Sorting algorithms/Quicksort
(Redirected from Quicksort)
You are encouraged to solve this task according to the task description, using any language you may know.
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
| This page uses content from Wikipedia. The original article was at Quicksort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance) |
- Task
Sort an array (or list) elements using the quicksort algorithm.
The elements must have a strict weak order and the index of the array can be of any discrete type.
For languages where this is not possible, sort an array of integers.
Quicksort, also known as partition-exchange sort, uses these steps.
- Choose any element of the array to be the pivot.
- Divide all other elements (except the pivot) into two partitions.
- All elements less than the pivot must be in the first partition.
- All elements greater than the pivot must be in the second partition.
- Use recursion to sort both partitions.
- Join the first sorted partition, the pivot, and the second sorted partition.
The best pivot creates partitions of equal length (or lengths differing by 1).
The worst pivot creates an empty partition (for example, if the pivot is the first or last element of a sorted array).
The run-time of Quicksort ranges from O(n log n) with the best pivots, to O(n2) with the worst pivots, where n is the number of elements in the array.
This is a simple quicksort algorithm, adapted from Wikipedia.
function quicksort(array)
less, equal, greater := three empty arrays
if length(array) > 1
pivot := select any element of array
for each x in array
if x < pivot then add x to less
if x = pivot then add x to equal
if x > pivot then add x to greater
quicksort(less)
quicksort(greater)
array := concatenate(less, equal, greater)
A better quicksort algorithm works in place, by swapping elements within the array, to avoid the memory allocation of more arrays.
function quicksort(array)
if length(array) > 1
pivot := select any element of array
left := first index of array
right := last index of array
while left ≤ right
while array[left] < pivot
left := left + 1
while array[right] > pivot
right := right - 1
if left ≤ right
swap array[left] with array[right]
left := left + 1
right := right - 1
quicksort(array from first index to right)
quicksort(array from left to last index)
Quicksort has a reputation as the fastest sort. Optimized variants of quicksort are common features of many languages and libraries. One often contrasts quicksort with merge sort, because both sorts have an average time of O(n log n).
- "On average, mergesort does fewer comparisons than quicksort, so it may be better when complicated comparison routines are used. Mergesort also takes advantage of pre-existing order, so it would be favored for using sort() to merge several sorted arrays. On the other hand, quicksort is often faster for small arrays, and on arrays of a few distinct values, repeated many times." — http://perldoc.perl.org/sort.html
Quicksort is at one end of the spectrum of divide-and-conquer algorithms, with merge sort at the opposite end.
- Quicksort is a conquer-then-divide algorithm, which does most of the work during the partitioning and the recursive calls. The subsequent reassembly of the sorted partitions involves trivial effort.
- Merge sort is a divide-then-conquer algorithm. The partioning happens in a trivial way, by splitting the input array in half. Most of the work happens during the recursive calls and the merge phase.
With quicksort, every element in the first partition is less than or equal to every element in the second partition. Therefore, the merge phase of quicksort is so trivial that it needs no mention!
This task has not specified whether to allocate new arrays, or sort in place. This task also has not specified how to choose the pivot element. (Common ways to are to choose the first element, the middle element, or the median of three elements.) Thus there is a variety among the following implementations.
11l
F _quicksort(&array, start, stop) -> Void
I stop - start > 0
V pivot = array[start]
V left = start
V right = stop
L left <= right
L array[left] < pivot
left++
L array[right] > pivot
right--
I left <= right
swap(&array[left], &array[right])
left++
right--
_quicksort(&array, start, right)
_quicksort(&array, left, stop)
F quicksort(&array)
_quicksort(&array, 0, array.len - 1)
V arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
quicksort(&arr)
print(arr)- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
360 Assembly
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- Output:
1 1 2 6 7 8 8 9 9 9 10 15 16 16 16 17 18 18 19 20
AArch64 Assembly
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program quickSort64.s */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeConstantesARM64.inc"
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessSortOk: .asciz "Table sorted.\n"
szMessSortNok: .asciz "Table not sorted !!!!!.\n"
sMessResult: .asciz "Value : @ \n"
szCarriageReturn: .asciz "\n"
.align 4
TableNumber: .quad 1,3,6,2,5,9,10,8,4,7,11
#TableNumber: .quad 10,9,8,7,6,-5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 8
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
sZoneConv: .skip 24
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: // entry of program
ldr x0,qAdrTableNumber // address number table
mov x1,0 // first element
mov x2,NBELEMENTS // number of élements
bl quickSort
ldr x0,qAdrTableNumber // address number table
bl displayTable
ldr x0,qAdrTableNumber // address number table
mov x1,NBELEMENTS // number of élements
bl isSorted // control sort
cmp x0,1 // sorted ?
beq 1f
ldr x0,qAdrszMessSortNok // no !! error sort
bl affichageMess
b 100f
1: // yes
ldr x0,qAdrszMessSortOk
bl affichageMess
100: // standard end of the program
mov x0,0 // return code
mov x8,EXIT // request to exit program
svc 0 // perform the system call
qAdrsZoneConv: .quad sZoneConv
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrsMessResult: .quad sMessResult
qAdrTableNumber: .quad TableNumber
qAdrszMessSortOk: .quad szMessSortOk
qAdrszMessSortNok: .quad szMessSortNok
/******************************************************************/
/* control sorted table */
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the number of elements > 0 */
/* x0 return 0 if not sorted 1 if sorted */
isSorted:
stp x2,lr,[sp,-16]! // save registers
stp x3,x4,[sp,-16]! // save registers
mov x2,0
ldr x4,[x0,x2,lsl 3]
1:
add x2,x2,1
cmp x2,x1
bge 99f
ldr x3,[x0,x2, lsl 3]
cmp x3,x4
blt 98f
mov x4,x3
b 1b
98:
mov x0,0 // not sorted
b 100f
99:
mov x0,1 // sorted
100:
ldp x3,x4,[sp],16 // restaur 2 registers
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/***************************************************/
/* Appel récursif Tri Rapide quicksort */
/***************************************************/
/* x0 contains the address of table */
/* x1 contains index of first item */
/* x2 contains the number of elements > 0 */
quickSort:
stp x2,lr,[sp,-16]! // save registers
stp x3,x4,[sp,-16]! // save registers
str x5, [sp,-16]! // save registers
sub x2,x2,1 // last item index
cmp x1,x2 // first > last ?
bge 100f // yes -> end
mov x4,x0 // save x0
mov x5,x2 // save x2
bl partition1 // cutting into 2 parts
mov x2,x0 // index partition
mov x0,x4 // table address
bl quickSort // sort lower part
add x1,x2,1 // index begin = index partition + 1
add x2,x5,1 // number of elements
bl quickSort // sort higter part
100: // end function
ldr x5, [sp],16 // restaur 1 register
ldp x3,x4,[sp],16 // restaur 2 registers
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* Partition table elements */
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains index of first item */
/* x2 contains index of last item */
partition1:
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
ldr x3,[x0,x2,lsl 3] // load value last index
mov x4,x1 // init with first index
mov x5,x1 // init with first index
1: // begin loop
ldr x6,[x0,x5,lsl 3] // load value
cmp x6,x3 // compare value
bge 2f
ldr x7,[x0,x4,lsl 3] // if < swap value table
str x6,[x0,x4,lsl 3]
str x7,[x0,x5,lsl 3]
add x4,x4,1 // and increment index 1
2:
add x5,x5,1 // increment index 2
cmp x5,x2 // end ?
blt 1b // no loop
ldr x7,[x0,x4,lsl 3] // swap value
str x3,[x0,x4,lsl 3]
str x7,[x0,x2,lsl 3]
mov x0,x4 // return index partition
100:
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* Display table elements */
/******************************************************************/
/* x0 contains the address of table */
displayTable:
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
mov x2,x0 // table address
mov x3,0
1: // loop display table
ldr x0,[x2,x3,lsl 3]
ldr x1,qAdrsZoneConv
bl conversion10S // décimal conversion
ldr x0,qAdrsMessResult
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc // insert result at // character
bl affichageMess // display message
add x3,x3,1
cmp x3,NBELEMENTS - 1
ble 1b
ldr x0,qAdrszCarriageReturn
bl affichageMess
mov x0,x2
100:
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"Value : +1 Value : +2 Value : +3 Value : +4 Value : +5 Value : +6 Value : +7 Value : +8 Value : +9 Value : +10 Value : +11 Table sorted.
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.
- Output:
[ 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:
> (qsort '(8 6 7 5 3 0 9))
(0 3 5 6 7 8 9)
Action!
Action! language does not support recursion. Therefore an iterative approach with a stack has been proposed.
DEFINE MAX_COUNT="100"
INT ARRAY stack(MAX_COUNT)
INT stackSize
PROC PrintArray(INT ARRAY a INT size)
INT i
Put('[)
FOR i=0 TO size-1
DO
IF i>0 THEN Put(' ) FI
PrintI(a(i))
OD
Put(']) PutE()
RETURN
PROC InitStack()
stackSize=0
RETURN
BYTE FUNC IsEmpty()
IF stackSize=0 THEN
RETURN (1)
FI
RETURN (0)
PROC Push(INT low,high)
stack(stackSize)=low stackSize==+1
stack(stackSize)=high stackSize==+1
RETURN
PROC Pop(INT POINTER low,high)
stackSize==-1 high^=stack(stackSize)
stackSize==-1 low^=stack(stackSize)
RETURN
INT FUNC Partition(INT ARRAY a INT low,high)
INT part,v,i,tmp
v=a(high)
part=low-1
FOR i=low TO high-1
DO
IF a(i)<=v THEN
part==+1
tmp=a(part) a(part)=a(i) a(i)=tmp
FI
OD
part==+1
tmp=a(part) a(part)=a(high) a(high)=tmp
RETURN (part)
PROC QuickSort(INT ARRAY a INT size)
INT low,high,part
InitStack()
Push(0,size-1)
WHILE IsEmpty()=0
DO
Pop(@low,@high)
part=Partition(a,low,high)
IF part-1>low THEN
Push(low,part-1)
FI
IF part+1<high THEN
Push(part+1,high)
FI
OD
RETURN
PROC Test(INT ARRAY a INT size)
PrintE("Array before sort:")
PrintArray(a,size)
QuickSort(a,size)
PrintE("Array after sort:")
PrintArray(a,size)
PutE()
RETURN
PROC Main()
INT ARRAY
a(10)=[1 4 65535 0 3 7 4 8 20 65530],
b(21)=[10 9 8 7 6 5 4 3 2 1 0
65535 65534 65533 65532 65531
65530 65529 65528 65527 65526],
c(8)=[101 102 103 104 105 106 107 108],
d(12)=[1 65535 1 65535 1 65535 1
65535 1 65535 1 65535]
Test(a,10)
Test(b,21)
Test(c,8)
Test(d,12)
RETURN- Output:
Screenshot from Atari 8-bit computer
Array before sort: [1 4 -1 0 3 7 4 8 20 -6] Array after sort: [-6 -1 0 1 3 4 4 7 8 20] Array before sort: [10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10] Array after sort: [-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10] Array before sort: [101 102 103 104 105 106 107 108] Array after sort: [101 102 103 104 105 106 107 108] Array before sort: [1 -1 1 -1 1 -1 1 -1 1 -1 1 -1] Array after sort: [-1 -1 -1 -1 -1 -1 1 1 1 1 1 1]
ActionScript
The functional programming way
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;
with Quick_Sort;
procedure Sort_Test is
type Days is (Mon, Tue, Wed, Thu, Fri, Sat, Sun);
type Sales is array (Days range <>) of Float;
procedure Sort_Days is new 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))
)- Output:
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 ;APL
qsort ← {1≥≢∪⍵:⍵ ⋄ p←⍵[?≢⍵] ⋄ (∇(⍵≤p)/⍵) , ∇(⍵>p)/⍵}
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 ⍋ (Grade Up) to sort (which will pick a sorting algorithm suited to the argument):
sort ← {⍵[⍋⍵]}
sort 31 4 1 5 9 2 6 5 3 5 8
1 2 3 4 5 5 5 6 8 9 31
AppleScript
Functional
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).
(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
- Output:
{5.7, 8.5, 11.8, 14.1, 16.7, 21.3}
Straightforward
Emphasising clarity, quick sorting, and correct AppleScript:
-- In-place Quicksort (basic algorithm).
-- Algorithm: S.A.R. (Tony) Hoare, 1960.
on quicksort(theList, l, r) -- Sort items l thru r of theList.
set listLength to (count theList)
if (listLength < 2) then return
-- Convert negative and/or transposed range indices.
if (l < 0) then set l to listLength + l + 1
if (r < 0) then set r to listLength + r + 1
if (l > r) then set {l, r} to {r, l}
-- Script object containing the list as a property (to allow faster references to its items)
-- and the recursive subhandler.
script o
property lst : theList
on qsrt(l, r)
set pivot to my lst's item ((l + r) div 2)
set i to l
set j to r
repeat until (i > j)
set lv to my lst's item i
repeat while (pivot > lv)
set i to i + 1
set lv to my lst's item i
end repeat
set rv to my lst's item j
repeat while (rv > pivot)
set j to j - 1
set rv to my lst's item j
end repeat
if (j > i) then
set my lst's item i to rv
set my lst's item j to lv
else if (i > j) then
exit repeat
end if
set i to i + 1
set j to j - 1
end repeat
if (j > l) then qsrt(l, j)
if (i < r) then qsrt(i, r)
end qsrt
end script
tell o to qsrt(l, r)
return -- nothing.
end quicksort
property sort : quicksort
-- Demo:
local aList
set aList to {28, 9, 95, 22, 67, 55, 20, 41, 60, 53, 100, 72, 19, 67, 14, 42, 29, 20, 74, 39}
sort(aList, 1, -1) -- Sort items 1 thru -1 of aList.
return aList
- Output:
{9, 14, 19, 20, 20, 22, 28, 29, 39, 41, 42, 53, 55, 60, 67, 67, 72, 74, 95, 100}
Arc
(def qs (seq)
(if (empty seq) nil
(let pivot (car seq)
(join (qs (keep [< _ pivot] (cdr seq)))
(list pivot)
(qs (keep [>= _ pivot] (cdr seq)))))))ARM Assembly
/* 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 0xCCCCCCCDArturo
quickSort: function [items][
if 2 > size items -> return items
pivot: first items
left: select slice items 1 (size items)-1 'x -> x < pivot
right: select slice items 1 (size items)-1 'x -> x >= pivot
((quickSort left) ++ pivot) ++ quickSort right
]
print quickSort [3 1 2 8 5 7 9 4 6]
- Output:
1 2 3 4 5 6 7 8 9
ATS
A quicksort working on non-linear linked lists
(*------------------------------------------------------------------*)
(* Quicksort in ATS2, for non-linear lists. *)
(*------------------------------------------------------------------*)
#include "share/atspre_staload.hats"
#define NIL list_nil ()
#define :: list_cons
(*------------------------------------------------------------------*)
(* A simple quicksort working on "garbage-collected" linked lists,
with first element as pivot. This is meant as a demonstration, not
as a superior sort algorithm.
It is based on the "not-in-place" task pseudocode. *)
datatype comparison_result =
| first_is_less_than_second of ()
| first_is_equal_to_second of ()
| first_is_greater_than_second of ()
extern fun {a : t@ype}
list_quicksort$comparison (x : a, y : a) :<> comparison_result
extern fun {a : t@ype}
list_quicksort {n : int}
(lst : list (a, n)) :<> list (a, n)
(* - - - - - - - - - - - - - - - - - - - - - - *)
implement {a}
list_quicksort {n} (lst) =
let
fun
partition {n : nat}
.<n>. (* Proof of termination. *)
(lst : list (a, n),
pivot : a)
:<> [n1, n2, n3 : int | n1 + n2 + n3 == n]
@(list (a, n1), list (a, n2), list (a, n3)) =
(* This implementation is *not* tail recursive. I may get a
scolding for using ATS to risk stack overflow! However, I
need more practice writing non-tail routines. :) Also, a lot
of programmers in other languages would do it this
way--especially if the lists are evaluated lazily. *)
case+ lst of
| NIL => @(NIL, NIL, NIL)
| head :: tail =>
let
val @(lt, eq, gt) = partition (tail, pivot)
prval () = lemma_list_param lt
prval () = lemma_list_param eq
prval () = lemma_list_param gt
in
case+ list_quicksort$comparison<a> (head, pivot) of
| first_is_less_than_second () => @(head :: lt, eq, gt)
| first_is_equal_to_second () => @(lt, head :: eq, gt)
| first_is_greater_than_second () => @(lt, eq, head :: gt)
end
fun
quicksort {n : nat}
.<n>. (* Proof of termination. *)
(lst : list (a, n))
:<> list (a, n) =
case+ lst of
| NIL => lst
| _ :: NIL => lst
| head :: tail =>
let
(* We are careful here to run "partition" on "tail" rather
than "lst", so the termination metric will be provably
decreasing. (Really the compiler *forces* us to take such
care, or else to change :<> to :<!ntm>) *)
val pivot = head
prval () = lemma_list_param tail
val @(lt, eq, gt) = partition {n - 1} (tail, pivot)
prval () = lemma_list_param lt
prval () = lemma_list_param eq
prval () = lemma_list_param gt
val eq = pivot :: eq
and lt = quicksort lt
and gt = quicksort gt
in
lt + (eq + gt)
end
prval () = lemma_list_param lst
in
quicksort {n} lst
end
(*------------------------------------------------------------------*)
val example_strings =
$list ("choose", "any", "element", "of", "the", "array",
"to", "be", "the", "pivot",
"divide", "all", "other", "elements", "except",
"the", "pivot", "into", "two", "partitions",
"all", "elements", "less", "than", "the", "pivot",
"must", "be", "in", "the", "first", "partition",
"all", "elements", "greater", "than", "the", "pivot",
"must", "be", "in", "the", "second", "partition",
"use", "recursion", "to", "sort", "both", "partitions",
"join", "the", "first", "sorted", "partition", "the",
"pivot", "and", "the", "second", "sorted", "partition")
implement
list_quicksort$comparison<string> (x, y) =
let
val i = strcmp (x, y)
in
if i < 0 then
first_is_less_than_second
else if i = 0 then
first_is_equal_to_second
else
first_is_greater_than_second
end
implement
main0 () =
let
val sorted_strings = list_quicksort<string> example_strings
fun
print_strings {n : nat} .<n>.
