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{{task|Sorting Algorithms}} {{Sorting Algorithm}} [[Category:Recursion]] {{Wikipedia|Quicksort}}
;Task: Sort an array (or list) elements using the [https://en.wikipedia.org/wiki/Quicksort ''quicksort''] algorithm.
The elements must have a [https://en.wikipedia.org/wiki/Weak_ordering 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 run-time of Quicksort ranges from ''[[O]](n ''log'' n)'' with the best pivots, to ''[O]'' 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|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
{{trans|REXX}} Structured version with ASM & ASSIST macros.
* Quicksort 14/09/2015 & 23/06/2016
QUICKSOR CSECT
USING QUICKSOR,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) prolog
ST R13,4(R15) "
ST R15,8(R13) "
LR R13,R15 "
MVC A,=A(1) a(1)=1
MVC B,=A(NN) b(1)=hbound(t)
L R6,=F'1' k=1
DO WHILE=(LTR,R6,NZ,R6) do while k<>0
### ============
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 ITERATE 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,LT,R3 if t(x)<t(l) ---+
IF CR,R5,LT,R4 if t(y)<t(x) |
LR R7,R4 p=t(x) |
L R1,X x |
SLA R1,2 ~ |
ST R3,T-4(R1) t(x)=t(l) |
ELSEIF CR,R5,GT,R3 elseif t(y)>t(l) |
LR R7,R3 p=t(l) |
ELSE , else |
LR R7,R5 p=t(y) |
L R1,Y y |
SLA R1,2 ~ |
ST R3,T-4(R1) t(y)=t(l) |
ENDIF , end if |
ELSE , else |
IF CR,R5,LT,R3 if t(y)<t(l) |
LR R7,R3 p=t(l) |
ELSEIF CR,R5,GT,R4 elseif t(y)>t(x) |
LR R7,R4 p=t(x) |
L R1,X x |
SLA R1,2 ~ |
ST R3,T-4(R1) t(x)=t(l) |
ELSE , else |
LR R7,R5 p=t(y) |
L R1,Y y |
SLA R1,2 ~ |
ST R3,T-4(R1) t(y)=t(l) |
ENDIF , end if |
ENDIF , end if ---+
LA R8,1(R10) i=l+1
L R9,X j=x
FOREVER EQU * do forever --------------------+
LR R1,R8 i |
SLA R1,2 ~ |
LA R2,T-4(R1) @t(i) |
L R0,0(R2) t(i) |
DO WHILE=(CR,R8,LE,R9,AND, while i<=j and ---+ | X
CR,R0,LE,R7) t(i)<=p | |
AH R8,=H'1' i=i+1 | |
AH R2,=H'4' @t(i) | |
L R0,0(R2) t(i) | |
ENDDO , end while ---+ |
LR R1,R9 j |
SLA R1,2 ~ |
LA R2,T-4(R1) @t(j) |
L R0,0(R2) t(j) |
DO WHILE=(CR,R8,LT,R9,AND, while i<j and ---+ | X
CR,R0,GE,R7) t(j)>=p | |
SH R9,=H'1' j=j-1 | |
SH R2,=H'4' @t(j) | |
L R0,0(R2) t(j) | |
ENDDO , end while ---+ |
CR R8,R9 if i>=j |
BNL LEAVE 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 end do forever ----------------+
LEAVE EQU *
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)
IF C,R8,LE,Y if i<=y ----+
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 |
ELSE , else |
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 |
ENDIF , end if ----+
ITERATE EQU *
ENDDO , end while
### ===============
* *** ********* print sorted table
LA R3,PG ibuffer
LA R4,T @t(i)
DO WHILE=(C,R4,LE,=A(TEND)) do i=1 to hbound(t)
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
ENDDO , end do
XPRNT PG,80 print buffer
L R13,4(0,R13) epilog
LM R14,R12,12(R13) "
XR R15,R15 "
BR R14 exit
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'
TEND DS 0F
NN EQU (TEND-T)/4)
A DS (NN)F same size as T
B DS (NN)F same size as T
X DS F
Y DS F
PG DS CL80
XD DS CL12
YREGS
END QUICKSOR
{{out}}
1 1 2 6 7 8 8 9 9 9 10 15 16 16 16 17 18 18 19 20
ABAP
This works for ABAP Version 7.40 and above
report z_quicksort.
data(numbers) = value int4_table( ( 4 ) ( 65 ) ( 2 ) ( -31 ) ( 0 ) ( 99 ) ( 2 ) ( 83 ) ( 782 ) ( 1 ) ).
perform quicksort changing numbers.
write `[`.
loop at numbers assigning field-symbol(<numbers>).
write <numbers>.
endloop.
write `]`.
form quicksort changing numbers type int4_table.
data(less) = value int4_table( ).
data(equal) = value int4_table( ).
data(greater) = value int4_table( ).
if lines( numbers ) > 1.
data(pivot) = numbers[ lines( numbers ) / 2 ].
loop at numbers assigning field-symbol(<number>).
if <number> < pivot.
append <number> to less.
elseif <number> = pivot.
append <number> to equal.
elseif <number> > pivot.
append <number> to greater.
endif.
endloop.
perform quicksort changing less.
perform quicksort changing greater.
clear numbers.
append lines of less to numbers.
append lines of equal to numbers.
append lines of greater to numbers.
endif.
endform.
{{out}}
[ 31- 0 1 2 2 4 65 83 99 782 ]
ACL2
(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)))))
Usage:
## ActionScript
{{works with|ActionScript|3}}
The functional programming way
```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; })));
}
The faster way
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));
}
Ada
This example is implemented as a generic procedure.
The procedure specification is:
-----------------------------------------------------------------------
-- Generic Quick_Sort procedure
-----------------------------------------------------------------------
generic
type Element is private;
type Index is (<>);
type Element_Array is array(Index range <>) of Element;
with function "<" (Left, Right : Element) return Boolean is <>;
procedure Quick_Sort(A : in out Element_Array);
The procedure body deals with any discrete index type, either an integer type or an enumerated type.
-----------------------------------------------------------------------
-- Generic Quick_Sort procedure
-----------------------------------------------------------------------
procedure Quick_Sort (A : in out Element_Array) is
procedure Swap(Left, Right : Index) is
Temp : Element := A (Left);
begin
A (Left) := A (Right);
A (Right) := Temp;
end Swap;
begin
if A'Length > 1 then
declare
Pivot_Value : Element := A (A'First);
Right : Index := A'Last;
Left : Index := A'First;
begin
loop
while Left < Right and not (Pivot_Value < A (Left)) loop
Left := Index'Succ (Left);
end loop;
while Pivot_Value < A (Right) loop
Right := Index'Pred (Right);
end loop;
exit when Right <= Left;
Swap (Left, Right);
Left := Index'Succ (Left);
Right := Index'Pred (Right);
end loop;
if Right = A'Last then
Right := Index'Pred (Right);
Swap (A'First, A'Last);
end if;
if Left = A'First then
Left := Index'Succ (Left);
end if;
Quick_Sort (A (A'First .. Right));
Quick_Sort (A (Left .. A'Last));
end;
end if;
end Quick_Sort;
An example of how this procedure may be used is:
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 Quick_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;
ALGOL 68
#--- 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))
)
{{out}}
Before: +73 +921 +179 +961 +50 +324 +82 +178 +243 +458
After: +50 +73 +82 +178 +179 +243 +324 +458 +921 +961
ALGOL W
% Quicksorts in-place the array of integers v, from lb to ub %
procedure quicksort ( integer array v( * )
; integer value lb, ub
) ;
if ub > lb then begin
% more than one element, so must sort %
integer left, right, pivot;
left := lb;
right := ub;
% choosing the middle element of the array as the pivot %
pivot := v( left + ( ( right + 1 ) - left ) div 2 );
while begin
while left <= ub and v( left ) < pivot do left := left + 1;
while right >= lb and v( right ) > pivot do right := right - 1;
left <= right
end do begin
integer swap;
swap := v( left );
v( left ) := v( right );
v( right ) := swap;
left := left + 1;
right := right - 1
end while_left_le_right ;
quicksort( v, lb, right );
quicksort( v, left, ub )
end quicksort ;
== {{header|APL}} == {{works with|Dyalog APL}}{{trans|J}}
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
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, since OS X Yosemite, to Foundation classes through the ObjC interface).
