Sorting algorithms/Quicksort: Difference between revisions

Content added Content deleted

Inline

Revision as of 23:05, 13 March 2016

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.

Choose any element of the array to be the pivot.
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.
Use recursion to sort both partitions.
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.

360 Assembly

Translation of: REXX

<lang 360asm>* quicksort 14/09/2015 QUICKSOR CSECT

        USING  QUICKSOR,R15       set base register

BEGIN MVC A,=F'1' a(1)=1

        MVC    B,=A((A-T)/4)      b(1)=hbound(t)
        L      R6,=F'1'           k=1

WHILEK LTR R6,R6 do while k^=0

        BZ     EWHILEK
        LR     R1,R6              k 
        SLA    R1,2               ~
        L      R10,A-4(R1)        l=a(k)
        LR     R1,R6              k
        SLA    R1,2               ~
        L      R11,B-4(R1)        m=b(k)
        BCTR   R6,0               k=k-1
        LR     R4,R11             m
        C      R4,=F'2'           if m<2 
        BL     WHILEK             then iterate
        LR     R2,R10             l
        AR     R2,R11             +m
        BCTR   R2,0               -1
        ST     R2,X               x=l+m-1
        LR     R2,R11             m
        SRA    R2,1               m/2
        AR     R2,R10             +l
        ST     R2,Y               y=l+m/2
        L      R1,X               x
        SLA    R1,2               ~
        L      R4,T-4(R1)         r4=t(x)
        L      R1,Y               y
        SLA    R1,2               ~
        L      R5,T-4(R1)         r5=t(y)
        LR     R1,R10             l
        SLA    R1,2               ~
        L      R3,T-4(R1)         r3=t(l)

IF CR R4,R3 if t(x)<t(l)

        BNL    ELSE
        CR     R5,R4              if t(y)<t(x) 
        BNL    IFX
        LR     R7,R4              p=t(x)
        L      R1,X               x
        SLA    R1,2               ~
        ST     R3,T-4(R1)         t(x)=t(l)
        B      EIFX

IFX CR R5,R3 if t(y)>t(l)

        BNH    IFXELIF
        LR     R7,R3              p=t(l)
        B      EIFX

IFXELIF LR R7,R5 p=t(y)

        L      R1,Y               y
        SLA    R1,2               ~
        ST     R3,T-4(R1)         t(y)=t(l)

EIFX B ENDIF ELSE CR R5,R3 if t(y)<t(l)

        BNL    IFY
        LR     R7,R3              p=t(l)
        B      ENDIF

IFY CR R5,R4 if t(y)>t(x)

        BNH    IFYELIF
        LR     R7,R4              p=t(x)
        L      R1,X               x
        SLA    R1,2               ~
        ST     R3,T-4(R1)         t(x)=t(l)
        B      ENDIF

IFYELIF LR R7,R5 p=t(y)

        L      R1,Y               y
        SLA    R1,2               ~
        ST     R3,T-4(R1)         t(y)=t(l)

ENDIF LA R8,1(R10) i=l+1

        L      R9,X               j=x

FOREVER EQU * LOOPWI CR R8,R9 i<=j

        BH     ELOOPWI
        LR     R1,R8              i
        SLA    R1,2               ~
        L      R2,T-4(R1)         t(i)
        CR     R2,R7              t(i)<=p
        BH     ELOOPWI
        LA     R8,1(R8)           i=i+1
        B      LOOPWI

ELOOPWI EQU * LOOPWJ CR R8,R9 i<j

        BNL    ELOOPWJ
        LR     R1,R9              j
        SLA    R1,2               ~
        L      R2,T-4(R1)         t(j)
        CR     R2,R7              t(j)>=p
        BL     ELOOPWJ
        BCTR   R9,0               j=j-1
        B      LOOPWJ

ELOOPWJ CR R8,R9 if i>=j

        BNL    EFOREVER           then leave    segment finished
        LR     R1,R8              i
        SLA    R1,2               ~
        LA     R2,T-4(R1)         @t(i)
        LR     R1,R9              j
        SLA    R1,2               ~
        LA     R3,T-4(R1)         @t(j)
        L      R0,0(R2)           w=t(i)
        MVC    0(4,R2),0(R3)      t(i)=t(j)     swap t(i),t(j)
        ST     R0,0(R3)           t(j)=w 
        B      FOREVER

EFOREVER LR R9,R8 j=i

        BCTR   R9,0               j=i-1
        LR     R1,R9              j
        SLA    R1,2               ~
        LA     R3,T-4(R1)         @t(j)
        L      R2,0(R3)           t(j)
        LR     R1,R10             l
        SLA    R1,2               ~
        ST     R2,T-4(R1)         t(l)=t(j)
        ST     R7,0(R3)           t(j)=p
        LA     R6,1(R6)           k=k+1
        LR     R1,R6              k
        SLA    R1,2               ~
        LA     R4,A-4(R1)         r4=@a(k)
        LA     R5,B-4(R1)         r5=@b(k)
        C      R8,Y               if i<=y
        BH     IFIHY
        ST     R8,0(R4)           a(k)=i
        L      R2,X               x
        SR     R2,R8              -i
        LA     R2,1(R2)           +1
        ST     R2,0(R5)           b(k)=x-i+1
        LA     R6,1(R6)           k=k+1
        ST     R10,4(R4)          a(k)=l
        LR     R2,R9              j
        SR     R2,R10             -l
        ST     R2,4(R5)           b(k)=j-l
        B      EIFIHY

IFIHY ST R10,4(R4) a(k)=l

        LR     R2,R9              j
        SR     R2,R10             -l
        ST     R2,0(R5)           b(k)=j-l
        LA     R6,1(R6)           k=k+1
        ST     R8,4(R4)           a(k)=i
        L      R2,X               x
        SR     R2,R8              -i
        LA     R2,1(R2)           +1
        ST     R2,4(R5)           b(k)=x-i+1

EIFIHY B WHILEK EWHILEK LA R3,PG ibuffer

        LA     R4,T               @t(i)

LOOPI C R4,=A(A) do i=1 to hbound(t)

        BH     ELOOPI
        L      R2,0(R4)           t(i)
        XDECO  R2,XD              edit t(i)
        MVC    0(4,R3),XD+8       put in buffer
        LA     R3,4(R3)           ibuffer=ibuffer+1
        LA     R4,4(R4)           i=i+1
        B      LOOPI

ELOOPI XPRNT PG,80 print bufffer RETURN XR R15,R15 set return code

        BR     R14                return to caller

T DC F'10',F'9',F'9',F'6',F'7',F'16',F'1',F'16',F'17',F'15'

        DC     F'1',F'9',F'18',F'16',F'8',F'20',F'18',F'2',F'19',F'8'

A DS ((A-T)/4)F same size as T B DS ((A-T)/4)F same size as T X DS F Y DS F PG DS CL80 XD DS CL12

        YREGS 
        END    QUICKSOR</lang>

Output:

   1   1   2   6   7   8   8   9   9   9  10  15  16  16  16  17  18  18  19  20

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 then
           Left := Index_Type'Succ(Left);
        end if;
        if Right > Item'First then
           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

<lang algol68>#--- Swap function ---# PROC swap = (REF []INT array, INT first, INT second) VOID: (

   INT temp := array[first];
   array[first] := array[second];
   array[second]:= temp

);

--- Quick sort 3 arg function ---#

PROC quick = (REF [] INT array, INT first, INT last) VOID: (

   INT smaller := first + 1,  
       larger  := last,
       pivot   := array[first];
 
   WHILE smaller <= larger DO
       WHILE array[smaller] < pivot   AND   smaller < last DO   
           smaller +:= 1        
       OD;
       WHILE array[larger]  > pivot   AND   larger > first DO   
           larger  -:= 1       
       OD; 
       IF smaller < larger THEN 
           swap(array, smaller, larger); 
           smaller +:= 1;
           larger  -:= 1
       ELSE
           smaller +:= 1
       FI
   OD;
   
   swap(array, first, larger);

   IF first < larger-1 THEN
       quick(array, first, larger-1)  
   FI;
   IF last > larger +1 THEN
       quick(array, larger+1, last)   
   FI

);

--- Quick sort 1 arg function ---#

PROC quicksort = (REF []INT array) VOID: (

 IF UPB array > 1 THEN
   quick(array, 1, UPB array) 
 FI

);

main: (

   [10]INT a; 
   FOR i FROM 1 TO UPB a DO 
       a[i] := ROUND(random*1000)
   OD;

   print(("Before:", a));
   quicksort(a);
   print((newline, newline));
   print(("After: ", a))

) </lang>

Output:

Before:        +73       +921       +179       +961        +50       +324        +82       +178       +243       +458
                                                                                                                     
After:         +50        +73        +82       +178       +179       +243       +324       +458       +921       +961

APL

Works with: Dyalog APL

Translation of: J

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

     qsort 31 4 1 5 9 2 6 5 3 5 8

1 2 3 4 5 5 5 6 8 9 31</lang>

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

AppleScript

Emphasising clarity and simplicity more than run-time performance. (Practical scripts will often delegate sorting to the OS X shell, or use an alternative scripting language).