(strings : list (string, n),
i : int) : void =
case+ strings of
| NIL => if i <> 1 then println! () else ()
| head :: tail =>
begin
print! head;
if i = 8 then
begin
println! ();
print_strings (tail, 1)
end
else
begin
print! " ";
print_strings (tail, succ i)
end
end
in
println! (length example_strings);
println! (length sorted_strings);
print_strings (sorted_strings, 1)
end
(*------------------------------------------------------------------*)- Output:
$ patscc -O3 -DATS_MEMALLOC_GCBDW quicksort_task_for_lists.dats -lgc && ./a.out 62 62 all all all and any array be be be both choose divide element elements elements elements except first first greater in in into join less must must of other partition partition partition partition partitions partitions pivot pivot pivot pivot pivot recursion second second sort sorted sorted than than the the the the the the the the the the to to two use
A quicksort working on linear linked lists
This program was derived from the quicksort for non-linear linked lists.
(*------------------------------------------------------------------*)
(* Quicksort in ATS2, for linear lists. *)
(*------------------------------------------------------------------*)
#include "share/atspre_staload.hats"
#define NIL list_vt_nil ()
#define :: list_vt_cons
(*------------------------------------------------------------------*)
(* A simple quicksort working on linear linked lists, with first
element as pivot. This is meant as a demonstration, not as a
superior sort algorithm.
It is based on the "not-in-place" task pseudocode. *)
#define FIRST_IS_LESS_THAN_SECOND 1
#define FIRST_IS_EQUAL_TO_SECOND 2
#define FIRST_IS_GREATER_THAN_SECOND 3
typedef comparison_result =
[i : int | (i == FIRST_IS_LESS_THAN_SECOND ||
i == FIRST_IS_EQUAL_TO_SECOND ||
i == FIRST_IS_GREATER_THAN_SECOND)]
int i
extern fun {a : vt@ype}
list_vt_quicksort$comparison (x : !a, y : !a) :<> comparison_result
extern fun {a : vt@ype}
list_vt_quicksort {n : int}
(lst : list_vt (a, n)) :<!wrt> list_vt (a, n)
(* - - - - - - - - - - - - - - - - - - - - - - *)
implement {a}
list_vt_quicksort {n} (lst) =
let
fun
partition {n : nat}
.<n>. (* Proof of termination. *)
(lst : list_vt (a, n),
pivot : !a)
:<> [n1, n2, n3 : int | n1 + n2 + n3 == n]
@(list_vt (a, n1), list_vt (a, n2), list_vt (a, n3)) =
(* This implementation is *not* tail recursive. I may get a
scolding for using ATS to risk stack overflow! However, I
need more practice writing non-tail routines. :) Also, a lot
of programmers in other languages would do it this
way--especially if the lists are evaluated lazily. *)
case+ lst of
| ~ NIL => @(NIL, NIL, NIL)
| ~ head :: tail =>
let
val @(lt, eq, gt) = partition (tail, pivot)
prval () = lemma_list_vt_param lt
prval () = lemma_list_vt_param eq
prval () = lemma_list_vt_param gt
in
case+ list_vt_quicksort$comparison<a> (head, pivot) of
| FIRST_IS_LESS_THAN_SECOND => @(head :: lt, eq, gt)
| FIRST_IS_EQUAL_TO_SECOND => @(lt, head :: eq, gt)
| FIRST_IS_GREATER_THAN_SECOND => @(lt, eq, head :: gt)
end
fun
quicksort {n : nat}
.<n>. (* Proof of termination. *)
(lst : list_vt (a, n))
:<!wrt> list_vt (a, n) =
case+ lst of
| NIL => lst
| _ :: NIL => lst
| ~ head :: tail =>
let
(* We are careful here to run "partition" on "tail" rather
than "lst", so the termination metric will be provably
decreasing. (Really the compiler *forces* us to take such
care, or else to add !ntm to the effects.) *)
val pivot = head
prval () = lemma_list_vt_param tail
val @(lt, eq, gt) = partition {n - 1} (tail, pivot)
prval () = lemma_list_vt_param lt
prval () = lemma_list_vt_param eq
prval () = lemma_list_vt_param gt
val eq = pivot :: eq
and lt = quicksort lt
and gt = quicksort gt
in
list_vt_append (lt, list_vt_append (eq, gt))
end
prval () = lemma_list_vt_param lst
in
quicksort {n} lst
end
(*------------------------------------------------------------------*)
implement
list_vt_quicksort$comparison<Strptr1> (x, y) =
let
val i = compare (x, y)
in
if i < 0 then
FIRST_IS_LESS_THAN_SECOND
else if i = 0 then
FIRST_IS_EQUAL_TO_SECOND
else
FIRST_IS_GREATER_THAN_SECOND
end
implement
list_vt_map$fopr<string><Strptr1> (s) = string0_copy s
implement
list_vt_freelin$clear<Strptr1> (x) = strptr_free x
implement
main0 () =
let
val example_strings =
$list_vt
("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")
val example_strptrs =
list_vt_map<string><Strptr1> (example_strings)
val sorted_strptrs = list_vt_quicksort<Strptr1> example_strptrs
fun
print_strptrs {n : nat} .<n>.
(strptrs : !list_vt (Strptr1, n),
i : int) : void =
case+ strptrs of
| NIL => if i <> 1 then println! () else ()
| @ head :: tail =>
begin
print! head;
if i = 8 then
begin
println! ();
print_strptrs (tail, 1)
end
else
begin
print! " ";
print_strptrs (tail, succ i)
end;
fold@ strptrs
end
in
println! (length example_strings);
println! (length sorted_strptrs);
print_strptrs (sorted_strptrs, 1);
list_vt_freelin<Strptr1> sorted_strptrs;
list_vt_free<string> example_strings
end
(*------------------------------------------------------------------*)- Output:
$ patscc -O3 -DATS_MEMALLOC_LIBC quicksort_task_for_list_vt.dats && ./a.out 62 62 all all all and any array be be be both choose divide element elements elements elements except first first greater in in into join less must must of other partition partition partition partition partitions partitions pivot pivot pivot pivot pivot recursion second second sort sorted sorted than than the the the the the the the the the the to to two use
A quicksort working on arrays of non-linear elements
(*------------------------------------------------------------------*)
(* Quicksort in ATS2, for arrays of non-linear values. *)
(*------------------------------------------------------------------*)
#include "share/atspre_staload.hats"
#define NIL list_nil ()
#define :: list_cons
(*------------------------------------------------------------------*)
(* A simple quicksort working on arrays of non-linear values, using
a programmer-selectible pivot.
It is based on the "in-place" task pseudocode. *)
extern fun {a : t@ype} (* A "less-than" predicate. *)
array_quicksort$lt (x : a, y : a) : bool
extern fun {a : t@ype}
array_quicksort$select_pivot {n : int}
{i, j : nat | i < j; j < n}
(arr : &array (a, n) >> _,
first : size_t i,
last : size_t j) : a
extern fun {a : t@ype}
array_quicksort {n : int}
(arr : &array (a, n) >> _,
n : size_t n) : void
(* - - - - - - - - - - - - - - - - - - - - - - *)
fn {a : t@ype}
swap {n : int}
{i, j : nat | i < n; j < n}
(arr : &array(a, n) >> _,
i : size_t i,
j : size_t j) : void =
{
val x = arr[i] and y = arr[j]
val () = (arr[i] := y) and () = (arr[j] := x)
}
implement {a}
array_quicksort {n} (arr, n) =
let
sortdef index = {i : nat | i < n}
typedef index (i : int) = [0 <= i; i < n] size_t i
typedef index = [i : index] index i
macdef lt = array_quicksort$lt<a>
fun
quicksort {i, j : index}
(arr : &array(a, n) >> _,
first : index i,
last : index j) : void =
if first < last then
{
val pivot : a =
array_quicksort$select_pivot<a> (arr, first, last)
fun
search_rightwards (arr : &array (a, n),
left : index) : index =
if arr[left] \lt pivot then
let
val () = assertloc (succ left <> n)
in
search_rightwards (arr, succ left)
end
else
left
fun
search_leftwards (arr : &array (a, n),
left : index,
right : index) : index =
if right < left then
right
else if pivot \lt arr[right] then
let
val () = assertloc (right <> i2sz 0)
in
search_leftwards (arr, left, pred right)
end
else
right
fun
partition (arr : &array (a, n) >> _,
left0 : index,
right0 : index) : @(index, index) =
let
val left = search_rightwards (arr, left0)
val right = search_leftwards (arr, left, right0)
in
if left <= right then
let
val () = assertloc (succ left <> n)
and () = assertloc (right <> i2sz 0)
in
swap (arr, left, right);
partition (arr, succ left, pred right)
end
else
@(left, right)
end
val @(left, right) = partition (arr, first, last)
val () = quicksort (arr, first, right)
and () = quicksort (arr, left, last)
}
in
if i2sz 2 <= n then
quicksort {0, n - 1} (arr, i2sz 0, pred n)
end
(*------------------------------------------------------------------*)
val example_strings =
$list ("choose", "any", "element", "of", "the", "array",
"to", "be", "the", "pivot",
"divide", "all", "other", "elements", "except",
"the", "pivot", "into", "two", "partitions",
"all", "elements", "less", "than", "the", "pivot",
"must", "be", "in", "the", "first", "partition",
"all", "elements", "greater", "than", "the", "pivot",
"must", "be", "in", "the", "second", "partition",
"use", "recursion", "to", "sort", "both", "partitions",
"join", "the", "first", "sorted", "partition", "the",
"pivot", "and", "the", "second", "sorted", "partition")
implement
array_quicksort$lt<string> (x, y) =
strcmp (x, y) < 0
implement
array_quicksort$select_pivot<string> {n} (arr, first, last) =
(* Median of three, with swapping around of elements during pivot
selection. See https://archive.ph/oYENx *)
let
macdef lt = array_quicksort$lt<string>
val middle = first + ((last - first) / i2sz 2)
val xfirst = arr[first]
and xmiddle = arr[middle]
and xlast = arr[last]
in
if (xmiddle \lt xfirst) xor (xlast \lt xfirst) then
begin
swap (arr, first, middle);
if xlast \lt xmiddle then
swap (arr, first, last);
xfirst
end
else if (xmiddle \lt xfirst) xor (xmiddle \lt xlast) then
begin
if xlast \lt xfirst then
swap (arr, first, last);
xmiddle
end
else
begin
swap (arr, middle, last);
if xmiddle \lt xfirst then
swap (arr, first, last);
xlast
end
end
implement
main0 () =
let
prval () = lemma_list_param example_strings
val n = length example_strings
val @(pf, pfgc | p) = array_ptr_alloc<string> (i2sz n)
macdef arr = !p
val () = array_initize_list (arr, n, example_strings)
val () = array_quicksort<string> (arr, i2sz n)
val sorted_strings = list_vt2t (array2list (arr, i2sz n))
val () = array_ptr_free (pf, pfgc | p)
fun
print_strings {n : nat} .<n>.
(strings : list (string, n),
i : int) : void =
case+ strings of
| NIL => if i <> 1 then println! () else ()
| head :: tail =>
begin
print! head;
if i = 8 then
begin
println! ();
print_strings (tail, 1)
end
else
begin
print! " ";
print_strings (tail, succ i)
end
end
in
println! (length example_strings);
println! (length sorted_strings);
print_strings (sorted_strings, 1)
end
(*------------------------------------------------------------------*)- Output:
$ patscc -O3 -DATS_MEMALLOC_GCBDW quicksort_task_for_arrays.dats -lgc && ./a.out 62 62 all all all and any array be be be both choose divide element elements elements elements except first first greater in in into join less must must of other partition partition partition partition partitions partitions pivot pivot pivot pivot pivot recursion second second sort sorted sorted than than the the the the the the the the the the to to two use
A quicksort working on arrays of linear elements
The quicksort for arrays of non-linear elements makes a copy of the pivot value, and compares this copy with array elements by value. Here, however, the array elements are linear values. They cannot be copied, unless a special "copy" procedure is provided. We do not want to require such a procedure. So we must do something else.
What we do is move the pivot to the last element of the array, by safely swapping it with the original last element. We partition the array to the left of the last element, comparing array elements with the pivot (that is, the last element) by reference.
(*------------------------------------------------------------------*)
(* Quicksort in ATS2, for arrays of (possibly) linear values. *)
(*------------------------------------------------------------------*)
#include "share/atspre_staload.hats"
#define NIL list_vt_nil ()
#define :: list_vt_cons
(*------------------------------------------------------------------*)
(* A simple quicksort working on arrays of non-linear values, using
a programmer-selectible pivot.
It is based on the "in-place" task pseudocode. *)
extern fun {a : vt@ype} (* A "less-than" predicate. *)
array_quicksort$lt {px, py : addr}
(pfx : !(a @ px),
pfy : !(a @ py) |
px : ptr px,
py : ptr py) : bool
extern fun {a : vt@ype}
array_quicksort$select_pivot_index {n : int}
{i, j : nat | i < j; j < n}
(arr : &array (a, n),
first : size_t i,
last : size_t j)
: [k : int | i <= k; k <= j] size_t k
extern fun {a : vt@ype}
array_quicksort {n : int}
(arr : &array (a, n) >> _,
n : size_t n) : void
(* - - - - - - - - - - - - - - - - - - - - - - *)
prfn (* Subdivide an array view into three views. *)
array_v_subdivide3 {a : vt@ype} {p : addr} {n1, n2, n3 : nat}
(pf : @[a][n1 + n2 + n3] @ p)
:<prf> @(@[a][n1] @ p,
@[a][n2] @ (p + n1 * sizeof a),
@[a][n3] @ (p + (n1 + n2) * sizeof a)) =
let
prval (pf1, pf23) =
array_v_split {a} {p} {n1 + n2 + n3} {n1} pf
prval (pf2, pf3) =
array_v_split {a} {p + n1 * sizeof a} {n2 + n3} {n2} pf23
in
@(pf1, pf2, pf3)
end
prfn (* Join three contiguous array views into one view. *)
array_v_join3 {a : vt@ype} {p : addr} {n1, n2, n3 : nat}
(pf1 : @[a][n1] @ p,
pf2 : @[a][n2] @ (p + n1 * sizeof a),
pf3 : @[a][n3] @ (p + (n1 + n2) * sizeof a))
:<prf> @[a][n1 + n2 + n3] @ p =
let
prval pf23 =
array_v_unsplit {a} {p + n1 * sizeof a} {n2, n3} (pf2, pf3)
prval pf = array_v_unsplit {a} {p} {n1, n2 + n3} (pf1, pf23)
in
pf
end
fn {a : vt@ype} (* Safely swap two elements of an array. *)
swap_elems_1 {n : int}
{i, j : nat | i <= j; j < n}
{p : addr}
(pfarr : !array_v(a, p, n) >> _ |
p : ptr p,
i : size_t i,
j : size_t j) : void =
let
fn {a : vt@ype}
swap {n : int}
{i, j : nat | i < j; j < n}
{p : addr}
(pfarr : !array_v(a, p, n) >> _ |
p : ptr p,
i : size_t i,
j : size_t j) : void =
{
(* Safely swapping linear elements requires that views of
those elements be split off from the rest of the
array. Why? Because those elements will temporarily be in
an uninitialized state. (Actually they will be "?!", but
the difference is unimportant here.)
Remember, a linear value is consumed by using it.