{{trans|JavaScript}} (Functional ES5 version)
-- quickSort :: (Ord a) => [a] -> [a]
on quickSort(xs)
if length of xs > 1 then
set {h, t} to uncons(xs)
-- lessOrEqual :: a -> Bool
script lessOrEqual
on |λ|(x)
x ≤ h
end |λ|
end script
set {less, more} to partition(lessOrEqual, t)
quickSort(less) & h & quickSort(more)
else
xs
end if
end quickSort
-- TEST -----------------------------------------------------------------------
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 ----------------------------------------------------------
-- partition :: predicate -> List -> (Matches, nonMatches)
-- partition :: (a -> Bool) -> [a] -> ([a], [a])
on partition(f, xs)
tell mReturn(f)
set lst to {{}, {}}
repeat with x in xs
set v to contents of x
set end of item ((|λ|(v) as integer) + 1) of lst to v
end repeat
return {item 2 of lst, item 1 of lst}
end tell
end partition
-- uncons :: [a] -> Maybe (a, [a])
on uncons(xs)
if length of xs > 0 then
{item 1 of xs, rest of xs}
else
missing value
end if
end uncons
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
{{Out}}
{5.7, 8.5, 11.8, 14.1, 16.7, 21.3}
ARM Assembly
{{works with|as|Raspberry Pi}}
/* ARM assembly Raspberry PI */
/* program quickSort.s */
/* look pseudo code in wikipedia quicksort */
/************************************/
/* Constantes */
/************************************/
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessSortOk: .asciz "Table sorted.\n"
szMessSortNok: .asciz "Table not sorted !!!!!.\n"
sMessResult: .ascii "Value : "
sMessValeur: .fill 11, 1, ' ' @ size => 11
szCarriageReturn: .asciz "\n"
.align 4
iGraine: .int 123456
.equ NBELEMENTS, 10
#TableNumber: .int 9,5,6,1,2,3,10,8,4,7
#TableNumber: .int 1,3,5,2,4,6,10,8,4,7
#TableNumber: .int 1,3,5,2,4,6,10,8,4,7
#TableNumber: .int 1,2,3,4,5,6,10,8,4,7
TableNumber: .int 10,9,8,7,6,5,4,3,2,1
#TableNumber: .int 13,12,11,10,9,8,7,6,5,4,3,2,1
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
1:
ldr r0,iAdrTableNumber @ address number table
mov r1,#0 @ indice first item
mov r2,#NBELEMENTS @ number of élements
bl triRapide @ call quicksort
ldr r0,iAdrTableNumber @ address number table
bl displayTable
ldr r0,iAdrTableNumber @ address number table
mov r1,#NBELEMENTS @ number of élements
bl isSorted @ control sort
cmp r0,#1 @ sorted ?
beq 2f
ldr r0,iAdrszMessSortNok @ no !! error sort
bl affichageMess
b 100f
2: @ yes
ldr r0,iAdrszMessSortOk
bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrsMessValeur: .int sMessValeur
iAdrszCarriageReturn: .int szCarriageReturn
iAdrsMessResult: .int sMessResult
iAdrTableNumber: .int TableNumber
iAdrszMessSortOk: .int szMessSortOk
iAdrszMessSortNok: .int szMessSortNok
/******************************************************************/
/* control sorted table */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements > 0 */
/* r0 return 0 if not sorted 1 if sorted */
isSorted:
push {r2-r4,lr} @ save registers
mov r2,#0
ldr r4,[r0,r2,lsl #2]
1:
add r2,#1
cmp r2,r1
movge r0,#1
bge 100f
ldr r3,[r0,r2, lsl #2]
cmp r3,r4
movlt r0,#0
blt 100f
mov r4,r3
b 1b
100:
pop {r2-r4,lr}
bx lr @ return
/***************************************************/
/* Appel récursif Tri Rapide quicksort */
/***************************************************/
/* r0 contains the address of table */
/* r1 contains index of first item */
/* r2 contains the number of elements > 0 */
triRapide:
push {r2-r5,lr} @ save registers
sub r2,#1 @ last item index
cmp r1,r2 @ first > last ?
bge 100f @ yes -> end
mov r4,r0 @ save r0
mov r5,r2 @ save r2
bl partition1 @ cutting into 2 parts
mov r2,r0 @ index partition
mov r0,r4 @ table address
bl triRapide @ sort lower part
add r1,r2,#1 @ index begin = index partition + 1
add r2,r5,#1 @ number of elements
bl triRapide @ sort higter part
100: @ end function
pop {r2-r5,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* Partition table elements */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains index of first item */
/* r2 contains index of last item */
partition1:
push {r1-r7,lr} @ save registers
ldr r3,[r0,r2,lsl #2] @ load value last index
mov r4,r1 @ init with first index
mov r5,r1 @ init with first index
1: @ begin loop
ldr r6,[r0,r5,lsl #2] @ load value
cmp r6,r3 @ compare value
ldrlt r7,[r0,r4,lsl #2] @ if < swap value table
strlt r6,[r0,r4,lsl #2]
strlt r7,[r0,r5,lsl #2]
addlt r4,#1 @ and increment index 1
add r5,#1 @ increment index 2
cmp r5,r2 @ end ?
blt 1b @ no loop
ldr r7,[r0,r4,lsl #2] @ swap value
str r3,[r0,r4,lsl #2]
str r7,[r0,r2,lsl #2]
mov r0,r4 @ return index partition
100:
pop {r1-r7,lr}
bx lr
/******************************************************************/
/* Display table elements */
/******************************************************************/
/* r0 contains the address of table */
displayTable:
push {r0-r3,lr} @ save registers
mov r2,r0 @ table address
mov r3,#0
1: @ loop display table
ldr r0,[r2,r3,lsl #2]
ldr r1,iAdrsMessValeur @ display value
bl conversion10 @ call function
ldr r0,iAdrsMessResult
bl affichageMess @ display message
add r3,#1
cmp r3,#NBELEMENTS - 1
ble 1b
ldr r0,iAdrszCarriageReturn
bl affichageMess
100:
pop {r0-r3,lr}
bx lr
/******************************************************************/
/* display text with size calculation */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {r0,r1,r2,r7,lr} @ save registres
mov r2,#0 @ counter length
1: @ loop length calculation
ldrb r1,[r0,r2] @ read octet start position + index
cmp r1,#0 @ if 0 its over
addne r2,r2,#1 @ else add 1 in the length
bne 1b @ and loop
@ so here r2 contains the length of the message
mov r1,r0 @ address message in r1
mov r0,#STDOUT @ code to write to the standard output Linux
mov r7, #WRITE @ code call system "write"
svc #0 @ call systeme
pop {r0,r1,r2,r7,lr} @ restaur des 2 registres */
bx lr @ return
/******************************************************************/
/* Converting a register to a decimal unsigned */
/******************************************************************/
/* r0 contains value and r1 address area */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes */
.equ LGZONECAL, 10
conversion10:
push {r1-r4,lr} @ save registers
mov r3,r1
mov r2,#LGZONECAL
1: @ start loop
bl divisionpar10U @ unsigned r0 <- dividende. quotient ->r0 reste -> r1
add r1,#48 @ digit
strb r1,[r3,r2] @ store digit on area
cmp r0,#0 @ stop if quotient = 0
subne r2,#1 @ else previous position
bne 1b @ and loop
@ and move digit from left of area
mov r4,#0
2:
ldrb r1,[r3,r2]
strb r1,[r3,r4]
add r2,#1
add r4,#1
cmp r2,#LGZONECAL
ble 2b
@ and move spaces in end on area
mov r0,r4 @ result length
mov r1,#' ' @ space
3:
strb r1,[r3,r4] @ store space in area
add r4,#1 @ next position
cmp r4,#LGZONECAL
ble 3b @ loop if r4 <= area size
100:
pop {r1-r4,lr} @ restaur registres
bx lr @return
/***************************************************/
/* division par 10 unsigned */
/***************************************************/
/* r0 dividende */
/* r0 quotient */
/* r1 remainder */
divisionpar10U:
push {r2,r3,r4, lr}
mov r4,r0 @ save value
//mov r3,#0xCCCD @ r3 <- magic_number lower raspberry 3
//movt r3,#0xCCCC @ r3 <- magic_number higter raspberry 3
ldr r3,iMagicNumber @ r3 <- magic_number raspberry 1 2
umull r1, r2, r3, r0 @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0)
mov r0, r2, LSR #3 @ r2 <- r2 >> shift 3
add r2,r0,r0, lsl #2 @ r2 <- r0 * 5
sub r1,r4,r2, lsl #1 @ r1 <- r4 - (r2 * 2) = r4 - (r0 * 10)
pop {r2,r3,r4,lr}
bx lr @ leave function
iMagicNumber: .int 0xCCCCCCCD
Arturo
quickSort [items]{
if $(size items) < 2 { items } {
$(quickSort|filter $(slice items 1) { & < items.0 }) + items.0 + $(quickSort|filter $(slice items 1) { & >= items.0 })
}
}
print $(quickSort #(3 1 2 8 5 7 9 4 6))
{{out}}
#(1 2 3 4 5 6 7 8 9)
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);
}
}
AutoHotkey
Translated from the python example:
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
}
Old implementation for AutoHotkey 1.0:
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
}
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.
