;
   else if (t2 < t3)
     return t3;
   else
     return t2;
 }

}

// helper object to get <= from < template<typename Order> struct non_strict_op:

 public std::binary_function<typename Order::second_argument_type,
                             typename Order::first_argument_type,
                             bool>

{

 non_strict_op(Order o): order(o) {}
 bool operator()(typename Order::second_argument_type arg1,
                 typename Order::first_argument_type arg2) const
 {
   return !order(arg2, arg1);
 }

private:

 Order order;

};

template<typename Order> non_strict_op<Order> non_strict(Order o) {

 return non_strict_op<Order>(o);

}

template<typename RandomAccessIterator,

        typename Order>
void quicksort(RandomAccessIterator first, RandomAccessIterator last, Order order)

{

 if (first != last && first+1 != last)
 {
   typedef typename std::iterator_traits<RandomAccessIterator>::value_type value_type;
   RandomAccessIterator mid = first + (last - first)/2;
   value_type pivot = median(*first, *mid, *(last-1));
   RandomAccessIterator split1 = std::partition(first, last, std::bind2nd(order, pivot));
   RandomAccessIterator split2 = std::partition(split1, last, std::bind2nd(non_strict(order), pivot));
   quicksort(first, split1, order);
   quicksort(split2, last, order);
 }

}

template<typename RandomAccessIterator>

void quicksort(RandomAccessIterator first, RandomAccessIterator last)

{

 quicksort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());

}</lang>

A simpler version of the above that just uses the first element as the pivot and only does one "partition". <lang cpp>#include <iterator>

1. include <algorithm> // for std::partition
2. include <functional> // for std::less

template<typename RandomAccessIterator,

        typename Order>
void quicksort(RandomAccessIterator first, RandomAccessIterator last, Order order)

{

 if (last - first > 1)
 {
   RandomAccessIterator split = std::partition(first+1, last, std::bind2nd(order, *first));
   std::iter_swap(first, split-1);
   quicksort(first, split-1, order);
   quicksort(split, last, order);
 }

}

template<typename RandomAccessIterator>

void quicksort(RandomAccessIterator first, RandomAccessIterator last)

{

 quicksort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());

}</lang>

C#

Note that actually Array.Sort and ArrayList.Sort both use an unstable implementation of the quicksort algorithm. <lang csharp>using System; using System.Collections.Generic;

namespace QuickSort {

   class Program
   {
       static void Main(string[] args)
       {
           List<int> unsorted = new List<int> { 1, 3, 5, 7, 9, 8, 6, 4, 2 };
           List<int> sorted = quicksort(unsorted);

           Console.WriteLine(string.Join(",", sorted));
           Console.ReadKey();
       }

       private static List<int> quicksort(List<int> arr)
       {
           List<int> loe = new List<int>(), gt = new List<int>();
           if (arr.Count < 2)
               return arr;
           int pivot = arr.Count / 2;
           int pivot_val = arr[pivot];
           arr.RemoveAt(pivot);
           foreach (int i in arr)
           {
               if (i <= pivot_val)
                   loe.Add(i);
               else if (i > pivot_val)
                   gt.Add(i);                
           }
                       
           List<int> resultSet = new List<int>();
           resultSet.AddRange(quicksort(loe));
           gt.Add(pivot_val);
           resultSet.AddRange(quicksort(gt));
           return resultSet;            
       }
   }

}</lang>

A very inefficient way to do qsort in C# to prove C# code can be just as compact and readable as any dynamic code

<lang csharp>using System; using System.Collections.Generic; using System.Linq;

namespace QSort {

   class QSorter
   {
       private static IEnumerable<IComparable> empty = new List<IComparable>();

       public static IEnumerable<IComparable> QSort(IEnumerable<IComparable> iEnumerable)
       {
           if(iEnumerable.Any())
           {
               var pivot = iEnumerable.First();
               return QSort(iEnumerable.Where((anItem) => pivot.CompareTo(anItem) > 0)).
                   Concat(iEnumerable.Where((anItem) => pivot.CompareTo(anItem) == 0)).
                   Concat(QSort(iEnumerable.Where((anItem) => pivot.CompareTo(anItem) < 0)));
           }
           return empty;
       }
   }

}</lang>

Clojure

A very Haskell-like solution using list comprehensions and lazy evaluation. <lang lisp>(defn qsort [L]

 (if (empty? L) 
     '()
     (let [[pivot & L2] L]
          (lazy-cat (qsort (for [y L2 :when (<  y pivot)] y))
                    (list pivot)
                    (qsort (for [y L2 :when (>= y pivot)] y))))))</lang>

Another short version (using quasiquote):

<lang lisp>(defn qsort pvt & rs

 (if pvt
   `(~@(qsort (filter #(<  % pvt) rs))
     ~pvt 
     ~@(qsort (filter #(>= % pvt) rs)))))</lang>

Another, more readable version (no macros):

<lang lisp>(defn qsort pivot & xs

 (when pivot
   (let [smaller #(< % pivot)]
     (lazy-cat (qsort (filter smaller xs))

[pivot] (qsort (remove smaller xs))))))</lang>

A 3-group quicksort (fast when many values are equal): <lang lisp>(defn qsort3 pvt :as coll

 (when pvt
   (let [{left -1 mid 0 right 1} (group-by #(compare % pvt) coll)]
     (lazy-cat (qsort3 left) mid (qsort3 right)))))</lang>

A lazier version of above (unlike group-by, filter returns (and reads) a lazy sequence) <lang lisp>(defn qsort3 pivot :as coll

 (when pivot
   (lazy-cat (qsort (filter #(< % pivot) coll))
             (filter #{pivot} coll)
             (qsort (filter #(> % pivot) coll)))))</lang>

CoffeeScript

<lang coffeescript>

1. This shows quicksort-in-place.

quicksort = (a) ->

 swap = (i, j) ->
   return if i == j
   [a[i], a[j]] = [a[j], a[i]]

 divide = (v, start, end) ->
   first_big = start
   j = start
   while j <= end
     if a[j] < v
       swap first_big, j
       first_big += 1
     j += 1
   first_big

 partition = (start, end) ->
   v = a[end]
   first_big = divide v, start, end-1
   swap first_big, end
   first_big

 qs = (start, end) ->
   return if start >= end
   m = partition start, end
   qs start, m-1
   qs m+1, end

 qs 0, a.length - 1

1. test

do ->

 a = [1, 3, 5, 7, 9, 8, 6, 4, 2, 0, 3.5]
 quicksort(a)
 console.log a # [ 0, 1, 2, 3, 3.5, 4, 5, 6, 7, 8, 9 ]

</lang>

Common Lisp

The functional programming way

<lang lisp>(defun quicksort (list &aux (pivot (car list)) )

 (if (cdr list)
     (nconc (quicksort (remove-if-not #'(lambda (x) (< x pivot)) list))
            (remove-if-not #'(lambda (x) (= x pivot)) list)
            (quicksort (remove-if-not #'(lambda (x) (> x pivot)) list)))
     list))</lang>

With macrolet

<lang lisp>(defun qs (list)

 (if (cdr list)
     (macrolet ((pivot (test) `(remove (car list) list :test-not #',test)))
       (nconc (qs (pivot >)) (pivot =) (qs (pivot <))))
     list))</lang>

In-place non-functional

<lang lisp>(defun quicksort (sequence)

 (labels ((swap (a b) (rotatef (elt sequence a) (elt sequence b)))
          (sub-sort (left right)
            (when (< left right)
              (let ((pivot (elt sequence right))
                    (index left))
                (loop for i from left below right
                      when (<= (elt sequence i) pivot)
                        do (swap i (prog1 index (incf index))))
                (swap right index)
                (sub-sort left (1- index))
                (sub-sort (1+ index) right)))))
   (sub-sort 0 (1- (length sequence)))
   sequence))</lang>

Curry

Copied from Curry: Example Programs. <lang curry>-- quicksort using higher-order functions:

qsort :: [Int] -> [Int] qsort [] = [] qsort (x:l) = qsort (filter (<x) l) ++ x : qsort (filter (>=x) l)

goal = qsort [2,3,1,0]</lang>

D

A high-level version: <lang d>import std.stdio;

T[] quickSort(T)(T[] items) {

   if (items.length <= 1)
       return items;
   T[] less, more;
   foreach (x; items[1 .. $])
       (x < items[0] ? less : more) ~= x;
   return quickSort(less) ~ items[0] ~ quickSort(more);

}

void main() {

   writeln(quickSort([4, 65, 2, -31, 0, 99, 2, 83, 782, 1]));

}</lang> Output:

[-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]

An in-place version: <lang d>import std.stdio; import std.algorithm;

void quickSort(T)(T[] items) {

   if (items.length >= 2) {
       auto parts = partition3(items, items[$ / 2]);
       quickSort(parts[0]);
       quickSort(parts[2]);
   }

}

void main() {

   auto items = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1];
   quickSort(items);
   writeln(items);

}</lang>

Dart

<lang dart>quickSort(List a) {

 if (a.length <= 1) {
   return a;
 }
 
 var pivot = a[0];
 var less = [];
 var more = [];
 var pivotList = [];
 
 // Partition
 a.forEach((var i){    
   if (i.compareTo(pivot) < 0) {
     less.add(i);
   } else if (i.compareTo(pivot) > 0) {
     more.add(i);
   } else {
     pivotList.add(i);
   }
 });
 
 // Recursively sort sublists
 less = quickSort(less);
 more = quickSort(more);
 
 // Concatenate results
 less.addAll(pivotList);
 less.addAll(more);
 return less;

}

void main() {

 var arr=[1,5,2,7,3,9,4,6,8];
 print("Before sort");
 arr.forEach((var i)=>print("$i"));
 arr = quickSort(arr);
 print("After sort");
 arr.forEach((var i)=>print("$i"));

}</lang>

E

<lang e>def quicksort := {

   def swap(container, ixA, ixB) {
       def temp := container[ixA]
       container[ixA] := container[ixB]
       container[ixB] := temp
   }

   def partition(array, var first :int, var last :int) {
       if (last <= first) { return }
 
       # Choose a pivot
       def pivot := array[def pivotIndex := (first + last) // 2]
 
       # Move pivot to end temporarily
       swap(array, pivotIndex, last)
 
       var swapWith := first
 
       # Scan array except for pivot, and...
       for i in first..!last {
           if (array[i] <= pivot) {   # items ≤ the pivot
               swap(array, i, swapWith) # are moved to consecutive positions on the left
               swapWith += 1
           }
       }
 
       # Swap pivot into between-partition position.
       # Because of the swapping we know that everything before swapWith is less
       # than or equal to the pivot, and the item at swapWith (since it was not
       # swapped) is greater than the pivot, so inserting the pivot at swapWith
       # will preserve the partition.
       swap(array, swapWith, last)
       return swapWith
   }

   def quicksortR(array, first :int, last :int) {
       if (last <= first) { return }
       def pivot := partition(array, first, last)
       quicksortR(array, first, pivot - 1)
       quicksortR(array, pivot + 1, last)
   }

   def quicksort(array) { # returned from block
       quicksortR(array, 0, array.size() - 1)
   }

}</lang>

Erlang

like haskell <lang erlang>qsort([]) -> []; qsort([X|Xs]) ->

  qsort([ Y || Y <- Xs, Y < X]) ++ [X] ++ qsort([ Y || Y <- Xs, Y >= X]).</lang>

F#

<lang fsharp> let rec qsort = function

   [] -> []
   | hd :: tl ->
       let less, greater = List.partition ((>=) hd) tl
       List.concat [qsort less; [hd]; qsort greater]

</lang>

Factor

<lang factor>: qsort ( seq -- seq )

   dup empty? [ 
     unclip [ [ < ] curry partition [ qsort ] bi@ ] keep
     prefix append
   ] unless ;</lang>

Fexl

<lang Fexl>

1. (sort keep compare xs) sorts the list xs using the three-way comparison
2. function. It keeps duplicates if the keep flag is true, otherwise it
3. discards them and returns only the unique entries.