The view for the whole array can be reassembled only after
new values have been stored, making the entire array once
again initialized. *)
prval @(pf1, pf2, pf3) =
array_v_subdivide3 {a} {p} {i, j - i, n - j} pfarr
prval @(pfi, pf2_) = array_v_uncons pf2
prval @(pfj, pf3_) = array_v_uncons pf3
val pi = ptr_add<a> (p, i)
and pj = ptr_add<a> (p, j)
val xi = ptr_get<a> (pfi | pi)
and xj = ptr_get<a> (pfj | pj)
val () = ptr_set<a> (pfi | pi, xj)
and () = ptr_set<a> (pfj | pj, xi)
prval pf2 = array_v_cons (pfi, pf2_)
prval pf3 = array_v_cons (pfj, pf3_)
prval () = pfarr := array_v_join3 (pf1, pf2, pf3)
}
in
if i < j then
swap {n} {i, j} {p} (pfarr | p, i, j)
else
() (* i = j must be handled specially, due to linear typing.*)
end
fn {a : vt@ype} (* Safely swap two elements of an array. *)
swap_elems_2 {n : int}
{i, j : nat | i <= j; j < n}
(arr : &array(a, n) >> _,
i : size_t i,
j : size_t j) : void =
swap_elems_1 (view@ arr | addr@ arr, i, j)
overload swap_elems with swap_elems_1
overload swap_elems with swap_elems_2
overload swap with swap_elems
fn {a : vt@ype} (* Safely compare two elements of an array. *)
lt_elems_1 {n : int}
{i, j : nat | i < n; j < n}
{p : addr}
(pfarr : !array_v(a, p, n) |
p : ptr p,
i : size_t i,
j : size_t j) : bool =
let
fn
compare {n : int}
{i, j : nat | i < j; j < n}
{p : addr}
(pfarr : !array_v(a, p, n) |
p : ptr p,
i : size_t i,
j : size_t j,
gt : bool) : bool =
let
prval @(pf1, pf2, pf3) =
array_v_subdivide3 {a} {p} {i, j - i, n - j} pfarr
prval @(pfi, pf2_) = array_v_uncons pf2
prval @(pfj, pf3_) = array_v_uncons pf3
val pi = ptr_add<a> (p, i)
and pj = ptr_add<a> (p, j)
val retval =
if gt then
array_quicksort$lt<a> (pfj, pfi | pj, pi)
else
array_quicksort$lt<a> (pfi, pfj | pi, pj)
prval pf2 = array_v_cons (pfi, pf2_)
prval pf3 = array_v_cons (pfj, pf3_)
prval () = pfarr := array_v_join3 (pf1, pf2, pf3)
in
retval
end
in
if i < j then
compare {n} {i, j} {p} (pfarr | p, i, j, false)
else if j < i then
compare {n} {j, i} {p} (pfarr | p, j, i, true)
else
false
end
fn {a : vt@ype} (* Safely compare two elements of an array. *)
lt_elems_2 {n : int}
{i, j : nat | i < n; j < n}
(arr : &array (a, n),
i : size_t i,
j : size_t j) : bool =
lt_elems_1 (view@ arr | addr@ arr, i, j)
overload lt_elems with lt_elems_1
overload lt_elems with lt_elems_2
implement {a}
array_quicksort {n} (arr, n) =
let
sortdef index = {i : nat | i < n}
typedef index (i : int) = [0 <= i; i < n] size_t i
typedef index = [i : index] index i
macdef lt = array_quicksort$lt<a>
fun
quicksort {i, j : index}
(arr : &array(a, n) >> _,
first : index i,
last : index j) : void =
if first < last then
{
val pivot =
array_quicksort$select_pivot_index<a> (arr, first, last)
(* Swap the pivot with the last element. *)
val () = swap (arr, pivot, last)
val pivot = last
fun
search_rightwards (arr : &array (a, n),
left : index) : index =
if lt_elems<a> (arr, left, pivot) then
let
val () = assertloc (succ left <> n)
in
search_rightwards (arr, succ left)
end
else
left
fun
search_leftwards (arr : &array (a, n),
left : index,
right : index) : index =
if right < left then
right
else if lt_elems<a> (arr, pivot, right) then
let
val () = assertloc (right <> i2sz 0)
in
search_leftwards (arr, left, pred right)
end
else
right
fun
partition (arr : &array (a, n) >> _,
left0 : index,
right0 : index) : @(index, index) =
let
val left = search_rightwards (arr, left0)
val right = search_leftwards (arr, left, right0)
in
if left <= right then
let
val () = assertloc (succ left <> n)
and () = assertloc (right <> i2sz 0)
in
swap (arr, left, right);
partition (arr, succ left, pred right)
end
else
@(left, right)
end
val @(left, right) = partition (arr, first, pred last)
val () = quicksort (arr, first, right)
and () = quicksort (arr, left, last)
}
in
if i2sz 2 <= n then
quicksort {0, n - 1} (arr, i2sz 0, pred n)
end
(*------------------------------------------------------------------*)
implement
array_quicksort$lt<Strptr1> (pfx, pfy | px, py) =
compare (!px, !py) < 0
implement
array_quicksort$select_pivot_index<Strptr1> {n} (arr, first, last) =
(* Median of three. *)
let
val middle = first + ((last - first) / i2sz 2)
in
if lt_elems<Strptr1> (arr, middle, first)
xor lt_elems<Strptr1> (arr, last, first) then
first
else if lt_elems<Strptr1> (arr, middle, first)
xor lt_elems<Strptr1> (arr, middle, last) then
middle
else
last
end
implement
list_vt_map$fopr<string><Strptr1> (s) = string0_copy s
implement
list_vt_freelin$clear<Strptr1> (x) = strptr_free x
implement
main0 () =
let
val example_strings =
$list_vt
("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")
val example_strptrs =
list_vt_map<string><Strptr1> (example_strings)
prval () = lemma_list_vt_param example_strptrs
val n = length example_strptrs
val @(pf, pfgc | p) = array_ptr_alloc<Strptr1> (i2sz n)
macdef arr = !p
val () = array_initize_list_vt<Strptr1> (arr, n, example_strptrs)
val () = array_quicksort<Strptr1> (arr, i2sz n)
val sorted_strptrs = array2list (arr, i2sz n)
fun
print_strptrs {n : nat} .<n>.
(strptrs : !list_vt (Strptr1, n),
i : int) : void =
case+ strptrs of
| NIL => if i <> 1 then println! () else ()
| @ head :: tail =>
begin
print! head;
if i = 8 then
begin
println! ();
print_strptrs (tail, 1)
end
else
begin
print! " ";
print_strptrs (tail, succ i)
end;
fold@ strptrs
end
in
println! (length example_strings);
println! (length sorted_strptrs);
print_strptrs (sorted_strptrs, 1);
list_vt_freelin<Strptr1> sorted_strptrs;
array_ptr_free (pf, pfgc | p);
list_vt_free<string> example_strings
end
(*------------------------------------------------------------------*)- Output:
$ patscc -O3 -DATS_MEMALLOC_LIBC quicksort_task_for_arrays_2.dats 62 62 all all all and any array be be be both choose divide element elements elements elements except first first greater in in into join less must must of other partition partition partition partition partitions partitions pivot pivot pivot pivot pivot recursion second second sort sorted sorted than than the the the the the the the the the the to to two use
A stable quicksort working on linear lists
See the code at the quickselect task.
- Output:
$ patscc -O3 -DATS_MEMALLOC_LIBC quickselect_task_for_list_vt.dats && ./a.out quicksort stable sort by first character: duck, deer, dolphin, elephant, earwig, giraffe, pronghorn, wildebeest, woodlouse, whip-poor-will
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
}
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);
}
}
BASIC
ANSI BASIC
100 REM Sorting algorithms/Quicksort
110 DECLARE EXTERNAL SUB QuickSort
120 DIM Arr(0 TO 19)
130 LET A = LBOUND(Arr)
140 LET B = UBOUND(Arr)
150 RANDOMIZE
160 FOR I = A TO B
170 LET Arr(I) = ROUND(INT(RND * 99))
180 NEXT I
190 PRINT "Unsorted:"
200 FOR I = A TO B
210 PRINT USING "## ": Arr(I);
220 NEXT I
230 PRINT
240 PRINT "Sorted:"
250 CALL QuickSort(Arr, A, B)
260 FOR I = A TO B
270 PRINT USING "## ": Arr(I);
280 NEXT I
290 PRINT
300 END
310 REM **
320 EXTERNAL SUB QuickSort (Arr(), L, R)
330 LET LIndex = L
340 LET RIndex = R
350 IF R > L THEN
360 LET Pivot = INT((L + R) / 2)
370 DO WHILE (LIndex <= Pivot) AND (RIndex >= Pivot)
380 DO WHILE (Arr(LIndex) < Arr(Pivot)) AND (LIndex <= Pivot)
390 LET LIndex = LIndex + 1
400 LOOP
410 DO WHILE (Arr(RIndex) > Arr(Pivot)) AND (RIndex >= Pivot)
420 LET RIndex = RIndex - 1
430 LOOP
440 LET Temp = Arr(LIndex)
450 LET Arr(LIndex) = Arr(RIndex)
460 LET Arr(RIndex) = Temp
470 LET LIndex = LIndex + 1
480 LET RIndex = RIndex - 1
490 IF (LIndex - 1) = Pivot THEN
500 LET RIndex = RIndex + 1
510 LET Pivot = RIndex
520 ELSEIF (RIndex + 1) = Pivot THEN
530 LET LIndex = LIndex - 1
540 LET Pivot = LIndex
550 END IF
560 LOOP
570 CALL QuickSort (Arr, L, Pivot - 1)
580 CALL QuickSort (Arr, Pivot + 1, R)
590 END IF
600 END SUB
- Output:
(example)
Unsorted: 17 79 23 91 28 91 29 58 47 59 8 35 93 23 34 28 35 31 7 25 Sorted: 7 8 17 23 23 25 28 28 29 31 34 35 35 47 58 59 79 91 91 93
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
- Output:
-31 0 1 2 2 4 65 83 99 782
Chipmunk Basic
100 dim array(15)
110 a = 0
120 b = ubound(array)
130 randomize timer
140 for i = a to b
150 array(i) = rnd(1)*1000
160 next i
170 print "unsort ";
180 for i = a to b
190 print using "####";array(i);
200 if i = b then print ""; else print ", ";
210 next i
220 quicksort(array(),a,b)
230 print : print " sort ";
240 for i = a to b
250 print using "####";array(i);
260 if i = b then print ""; else print ", ";
270 next i
280 print
290 end
300 sub quicksort(array(),l,r)
310 size = r-l+1
320 if size < 2 then return
330 i = l
340 j = r
350 pivot = array(l+int(size/2))
360 rem repeat
370 while array(i) < pivot
380 i = i+1
390 wend
400 while pivot < array(j)
410 j = j-1
420 wend
430 if i <= j then temp = array(i) : array(i) = array(j) : array(j) = temp : i = i+1 : j = j-1
440 if i <= j then goto 360
450 if l < j then quicksort(array(),l,j)
460 if i < r then quicksort(array(),i,r)
470 end sub
Craft Basic
define size = 10, point = 0, top = 0
define high = 0, low = 0, pivot = 0
dim list[size]
dim stack[size]
gosub fill
gosub sort
gosub show
end
sub fill
for i = 0 to size - 1
let list[i] = int(rnd * 100)
next i
return
sub sort
let low = 0
let high = size - 1
let top = -1
let top = top + 1
let stack[top] = low
let top = top + 1
let stack[top] = high
do
if top < 0 then
break
endif
let high = stack[top]
let top = top - 1
let low = stack[top]
let top = top - 1
let i = low - 1
for j = low to high - 1
if list[j] <= list[high] then
let i = i + 1
let t = list[i]
let list[i] = list[j]
let list[j] = t
endif
next j
let point = i + 1
let t = list[point]
let list[point] = list[high]
let list[high] = t
let pivot = i + 1
if pivot - 1 > low then
let top = top + 1
let stack[top] = low
let top = top + 1
let stack[top] = pivot - 1
endif
if pivot + 1 < high then
let top = top + 1
let stack[top] = pivot + 1
let top = top + 1
let stack[top] = high
endif
wait
loop top >= 0
return
sub show
for i = 0 to size - 1
print i, ": ", list[i]
next i
return
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
- Output:
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
FutureBasic
include "NSLog.incl"
local fn Quicksort( qs as CFMutableArrayRef, l as NSInteger, r as NSInteger )
UInt64 size = r - l + 1
if size < 2 then exit fn
NSinteger i = l, j = r
NSinteger pivot = fn NumberIntegerValue( qs[l+size / 2] )
do
while fn NumberIntegerValue( qs[i] ) < pivot
i++
wend
while pivot < fn NumberIntegerValue( qs[j] )
j--
wend
if ( i <= j )
MutableArrayExchangeObjects( qs, i, j )
i++
j--
end if
until i > j
if l < j then fn Quicksort( qs, l, j )
if i < r then fn Quicksort( qs, i, r )
end fn
CFMutableArrayRef qs
CFArrayRef unsorted
NSUInteger i, amount
qs = fn MutableArrayWithCapacity(0)
for i = 0 to 25
if i mod 2 == 0 then amount = 100 else amount = 10000
MutableArrayInsertObjectAtIndex( qs, fn NumberWithInteger( rnd(amount) ), i )
next
unsorted = fn ArrayWithArray( qs )
fn QuickSort( qs, 0, len(qs) - 1 )
NSLog( @"\n-----------------\nUnsorted : Sorted\n-----------------" )
for i = 0 to 25
NSLog( @"%8ld : %-8ld", fn NumberIntegerValue( unsorted[i] ), fn NumberIntegerValue( qs[i] ) )
next
randomize
HandleEvents- Output:
-----------------
Unsorted : Sorted
-----------------
97 : 5
6168 : 30
61 : 34
8847 : 40
55 : 46
2570 : 49
40 : 55
4676 : 61
94 : 62
693 : 67
62 : 79
3419 : 94
30 : 97
936 : 693
5 : 733
9910 : 936
67 : 1395
8460 : 1796
79 : 2570
9352 : 3419
49 : 4676
1395 : 6168
34 : 8460
733 : 8847
46 : 9352
1796 : 9910
IS-BASIC
100 PROGRAM "QuickSrt.bas"
110 RANDOMIZE
120 NUMERIC A(5 TO 19)
130 CALL INIT(A)
140 CALL WRITE(A)
150 CALL QSORT(LBOUND(A),UBOUND(A))
160 CALL WRITE(A)
170 DEF INIT(REF A)
180 FOR I=LBOUND(A) TO UBOUND(A)
190 LET A(I)=RND(98)+1
200 NEXT
210 END DEF
220 DEF WRITE(REF A)
230 FOR I=LBOUND(A) TO UBOUND(A)
240 PRINT A(I);
250 NEXT
260 PRINT
270 END DEF
280 DEF QSORT(AH,FH)
290 NUMERIC E
300 LET E=AH:LET U=FH:LET K=A(E)
310 DO UNTIL E=U
320 DO UNTIL E=U OR A(U)<K
330 LET U=U-1
340 LOOP
350 IF E<U THEN
360 LET A(E)=A(U):LET E=E+1
370 DO UNTIL E=U OR A(E)>K
380 LET E=E+1
390 LOOP
400 IF E<U THEN LET A(U)=A(E):LET U=U-1
410 END IF
420 LOOP
430 LET A(E)=K
440 IF AH<E-1 THEN CALL QSORT(AH,E-1)
450 IF E+1<FH THEN CALL QSORT(E+1,FH)
460 END DEFPureBasic
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
QB64
' Written by Sanmayce, 2021-Oct-29
' The indexes are signed, but the elements are unsigned.
_Define A-Z As _INTEGER64
Sub Quicksort_QB64 (QWORDS~&&())
Left = LBound(QWORDS~&&)
Right = UBound(QWORDS~&&)
LeftMargin = Left
ReDim Stack&&(Left To Right)
StackPtr = 0
StackPtr = StackPtr + 1
Stack&&(StackPtr + LeftMargin) = Left
StackPtr = StackPtr + 1
Stack&&(StackPtr + LeftMargin) = Right
Do 'Until StackPtr = 0
Right = Stack&&(StackPtr + LeftMargin)
StackPtr = StackPtr - 1
Left = Stack&&(StackPtr + LeftMargin)
StackPtr = StackPtr - 1
Do 'Until Left >= Right
Pivot~&& = QWORDS~&&((Left + Right) \ 2)
Indx = Left
Jndx = Right
Do
Do While (QWORDS~&&(Indx) < Pivot~&&)
Indx = Indx + 1
Loop
Do While (QWORDS~&&(Jndx) > Pivot~&&)
Jndx = Jndx - 1
Loop
If Indx <= Jndx Then
If Indx < Jndx Then Swap QWORDS~&&(Indx), QWORDS~&&(Jndx)
Indx = Indx + 1
Jndx = Jndx - 1
End If
Loop While Indx <= Jndx
If Indx < Right Then
StackPtr = StackPtr + 1
Stack&&(StackPtr + LeftMargin) = Indx
StackPtr = StackPtr + 1
Stack&&(StackPtr + LeftMargin) = Right
End If
Right = Jndx
Loop Until Left >= Right
Loop Until StackPtr = 0
End SubQuickBASIC
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
Run BASIC
' -------------------------------
' 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 iTrue BASIC
SUB quicksort (arr(), l, r)
LET lidx = round(l)
LET ridx = round(r)
IF (r-l) > 0 THEN
LET pivot = round((l+r)/2)
DO WHILE (lidx <= pivot) AND (ridx >= pivot)
DO WHILE (arr(lidx) < arr(pivot)) AND (lidx <= pivot)
LET lidx = lidx+1
LOOP
DO WHILE (arr(ridx) > arr(pivot)) AND (ridx >= pivot)
LET ridx = ridx-1
LOOP
LET temp = arr(lidx)
LET arr(lidx) = arr(ridx)
LET arr(ridx) = temp
LET lidx = lidx+1
LET ridx = ridx-1
IF (lidx-1) = pivot THEN
LET ridx = ridx+1
LET pivot = ridx
ELSEIF (ridx+1) = pivot THEN
LET lidx = lidx-1
LET pivot = lidx
END IF
LOOP
CALL quicksort (arr(), l, pivot-1)
CALL quicksort (arr(), pivot+1, r)
END IF
END SUB
DIM arr(15)
LET a = round(LBOUND(arr))
LET b = round(UBOUND(arr))
RANDOMIZE
FOR n = a TO b
LET arr(n) = round(INT(RND*99))
NEXT n
PRINT "unsort ";
FOR n = a TO b
PRINT arr(n); " ";
NEXT n
PRINT
PRINT " sort ";
CALL quicksort (arr(), a, b)
FOR n = a TO b
PRINT arr(n); " ";
NEXT n
END
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
VBA
This is the "simple" quicksort, using temporary arrays.