Translation of: JavaScript

(Functional ES5 version)

<lang AppleScript>-- quickSort :: (Ord a) => [a] -> [a] on quickSort(xxs)

   script mf
       -- qs :: (Ord a) => [a] -> [a]
       on qs(xxs)
           set headTail to uncons(xxs)
           if headTail is not missing value then
               set {x, xs} to headTail
               
               set less to qs(filter(mClosure(my lessOrEqual, {x:x}), xs))
               set more to qs(filter(mClosure(my moreThan, {x:x}), xs))
               
               less & {x} & more
           else
               xxs
           end if
       end qs
       
       -- lessOrEqual :: a -> Bool
       on lessOrEqual(a)
           a ≤ my closure's x
       end lessOrEqual
       
       -- moreThan :: a -> Bool
       on moreThan(a)
           a > my closure's x
       end moreThan
   end script
   
   mf's qs(xxs)

end quickSort

on run

   quickSort([11.8, 14.1, 21.3, 8.5, 16.7, 5.7])
   
   --> {5.7, 8.5, 11.8, 14.1, 16.7, 21.3}

end run

-- GENERIC FUNCTIONS

-- uncons :: [a] -> Maybe (a, [a]) on uncons(xs)

   set lng to length of xs
   if lng > 0 then
       if lng > 1 then
           {item 1 of xs, items 2 thru -1 of xs}
       else
           {item 1 of xs, {}}
       end if
   else
       missing value
   end if

end uncons

-- filter :: (a -> Bool) -> [a] -> [a] -- filter :: (a -> Int -> Bool) -> [a] -> [a] -- filter :: (a -> Int -> [a] -> Bool) -> [a] -> [a] on filter(f, xs)

   set mf to mReturn(f)
   
   set lst to {}
   set lng to length of xs
   repeat with i from 1 to lng
       set v to item i of xs
       if mf's lambda(v, i, xs) then
           set end of lst to v
       end if
   end repeat
   return lst

end filter

-- Lift 2nd class function into 1st class wrapper -- handler function --> first class script object on mReturn(f)

   if class of f is script then return f
   script
       property lambda : f
   end script

end mReturn

-- Handler -> Record -> Script on mClosure(f, recBindings)

   script
       property closure : recBindings
       property lambda : f
   end script

end mClosure</lang>

Output:

{5.7, 8.5, 11.8, 14.1, 16.7, 21.3}

AWK

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

function qsortArbIndByValue(Arr, k,

                           ArrInd, ElNum)

{

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

}

qsortSegment(): Sort a segment of an array.
Input variables:
Arr[] contains data with arbitrary indices.
k[] has indices 1..nelem, with the indices of Arr[] as values.
Output variables:
k[] is modified by this function. The elements of Arr[] that are pointed to
by k[start..end] are sorted, with the values of elements of k[] swapped
so that when this function returns, Arr[k[start..end]] will be in order.
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 the python example: <lang AutoHotkey>a := [4, 65, 2, -31, 0, 99, 83, 782, 7] for k, v in QuickSort(a) Out .= "," v MsgBox, % SubStr(Out, 2) return

QuickSort(a) { if (a.MaxIndex() <= 1) return a Less := [], Same := [], More := [] Pivot := a[1] for k, v in a { if (v < Pivot) less.Insert(v) else if (v > Pivot) more.Insert(v) else same.Insert(v) } Less := QuickSort(Less) Out := QuickSort(More) if (Same.MaxIndex()) Out.Insert(1, Same*) ; insert all values of same at index 1 if (Less.MaxIndex()) Out.Insert(1, Less*) ; insert all values of less at index 1 return Out }</lang>

Old implementation for AutoHotkey 1.0: <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)

   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>
Bracmat
Instead of comparing elements explicitly, this solution puts the two elements-to-compare in a sum. After evaluating the sum its terms are sorted. Numbers are sorted numerically, strings alphabetically and compound expressions by comparing nodes and leafs in a left-to right order. Now there are three cases: either the terms stayed put, or they were swapped, or they were equal and were combined into one term with a factor 2 in front. To not let the evaluator add numbers together, each term is constructed as a dotted list. <lang bracmat>( ( Q
= Less Greater Equal pivot element . !arg:%(?pivot:?Equal) %?arg & :?Less:?Greater & whl ' ( !arg:%?element ?arg & (.!element)+(.!pivot) { BAD: 1900+90 adds to 1990, GOOD: (.1900)+(.90) is sorted to (.90)+(.1900) } : ( (.!element)+(.!pivot) & !element !Less:?Less | (.!pivot)+(.!element) & !element !Greater:?Greater | ?&!element !Equal:?Equal ) ) & Q$!Less !Equal Q$!Greater | !arg )
& out$Q$(1900 optimized variants of 4001/2 Quicksort (quick,sort) are (quick,sober) features of 90 languages) );</lang>

Output:
90 1900 4001/2 Quicksort are features languages of of optimized variants (quick,sober) (quick,sort)
C
<lang c>#include <stdio.h>
void quick_sort (int *a, int n) {
int i, j, p, t; if (n < 2) return; p = a[n / 2]; for (i = 0, j = n - 1;; i++, j--) { while (a[i] < p) i++; while (p < a[j]) j--; if (i >= j) break; t = a[i]; a[i] = a[j]; a[j] = t; } quick_sort(a, i); quick_sort(a + i, n - i);
}
int main (void) {
int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1}; int n = sizeof a / sizeof a[0]; int i; for (i = 0; i < n; i++) printf("%d%s", a[i], i == n - 1 ? "\n" : " "); quick_sort(a, n); for (i = 0; i < n; i++) printf("%d%s", a[i], i == n - 1 ? "\n" : " "); return 0;
}</lang>

Output:
4 65 2 -31 0 99 2 83 782 1 -31 0 1 2 2 4 65 83 99 782
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>
include <algorithm> // for std::partition

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>
include <algorithm> // for std::partition

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 Array.Sort and ArrayList.Sort both use an unstable implementation of the quicksort algorithm. <lang csharp>namespace Sort {
using System;
class QuickSort<T> where T : IComparable { #region Constants private const Int32 insertionLimitDefault = 16; private const Int32 pivotSamples = 5; #endregion
#region Properties public Int32 InsertionLimit { get; set; } protected Random Random { get; set; } #endregion
#region Constructors public QuickSort() : this(insertionLimitDefault, new Random()) { }
public QuickSort(Int32 insertionLimit, Random random) { InsertionLimit = insertionLimit; Random = random; } #endregion
#region Sort Methods public void Sort(T[] entries) { Sort(entries, 0, entries.Length - 1); }
public void Sort(T[] entries, Int32 first, Int32 last) { var length = last + 1 - first; // Elide tail recursion by looping over the longer partition while (length > 1) { if (length < InsertionLimit) { InsertionSort<T>.Sort(entries, first, last); return; }
var median = pivot(entries, first, last);
var left = first; var right = last; partition(entries, median, ref left, ref right);
var leftLength = right + 1 - first; var rightLength = last + 1 - left;
if (leftLength < rightLength) { Sort(entries, first, right); first = left; length = rightLength; } else { Sort(entries, left, last); last = right; length = leftLength; } } }
private T pivot(T[] entries, Int32 first, Int32 last) { var length = last + 1 - first; var sampleSize = Math.Min(pivotSamples, length); var right = first + sampleSize - 1; for (var left = first; left <= right; left++) { // Random sampling avoids pathological cases var random = Random.Next(left, last + 1); // Sample without replacement if (left != random) Swap(entries, left, random); }
InsertionSort<T>.Sort(entries, first, right); return entries[first + sampleSize / 2]; }
private static void partition(T[] entries, T pivot, ref Int32 left, ref Int32 right) { while (left <= right) { while (pivot.CompareTo(entries[left]) > 0) left++; // pivot follows entry while (pivot.CompareTo(entries[right]) < 0) right--; // pivot precedes entry
if (left < right) // Move entries to their correct partition Swap(entries, left++, right--); else if (left == right) { // No swap needed left++; right--; } } }
public static void Swap(T[] entries, Int32 index1, Int32 index2) { var entry = entries[index1]; entries[index1] = entries[index2]; entries[index2] = entry; } #endregion }
#region Insertion Sort static class InsertionSort<T> where T : IComparable { public static void Sort(T[] entries, Int32 first, Int32 last) { for (var i = first + 1; i <= last; i++) { var entry = entries[i]; var j = i; while (j > first && entries[j - 1].CompareTo(entry) > 0) entries[j] = entries[--j]; entries[j] = entry; } } } #endregion
}</lang> Example: <lang csharp> using Sort;
using System;
class Program { static void Main(String[] args) { var entries = new Int32[] { 1, 3, 5, 7, 9, 8, 6, 4, 2 }; var sorter = new QuickSort<Int32>(); sorter.Sort(entries); Console.WriteLine(String.Join(" ", entries)); } }</lang>