\sort ==

   (\keep\compare\xs
   xs end \x\xs 

   \lo = (filter (\y compare y x T F F) xs)
   \hi = (filter (\y compare y x F keep T) xs)

   append (sort keep compare lo); 
   item x;
   sort keep compare hi
   )

</lang>

Forth

<lang forth>defer lessthan ( a@ b@ -- ? ) ' < is lessthan

mid ( l r -- mid ) over - 2/ -cell and + ;

exch ( addr1 addr2 -- ) dup @ >r over @ swap ! r> swap ! ;

partition ( l r -- l r r2 l2 )

 2dup mid @ >r ( r: pivot )
 2dup begin
   swap begin dup @  r@ lessthan while cell+ repeat
   swap begin r@ over @ lessthan while cell- repeat
   2dup <= if 2dup exch >r cell+ r> cell- then
 2dup > until  r> drop ;

qsort ( l r -- )

 partition  swap rot
 \ 2over 2over - + < if 2swap then
 2dup < if recurse else 2drop then
 2dup < if recurse else 2drop then ;

sort ( array len -- )

 dup 2 < if 2drop exit then
 1- cells over + qsort ;</lang>

Fortran

This example is in need of improvement: Apparently does not work under gfortran on OSX Lion.

Works with: Fortran version 90 and later

<lang fortran>MODULE Qsort_Module

IMPLICIT NONE

CONTAINS

RECURSIVE SUBROUTINE Qsort(a)

 INTEGER, INTENT(IN OUT) :: a(:)
 INTEGER :: split

 IF(size(a) > 1) THEN
    CALL Partition(a, split)
    CALL Qsort(a(:split-1))
    CALL Qsort(a(split:))
 END IF
 

END SUBROUTINE Qsort

SUBROUTINE Partition(a, marker)

 INTEGER, INTENT(IN OUT) :: a(:)
 INTEGER, INTENT(OUT) :: marker
 INTEGER :: left, right, pivot, temp
 
 pivot = (a(1) + a(size(a))) / 2  ! Average of first and last elements to prevent quadratic 
 left = 0                         ! behavior with sorted or reverse sorted data
 right = size(a) + 1

 DO WHILE (left < right)
    right = right - 1
    DO WHILE (a(right) > pivot)
       right = right-1
    END DO
    left = left + 1
    DO WHILE (a(left) < pivot)
       left = left + 1
    END DO
    IF (left < right) THEN 
       temp = a(left)
       a(left) = a(right)
       a(right) = temp
    END IF
 END DO

 IF (left == right) THEN
    marker = left + 1
 ELSE
    marker = left
 END IF

END SUBROUTINE Partition

END MODULE Qsort_Module

PROGRAM Quicksort

 USE Qsort_Module
 
 IMPLICIT NONE
 INTEGER, PARAMETER :: n = 100
 INTEGER :: array(n)
 INTEGER :: i
 REAL :: x
   CALL RANDOM_SEED
 DO i = 1, n
    CALL RANDOM_NUMBER(x)
    array(i) = INT(x * 10000)
 END DO
 
 WRITE (*, "(A)") "array is :-"
 WRITE (*, "(10I5)") array
 CALL Qsort(array)
 WRITE (*,*)
 WRITE (*, "(A)") "sorted array is :-"  
 WRITE (*,"(10I5)") array
 

END PROGRAM Quicksort</lang>

FPr

<lang FPr>qsort==nilp->id; ((qsort°3)++1,qsort°4) °((not°nilp°2)->*1,(tail°2),(1>1°2)->(((1°2),3),4,nil);3,((1°2),4),nil) °1,tail,(nil as _1),(nil as _1),nil </lang>

Go

Old school, following Hoare's 1962 paper.

As a nod to the task request to work for all types with weak strict ordering, code below uses the < operator when comparing key values. The three points are noted in the code below.

Actually supporting arbitrary types would then require at a minimum a user supplied less-than function, and values referenced from an array of interface{} types. More efficient and flexible though is the sort interface of the Go sort package. Replicating that here seemed beyond the scope of the task so code was left written to sort an array of ints.

Go has no language support for indexing with discrete types other than integer types, so this was not coded.

Finally, the choice of a recursive closure over passing slices to a recursive function is really just a very small optimization. Slices are cheap because they do not copy the underlying array, but there's still a tiny bit of overhead in constructing the slice object. Passing just the two numbers is in the interest of avoiding that overhead. <lang go>package main

import "fmt"

func main() {

   list := []int{31, 41, 59, 26, 53, 58, 97, 93, 23, 84}
   fmt.Println("unsorted:", list)

   quicksort(list)
   fmt.Println("sorted!  ", list)

}

func quicksort(a []int) {

   var pex func(int, int)
   pex = func(lower, upper int) {
       for {
           switch upper - lower {
           case -1, 0: // 0 or 1 item in segment.  nothing to do here!
               return
           case 1: // 2 items in segment
               // < operator respects strict weak order
               if a[upper] < a[lower] {
                   // a quick exchange and we're done.
                   a[upper], a[lower] = a[lower], a[upper]
               }
               return
           // Hoare suggests optimized sort-3 or sort-4 algorithms here,
           // but does not provide an algorithm.
           }

           // Hoare stresses picking a bound in a way to avoid worst case
           // behavior, but offers no suggestions other than picking a
           // random element.  A function call to get a random number is
           // relatively expensive, so the method used here is to simply
           // choose the middle element.  This at least avoids worst case
           // behavior for the obvious common case of an already sorted list.
           bx := (upper + lower) / 2
           b := a[bx]  // b = Hoare's "bound" (aka "pivot")
           lp := lower // lp = Hoare's "lower pointer"
           up := upper // up = Hoare's "upper pointer"
       outer:
           for {
               // use < operator to respect strict weak order
               for lp < upper && !(b < a[lp]) {
                   lp++
               }
               for {
                   if lp > up {
                       // "pointers crossed!"
                       break outer
                   }
                   // < operator for strict weak order
                   if a[up] < b {
                       break // inner
                   }
                   up--
               }
               // exchange
               a[lp], a[up] = a[up], a[lp]
               lp++
               up--
           }
           // segment boundary is between up and lp, but lp-up might be
           // 1 or 2, so just call segment boundary between lp-1 and lp.
           if bx < lp {
               // bound was in lower segment
               if bx < lp-1 {
                   // exchange bx with lp-1
                   a[bx], a[lp-1] = a[lp-1], b
               }
               up = lp - 2
           } else {
               // bound was in upper segment
               if bx > lp {
                   // exchange
                   a[bx], a[lp] = a[lp], b
               }
               up = lp - 1
               lp++
           }
           // "postpone the larger of the two segments" = recurse on
           // the smaller segment, then iterate on the remaining one.
           if up-lower < upper-lp {
               pex(lower, up)
               lower = lp
           } else {
               pex(lp, upper)
               upper = up
           }
       }
   }
   pex(0, len(a)-1)

}</lang> Output:

unsorted: [31 41 59 26 53 58 97 93 23 84]
sorted!   [23 26 31 41 53 58 59 84 93 97]

Haskell

The famous two-liner, reflecting the underlying algorithm directly: <lang haskell>qsort [] = [] qsort (x:xs) = qsort [y | y <- xs, y < x] ++ [x] ++ qsort [y | y <- xs, y >= x]</lang> A more efficient version, doing only one comparison per element: <lang haskell>import Data.List

qsort [] = [] qsort (x:xs) = qsort ys ++ x : qsort zs where (ys, zs) = partition (< x) xs</lang>

IDL

IDL has a powerful optimized sort() built-in. The following is thus merely for demonstration. <lang idl>function qs, arr

 if (count = n_elements(arr)) lt 2 then return,arr
 pivot = total(arr) / count ; use the average for want of a better choice
 return,[qs(arr[where(arr le pivot)]),qs(arr[where(arr gt pivot)])]
end</lang>

Example:

IDL> print,qs([3,17,-5,12,99])
     -5       3      12      17      99

Icon and Unicon

<lang Icon>procedure main() #: demonstrate various ways to sort a list and string

  demosort(quicksort,[3, 14, 1, 5, 9, 2, 6, 3],"qwerty")

end

procedure quicksort(X,op,lower,upper) #: return sorted list local pivot,x

  if /lower := 1 then {                                   # top level call setup
     upper := *X   
     op := sortop(op,X)                                   # select how and what we sort
     }

  if upper - lower > 0 then {
     every x := quickpartition(X,op,lower,upper) do       # find a pivot and sort ...
         /pivot | X := x                                  # ... how to return 2 values w/o a structure
     X := quicksort(X,op,lower,pivot-1)                   # ... left            
     X := quicksort(X,op,pivot,upper)                     # ... right
     }

  return X                                             

end

procedure quickpartition(X,op,lower,upper) #: quicksort partitioner helper local pivot static pivotL initial pivotL := list(3)

  pivotL[1] := X[lower]                                   # endpoints
  pivotL[2] := X[upper]                                   # ... and
  pivotL[3] := X[lower+?(upper-lower)]                    # ... random midpoint
  if op(pivotL[2],pivotL[1]) then pivotL[2] :=: pivotL[1] # mini-
  if op(pivotL[3],pivotL[2]) then pivotL[3] :=: pivotL[2] # ... sort
  pivot := pivotL[2]                                      # median is pivot

  lower -:= 1
  upper +:= 1
  while lower < upper do {                                # find values on wrong side of pivot ...
     while op(pivot,X[upper -:= 1])                       # ... rightmost 
     while op(X[lower +:=1],pivot)                        # ... leftmost
     if lower < upper then                                # not crossed yet
        X[lower] :=: X[upper]                             # ... swap 
     }

  suspend lower                                           # 1st return pivot point
  suspend X                                               # 2nd return modified X (in case immutable)

end</lang>

Implementation notes:

• Since this transparently sorts both string and list arguments the result must 'return' to bypass call by value (strings)
• The partition procedure must "return" two values - 'suspend' is used to accomplish this

Algorithm notes:

• The use of a type specific sorting operator meant that a general pivot choice need to be made. The median of the ends and random middle seemed reasonable. It turns out to have been suggested by Sedgewick.
• Sedgewick's suggestions for tail calling to recurse into the larger side and using insertion sort below a certain size were not implemented. (Q: does Icon/Unicon has tail calling optimizations?)

Note: This example relies on the supporting procedures 'sortop', and 'demosort' in Bubble Sort. The full demosort exercises the named sort of a list with op = "numeric", "string", ">>" (lexically gt, descending),">" (numerically gt, descending), a custom comparator, and also a string.

Abbreviated sample output:

Sorting Demo using procedure quicksort
  on list : [ 3 14 1 5 9 2 6 3 ]
    with op = &null:         [ 1 2 3 3 5 6 9 14 ]   (0 ms)
  ...
  on string : "qwerty"
    with op = &null:         "eqrtwy"   (0 ms)

Io

<lang io>List do(

   quickSort := method(
       if(size > 1) then(
           pivot := at(size / 2 floor)
           return select(x, x < pivot) quickSort appendSeq(
               select(x, x == pivot) appendSeq(select(x, x > pivot) quickSort)
           )
       ) else(return self)
   )

   quickSortInPlace := method(
       copy(quickSort)
   )

)

lst := list(5, -1, -4, 2, 9) lst quickSort println # ==> list(-4, -1, 2, 5, 9) lst quickSortInPlace println # ==> list(-4, -1, 2, 5, 9)</lang> Another more low-level Quicksort implementation can be found in Io's [github ] repository.

J

Generally, this task should be accomplished in J using /:~. Here we take an approach that's more comparable with the other examples on this page.

<lang j>sel=: 1 : 'x # ['

quicksort=: 3 : 0

if.
 1 >: #y
do.
 y
else.
 e=. y{~?#y
 (quicksort y <sel e),(y =sel e),quicksort y >sel e
end.

)</lang>

See the Quicksort essay in the J Wiki for additional explanations and examples.