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
- Output:
quicksorttest 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 a-stuff b-stuff c-stuff d-stuff e-stuff f-stuff g-stuff h-stuff i-stuff j-stuff k-stuff l-stuff m-stuff n-stuff o-stuff p-stuff q-stuff r-stuff s-stuff t-stuff u-stuff v-stuff w-stuff x-stuff y-stuff z-stuff
Note: the "quicksort in place"
VBScript
Function quicksort(arr,s,n)
If n < 2 Then
Exit Function
End If
t = s + n - 1
l = s
r = t
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,",")
- Output:
-1,0,1,2,3,4,5,5,6,7,8,9
Visual Basic
QuickSort without swapping
Sub QuickSort(arr() As Integer, ByVal f As Integer, ByVal l As Integer)
i = f 'First
j = l 'Last
Key = arr(i) 'Pivot
Do While i < j
Do While i < j And Key < arr(j)
j = j - 1
Loop
If i < j Then arr(i) = arr(j): i = i + 1
Do While i < j And Key > arr(i)
i = i + 1
Loop
If i < j Then arr(j) = arr(i): j = j - 1
Loop
arr(i) = Key
If i - 1 > f Then QuickSort arr(), f, i - 1
If j + 1 < l Then QuickSort arr(), j + 1, l
End Sub
XBasic
Note. XBasic has also a standard function XstQuickSort in the xst library.
' Sorting algorithms/Quicksort
PROGRAM "quicksort"
VERSION "1.0"
IMPORT "xst"
DECLARE FUNCTION Entry ()
DECLARE FUNCTION QuickSort (@arr%[], l%%, r%%)
' Pseudo-random number generator
' Based on the rand, srand functions from Kernighan & Ritchie's book
' 'The C Programming Language'
DECLARE FUNCTION Rand()
DECLARE FUNCTION SRand(seed%%)
FUNCTION Entry ()
DIM arr%[19]
a%% = 0
b%% = UBOUND(arr%[])
XstGetSystemTime (@msec)
SRand(INT(msec) MOD 32768)
FOR i%% = a%% TO b%%
arr%[i%%] = INT(Rand() / 32768.0 * 99.0)
NEXT i%%
PRINT "Unsorted:"
FOR i%% = a%% TO b%%
PRINT FORMAT$("## ", arr%[i%%]);
NEXT i%%
PRINT
PRINT "Sorted:"
QuickSort(@arr%[], a%%, b%%)
FOR i%% = a%% TO b%%
PRINT FORMAT$("## ", arr%[i%%]);
NEXT i%%
PRINT
END FUNCTION
FUNCTION QuickSort (@arr%[], l%%, r%%)
leftIndex%% = l%%
rightIndex%% = r%%
IF r%% > l%% THEN
pivot%% = (l%% + r%%) \ 2
DO WHILE (leftIndex%% <= pivot%%) AND (rightIndex%% >= pivot%%)
DO WHILE (arr%[leftIndex%%] < arr%[pivot%%]) AND (leftIndex%% <= pivot%%)
INC leftIndex%%
LOOP
DO WHILE (arr%[rightIndex%%] > arr%[pivot%%]) AND (rightIndex%% >= pivot%%)
DEC rightIndex%%
LOOP
SWAP arr%[leftIndex%%], arr%[rightIndex%%]
INC leftIndex%%
DEC rightIndex%%
SELECT CASE TRUE
CASE leftIndex%% - 1 = pivot%%:
INC rightIndex%%
pivot%% = rightIndex%%
CASE rightIndex%% + 1 = pivot%%:
DEC leftIndex%%
pivot%% = leftIndex%%
END SELECT
LOOP
QuickSort (@arr%[], l%%, pivot%% - 1)
QuickSort (@arr%[], pivot%% + 1, r%%)
END IF
END FUNCTION
' Return pseudo-random integer on 0..32767
FUNCTION Rand()
#next&& = #next&& * 1103515245 + 12345
END FUNCTION USHORT(#next&& / 65536) MOD 32768
' Set seed for Rand()
FUNCTION SRand(seed%%)
#next&& = seed%%
END FUNCTION
END PROGRAM
- Output:
(example)
Unsorted: 18 37 79 14 23 13 64 37 84 37 22 64 25 43 26 13 12 83 21 41 Sorted: 12 13 13 14 18 21 22 23 25 26 37 37 37 41 43 64 64 79 83 84
Yabasic
Rosetta Code problem: https://rosettacode.org/wiki/Sorting_algorithms/Quicksort
by Jjuanhdez, 03/2023
dim array(15)
a = 0
b = arraysize(array(),1)
for i = a to b
array(i) = ran(1000)
next i
print "unsort ";
for i = a to b
print array(i) using("####");
if i = b then print ""; else print ", "; : fi
next i
quickSort(array(), a, b)
print "\n sort ";
for i = a to b
print array(i) using("####");
if i = b then print ""; else print ", "; : fi
next i
print
end
sub quickSort(array(), l, r)
local asize, i, j, pivot
size = r - l +1
if size < 2 return
i = l
j = r
pivot = array(l + int(size / 2))
repeat
while array(i) < pivot
i = i + 1
wend
while pivot < array(j)
j = j - 1
wend
if i <= j then
temp = array(i)
array(i) = array(j)
array(j) = temp
i = i + 1
j = j - 1
fi
until i > j
if l < j quickSort(array(), l, j)
if i < r quickSort(array(), i, r)
end sub
- Output:
unsort 582, 796, 598, 478, 27, 125, 477, 679, 133, 513, 154, 93, 451, 463, 20 sort 20, 27, 93, 125, 133, 154, 451, 463, 477, 478, 513, 582, 598, 679, 796
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()
}Beads
beads 1 program Quicksort
calc main_init
var arr = [1, 3, 5, 1, 7, 9, 8, 6, 4, 2]
var arr2 = arr
quicksort(arr, 1, tree_count(arr))
var tempStr : str
loop across:arr index:ix
tempStr = tempStr & ' ' & to_str(arr[ix])
log tempStr
calc quicksort(
arr:array of num
startIndex
highIndex
)
if (startIndex < highIndex)
var partitionIndex = partition(arr, startIndex, highIndex)
quicksort(arr, startIndex, partitionIndex - 1)
quicksort(arr, partitionIndex+1, highIndex)
calc partition(
arr:array of num
startIndex
highIndex
):num
var pivot = arr[highIndex]
var i = startIndex - 1
var j = startIndex
loop while:(j <= highIndex - 1)
if arr[j] < pivot
inc i
swap arr[i] <=> arr[j]
inc j
swap arr[i+1] <=> arr[highIndex]
return (i+1)- Output:
1 1 2 3 4 5 6 7 8 9
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)
);- Output:
90 1900 4001/2 Quicksort are features languages of of optimized variants (quick,sober) (quick,sort)
Bruijn
:import std/Combinator .
:import std/Number .
:import std/List .
sort y [[0 [[[case-sort]]] case-end]]
case-sort (4 lesser) ++ (2 : (4 greater))
lesser (\lt? 2) <#> 1
greater (\ge? 2) <#> 1
case-end empty
:test (sort ((+3) : ((+2) : {}(+1)))) ((+1) : ((+2) : {}(+3)))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);
}
- Output:
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 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 RosettaCode {
using System;
using System.Diagnostics;
public class QuickSort<T> where T : IComparable {
#region Constants
public const UInt32 INSERTION_LIMIT_DEFAULT = 12;
private const Int32 SAMPLES_MAX = 19;
#endregion
#region Properties
public UInt32 InsertionLimit { get; }
private T[] Samples { get; }
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(UInt32 insertionLimit = INSERTION_LIMIT_DEFAULT) {
this.InsertionLimit = insertionLimit;
this.Samples = new T[SAMPLES_MAX];
}
#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;
var median = pivot(entries);
partition(median, 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;
}
}
}
/// <summary>Return an odd sample size proportional to the log of a large interval size.</summary>
private static Int32 sampleSize(Int32 length, Int32 max = SAMPLES_MAX) {
var logLen = (Int32)Math.Log10(length);
var samples = Math.Min(2 * logLen + 1, max);
return Math.Min(samples, length);
}
/// <summary>Estimate the median value of entries[Left:Right]</summary>
/// <remarks>A sample median is used as an estimate the true median.</remarks>
private T pivot(T[] entries) {
var length = Right + 1 - Left;
var samples = sampleSize(length);
// Sample Linearly:
for (var sample = 0; sample < samples; sample++) {
// Guard against Arithmetic Overflow:
var index = (Int64)length * sample / samples + Left;
Samples[sample] = entries[index];
}
InsertionSort<T>.Sort(Samples, 0, samples - 1);
return Samples[samples / 2];
}
private void partition(T median, 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(median, 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 median, 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--);
}
/// <summary>Swap entries at the left and right indicies.</summary>
public void Swap(T[] entries, Int32 left, Int32 right) {
Swap(ref entries[left], ref entries[right]);
}
/// <summary>Swap two entities of type T.</summary>
public static void Swap(ref T e1, ref T e2) {
var e = e1;
e1 = e2;
e2 = e;
}
#endregion
}
#region Insertion Sort
static class InsertionSort<T> where T : IComparable {
public static void Sort(T[] entries, Int32 first, Int32 last) {
for (var next = first + 1; next <= last; next++)
insert(entries, first, next);
}
/// <summary>Bubble next entry up to its sorted location, assuming entries[first:next - 1] are already sorted.</summary>
private static void insert(T[] entries, Int32 first, Int32 next) {
var entry = entries[next];
while (next > first && entries[next - 1].CompareTo(entry) > 0)
entries[next] = entries[--next];
entries[next] = 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));
}
}
- Output:
1 2 3 4 5 6 7 8 9
A very inefficient way to do qsort in C# to prove C# code can be just as compact and readable as any dynamic code
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;
}
}
}
CafeOBJ
There is no builtin list type in CafeOBJ, so a user written list module is included.
mod! SIMPLE-LIST(X :: TRIV){
[NeList < List ]
op [] : -> List
op [_] : Elt -> List
op (_:_) : Elt List -> NeList -- consr
op _++_ : List List -> List {assoc} -- concatenate
var E : Elt
vars L L' : List
eq [ E ] = E : [] .
eq [] ++ L = L .
eq (E : L) ++ L' = E : (L ++ L') .
}
mod! QUICKSORT{
pr(SIMPLE-LIST(NAT))
op qsort_ : List -> List
op smaller__ : List Nat -> List
op larger__ : List Nat -> List
vars x y : Nat
vars xs ys : List
eq qsort [] = [] .
eq qsort (x : xs) = (qsort (smaller xs x)) ++ [ x ] ++ (qsort (larger xs x)) .
eq smaller [] x = [] .
eq smaller (x : xs) y = if x <= y then (x : (smaller xs y)) else (smaller xs y) fi .
eq larger [] x = [] .
eq larger (x : xs) y = if x <= y then (larger xs y) else (x : (larger xs y)) fi .
}
open QUICKSORT .
red qsort(5 : 4 : 3 : 2 : 1 : 0 : []) .
red qsort(5 : 5 : 4 : 3 : 5 : 2 : 1 : 1 : 0 : []) .
eofC++
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>());
}
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
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))))))
Cowgol
include "cowgol.coh";
# Comparator interface, on the model of C, i.e:
# foo < bar => -1, foo == bar => 0, foo > bar => 1
typedef CompRslt is int(-1, 1);
interface Comparator(foo: intptr, bar: intptr): (rslt: CompRslt);
# Quicksort an array of pointer-sized integers given a comparator function
# (This is the closest you can get to polymorphism in Cowgol).
# Because Cowgol does not support recursion, a pointer to free memory
# for a stack must also be given.
sub qsort(A: [intptr], len: intptr, comp: Comparator, stack: [intptr]) is
# The partition function can be taken almost verbatim from Wikipedia
sub partition(lo: intptr, hi: intptr): (p: intptr) is
# This is not quite as bad as it looks: /2 compiles into a single shift
# and "@bytesof intptr" is always power of 2 so compiles into shift(s).
var pivot := [A + (hi/2 + lo/2) * @bytesof intptr];
var i := lo - 1;
var j := hi + 1;
loop
loop
i := i + 1;
if comp([A + i*@bytesof intptr], pivot) != -1 then
break;
end if;
end loop;
loop
j := j - 1;
if comp([A + j*@bytesof intptr], pivot) != 1 then
break;
end if;
end loop;
if i >= j then
p := j;
return;
end if;
var ii := i * @bytesof intptr;
var jj := j * @bytesof intptr;
var t := [A+ii];
[A+ii] := [A+jj];
[A+jj] := t;
end loop;
end sub;
# Cowgol lacks recursion, so we'll have to solve it by implementing
# the stack ourselves.
var sp: intptr := 0; # stack index
sub push(n: intptr) is
sp := sp + 1;
[stack] := n;
stack := @next stack;
end sub;
sub pop(): (n: intptr) is
sp := sp - 1;
stack := @prev stack;
n := [stack];
end sub;
# start by sorting [0..length-1]
push(len-1);
push(0);
while sp != 0 loop
var lo := pop();
var hi := pop();
if lo < hi then
var p := partition(lo, hi);
push(hi); # note the order - we need to push the high pair
push(p+1); # first for it to be done last
push(p);
push(lo);
end if;
end loop;
end sub;
# Test: sort a list of numbers
sub NumComp implements Comparator is
# Compare the inputs as numbers
if foo < bar then rslt := -1;
elseif foo > bar then rslt := 1;
else rslt := 0;
end if;
end sub;
# Numbers
var numbers: intptr[] := {
65,13,4,84,29,5,96,73,5,11,17,76,38,26,44,20,36,12,44,51,79,8,99,7,19,95,26
};
# Room for the stack
var stackbuf: intptr[256];
# Sort the numbers in place
qsort(&numbers as [intptr], @sizeof numbers, NumComp, &stackbuf as [intptr]);
# Print the numbers (hopefully in order)
var i: @indexof numbers := 0;
while i < @sizeof numbers loop
print_i32(numbers[i] as uint32);
print_char(' ');
i := i + 1;
end loop;
print_nl();- Output:
4 5 5 7 8 11 12 13 17 19 20 26 26 29 36 38 44 44 51 65 73 76 79 84 95 96 99
Crystal
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 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 : writefln, writeln;
import std.algorithm: filter;
import std.array;
T[] quickSort(T)(T[] xs) =>
xs.length == 0 ? [] :
xs[1 .. $].filter!(x => x< xs[0]).array.quickSort ~
xs[0 .. 1] ~
xs[1 .. $].filter!(x => x>=xs[0]).array.quickSort;
void main() =>
[4, 65, 2, -31, 0, 99, 2, 83, 782, 1].quickSort.writeln;
- Output:
[-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;
}
Delphi
This quick sort routine is infinitely versatile. It sorts an array of pointers. The advantage of this is that pointers can contain anything, ranging from integers, to strings, to floating point numbers to objects. The way each pointer is interpreted is through the compare routine, which is customized for the particular situation. The compare routine can interpret each pointer as a string, an integer, a float or an object and it can treat those items in different ways. For example, the order in which it compares strings controls whether the sort is alphabetical or reverse alphabetical. In this case, I show an integer sort, an alphabetic string sort, a reverse alphabetical string sort and a string sort by length.