Output:
1 2 3 4 5 6 7 8 9
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>
COBOL
Works with: Visual COBOL
<lang cobol> IDENTIFICATION DIVISION.
PROGRAM-ID. quicksort RECURSIVE. DATA DIVISION. LOCAL-STORAGE SECTION. 01 temp PIC S9(8). 01 pivot PIC S9(8). 01 left-most-idx PIC 9(5). 01 right-most-idx PIC 9(5). 01 left-idx PIC 9(5). 01 right-idx PIC 9(5). LINKAGE SECTION. 78 Arr-Length VALUE 50. 01 arr-area. 03 arr PIC S9(8) OCCURS Arr-Length TIMES. 01 left-val PIC 9(5). 01 right-val PIC 9(5). PROCEDURE DIVISION USING REFERENCE arr-area, OPTIONAL left-val, OPTIONAL right-val. IF left-val IS OMITTED OR right-val IS OMITTED MOVE 1 TO left-most-idx, left-idx MOVE Arr-Length TO right-most-idx, right-idx ELSE MOVE left-val TO left-most-idx, left-idx MOVE right-val TO right-most-idx, right-idx END-IF IF right-most-idx - left-most-idx < 1 GOBACK END-IF COMPUTE pivot = arr ((left-most-idx + right-most-idx) / 2) PERFORM UNTIL left-idx > right-idx PERFORM VARYING left-idx FROM left-idx BY 1 UNTIL arr (left-idx) >= pivot END-PERFORM PERFORM VARYING right-idx FROM right-idx BY -1 UNTIL arr (right-idx) <= pivot END-PERFORM IF left-idx <= right-idx MOVE arr (left-idx) TO temp MOVE arr (right-idx) TO arr (left-idx) MOVE temp TO arr (right-idx) ADD 1 TO left-idx SUBTRACT 1 FROM right-idx END-IF END-PERFORM CALL "quicksort" USING REFERENCE arr-area, CONTENT left-most-idx, right-idx CALL "quicksort" USING REFERENCE arr-area, CONTENT left-idx, right-most-idx GOBACK .</lang>
CoffeeScript
<lang coffeescript> quicksort = ([x, xs...]) ->
return [] unless x? smallerOrEqual = (a for a in xs when a <= x) larger = (a for a in xs when a > x) (quicksort smallerOrEqual).concat(x).concat(quicksort larger)
</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 flet
<lang lisp>(defun qs (list)
(if (cdr list) (flet ((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 functional version: <lang d>import std.stdio, std.algorithm, std.range, std.array;
auto quickSort(T)(T[] items) pure nothrow @safe {
if (items.length < 2) return items; immutable pivot = items[0]; return items[1 .. $].filter!(x => x < pivot).array.quickSort ~ pivot ~ items[1 .. $].filter!(x => x >= pivot).array.quickSort;
}
void main() {
[4, 65, 2, -31, 0, 99, 2, 83, 782, 1].quickSort.writeln;
}</lang>

Output:
[-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]
A simple high-level version (same output): <lang d>import std.stdio, std.array;
T[] quickSort(T)(T[] items) pure nothrow {
if (items.empty) return items; T[] less, notLess; foreach (x; items[1 .. $]) (x < items[0] ? less : notLess) ~= x; return less.quickSort ~ items[0] ~ notLess.quickSort;
}
void main() {
[4, 65, 2, -31, 0, 99, 2, 83, 782, 1].quickSort.writeln;
}</lang>
Often short functional sieves are not a true implementations of the Sieve of Eratosthenes: http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf
Similarly, one could argue that a true QuickSort is in-place, as this more efficient version (same output): <lang d>import std.stdio, std.algorithm;
void quickSort(T)(T[] items) pure nothrow @safe @nogc {
if (items.length >= 2) { auto parts = partition3(items, items[$ / 2]); parts[0].quickSort; parts[2].quickSort; }
}
void main() {
auto items = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]; items.quickSort; items.writeln;
}</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>
EchoLisp
<lang scheme> (lib 'list) ;; list-partition
(define compare 0) ;; counter
(define (quicksort L compare-predicate: proc aux: (part null)) (if (<= (length L) 1) L
(begin ;; counting the number of comparisons (set! compare (+ compare (length (rest L)))) ;; pivot = first element of list (set! part (list-partition (rest L) proc (first L))) (append (quicksort (first part) proc ) (list (first L)) (quicksort (second part) proc)))))
</lang>

Output:
<lang scheme> (shuffle (iota 15))
→ (10 0 14 11 13 9 2 5 4 8 1 7 12 3 6)
(quicksort (shuffle (iota 15)) <)
→ (0 1 2 3 4 5 6 7 8 9 10 11 12 13 14)
random list of numbers in [0 .. n[

count number of comparisons
(define (qtest (n 10000)) (set! compare 0) (quicksort (shuffle (iota n)) >) (writeln 'n n 'compare# compare ))
(qtest 1000)
n 1000 compare# 12764
(qtest 10000)
n 10000 compare# 277868
(qtest 100000)
n 100000 compare# 6198601
</lang>
Eero
Translated from Objective-C example on this page. <lang objc>#import <Foundation/Foundation.h>
void quicksortInPlace(MutableArray array, const long first, const long last)
if first >= last return Value pivot = array[(first + last) / 2] left := first right := last while left <= right while array[left] < pivot left++ while array[right] > pivot right-- if left <= right array.exchangeObjectAtIndex: left++, withObjectAtIndex: right--
quicksortInPlace(array, first, right) quicksortInPlace(array, left, last)
Array quicksort(Array unsorted)
a := [] a.addObjectsFromArray: unsorted quicksortInPlace(a, 0, a.count - 1) return a

int main(int argc, const char * argv[])
autoreleasepool a := [1, 3, 5, 7, 9, 8, 6, 4, 2] Log( 'Unsorted: %@', a) Log( 'Sorted: %@', quicksort(a) ) b := ['Emil', 'Peg', 'Helen', 'Juergen', 'David', 'Rick', 'Barb', 'Mike', 'Tom'] Log( 'Unsorted: %@', b) Log( 'Sorted: %@', quicksort(b) )
return 0</lang>
Alternative implementation (not necessarily as efficient, but very readable)
<lang objc>#import <Foundation/Foundation.h>
implementation Array (Quicksort)
plus: Array array, return Array = self.arrayByAddingObjectsFromArray: array
filter: BOOL (^)(id) predicate, return Array array := [] for id item in self if predicate(item) array.addObject: item return array.copy
quicksort, return Array = self if self.count > 1 id x = self[self.count / 2] lesser := self.filter: (id y | return y < x) greater := self.filter: (id y | return y > x) return lesser.quicksort + [x] + greater.quicksort
end
int main()
autoreleasepool a := [1, 3, 5, 7, 9, 8, 6, 4, 2] Log( 'Unsorted: %@', a) Log( 'Sorted: %@', a.quicksort ) b := ['Emil', 'Peg', 'Helen', 'Juergen', 'David', 'Rick', 'Barb', 'Mike', 'Tom'] Log( 'Unsorted: %@', b) Log( 'Sorted: %@', b.quicksort )
return 0</lang>