Java

Works with: Java version 1.5+

Translation of: Python

<lang java5>public static <E extends Comparable<? super E>> List<E> quickSort(List<E> arr) {

   if (arr.size() <= 1)
       return arr;
   E pivot = arr.getFirst(); //This pivot can change to get faster results

   List<E> less = new LinkedList<E>();
   List<E> pivotList = new LinkedList<E>();
   List<E> more = new LinkedList<E>();

   // Partition
   for (E i: arr) {
       if (i.compareTo(pivot) < 0)
           less.add(i);
       else if (i.compareTo(pivot) > 0)
           more.add(i);
       else
           pivotList.add(i);
   }

   // Recursively sort sublists
   less = quickSort(less);
   more = quickSort(more);

   // Concatenate results
   less.addAll(pivotList);
   less.addAll(more);
   return less;

}</lang>

JavaScript

<lang javascript>function sort(array, less) {

 function swap(i, j) { var t=array[i]; array[i]=array[j]; array[j]=t }

 function quicksort(left, right) {

   if (left < right) {

     var pivot = array[(left + right) >> 1];
     var left_new = left, right_new = right;

     do {
       while (less(array[left_new], pivot)
         left_new++;
       while (less(pivot, array[right_new])
         right_new--;
       if (left_new  <= right_new)
         swap(left_new++, right_new--);
     } while (left_new  <= right_new);

     quicksort(left, right_new);
     quicksort(left_new, right);

   }
 }

 quicksort(0, array.length-1);

 return array;

}</lang>

The functional programming way

<lang javascript>Array.prototype.quick_sort = function () {

   if (this.length <= 1)
       return this;

   var pivot = this[Math.round(this.length / 2)];

   return this.filter(function (x) { return x <  pivot }).quick_sort().concat(
          this.filter(function (x) { return x == pivot })).concat(
          this.filter(function (x) { return x >  pivot }).quick_sort());

}</lang>

Joy

<lang joy> DEFINE qsort ==

 [small]            # termination condition: 0 or 1 element
 []                 # do nothing
 [uncons [>] split] # pivot and two lists
 [enconcat]         # insert the pivot after the recursion
 binrec.            # recursion on the two lists

</lang>

K

<lang K>quicksort:{f:*x@1?#x;:[0=#x;x;,/(_f x@&x<f;x@&x=f;_f x@&x>f)]}</lang>

Example:

<lang K>

   quicksort 1 3 5 7 9 8 6 4 2

</lang>

Output:

<lang K> 1 2 3 4 5 6 7 8 9 </lang>

Explanation:

<lang K>

 _f()

</lang>

is the current function called recursively.

<lang K>

  :[....] 

</lang>

generally means :[condition1;then1;condition2;then2;....;else]. Though here it is used as :[if;then;else].

This construct

<lang K>

  f:*x@1?#x

</lang>

assigns a random element in x (the argument) to f, as the pivot value.

And here is the full if/then/else clause:

<lang K>

   :[
       0=#x;           / if length of x is zero 
       x;              / then return x
                       / else
       ,/(             / join the results of: 
         _f x@&x<f         / sort (recursively) elements less than f (pivot)
         x@&x=f            / element equal to f 
         _f x@&x>f)        / sort (recursively) elements greater than f 
    ]

</lang>

Though - as with APL and J - for larger arrays it's much faster to sort using "<" (grade up) which gives the indices of the list sorted ascending, i.e.

<lang K>

  t@<t:1 3 5 7 9 8 6 4 2

</lang>

Logo

<lang logo>; quicksort (lists, functional)

to small? :list

 output or [empty? :list] [empty? butfirst :list]

end to quicksort :list

 if small? :list [output :list]
 localmake "pivot first :list
 output (sentence
   quicksort filter [? < :pivot] butfirst :list
             filter [? = :pivot]          :list
   quicksort filter [? > :pivot] butfirst :list
 )

end

show quicksort [1 3 5 7 9 8 6 4 2]</lang> <lang logo>; quicksort (arrays, in-place)

to incr :name

 make :name (thing :name) + 1

end to decr :name

 make :name (thing :name) - 1

end to swap :i :j :a

 localmake "t item :i :a
 setitem :i :a item :j :a
 setitem :j :a :t

end

to quick :a :low :high

 if :high <= :low [stop]
 localmake "l :low
 localmake "h :high
 localmake "pivot item ashift (:l + :h) -1  :a
 do.while [
   while [(item :l :a) < :pivot] [incr "l]
   while [(item :h :a) > :pivot] [decr "h]
   if :l <= :h [swap :l :h :a  incr "l  decr "h]
 ] [:l <= :h]
 quick :a :low :h
 quick :a :l :high

end to sort :a

 quick :a first :a count :a

end

make "test {1 3 5 7 9 8 6 4 2} sort :test show :test</lang>

Logtalk

<lang logtalk>quicksort(List, Sorted) :-

   quicksort(List, [], Sorted).

quicksort([], Sorted, Sorted). quicksort([Pivot| Rest], Acc, Sorted) :-

   partition(Rest, Pivot, Smaller0, Bigger0),
   quicksort(Smaller0, [Pivot| Bigger], Sorted),
   quicksort(Bigger0, Acc, Bigger).

partition([], _, [], []). partition([X| Xs], Pivot, Smalls, Bigs) :-

   (   X @< Pivot ->
       Smalls = [X| Rest],
       partition(Xs, Pivot, Rest, Bigs)
   ;   Bigs = [X| Rest],
       partition(Xs, Pivot, Smalls, Rest)
   ).</lang>

Lua

<lang lua>--in-place quicksort function quicksort(t, start, endi)

 start, endi = start or 1, endi or #t
 --partition w.r.t. first element
 if(endi - start < 2) then return t end
 local pivot = start
 for i = start + 1, endi do
   if t[i] <= t[pivot] then
     local temp = t[pivot + 1]
     t[pivot + 1] = t[pivot]
     if(i == pivot + 1) then
       t[pivot] = temp
     else
       t[pivot] = t[i]
       t[i] = temp
     end
     pivot = pivot + 1
   end
 end
 t = quicksort(t, start, pivot - 1)
 return quicksort(t, pivot + 1, endi)

end

--example print(unpack(quicksort{5, 2, 7, 3, 4, 7, 1}))</lang>

Lucid

[1] <lang lucid>qsort(a) = if eof(first a) then a else follow(qsort(b0),qsort(b1)) fi

where
   p = first a < a;
   b0 = a whenever p;
   b1 = a whenever not p;
   follow(x,y) = if xdone then y upon xdone else x fi
                   where
                      xdone = iseod x fby xdone or iseod x; 
                   end;
end</lang>

M4

<lang M4>dnl return the first element of a list when called in the funny way seen below define(`arg1', `$1')dnl dnl dnl append lists 1 and 2 define(`append',

  `ifelse(`$1',`()',
     `$2',
     `ifelse(`$2',`()',
        `$1',
        `substr($1,0,decr(len($1))),substr($2,1)')')')dnl

dnl dnl separate list 2 based on pivot 1, appending to left 3 and right 4, dnl until 2 is empty, and then combine the sort of left with pivot with dnl sort of right define(`sep',

  `ifelse(`$2', `()',
     `append(append(quicksort($3),($1)),quicksort($4))',
     `ifelse(eval(arg1$2<=$1),1,
        `sep($1,(shift$2),append($3,(arg1$2)),$4)',
        `sep($1,(shift$2),$3,append($4,(arg1$2)))')')')dnl

dnl dnl pick first element of list 1 as pivot and separate based on that define(`quicksort',

  `ifelse(`$1', `()',
     `()',
     `sep(arg1$1,(shift$1),`()',`()')')')dnl

dnl quicksort((3,1,4,1,5,9))</lang>

Output:

(1,1,3,4,5,9)

Mathematica

<lang Mathematica>QuickSort[x_List] := Module[{pivot},

 If[Length@x <= 1, Return[x]];
 pivot = RandomChoice@x;
 Flatten@{QuickSort[Cases[x, j_ /; j < pivot]], Cases[x, j_ /; j == pivot], QuickSort[Cases[x, j_ /; j > pivot]]}
 ]</lang>

MATLAB

This implements the pseudo-code in the specification. The input can be either a row or column vector, but the returned vector will always be a row vector. This can be modified to operate on any built-in primitive or user defined class by replacing the "<=" and ">" comparisons with "le" and "gt" functions respectively. This is because operators can not be overloaded, but the functions that are equivalent to the operators can be overloaded in class definitions.

This should be placed in a file named quickSort.m. <lang Matlab>function sortedArray = quickSort(array)

   if numel(array) <= 1 %If the array has 1 element then it can't be sorted       
       sortedArray = array;
       return
   end
   
   pivot = array(end);
   array(end) = [];
       
   %Create two new arrays which contain the elements that are less than or
   %equal to the pivot called "less" and greater than the pivot called
   %"greater"
   less = array( array <= pivot );
   greater = array( array > pivot );
   
   %The sorted array is the concatenation of the sorted "less" array, the
   %pivot and the sorted "greater" array in that order
   sortedArray = [quickSort(less) pivot quickSort(greater)];
   

end</lang>

A slightly more vectorized version of the above code that removes the need for the less and greater arrays: <lang Matlab>function sortedArray = quickSort(array)

   if numel(array) <= 1 %If the array has 1 element then it can't be sorted       
       sortedArray = array;
       return
   end
   
   pivot = array(end);
   array(end) = [];
   
   sortedArray = [quickSort( array(array <= pivot) ) pivot quickSort( array(array > pivot) )];
   

end</lang>

Sample usage: <lang MATLAB>quickSort([4,3,7,-2,9,1])

ans =

   -2     1     3     4     7     9</lang>

MAXScript

<lang maxscript>fn quickSort arr = (

   less = #()
   pivotList = #()
   more = #()
   if arr.count <= 1 then
   (
       arr
   )
   else
   (
       pivot = arr[arr.count/2]
       for i in arr do
       (
           case of
           (
               (i < pivot):	(append less i)
               (i == pivot):	(append pivotList i)
               (i > pivot):	(append more i)
           )
       )
       less = quickSort less
       more = quickSort more
       less + pivotList + more
   )

) a = #(4, 89, -3, 42, 5, 0, 2, 889) a = quickSort a</lang>

Modula-2

The definition module exposes the interface. This one uses the procedure variable feature to pass a caller defined compare callback function so that it can sort various simple and structured record types.

This Quicksort assumes that you are working with an an array of pointers to an arbitrary type and are not moving the record data itself but only the pointers. The M2 type "ADDRESS" is considered compatible with any pointer type.

The use of type ADDRESS here to achieve genericity is something of a chink the the normal strongly typed flavor of Modula-2. Unlike the other language types, "system" types such as ADDRESS or WORD must be imported explicity from the SYSTEM MODULE. The ISO standard for the "Generic Modula-2" language extension provides genericity without the chink, but most compilers have not implemented this extension.

<lang Modula2>(*#####################*)

DEFINITION MODULE QSORT; 

(*#####################*)

FROM SYSTEM IMPORT ADDRESS;

TYPE CmpFuncPtrs = PROCEDURE(ADDRESS, ADDRESS):INTEGER;

PROCEDURE QuickSortPtrs(VAR Array:ARRAY OF ADDRESS; N:CARDINAL;
                        Compare:CmpFuncPtrs);

END QSORT.

</lang>

The implementation module is not visible to clients, so it may be changed without worry so long as it still implements the definition.

Sedgewick suggests that faster sorting will be achieved if you drop back to an insertion sort once the partitions get small.

<lang Modula2>(*##########################*)

IMPLEMENTATION MODULE QSORT; 

(*##########################*)

FROM SYSTEM IMPORT ADDRESS;

CONST SmallPartition = 9;

(* NOTE

       1.Reference on QuickSort: "Implementing Quicksort Programs", Robert
         Sedgewick, Communications of the ACM, Oct 78, v21 #10.