{Dynamic array of pointers}
type TPointerArray = array of Pointer;
procedure QuickSort(SortList: TPointerArray; L, R: Integer; SCompare: TListSortCompare);
{Do quick sort on items held in TPointerArray}
{SCompare controls how the pointers are interpreted}
var I, J: Integer;
var P,T: Pointer;
begin
repeat
begin
I := L;
J := R;
P := SortList[(L + R) shr 1];
repeat
begin
while SCompare(SortList[I], P) < 0 do Inc(I);
while SCompare(SortList[J], P) > 0 do Dec(J);
if I <= J then
begin
{Exchange itesm}
T:=SortList[I];
SortList[I]:=SortList[J];
SortList[J]:=T;
if P = SortList[I] then P := SortList[J]
else if P = SortList[J] then P := SortList[I];
Inc(I);
Dec(J);
end;
end
until I > J;
if L < J then QuickSort(SortList, L, J, SCompare);
L := I;
end
until I >= R;
end;
procedure DisplayStrings(Memo: TMemo; PA: TPointerArray);
{Display pointers as strings}
var I: integer;
var S: string;
begin
S:='[';
for I:=0 to High(PA) do
begin
if I>0 then S:=S+' ';
S:=S+string(PA[I]^);
end;
S:=S+']';
Memo.Lines.Add(S);
end;
procedure DisplayIntegers(Memo: TMemo; PA: TPointerArray);
{Display pointer array as integers}
var I: integer;
var S: string;
begin
S:='[';
for I:=0 to High(PA) do
begin
if I>0 then S:=S+' ';
S:=S+IntToStr(Integer(PA[I]));
end;
S:=S+']';
Memo.Lines.Add(S);
end;
function IntCompare(Item1, Item2: Pointer): Integer;
{Compare for integer sort}
begin
Result:=Integer(Item1)-Integer(Item2);
end;
function StringCompare(Item1, Item2: Pointer): Integer;
{Compare for alphabetical string sort}
begin
Result:=AnsiCompareText(string(Item1^),string(Item2^));
end;
function StringRevCompare(Item1, Item2: Pointer): Integer;
{Compare for reverse alphabetical order}
begin
Result:=AnsiCompareText(string(Item2^),string(Item1^));
end;
function StringLenCompare(Item1, Item2: Pointer): Integer;
{Compare for string length sort}
begin
Result:=Length(string(Item1^))-Length(string(Item2^));
end;
{Arrays of strings and integers}
var IA: array [0..9] of integer = (23, 14, 62, 28, 56, 91, 33, 30, 75, 5);
var SA: array [0..15] of string = ('Now','is','the','time','for','all','good','men','to','come','to','the','aid','of','the','party.');
procedure ShowQuickSort(Memo: TMemo);
var L: TStringList;
var PA: TPointerArray;
var I: integer;
begin
Memo.Lines.Add('Integer Sort');
SetLength(PA,Length(IA));
for I:=0 to High(IA) do PA[I]:=Pointer(IA[I]);
Memo.Lines.Add('Before Sorting');
DisplayIntegers(Memo,PA);
QuickSort(PA,0,High(PA),IntCompare);
Memo.Lines.Add('After Sorting');
DisplayIntegers(Memo,PA);
Memo.Lines.Add('');
Memo.Lines.Add('String Sort - Alphabetical');
SetLength(PA,Length(SA));
for I:=0 to High(SA) do PA[I]:=Pointer(@SA[I]);
Memo.Lines.Add('Before Sorting');
DisplayStrings(Memo,PA);
QuickSort(PA,0,High(PA),StringCompare);
Memo.Lines.Add('After Sorting');
DisplayStrings(Memo,PA);
Memo.Lines.Add('');
Memo.Lines.Add('String Sort - Reverse Alphabetical');
QuickSort(PA,0,High(PA),StringRevCompare);
Memo.Lines.Add('After Sorting');
DisplayStrings(Memo,PA);
Memo.Lines.Add('');
Memo.Lines.Add('String Sort - By Length');
QuickSort(PA,0,High(PA),StringLenCompare);
Memo.Lines.Add('After Sorting');
DisplayStrings(Memo,PA);
end;
- Output:
Integer Sort Before Sorting [23 14 62 28 56 91 33 30 75 5] After Sorting [5 14 23 28 30 33 56 62 75 91] String Sort - Alphabetical Before Sorting [Now is the time for all good men to come to the aid of the party.] After Sorting [aid all come for good is men Now party. of the the the time to to] String Sort - Reverse Alphabetical After Sorting [to to time the the the party. of Now men is good for come all aid] String Sort - By Length After Sorting [of is to to men aid all for Now the the the time come good party.] Elapsed Time: 16.478 ms.
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
proc qsort left right . d[] .
if left >= right
return
.
mid = left
for i = left + 1 to right
if d[i] < d[left]
mid += 1
swap d[i] d[mid]
.
.
swap d[left] d[mid]
qsort left mid - 1 d[]
qsort mid + 1 right d[]
.
proc sort . d[] .
qsort 1 len d[] d[]
.
d[] = [ 29 4 72 44 55 26 27 77 92 5 ]
sort d[]
print d[]
- Output:
[ 4 5 26 27 29 44 55 72 77 92 ]
EchoLisp
(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)))))
- Output:
(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.
#import <Foundation/Foundation.h>
void quicksortInPlace(MutableArray array, const long first, const long last)
if first >= last
return
Value pivot = array[(first + last) / 2]
left := first
right := last
while left <= right
while array[left] < pivot
left++
while array[right] > pivot
right--
if left <= right
array.exchangeObjectAtIndex: left++, withObjectAtIndex: right--
quicksortInPlace(array, first, right)
quicksortInPlace(array, left, last)
Array quicksort(Array unsorted)
a := []
a.addObjectsFromArray: unsorted
quicksortInPlace(a, 0, a.count - 1)
return a
int main(int argc, const char * argv[])
autoreleasepool
a := [1, 3, 5, 7, 9, 8, 6, 4, 2]
Log( 'Unsorted: %@', a)
Log( 'Sorted: %@', quicksort(a) )
b := ['Emil', 'Peg', 'Helen', 'Juergen', 'David', 'Rick', 'Barb', 'Mike', 'Tom']
Log( 'Unsorted: %@', b)
Log( 'Sorted: %@', quicksort(b) )
return 0
Alternative implementation (not necessarily as efficient, but very readable)
#import <Foundation/Foundation.h>
implementation Array (Quicksort)
plus: Array array, return Array =
self.arrayByAddingObjectsFromArray: array
filter: BOOL (^)(id) predicate, return Array
array := []
for id item in self
if predicate(item)
array.addObject: item
return array.copy
quicksort, return Array = self
if self.count > 1
id x = self[self.count / 2]
lesser := self.filter: (id y | return y < x)
greater := self.filter: (id y | return y > x)
return lesser.quicksort + [x] + greater.quicksort
end
int main()
autoreleasepool
a := [1, 3, 5, 7, 9, 8, 6, 4, 2]
Log( 'Unsorted: %@', a)
Log( 'Sorted: %@', a.quicksort )
b := ['Emil', 'Peg', 'Helen', 'Juergen', 'David', 'Rick', 'Barb', 'Mike', 'Tom']
Log( 'Unsorted: %@', b)
Log( 'Sorted: %@', b.quicksort )
return 0
- Output:
2013-09-04 16:54:31.780 a.out[2201:507] Unsorted: (
1,
3,
5,
7,
9,
8,
6,
4,
2
)
2013-09-04 16:54:31.781 a.out[2201:507] Sorted: (
1,
2,
3,
4,
5,
6,
7,
8,
9
)
2013-09-04 16:54:31.781 a.out[2201:507] Unsorted: (
Emil,
Peg,
Helen,
Juergen,
David,
Rick,
Barb,
Mike,
Tom
)
2013-09-04 16:54:31.782 a.out[2201:507] Sorted: (
Barb,
David,
Emil,
Helen,
Juergen,
Mike,
Peg,
Rick,
Tom
)
Eiffel
The
QUICKSORT
class:
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 6.x :
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());
}- Output:
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.
Emacs Lisp
Unoptimized
(require 'seq)
(defun quicksort (xs)
(if (null xs)
()
(let* ((head (car xs))
(tail (cdr xs))
(lower-part (quicksort (seq-filter (lambda (x) (<= x head)) tail)))
(higher-part (quicksort (seq-filter (lambda (x) (> x head)) tail))))
(append lower-part (list head) higher-part))))
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 PROGRAMF#
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 ;
Fe
; utility for list joining
(= join (fn (a b)
(if (is a nil) b (is b nil) a (do
(let res a)
(while (cdr a) (= a (cdr a)))
(setcdr a b)
res))))
(= quicksort (fn (lst)
(if (not (cdr lst)) lst (do
(let pivot (car lst))
(let less nil)
(let equal nil)
(let greater nil)
; filter list for less than pivot, equal to pivot and greater than pivot
(while lst
(let x (car lst))
(if (< x pivot) (= less (cons x less))
(< pivot x) (= greater (cons x greater))
(= equal (cons x equal)))
(= lst (cdr lst)))
; sort 'less' and 'greater' partitions ('equal' partition is always sorted)
(= less (quicksort less))
(= greater (quicksort greater))
; join partitions to one
(join less (join equal greater))))))
(print '(4 65 0 2 -31 99 2 0 83 782 1))
(print (quicksort '(4 65 0 2 -31 99 2 0 83 782 1)))
Outputs:
(4 65 0 2 -31 99 2 0 83 782 1)
(-31 0 0 1 2 2 4 65 83 99 782)
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
recursive subroutine fsort(a)
use inserts, only:insertion_sort !Not included in this posting
implicit none
!
! PARAMETER definitions
!
integer, parameter :: changesize = 64
!
! Dummy arguments
!
real, dimension(:) ,contiguous :: a
intent (inout) a
!
! Local variables
!
integer :: first = 1
integer :: i
integer :: j
integer :: last
logical :: stay
real :: t
real :: x
!
!*Code
!
last = size(a, 1)
if( (last - first)<changesize )then
call insertion_sort(a(first:last))
return
end if
j = shiftr((first + last), 1) + 1
!
x = a(j)
i = first
j = last
stay = .true.
do while ( stay )
do while ( a(i)<x )
i = i + 1
end do
do while ( x<a(j) )
j = j - 1
end do
if( j<i )then
stay = .false.
else
t = a(i) ! Swap the values
a(i) = a(j)
a(j) = t
i = i + 1 ! Adjust the pointers (PIVOT POINTS)
j = j - 1
end if
end do
if( first<i - 1 )call fsort(a(first:i - 1)) ! We still have some left to do on the lower
if( j + 1<last )call fsort(a(j + 1:last)) ! We still have some left to do on the upper
return
end subroutine fsort
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"]) )- Output:
[0, 1, 2, 2, 3, 4] [Daniel, Ethan, Jacob, Juan, Liam, Miguel, William]
Go
Note that Go's sort.Sort function is a Quicksort so in practice it would be just be used.
It's actually a combination of quick sort, heap sort, and insertion sort.
It starts with a quick sort, after a depth of 2*ceil(lg(n+1)) it switches to heap sort, or once a partition becomes small (less than eight items) it switches to insertion sort.
Old school, following Hoare's 1962 paper.
As a nod to the task request to work for all types with weak strict ordering, code below uses the < operator when comparing key values. The three points are noted in the code below.
Actually supporting arbitrary types would then require at a minimum a user supplied less-than function, and values referenced from an array of interface{} types. More efficient and flexible though is the sort interface of the Go sort package. Replicating that here seemed beyond the scope of the task so code was left written to sort an array of ints.
Go has no language support for indexing with discrete types other than integer types, so this was not coded.
Finally, the choice of a recursive closure over passing slices to a recursive function is really just a very small optimization. Slices are cheap because they do not copy the underlying array, but there's still a tiny bit of overhead in constructing the slice object. Passing just the two numbers is in the interest of avoiding that overhead.
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)
}
- Output:
unsorted: [31 41 59 26 53 58 97 93 23 84] sorted! [23 26 31 41 53 58 59 84 93 97]
More traditional version of quicksort. It work generically with any container that conforms to sort.Interface.
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)
}
- Output:
Unsorted: [1 3 5 7 9 8 6 4 2] Sorted: [1 2 3 4 5 6 7 8 9] Unsorted: [Emil Peg Helen Juergen David Rick Barb Mike Tom] Sorted: [Barb David Emil Helen Juergen Mike Peg Rick Tom]
Haskell
The famous two-liner, reflecting the underlying algorithm directly:
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
Icon and Unicon
Implementation notes:
- Since this transparently sorts both string and list arguments the result must 'return' to bypass call by value (strings)
- The partition procedure must "return" two values - 'suspend' is used to accomplish this
Algorithm notes:
- The use of a type specific sorting operator meant that a general pivot choice need to be made. The median of the ends and random middle seemed reasonable. It turns out to have been suggested by Sedgewick.
- Sedgewick's suggestions for tail calling to recurse into the larger side and using insertion sort below a certain size were not implemented. (Q: does Icon/Unicon has tail calling optimizations?)
Note: This example relies on the supporting procedures 'sortop', and 'demosort' in Bubble Sort. The full demosort exercises the named sort of a list with op = "numeric", "string", ">>" (lexically gt, descending),">" (numerically gt, descending), a custom comparator, and also a string.
- Output:
Abbreviated
Sorting Demo using procedure quicksort
on list : [ 3 14 1 5 9 2 6 3 ]
with op = &null: [ 1 2 3 3 5 6 9 14 ] (0 ms)
...
on string : "qwerty"
with op = &null: "eqrtwy" (0 ms)
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
Idris
quicksort : Ord elem => List elem -> List elem
quicksort [] = []
quicksort (x :: xs) =
let lesser = filter (< x) xs
greater = filter(>= x) xs in
(quicksort lesser) ++ [x] ++ (quicksort greater)
Example:
*quicksort> quicksort [1, 3, 7, 2, 5, 4, 9, 6, 8, 0] [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] : List Integer
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 [github ] repository.
Isabelle
theory Quicksort
imports Main
begin
fun quicksort :: "('a :: linorder) list ⇒ 'a list" where
"quicksort [] = []"
| "quicksort (x#xs) = (quicksort [y←xs. y<x]) @ [x] @ (quicksort [y←xs. y>x])"
lemma "quicksort [4::int, 2, 7, 1] = [1, 2, 4, 7]"
by(code_simp)
lemma set_first_second_partition:
fixes x :: "'a :: linorder"
shows "{y ∈ ys. y < x} ∪ {x} ∪ {y ∈ ys. x < y} =
insert x ys"
by fastforce
lemma set_quicksort: "set (quicksort xs) = set xs"
by(induction xs rule: quicksort.induct)
(simp add: set_first_second_partition[simplified])+
theorem "sorted (quicksort xs)"
proof(induction xs rule: quicksort.induct)
case 1
show "sorted (quicksort [])" by simp
next
case (2 x xs)
assume IH_less: "sorted (quicksort [y←xs. y<x])"
assume IH_greater: "sorted (quicksort [y←xs. y>x])"
have pivot_geq_first_partition:
"∀z∈set (quicksort [y←xs. y<x]). z ≤ x"
by (simp add: set_quicksort less_imp_le)
have pivot_leq_second_partition:
"∀z ∈ (set (quicksort [y←xs. y>x])). (x ≤ z)"
by (simp add: set_quicksort less_imp_le)
have first_partition_leq_second_partition:
"∀p∈set (quicksort [y←xs. y<x]).
∀z ∈ (set (quicksort [y←xs. y>x])). (p ≤ z)"
by (auto simp add: set_quicksort)
from IH_less IH_greater
pivot_geq_first_partition pivot_leq_second_partition
first_partition_leq_second_partition
show "sorted (quicksort (x # xs))" by(simp add: sorted_append)
qed
text‹
The specification on rosettacode says
▪ All elements less than the pivot must be in the first partition.
▪ All elements greater than the pivot must be in the second partition.
Since this specification neither says "less than or equal" nor
"greater or equal", this quicksort implementation removes duplicate elements.
›
lemma "quicksort [1::int, 1, 1, 2, 2, 3] = [1, 2, 3]"
by(code_simp)
text‹If we try the following, we automatically get a counterexample›
lemma "length (quicksort xs) = length xs"
(*
Auto Quickcheck found a counterexample:
xs = [a⇩1, a⇩1]
Evaluated terms:
length (quicksort xs) = 1
length xs = 2
*)
oops
end
J
A two-partition tacit version with random pivot:
qsort=: (((<:#[) ,&$: (>#[)) (?@#{]))^:(1<#@~.)
Use:
qsort 7 4 1 5 9 8 2 4 6
- Output:
1 2 4 4 5 6 7 8 9
A three-partition explicit version broken into smaller steps:
sel=: 1 : 'u # ]'
quicksort=: 3 : 0
if.
1 >: #y
do.
y
else.
p=. y{~?#y
(quicksort y <sel p),(y =sel p),quicksort y >sel p
end.
)
See the Quicksort essay in the J Wiki for additional explanations and examples.