DECLARE SUB quicksort (arr() AS INTEGER, leftN AS INTEGER, rightN AS INTEGER)
DIM q(99) AS INTEGER
DIM n AS INTEGER
RANDOMIZE TIMER
FOR n = 0 TO 99
q(n) = INT(RND * 9999)
NEXT
OPEN "output.txt" FOR OUTPUT AS 1
FOR n = 0 TO 99
PRINT #1, q(n),
NEXT
PRINT #1,
quicksort q(), 0, 99
FOR n = 0 TO 99
PRINT #1, q(n),
NEXT
CLOSE
SUB quicksort (arr() AS INTEGER, leftN AS INTEGER, rightN AS INTEGER)
DIM pivot AS INTEGER, leftNIdx AS INTEGER, rightNIdx AS INTEGER
leftNIdx = leftN
rightNIdx = rightN
IF (rightN - leftN) > 0 THEN
pivot = (leftN + rightN) / 2
WHILE (leftNIdx <= pivot) AND (rightNIdx >= pivot)
WHILE (arr(leftNIdx) < arr(pivot)) AND (leftNIdx <= pivot)
leftNIdx = leftNIdx + 1
WEND
WHILE (arr(rightNIdx) > arr(pivot)) AND (rightNIdx >= pivot)
rightNIdx = rightNIdx - 1
WEND
SWAP arr(leftNIdx), arr(rightNIdx)
leftNIdx = leftNIdx + 1
rightNIdx = rightNIdx - 1
IF (leftNIdx - 1) = pivot THEN
rightNIdx = rightNIdx + 1
pivot = rightNIdx
ELSEIF (rightNIdx + 1) = pivot THEN
leftNIdx = leftNIdx - 1
pivot = leftNIdx
END IF
WEND
quicksort arr(), leftN, pivot - 1
quicksort arr(), pivot + 1, rightN
END IF
END SUB
=
BBC BASIC
=
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
{{out}}
-31 0 1 2 2 4 65 83 99 782
==={{header|IS-BASIC}}===
## BCPL
```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 -> 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()
}
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.
( ( 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)
);
{{out}}
90
1900
4001/2
Quicksort
are
features
languages
of
of
optimized
variants
(quick,sober)
(quick,sort)
C
#include <stdio.h>
void quicksort(int *A, int len);
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 ", a[i]);
}
printf("\n");
quicksort(a, n);
for (i = 0; i < n; i++) {
printf("%d ", a[i]);
}
printf("\n");
return 0;
}
void quicksort(int *A, int len) {
if (len < 2) return;
int pivot = A[len / 2];
int i, j;
for (i = 0, j = len - 1; ; i++, j--) {
while (A[i] < pivot) i++;
while (A[j] > pivot) j--;
if (i >= j) break;
int temp = A[i];
A[i] = A[j];
A[j] = temp;
}
quicksort(A, i);
quicksort(A + i, len - i);
}
{{out}}
4 65 2 -31 0 99 2 83 782 1
-31 0 1 2 2 4 65 83 99 782
Randomized sort with separated components.
#include <stdlib.h> // REQ: rand()
void swap(int *a, int *b) {
int c = *a;
*a = *b;
*b = c;
}
int partition(int A[], int p, int q) {
swap(&A[p + (rand() % (q - p + 1))], &A[q]); // PIVOT = A[q]
int i = p - 1;
for(int j = p; j <= q; j++) {
if(A[j] <= A[q]) {
swap(&A[++i], &A[j]);
}
}
return i;
}
void quicksort(int A[], int p, int q) {
if(p < q) {
int pivotIndx = partition(A, p, q);
quicksort(A, p, pivotIndx - 1);
quicksort(A, pivotIndx + 1, q);
}
}
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).
#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>());
}
A simpler version of the above that just uses the first element as the pivot and only does one "partition".
#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>());
}
C#
Note that Array.Sort and ArrayList.Sort both use an unstable implementation of the quicksort algorithm.
//
// The Tripartite conditional enables Bentley-McIlroy 3-way Partitioning.
// This performs additional compares to isolate islands of keys equal to
// the pivot value. Use unless key-equivalent classes are of small size.
//
#define Tripartite
namespace Sort {
using System;
using System.Diagnostics;
class QuickSort<T> where T : IComparable {
#region Constants
private const Int32 INSERTION_LIMIT_DEFAULT = 12;
#endregion
#region Properties
public Int32 InsertionLimit { get; set; }
private Random Random { get; set; }
private T Median { get; set; }
private Int32 Left { get; set; }
private Int32 Right { get; set; }
private Int32 LeftMedian { get; set; }
private Int32 RightMedian { get; set; }
#endregion
#region Constructors
public QuickSort(Int32 insertionLimit, Random random) {
this.InsertionLimit = insertionLimit;
this.Random = random;
}
public QuickSort(Int32 insertionLimit)
: this(insertionLimit, new Random()) {
}
public QuickSort()
: this(INSERTION_LIMIT_DEFAULT) {
}
#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;
while (length > 1) {
if (length < InsertionLimit) {
InsertionSort<T>.Sort(entries, first, last);
return;
}
Left = first;
Right = last;
pivot(entries);
partition(entries);
//[Note]Right < Left
var leftLength = Right + 1 - first;
var rightLength = last + 1 - Left;
//
// First recurse over shorter partition, then loop
// on the longer partition to elide tail recursion.
//
if (leftLength < rightLength) {
Sort(entries, first, Right);
first = Left;
length = rightLength;
}
else {
Sort(entries, Left, last);
last = Right;
length = leftLength;
}
}
}
private void pivot(T[] entries) {
//
// An odd sample size is chosen based on the log of the interval size.
// The median of a randomly chosen set of samples is then returned as
// an estimate of the true median.
//
var length = Right + 1 - Left;
var logLen = (Int32)Math.Log10(length);
var pivotSamples = 2 * logLen + 1;
var sampleSize = Math.Min(pivotSamples, length);
var last = Left + sampleSize - 1;
// Sample without replacement
for (var first = Left; first <= last; first++) {
// Random sampling avoids pathological cases
var random = Random.Next(first, Right + 1);
Swap(entries, first, random);
}
InsertionSort<T>.Sort(entries, Left, last);
Median = entries[Left + sampleSize / 2];
}
private void partition(T[] entries) {
var first = Left;
var last = Right;
#if Tripartite
LeftMedian = first;
RightMedian = last;
#endif
while (true) {
//[Assert]There exists some index >= Left where entries[index] >= Median
//[Assert]There exists some index <= Right where entries[index] <= Median
// So, there is no need for Left or Right bound checks
while (Median.CompareTo(entries[Left]) > 0) Left++;
while (Median.CompareTo(entries[Right]) < 0) Right--;
//[Assert]entries[Right] <= Median <= entries[Left]
if (Right <= Left) break;
Swap(entries, Left, Right);
swapOut(entries);
Left++;
Right--;
//[Assert]entries[first:Left - 1] <= Median <= entries[Right + 1:last]
}
if (Left == Right) {
Left++;
Right--;
}
//[Assert]Right < Left
swapIn(entries, first, last);
//[Assert]entries[first:Right] <= Median <= entries[Left:last]
//[Assert]entries[Right + 1:Left - 1] == Median when non-empty
}
#endregion
#region Swap Methods
[Conditional("Tripartite")]
private void swapOut(T[] entries) {
if (Median.CompareTo(entries[Left]) == 0) Swap(entries, LeftMedian++, Left);
if (Median.CompareTo(entries[Right]) == 0) Swap(entries, Right, RightMedian--);
}
[Conditional("Tripartite")]
private void swapIn(T[] entries, Int32 first, Int32 last) {
// Restore Median entries
while (first < LeftMedian) Swap(entries, first++, Right--);
while (RightMedian < last) Swap(entries, Left++, last--);
}
public static void Swap(T[] entries, Int32 index1, Int32 index2) {
if (index1 != 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 index = first + 1; index <= last; index++)
insert(entries, first, index);
}
private static void insert(T[] entries, Int32 first, Int32 index) {
var entry = entries[index];
while (index > first && entries[index - 1].CompareTo(entry) > 0)
entries[index] = entries[--index];
entries[index] = entry;
}
}
#endregion
}
'''Example''':
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));
}
}
{{out}}
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
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;
}
}
}
Clojure
A very Haskell-like solution using list comprehensions and lazy evaluation.