• )

(*==============================================================*)

PROCEDURE QuickSortPtrs(VAR Array:ARRAY OF ADDRESS; N:CARDINAL;
                        Compare:CmpFuncPtrs);

(*==============================================================*)

        (*-----------------------------*)
         PROCEDURE Swap(VAR A,B:ADDRESS);
        (*-----------------------------*)

        VAR  temp :ADDRESS;

        BEGIN

        temp := A; A := B; B := temp;

        END Swap;

        (*-------------------------------*)
         PROCEDURE TstSwap(VAR A,B:ADDRESS);
        (*-------------------------------*)

        VAR  temp   :ADDRESS;

        BEGIN

        IF Compare(A,B) > 0 THEN
           temp := A; A := B; B := temp;
        END;

        END TstSwap;

        (*--------------*)
         PROCEDURE Isort;
        (*--------------*)
        (*
                Insertion sort.
        *)

        VAR  i,j    :CARDINAL;
             temp   :ADDRESS;

        BEGIN

        IF N < 2 THEN RETURN END;

        FOR i := N-2 TO 0 BY -1 DO
           IF Compare(Array[i],Array[i+1]) > 0 THEN
              temp := Array[i];
              j := i+1;
              REPEAT
                 Array[j-1] := Array[j];
                 INC(j);
              UNTIL (j = N) OR (Compare(Array[j],temp) >= 0);
              Array[j-1] := temp;
           END;
        END;

        END Isort;

        (*----------------------------------*)
         PROCEDURE Quick(left,right:CARDINAL);
        (*----------------------------------*)

        VAR
             i,j,
             second     :CARDINAL;
             Partition  :ADDRESS;

        BEGIN

        IF right > left THEN
           i := left; j := right;

           Swap(Array[left],Array[(left+right) DIV 2]);

           second := left+1;                          (* insure 2nd element is in   *)
           TstSwap(Array[second], Array[right]);      (* the lower part, last elem  *)
           TstSwap(Array[left], Array[right]);        (* in the upper part          *)
           TstSwap(Array[second], Array[left]);       (* THUS, only one test is     *)
                                                      (* needed in repeat loops     *)
           Partition := Array[left];

           LOOP
              REPEAT INC(i) UNTIL Compare(Array[i],Partition) >= 0;
              REPEAT DEC(j) UNTIL Compare(Array[j],Partition) <= 0;
              IF j < i THEN
                 EXIT
              END;
              Swap(Array[i],Array[j]);
           END; (*loop*)
           Swap(Array[left],Array[j]);

           IF (j > 0) AND (j-1-left >= SmallPartition) THEN
              Quick(left,j-1);
           END;
           IF right-i >= SmallPartition THEN
              Quick(i,right);
           END;
        END;

        END Quick;

BEGIN (* QuickSortPtrs --------------------------------------------------*)

IF N > SmallPartition THEN (* won't work for 2 elements *)

  Quick(0,N-1);

END;

Isort;

END QuickSortPtrs;

END QSORT. </lang>

Modula-3

This code is taken from libm3, which is basically Modula-3's "standard library". Note that this code uses Insertion sort when the array is less than 9 elements long.

<lang modula3>GENERIC INTERFACE ArraySort(Elem);

PROCEDURE Sort(VAR a: ARRAY OF Elem.T; cmp := Elem.Compare);

END ArraySort.</lang>

<lang modula3>GENERIC MODULE ArraySort (Elem);

PROCEDURE Sort (VAR a: ARRAY OF Elem.T; cmp := Elem.Compare) =

 BEGIN
   QuickSort (a, 0, NUMBER (a), cmp);
   InsertionSort (a, 0, NUMBER (a), cmp);
 END Sort;

PROCEDURE QuickSort (VAR a: ARRAY OF Elem.T; lo, hi: INTEGER;

                    cmp := Elem.Compare) =
 CONST CutOff = 9;
 VAR i, j: INTEGER;  key, tmp: Elem.T;
 BEGIN
   WHILE (hi - lo > CutOff) DO (* sort a[lo..hi) *)

     (* use median-of-3 to select a key *)
     i := (hi + lo) DIV 2;
     IF cmp (a[lo], a[i]) < 0 THEN
       IF cmp (a[i], a[hi-1]) < 0 THEN
         key := a[i];
       ELSIF cmp (a[lo], a[hi-1]) < 0 THEN
         key := a[hi-1];  a[hi-1] := a[i];  a[i] := key;
       ELSE
         key := a[lo];  a[lo] := a[hi-1];  a[hi-1] := a[i];  a[i] := key;
       END;
     ELSE (* a[lo] >= a[i] *)
       IF cmp (a[hi-1], a[i]) < 0 THEN
         key := a[i];  tmp := a[hi-1];  a[hi-1] := a[lo];  a[lo] := tmp;
       ELSIF cmp (a[lo], a[hi-1]) < 0 THEN
         key := a[lo];  a[lo] := a[i];  a[i] := key;
       ELSE
         key := a[hi-1];  a[hi-1] := a[lo];  a[lo] := a[i];  a[i] := key;
       END;
     END;

     (* partition the array *)
     i := lo+1;  j := hi-2;

     (* find the first hole *)
     WHILE cmp (a[j], key) > 0 DO DEC (j) END;
     tmp := a[j];
     DEC (j);

     LOOP
       IF (i > j) THEN EXIT END;

       WHILE i < hi AND cmp (a[i], key) < 0 DO INC (i) END;
       IF (i > j) THEN EXIT END;
       a[j+1] := a[i];
       INC (i);

       WHILE j > lo AND cmp (a[j], key) > 0 DO DEC (j) END;
       IF (i > j) THEN  IF (j = i-1) THEN  DEC (j)  END;  EXIT  END;
       a[i-1] := a[j];
       DEC (j);
     END;

     (* fill in the last hole *)
     a[j+1] := tmp;
     i := j+2;

     (* then, recursively sort the smaller subfile *)
     IF (i - lo < hi - i)
       THEN  QuickSort (a, lo, i-1, cmp);   lo := i;
       ELSE  QuickSort (a, i, hi, cmp);     hi := i-1;
     END;

   END; (* WHILE (hi-lo > CutOff) *)
 END QuickSort;

PROCEDURE InsertionSort (VAR a: ARRAY OF Elem.T; lo, hi: INTEGER;

                        cmp := Elem.Compare) =
 VAR j: INTEGER;  key: Elem.T;
 BEGIN
   FOR i := lo+1 TO hi-1 DO
     key := a[i];
     j := i-1;
     WHILE (j >= lo) AND cmp (key, a[j]) < 0 DO
       a[j+1] := a[j];
       DEC (j);
     END;
     a[j+1] := key;
   END;
 END InsertionSort;

BEGIN END ArraySort.</lang>

To use this generic code to sort an array of text, we create two files called TextSort.i3 and TextSort.m3, respectively.

<lang modula3>INTERFACE TextSort = ArraySort(Text) END TextSort.</lang> <lang modula3>MODULE TextSort = ArraySort(Text) END TextSort.</lang>

Then, as an example: <lang modula3>MODULE Main;

IMPORT IO, TextSort;

VAR arr := ARRAY [1..10] OF TEXT {"Foo", "bar", "!ooF", "Modula-3", "hickup",

                                "baz", "quuz", "Zeepf", "woo", "Rosetta Code"};

BEGIN

 TextSort.Sort(arr);
 FOR i := FIRST(arr) TO LAST(arr) DO
   IO.Put(arr[i] & "\n");
 END;

END Main.</lang>

Nemerle

Translation of: Haskell

A little less clean and concise than Haskell, but essentially the same. <lang Nemerle>using System; using System.Console; using Nemerle.Collections.NList;

module Quicksort {

   Qsort[T] (x : list[T]) : list[T]
     where T : IComparable
   {
       |[]    => []
       |x::xs => Qsort($[y|y in xs, (y.CompareTo(x) < 0)]) + [x] + Qsort($[y|y in xs, (y.CompareTo(x) > 0)])
   }
   
   Main() : void
   {
       def empty = [];
       def single = [2];
       def several = [2, 6, 1, 7, 3, 9, 4];
       WriteLine(Qsort(empty));
       WriteLine(Qsort(single));
       WriteLine(Qsort(several));
   }

}</lang>

NetRexx

This sample implements both the simple and in place algorithms as described in the task's description: <lang NetRexx>/* NetRexx */ options replace format comments java crossref savelog symbols binary

import java.util.List

placesList = [String -

   "UK  London",     "US  New York",   "US  Boston",     "US  Washington" -
 , "UK  Washington", "US  Birmingham", "UK  Birmingham", "UK  Boston"     -

] lists = [ -

   placesList -
 , quickSortSimple(String[] Arrays.copyOf(placesList, placesList.length)) -
 , quickSortInplace(String[] Arrays.copyOf(placesList, placesList.length)) -

]

loop ln = 0 to lists.length - 1

 cl = lists[ln]
 loop ct = 0 to cl.length - 1
   say cl[ct]
   end ct
   say
 end ln

return

method quickSortSimple(array = String[]) public constant binary returns String[]

 rl = String[array.length]
 al = List quickSortSimple(Arrays.asList(array))
 al.toArray(rl)

 return rl

method quickSortSimple(array = List) public constant binary returns ArrayList

 if array.size > 1 then do
   less    = ArrayList()
   equal   = ArrayList()
   greater = ArrayList()

   pivot = array.get(Random().nextInt(array.size - 1))
   loop x_ = 0 to array.size - 1
     if (Comparable array.get(x_)).compareTo(Comparable pivot) < 0 then less.add(array.get(x_))
     if (Comparable array.get(x_)).compareTo(Comparable pivot) = 0 then equal.add(array.get(x_))
     if (Comparable array.get(x_)).compareTo(Comparable pivot) > 0 then greater.add(array.get(x_))
     end x_
   less    = quickSortSimple(less)
   greater = quickSortSimple(greater)
   out = ArrayList(array.size)
   out.addAll(less)
   out.addAll(equal)
   out.addAll(greater)

   array = out
   end

 return ArrayList array

method quickSortInplace(array = String[]) public constant binary returns String[]

 rl = String[array.length]
 al = List quickSortInplace(Arrays.asList(array))
 al.toArray(rl)

 return rl

method quickSortInplace(array = List, ixL = int 0, ixR = int array.size - 1) public constant binary returns ArrayList

 if ixL < ixR then do
   ixP = int ixL + (ixR - ixL) % 2
   ixP = quickSortInplacePartition(array, ixL, ixR, ixP)
   quickSortInplace(array, ixL, ixP - 1)
   quickSortInplace(array, ixP + 1, ixR)
   end

 array = ArrayList(array)
 return ArrayList array

method quickSortInplacePartition(array = List, ixL = int, ixR = int, ixP = int) public constant binary returns int

 pivotValue = array.get(ixP)
 rValue     = array.get(ixR)
 array.set(ixP, rValue)
 array.set(ixR, pivotValue)
 ixStore = ixL
 loop i_ = ixL to ixR - 1
   iValue = array.get(i_)
   if (Comparable iValue).compareTo(Comparable pivotValue) < 0 then do
     storeValue = array.get(ixStore)
     array.set(i_, storeValue)
     array.set(ixStore, iValue)
     ixStore = ixStore + 1
     end
   end i_
 storeValue = array.get(ixStore)
 rValue     = array.get(ixR)
 array.set(ixStore, rValue)
 array.set(ixR, storeValue)

 return ixStore

</lang>

Output

UK  London
US  New York
US  Boston
US  Washington
UK  Washington
US  Birmingham
UK  Birmingham
UK  Boston

UK  Birmingham
UK  Boston
UK  London
UK  Washington
US  Birmingham
US  Boston
US  New York
US  Washington

UK  Birmingham
UK  Boston
UK  London
UK  Washington
US  Birmingham
US  Boston
US  New York
US  Washington

Nial

<lang nial>quicksort is fork [ >= [1 first,tally],

 pass,
 link [
     quicksort sublist [ < [pass, first], pass ],
     sublist [ match [pass,first],pass ],
     quicksort sublist [ > [pass,first], pass ]
 ]

]</lang>

Using it. <lang nial>|quicksort [5, 8, 7, 4, 3] =3 4 5 7 8</lang>

Nimrod

<lang python>proc QuickSort(list: seq[int]): seq[int] =

   if len(list) == 0:
       return @[]

   var pivot = list[0]

   var left: seq[int] = @[]
   var right: seq[int] = @[]
   for i in low(list)+1..high(list):
       if list[i] <= pivot:
           left.add(list[i])
       elif list[i] > pivot:
           right.add(list[i])

   result = QuickSort(left) 
   result.add(pivot)
   result.add(QuickSort(right))</lang>