Java
Imperative
public static <E extends Comparable<? super E>> List<E> 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
public static <E extends Comparable<E>> List<E> 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; });
- Output:
[ 1, 3, 10, 11, 15, 19 ]
Functional
ES6
Using destructuring and satisfying immutability we can propose a single expresion solution (from https://github.com/ddcovery/expressive_sort)
const qsort = ([pivot, ...others]) =>
pivot === void 0 ? [] : [
...qsort(others.filter(n => n < pivot)),
pivot,
...qsort(others.filter(n => n >= pivot))
];
qsort( [ 11.8, 14.1, 21.3, 8.5, 16.7, 5.7 ] )
- Output:
[ 5.7, 8.5, 11.8, 14.1, 16.7, 21.3 ]
ES5
Unlike what happens with ES6, there are no destructuring nor lambdas, but we can ensure immutability and propose a single expression solution with standard anonymous functions
function qsort( xs ){
return xs.length === 0 ? [] : [].concat(
qsort( xs.slice(1).filter(function(x){ return x< xs[0] })),
xs[0],
qsort( xs.slice(1).filter(function(x){ return x>= xs[0] }))
)
}
qsort( [ 11.8, 14.1, 21.3, 8.5, 16.7, 5.7 ] )
- Output:
[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 listsjq
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- Output:
[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] += [$x] # add x to greater
end
)
| (.[0] | quicksort ) + .[1] + (.[2] | quicksort )
end ;Fortunately, the example input used above produces the same output,
and so both are omitted here.
Julia
Built-in function for in-place sorting via quicksort (the code from the standard library is quite readable):
sort!(A, alg=QuickSort)
A simple polymorphic implementation of an in-place recursive quicksort (based on the pseudocode above):
function quicksort!(A,i=1,j=length(A))
if j > i
pivot = A[rand(i:j)] # random element of A
left, right = i, j
while left <= right
while A[left] < pivot
left += 1
end
while A[right] > pivot
right -= 1
end
if left <= right
A[left], A[right] = A[right], A[left]
left += 1
right -= 1
end
end
quicksort!(A,i,right)
quicksort!(A,left,j)
end
return A
end
A one-line (but rather inefficient) implementation based on the Haskell version, which operates out-of-place and allocates temporary arrays:
qsort(L) = isempty(L) ? L : vcat(qsort(filter(x -> x < L[1], L[2:end])), L[1:1], qsort(filter(x -> x >= L[1], L[2:end])))
- Output:
julia> A = [84,77,20,60,47,20,18,97,41,49,31,39,73,68,65,52,1,92,15,9] julia> qsort(A) [1,9,15,18,20,20,31,39,41,47,49,52,60,65,68,73,77,84,92,97] julia> quicksort!(copy(A)) [1,9,15,18,20,20,31,39,41,47,49,52,60,65,68,73,77,84,92,97] julia> qsort(A) == quicksort!(copy(A)) == sort(A) == sort(A, alg=QuickSort) true
K
qsort:{$[2>#?x;x;,/o'x@&'~:\x<*1?x]}
This version partitions the array into [elements greater than or equal to the pivot], and [those less than the pivot], stopping recursion when the subarray contains only one unique element.
The $[...] works as $[if;then;else].
x<*1?x
selects a random pivot and gives a logical mask (vector of 0’s and 1’s) where a 1 at index n indicates that the element at n is less than the pivot.
f\
successively applies f until the result converges (i.e., yields a result from a prior iteration), and collects the intermediate results (including the initial argument). Since f is negation here, this happens after one iteration. Each mask is coupled with its negation, e.g., ~:\0 1 1 produces (0 1 1;1 0 0).
x@&'
converts each logical mask into corresponding indices, and uses them to index into array x, yielding the two partitions.
Finally,
,/o'
recurses on each partition and joins the results.
A 3-partition version (faster if many elements are equal):
quicksort:{p:*x[1?#x];:[0=#x;x;,/(_f x[&x<p];x[&x=p];_f x[&x>p])]}
Example:
quicksort 1 3 5 7 9 8 6 4 2
- Output:
1 2 3 4 5 6 7 8 9
Explanation:
_fis the current function called recursively.
:[....]generally means :[condition1;then1;condition2;then2;....;else]. Here it is used as :[if;then;else].
This construct
p:*x[1?#x]assigns a random element in x (the argument) to p, 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<p] / sort (recursively) elements less than pivot p
x[&x=p] / elements equal to p
_f x[&x>p]) / sort (recursively) elements greater than p
]Note that - 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 2Koka
Haskell-like solution
fun qsort( xs : list<int> ) : div list<int> {
match(xs) {
Cons(x,xx) -> {
val ys = xx.filter fn(el) { el < x }
val zs = xx.filter fn(el) { el >= x }
qsort(ys) ++ [x] ++ qsort(zs)
}
Nil -> Nil
}
}or using standard partition function
fun qsort( xs : list<int> ) : div list<int> {
match(xs) {
Cons(x,xx) -> {
val (ys, zs) = xx.partition fn(el) { el < x }
qsort(ys) ++ [x] ++ qsort(zs)
}
Nil -> Nil
}
}Example:
fun main() {
val arr = [24,63,77,26,84,64,56,80,85,17]
println(arr.qsort.show)
}- Output:
[17,24,26,56,63,64,77,80,84,85]
Kotlin
A version that reflects the algorithm directly:
fun <E : Comparable<E>> List<E>.qsort(): List<E> =
if (size < 2) this
else filter { it < first() }.qsort() +
filter { it == first() } +
filter { it > first() }.qsort()A more efficient version that does only one comparison per element:
fun <E : Comparable<E>> List<E>.qsort(): List<E> =
if (size < 2) this
else {
val (less, high) = subList(1, size).partition { it < first() }
less.qsort() + first() + high.qsort()
}Lambdatalk
We create a binary tree from a random array, then we walk the canopy.
1) three functions for readability:
{def BT.data {lambda {:t} {A.get 0 :t}}} -> BT.data
{def BT.left {lambda {:t} {A.get 1 :t}}} -> BT.left
{def BT.right {lambda {:t} {A.get 2 :t}}} -> BT.right
2) adding a leaf to the tree:
{def BT.add {lambda {:x :t}
{if {A.empty? :t}
then {A.new :x {A.new} {A.new}}
else {if {= :x {BT.data :t}}
then :t
else {if {< :x {BT.data :t}}
then {A.new {BT.data :t}
{BT.add :x {BT.left :t}}
{BT.right :t}}
else {A.new {BT.data :t}
{BT.left :t}
{BT.add :x {BT.right :t}} }}}}}}
-> BT.add
3) creating the tree from an array of numbers:
{def BT.create
{def BT.create.rec
{lambda {:l :t}
{if {A.empty? :l}
then :t
else {BT.create.rec {A.rest :l}
{BT.add {A.first :l} :t}} }}}
{lambda {:l}
{BT.create.rec :l {A.new}} }}
-> BT.create
4) walking the canopy -> sorting in increasing order:
{def BT.sort
{lambda {:t}
{if {A.empty? :t}
then else {BT.sort {BT.left :t}}
{BT.data :t}
{BT.sort {BT.right :t}} }}}
-> BT.sort
Testing
1) generating random numbers:
{def L {A.new
{S.map {lambda {:n} {floor {* {random} 100000}}} {S.serie 1 100}}}}
-> L = [1850,7963,50540,92667,72892,47361,19018,40640,10126,80235,48407,51623,63597,71675,27814,63478,18985,88032,46585,85209,
74053,95005,27592,9575,22162,35904,70467,38527,89715,36594,54309,39950,89345,72224,7772,65756,68766,43942,52422,85144,
66010,38961,21647,53194,72166,33545,49037,23218,27969,83566,19382,53120,55291,77374,27502,66648,99637,37322,9815,432,90565,
37831,26503,99232,87024,65625,75155,55382,30120,58117,70031,13011,81375,10490,39786,1926,71311,4213,55183,2583,22075,90411,
92928,61120,94259,433,93332,88423,64119,40850,94318,27816,84818,90632,5094,36696,94705,50602,45818,61365]
2) creating the tree is the main work:
{def T {BT.create {L}}}
-> T = [1850,[432,],[433,],]]],[7963,[7772,[1926,],[4213,[2583,],]],[5094,],]]]],]],[50540,[47361,[19018,[10126,[9575,],
[9815,],]]],[18985,[13011,[10490,],]],]],]]],[40640,[27814,[27592,[22162,[21647,[19382,],]],[22075,],]]],[23218,],
[27502,[26503,],]],]]]],]],[35904,[33545,[27969,[27816,],]],[30120,],]]],]],[38527,[36594,],[37322,[36696,],]],[37831,],]]]],
[39950,[38961,],[39786,],]]],]]]]],[46585,[43942,[40850,],]],[45818,],]]],]]]],[48407,],[49037,],]]]],[92667,[72892,
[51623,[50602,],]],[63597,[63478,[54309,[52422,],[53194,[53120,],]],]]],[55291,[55183,],]],[55382,],[58117,],[61120,],[61365,],]]]]]]],]],[71675,[70467,[65756,[65625,[64119,],]],]],[68766,[66010,],[66648,],]]],[70031,],]]]],[71311,],]]],
[72224,[72166,],]],]]]]],[80235,[74053,],[77374,[75155,],]],]]],[88032,[85209,[85144,[83566,[81375,],]],[84818,],]]],]],
[87024,],]]],[89715,[89345,[88423,],]],]],[90565,[90411,],]],[90632,],]]]]]]],[95005,[92928,],[94259,[93332,],]],[94318,],
[94705,],]]]]],[99637,[99232,],]],]]]]]]]
3) walking the canopy is fast:
{BT.sort {T}}
-> 432 433 1850 1926 2583 4213 5094 7772 7963 9575 9815 10126 10490 13011 18985 19018 19382 21647 22075 22162 23218 26503
27502 27592 27814 27816 27969 30120 33545 35904 36594 36696 37322 37831 38527 38961 39786 39950 40640 40850 43942 45818
46585 47361 48407 49037 50540 50602 51623 52422 53120 53194 54309 55183 55291 55382 58117 61120 61365 63478 63597 64119
65625 65756 66010 66648 68766 70031 70467 71311 71675 72166 72224 72892 74053 75155 77374 80235 81375 83566 84818 85144
85209 87024 88032 88423 89345 89715 90411 90565 90632 92667 92928 93332 94259 94318 94705 95005 99232 99637
4) walking with new leaves is fast:
{BT.sort {BT.add -1 {T}}}
-> -1 432 433 1850 1926 2583 4213 5094 7772 7963 9575 9815 10126 10490 13011 18985 19018 19382 21647 22075 22162 23218 26503
27502 27592 27814 27816 27969 30120 33545 35904 36594 36696 37322 37831 38527 38961 39786 39950 40640 40850 43942 45818 46585
47361 48407 49037 50540 50602 51623 52422 53120 53194 54309 55183 55291 55382 58117 61120 61365 63478 63597 64119 65625 65756
66010 66648 68766 70031 70467 71311 71675 72166 72224 72892 74053 75155 77374 80235 81375 83566 84818 85144 85209 87024 88032
88423 89345 89715 90411 90565 90632 92667 92928 93332 94259 94318 94705 95005 99232 99637
{BT.sort {BT.add 50000 {T}}}
-> 432 433 1850 1926 2583 4213 5094 7772 7963 9575 9815 10126 10490 13011 18985 19018 19382 21647 22075 22162 23218 26503
27502 27592 27814 27816 27969 30120 33545 35904 36594 36696 37322 37831 38527 38961 39786 39950 40640 40850 43942 45818 46585
47361 48407 49037 50000 50540 50602 51623 52422 53120 53194 54309 55183 55291 55382 58117 61120 61365 63478 63597 64119 65625
65756 66010 66648 68766 70031 70467 71311 71675 72166 72224 72892 74053 75155 77374 80235 81375 83566 84818 85144 85209 87024
88032 88423 89345 89715 90411 90565 90632 92667 92928 93332 94259 94318 94705 95005 99232 99637
{BT.sort {BT.add 100000 {T}}}
-> 432 433 1850 1926 2583 4213 5094 7772 7963 9575 9815 10126 10490 13011 18985 19018 19382 21647 22075 22162 23218 26503
27502 27592 27814 27816 27969 30120 33545 35904 36594 36696 37322 37831 38527 38961 39786 39950 40640 40850 43942 45818 46585
47361 48407 49037 50540 50602 51623 52422 53120 53194 54309 55183 55291 55382 58117 61120 61365 63478 63597 64119 65625 65756
66010 66648 68766 70031 70467 71311 71675 72166 72224 72892 74053 75155 77374 80235 81375 83566 84818 85144 85209 87024 88032
88423 89345 89715 90411 90565 90632 92667 92928 93332 94259 94318 94705 95005 99232 99637 100000
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 sortedLogo
; 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 :testLogtalk
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
endLucid
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;
endM2000 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()
}
Checkit1Recursive 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$())-1)
Print A$()
}
Checkit2Non 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$())-1)
Print A$()
}
Checkit3M4
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))- Output:
(1,1,3,4,5,9)
Maclisp
;; While not strictly required, it simplifies the
;; implementation considerably to use filter. MACLisp
;; Doesn't have one out of the box, so we bring our own
(DEFUN FILTER (F LIST)
(COND
((EQ LIST NIL) NIL)
((FUNCALL F (CAR LIST))
(CONS (CAR LIST) (FILTER F (CDR LIST))))
(T
(FILTER F (CDR LIST)))))
;; And then, quicksort.
(DEFUN QUICKSORT (LIST)
(COND
((OR (EQ LIST ())
(EQ (CDR LIST) ()))
LIST)
(T
(LET
((PIVOT (CAR LIST))
(REST (CDR LIST)))
(APPEND
(QUICKSORT (FILTER #'(LAMBDA (X) (<= X PIVOT)) REST))
(LIST PIVOT)
(QUICKSORT (FILTER #'(LAMBDA (X) (> X PIVOT)) REST)))))))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;- Output:
[0, 1, 2, 4, 12]
Mathematica /Wolfram Language
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)];
endA 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) )];
endSample usage:
quickSort([4,3,7,-2,9,1])
ans =
-2 1 3 4 7 9MAXScript
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 aMercury
A quicksort that works on linked lists
%%%-------------------------------------------------------------------
:- module quicksort_task_for_lists.
:- interface.
:- import_module io.
:- pred main(io, io).
:- mode main(di, uo) is det.
:- implementation.
:- import_module int.
:- import_module list.
%%%-------------------------------------------------------------------
%%%
%%% Partitioning a list into three:
%%%
%%% Left elements less than the pivot
%%% Middle elements equal to the pivot
%%% Right elements greater than the pivot
%%%
%%% The implementation is tail-recursive.
%%%
:- pred partition(comparison_func(T), T, list(T),
list(T), list(T), list(T)).
:- mode partition(in, in, in, out, out, out) is det.
partition(Compare, Pivot, Lst, Left, Middle, Right) :-
partition(Compare, Pivot, Lst, [], Left, [], Middle, [], Right).
:- pred partition(comparison_func(T), T, list(T),
list(T), list(T),
list(T), list(T),
list(T), list(T)).
:- mode partition(in, in, in,
in, out,
in, out,
in, out) is det.
partition(_, _, [], Left0, Left, Middle0, Middle, Right0, Right) :-
Left = Left0,
Middle = Middle0,
Right = Right0.
partition(Compare, Pivot, [Head | Tail], Left0, Left,
Middle0, Middle, Right0, Right) :-
Compare(Head, Pivot) = Cmp,
(if (Cmp = (<))
then partition(Compare, Pivot, Tail,
[Head | Left0], Left,
Middle0, Middle,
Right0, Right)
else if (Cmp = (=))
then partition(Compare, Pivot, Tail,
Left0, Left,
[Head | Middle0], Middle,
Right0, Right)
else partition(Compare, Pivot, Tail,
Left0, Left,
Middle0, Middle,
[Head | Right0], Right)).
%%%-------------------------------------------------------------------
%%%
%%% Quicksort using the first element as pivot.
%%%
%%% This is not the world's best choice of pivot, but it is the
%%% easiest one to get from a linked list.
%%%
%%% This implementation is *not* tail-recursive--as most quicksort
%%% implementations also are not. (However, do an online search on
%%% "quicksort fortran 77" and you will find some "tail-recursive"
%%% implementations, with the tail recursions expressed as gotos.)
%%%
:- func quicksort(comparison_func(T), list(T)) = list(T).
quicksort(_, []) = [].
quicksort(Compare, [Pivot | Tail]) = Sorted_Lst :-
partition(Compare, Pivot, Tail, Left, Middle, Right),
quicksort(Compare, Left) = Sorted_Left,
quicksort(Compare, Right) = Sorted_Right,
Sorted_Left ++ [Pivot | Middle] ++ Sorted_Right = Sorted_Lst.
%%%-------------------------------------------------------------------
:- func example_numbers = list(int).
example_numbers = [1, 3, 9, 5, 8, 6, 5, 1, 7, 9, 8, 6, 4, 2].
:- func int_compare(int, int) = comparison_result.
int_compare(I, J) = Cmp :-
if (I < J) then (Cmp = (<))
else if (I = J) then (Cmp = (=))
else (Cmp = (>)).
main(!IO) :-
quicksort(int_compare, example_numbers) = Sorted_Numbers,
print("unsorted: ", !IO),
print_line(example_numbers, !IO),
print("sorted: ", !IO),
print_line(Sorted_Numbers, !IO).