(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))))))
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))))))
A 3-group quicksort (fast when many values are equal):
(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)))))
A lazier version of above (unlike group-by, filter returns (and reads) a lazy sequence)
(defn qsort3 [[pivot :as coll]]
(when pivot
(lazy-cat (qsort (filter #(< % pivot) coll))
(filter #{pivot} coll)
(qsort (filter #(> % pivot) coll)))))
COBOL
{{works with|Visual 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
.
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)
Common Lisp
The functional programming way
(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))
With flet
(defun qs (list)
(if (cdr list)
(flet ((pivot (test)
(remove (car list) list :test-not test)))
(nconc (qs (pivot #'>)) (pivot #'=) (qs (pivot #'<))))
list))
In-place non-functional
(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))
Functional with destructuring
(defun quicksort (list)
(when list
(destructuring-bind (x . xs) list
(nconc (quicksort (remove-if (lambda (a) (> a x)) xs))
`(,x)
(quicksort (remove-if (lambda (a) (<= a x)) xs))))))
Crystal
{{trans|Ruby}}
def quick_sort(a : Array(Int32)) : Array(Int32)
return a if a.size <= 1
p = a[0]
lt, rt = a[1 .. -1].partition { |x| x < p }
return quick_sort(lt) + [p] + quick_sort(rt)
end
a = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
puts quick_sort(a) # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Curry
Copied from [http://www.informatik.uni-kiel.de/~curry/examples/ Curry: Example Programs].
-- 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]
D
A functional version:
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;
}
{{out}}
[-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]
A simple high-level version (same output):
import std.stdio, std.array;
T[] quickSort(T)(T[] items) pure nothrow {
if (items.empty)
return items;
T[] less, notLess;
foreach (x; items[1 .. $])
(x < items[0] ? less : notLess) ~= x;
return less.quickSort ~ items[0] ~ notLess.quickSort;
}
void main() {
[4, 65, 2, -31, 0, 99, 2, 83, 782, 1].quickSort.writeln;
}
Often short functional sieves are not a true implementations of the Sieve of Eratosthenes: http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf
Similarly, one could argue that a true QuickSort is in-place, as this more efficient version (same output):
import std.stdio, std.algorithm;
void quickSort(T)(T[] items) pure nothrow @safe @nogc {
if (items.length >= 2) {
auto parts = partition3(items, items[$ / 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;
}
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"));
}
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)
}
}
EasyLang
func qsort left right . . while left < right swap data[(left + right) / 2] data[left] mid = left for i = left + 1 to right if data[i] < data[left] mid += 1 swap data[i] data[mid] . . swap data[left] data[mid] call qsort left mid - 1 left = mid + 1 . .
call qsort 0 len data[] - 1 print data[]
## EchoLisp
```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)))))
{{out}}
(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
Eero
Translated from Objective-C example on this page.
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
Alternative implementation (not necessarily as efficient, but very readable)
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
{{out}}
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
class:
```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
A test application:
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
Elena
ELENA 4.1 :
import extensions;
import system'routines;
import system'collections;
extension op
{
quickSort()
{
if (self.isEmpty()) { ^ self };
var pivot := self[0];
auto less := new ArrayList();
auto pivotList := new ArrayList();
auto more := new ArrayList();
self.forEach:(item)
{
if (item < pivot)
{
less.append(item)
}
else if (item > pivot)
{
more.append(item)
}
else
{
pivotList.append(item)
}
};
less := less.quickSort();
more := more.quickSort();
less.appendRange(pivotList);
less.appendRange(more);
^ less
}
}
public program()
{
var list := new int[]::(3, 14, 1, 5, 9, 2, 6, 3);
console.printLine("before:", list.asEnumerable());
console.printLine("after :", list.quickSort().asEnumerable());
}
{{out}}
before:3,14,1,5,9,2,6,3
after :1,2,3,3,5,6,9,14
Elixir
defmodule Sort do
def qsort([]), do: []
def qsort([h | t]) do
{lesser, greater} = Enum.split_with(t, &(&1 < h))
qsort(lesser) ++ [h] ++ qsort(greater)
end
end
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]]
-module( quicksort ).
-export( [qsort/1] ).
qsort([]) -> [];
qsort([X|Xs]) ->
qsort([ Y || Y <- Xs, Y < X]) ++ [X] ++ qsort([ Y || Y <- Xs, Y >= X]).
multi-process implementation (number processes = number of processor cores):
quick_sort(L) -> qs(L, trunc(math:log2(erlang:system_info(schedulers)))).
qs([],_) -> [];
qs([H|T], N) when N > 0 ->
{Parent, Ref} = {self(), make_ref()},
spawn(fun()-> Parent ! {l1, Ref, qs([E||E<-T, E<H], N-1)} end),
spawn(fun()-> Parent ! {l2, Ref, qs([E||E<-T, H =< E], N-1)} end),
{L1, L2} = receive_results(Ref, undefined, undefined),
L1 ++ [H] ++ L2;
qs([H|T],_) ->
qs([E||E<-T, E<H],0) ++ [H] ++ qs([E||E<-T, H =< E],0).
receive_results(Ref, L1, L2) ->
receive
{l1, Ref, L1R} when L2 == undefined -> receive_results(Ref, L1R, L2);
{l2, Ref, L2R} when L1 == undefined -> receive_results(Ref, L1, L2R);
{l1, Ref, L1R} -> {L1R, L2};
{l2, Ref, L2R} -> {L1, L2R}
after 5000 -> receive_results(Ref, L1, L2)
end.
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
=={{header|F Sharp|F#}}==
let rec qsort = function
hd :: tl ->
let less, greater = List.partition ((>=) hd) tl
List.concat [qsort less; [hd]; qsort greater]
| _ -> []
Factor
: qsort ( seq -- seq )
dup empty? [
unclip [ [ < ] curry partition [ qsort ] bi@ ] keep
prefix append
] unless ;
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
)
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 ;
Fortran
{{Works with|Fortran|90 and later}}
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
{{out}}
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 [http://balfortran.org balfortran.org]
FreeBASIC
' version 23-10-2016
' compile with: fbc -s console
' sort from lower bound to the highter bound
' array's can have subscript range from -2147483648 to +2147483647
Sub quicksort(qs() As Long, l As Long, r As Long)
Dim As ULong size = r - l +1
If size < 2 Then Exit Sub
Dim As Long i = l, j = r
Dim As Long pivot = qs(l + size \ 2)
Do
While qs(i) < pivot
i += 1
Wend
While pivot < qs(j)
j -= 1
Wend
If i <= j Then
Swap qs(i), qs(j)
i += 1
j -= 1
End If
Loop Until i > j
If l < j Then quicksort(qs(), l, j)
If i < r Then quicksort(qs(), i, r)
End Sub
' ------=< MAIN >=------
Dim As Long i, array(-7 To 7)
Dim As Long a = LBound(array), b = UBound(array)
Randomize Timer
For i = a To b : array(i) = i : Next
For i = a To b ' little shuffle
Swap array(i), array(Int(Rnd * (b - a +1)) + a)
Next
Print "unsorted ";
For i = a To b : Print Using "####"; array(i); : Next : Print
quicksort(array(), LBound(array), UBound(array))
Print " sorted ";
For i = a To b : Print Using "####"; array(i); : Next : Print
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
{{out}}
unsorted -5 -6 -1 0 2 -4 -7 6 -2 -3 4 7 5 1 3
sorted -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
FunL
def
qsort( [] ) = []
qsort( p:xs ) = qsort( xs.filter((< p)) ) + [p] + qsort( xs.filter((>= p)) )
Here is a more efficient version using the partition function.
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"]) )
{{out}}
[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 [http://comjnl.oxfordjournals.org/cgi/content/short/5/1/10 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 [http://golang.org/pkg/sort/#Interface 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.
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)
}
{{out}}
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.
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)
}
{{out}}
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:
qsort [] = []
qsort (x:xs) = qsort [y | y <- xs, y < x] ++ [x] ++ qsort [y | y <- xs, y >= x]
A more efficient version, doing only one comparison per element:
import Data.List (partition)
qsort :: Ord a => [a] -> [a]
qsort [] = []
qsort (x:xs) = qsort ys ++ x : qsort zs
where
(ys, zs) = partition (< x) xs
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
=={{header|Icon}} and {{header|Unicon}}==
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
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 [[Sorting_algorithms/Bubble_sort#Icon| 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.