Usage: <lang python>var sorted: seq[int] = QuickSort(@[5,2,1,6,2,3,1,2,123,21,54,6,1]) for i in items(sorted):

 echo(i)</lang>

Objeck

<lang objeck> class QuickSort {

 function : Main(args : String[]) ~ Nil {
   array := [1, 3, 5, 7, 9, 8, 6, 4, 2];
   Sort(array);
   each(i : array) {
     array[i]->PrintLine();
   };
 }

 function : Sort(array : Int[]) ~ Nil {
   size := array->Size();
   if(size <= 1) {
     return;
   };
   Sort(array, 0, size - 1);
 }

 function : native : Sort(array : Int[], low : Int, high : Int) ~ Nil {
   i := low; j := high;
   pivot := array[low + (high-low)/2];

   while(i <= j) {
     while(array[i] < pivot) {
       i+=1;
     };

     while(array[j] > pivot) {
       j-=1;
     };

     if (i <= j) {
       temp := array[i];
       array[i] := array[j];
       array[j] := temp;
       i+=1; j-=1;
     };
   };

   if(low < j) {
     Sort(array, low, j);
   };

   if(i < high) {
     Sort(array, i, high);
   };
 }

} </lang>

Objective C

The latest XCode compiler is assumed with ARC enabled. <lang objc>void quicksortInPlace(NSMutableArray *array, const long first, const long last) {

   if (first >= last) return;
   NSValue *pivot = array[(first + last) / 2];
   long left = first;
   long right = last;
   while (left <= right) {
       while ([array[left] isLessThan:pivot])
           left++;
       while ([array[right] isGreaterThan:pivot])
           right--;
       if (left <= right)
           [array exchangeObjectAtIndex:left++ withObjectAtIndex:right--];
   }
   quicksortInPlace(array, first, right);
   quicksortInPlace(array, left, last);

}

NSArray* quicksort(NSArray *unsorted) {

   NSMutableArray *a = [NSMutableArray arrayWithArray:unsorted];
   quicksortInPlace(a, 0, a.count - 1);
   return a;

}

int main(int argc, const char * argv[]) {

   @autoreleasepool {
       NSArray *a = @[ @1, @3, @5, @7, @9, @8, @6, @4, @2 ];
       NSLog(@"Unsorted: %@", a);
       NSLog(@"Sorted: %@", quicksort(a));
       NSArray *b = @[ @"Emil", @"Peg", @"Helen", @"Juergen", @"David", @"Rick", @"Barb", @"Mike", @"Tom" ];
       NSLog(@"Unsorted: %@", b);
       NSLog(@"Sorted: %@", quicksort(b));
   }
   return 0;

}</lang>

Output:

Unsorted: (
    1,
    3,
    5,
    7,
    9,
    8,
    6,
    4,
    2
)
Sorted: (
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9
)
Unsorted: (
    Emil,
    Peg,
    Helen,
    Juergen,
    David,
    Rick,
    Barb,
    Mike,
    Tom
)
Sorted: (
    Barb,
    David,
    Emil,
    Helen,
    Juergen,
    Mike,
    Peg,
    Rick,
    Tom
)

OCaml

<lang ocaml>let rec quicksort gt = function

 | [] -> []
 | x::xs ->
     let ys, zs = List.partition (gt x) xs in
     (quicksort gt ys) @ (x :: (quicksort gt zs))

let _ =

 quicksort (>) [4; 65; 2; -31; 0; 99; 83; 782; 1]</lang>

Octave

Translation of: MATLAB

(The MATLAB version works as is in Octave, provided that the code is put in a file named quicksort.m, and everything below the return must be typed in the prompt of course)

<lang octave>function f=quicksort(v)  % v must be a column vector

 f = v; n=length(v);
 if(n > 1)
    vl = min(f); vh = max(f);                  % min, max
    p  = (vl+vh)*0.5;                          % pivot
    ia = find(f < p); ib = find(f == p); ic=find(f > p);
    f  = [quicksort(f(ia)); f(ib); quicksort(f(ic))];
 end

endfunction

N=30; v=rand(N,1); tic,u=quicksort(v); toc u</lang>

ooRexx

Translation of: Python

<lang ooRexx>

   a = .array~Of(4, 65, 2, -31, 0, 99, 83, 782, 1)
   a = quickSort(a)
   say a~toString( ,', ')
   exit

routine quickSort

   use arg arr -- the array to be sorted
   less = .array~new
   pivotList = .array~new
   more = .array~new
   if arr~items <= 1 then
       return arr
   else do
       pivot = arr[1]
       do i over arr
           if i < pivot then
               less~append(i)
           else if i > pivot then
               more~append(i)
           else
               pivotList~append(i)
       end
       less = quickSort(less)
       more = quickSort(more)
       return less~~appendAll(pivotList)~~appendAll(more)
   end</lang>

Oz

<lang oz>declare

 fun {QuickSort Xs}
    case Xs of nil then nil
    [] Pivot|Xr then

fun {IsSmaller X} X < Pivot end

       Smaller Larger
    in

{List.partition Xr IsSmaller ?Smaller ?Larger}

       {Append {QuickSort Smaller} Pivot|{QuickSort Larger}}
    end
 end

in

 {Show {QuickSort [3 1 4 1 5 9 2 6 5]}}</lang>

PARI/GP

<lang parigp>quickSort(v)={

 if(#v<2, return(v));
 my(less=List(),more=List(),same=List(),pivot);
 pivot=median([v[random(#v)+1],v[random(#v)+1],v[random(#v)+1]]); \\ Middle-of-three
 for(i=1,#v,
   if(v[i]<pivot,
     listput(less, v[i]),
     if(v[i]==pivot, listput(same, v[i]), listput(more, v[i]))
   )
 );
 concat(quickSort(Vec(less)), concat(Vec(same), quickSort(Vec(more))))

}; median(v)={

 vecsort(v)[#v>>1]

};</lang>

Pascal

<lang pascal> { X is array of LongInt } Procedure QuickSort ( Left, Right : LongInt ); Var

 i, j : LongInt;
 tmp, pivot : LongInt;         { tmp & pivot are the same type as the elements of array }

Begin

 i:=Left;
 j:=Right;
 pivot := X[(Left + Right) shr 1]; // pivot := X[(Left + Rigth) div 2] 
 Repeat
   While pivot > X[i] Do i:=i+1;
   While pivot < X[j] Do j:=j-1;
   If i<j Then Begin
     tmp:=X[i];
     X[i]:=X[j];
     X[j]:=tmp;
     j:=j-1;
     i:=i+1;
   End;
 Until i>j;
 If Left<j Then QuickSort(Left,j);
 If i<Right Then QuickSort(i,Right);

End; </lang>

Perl

<lang perl> sub quick_sort {

   my @a = @_;
   return @a if @a < 2;
   my $p = pop @a;
   quick_sort(grep $_ < $p, @a), $p, quick_sort(grep $_ >= $p, @a);

}

my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1); @a = quick_sort @a; print "@a\n"; </lang>

Perl 6

<lang perl6># Empty list sorts to the empty list

multi quicksort([]) { () }

# Otherwise, extract first item as pivot...
multi quicksort([$pivot, *@rest]) {
    # Partition.
    my @before := @rest.grep(* before $pivot);
    my @after  := @rest.grep(* !before $pivot);

    # Sort the partitions.
    (quicksort(@before), $pivot, quicksort(@after))
}</lang>

Note that @before and @after are bound to lazy lists, so the partitions can (at least in theory) be sorted in parallel.

PHP

<lang php>function quicksort($arr){ $loe = $gt = array(); if(count($arr) < 2){ return $arr; } $pivot_key = key($arr); $pivot = array_shift($arr); foreach($arr as $val){ if($val <= $pivot){ $loe[] = $val; }elseif ($val > $pivot){ $gt[] = $val; } } return array_merge(quicksort($loe),array($pivot_key=>$pivot),quicksort($gt)); }

$arr = array(1, 3, 5, 7, 9, 8, 6, 4, 2); $arr = quicksort($arr); echo implode(',',$arr);</lang>

1,2,3,4,5,6,7,8,9

PicoLisp

<lang lisp>(de quicksort (L)

  (if (cdr L)
     (let Pivot (car L)
         (append (quicksort (filter '((A) (< A Pivot)) (cdr L)))
                            (filter '((A) (= A Pivot))      L )
                 (quicksort (filter '((A) (> A Pivot)) (cdr L)))) )
     L) )</lang>

PL/I

<lang pli>DCL (T(20)) FIXED BIN(31); /* scratch space of length N */

QUICKSORT: PROCEDURE (A,AMIN,AMAX,N) RECURSIVE ;

  DECLARE (A(*))              FIXED BIN(31);
  DECLARE (N,AMIN,AMAX)       FIXED BIN(31) NONASGN;
  DECLARE (I,J,IA,IB,IC,PIV)  FIXED BIN(31);
  DECLARE (P,Q)               POINTER;
  DECLARE (AP(1))             FIXED BIN(31) BASED(P);
  
  IF(N <= 1)THEN RETURN;
  IA=0; IB=0; IC=N+1;
  PIV=(AMIN+AMAX)/2;
  DO I=1 TO N;
     IF(A(I) < PIV)THEN DO;
        IA+=1; A(IA)=A(I);
     END; ELSE IF(A(I) > PIV) THEN DO;
        IC-=1; T(IC)=A(I);
     END; ELSE DO;
        IB+=1; T(IB)=A(I);
     END;
  END;
  DO I=1  TO IB; A(I+IA)=T(I);   END;
  DO I=IC TO N;  A(I)=T(N+IC-I); END;
  P=ADDR(A(IC));
  IC=N+1-IC;
  IF(IA > 1) THEN CALL QUICKSORT(A, AMIN, PIV-1,IA);
  IF(IC > 1) THEN CALL QUICKSORT(AP,PIV+1,AMAX, IC);
  RETURN;

END QUICKSORT;

MINMAX: PROC(A,AMIN,AMAX,N);
  DCL (AMIN,AMAX) FIXED BIN(31),
      (N,A(*))    FIXED BIN(31) NONASGN ;
  DCL (I,X,Y) FIXED BIN(31);
  
  AMIN=A(N); AMAX=AMIN;
  DO I=1 TO N-1;
     X=A(I); Y=A(I+1);
     IF (X < Y)THEN DO;
        IF (X < AMIN) THEN AMIN=X;
        IF (Y > AMAX) THEN AMAX=Y;
      END; ELSE DO;
         IF (X > AMAX) THEN AMAX=X;
         IF (Y < AMIN) THEN AMIN=Y;
      END;
  END;
  RETURN;

END MINMAX; CALL MINMAX(A,AMIN,AMAX,N); CALL QUICKSORT(A,AMIN,AMAX,N);</lang>

PowerShell

<lang PowerShell>Function SortThree( [Array] $data ) { if( $data[ 0 ] -gt $data[ 1 ] ) { if( $data[ 0 ] -lt $data[ 2 ] ) { $data = $data[ 1, 0, 2 ] } elseif ( $data[ 1 ] -lt $data[ 2 ] ){ $data = $data[ 1, 2, 0 ] } else { $data = $data[ 2, 1, 0 ] } } else { if( $data[ 0 ] -gt $data[ 2 ] ) { $data = $data[ 2, 0, 1 ] } elseif( $data[ 1 ] -gt $data[ 2 ] ) { $data = $data[ 0, 2, 1 ] } } $data }

Function QuickSort( [Array] $data, $rand = ( New-Object Random ) ) { $datal = $data.length if( $datal -gt 3 ) { [void] $datal-- $median = ( SortThree $data[ 0, ( $rand.Next( 1, $datal - 1 ) ), -1 ] )[ 1 ] $lt = @() $eq = @() $gt = @() $data | ForEach-Object { if( $_ -lt $median ) { $lt += $_ } elseif( $_ -eq $median ) { $eq += $_ } else { $gt += $_ } } $lt = ( QuickSort $lt $rand ) $gt = ( QuickSort $gt $rand ) $data = @($lt) + $eq + $gt } elseif( $datal -eq 3 ) { $data = SortThree( $data ) } elseif( $datal -eq 2 ) { if( $data[ 0 ] -gt $data[ 1 ] ) { $data = $data[ 1, 0 ] } } $data }

QuickSort 5,3,1,2,4 QuickSort 'e','c','a','b','d' QuickSort 0.5,0.3,0.1,0.2,0.4 $l = 100; QuickSort ( 1..$l | ForEach-Object { $Rand = New-Object Random }{ $Rand.Next( 0, $l - 1 ) } )</lang>

Prolog

<lang prolog>qsort( [], [] ). qsort( [H|U], S ) :- splitBy(H, U, L, R), qsort(L, SL), qsort(R, SR), append(SL, [H|SR], S).