%%%-------------------------------------------------------------------
%%% local variables:
%%% mode: mercury
%%% prolog-indent-width: 2
%%% end:- Output:
$ mmc quicksort_task_for_lists.m && ./quicksort_task_for_lists unsorted: [1, 3, 9, 5, 8, 6, 5, 1, 7, 9, 8, 6, 4, 2] sorted: [1, 1, 2, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9]
A quicksort that works on arrays
The in-place partitioning algorithm here is similar to but not quite the same as that of the task pseudocode. I wrote it by referring to some Fortran code I wrote several months ago for a quickselect. (That quickselect had a random pivot, however.)
%%%-------------------------------------------------------------------
:- module quicksort_task_for_arrays.
:- interface.
:- import_module io.
:- pred main(io, io).
:- mode main(di, uo) is det.
:- implementation.
:- import_module array.
:- import_module int.
:- import_module list.
%%%-------------------------------------------------------------------
%%%
%%% Partitioning a subarray into two halves: one with elements less
%%% than or equal to a pivot, the other with elements greater than or
%%% equal to a pivot.
%%%
%%% The implementation is tail-recursive.
%%%
:- pred partition(pred(T, T), T, int, int, array(T), array(T), int).
:- mode partition(pred(in, in) is semidet, in, in, in,
array_di, array_uo, out).
partition(Less_than, Pivot, I_first, I_last, Arr0, Arr, I_pivot) :-
I = I_first - 1,
J = I_last + 1,
partition_loop(Less_than, Pivot, I, J, Arr0, Arr, I_pivot).
:- pred partition_loop(pred(T, T), T, int, int,
array(T), array(T), int).
:- mode partition_loop(pred(in, in) is semidet, in, in, in,
array_di, array_uo, out).
partition_loop(Less_than, Pivot, I, J, Arr0, Arr, Pivot_index) :-
if (I = J) then (Arr = Arr0,
Pivot_index = I)
else (I1 = I + 1,
I2 = search_right(Less_than, Pivot, I1, J, Arr0),
(if (I2 = J) then (Arr = Arr0,
Pivot_index = J)
else (J1 = J - 1,
J2 = search_left(Less_than, Pivot, I2, J1, Arr0),
swap(I2, J2, Arr0, Arr1),
partition_loop(Less_than, Pivot, I2, J2, Arr1, Arr,
Pivot_index)))).
:- func search_right(pred(T, T), T, int, int, array(T)) = int.
:- mode search_right(pred(in, in) is semidet,
in, in, in, in) = out is det.
search_right(Less_than, Pivot, I, J, Arr0) = K :-
if (I = J) then (I = K)
else if Less_than(Pivot, Arr0^elem(I)) then (I = K)
else (search_right(Less_than, Pivot, I + 1, J, Arr0) = K).
:- func search_left(pred(T, T), T, int, int, array(T)) = int.
:- mode search_left(pred(in, in) is semidet,
in, in, in, in) = out is det.
search_left(Less_than, Pivot, I, J, Arr0) = K :-
if (I = J) then (J = K)
else if Less_than(Arr0^elem(J), Pivot) then (J = K)
else (search_left(Less_than, Pivot, I, J - 1, Arr0) = K).
%%%-------------------------------------------------------------------
%%%
%%% Quicksort with median of three as pivot.
%%%
%%% Like most quicksort implementations, this one is *not*
%%% tail-recursive.
%%%
%% quicksort/3 sorts an entire array.
:- pred quicksort(pred(T, T), array(T), array(T)).
:- mode quicksort(pred(in, in) is semidet, array_di, array_uo) is det.
quicksort(Less_than, Arr0, Arr) :-
bounds(Arr0, I_first, I_last),
quicksort(Less_than, I_first, I_last, Arr0, Arr).
%% quicksort/5 sorts a subarray.
:- pred quicksort(pred(T, T), int, int, array(T), array(T)).
:- mode quicksort(pred(in, in) is semidet, in, in,
array_di, array_uo) is det.
quicksort(Less_than, I_first, I_last, Arr0, Arr) :-
if (I_last - I_first >= 2)
then (median_of_three(Less_than, I_first, I_last,
Arr0, Arr1, Pivot),
%% Partition only from I_first to I_last - 1.
partition(Less_than, Pivot, I_first, I_last - 1,
Arr1, Arr2, K),
%% Now everything that is less than the pivot is to the
%% left of K.
%% Put the pivot at K, moving the element that had been there
%% to the end. If K = I_last, then this element is actually
%% garbage and will be overwritten with the pivot, which turns
%% out to be the greatest element. Otherwise, the moved
%% element is not less than the pivot and so the partitioning
%% is preserved.
Arr2^elem(K) = Elem_to_move,
(Arr2^elem(I_last) := Elem_to_move) = Arr3,
(Arr3^elem(K) := Pivot) = Arr4,
%% Sort the subarray on either side of the pivot.
quicksort(Less_than, I_first, K - 1, Arr4, Arr5),
quicksort(Less_than, K + 1, I_last, Arr5, Arr))
else if (I_last - I_first = 1) % Two elements.
then (Elem_first = Arr0^elem(I_first),
Elem_last = Arr0^elem(I_last),
(if Less_than(Elem_first, Elem_last)
then (Arr = Arr0)
else ((Arr0^elem(I_first) := Elem_last) = Arr1,
(Arr1^elem(I_last) := Elem_first) = Arr)))
else (Arr = Arr0). % Zero or one element.
%% median_of_three/6 both chooses a pivot and rearranges the array
%% elements so one may partition them from I_first to I_last - 1,
%% leaving the pivot element out of the array.
:- pred median_of_three(pred(T, T), int, int, array(T), array(T), T).
:- mode median_of_three(pred(in, in) is semidet, in, in,
array_di, array_uo, out) is det.
median_of_three(Less_than, I_first, I_last, Arr0, Arr, Pivot) :-
I_middle = I_first + ((I_last - I_first) // 2),
Elem_first = Arr0^elem(I_first),
Elem_middle = Arr0^elem(I_middle),
Elem_last = Arr0^elem(I_last),
(if pred_xor(Less_than, Less_than,
Elem_middle, Elem_first,
Elem_last, Elem_first)
then (Pivot = Elem_first,
(if Less_than(Elem_middle, Elem_last)
then (Arr1 = (Arr0^elem(I_first) := Elem_middle),
Arr = (Arr1^elem(I_middle) := Elem_last))
else (Arr = (Arr0^elem(I_first) := Elem_last))))
else if pred_xor(Less_than, Less_than,
Elem_middle, Elem_first,
Elem_middle, Elem_last)
then (Pivot = Elem_middle,
(if Less_than(Elem_first, Elem_last)
then (Arr = (Arr0^elem(I_middle) := Elem_last))
else (Arr1 = (Arr0^elem(I_first) := Elem_last),
Arr = (Arr1^elem(I_middle) := Elem_first))))
else (Pivot = Elem_last,
(if Less_than(Elem_first, Elem_middle)
then (Arr = Arr0)
else (Arr1 = (Arr0^elem(I_first) := Elem_middle),
Arr = (Arr1^elem(I_middle) := Elem_first))))).
:- pred pred_xor(pred(T, T), pred(T, T), T, T, T, T).
:- mode pred_xor(pred(in, in) is semidet,
pred(in, in) is semidet,
in, in, in, in) is semidet.
pred_xor(P, Q, W, X, Y, Z) :-
if P(W, X) then (not Q(Y, Z)) else Q(Y, Z).
%%%-------------------------------------------------------------------
:- func example_numbers = list(int).
example_numbers = [1, 3, 9, 5, 8, 6, 5, 0, 1, 7, 9, 8, 6, 4, 2, -28,
30, 31, 1, 3, 9, 5, 8, 6, 5, 1, 6, 4, 2, -28, 30,
-50, 500, -1234, 1234, 12].
main(!IO) :-
(array.from_list(example_numbers, Arr0)),
print_line("", !IO),
print_line(Arr0, !IO),
print_line("", !IO),
print_line(" |", !IO),
print_line(" V", !IO),
print_line("", !IO),
quicksort(<, Arr0, Arr1),
print_line(Arr1, !IO),
print_line("", !IO).
%%%-------------------------------------------------------------------
%%% local variables:
%%% mode: mercury
%%% prolog-indent-width: 2
%%% end:- Output:
$ mmc quicksort_task_for_arrays.m && ./quicksort_task_for_arrays
array([1, 3, 9, 5, 8, 6, 5, 0, 1, 7, 9, 8, 6, 4, 2, -28, 30, 31, 1, 3, 9, 5, 8, 6, 5, 1, 6, 4, 2, -28, 30, -50, 500, -1234, 1234, 12])
|
V
array([-1234, -50, -28, -28, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 8, 8, 8, 9, 9, 9, 12, 30, 30, 31, 500, 1234])
MiniScript
Quick implementation for Miniscript, simply goes through the list reference and swaps the positions
Partition = function(a, low, high)
pivot = a[low]
leftwall = low
for i in range(low + 1, high)
if a[i] < pivot then
leftwall = leftwall + 1
temp = a[leftwall]
a[leftwall] = a[i]
a[i] = temp
end if
end for
temp = a[leftwall]
a[leftwall] = pivot
a[low] = temp
return leftwall
end function
QuickSort = function(a, low=null, high=null)
if not low then low = 0
if not high then high = a.len - 1
if low < high then
pivot_location = Partition(a, low, high)
QuickSort a, low, pivot_location - 1
QuickSort a, pivot_location + 1, high
end if
return a
end function
print QuickSort([3, 5, 2, 4, 1])- Output:
[1, 2, 3, 4, 5]
Miranda
main :: [sys_message]
main = [Stdout ("Before: " ++ show testlist ++ "\n"),
Stdout ("After: " ++ show (quicksort testlist) ++ "\n")]
where testlist = [4,65,2,-31,0,99,2,83,782,1]
quicksort [] = []
quicksort [x] = [x]
quicksort xs = (quicksort less) ++ equal ++ (quicksort more)
where pivot = hd xs
less = [x | x<-xs; x<pivot]
equal = [x | x<-xs; x=pivot]
more = [x | x<-xs; x>pivot]- Output:
Before: [4,65,2,-31,0,99,2,83,782,1] After: [-31,0,1,2,2,4,65,83,99,782]
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.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 );- Output:
[ 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()- Output:
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
Nanoquery
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)
else if i > pivot
more.append(i)
else
pivotList.append(i)
end
end
less = quickSort(less)
more = quickSort(more)
return less + pivotList + more
end
endNemerle
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- Output:
UK London US New York US Boston US Washington UK Washington US Birmingham UK Birmingham UK Boston UK Birmingham UK Boston UK London UK Washington US Birmingham US Boston US New York US Washington UK Birmingham UK Boston UK London UK Washington US Birmingham US Boston US New York US Washington
Nial
quicksort is fork [ >= [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 8Nim
Procedural (in place) algorithm
proc quickSortImpl[T](a: var openarray[T], start, stop: int) =
if stop - start > 0:
let pivot = a[start]
var left = start
var right = stop
while left <= right:
while cmp(a[left], pivot) < 0:
inc(left)
while cmp(a[right], pivot) > 0:
dec(right)
if left <= right:
swap(a[left], a[right])
inc(left)
dec(right)
quickSortImpl(a, start, right)
quickSortImpl(a, left, stop)
proc quickSort[T](a: var openarray[T]) =
quickSortImpl(a, 0, a.len - 1)
var a = @[4, 65, 2, -31, 0, 99, 2, 83, 782]
a.quickSort()
echo aFunctional (inmmutability) algorithm
import sequtils,sugar
func sorted[T](xs:seq[T]): seq[T] =
if xs.len==0: @[] else: concat(
xs[1..^1].filter(x=>x<xs[0]).sorted,
@[xs[0]],
xs[1..^1].filter(x=>x>=xs[0]).sorted
)
@[4, 65, 2, -31, 0, 99, 2, 83, 782].sorted.echo- Output:
@[-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]- Output:
[ -31 0 2 4 65 83 99 782 ]
Oberon-2
MODULE QS;
IMPORT Out;
TYPE
TItem = INTEGER;
CONST
N = 10;
VAR
I:LONGINT;
A:ARRAY N OF INTEGER;
PROCEDURE Init(VAR A:ARRAY OF TItem);
BEGIN
A[0] := 4; A[1] := 65; A[2] := 2; A[3] := -31; A[4] := 0;
A[5] := 99; A[6] := 2; A[7] := 83; A[8] := 782; A[9] := 1;
END Init;
PROCEDURE QuickSort(VAR A:ARRAY OF TItem; Left,Right:LONGINT);
VAR
I,J:LONGINT;
Pivot,Temp:TItem;
BEGIN
I := Left;
J := Right;
Pivot := A[(Left + Right) DIV 2];
REPEAT
WHILE Pivot > A[I] DO INC(I) END;
WHILE Pivot < A[J] DO DEC(J) END;
IF I <= J THEN
Temp := A[I];
A[I] := A[J];
A[J] := Temp;
INC(I);
DEC(J);
END;
UNTIL I > J;
IF Left < J THEN QuickSort(A, Left, J) END;
IF I < Right THEN QuickSort(A, I, Right) END;
END QuickSort;
BEGIN
Init(A);
FOR I := 0 TO LEN(A)-1 DO
Out.Int(A[I], 0); Out.Char(' ');
END;
Out.Ln;
QuickSort(A, 0, LEN(A)-1);
FOR I := 0 TO LEN(A)-1 DO
Out.Int(A[I], 0); Out.Char(' ');
END;
Out.Ln;
END QS.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);
};
}
}Objective-C
The latest XCode compiler is assumed with 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;
}- Output:
Unsorted: (
1,
3,
5,
7,
9,
8,
6,
4,
2
)
Sorted: (
1,
2,
3,
4,
5,
6,
7,
8,
9
)
Unsorted: (
Emil,
Peg,
Helen,
Juergen,
David,
Rick,
Barb,
Mike,
Tom
)
Sorted: (
Barb,
David,
Emil,
Helen,
Juergen,
Mike,
Peg,
Rick,
Tom
)
OCaml
Declarative and purely functional
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]The list based implementation is elegant and perspicuous, but inefficient in time (because partition and @ are linear) and in space (since it creates numerous new lists along the way).
Imperative and in place
Using aliased array slices from the Containers library.
module Slice = CCArray_slice
let quicksort : int Array.t -> unit = fun arr ->
let rec quicksort' : int Slice.t -> unit = fun slice ->
let len = Slice.length slice in
if len > 1 then begin
let pivot = Slice.get slice (len / 2)
and i = ref 0
and j = ref (len - 1)
in
while !i < !j do
while Slice.get slice !i < pivot do incr i done;
while Slice.get slice !j > pivot do decr j done;
if !i < !j then begin
let i_val = Slice.get slice !i in
Slice.set slice !i (Slice.get slice !j);
Slice.set slice !j i_val;
incr i;
decr j;
end
done;
quicksort' (Slice.sub slice 0 !i);
quicksort' (Slice.sub slice !i (len - !i));
end
in
(* Take the array into an aliased array slice *)
Slice.full arr |> quicksort'Octave
(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
uOforth
Oforth built-in sort uses quick sort algorithm (see lang/collect/ListBuffer.of for implementation) :
[ 5, 8, 2, 3, 4, 1 ] sortOl
(define (quicksort l ??)
(if (null? l)
'()
(append (quicksort (filter (lambda (x) (?? (car l) x)) (cdr l)) ??)
(list (car l))
(quicksort (filter (lambda (x) (not (?? (car l) x))) (cdr l)) ??))))