{{out}} 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
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)
Another more low-level Quicksort implementation can be found in Io's [[http://github.com/stevedekorte/io/blob/master/samples/misc/qsort.io github ]] repository.
J
{{eff note|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.
)
See the [[j:Essays/Quicksort|Quicksort essay]] in the J Wiki for additional explanations and examples.
Java
Imperative
{{works with|Java|1.5+}}
{{trans|Python}}
quickSort(List<E> arr) {
if (arr.isEmpty())
return arr;
else {
E pivot = arr.get(0);
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;
}
}
Functional
{{works with|Java|1.8}}
sort(List<E> col) {
if (col == null || col.isEmpty())
return Collections.emptyList();
else {
E pivot = col.get(0);
Map<Integer, List<E>> grouped = col.stream()
.collect(Collectors.groupingBy(pivot::compareTo));
return Stream.of(sort(grouped.get(1)), grouped.get(0), sort(grouped.get(-1)))
.flatMap(Collection::stream).collect(Collectors.toList());
}
}
JavaScript
Imperative
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 - left) / 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;
}
Example:
var test_array = [10, 3, 11, 15, 19, 1];
var sorted_array = sort(test_array, function(a,b) { return a<b; });
{{Out}}
[ 1, 3, 10, 11, 15, 19 ]
Functional
=ES5=
Emphasising clarity more than run-time optimisation (for which Array.sort() would be a better option)
(function () {
'use strict';
// quickSort :: (Ord a) => [a] -> [a]
function quickSort(xs) {
if (xs.length) {
var h = xs[0],
t = xs.slice(1),
lessMore = partition(function (x) {
return x <= h;
}, t),
less = lessMore[0],
more = lessMore[1];
return [].concat.apply(
[], [quickSort(less), h, quickSort(more)]
);
} else return [];
}
// partition :: Predicate -> List -> (Matches, nonMatches)
// partition :: (a -> Bool) -> [a] -> ([a], [a])
function partition(p, xs) {
return xs.reduce(function (a, x) {
return (
a[p(x) ? 0 : 1].push(x),
a
);
}, [[], []]);
}
return quickSort([11.8, 14.1, 21.3, 8.5, 16.7, 5.7])
})();
{{Out}}
[5.7, 8.5, 11.8, 14.1, 16.7, 21.3]
=ES6=
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());
};
Or, expressed in terms of a single partition, rather than two consecutive filters:
(() => {
'use strict';
// QUICKSORT --------------------------------------------------------------
// quickSort :: (Ord a) => [a] -> [a]
const quickSort = xs =>
xs.length > 1 ? (() => {
const
h = xs[0],
[less, more] = partition(x => x <= h, xs.slice(1));
return [].concat.apply(
[], [quickSort(less), h, quickSort(more)]
);
})() : xs;
// GENERIC ----------------------------------------------------------------
// partition :: Predicate -> List -> (Matches, nonMatches)
// partition :: (a -> Bool) -> [a] -> ([a], [a])
const partition = (p, xs) =>
xs.reduce((a, x) =>
p(x) ? [a[0].concat(x), a[1]] : [a[0], a[1].concat(x)], [
[],
[]
]);
// TEST -------------------------------------------------------------------
return quickSort([11.8, 14.1, 21.3, 8.5, 16.7, 5.7]);
})();
{{Out}}
[5.7, 8.5, 11.8, 14.1, 16.7, 21.3]
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
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:
[1, 1.1, [1,2], true, false, null, {"a":1}, null] | sort
{{Out}}
[null,null,false,true,1,1.1,[1,2],{"a":1}]
Here is an implementation in jq of the pseudo-code (and comments :-) given at the head of this article:
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 ;
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 [https://github.com/JuliaLang/julia/blob/2364748377f2a79c0485fdd5155ec2116c9f0d37/base/sort.jl#L259-L296 code from the standard library is quite readable]):
sort!(A, alg=QuickSort)
A simple polymorphic implementation of an in-place recursive quicksort (based on the pseudocode above):
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
A one-line (but rather inefficient) implementation based on the Haskell version, which operates out-of-place and allocates temporary arrays:
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])))
{{out}}
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
quicksort:{f:*x@1?#x;:[0=#x;x;,/(_f x@&x<f;x@&x=f;_f x@&x>f)]}
Example:
quicksort 1 3 5 7 9 8 6 4 2
{{out}}
1 2 3 4 5 6 7 8 9
Explanation:
_f()
is the current function called recursively.
:[....]
generally means :[condition1;then1;condition2;then2;....;else]. Though here it is used as :[if;then;else].
This construct
f:*x@1?#x
assigns a random element in x (the argument) to f, as the pivot value.
And here is the full if/then/else clause:
:[
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
]
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.
t@<t:1 3 5 7 9 8 6 4 2
Kotlin
import java.util.*
import java.util.Comparator
fun <T> quickSort(a: List<T>, c: Comparator<T>): ArrayList<T> {
if (a.isEmpty()) return ArrayList(a)
val boxes = Array(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) }
arrayOf(0, 2).forEach { boxes[it] = quickSort(boxes[it], c) }
return boxes.flatMapTo(ArrayList<T>()) { it }
}
Another version of the code:
quicksort(list: List<T>): List<T> {
if (list.isEmpty()) return emptyList()
val head = list.first()
val tail = list.takeLast(list.size - 1)
val (less, high) = tail.partition { it < head }
return less + head + high
}
fun main(args: Array<String>) {
val nums = listOf(9, 7, 9, 8, 1, 2, 3, 4, 1, 9, 8, 9, 2, 4, 2, 4, 6, 3)
println(quicksort(nums))
}
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
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]
; 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
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)
).
Lua
NOTE: If you want to use quicksort in a Lua script, you don't need to implement it yourself. Just do:
table.sort(tableName)
===in-place===
--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}))
===non in-place===
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
Lucid
[http://i.csc.uvic.ca/home/hei/lup/06.html]
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
M2000 Interpreter
Recursive calling Functions
Module Checkit1 {
Group Quick {
Private:
Function partition {
Read &A(), p, r
x = A(r)
i = p-1
For j=p to r-1 {
If .LE(A(j), x) Then {
i++
Swap A(i),A(j)
}
}
Swap A(i+1),A(r)
= i+1
}
Public:
LE=Lambda->Number<=Number
Function quicksort {
Read &A(), p, r
If p < r Then {
q = .partition(&A(), p, r)
Call .quicksort(&A(), p, q - 1)
Call .quicksort(&A(), q + 1, r)
}
}
}
Dim A(10)<<Random(50, 100)
Print A()
Call Quick.quicksort(&A(), 0, Len(A())-1)
Print A()
}
Checkit1
Recursive calling Subs
Variables p, r, q removed from quicksort function. we use stack for values. Also Partition push to stack now. Works for string arrays too.
Module Checkit2 {
Class Quick {
Private:
partition=lambda-> {
Read &A(), p, r : i = p-1 : x=A(r)
For j=p to r-1 {If .LE(A(j), x) Then i++:Swap A(i),A(j)
} : Swap A(i+1), A(r) : Push i+1
}
Public:
LE=Lambda->Number<=Number
Module ForStrings {
.partition<=lambda-> {
Read &A$(), p, r : i = p-1 : x$=A$(r)
For j=p to r-1 {If A$(j)<= x$ Then i++:Swap A$(i),A$(j)
} : Swap A$(i+1), A$(r) : Push i+1
}
}
Function quicksort (ref$) {
myQuick()
sub myQuick()
If Stackitem() >= stackitem(2) Then drop 2 : Exit Sub
Over 2, 2 : Call .partition(ref$) : Over : Shiftback 3, 2
myQuick(number, number - 1)
myQuick( number + 1, number)
End Sub
}
}
Quick=Quick()
Dim A(10)
A(0):=57, 83, 74, 98, 51, 73, 85, 76, 65, 92
Print A()
Call Quick.quicksort(&A(), 0, Len(A())-1)
Print A()
Quick=Quick()
Quick.ForStrings
Dim A$()
A$()=("one","two", "three","four", "five")
Print A$()
Call Quick.quicksort(&A$(), 0, Len(A$())-1)
Print A$()
}
Checkit2
Non Recursive
Partition function return two values (where we want q, and use it as q-1 an q+1 now Partition() return final q-1 and q+1_ Example include numeric array, array of arrays (we provide a lambda for comparison) and string array.