Output:
2013-09-04 16:54:31.780 a.out[2201:507] Unsorted: ( 1, 3, 5, 7, 9, 8, 6, 4, 2 ) 2013-09-04 16:54:31.781 a.out[2201:507] Sorted: ( 1, 2, 3, 4, 5, 6, 7, 8, 9 ) 2013-09-04 16:54:31.781 a.out[2201:507] Unsorted: ( Emil, Peg, Helen, Juergen, David, Rick, Barb, Mike, Tom ) 2013-09-04 16:54:31.782 a.out[2201:507] Sorted: ( Barb, David, Emil, Helen, Juergen, Mike, Peg, Rick, Tom )
Eiffel
The <lang eiffel>QUICKSORT</lang> class: <lang eiffel> class QUICKSORT [G -> COMPARABLE]
create make
feature {NONE} --Implementation
is_sorted (list: ARRAY [G]): BOOLEAN require not_void: list /= Void local i: INTEGER do Result := True from i := list.lower + 1 invariant i >= list.lower + 1 and i <= list.upper + 1 until i > list.upper loop Result := Result and list [i - 1] <= list [i] i := i + 1 variant list.upper + 1 - i end end
concatenate_array (a: ARRAY [G] b: ARRAY [G]): ARRAY [G] require not_void: a /= Void and b /= Void do create Result.make_from_array (a) across b as t loop Result.force (t.item, Result.upper + 1) end ensure same_size: a.count + b.count = Result.count end
quicksort_array (list: ARRAY [G]): ARRAY [G] require not_void: list /= Void local less_a: ARRAY [G] equal_a: ARRAY [G] more_a: ARRAY [G] pivot: G do create less_a.make_empty create more_a.make_empty create equal_a.make_empty create Result.make_empty if list.count <= 1 then Result := list else pivot := list [list.lower] across list as li invariant less_a.count + equal_a.count + more_a.count <= list.count loop if li.item < pivot then less_a.force (li.item, less_a.upper + 1) elseif li.item = pivot then equal_a.force (li.item, equal_a.upper + 1) elseif li.item > pivot then more_a.force (li.item, more_a.upper + 1) end end Result := concatenate_array (Result, quicksort_array (less_a)) Result := concatenate_array (Result, equal_a) Result := concatenate_array (Result, quicksort_array (more_a)) end ensure same_size: list.count = Result.count sorted: is_sorted (Result) end
feature -- Initialization
make do end
quicksort (a: ARRAY [G]): ARRAY [G] do Result := quicksort_array (a) end
end </lang> A test application: <lang eiffel> class APPLICATION
create make
feature {NONE} -- Initialization
make -- Run application. local test: ARRAY [INTEGER] sorted: ARRAY [INTEGER] sorter: QUICKSORT [INTEGER] do create sorter.make test := <<1, 3, 2, 4, 5, 5, 7, -1>> sorted := sorter.quicksort (test) across sorted as s loop print (s.item) print (" ") end print ("%N") end
end </lang>
Elixir
<lang elixir> defmodule QuickSort do
def qsort([]) do [] end def qsort([pivot | rest]) do { left, right } = Enum.partition(rest, fn(x) -> x < pivot end) qsort(left) ++ [pivot] ++ qsort(right) end
end </lang>
Erlang
like haskell. Used by Measure_relative_performance_of_sorting_algorithms_implementations. If changed keep the interface or change Measure_relative_performance_of_sorting_algorithms_implementations <lang erlang> -module( quicksort ).
-export( [qsort/1] ).
qsort([]) -> []; qsort([X|Xs]) ->
qsort([ Y || Y <- Xs, Y < X]) ++ [X] ++ qsort([ Y || Y <- Xs, Y >= X]).
</lang>
ERRE
<lang ERRE> PROGRAM QUICKSORT_DEMO
DIM ARRAY[21]
!$DYNAMIC DIM QSTACK[0]
!$INCLUDE="PC.LIB"
PROCEDURE QSORT(ARRAY[],START,NUM)
FIRST=START ! initialize work variables LAST=START+NUM-1 LOOP REPEAT TEMP=ARRAY[(LAST+FIRST) DIV 2] ! seek midpoint I=FIRST J=LAST REPEAT ! reverse both < and > below to sort descending WHILE ARRAY[I]<TEMP DO I=I+1 END WHILE WHILE ARRAY[J]>TEMP DO J=J-1 END WHILE EXIT IF I>J IF I<J THEN SWAP(ARRAY[I],ARRAY[J]) END IF I=I+1 J=J-1 UNTIL NOT(I<=J) IF I<LAST THEN ! Done QSTACK[SP]=I ! Push I QSTACK[SP+1]=LAST ! Push Last SP=SP+2 END IF LAST=J UNTIL NOT(FIRST<LAST)
EXIT IF SP=0 SP=SP-2 FIRST=QSTACK[SP] ! Pop First LAST=QSTACK[SP+1] ! Pop Last END LOOP
END PROCEDURE
BEGIN
RANDOMIZE(TIMER) ! generate a new series each run
! create an array FOR X=1 TO 21 DO ! fill with random numbers ARRAY[X]=RND(1)*500 ! between 0 and 500 END FOR PRIMO=6 ! sort starting here NUM=10 ! sort this many elements CLS PRINT("Before Sorting:";TAB(31);"After sorting:") PRINT("===============";TAB(31);"==============") FOR X=1 TO 21 DO ! show them before sorting IF X>=PRIMO AND X<=PRIMO+NUM-1 THEN PRINT("==>";) END IF PRINT(TAB(5);) WRITE("###.##";ARRAY[X]) END FOR
! create a stack !$DIM QSTACK[INT(NUM/5)+10]
QSORT(ARRAY[],PRIMO,NUM)
!$ERASE QSTACK
LOCATE(2,1) FOR X=1 TO 21 DO ! print them after sorting LOCATE(2+X,30) IF X>=PRIMO AND X<=PRIMO+NUM-1 THEN PRINT("==>";) ! point to sorted items END IF LOCATE(2+X,35) WRITE("###.##";ARRAY[X]) END FOR
END PROGRAM </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># (sort xs) is the ordered list of all elements in list xs.
This version preserves duplicates.
\sort==
(\xs xs [] \x\xs append (sort; filter (gt x) xs); # all the items less than x cons x; append (filter (eq x) xs); # all the items equal to x sort; filter (lt x) xs # all the items greater than x )
(unique xs) is the ordered list of unique elements in list xs.
\unique==
(\xs xs [] \x\xs append (unique; filter (gt x) xs); # all the items less than x cons x; # x itself unique; filter (lt x) xs # all the items greater than x )
</lang>
Forth
<lang forth>: 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@ < while cell+ repeat swap begin r@ over @ < 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
Works with: Fortran version 90 and later
<lang fortran>module qsort_mod
implicit none
type group
integer :: order ! original order of unsorted data real :: value ! values to be sorted by
end type group
contains
recursive subroutine QSort(a,na)
! DUMMY ARGUMENTS integer, intent(in) :: nA type (group), dimension(nA), intent(in out) :: A
! LOCAL VARIABLES integer :: left, right real :: random real :: pivot type (group) :: temp integer :: marker
if (nA > 1) then
call random_number(random) pivot = A(int(random*real(nA-1))+1)%value ! random pivor (not best performance, but avoids worst-case) left = 0 right = nA + 1
do while (left < right) right = right - 1 do while (A(right)%value > pivot) right = right - 1 end do left = left + 1 do while (A(left)%value < 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
call QSort(A(:marker-1),marker-1) call QSort(A(marker:),nA-marker+1)
end if
end subroutine QSort
end module qsort_mod
! Test Qsort Module program qsort_test use qsort_mod implicit none
integer, parameter :: l = 8 type (group), dimension(l) :: A integer, dimension(12) :: seed = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] integer :: i real :: random
write (*,*) "Unsorted Values:" call random_seed(put = seed) do i = 1, l call random_number(random) A(i)%value = random A(i)%order = i if (mod(i,4) == 0) write (*,"(4(I5,1X,F8.6))") A(i-3:i) end do
call QSort(A,l) write (*,*) "Sorted Values:" do i = 4, l, 4 if (mod(i,4) == 0) write (*,"(4(I5,1X,F8.6))") A(i-3:i) end do
end program qsort_test</lang>

Output:
Compiled with GNU Fortran 4.6.3 Unsorted Values: 1 0.228570 2 0.352733 3 0.167898 4 0.883237 5 0.968189 6 0.806234 7 0.117714 8 0.487401 Sorted Values: 7 0.117714 3 0.167898 1 0.228570 2 0.352733 8 0.487401 6 0.806234 4 0.883237 5 0.968189
A discussion about Quicksort pivot options, free source code for an optimized quicksort using insertion sort as a finisher, and an OpenMP multi-threaded quicksort is found at balfortran.org
FunL
<lang funl>def
qsort( [] ) = [] qsort( p:xs ) = qsort( xs.filter((< p)) ) + [p] + qsort( xs.filter((>= p)) )</lang>
Here is a more efficient version using the partition function.
<lang funl>def
qsort( [] ) = [] qsort( x:xs ) = val (ys, zs) = xs.partition( (< x) ) qsort( ys ) + (x : qsort( zs ))
println( qsort([4, 2, 1, 3, 0, 2]) ) println( qsort(["Juan", "Daniel", "Miguel", "William", "Liam", "Ethan", "Jacob"]) )</lang>

Output:
[0, 1, 2, 2, 3, 4] [Daniel, Ethan, Jacob, Juan, Liam, Miguel, William]
Go
Note that Go's sort.Sort function is a Quicksort so in practice it would be just be used. It's actually a combination of quick sort, heap sort, and insertion sort. It starts with a quick sort, after a depth of 2*ceil(lg(n+1)) it switches to heap sort, or once a partition becomes small (less than eight items) it switches to insertion sort.