% splitBy( H, U, LS, RS ) % True if LS = { L in U | L <= H }; RS = { R in U | R > H } splitBy( _, [], [], []). splitBy( H, [U|T], [U|LS], RS ) :- U =< H, splitBy(H, T, LS, RS). splitBy( H, [U|T], LS, [U|RS] ) :- U > H, splitBy(H, T, LS, RS). </lang>

PureBasic

<lang PureBasic>Procedure qSort(Array a(1), firstIndex, lastIndex)

 Protected  low, high, pivotValue

 low = firstIndex
 high = lastIndex
 pivotValue = a((firstIndex + lastIndex) / 2)
 
 Repeat
   
   While a(low) < pivotValue
     low + 1
   Wend
   
   While a(high) > pivotValue
     high - 1
   Wend
   
   If low <= high
     Swap a(low), a(high)
     low + 1
     high - 1
   EndIf
   
 Until low > high
 
 If firstIndex < high
   qSort(a(), firstIndex, high)
 EndIf
 
 If low < lastIndex
   qSort(a(), low, lastIndex)
 EndIf

EndProcedure

Procedure quickSort(Array a(1))

 qSort(a(),0,ArraySize(a()))

EndProcedure</lang>

Python

<lang python>def quickSort(arr):

   less = []
   pivotList = []
   more = []
   if len(arr) <= 1:
       return arr
   else:
       pivot = arr[0]
       for i in arr:
           if i < pivot:
               less.append(i)
           elif i > pivot:
               more.append(i)
           else:
               pivotList.append(i)
       less = quickSort(less)
       more = quickSort(more)
       return less + pivotList + more

a = [4, 65, 2, -31, 0, 99, 83, 782, 1] a = quickSort(a)</lang>

In a Haskell fashion -- <lang python>def qsort(L):

   return (qsort([y for y in L[1:] if y <  L[0]]) + 
           L[:1] + 
           qsort([y for y in L[1:] if y >= L[0]])) if len(L) > 1 else L</lang>

More readable, but still using list comprehensions: <lang python>def qsort(list):

   if not list:
       return []
   else:
       pivot = list[0]
       less = [x for x in list     if x <  pivot]
       more = [x for x in list[1:] if x >= pivot]
       return qsort(less) + [pivot] + qsort(more)</lang>

Qi

<lang Qi>(define keep

 _    []       -> []
 Pred [A|Rest] -> [A | (keep Pred Rest)] where (Pred A)
 Pred [_|Rest] -> (keep Pred Rest))

(define quicksort

 []    -> []
 [A|R] -> (append (quicksort (keep (>= A) R))
                  [A]
                  (quicksort (keep (< A) R))))

(quicksort [6 8 5 9 3 2 2 1 4 7]) </lang>

R

Translation of: Octave

<lang R>qsort <- function(v) {

 if ( length(v) > 1 ) 
 {
   pivot <- (min(v) + max(v))/2.0                            # Could also use pivot <- median(v)
   c(qsort(v[v < pivot]), v[v == pivot], qsort(v[v > pivot])) 
 } else v

}

N <- 100 vs <- runif(N) system.time(u <- qsort(vs)) print(u)</lang>

REXX

version 1

<lang rexx>/*REXX program sorts a stemmed array using the quicksort method. */ call gen@ /*generate the array elements. */ call show@ 'before sort' /*show before array elements.*/ call quickSort highItem /*here come da judge, here come..*/ call show@ ' after sort' /*show after array elements.*/ exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────QUICKSORT subroutine────────────────*/ quickSort: procedure expose @. /*access the caller's local var. */ a.1=1; b.1=arg(1); $=1

 do while $\==0;   l=a.$;   t=b.$;   $=$-1
 if t<2 then iterate
 h=l+t-1
 ?=l+t%2
 if @.h<@.l then if @.?<@.h then do; p=@.h; @.h=@.l; end
                            else if @.?>@.l then p=@.l
                                            else do; p=@.?; @.?=@.l; end
            else if @.?<@.l then p=@.l
                            else if @.?>@.h then do; p=@.h; @.h=@.l; end
                                            else do; p=@.?; @.?=@.l; end
 j=l+1
 k=h
       do forever
           do j=j       while j<=k & @.j<=p; end    /*a tinie-tiny loop*/
           do k=k by -1 while j <k & @.k>=p; end    /*another tiny loop*/
       if j>=k then leave
       _=@.j; @.j=@.k; @.k=_
       end   /*forever*/

 k=j-1;  @.l=@.k;  @.k=p
 $=$+1
 if j<=? then do;   a.$=j;  b.$=h-j+1;  $=$+1;  a.$=l;  b.$=k-l;     end
         else do;   a.$=l;  b.$=k-l;    $=$+1;  a.$=j;  b.$=h-j+1;   end
 end   /*while $\==0*/

return /*──────────────────────────────────GEN@ subroutine─────────────────────*/ gen@: @.=; maxL=0 /*assign default value. */ @.1 =" Rivers that form part of a state's (USA) border " @.2 ='=' @.3 ="Chattahoochee River: Alabama, Georgia" @.4 ="Colorado River: Arizona, Nevada, California, Baja California (Mexico)" @.5 ="St. Francis River: Arkansas, Missouri" @.6 ="Poteau River: Arkansas, Oklahoma" @.7 ="Byram River: Connecticut, New York" @.8 ="Pawcatuck River: Connecticut, Rhode Island" @.9 ="Perdido River: Florida, Alabama" @.10="St. Marys River: Florida, Georgia" @.11="Chattooga River: Georgia, South Carolina" @.12="Tugaloo River: Georgia, South Carolina" @.13="Snake River: Idaho, Washington, Oregon" @.14="Wabash River: Illinois, Indiana" @.15="Ohio River: Illinois, Indiana, Ohio, Kentucky, West Virginia" @.16="Des Moines River: Iowa, Missouri" @.17="Tennessee River: Kentucky, Tennessee, Mississippi, Alabama" @.18="Big Sandy River: Kentucky, West Virginia" @.19="Tug Fork River: Kentucky, West Virginia, Virginia" @.20="Monument Creek: Maine, New Brunswick (Canda)" @.21="St. Croix River: Maine, New Brunswick (Canda)" @.22="Piscataqua River: Maine, New Hampshire" @.23="St. Francis River: Maine, Quebec (Canada)" @.24="St. John River: Maine, Quebec (Canada)" @.25="Pocomoke River: Maryland, Virginia" @.26="Potomac River: Maryland, Virginia, city of Washington (District of Columbia), West Virginia" @.27="Montreal River: Michigan (upper peninsula ), Wisconsin" @.28="Detroit River: Michigan, Ontario (Canada)" @.29="St. Clair River: Michigan, Ontario (Canada)" @.30="St. Marys River: Michigan, Ontario (Canada)" @.31="Brule River: Michigan, Wisconsin" @.32="Menominee River: Michigan, Wisconsin" @.33="Pigeon River: Minnesota, Ontario (Canada)" @.34="Rainy River: Minnesota, Ontario (Canada)" @.35="St. Croix River: Minnesota, Wisconsin" @.36="St. Louis River: Minnesota, Wisconsin" @.37="Mississippi River: Minnesota, Wisconsin, Iowa, Illinois, Missouri, Kentucky, Tennesse, Arkansas, Mississippi, Louisiana" @.38="Pearl River: Mississippi, Louisiana" @.39="Halls Stream: New Hampshire, Canada" @.40="Salmon Falls River: New Hampshire, Maine" @.41="Connecticut River: New Hampshire, Vermont" @.42="Hudson River (lower part only): New Jersey, New York" @.43="Arthur Kill: New Jersey, New York (tidal strait)" @.44="Kill Van Kull: New Jersey, New York (tidal strait)" @.45="Rio Grande: New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila De Zaragoza (Mexico), Chihuahua (Mexico)" @.46="Niagara River: New York, Ontario (Canada)" @.47="St. Lawrence River: New York, Ontario (Canada)" @.48="Delaware River: New York, Pennsylvania, New Jersey, Delaware" @.49="Catawba River: North Carolina, South Carolina" @.50="Red River of the North: North Dakota, Minnesota" @.51="Great Miami River (mouth only): Ohio, Indiana" @.52="Arkansas River: Oklahoma, Arkansas" @.53="Palmer River: Rhode Island, Massachusetts" @.54="Runnins River: Rhode Island, Massachusetts" @.55="Savannah River: South Carolina, Georgia" @.56="Big Sioux River: South Dakota, Iowa" @.57="Bois de Sioux River: South Dakota, Minnesota, North Dakota" @.58="Missouri River: South Dakota, Nebraska, Iowa, Missouri, Kansas" @.59="Sabine River: Texas, Louisiana" @.60="Red River (Mississippi watershed): Texas, Oklahoma, Arkansas" @.61="Poultney River: Vermont, New York" @.62="Blackwater River: Virginia, North Carolina" @.63="Columbia River: Washington, Oregon"

 do highItem=1 while @.highItem\==  /*find how many entries, and also*/
 maxL=max(maxL,length(@.highItem))    /*  find the maximum width entry.*/
 end

highItem=highItem-1 /*adjust highItem slightly. */ @.1=centre(@.1,maxL,'-') /*adjust the header information. */ @.2=copies(@.2,maxL) /*adjust the header separator. */ return /*──────────────────────────────────SHOW@ subroutine────────────────────*/ show@: widthH=length(highItem) /*maximum width of any line. */

                    do j=1 for highItem         /*show each array item.*/
                    say  'element'  right(j,widthH)  arg(1)':'  @.j
                    end