Module Checkit3 {
Class Quick {
Private:
partition=lambda-> {
Read &A(), p, r : i = p-1 : x=A(r)
For j=p to r-1 {If .LE(A(j), x) Then i++:Swap A(i),A(j)
} : Swap A(i+1), A(r) : Push i+2, i
}
Public:
LE=Lambda->Number<=Number
Module ForStrings {
.partition<=lambda-> {
Read &A$(), p, r : i = p-1 : x$=A$(r)
For j=p to r-1 {If A$(j)<= x$ Then i++:Swap A$(i),A$(j)
} : Swap A$(i+1), A$(r) : Push i+2, i
}
}
Function quicksort {
Read ref$
{
loop : If Stackitem() >= Stackitem(2) Then Drop 2 : if empty then {Break} else continue
over 2,2 : call .partition(ref$) :shift 3
}
}
}
Quick=Quick()
Dim A(10)<<Random(50, 100)
Print A()
Call Quick.quicksort(&A(), 0, Len(A())-1)
Print A()
Quick=Quick()
Function join$(a$()) {
n=each(a$(), 1, -2)
k$=""
while n {
overwrite k$, ".", n^:=array$(n)
}
=k$
}
Stack New {
Data "1.3.6.1.4.1.11.2.17.19.3.4.0.4" , "1.3.6.1.4.1.11.2.17.19.3.4.0.1", "1.3.6.1.4.1.11150.3.4.0.1"
Data "1.3.6.1.4.1.11.2.17.19.3.4.0.10", "1.3.6.1.4.1.11.2.17.5.2.0.79", "1.3.6.1.4.1.11150.3.4.0"
Dim Base 0, arr(Stack.Size)
Link arr() to arr$()
i=0 : While not Empty {arr$(i)=piece$(letter$+".", ".") : i++ }
}
\\ change comparison function
Quick.LE=lambda (a, b)->{
Link a, b to a$(), b$()
def i=-1
do {
i++
} until a$(i)="" or b$(i)="" or a$(i)<>b$(i)
if b$(i)="" then =a$(i)="":exit
if a$(i)="" then =true:exit
=val(a$(i))<=val(b$(i))
}
Call Quick.quicksort(&arr(), 0, Len(arr())-1)
For i=0 to len(arr())-1 {
Print join$(arr(i))
}
\\ Fresh load
Quick=Quick()
Quick.ForStrings
Dim A$()
A$()=("one","two", "three","four", "five")
Print A$()
Call Quick.quicksort(&A$(), 0, Len(A$())-1)
Print A$()
}
Checkit3
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))
{{out}}
(1,1,3,4,5,9)
Maple
swap := proc(arr, a, b)
local temp := arr[a]:
arr[a] := arr[b]:
arr[b] := temp:
end proc:
quicksort := proc(arr, low, high)
local pi:
if (low < high) then
pi := qpart(arr,low,high):
quicksort(arr, low, pi-1):
quicksort(arr, pi+1, high):
end if:
end proc:
qpart := proc(arr, low, high)
local i,j,pivot;
pivot := arr[high]:
i := low-1:
for j from low to high-1 by 1 do
if (arr[j] <= pivot) then
i++:
swap(arr, i, j):
end if;
end do;
swap(arr, i+1, high):
return (i+1):
end proc:
a:=Array([12,4,2,1,0]);
quicksort(a,1,5);
a;
{{Out|Output}}
[0, 1, 2, 4, 12]
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]]}
]
qsort[{}] = {};
qsort[{x_, xs___}] := Join[qsort@Select[{xs}, # <= x &], {x}, qsort@Select[{xs}, # > x &]];
QuickSort[{}] := {}
QuickSort[list: {__}] := With[{pivot=RandomChoice[list]},
Join[ <|1->{}, -1->{}|>, GroupBy[list,Order[#,pivot]&] ] // Catenate[ {QuickSort@#[1], #[0], QuickSort@#[-1]} ]&
]
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''.
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
A slightly more vectorized version of the above code that removes the need for the ''less'' and ''greater'' arrays:
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
Sample usage:
quickSort([4,3,7,-2,9,1])
ans =
-2 1 3 4 7 9
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
=={{header|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.
(*#####################*)
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.
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.
(*##########################*)
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.
=={{header|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.
GENERIC INTERFACE ArraySort(Elem);
PROCEDURE Sort(VAR a: ARRAY OF Elem.T; cmp := Elem.Compare);
END ArraySort.
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.
To use this generic code to sort an array of text, we create two files called TextSort.i3 and TextSort.m3, respectively.
INTERFACE TextSort = ArraySort(Text) END TextSort.
MODULE TextSort = ArraySort(Text) END TextSort.
Then, as an example:
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.
Mond
Implements the simple quicksort algorithm.
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;
}
;Usage
var array = [ 532, 16, 153, 3, 63.60, 925, 0.214 ];
var sorted = quicksort( array );
printLn( sorted );
{{out}}
[
0.214,
3,
16,
63.6,
153,
532,
925
]
MUMPS
Shows quicksort on a 16-element array.
main
new collection,size
set size=16
set collection=size for i=0:1:size-1 set collection(i)=$random(size)
write "Collection to sort:",!!
zwrite collection ; This will only work on Intersystem's flavor of MUMPS
do quicksort(.collection,0,collection-1)
write:$$isSorted(.collection) !,"Collection is sorted:",!!
zwrite collection ; This will only work on Intersystem's flavor of MUMPS
q
quicksort(array,low,high)
if low<high do
. set pivot=$$partition(.array,low,high)
. do quicksort(.array,low,pivot-1)
. do quicksort(.array,pivot+1,high)
q
partition(A,p,r)
set pivot=A(r)
set i=p-1
for j=p:1:r-1 do
. i A(j)<=pivot do
. . set i=i+1
. . set helper=A(j)
. . set A(j)=A(i)
. . set A(i)=helper
set helper=A(r)
set A(r)=A(i+1)
set A(i+1)=helper
quit i+1
isSorted(array)
set sorted=1
for i=0:1:array-2 do quit:sorted=0
. for j=i+1:1:array-1 do quit:sorted=0
. . set:array(i)>array(j) sorted=0
quit sorted
;Usage
do main()
{{out}}
Collection to sort:
collection=16
collection(0)=4
collection(1)=0
collection(2)=6
collection(3)=14
collection(4)=4
collection(5)=0
collection(6)=10
collection(7)=5
collection(8)=11
collection(9)=4
collection(10)=12
collection(11)=9
collection(12)=13
collection(13)=4
collection(14)=14
collection(15)=0
Collection is sorted:
collection=16
collection(0)=0
collection(1)=0
collection(2)=0
collection(3)=4
collection(4)=4
collection(5)=4
collection(6)=4
collection(7)=5
collection(8)=6
collection(9)=9
collection(10)=10
collection(11)=11
collection(12)=12
collection(13)=13
collection(14)=14
collection(15)=14
Nemerle
{{trans|Haskell}} A little less clean and concise than Haskell, but essentially the same.
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));
}
}
NetRexx
This sample implements both the '''simple''' and '''in place''' algorithms as described in the task's description:
/* 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
{{out}}
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
= [1 first,tally],
pass,
link [
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
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
{{out}}
@[-31, 0, 2, 2, 4, 65, 83, 99, 782]
Nix
let
qs = l:
if l == [] then []
else
with builtins;
let x = head l;
xs = tail l;
low = filter (a: a < x) xs;
high = filter (a: a >= x) xs;
in qs low ++ [x] ++ qs high;
in
qs [4 65 2 (-31) 0 99 83 782]
{{out}}
[ -31 0 2 4 65 83 99 782 ]
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);
};
}
}
=={{header|Objective-C}}== The [http://weblog.bignerdranch.com/398-objective-c-literals-part-1/ latest XCode compiler] is assumed with [http://en.wikipedia.org/wiki/Automatic_Reference_Counting ARC] enabled.
