# Sorting algorithms/Quicksort

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

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

O(n logn) sorts

O(n log2n) sorts
Shell Sort

In this task, the goal is to sort an array (or list) of 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. The algorithm goes like this (from the wiki):

```function quicksort(array)
var list lessOrEqual, greater
if length(array) ≤ 1
return array
select a pivot value pivot
for each x in array
if x ≤ pivot then add x to lessOrEqual
if x > pivot then add x to greater
return concatenate(quicksort(lessOrEqual), quicksort(greater))
```

The "pivot" separates the dataset into two groups: those that are less than or equal to the value at the pivot and those that are greater than the pivot. An optimally selected pivot will result in partitions of equal length (or lengths differing by 1). The partitioning step may be thought of as a special sorting step using the attribute x ≤ pivot as the sort key, with possible values <true, false>. Quicksort's worst case time is O(n2),e.g., for a completely sorted set with the pivot chosen as the first or last element, but otherwise it is O(n * log n). Its average time is slightly faster than that of the merge sort in most cases, even though they are both O(n * log n) sorts.

Quicksort may be thought of as being situated at one end of the spectrum of divide-conquer algorithms, with Mergesort at the other end. In Quicksort, which some have called a conquer-divide algorithm, most of the work is done in the partitioning and recursive calls. The subsequent reassembly of the sorted segments involves trivial effort. In Mergesort, in contrast, the partitioning is done in a trivial way by splitting the input array in half. In Quicksort, every element in the first partition is less or equal to every element in the second partition. It is this property that makes the merge phase of Quicksort so trivial that it does not even need mentioning.

## 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>

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

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);
Sort_Days(Weekly_Sales);
Print(Weekly_Sales);

end Sort_Test;</lang>
```

## ALGOL 68

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

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

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

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

## APL

Works with: Dyalog APL
Translation of: J
```      qsort ← {1≥⍴⍵:⍵⋄e←⍵[?⍴⍵]⋄ (∇(⍵<e)/⍵) , ((⍵=e)/⍵) , ∇(⍵>e)/⍵}
qsort 1 3 5 7 9 8 6 4 2
1 2 3 4 5 6 7 8 9
```

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

## AutoHotkey

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

quicksort(list) {

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

} </lang>

## C

<lang c>void quick(int *left, int *right) {

``` if (right > left) {
int pivot = left[(right-left)/2];
int *r = right, *l = left;
do {
while (*l < pivot) l++;
while (*r > pivot) r--;
if (l <= r) {
int t = *l;
*l++ = *r;
*r-- = t;
}
} while (l <= r);
quick(left, r);
quick(l, right);
}
```

} void sort(int *array, int length) {

``` quick(array, array+length-1);
```

}</lang>

## C++

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

1. include <iterator>
2. include <algorithm> // for std::partition
3. 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>

1. include <iterator>
2. include <algorithm> // for std::partition
3. 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>

## Clojure

A very Haskell-like solution using list comprehensions and lazy evaluation.

```(defn qsort [L]
(if (nil? 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))))))
```

Another short version (using quasiquote):

```(defn qsort [[pvt & rs]]
(if pvt
`(~@(qsort (filter #(<  % pvt) rs))
~pvt
~@(qsort (filter #(>= % pvt) rs)))))
```

Another, more readable version (no macros):

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

## Common Lisp

The functional programming way

<lang lisp>(defun quicksort (list)

``` (if (<= (length list) 1)
list
(let ((pivot (first list)))
```

(append (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))))))</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>
```

## D

An implementation much similar to the C one is possible too, this is slower and simpler, derived from the Python one. This is a function template: <lang d>import std.stdio;

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

```   T[] less, more;
if (items.length <= 1)
return items;
else {
T pivot = items[0];
foreach(el; items[1 .. \$])
if (el < pivot)
less ~= el;
else
more ~= el;
return quickSort(less) ~ pivot ~ quickSort(more);
}
```

}

void main() {

```   auto a1 = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1];
writefln(quickSort(a1));
auto a2 = [4.0,65.0,2.0,-31.0,0.0,99.0,2.0,83.0,782.0,1.0];
writefln(quickSort(a2));
```