say copies('█',maxL+widthH+22) /*show a separator line. */ return</lang> output

element  1 before sort: ------------------------------------------------ Rivers that form part of a state's (USA) border -------------------------------------------------
element  2 before sort: ==================================================================================================================================================
element  3 before sort: Chattahoochee River:                Alabama, Georgia
element  4 before sort: Colorado River:                     Arizona, Nevada, California, Baja California (Mexico)
element  5 before sort: St. Francis River:                  Arkansas, Missouri
element  6 before sort: Poteau River:                       Arkansas, Oklahoma
element  7 before sort: Byram River:                        Connecticut, New York
element  8 before sort: Pawcatuck River:                    Connecticut, Rhode Island
element  9 before sort: Perdido River:                      Florida, Alabama
element 10 before sort: St. Marys River:                    Florida, Georgia
element 11 before sort: Chattooga River:                    Georgia, South Carolina
element 12 before sort: Tugaloo River:                      Georgia, South Carolina
element 13 before sort: Snake River:                        Idaho, Washington, Oregon
element 14 before sort: Wabash River:                       Illinois, Indiana
element 15 before sort: Ohio River:                         Illinois, Indiana, Ohio, Kentucky, West Virginia
element 16 before sort: Des Moines River:                   Iowa, Missouri
element 17 before sort: Tennessee River:                    Kentucky, Tennessee, Mississippi, Alabama
element 18 before sort: Big Sandy River:                    Kentucky, West Virginia
element 19 before sort: Tug Fork River:                     Kentucky, West Virginia, Virginia
element 20 before sort: Monument Creek:                     Maine, New Brunswick (Canda)
element 21 before sort: St. Croix River:                    Maine, New Brunswick (Canda)
element 22 before sort: Piscataqua River:                   Maine, New Hampshire
element 23 before sort: St. Francis River:                  Maine, Quebec (Canada)
element 24 before sort: St. John River:                     Maine, Quebec (Canada)
element 25 before sort: Pocomoke River:                     Maryland, Virginia
element 26 before sort: Potomac River:                      Maryland, Virginia, city of Washington (District of Columbia), West Virginia
element 27 before sort: Montreal River:                     Michigan (upper peninsula ), Wisconsin
element 28 before sort: Detroit River:                      Michigan, Ontario (Canada)
element 29 before sort: St. Clair River:                    Michigan, Ontario (Canada)
element 30 before sort: St. Marys River:                    Michigan, Ontario (Canada)
element 31 before sort: Brule River:                        Michigan, Wisconsin
element 32 before sort: Menominee River:                    Michigan, Wisconsin
element 33 before sort: Pigeon River:                       Minnesota, Ontario (Canada)
element 34 before sort: Rainy River:                        Minnesota, Ontario (Canada)
element 35 before sort: St. Croix River:                    Minnesota, Wisconsin
element 36 before sort: St. Louis River:                    Minnesota, Wisconsin
element 37 before sort: Mississippi River:                  Minnesota, Wisconsin, Iowa, Illinois, Missouri, Kentucky, Tennesse, Arkansas, Mississippi, Louisiana
element 38 before sort: Pearl River:                        Mississippi, Louisiana
element 39 before sort: Halls Stream:                       New Hampshire, Canada
element 40 before sort: Salmon Falls River:                 New Hampshire, Maine
element 41 before sort: Connecticut River:                  New Hampshire, Vermont
element 42 before sort: Hudson River (lower part only):     New Jersey, New York
element 43 before sort: Arthur Kill:                        New Jersey, New York (tidal strait)
element 44 before sort: Kill Van Kull:                      New Jersey, New York (tidal strait)
element 45 before sort: Rio Grande:                         New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila De Zaragoza (Mexico), Chihuahua (Mexico)
element 46 before sort: Niagara River:                      New York, Ontario (Canada)
element 47 before sort: St. Lawrence River:                 New York, Ontario (Canada)
element 48 before sort: Delaware River:                     New York, Pennsylvania, New Jersey, Delaware
element 49 before sort: Catawba River:                      North Carolina, South Carolina
element 50 before sort: Red River of the North:             North Dakota, Minnesota
element 51 before sort: Great Miami River (mouth only):     Ohio, Indiana
element 52 before sort: Arkansas River:                     Oklahoma, Arkansas
element 53 before sort: Palmer River:                       Rhode Island, Massachusetts
element 54 before sort: Runnins River:                      Rhode Island, Massachusetts
element 55 before sort: Savannah River:                     South Carolina, Georgia
element 56 before sort: Big Sioux River:                    South Dakota, Iowa
element 57 before sort: Bois de Sioux River:                South Dakota, Minnesota, North Dakota
element 58 before sort: Missouri River:                     South Dakota, Nebraska, Iowa, Missouri, Kansas
element 59 before sort: Sabine River:                       Texas, Louisiana
element 60 before sort: Red River (Mississippi watershed):  Texas, Oklahoma, Arkansas
element 61 before sort: Poultney River:                     Vermont, New York
element 62 before sort: Blackwater River:                   Virginia, North Carolina
element 63 before sort: Columbia River:                     Washington, Oregon
██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████
element  1  after sort: ------------------------------------------------ Rivers that form part of a state's (USA) border -------------------------------------------------
element  2  after sort: ==================================================================================================================================================
element  3  after sort: Arkansas River:                     Oklahoma, Arkansas
element  4  after sort: Arthur Kill:                        New Jersey, New York (tidal strait)
element  5  after sort: Big Sandy River:                    Kentucky, West Virginia
element  6  after sort: Big Sioux River:                    South Dakota, Iowa
element  7  after sort: Blackwater River:                   Virginia, North Carolina
element  8  after sort: Bois de Sioux River:                South Dakota, Minnesota, North Dakota
element  9  after sort: Brule River:                        Michigan, Wisconsin
element 10  after sort: Byram River:                        Connecticut, New York
element 11  after sort: Catawba River:                      North Carolina, South Carolina
element 12  after sort: Chattahoochee River:                Alabama, Georgia
element 13  after sort: Chattooga River:                    Georgia, South Carolina
element 14  after sort: Colorado River:                     Arizona, Nevada, California, Baja California (Mexico)
element 15  after sort: Columbia River:                     Washington, Oregon
element 16  after sort: Connecticut River:                  New Hampshire, Vermont
element 17  after sort: Delaware River:                     New York, Pennsylvania, New Jersey, Delaware
element 18  after sort: Des Moines River:                   Iowa, Missouri
element 19  after sort: Detroit River:                      Michigan, Ontario (Canada)
element 20  after sort: Great Miami River (mouth only):     Ohio, Indiana
element 21  after sort: Halls Stream:                       New Hampshire, Canada
element 22  after sort: Hudson River (lower part only):     New Jersey, New York
element 23  after sort: Kill Van Kull:                      New Jersey, New York (tidal strait)
element 24  after sort: Menominee River:                    Michigan, Wisconsin
element 25  after sort: Mississippi River:                  Minnesota, Wisconsin, Iowa, Illinois, Missouri, Kentucky, Tennesse, Arkansas, Mississippi, Louisiana
element 26  after sort: Missouri River:                     South Dakota, Nebraska, Iowa, Missouri, Kansas
element 27  after sort: Montreal River:                     Michigan (upper peninsula ), Wisconsin
element 28  after sort: Monument Creek:                     Maine, New Brunswick (Canda)
element 29  after sort: Niagara River:                      New York, Ontario (Canada)
element 30  after sort: Ohio River:                         Illinois, Indiana, Ohio, Kentucky, West Virginia
element 31  after sort: Palmer River:                       Rhode Island, Massachusetts
element 32  after sort: Pawcatuck River:                    Connecticut, Rhode Island
element 33  after sort: Pearl River:                        Mississippi, Louisiana
element 34  after sort: Perdido River:                      Florida, Alabama
element 35  after sort: Pigeon River:                       Minnesota, Ontario (Canada)
element 36  after sort: Piscataqua River:                   Maine, New Hampshire
element 37  after sort: Pocomoke River:                     Maryland, Virginia
element 38  after sort: Poteau River:                       Arkansas, Oklahoma
element 39  after sort: Potomac River:                      Maryland, Virginia, city of Washington (District of Columbia), West Virginia
element 40  after sort: Poultney River:                     Vermont, New York
element 41  after sort: Rainy River:                        Minnesota, Ontario (Canada)
element 42  after sort: Red River (Mississippi watershed):  Texas, Oklahoma, Arkansas
element 43  after sort: Red River of the North:             North Dakota, Minnesota
element 44  after sort: Rio Grande:                         New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila De Zaragoza (Mexico), Chihuahua (Mexico)
element 45  after sort: Runnins River:                      Rhode Island, Massachusetts
element 46  after sort: Sabine River:                       Texas, Louisiana
element 47  after sort: Salmon Falls River:                 New Hampshire, Maine
element 48  after sort: Savannah River:                     South Carolina, Georgia
element 49  after sort: Snake River:                        Idaho, Washington, Oregon
element 50  after sort: St. Clair River:                    Michigan, Ontario (Canada)
element 51  after sort: St. Croix River:                    Maine, New Brunswick (Canda)
element 52  after sort: St. Croix River:                    Minnesota, Wisconsin
element 53  after sort: St. Francis River:                  Arkansas, Missouri
element 54  after sort: St. Francis River:                  Maine, Quebec (Canada)
element 55  after sort: St. John River:                     Maine, Quebec (Canada)
element 56  after sort: St. Lawrence River:                 New York, Ontario (Canada)
element 57  after sort: St. Louis River:                    Minnesota, Wisconsin
element 58  after sort: St. Marys River:                    Florida, Georgia
element 59  after sort: St. Marys River:                    Michigan, Ontario (Canada)
element 60  after sort: Tennessee River:                    Kentucky, Tennessee, Mississippi, Alabama
element 61  after sort: Tug Fork River:                     Kentucky, West Virginia, Virginia
element 62  after sort: Tugaloo River:                      Georgia, South Carolina
element 63  after sort: Wabash River:                       Illinois, Indiana
██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████

version 2

Translation of: Python

The Python code translates very well to ooRexx but here is a way to implement it in classic REXX as well.

<lang Rexx> a = '4 65 2 -31 0 99 83 782 1'

   do i = 1 to words(a)
       queue word(a, i)
   end
   call quickSort
   parse pull item
   do queued()
       call charout ,item', '
       parse pull item
   end
   say item
   exit

quickSort: procedure /* In classic Rexx, arguments are passed by value, not by reference so stems

   cannot be passed as arguments nor used as return values.  Putting their
   contents on the external data queue is a way to bypass this issue. */

   /* construct the input stem */
   arr.0 = queued()
   do i = 1 to arr.0
       parse pull arr.i
   end
   less.0 = 0
   pivotList.0 = 0
   more.0 = 0
   if arr.0 <= 1 then do
       if arr.0 = 1 then
           queue arr.1
       return
   end
   else do
       pivot = arr.1
       do i = 1 to arr.0
           item = arr.i
           select
               when item < pivot then do
                   j = less.0 + 1
                   less.j = item
                   less.0 = j
               end
               when item > pivot then do
                   j = more.0 + 1
                   more.j = item
                   more.0 = j
               end
               otherwise
                   j = pivotList.0 + 1
                   pivotList.j = item
                   pivotList.0 = j
           end
       end
   end
   /* recursive call to sort the less. stem */
   do i = 1 to less.0
       queue less.i
   end
   if queued() > 0 then do
       call quickSort
       less.0 = queued()
       do i = 1 to less.0
           parse pull less.i
       end
   end
   /* recursive call to sort the more. stem */
   do i = 1 to more.0
       queue more.i
   end
   if queued() > 0 then do
       call quickSort
       more.0 = queued()
       do i = 1 to more.0
           parse pull more.i
       end
   end
   /* put the contents of all 3 stems on the queue in order */
   do i = 1 to less.0
       queue less.i
   end
   do i = 1 to pivotList.0
       queue pivotList.i
   end
   do i = 1 to more.0
       queue more.i
   end
   return</lang>

Ruby

<lang ruby>class Array

 def quick_sort
   return self if length <= 1
   pivot = self[length / 2]
   find_all { |i| i <  pivot }.quick_sort +
     find_all { |i| i == pivot } +
     find_all { |i| i >  pivot }.quick_sort
 end

end</lang> or <lang ruby>class Array

 def quick_sort
   return self if length <= 1
   pivot = self[0]
   less, greatereq = self[1..-1].partition { |x| x < pivot }
   less.quick_sort +
     [pivot] +
     greatereq.quick_sort
 end

end</lang>

Run BASIC

<lang runbasic>' ------------------------------- ' quick sort ' ------------------------------- size = 50 dim s(size) ' array to sort for i = 1 to size ' fill it with some random numbers

s(i) = rnd(0) * 100

next i

lft = 1 rht = size

[qSort]

 lftHold = lft
 rhtHold = rht
 pivot   = s(lft)
 while lft < rht
   while (s(rht) >= pivot) and (lft < rht) : rht = rht - 1 :wend
   if lft <> rht then
     s(lft) = s(rht)
     lft    = lft + 1
   end if
   while (s(lft) <= pivot) and (lft < rht) : lft = lft + 1 :wend
   if lft <> rht then
     s(rht) = s(lft)
     rht    = rht - 1
   end if
 wend

 s(lft) = pivot
 pivot  = lft
 lft    = lftHold
 rht    = rhtHold
 if lft < pivot then
   rht = pivot - 1
   goto [qSort]
 end if 
if rht > pivot then
   lft = pivot + 1
   goto [qSort]
end if

for i = 1 to size

print i;"-->";s(i)

next i</lang>

Sather

<lang sather>class SORT{T < $IS_LT{T}} is

 private afilter(a:ARRAY{T}, cmp:ROUT{T,T}:BOOL, p:T):ARRAY{T} is
   filtered ::= #ARRAY{T};
   loop v ::= a.elt!;
     if cmp.call(v, p) then
       filtered := filtered.append(|v|);
     end;
   end;
   return filtered;
 end;

 private mlt(a, b:T):BOOL is return a < b; end;
 private mgt(a, b:T):BOOL is return a > b; end;
 quick_sort(inout a:ARRAY{T}) is
   if a.size < 2 then return; end;
   pivot ::= a.median;
   left:ARRAY{T} := afilter(a, bind(mlt(_,_)), pivot);
   right:ARRAY{T} := afilter(a, bind(mgt(_,_)), pivot);
   quick_sort(inout left);
   quick_sort(inout right);
   res ::= #ARRAY{T};
   res := res.append(left, |pivot|,  right);
   a := res;
 end;

end;</lang>

<lang sather>class MAIN is

 main is
   a:ARRAY{INT} := |10, 9, 8, 7, 6, -10, 5, 4, 656, -11|;
   b ::= a.copy;
   SORT{INT}::quick_sort(inout a);
   #OUT + a + "\n" + b.sort + "\n";
 end;

end;</lang>

The ARRAY class has a builtin sorting method, which is quicksort (but under certain condition an insertion sort is used instead), exactly quicksort_range; this implementation is original.

Scala

I'll show a progression on genericity here.