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;
}
{{out}}
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
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]
Octave
{{trans|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)
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
Oforth
Oforth built-in sort uses quick sort algorithm (see lang/collect/ListBuffer.of for implementation) :
[ 5, 8, 2, 3, 4, 1 ] sort
ooRexx
{{trans|Python}}
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
{{out}}
before: 4, 65, 2, -31, 0, 99, 83, 782, 1
after: -31, 0, 1, 2, 4, 65, 83, 99, 782
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]}}
PARI/GP
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]
};
Pascal
{ X is array of LongInt }
Procedure QuickSort ( Left, Right : LongInt );
Var
i, j,
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 inc(i); // i:=i+1;
While pivot < X[j] Do dec(j); // j:=j-1;
If i<=j Then Begin
tmp:=X[i];
X[i]:=X[j];
X[j]:=tmp;
dec(j); // j:=j-1;
inc(i); // i:=i+1;
End;
Until i>j;
If Left<j Then QuickSort(Left,j);
If i<Right Then QuickSort(i,Right);
End;
Perl
sub quick_sort {
return @_ if @_ < 2;
my $p = splice @_, int rand @_, 1;
quick_sort(grep $_ < $p, @_), $p, quick_sort(grep $_ >= $p, @_);
}
my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1);
@a = quick_sort @a;
print "@a\n";
Perl 6
# Empty list sorts to the empty list
multi quicksort([]) { () }
# Otherwise, extract first item as pivot...
multi quicksort([$pivot, *@rest]) {
# Partition.
my $before := @rest.grep(* before $pivot);
my $after := @rest.grep(* !before $pivot);
# Sort the partitions.
flat quicksort($before), $pivot, quicksort($after)
}
Note that $before and $after are bound to lazy lists, so the partitions can (at least in theory) be sorted in parallel.
Phix
function quick_sort(sequence x)
--
-- put x into ascending order using recursive quick sort
--
integer n, last, mid
object xi, midval
n = length(x)
if n<2 then
return x -- already sorted (trivial case)
end if
mid = floor((n+1)/2)
midval = x[mid]
x[mid] = x[1]
last = 1
for i=2 to n do
xi = x[i]
if xi<midval then
last += 1
x[i] = x[last]
x[last] = xi
end if
end for
return quick_sort(x[2..last]) & {midval} & quick_sort(x[last+1..n])
end function
?quick_sort({5,"oranges","and",3,"apples"})
{{out}}
{3,5,"and","apples","oranges"}
PHP
function quicksort($arr){
$lte = $gt = array();
if(count($arr) < 2){
return $arr;
}
$pivot_key = key($arr);
$pivot = array_shift($arr);
foreach($arr as $val){
if($val <= $pivot){
$lte[] = $val;
} else {
$gt[] = $val;
}
}
return array_merge(quicksort($lte),array($pivot_key=>$pivot),quicksort($gt));
}
$arr = array(1, 3, 5, 7, 9, 8, 6, 4, 2);
$arr = quicksort($arr);
echo implode(',',$arr);
1,2,3,4,5,6,7,8,9
function quickSort(array $array) {
// base case
if (empty($array)) {
return $array;
}
$head = array_shift($array);
$tail = $array;
$lesser = array_filter($tail, function ($item) use ($head) {
return $item <= $head;
});
$bigger = array_filter($tail, function ($item) use ($head) {
return $item > $head;
});
return array_merge(quickSort($lesser), [$head], quickSort($bigger));
}
$testCase = [1, 4, 8, 2, 8, 0, 2, 8];
$result = quickSort($testCase);
echo sprintf("[%s] ==> [%s]\n", implode(', ', $testCase), implode(', ', $result));
[1, 4, 8, 2, 8, 0, 2, 8] ==> [0, 1, 2, 2, 4, 8, 8, 8]
PicoLisp
(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) )
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;
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);
PowerShell
First solution
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, $l - 1 ) } )
Another solution
function quicksort($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)"
The output is: 3 8 11 19 21 36 60 63 80 87 100
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).
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
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)
In a Haskell fashion --
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
More readable, but still using list comprehensions:
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)
More correctly in some tests:
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])
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
Returning a new list:
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
Sorting a list in place:
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)
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])
R
{{trans|Octave}}
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)
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)))]))
Examples
(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")
Red
Red []
;;-------------------------------
;; we have to use function not func here, otherwise we'd have to define all "vars" as local...
qsort: function [list][
;;-------------------------------
if 1 >= length? list [ return list ]
left: copy []
right: copy []
eq: copy [] ;; "equal"
pivot: list/2 ;; simply choose second element as pivot element
foreach ele list [
case [
ele < pivot [ append left ele ]
ele > pivot [ append right ele ]
true [append eq ele ]
]
]
;; this is the last expression of the function, so coding "return" here is not necessary
reduce [qsort left eq qsort right]
]
;; lets test the function with an array of 100k integers, range 1..1000
list: []
loop 100000 [append list random 1000]
t0: now/time/precise ;; start timestamp
qsort list ;; the return value (block) contains the sorted list, original list has not changed
print ["time1: " now/time/precise - t0] ;; about 1.1 sec on my machine
t0: now/time/precise
sort list ;; just for fun time the builtin function also ( also implementation of quicksort )
print ["time2: " now/time/precise - t0]
REXX
version 1
/*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 qSort # /*invoke the quicksort subroutine. */
call show@ ' after sort' /*show the after array elements. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
qSort: procedure expose @.; a.1=1; parse arg b.1 /*access the caller's local variable. */
$=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@: w=length(#); do j=1 for #; say 'element' right(j,w) arg(1)":" @.j; end
say copies('▒', maxL + w + 22) /*display a separator (between outputs)*/
return
/*───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
gen@: @.=; maxL=0 /*assign a default value for the 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 until @.#=='' /*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
'''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
{{trans|Python}}The Python code translates very well to [[ooRexx]] but here is a way to implement it in classic REXX as well.
```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
```
## Ring
```ring
# Project : Sorting algorithms/Quicksort
test = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
see "before sort:" + nl
showarray(test)
quicksort(test, 1, 10)
see "after sort:" + nl
showarray(test)
func quicksort(a, s, n)
if n < 2
return
ok
t = s + n - 1
l = s
r = t
p = a[floor((l + r) / 2)]
while l <= r
while a[l] < p
l = l + 1
end
while a[r] > p
r = r - 1
end
if l <= r
temp = a[l]
a[l] = a[r]
a[r] = temp
l = l + 1
r = r - 1
ok
end
if s < r
quicksort(a, s, r - s + 1)
ok
if l < t
quicksort(a, l, t - l + 1 )
ok
func showarray(vect)
svect = ""
for n = 1 to len(vect)
svect = svect + vect[n] + " "
next
svect = left(svect, len(svect) - 1)
see svect + nl
```
Output:
```txt
before sort:
4 65 2 -31 0 99 2 83 782 1
after sort:
-31 0 1 2 2 4 65 83 99 782
```
## Ruby
```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
```
or
```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
```
or functionally
```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
```
## Run BASIC
```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
```
## Rust
```rust
fn main() {
println!("Sort numbers in descending order");
let mut numbers = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1];
println!("Before: {:?}", numbers);
quick_sort(&mut numbers, &|x,y| x > y);
println!("After: {:?}\n", numbers);
println!("Sort strings alphabetically");
let mut strings = ["beach", "hotel", "airplane", "car", "house", "art"];
println!("Before: {:?}", strings);
quick_sort(&mut strings, &|x,y| x < y);
println!("After: {:?}\n", strings);
println!("Sort strings by length");
println!("Before: {:?}", strings);
quick_sort(&mut strings, &|x,y| x.len() < y.len());
println!("After: {:?}", strings);
}
fn quick_sort(v: &mut [T], f: &F)
where F: Fn(&T,&T) -> bool
{
let len = v.len();
if len >= 2 {
let pivot_index = partition(v, f);
quick_sort(&mut v[0..pivot_index], f);
quick_sort(&mut v[pivot_index + 1..len], f);
}
}
fn partition(v: &mut [T], f: &F) -> usize
where F: Fn(&T,&T) -> bool
{
let len = v.len();
let pivot_index = len / 2;
let last_index = len - 1;
v.swap(pivot_index, last_index);
let mut store_index = 0;
for i in 0..last_index {
if f(&v[i], &v[last_index]) {
v.swap(i, store_index);
store_index += 1;
}
}
v.swap(store_index, len - 1);
store_index
}
```
{{out}}
```txt
Sort numbers in descending order
Before: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
After: [782, 99, 83, 65, 4, 2, 2, 1, 0, -31]
Sort strings alphabetically
Before: ["beach", "hotel", "airplane", "car", "house", "art"]
After: ["airplane", "art", "beach", "car", "hotel", "house"]
Sort strings by length
Before: ["airplane", "art", "beach", "car", "hotel", "house"]
After: ["car", "art", "house", "hotel", "beach", "airplane"]
```
## SASL
Copied from SASL manual, Appendix II, solution (2)(b)
```SASL
DEF || this rather nice solution is due to Silvio Meira
sort () = ()
sort (a : x) = sort {b <- x; b <= a } ++ a : sort { b <- x; b>a}
?
```
## Sather
```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;
```
```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;
```
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
What follows is a progression on genericity here.