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]
More traditional version of quicksort. It work generically with any container that conforms to sort.Interface.
<lang go>package main
import (
"fmt" "sort" "math/rand"
)
func partition(a sort.Interface, first int, last int, pivotIndex int) int {
a.Swap(first, pivotIndex) // move it to beginning left := first+1 right := last for left <= right { for left <= last && a.Less(left, first) { left++ } for right >= first && a.Less(first, right) { right-- } if left <= right { a.Swap(left, right) left++ right-- } } a.Swap(first, right) // swap into right place return right
}
func quicksortHelper(a sort.Interface, first int, last int) {
if first >= last { return } pivotIndex := partition(a, first, last, rand.Intn(last - first + 1) + first) quicksortHelper(a, first, pivotIndex-1) quicksortHelper(a, pivotIndex+1, last)
}
func quicksort(a sort.Interface) {
quicksortHelper(a, 0, a.Len()-1)
}
func main() {
a := []int{1, 3, 5, 7, 9, 8, 6, 4, 2} fmt.Printf("Unsorted: %v\n", a) quicksort(sort.IntSlice(a)) fmt.Printf("Sorted: %v\n", a) b := []string{"Emil", "Peg", "Helen", "Juergen", "David", "Rick", "Barb", "Mike", "Tom"} fmt.Printf("Unsorted: %v\n", b) quicksort(sort.StringSlice(b)) fmt.Printf("Sorted: %v\n", b)
}</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]
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.

Output:

Abbreviated

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.isEmpty()) {
E pivot = arr.get(0); //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; }
return arr;
}</lang>
JavaScript
Imperative
<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 + Math.floor((right - right) / 2)], left_new = left, right_new = right;
do { while (less(array[left_new], pivot)) { left_new += 1; } while (less(pivot, array[right_new])) { right_new -= 1; } if (left_new <= right_new) { swap(left_new, right_new); left_new += 1; right_new -= 1; } } while (left_new <= right_new);
quicksort(left, right_new); quicksort(left_new, right);
} }
quicksort(0, array.length - 1);
return array;
}</lang>
Example:<lang javascript>var test_array = [10, 3, 11, 15, 19, 1]; var sorted_array = sort(test_array, function(a,b) { return a<b; });</lang>

Output:

<lang javascript>[ 1, 3, 10, 11, 15, 19 ]</lang>

Functional
ES5
Emphasising clarity more than run-time optimisation (for which Array.sort() would be a better option)
<lang JavaScript>// quickSort :: (Ord a) => [a] -> [a] function quickSort(xxs) {
if (xxs.length) { var x = xxs[0], xs = xxs.slice(1),
less = quickSort(xs.filter(function (a) { return a <= x; })),
more = quickSort(xs.filter(function (a) { return a > x; }));
return less .concat([x]) .concat(more);
} else return xxs;
}
// TEST quickSort([11.8, 14.1, 21.3, 8.5, 16.7, 5.7])</lang>

Output:
[5.7, 8.5, 11.8, 14.1, 16.7, 21.3]
ES6
<lang javascript>Array.prototype.quick_sort = function () {
if (this.length < 2) { return this; }
var pivot = this[Math.round(this.length / 2)];
return this.filter(x => x < pivot) .quick_sort() .concat(this.filter(x => x == pivot)) .concat(this.filter(x => 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>
jq
jq's built-in sort currently (version 1.4) uses the standard C qsort, a quicksort. sort can be used on any valid JSON array.

Example:<lang jq>[1, 1.1, [1,2], true, false, null, {"a":1}, null] | sort</lang>

Output:

<lang jq>[null,null,false,true,1,1.1,[1,2],{"a"

1}]</lang>
Here is an implementation in jq of the pseudo-code (and comments :-) given at the head of this article:<lang jq>def quicksort:
if length < 2 then . # it is already sorted else .[0] as $pivot | reduce .[] as $x # state: [less, equal, greater] ( [ [], [], [] ]; # three empty arrays: if $x < $pivot then .[0] += [$x] # add x to less elif $x == $pivot then .[1] += [$x] # add x to equal else .[2] += [$x] # add x to greater end ) | (.[0] | quicksort ) + .[1] + (.[2] | quicksort ) end ;
</lang>Fortunately, the example input used above produces the same output, and so both are omitted here.
Julia
Built-in function for in-place sorting via quicksort (the code from the standard library is quite readable): <lang julia>sort!(A, alg=QuickSort)</lang> A simple polymorphic implementation of an in-place recursive quicksort (based on the pseudocode above): <lang julia>function quicksort!(A,i=1,j=length(A))
if j > i pivot = A[rand(i:j)] # random element of A left, right = i, j while left <= right while A[left] < pivot left += 1 end while A[right] > pivot right -= 1 end if left <= right A[left], A[right] = A[right], A[left] left += 1 right -= 1 end end quicksort!(A,i,right) quicksort!(A,left,j) end return A
end</lang> A one-line (but rather inefficient) implementation based on the Haskell version, which operates out-of-place and allocates temporary arrays: <lang julia>qsort(L) = isempty(L) ? L : vcat(qsort(filter(x -> x < L[1], L[2:end])), L[1:1], qsort(filter(x -> x >= L[1], L[2:end])))</lang>

Output:
julia> A = [84,77,20,60,47,20,18,97,41,49,31,39,73,68,65,52,1,92,15,9] julia> qsort(A) [1,9,15,18,20,20,31,39,41,47,49,52,60,65,68,73,77,84,92,97] julia> quicksort!(copy(A)) [1,9,15,18,20,20,31,39,41,47,49,52,60,65,68,73,77,84,92,97] julia> qsort(A) == quicksort!(copy(A)) == sort(A) == sort(A, alg=QuickSort) true
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:
1 2 3 4 5 6 7 8 9

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>
Kotlin
<lang kotlin>import java.util.Comparator import java.util.ArrayList
fun <T> quickSort(a : List<T>, c : Comparator<T>) : ArrayList<T> {
return if (a.size == 0) ArrayList(a) else { val boxes = Array<ArrayList<T>>(3, {ArrayList<T>()}) fun normalise(i : Int) = i / Math.max(1, Math.abs(i)) a forEach {boxes[normalise(c.compare(it, a[0])) + 1] add(it)} array(0, 2) forEach {boxes[it] = quickSort(boxes[it], c)} boxes.flatMapTo(ArrayList<T>()) {it} }
}</lang>
Lobster
<lang lobster>include "std.lobster"
def quicksort(xs, lt):
if xs.length <= 1: xs else: pivot := xs[0] tail := xs.slice(1, -1) f1 := filter tail: lt(_, pivot) f2 := filter tail: !lt(_, pivot) append(append(quicksort(f1, lt), [ pivot ]), quicksort(f2, lt))
sorted := [ 3, 9, 5, 4, 1, 3, 9, 5, 4, 1 ].quicksort(): _a < _b print sorted</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
in-place
<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 < 1) then return t end local pivot = start for i = start + 1, endi do if t[i] <= t[pivot] then if i == pivot + 1 then t[pivot],t[pivot+1] = t[pivot+1],t[pivot] else t[pivot],t[pivot+1],t[i] = t[i],t[pivot],t[pivot+1] 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>
non in-place
<lang lua>function quicksort(t)
if #t<2 then return t end local pivot=t[1] local a,b,c={},{},{} for _,v in ipairs(t) do if v<pivot then a[#a+1]=v elseif v>pivot then c[#c+1]=v else b[#b+1]=v end end a=quicksort(a) c=quicksort(c) for _,v in ipairs(b) do a[#a+1]=v end for _,v in ipairs(c) do a[#a+1]=v end return a
end</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>
<lang Mathematica>qsort[{}] = {}; qsort[{x_, xs___}] := Join[qsort@Select[{xs}, # <= x &], {x}, qsort@Select[{xs}, # > x &]];</lang>
<lang Mathematica>QuickSort[{}] := {} QuickSort[list: {__}] := With[{pivot=RandomChoice[list]}, Join[ <|1->{}, -1->{}|>, GroupBy[list,Order[#,pivot]&] ] // Catenate[ {QuickSort@#[1], #[0], QuickSort@#[-1]} ]& ]</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>
Mond
Implements the simple quicksort algorithm.
<lang Mond>fun quicksort( arr, cmp ) {
if( arr.length() < 2 ) return arr; if( !cmp ) cmp = ( a, b ) -> a - b; var a = [ ], b = [ ]; var pivot = arr[0]; var len = arr.length(); for( var i = 1; i < len; ++i ) { var item = arr[i]; if( cmp( item, pivot ) < cmp( pivot, item ) ) a.add( item ); else b.add( item ); } a = quicksort( a, cmp ); b = quicksort( b, cmp ); a.add( pivot ); foreach( var item in b ) a.add( item ); return a;
}</lang>
Usage
<lang Mond>var array = [ 532, 16, 153, 3, 63.60, 925, 0.214 ]; var sorted = quicksort( array );
printLn( sorted );</lang>