First, a quick sort of a list of integers:

<lang scala>def quicksortInt(coll: List[Int]): List[Int] =

 if (coll.isEmpty) {
   coll
 } else {
   val (smaller, bigger) = coll.tail partition (_ < coll.head)
   quicksortInt(smaller) ::: coll.head :: quicksortInt(bigger)
 }</lang>

Next, a quick sort of a list of some type T, given a lessThan function:

<lang scala>def quicksortFunc[T](coll: List[T], lessThan: (T, T) => Boolean): List[T] =

 if (coll.isEmpty) {
   coll
 } else {
   val (smaller, bigger) = coll.tail partition (lessThan(_, coll.head))
   quicksortFunc(smaller, lessThan) ::: coll.head :: quicksortFunc(bigger, lessThan)
 }</lang>

To take advantage of known orderings, a quick sort of a list of some type T, for which exists an implicit (or explicit) Ordered[T]:

<lang scala>def quicksortOrd[T <% Ordered[T]](coll: List[T]): List[T] =

 if (coll.isEmpty) {
   coll
 } else {
   val (smaller, bigger) = coll.tail partition (_ < coll.head)
   quicksortOrd(smaller) ::: coll.head :: quicksortOrd(bigger)
 }</lang>

That last one could have worked with Ordering, but Ordering is Java, and doesn't have the less than operator. Ordered is Scala-specific, and provides it.

What hasn't changed in all these examples is that I'm ordering a list. It is possible to write a generic quicksort in Scala, which will order any kind of collection. To do so, however, requires that the type of the collection, itself, be made a parameter to the function. Let's see it below, and then remark upon it:

<lang scala>def quicksort

 [T, CC[X] <: Seq[X] with SeqLike[X, CC[X]]]       // My type parameters
 (coll: CC[T])                                                     // My explicit parameter
 (implicit o: T => Ordered[T], cbf: CanBuildFrom[CC[T], T, CC[T]]) // My implicit parameters
 : CC[T] =                                                         // My return type
 if (coll.isEmpty) {
   coll
 } else {
   val (smaller, bigger) = coll.tail partition (_ < coll.head)
   quicksort(smaller) ++ (coll.head +: quicksort(bigger))
 }</lang>

That will only work starting with Scala 2.8. The type of our collection is "CC", and, by providing CC[X] as a type parameter to TraversableLike, we ensure CC is capable of returing instances of type CC. Traversable is the base type of all collections, and TraversableLike is a trait which contains the implementation of most Traversable methods.

We need another parameter, though, which is a factory capable of building a CC collection. That is being passed implicitly, so callers to this method do not need to provide them, as the collection they are using should already provide such implicit. Because we need that implicit, then we need to ask for the "T => Ordered[T]" as well, as the "T <% Ordered[T]" which provides it cannot be used in conjunction with implicit parameters.

The body of the function is pretty much the same of the body for the list variant, but using "++" instead of list-specific methods "::" and ":::", and using "coll.companion" to build a collection out of one element.

We can also use pattern matching here - the first version of quicksortInt would look like that: <lang scala>def quicksortInt(list: List[Int]): List[Int] = list match {

   case head :: tail =>
     val (smaller, bigger) = tail partition (_ < head)
     quicksortInt(smaller) ::: head :: quicksortInt(bigger)
   case list => list
 }</lang>

Scheme

<lang scheme>(define (split-by l p k)

 (let loop ((low '())
            (high '())
            (l l))
   (cond ((null? l)
          (k low high))
         ((p (car l))
          (loop low (cons (car l) high) (cdr l)))
         (else
          (loop (cons (car l) low) high (cdr l))))))

(define (quicksort l gt?)

 (if (null? l)
     '()
     (split-by (cdr l) 
               (lambda (x) (gt? x (car l)))
               (lambda (low high)
                 (append (quicksort low gt?)
                         (list (car l))
                         (quicksort high gt?))))))

(quicksort '(1 3 5 7 9 8 6 4 2) >)</lang>

With srfi-1: <lang scheme>(define (quicksort l gt?)

 (if (null? l)
     '()
     (append (quicksort (filter (lambda (x) (gt? (car l) x)) (cdr l)) gt?)
             (list (car l))
             (quicksort (filter (lambda (x) (not (gt? (car l) x))) (cdr l)) gt?))))

(quicksort '(1 3 5 7 9 8 6 4 2) >) </lang>

Seed7

<lang seed7>const proc: quickSort (inout array elemType: arr, in integer: left, in integer: right) is func

 local
   var elemType: compare_elem is elemType.value;
   var integer: less_idx is 0;
   var integer: greater_idx is 0;
   var elemType: help is elemType.value;
 begin
   if right > left then
     compare_elem := arr[right];
     less_idx := pred(left);
     greater_idx := right;
     repeat
       repeat
         incr(less_idx);
       until arr[less_idx] >= compare_elem;
       repeat
         decr(greater_idx);
       until arr[greater_idx] <= compare_elem or greater_idx = left;
       if less_idx < greater_idx then
         help := arr[less_idx];
         arr[less_idx] := arr[greater_idx];
         arr[greater_idx] := help;
       end if;
     until less_idx >= greater_idx;
     arr[right] := arr[less_idx];
     arr[less_idx] := compare_elem;
     quickSort(arr, left, pred(less_idx));
     quickSort(arr, succ(less_idx), right);
   end if;
 end func;

const proc: quickSort (inout array elemType: arr) is func

 begin
   quickSort(arr, 1, length(arr));
 end func;</lang>

Original source: [2]

SETL

In-place sort (looks much the same as the C version) <lang SETL>a := [2,5,8,7,0,9,1,3,6,4]; qsort(a); print(a);

proc qsort(rw a);

 if #a > 1 then
   pivot := a(#a div 2 + 1);
   l := 1;
   r := #a;
   (while l < r)
     (while a(l) < pivot) l +:= 1; end;
     (while a(r) > pivot) r -:= 1; end;
     swap(a(l), a(r));
   end;
   qsort(a(1..l-1));
   qsort(a(r+1..#a));
 end if;

end proc;

proc swap(rw x, rw y);

 [y,x] := [x,y];

end proc;</lang>

Copying sort using comprehensions:

<lang SETL>a := [2,5,8,7,0,9,1,3,6,4]; print(qsort(a));

proc qsort(a);

 if #a > 1 then
   pivot := a(#a div 2 + 1);
   a := qsort([x in a | x < pivot]) +
        [x in a | x = pivot] +
        qsort([x in a | x > pivot]);
 end if;
 return a;

end proc;</lang>

Standard ML

<lang sml>fun quicksort [] = []

 | quicksort (x::xs) =
   let 
       val (left, right) = List.partition (fn y => y<x) xs
   in
       quicksort left @ [x] @ quicksort right
   end</lang>

Tcl

<lang tcl>package require Tcl 8.5

proc quicksort {m} {

   if {[llength $m] <= 1} {
       return $m
   }
   set pivot [lindex $m 0]
   set less [set equal [set greater [list]]]
   foreach x $m {
       lappend [expr {$x < $pivot ? "less" : $x > $pivot ? "greater" : "equal"}] $x
   }
   return [concat [quicksort $less] $equal [quicksort $greater]]

}

puts [quicksort {8 6 4 2 1 3 5 7 9}] ;# => 1 2 3 4 5 6 7 8 9</lang>

UnixPipes

Works with: Zsh

<lang bash>split() {

 (while read n ; do
     test $1 -gt $n && echo $n > $2 || echo $n > $3
 done)

}

qsort() {

(read p; test -n "$p" && (
    lc="1.$1" ; gc="2.$1"
    split $p >(qsort $lc >$lc) >(qsort $gc >$gc);
    cat $lc <(echo $p) $gc
    rm -f $lc $gc;
))

}

cat to.sort | qsort</lang>

Ursala

The distributing bipartition operator, *|, is useful for this algorithm. The pivot is chosen as the greater of the first two items, this being the least sophisticated method sufficient to ensure termination. The quicksort function is a higher order function parameterized by the relational predicate p, which can be chosen appropriately for the type of items in the list being sorted. This example demonstrates sorting a list of natural numbers.

<lang Ursala>#import nat

quicksort "p" = ~&itB^?a\~&a ^|WrlT/~& "p"*|^\~& "p"?hthPX/~&th ~&h

1. cast %nL

example = quicksort(nleq) <694,1377,367,506,3712,381,1704,1580,475,1872></lang> output:

<367,381,475,506,694,1377,1580,1704,1872,3712>

V

<lang v>[qsort

 [joinparts [p [*l1] [*l2] : [*l1 p *l2]] view].
 [split_on_first uncons [>] split].
 [small?]
   []
   [split_on_first [l1 l2 : [l1 qsort l2 qsort joinparts]] view i]
 ifte].</lang>

The way of joy (using binrec) <lang v>[qsort

  [small?] []
    [uncons [>] split]
    [[p [*l] [*g] : [*l p *g]] view]
   binrec].</lang>

VBA

This is the "simple" quicksort, using temporary arrays.

<lang VBA> Public Sub Quick(a() As Variant, last As Integer) ' quicksort a Variant array (1-based, numbers or strings) Dim aLess() As Variant Dim aEq() As Variant Dim aGreater() As Variant Dim pivot As Variant Dim naLess As Integer Dim naEq As Integer Dim naGreater As Integer

If last > 1 Then

   'choose pivot in the middle of the array
   pivot = a(Int((last + 1) / 2))
   'construct arrays
   naLess = 0
   naEq = 0
   naGreater = 0
   For Each el In a()
     If el > pivot Then
       naGreater = naGreater + 1
       ReDim Preserve aGreater(1 To naGreater)
       aGreater(naGreater) = el
     ElseIf el < pivot Then
       naLess = naLess + 1
       ReDim Preserve aLess(1 To naLess)
       aLess(naLess) = el
     Else
       naEq = naEq + 1
       ReDim Preserve aEq(1 To naEq)
       aEq(naEq) = el
     End If
   Next
   'sort arrays "less" and "greater"
   Quick aLess(), naLess
   Quick aGreater(), naGreater
   'concatenate
   P = 1
   For i = 1 To naLess
     a(P) = aLess(i): P = P + 1
   Next
   For i = 1 To naEq
     a(P) = aEq(i): P = P + 1
   Next
   For i = 1 To naGreater
     a(P) = aGreater(i): P = P + 1
   Next

End If End Sub

Public Sub QuicksortTest() Dim a(1 To 26) As Variant

'populate a with numbers in descending order, then sort
For i = 1 To 26: a(i) = 26 - i: Next
Quick a(), 26
For i = 1 To 26: Debug.Print a(i);: Next
Debug.Print
'now populate a with strings in descending order, then sort
For i = 1 To 26: a(i) = Chr$(Asc("z") + 1 - i) & "-stuff": Next
Quick a(), 26
For i = 1 To 26: Debug.Print a(i); " ";: Next
Debug.Print

End Sub

</lang>

Output:

quicksorttest
 0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25 
a-stuff b-stuff c-stuff d-stuff e-stuff f-stuff g-stuff h-stuff i-stuff j-stuff k-stuff l-stuff m-stuff n-stuff o-stuff p-stuff q-stuff r-stuff s-stuff t-stuff u-stuff v-stuff w-stuff x-stuff y-stuff z-stuff 

Note: the "quicksort in place"

XPL0

<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations string 0; \use zero-terminated strings instead of MSb-terminated

proc QSort(Array, Num, Size); \Quicksort Array into ascending order char Array; \address of array to sort int Num, \number of elements in the array

       Size;           \size (in bytes) of each element

int I, J, Mid, Temp; [I:= 0; J:= Num-1; Mid:= Array(J>>1); while I <= J do

      [while Array(I) < Mid do I:= I+1;
       while Array(J) > Mid do J:= J-1;
       if I <= J then
               [Temp:= Array(I);  Array(I):= Array(J);  Array(J):= Temp;
               I:= I+1;
               J:= J-1;
               ];
       ];

if I < Num-1 then QSort(Array+I*Size, Num-I, Size); \recurse if J > 0 then QSort(Array, J+1, Size); ]; \QSort

func StrLen(Str); \Return number of characters in an ASCIIZ string char Str; int I; for I:= 0 to -1>>1-1 do

       if Str(I) = 0 then return I;

char Str; [Str:= "Pack my box with five dozen liquor jugs."; QSort(Str, StrLen(Str), 1); Text(0, Str); CrLf(0); ]</lang>

Output:

"       .Pabcdeefghiiijklmnoooqrstuuvwxyz"