First, a quick sort of a list of integers:
```scala
def sort(xs: List[Int]): List[Int] = xs match {
case Nil => Nil
case head :: tail =>
val (less, notLess) = tail.partition(_ < head) // Arbitrarily partition list in two
sort(less) ++ (head :: sort(notLess)) // Sort each half
}
```
Next, a quick sort of a list of some type T, given a lessThan function:
```scala
def sort[T](xs: List[T], lessThan: (T, T) => Boolean): List[T] = xs match {
case Nil => Nil
case x :: xx =>
val (lo, hi) = xx.partition(lessThan(_, x))
sort(lo, lessThan) ++ (x :: sort(hi, lessThan))
}
```
To take advantage of known orderings, a quick sort of a list of some type T,
for which exists an implicit (or explicit) Ordering[T]:
```scala
def sort[T](xs: List[T])(implicit ord: Ordering[T]): List[T] = xs match {
case Nil => Nil
case x :: xx =>
val (lo, hi) = xx.partition(ord.lt(_, x))
sort[T](lo) ++ (x :: sort[T](hi))
}
```
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.
```scala
def sort[T <: Ordered[T]](xs: List[T]): List[T] = xs match {
case Nil => Nil
case x :: xx =>
val (lo, hi) = xx.partition(_ < x)
sort(lo) ++ (x :: sort(hi))
}
```
What hasn't changed in all these examples is 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:
```scala
def sort[T, C[T] <: scala.collection.TraversableLike[T, C[T]]]
(xs: C[T])
(implicit ord: scala.math.Ordering[T],
cbf: scala.collection.generic.CanBuildFrom[C[T], T, C[T]]): C[T] = {
// Some collection types can't pattern match
if (xs.isEmpty) {
xs
} else {
val (lo, hi) = xs.tail.partition(ord.lt(_, xs.head))
val b = cbf()
b.sizeHint(xs.size)
b ++= sort(lo)
b += xs.head
b ++= sort(hi)
b.result()
}
}
```
The type of our collection is "C[T]", and,
by providing C[T] as a type parameter to TraversableLike, we ensure C[T] is capable
of returning instances of type C[T]. 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 C[T] 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 one as such implicitly. Because we need that
implicitly, then we need to ask for the "T => Ordering[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 from the list variant, since many of the Traversable
collection types don't support pattern matching, "+:" or "::".
## Scheme
```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) >)
```
With srfi-1:
```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) >)
```
## Seed7
```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: [http://seed7.sourceforge.net/algorith/sorting.htm#quickSort]
## SETL
In-place sort (looks much the same as the C version)
```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;
```
Copying sort using comprehensions:
```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;
```
## Sidef
```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});
}
```
## Simula
```simula
PROCEDURE QUICKSORT(A); REAL ARRAY A;
BEGIN
PROCEDURE QS(A, FIRST, LAST); REAL ARRAY A; INTEGER FIRST, LAST;
BEGIN
INTEGER LEFT, RIGHT;
LEFT := FIRST; RIGHT := LAST;
IF RIGHT - LEFT + 1 > 1 THEN
BEGIN
REAL PIVOT;
PIVOT := A((LEFT + RIGHT) // 2);
WHILE LEFT <= RIGHT DO
BEGIN
WHILE A(LEFT) < PIVOT DO LEFT := LEFT + 1;
WHILE A(RIGHT) > PIVOT DO RIGHT := RIGHT - 1;
IF LEFT <= RIGHT THEN
BEGIN
REAL SWAP;
SWAP := A(LEFT); A(LEFT) := A(RIGHT); A(RIGHT) := SWAP;
LEFT := LEFT + 1; RIGHT := RIGHT - 1;
END;
END;
QS(A, FIRST, RIGHT);
QS(A, LEFT, LAST);
END;
END QS;
QS(A, LOWERBOUND(A, 1), UPPERBOUND(A, 1));
END QUICKSORT;
```
## Standard ML
```sml
fun quicksort [] = []
| quicksort (x::xs) =
let
val (left, right) = List.partition (fn y => yfunc quicksort) {
if (range.endIndex - range.startIndex > 1) {
let pivotIndex = partition(&elements, range)
quicksort(&elements, range.startIndex ..< pivotIndex)
quicksort(&elements, pivotIndex+1 ..< range.endIndex)
}
}
func quicksort(inout elements: [T]) {
quicksort(&elements, indices(elements))
}
```
## Tailspin
Simple recursive quicksort:
```tailspin
templates quicksort
@: [];
$ -> #
<[](2..)>
def pivot: $(1);
[ [ $(2..-1)... -> (
<..$pivot>
$ !
<>
..|@quicksort: $;
)] -> quicksort..., $pivot, $@ -> quicksort... ] !
<>
$ !
end quicksort
[4,5,3,8,1,2,6,7,9,8,5] -> quicksort -> !OUT::write
```
In place:
```tailspin
templates quicksort
templates partial
def first: $(1);
def last: $(2);
def pivot: $@quicksort($first);
[ $(1) + 1, $(2) ] -> #
)>
def limit: $(2);
@quicksort($first): $@quicksort($limit);
@quicksort($limit): $pivot;
[ $first, $limit - 1 ] !
[ $limit + 1, $last ] !
)>
[ $(1), $(2) - 1] -> #
)>
[ $(1) + 1, $(2)] -> #
<>
def temp: $@quicksort($(1));
@quicksort($(1)): $@quicksort($(2));
@quicksort($(2)): $temp;
[ $(1) + 1, $(2) - 1] -> #
end partial
@: $;
[1, $@::length] -> #
$@ !
)>
$ -> partial -> #
end quicksort
[4,5,3,8,1,2,6,7,9,8,5] -> quicksort -> !OUT::write
```
## Tcl
```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
```
## TypeScript
/**
Generic quicksort function using typescript generics.
Follows quicksort as done in CLRS.
*/
export type Comparator = (o1: T, o2: T) => number;
export function quickSort(array: T[], compare: Comparator) {
if (array.length <= 1 || array == null) {
return;
}
sort(array, compare, 0, array.length - 1);
}
function sort(
array: T[], compare: Comparator, low: number, high: number) {
if (low < high) {
const partIndex = partition(array, compare, low, high);
sort(array, compare, low, partIndex - 1);
sort(array, compare, partIndex + 1, high);
}
}
function partition(
array: T[], compare: Comparator, low: number, high: number): number {
const pivot: T = array[high];
let i: number = low - 1;
for (let j = low; j <= high - 1; j++) {
if (compare(array[j], pivot) == -1) {
i = i + 1;
swap(array, i, j)
}
}
if (compare(array[high], array[i + 1]) == -1) {
swap(array, i + 1, high);
}
return i + 1;
}
function swap(array: T[], i: number, j: number) {
const newJ: T = array[i];
array[i] = array[j];
array[j] = newJ;
}
export function testQuickSort(): void {
function numberComparator(o1: number, o2: number): number {
if (o1 < o2) {
return -1;
} else if (o1 == o2) {
return 0;
}
return 1;
}
let tests: number[][] = [
[], [1], [2, 1], [-1, 2, -3], [3, 16, 8, -5, 6, 4], [1, 2, 3, 4, 5, 6],
[1, 2, 3, 4, 5]
];
for (let testArray of tests) {
quickSort(testArray, numberComparator);
console.log(testArray);
}
}
```
## uBasic/4tH
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
```
## UnixPipes
{{works with|Zsh}}
```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
```
## 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.
```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>
```
{{out}}
```txt
<367,381,475,506,694,1377,1580,1704,1872,3712>
```
## V
```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)
```v
[qsort
[small?] []
[uncons [>] split]
[[p [*l] [*g] : [*l p *g]] view]
binrec].
```
{{omit from|GUISS}}
## VBA
This is the "simple" quicksort, using temporary arrays.
```vb
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
```
{{out}}
```txt
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
{{trans|BBC BASIC}}
```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,",")
```
{{out}}
```txt
-1,0,1,2,3,4,5,5,6,7,8,9
```
## Wart
```python
def (qsort (pivot ... ns))
(+ (qsort+keep (fn(_) (_ < pivot)) ns)
list.pivot
(qsort+keep (fn(_) (_ > pivot)) ns))
def (qsort x) :case x=nil
nil
```
## XPL0
```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);
]
```
{{out}}
```txt
.Pabcdeefghiiijklmnoooqrstuuvwxyz
```
## zkl
These are the Wikipedia algorithms.
Quick sort immutable sequence using crappy pivot choice:
```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);
}
```
In place quick sort:
```zkl
fcn qiSort(list,cmp='<){ // in place quick sort
fcn(list,left,right,cmp){
if (left