Output:
[ 0.214, 3, 16, 63.6, 153, 532, 925 ]
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>
Nim
<lang nim> proc quickSort[T](a: var openarray[T], inl = 0, inr = -1) =
var r = if inr >= 0: inr else: a.high var l = inl let n = r - l + 1 if n < 2: return let p = a[l + 3 * n div 4] while l <= r: if a[l] < p: inc l continue if a[r] > p: dec r continue if l <= r: swap a[l], a[r] inc l dec r quickSort(a, inl, r) quickSort(a, l, inr)
var a = @[4, 65, 2, -31, 0, 99, 2, 83, 782] quickSort a echo a</lang>

Output:
@[-31, 0, 2, 2, 4, 65, 83, 99, 782]
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, NSInteger first, NSInteger last, NSComparator comparator) {
if (first >= last) return; id pivot = array[(first + last) / 2]; NSInteger left = first; NSInteger right = last; while (left <= right) { while (comparator(array[left], pivot) == NSOrderedAscending) left++; while (comparator(array[right], pivot) == NSOrderedDescending) right--; if (left <= right) [array exchangeObjectAtIndex:left++ withObjectAtIndex:right--]; } quicksortInPlace(array, first, right, comparator); quicksortInPlace(array, left, last, comparator);
}
NSArray* quicksort(NSArray *unsorted, NSComparator comparator) {
NSMutableArray *a = [NSMutableArray arrayWithArray:unsorted]; quicksortInPlace(a, 0, a.count - 1, comparator); 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, ^(id x, id y) { return [x compare:y]; })); NSArray *b = @[ @"Emil", @"Peg", @"Helen", @"Juergen", @"David", @"Rick", @"Barb", @"Mike", @"Tom" ]; NSLog(@"Unsorted: %@", b); NSLog(@"Sorted: %@", quicksort(b, ^(id x, id y) { return [x compare:y]; })); } 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>
Oforth
Oforth built-in sort uses quick sort algorithm (see lang/collect/ListBuffer.of for implementation) :
<lang Oforth>[ 5, 8, 2, 3, 4, 1 ] sort</lang>
ooRexx
Translation of: Python
<lang ooRexx> a = .array~Of(4, 65, 2, -31, 0, 99, 83, 782, 1)
say 'before:' a~toString( ,', ') a = quickSort(a) say ' after:' 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>

Output:
before: 4, 65, 2, -31, 0, 99, 83, 782, 1 after: -31, 0, 1, 2, 4, 65, 83, 99, 782
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 {
return @_ if @_ < 2; my $p = splice @_, int rand @_, 1; quick_sort(grep $_ < $p, @_), $p, quick_sort(grep $_ >= $p, @_);
}
my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1); @a = quick_sort @a; print "@a\n"; </lang>
Perl 6
<lang perl6># Empty list sorts to the empty list
multi quicksort([]) { () } # Otherwise, extract first item as pivot... multi quicksort([$pivot, *@rest]) { # Partition. my $before := @rest.grep(* before $pivot); my $after := @rest.grep(* !before $pivot); # Sort the partitions. flat quicksort($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
First solution
<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>

Another solution
<lang powershell> function quicksort($array) {
$less, $equal, $greater = @(), @(), @() if( $array.Count -gt 1 ) { $pivot = $array[0] foreach( $x in $array) { if($x -lt $pivot) { $less += @($x) } elseif ($x -eq $pivot) { $equal += @($x)} else { $greater += @($x) } } $array = (@(quicksort $less) + @($equal) + @(quicksort $greater)) } $array
} $array = @(60, 21, 19, 36, 63, 8, 100, 80, 3, 87, 11) "$(quicksort $array)" </lang>
The output is: 3 8 11 19 21 36 60 63 80 87 100
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>
More correctly in some tests: <lang python>from random import *
def qSort(a):
if len(a) <= 1: return a else: q = choice(a) return qSort([elem for elem in a if elem < q]) + [q] * a.count(q) + qSort([elem for elem in a if elem > q])</lang>