} </lang>

## E

<lang e>def quicksort := {

```   def swap(container, ixA, ixB) {
def temp := container[ixA]
container[ixA] := container[ixB]
container[ixB] := temp
}
```
```   def partition(array, var first :int, var last :int) {
if (last <= first) { return }

# Choose a pivot
def pivot := array[def pivotIndex := (first + last) // 2]

# Move pivot to end temporarily
swap(array, pivotIndex, last)

var swapWith := first

# Scan array except for pivot, and...
for i in first..!last {
if (array[i] <= pivot) {   # items ≤ the pivot
swap(array, i, swapWith) # are moved to consecutive positions on the left
swapWith += 1
}
}

# Swap pivot into between-partition position.
# Because of the swapping we know that everything before swapWith is less
# than or equal to the pivot, and the item at swapWith (since it was not
# swapped) is greater than the pivot, so inserting the pivot at swapWith
# will preserve the partition.
swap(array, swapWith, last)
return swapWith
}
```
```   def quicksortR(array, first :int, last :int) {
if (last <= first) { return }
def pivot := partition(array, first, last)
quicksortR(array, first, pivot - 1)
quicksortR(array, pivot + 1, last)
}
```
```   def quicksort(array) { # returned from block
quicksortR(array, 0, array.size() - 1)
}
```

}</lang>

## Erlang

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

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

## Forth

```defer lessthan ( a@ b@ -- ? )   ' < is lessthan

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

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

: partition ( l r -- l r r2 l2 )
2dup mid @ >r ( r: pivot )
2dup begin
swap begin dup @  r@ lessthan while cell+ repeat
swap begin r@ over @ lessthan while cell- repeat
2dup <= if 2dup exch >r cell+ r> cell- then
2dup > until  r> drop ;

: qsort ( l r -- )
partition  swap rot
\ 2over 2over - + < if 2swap then
2dup < if recurse else 2drop then
2dup < if recurse else 2drop then ;

: sort ( array len -- )
dup 2 < if 2drop exit then
1- cells over + qsort ;
```

## Fortran

Works with: Fortran version 90 and later

<lang fortran>MODULE Qsort_Module

IMPLICIT NONE

CONTAINS

RECURSIVE SUBROUTINE Qsort(a)

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

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

```

END SUBROUTINE Qsort

SUBROUTINE Partition(a, marker)

``` INTEGER, INTENT(IN OUT) :: a(:)
INTEGER, INTENT(OUT) :: marker
INTEGER :: left, right, pivot, temp

pivot = (a(1) + a(size(a))) / 2  ! Average of first and last elements to prevent quadratic
left = 0                         ! behavior with sorted or reverse sorted data
right = size(a) + 1

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

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

```

END SUBROUTINE Partition

END MODULE Qsort_Module

PROGRAM Quicksort

``` USE Qsort_Module

IMPLICIT NONE
INTEGER, PARAMETER :: n = 100
INTEGER :: array(n)
INTEGER :: i
REAL :: x
CALL RANDOM_SEED
DO i = 1, n
CALL RANDOM_NUMBER(x)
array(i) = INT(x * 10000)
END DO

WRITE (*, "(A)") "array is :-"
WRITE (*, "(10I5)") array
CALL Qsort(array)
WRITE (*,*)
WRITE (*, "(A)") "sorted array is :-"
WRITE (*,"(10I5)") array

```

END PROGRAM Quicksort</lang>

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.

```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
```

Example:

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

## 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. (quicksort y <sel e),(y =sel e),quicksort y >sel e=.y{~?#y end.
```

)</lang>

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

## Java

Works with: Java version 1.5+

Translation of: Python

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

```   if (arr.size() <= 1)
return arr;
E pivot = arr.getFirst(); //This pivot can change to get faster results
```
```   List<E> less = new LinkedList<E>();
```
```   // Partition
for (E i: arr) {
if (i.compareTo(pivot) < 0)
else if (i.compareTo(pivot) > 0)
else
}
```
```   // Recursively sort sublists
less = quickSort(less);
more = quickSort(more);
```
```   // Concatenate results
return less;
```

}</lang>

## JavaScript

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

``` function swap(i,j) { var t=a[i]; a[i]=a[j]; a[j]=t }
function qs(l,r) {
if (l<r) {
var pivot = a[(l+r)>>1];
var l2=l, r2=r;
do {
while (less(a[l2], pivot) ++l2;
while (less(pivot, a[r2]) --r2;
if (l2 <= r2) swap(l2++, r2--);
} while (l2 <= r2);
qs(l, r2);
qs(l2, r);
}
}
qs(0, a.length-1);
return a;
```