<lang python>def quickSort(a):
if len(a) <= 1: return a else: less = [] more = [] pivot = choice(a) for i in a: if i < pivot: less.append(i) if i > pivot: more.append(i) less = quickSort(less) more = quickSort(more) return less + [pivot] * a.count(pivot) + more</lang>
Returning a new list:
<lang python>def qsort(array):
if len(array) < 2: return array head, *tail = array less = qsort([i for i in tail if i < head]) more = qsort([i for i in tail if i >= head]) return less + [head] + more</lang>
Sorting a list in place:
<lang python>def quicksort(array):
_quicksort(array, 0, len(array) - 1)
def _quicksort(array, start, stop):
if stop - start > 0: pivot, left, right = array[start], start, stop while left <= right: while array[left] < pivot: left += 1 while array[right] > pivot: right -= 1 if left <= right: array[left], array[right] = array[right], array[left] left += 1 right -= 1 _quicksort(array, start, right) _quicksort(array, left, stop)</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>
Racket
<lang Racket>#lang racket (define (quicksort < l)
(match l ['() '()] [(cons x xs) (let-values ([(xs-gte xs-lt) (partition (curry < x) xs)]) (append (quicksort < xs-lt) (list x) (quicksort < xs-gte)))]))</lang>
Examples
<lang Racket>(quicksort < '(8 7 3 6 4 5 2))
returns '(2 3 4 5 6 7 8)
(quicksort string<? '("Mergesort" "Quicksort" "Bubblesort"))
returns '("Bubblesort" "Mergesort" "Quicksort")</lang>
REXX
version 1
<lang rexx>/*REXX program sorts a stemmed array using the quicksort algorithm. */ call gen@ /*generate the elements for the array. */ call show@ 'before sort' /*show the before array elements. */ call quickSort # /*invoke the quicksort subroutine. */ call show@ ' after sort' /*show the after array elements. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ quickSort: procedure expose @. /*access the caller's local variable. */
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 " " */ if j>=k then leave /*segment finished? */ _=@.j; @.j=@.k; @.k=_ /*swap J&K elements.*/ end /*forever*/ $=$+1 k=j-1; @.L=@.k; @.k=p 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
/*──────────────────────────────────────────────────────────────────────────────────────*/ show@: widthH=length(#) /*maximum width of any line of output. */
do j=1 for # /*display each item in the array. */ say 'element' right(j,widthH) arg(1)':' @.j end /*j*/ say copies('▒', maxL + widthH + 22) /*display a separator (between outputs)*/ return
/*──────────────────────────────────GEN@ subroutine──────────────────────────────────────────────────────────────────────────────────────────────────────*/ gen@: @.=; maxL=0 /*assign default value for array.*/ @.1 = " Rivers that form part of a (USA) state's border " /*this value is adjusted later to include a prefix & suffix.*/ @.2 = '=' /*this value is expanded later. */ @.3 = "Perdido River Alabama, Florida" @.4 = "Chattahoochee River Alabama, Georgia" @.5 = "Tennessee River Alabama, Kentucky, Mississippi, Tennessee" @.6 = "Colorado River Arizona, California, Nevada, Baja California (Mexico)" @.7 = "Mississippi River Arkansas, Illinois, Iowa, Kentucky, Minnesota, Mississippi, Missouri, Tennessee, Louisiana, Wisconsin" @.8 = "St. Francis River Arkansas, Missouri" @.9 = "Poteau River Arkansas, Oklahoma" @.10 = "Arkansas River Arkansas, Oklahoma" @.11 = "Red River (Mississippi watershed) Arkansas, Oklahoma, Texas" @.12 = "Byram River Connecticut, New York" @.13 = "Pawcatuck River Connecticut, Rhode Island and Providence Plantations" @.14 = "Delaware River Delaware, New Jersey, New York, Pennsylvania" @.15 = "Potomac River District of Columbia, Maryland, Virginia, West Virginia" @.16 = "St. Marys River Florida, Georgia" @.17 = "Chattooga River Georgia, South Carolina" @.18 = "Tugaloo River Georgia, South Carolina" @.19 = "Savannah River Georgia, South Carolina" @.20 = "Snake River Idaho, Oregon, Washington" @.21 = "Wabash River Illinois, Indiana" @.22 = "Ohio River Illinois, Indiana, Kentucky, Ohio, West Virginia" @.23 = "Great Miami River (mouth only) Indiana, Ohio" @.24 = "Des Moines River Iowa, Missouri" @.25 = "Big Sioux River Iowa, South Dakota" @.26 = "Missouri River Kansas, Iowa, Missouri, Nebraska, South Dakota" @.27 = "Tug Fork River Kentucky, Virginia, West Virginia" @.28 = "Big Sandy River Kentucky, West Virginia" @.29 = "Pearl River Louisiana, Mississippi" @.30 = "Sabine River Louisiana, Texas" @.31 = "Monument Creek Maine, New Brunswick (Canada)" @.32 = "St. Croix River Maine, New Brunswick (Canada)" @.33 = "Piscataqua River Maine, New Hampshire" @.34 = "St. Francis River Maine, Quebec (Canada)" @.35 = "St. John River Maine, Quebec (Canada)" @.36 = "Pocomoke River Maryland, Virginia" @.37 = "Palmer River Massachusetts, Rhode Island and Providence Plantations" @.38 = "Runnins River Massachusetts, Rhode Island and Providence Plantations" @.39 = "Montreal River Michigan (upper peninsula), Wisconsin" @.40 = "Detroit River Michigan, Ontario (Canada)" @.41 = "St. Clair River Michigan, Ontario (Canada)" @.42 = "St. Marys River Michigan, Ontario (Canada)" @.43 = "Brule River Michigan, Wisconsin" @.44 = "Menominee River Michigan, Wisconsin" @.45 = "Red River of the North Minnesota, North Dakota" @.46 = "Bois de Sioux River Minnesota, North Dakota, South Dakota" @.47 = "Pigeon River Minnesota, Ontario (Canada)" @.48 = "Rainy River Minnesota, Ontario (Canada)" @.49 = "St. Croix River Minnesota, Wisconsin" @.50 = "St. Louis River Minnesota, Wisconsin" @.51 = "Halls Stream New Hampshire, Canada" @.52 = "Salmon Falls River New Hampshire, Maine" @.53 = "Connecticut River New Hampshire, Vermont" @.54 = "Arthur Kill New Jersey, New York (tidal strait)" @.55 = "Kill Van Kull New Jersey, New York (tidal strait)" @.56 = "Hudson River (lower part only) New Jersey, New York" @.57 = "Rio Grande New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila de Zaragoza (Mexico), Chihuahua (Mexico)" @.58 = "Niagara River New York, Ontario (Canada)" @.59 = "St. Lawrence River New York, Ontario (Canada)" @.60 = "Poultney River New York, Vermont" @.61 = "Catawba River North Carolina, South Carolina" @.62 = "Blackwater River North Carolina, Virginia" @.63 = "Columbia River Oregon, Washington"
do #=1 while @.#\== /*find how many entries in array, and */ maxL=max(maxL, length(@.#)) /* also find the maximum width entry.*/ end /*#*/
=#-1 /*adjust the highest element number. */
@.1=center(@.1, maxL, '-') /* " " header information. */ @.2=copies(@.2, maxL) /* " " " separator. */ return</lang> output
element 1 before sort: ------------------------------------------------ Rivers that form part of a (USA) state's border ------------------------------------------------- element 2 before sort: ================================================================================================================================================== element 3 before sort: Perdido River Alabama, Florida element 4 before sort: Chattahoochee River Alabama, Georgia element 5 before sort: Tennessee River Alabama, Kentucky, Mississippi, Tennessee element 6 before sort: Colorado River Arizona, California, Nevada, Baja California (Mexico) element 7 before sort: Mississippi River Arkansas, Illinois, Iowa, Kentucky, Minnesota, Mississippi, Missouri, Tennessee, Louisiana, Wisconsin element 8 before sort: St. Francis River Arkansas, Missouri element 9 before sort: Poteau River Arkansas, Oklahoma element 10 before sort: Arkansas River Arkansas, Oklahoma element 11 before sort: Red River (Mississippi watershed) Arkansas, Oklahoma, Texas element 12 before sort: Byram River Connecticut, New York element 13 before sort: Pawcatuck River Connecticut, Rhode Island and Providence Plantations element 14 before sort: Delaware River Delaware, New Jersey, New York, Pennsylvania element 15 before sort: Potomac River District of Columbia, Maryland, Virginia, West Virginia element 16 before sort: St. Marys River Florida, Georgia element 17 before sort: Chattooga River Georgia, South Carolina element 18 before sort: Tugaloo River Georgia, South Carolina element 19 before sort: Savannah River Georgia, South Carolina element 20 before sort: Snake River Idaho, Oregon, Washington element 21 before sort: Wabash River Illinois, Indiana element 22 before sort: Ohio River Illinois, Indiana, Kentucky, Ohio, West Virginia element 23 before sort: Great Miami River (mouth only) Indiana, Ohio element 24 before sort: Des Moines River Iowa, Missouri element 25 before sort: Big Sioux River Iowa, South Dakota element 26 before sort: Missouri River Kansas, Iowa, Missouri, Nebraska, South Dakota element 27 before sort: Tug Fork River Kentucky, Virginia, West Virginia element 28 before sort: Big Sandy River Kentucky, West Virginia element 29 before sort: Pearl River Louisiana, Mississippi element 30 before sort: Sabine River Louisiana, Texas element 31 before sort: Monument Creek Maine, New Brunswick (Canada) element 32 before sort: St. Croix River Maine, New Brunswick (Canada) element 33 before sort: Piscataqua River Maine, New Hampshire element 34 before sort: St. Francis River Maine, Quebec (Canada) element 35 before sort: St. John River Maine, Quebec (Canada) element 36 before sort: Pocomoke River Maryland, Virginia element 37 before sort: Palmer River Massachusetts, Rhode Island and Providence Plantations element 38 before sort: Runnins River Massachusetts, Rhode Island and Providence Plantations element 39 before sort: Montreal River Michigan (upper peninsula), Wisconsin element 40 before sort: Detroit River Michigan, Ontario (Canada) element 41 before sort: St. Clair River Michigan, Ontario (Canada) element 42 before sort: St. Marys River Michigan, Ontario (Canada) element 43 before sort: Brule River Michigan, Wisconsin element 44 before sort: Menominee River Michigan, Wisconsin element 45 before sort: Red River of the North Minnesota, North Dakota element 46 before sort: Bois de Sioux River Minnesota, North Dakota, South Dakota element 47 before sort: Pigeon River Minnesota, Ontario (Canada) element 48 before sort: Rainy River Minnesota, Ontario (Canada) element 49 before sort: St. Croix River Minnesota, Wisconsin element 50 before sort: St. Louis River Minnesota, Wisconsin element 51 before sort: Halls Stream New Hampshire, Canada element 52 before sort: Salmon Falls River New Hampshire, Maine element 53 before sort: Connecticut River New Hampshire, Vermont element 54 before sort: Arthur Kill New Jersey, New York (tidal strait) element 55 before sort: Kill Van Kull New Jersey, New York (tidal strait) element 56 before sort: Hudson River (lower part only) New Jersey, New York element 57 before sort: Rio Grande New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila De Zaragoza (Mexico), Chihuahua (Mexico) element 58 before sort: Niagara River New York, Ontario (Canada) element 59 before sort: St. Lawrence River New York, Ontario (Canada) element 60 before sort: Poultney River New York, Vermont element 61 before sort: Catawba River North Carolina, South Carolina element 62 before sort: Blackwater River North Carolina, Virginia element 63 before sort: Columbia River Oregon, Washington ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ element 1 after sort: ------------------------------------------------ Rivers that form part of a (USA) state's border ------------------------------------------------- element 2 after sort: ================================================================================================================================================== element 3 after sort: Arkansas River Arkansas, Oklahoma 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 Iowa, South Dakota element 7 after sort: Blackwater River North Carolina, Virginia element 8 after sort: Bois de Sioux River Minnesota, North Dakota, South 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, California, Nevada, Baja California (Mexico) element 15 after sort: Columbia River Oregon, Washington element 16 after sort: Connecticut River New Hampshire, Vermont element 17 after sort: Delaware River Delaware, New Jersey, New York, Pennsylvania 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) Indiana, Ohio 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 Arkansas, Illinois, Iowa, Kentucky, Minnesota, Mississippi, Missouri, Tennessee, Louisiana, Wisconsin element 26 after sort: Missouri River Kansas, Iowa, Missouri, Nebraska, South Dakota element 27 after sort: Montreal River Michigan (upper peninsula), Wisconsin element 28 after sort: Monument Creek Maine, New Brunswick (Canada) element 29 after sort: Niagara River New York, Ontario (Canada) element 30 after sort: Ohio River Illinois, Indiana, Kentucky, Ohio, West Virginia element 31 after sort: Palmer River Massachusetts, Rhode Island and Providence Plantations element 32 after sort: Pawcatuck River Connecticut, Rhode Island and Providence Plantations element 33 after sort: Pearl River Louisiana, Mississippi element 34 after sort: Perdido River Alabama, Florida 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 District of Columbia, Maryland, Virginia, West Virginia element 40 after sort: Poultney River New York, Vermont element 41 after sort: Rainy River Minnesota, Ontario (Canada) element 42 after sort: Red River (Mississippi watershed) Arkansas, Oklahoma, Texas element 43 after sort: Red River of the North Minnesota, North Dakota 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 Massachusetts, Rhode Island and Providence Plantations element 46 after sort: Sabine River Louisiana, Texas element 47 after sort: Salmon Falls River New Hampshire, Maine element 48 after sort: Savannah River Georgia, South Carolina element 49 after sort: Snake River Idaho, Oregon, Washington element 50 after sort: St. Clair River Michigan, Ontario (Canada) element 51 after sort: St. Croix River Maine, New Brunswick (Canada) 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 Alabama, Kentucky, Mississippi, Tennessee element 61 after sort: Tug Fork River Kentucky, Virginia, West 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[0] less, greatereq = self[1..-1].partition { |x| x < pivot } less.quick_sort + [pivot] + greatereq.quick_sort end
end</lang> or <lang ruby>class Array
def quick_sort return self if length <= 1 pivot = sample group = group_by{ |x| x <=> pivot } group.default = [] group[-1].quick_sort + group[0] + group[1].quick_sort end
end</lang> or functionally <lang ruby>class Array
def quick_sort h, *t = self h ? t.partition { |e| e < h }.inject { |l, r| l.quick_sort + [h] + r.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>
Rust
<lang rust>// Type alias for function that returns true if arguments should be swapped type OrderFunc<T> = Fn(&T, &T) -> bool;
fn main() {
// Sort numbers let mut numbers = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]; println!("Before: {:?}", numbers);
quick_sort(&mut numbers, &is_less); println!("After: {:?}", numbers);
// Sort strings let mut strings = ["beach", "hotel", "airplane", "car", "house", "art"]; println!("Before: {:?}", strings);
quick_sort(&mut strings, &is_less); println!("After: {:?}", strings);
}

// Example OrderFunc which is used to order items from least to greatest
[inline(always)]
fn is_less<T: Ord>(x: &T, y: &T) -> bool {
x < y
}
fn quick_sort<T>(v: &mut [T], f: &OrderFunc<T>) {
let len = v.len(); if len < 2 { return; }
let pivot_index = partition(v, f);
// Sort the left side quick_sort(&mut v[0..pivot_index], f);
// Sort the right side quick_sort(&mut v[pivot_index + 1..len], f);
}
fn partition<T>(v: &mut [T], f: &OrderFunc<T>) -> usize {
let len = v.len(); let pivot_index = len / 2;
v.swap(pivot_index, len - 1);
let mut store_index = 0; for i in 0..len - 1 { if f(&v[i], &v[len - 1]) { v.swap(i, store_index); store_index += 1; } }
v.swap(store_index, len - 1); store_index
}</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 List(head) => list case head :: tail => val (smaller, bigger) = tail partition (_ < head) quicksortInt(smaller) ::: head :: quicksortInt(bigger) case _ => 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>
Sidef
<lang ruby>func quicksort (a) {
a.len < 2 && return(a); var p = a.pop_rand; # to avoid the worst cases __FUNC__(a.grep{ .< p}) + [p] + __FUNC__(a.grep{ .>= p});
}</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>
Swift
<lang swift>func quicksort<T where T : Comparable>(inout elements: [T], range: Range<Int>) {
if (range.endIndex - range.startIndex > 1) { let pivotIndex = partition(&elements, range) quicksort(&elements, range.startIndex ..< pivotIndex) quicksort(&elements, pivotIndex+1 ..< range.endIndex) }
}
func quicksort<T where T : Comparable>(inout elements: [T]) {
quicksort(&elements, indices(elements))
}</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>
uBasic/4tH
<lang>PRINT "Quick sort:"
n = FUNC (_InitArray) PROC _ShowArray (n) PROC _Quicksort (n) PROC _ShowArray (n)
PRINT
END

_InnerQuick PARAM(2)
LOCAL(4)
IF b@ < 2 THEN RETURN f@ = a@ + b@ - 1 c@ = a@ e@ = f@ d@ = @((c@ + e@) / 2)
DO DO WHILE @(c@) < d@ c@ = c@ + 1 LOOP
DO WHILE @(e@) > d@ e@ = e@ - 1 LOOP
IF c@ - 1 < e@ THEN PROC _Swap (c@, e@) c@ = c@ + 1 e@ = e@ - 1 ENDIF
UNTIL c@ > e@ LOOP
IF a@ < e@ THEN PROC _InnerQuick (a@, e@ - a@ + 1) IF c@ < f@ THEN PROC _InnerQuick (c@, f@ - c@ + 1)
RETURN

_Quicksort PARAM(1) ' Quick sort
PROC _InnerQuick (0, a@)
RETURN

_Swap PARAM(2) ' Swap two array elements
PUSH @(a@) @(a@) = @(b@) @(b@) = POP()
RETURN

_InitArray ' Init example array
PUSH 4, 65, 2, -31, 0, 99, 2, 83, 782, 1 FOR i = 0 TO 9 @(i) = POP() NEXT
RETURN (i)

_ShowArray PARAM (1) ' Show array subroutine
FOR i = 0 TO a@-1 PRINT @(i), NEXT PRINT
RETURN</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
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"
VBScript
Translation of: BBC BASIC
<lang vb>Function quicksort(arr,s,n) l = s r = s + n - 1 p = arr(Int((l + r)/2)) Do Until l > r Do While arr(l) < p l = l + 1 Loop Do While arr(r) > p r = r -1 Loop If l <= r Then tmp = arr(l) arr(l) = arr(r) arr(r) = tmp l = l + 1 r = r - 1 End If Loop If s < r Then Call quicksort(arr,s,r-s+1) End If If l < t Then Call quicksort(arr,l,t-l+1) End If quicksort = arr End Function
myarray=Array(9,8,7,6,5,5,4,3,2,1,0,-1) m = quicksort(myarray,0,12) WScript.Echo Join(m,",")</lang>

Output:
-1,0,1,2,3,4,5,5,6,7,8,9
Wart
<lang python>def (qsort (pivot ... ns))
(+ (qsort+keep (fn(_) (_ < pivot)) ns) list.pivot (qsort+keep (fn(_) (_ > pivot)) ns))
def (qsort x) :case x=nil
nil</lang>
XPL0
<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations string 0; \use zero-terminated strings
proc QSort(Array, Num); \Quicksort Array into ascending order char Array; \address of array to sort int Num; \number of elements in the array 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), Num-I); if J > 0 then QSort(Array, J+1); ]; \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
zkl
These are the Wikipedia algorithms.
Quick sort immutable sequence using crappy pivot choice: <lang zkl>fcn qtSort(list,cmp=Op("<")){ // sort immutable lists
fcn(list,cmp,N){ // spendy to keep recreating cmp reg pivot=list[0], rest=list[1,*]; left,right:=rest.filter22(cmp,pivot); N+=1; T.extend(self.fcn(left,cmp,N),T(pivot),self.fcn(right,cmp,N)); }(list,cmp,0);
}</lang> In place quick sort: <lang zkl>fcn qiSort(list,cmp='<){ // in place quick sort
fcn(list,left,right,cmp){ if (left<right){
// partition list pivotIndex:=(left+right)/2; // or median of first,middle,last pivot:=list[pivotIndex]; list.swap(pivotIndex,right); // move pivot to end pivotIndex:=left; i:=left; do(right-left){ // foreach i in ([left..right-1]) if(cmp(list[i],pivot)){ // not cheap list.swap(i,pivotIndex); pivotIndex+=1; } i+=1; } list.swap(pivotIndex,right); // move pivot to final place
// sort the partitions
self.fcn(list,left,pivotIndex-1,cmp);
return(self.fcn(list,pivotIndex+1,right,cmp));
} }(list,0,list.len()-1,cmp); list;
}</lang>