}</lang>

The functional programming way

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

```   if (this.length <= 1)
return this;
```
```   var pivot = this[Math.round(this.length / 2)];
```
```   return this.filter(function (x) { return x <  pivot }).quick_sort().concat(
this.filter(function (x) { return x == pivot })).concat(
this.filter(function (x) { return x >  pivot }).quick_sort());
```

}</lang>

## Joy

<lang joy> DEFINE qsort ==

```  [small]
[]
[uncons [>] split]
[swapd cons concat]
binrec .
```

</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>

## 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
```

## 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)
```

## MATLAB

<lang Matlab> 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 return

N=256*256; v=rand(N,1); tic,u=quicksort(v); toc issorted(u) </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
```

## Nial

```quicksort is fork [ >= [1 first,tally],
pass,
quicksort sublist [ < [pass, first], pass ],
sublist [ match [pass,first],pass ],
quicksort sublist [ > [pass,first], pass ]
]
]
```

Using it.

```|quicksort [5, 8, 7, 4, 3]
=3 4 5 7 8
```

## 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>

## Perl

<lang perl> sub quick_sort {

```  \$arr = shift;
local \$less = [];
local \$pivot_list = [];
local \$more = [];
if (\$#{\$arr} <= 0) {
return \$arr;
} else {
\$pivot = \$arr->[0];
foreach my \$i (@{\$arr}) {
if (\$i < \$pivot) {
push @{\$less}, \$i;
} elsif (\$i > \$pivot) {
push @{\$more}, \$i;
} else {
push @{\$pivot_list}, \$i;
}
}
\$less = quick_sort(\$less);
\$more = quick_sort(\$more);
return [@{\$less}, @{\$pivot_list}, @{\$more}];
}
}

print join(' ', @{quick_sort([4, 65, 2, -31, 0, 99, 83, 782, 1])}), "\n";</lang>
```

Output:

```-31 0 1 2 4 65 83 99 782
```

In a more functional style: <lang perl> sub quicksort { @_ <= 1 ? @_ : do { my \$pivot = pop; quicksort( grep {\$_ <= \$pivot} @_ ), \$pivot, quicksort( grep {\$_ > \$pivot} @_ ) } } </lang> Accepting a sort function: <lang perl> sub quicksort (&@) { my \$c = shift; @_ <= 1 ? @_ : do { local (\$a, \$b) = splice @_, rand @_, 1; my (@low, @high); for \$b (@_) { \$c->() <= 0 ? \$high[@high] : \$low[@low] = \$b } quicksort( \$c => @low ), \$a, quicksort( \$c => @high ) } }

print join ', ' => quicksort { \$a <=> \$b } 3, 5, 7, 1, -6, 12, 2; </lang>

## PL/I

<lang PL/I>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;
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>

## Prolog

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

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

% combine( H, L, R, S ) % True if S is L ++ [H] ++ R (in Haskell notation) combine( H, L, R, S ) :- append(L, [H|R], S).</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>

## 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>

## Ruby

<lang ruby>class Array

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

end</lang>

## Scheme

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

``` (let loop ((low (list)) (high (list)) (l l))
(if (null? l)
(cons low high)
(if (p (car l))
(loop low (cons (car l) high) (cdr l))
(loop (cons (car l) low) high (cdr l))))))

```

(define (quicksort l gt?)

``` (let q ((l l))
(if (null? l)
l
(let ((s (split-by (cdr l) (lambda (x) (gt? x (car l))))))
(append (q (car s)) (list (car l)) (q (cdr s)))))))
(quicksort (list 1 3 5 7 9 8 6 4 2) >)</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;
```

Original source: [2]

## SETL

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

proc qsort(rw a);

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

end proc;

proc swap(rw x, rw y);

``` [y,x] := [x,y];
```

end proc;</lang>

Copying sort using comprehensions:

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

proc qsort(a);

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

end proc;</lang>

## Standard ML

<lang ocaml>fun quicksort [] = []

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

## Tcl

<lang tcl>package require Tcl 8.5

proc quicksort {m} {

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

}

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

## UnixPipes

Works with: Zsh
```split() {
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
```

## 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>

1. import nat

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

1. cast %nL

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

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

## V

```[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].
```

The way of joy (using binrec)

```[qsort
[small?] []
[uncons [>] split]
[[p [*l] [*g] : [*l p *g]] view]
binrec].
```