(print
(quicksort (list 1 3 5 9 8 6 4 3 2) >))
(print
(quicksort (iota 100) >))
(print
(quicksort (iota 100) <))- Output:
(1 2 3 3 4 5 6 8 9) (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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99) (99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0)
ooRexx
a = .array~Of(4, 65, 2, -31, 0, 99, 83, 782, 1)
say 'before:' a~toString( ,', ')
a = quickSort(a)
say ' after:' a~toString( ,', ')
exit
::routine quickSort
use arg arr -- the array to be sorted
less = .array~new
pivotList = .array~new
more = .array~new
if arr~items <= 1 then
return arr
else do
pivot = arr[1]
do i over arr
if i < pivot then
less~append(i)
else if i > pivot then
more~append(i)
else
pivotList~append(i)
end
less = quickSort(less)
more = quickSort(more)
return less~~appendAll(pivotList)~~appendAll(more)
end- Output:
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
program QSortDemo;
{$mode objfpc}{$h+}{$b-}
procedure QuickSort(var A: array of Integer);
procedure QSort(L, R: Integer);
var
I, J, Tmp, Pivot: Integer;
begin
if R - L < 1 then exit;
I := L; J := R;
{$push}{$q-}{$r-}Pivot := A[(L + R) shr 1];{$pop}
repeat
while A[I] < Pivot do Inc(I);
while A[J] > Pivot do Dec(J);
if I <= J then begin
Tmp := A[I];
A[I] := A[J];
A[J] := Tmp;
Inc(I); Dec(J);
end;
until I > J;
QSort(L, J);
QSort(I, R);
end;
begin
QSort(0, High(A));
end;
procedure PrintArray(const A: array of Integer);
var
I: Integer;
begin
Write('[');
for I := 0 to High(A) - 1 do
Write(A[I], ', ');
WriteLn(A[High(A)], ']');
end;
var
a: array[-7..6] of Integer = (-34, -20, 30, 13, 36, -10, 5, -25, 9, 19, 35, -50, 29, 11);
begin
QuickSort(a);
PrintArray(a);
end.- Output:
[-50, -34, -25, -20, -10, 5, 9, 11, 13, 19, 29, 30, 35, 36]
PascalABC.NET
function Partition(a: array of integer; l,r: integer): integer;
begin
var i := l - 1;
var j := r + 1;
var x := a[l];
while True do
begin
repeat
i += 1;
until a[i]>=x;
repeat
j -= 1;
until a[j]<=x;
if i<j then
Swap(a[i],a[j])
else
begin
Result := j;
exit;
end;
end;
end;
procedure QuickSort(a: array of integer; l,r: integer);
begin
if l>=r then exit;
var j := Partition(a,l,r);
QuickSort(a,l,j);
QuickSort(a,j+1,r);
end;
const n = 20;
begin
var a := ArrRandom(n);
Println('Before: ');
Println(a);
QuickSort(a,0,a.Length-1);
Println('After sorting: ');
Println(a);
end.- Output:
Before: [67,95,79,96,14,56,25,9,4,56,70,62,33,52,13,12,73,19,8,72] After sorting: [4,8,9,12,13,14,19,25,33,52,56,56,62,67,70,72,73,79,95,96]
Perl
sub quick_sort {
return @_ if @_ < 2;
my $p = splice @_, int rand @_, 1;
quick_sort(grep $_ < $p, @_), $p, quick_sort(grep $_ >= $p, @_);
}
my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1);
@a = quick_sort @a;
print "@a\n";Phix
with javascript_semantics function quick_sort(sequence x) -- -- put x into ascending order using recursive quick sort -- integer n = length(x) if n<2 then return x -- already sorted (trivial case) end if integer mid = floor((n+1)/2), last = 1 object midval = x[mid] x[mid] = x[1] for i=2 to n do object xi = x[i] if xi<midval then last += 1 x[i] = x[last] x[last] = xi end if end for return quick_sort(x[2..last]) & {midval} & quick_sort(x[last+1..n]) end function ?quick_sort({5,"oranges","and",3,"apples"})
- Output:
{3,5,"and","apples","oranges"}
PHP
function quicksort($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]
Picat
Function
qsort([]) = [].
qsort([H|T]) = qsort([E : E in T, E =< H])
++ [H] ++
qsort([E : E in T, E > H]).Recursion
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).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 $array)"The output is: 3 8 11 19 21 36 60 63 80 87 100
Yet another solution
function quicksort($in) {
$n = $in.count
switch ($n) {
0 {}
1 { $in[0] }
2 { if ($in[0] -lt $in[1]) {$in[0], $in[1]} else {$in[1], $in[0]} }
default {
$pivot = $in | get-random
$lt = $in | ? {$_ -lt $pivot}
$eq = $in | ? {$_ -eq $pivot}
$gt = $in | ? {$_ -gt $pivot}
@(quicksort $lt) + @($eq) + @(quicksort $gt)
}
}
}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).Python
def quick_sort(sequence):
lesser = []
equal = []
greater = []
if len(sequence) <= 1:
return sequence
pivot = sequence[0]
for element in sequence:
if element < pivot:
lesser.append(element)
elif element > pivot:
greater.append(element)
else:
equal.append(element)
lesser = quick_sort(lesser)
greater = quick_sort(greater)
return lesser + equal + greater
a = [4, 65, 2, -31, 0, 99, 83, 782, 1]
a = quick_sort(a)In a Haskell fashion --
def qsort(L):
return (qsort([y for y in L[1:] if y < L[0]]) +
[L[0]] +
qsort([y for y in L[1:] if y >= L[0]])) if len(L) > 1 else LMore readable, but still using list comprehensions:
def qsort(list):
if not list:
return []
else:
pivot = list[0]
less = [x for x in list[1:] 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) + moreReturning 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] + moreSorting 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)Functional Style (no for or while loops, constants only):
def quicksort(unsorted_list):
if len(unsorted_list) == 0:
return []
pivot = unsorted_list[0]
less = list(filter(lambda x: x < pivot, unsorted_list))
same = list(filter(lambda x: x == pivot, unsorted_list))
more = list(filter(lambda x: x > pivot, unsorted_list))
return quicksort(less) + same + quicksort(more)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])Quackery
Sort a nest of numbers.
[ stack ] is less ( --> s )
[ stack ] is same ( --> s )
[ stack ] is more ( --> s )
[ - -1 1 clamp 1+ ] is <=> ( n n --> n )
[ tuck take join swap put ] is append ( x s --> )
[ dup size 2 < if done
[] less put
[] same put
[] more put
behead swap witheach
[ 2dup swap <=>
[ table less same more ]
append ]
same append
less take recurse
same take join
more take recurse join ] is quicksort ( [ --> [ )
[] 10 times [ i^ join ] 3 of
dup echo cr
quicksort echo crOutput:
[ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 ] [ 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 ]
R
qsort <- function(v) {
if ( length(v) > 1 )
{
pivot <- (min(v) + max(v))/2.0 # Could also use pivot <- median(v)
c(qsort(v[v < pivot]), v[v == pivot], qsort(v[v > pivot]))
} else v
}
N <- 100
vs <- runif(N)
system.time(u <- qsort(vs))
print(u)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")Raku
#| Recursive, single-thread, random pivot, single-pass, quicksort implementation
multi quicksort(\a where a.elems < 2) { a }
multi quicksort(\a, \pivot = a.pick) {
my %prt{Order} is default([]) = a.classify: * cmp pivot;
|samewith(%prt{Less}), |%prt{Same}, |samewith(%prt{More})
}concurrent implementation
The partitions can be sorted in parallel.
#| Recursive, parallel, random pivot, single-pass, quicksort implementation
multi quicksort-parallel-naive(\a where a.elems < 2) { a }
multi quicksort-parallel-naive(\a, \pivot = a.pick) {
my %prt{Order} is default([]) = a.classify: * cmp pivot;
my Promise $less = start { samewith(%prt{Less}) }
my $more = samewith(%prt{More});
await $less andthen |$less.result, |%prt{Same}, |$more;
}Let's tune the parallel execution by applying a minimum batch size in order to spawn a new thread.
#| Recursive, parallel, batch tuned, single-pass, quicksort implementation
sub quicksort-parallel(@a, $batch = 2**9) {
return @a if @a.elems < 2;
# separate unsorted input into Order Less, Same and More compared to a random $pivot
my $pivot = @a.pick;
my %prt{Order} is default([]) = @a.classify( * cmp $pivot );
# decide if we sort the Less partition on a new thread
my $less = %prt{Less}.elems >= $batch
?? start { samewith(%prt{Less}, $batch) }
!! samewith(%prt{Less}, $batch);
# meanwhile use current thread for sorting the More partition
my $more = samewith(%prt{More}, $batch);
# if we went parallel, we need to await the result
await $less andthen $less = $less.result if $less ~~ Promise;
# concat all sorted partitions into a list and return
|$less, |%prt{Same}, |$more;
}testing
Let's run some tests.
say "x" x 10 ~ " Testing " ~ "x" x 10;
use Test;
my @functions-under-test = &quicksort, &quicksort-parallel-naive, &quicksort-parallel;
my @testcases =
() => (),
<a>.List => <a>.List,
<a a> => <a a>,
("b", "a", 3) => (3, "a", "b"),
<h b a c d f e g> => <a b c d e f g h>,
<a 🎮 3 z 4 🐧> => <a 🎮 3 z 4 🐧>.sort
;
plan @testcases.elems * @functions-under-test.elems;
for @functions-under-test -> &fun {
say &fun.name;
is-deeply &fun(.key), .value, .key ~ " => " ~ .value for @testcases;
}
done-testing;xxxxxxxxxx Testing xxxxxxxxxx 1..18 quicksort ok 1 - => ok 2 - a => a ok 3 - a a => a a ok 4 - b a 3 => 3 a b ok 5 - h b a c d f e g => a b c d e f g h ok 6 - a 🎮 3 z 4 🐧 => 3 4 a z 🎮 🐧 quicksort-parallel-naive ok 7 - => ok 8 - a => a ok 9 - a a => a a ok 10 - b a 3 => 3 a b ok 11 - h b a c d f e g => a b c d e f g h ok 12 - a 🎮 3 z 4 🐧 => 3 4 a z 🎮 🐧 quicksort-parallel ok 13 - => ok 14 - a => a ok 15 - a a => a a ok 16 - b a 3 => 3 a b ok 17 - h b a c d f e g => a b c d e f g h ok 18 - a 🎮 3 z 4 🐧 => 3 4 a z 🎮 🐧
benchmarking
and some benchmarking
say "x" x 11 ~ " Benchmarking " ~ "x" x 11;
use Benchmark;
my $runs = 5;
my $elems = 10 * Kernel.cpu-cores * 2**10;
my @unsorted of Str = ('a'..'z').roll(8).join xx $elems;
my UInt $l-batch = 2**13;
my UInt $m-batch = 2**11;
my UInt $s-batch = 2**9;
my UInt $t-batch = 2**7;
say "elements: $elems, runs: $runs, cpu-cores: {Kernel.cpu-cores}, large/medium/small/tiny-batch: $l-batch/$m-batch/$s-batch/$t-batch";
my %results = timethese $runs, {
single-thread => { quicksort(@unsorted) },
parallel-naive => { quicksort-parallel-naive(@unsorted) },
parallel-tiny-batch => { quicksort-parallel(@unsorted, $t-batch) },
parallel-small-batch => { quicksort-parallel(@unsorted, $s-batch) },
parallel-medium-batch => { quicksort-parallel(@unsorted, $m-batch) },
parallel-large-batch => { quicksort-parallel(@unsorted, $l-batch) },
}, :statistics;
my @metrics = <mean median sd>;
my $msg-row = "%.4f\t" x @metrics.elems ~ '%s';
say @metrics.join("\t");
for %results.kv -> $name, %m {
say sprintf($msg-row, %m{@metrics}, $name);
}xxxxxxxxxxx Benchmarking xxxxxxxxxxx elements: 40960, runs: 5, cpu-cores: 4, large/medium/small/tiny-batch: 8192/2048/512/128 mean median sd 2.9503 2.8907 0.2071 parallel-small-batch 3.2054 3.1727 0.2078 parallel-tiny-batch 5.6524 5.0980 1.2628 parallel-naive 3.4717 3.3353 0.3622 parallel-medium-batch 4.6275 4.7793 0.4930 parallel-large-batch 6.5401 6.2832 0.5585 single-thread
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 qSort
This REXX version doesn't use or modify the program stack.
It is over 400% times faster then the 2nd REXX version (using the exact same random numbers).
See at the end of this entry for timing all versions with larger stems.
/*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. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
inOrder: parse arg n; do j=1 for n-1; k= j+1; if @.j>@.k then return 0; end; return 1
/*──────────────────────────────────────────────────────────────────────────────────────*/
qSort: procedure expose @.; a.1=1; parse arg b.1; $= 1 /*access @.; get @. size; pivot.*/
if inOrder(b.1) then return /*Array already in order? Return*/
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 teeny─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 when using the internal default input:
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 quickSort
The Python code translates very well to ooRexx but here is a way to implement it in classic REXX as well.
This REXX version doesn't handle numbers with leading/trailing/embedded blanks, or textual values that have blanks (or whitespace) in them.
/*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
returnVersion 3 Elegant
A basic quicksort using the stack, but only for the pending partitions. Short and elegant.
Elegant:
procedure expose stem.
push 1 stem.0
do while queued() > 0
pull l r
if l < r then do
m = (l+r)%2; p = stem.m; i = l-1; j = r+1
do forever
do until stem.j <= p
j = j-1
end
do until stem.i >= p
i = i+1
end
if i < j then do
t = stem.i; stem.i = stem.j; stem.j = t
end
else
leave
end
push l j; push j+1 r
end
end
returnVersion 4 Recursive
Also a basic quicksort, but now using recursion as stated in the task. No stack usage.
Recursive:
procedure expose stem.
arg l r
m = (l+r)%2; p = stem.m
i = l; j = r
do while i <= j
do i = i while stem.i < p
end
do j = j by -1 while stem.j > p
end
if i <= j then do
t = stem.i; stem.i = stem.j; stem.j = t
i = i+1; j = j-1
end
end
if l < j then
call Recursive l j
if i < r then
call Recursive i r
returnVersion 5 Optimized
The fastest. As in Version 1, no recursion and no stack usage. The pending partitions are kept in small stems. For partitions < 11 items, a selection sort is employed. Pivot choice is optimized to prevent 'worst case' scenarios.
Optimized:
procedure expose stem.
n = stem.0; s = 1; sl.1 = 1; sr.1 = n
do until s = 0
l = sl.s; r = sr.s; s = s-1
do until l >= r
if r-l < 11 then do
do i = l+1 to r
a = stem.i
do j=i-1 by -1 to l while stem.j > a
k = j+1; stem.k = stem.j
end
k = j+1; stem.k = a
end
if s = 0 then
leave
l = sl.s; r = sr.s; s = s-1
end
else do
m = (l+r)%2
if stem.l > stem.m then do
t = stem.l; stem.l = stem.m; stem.m = t
end
if stem.l > stem.r then do
t = stem.l; stem.l = stem.r; stem.r = t
end
if stem.m > stem.r then do
t = stem.m; stem.m = stem.r; stem.r = t
end
i = l; j = r; p = stem.m
do until i > j
do i = i while stem.i < p
end
do j = j by -1 while stem.j > p
end
if i <= j then do
t = stem.i; stem.i = stem.j; stem.j = t
i = i+1; j = j-1
end
end
if j-l < r-i then do
if i < r then do
s = s+1; sl.s = i; sr.s = r
end
r = j
end
else do
if l < j then do
s = s+1; sl.s = l; sr.s = j
end
l = i
end
end
end
end
returnTiming all versions
Using following program, with all versions copied in (but not shown here).
numeric digits 9
parse version version; say version Digits() 'digits'
arg n v
if n = '' then n = 10
if v = '' then v = 1
show = (n > 0); n = Abs(n)
say 'Quicksort: Timing Version' v 'for' n 'random numbers'
call Generate
if show then call ShowSave
select
when v = 1 then do
call Save2Stem
call Time 'r'; call Qsort n; say 'Qsort' format(time('e'),3,3) 'seconds'
if show then call ShowStem
end
when v = 2 then do
call Time 'r'; call Save2Stack; say 'Save2Stack' format(time('e'),3,3) 'seconds'
call Time 'r'; call Quicksort; say 'Quicksort ' format(time('e'),3,3) 'seconds'
call Time 'r'; call Stack2Stem; say 'Stack2Stem' format(time('e'),3,3) 'seconds'
if show then call ShowStem
end
when v = 3 then do
call Save2Stem
call Time 'r'; call Elegant; say 'Elegant' format(time('e'),3,3) 'seconds'
if show then call ShowStem
end
when v = 4 then do
call Save2Stem
call Time 'r'; call Recursive 1 n; say 'Recursive' format(time('e'),3,3) 'seconds'
if show then call ShowStem
end
when v = 5 then do
call Save2Stem
call Time 'r'; call Optimized; say 'Optimized' format(time('e'),3,3) 'seconds'
if show then call ShowStem
end
otherwise nop
end
say
exit
Generate:
do x = 1 to n
save.x = 10000*Random(0,9999)+Random(0,9999)
end
save.0 = n
return
ShowSave:
do x = 1 to 5
say x save.x
end
do x = n-4 to n
say x save.x
end
return
ShowStem:
do x = 1 to 5
say x stem.x
end
do x = n-4 to n
say x stem.x
end
return
Save2Stem:
do x = 0 to n
stem.x = save.x
end
return
/* Sorting procedures follow, not shown here */Running under Regina with some values for n and v.
- Output:
REXX-Regina_3.9.6(MT) 5.00 29 Apr 2024 9 digits Quicksort: Timing Version 1 for 1000 random numbers Qsort 0.005 seconds Quicksort: Timing Version 2 for 1000 random numbers Save2Stack 0.001 seconds Quicksort 0.016 seconds Stack2Stem 0.000 seconds Quicksort: Timing Version 3 for 1000 random numbers Elegant 0.005 seconds Quicksort: Timing Version 4 for 1000 random numbers Recursive 0.005 seconds Quicksort: Timing Version 5 for 1000 random numbers Optimized 0.004 seconds Quicksort: Timing Version 1 for 10000 random numbers Qsort 0.055 seconds Quicksort: Timing Version 2 for 10000 random numbers Save2Stack 0.002 seconds Quicksort 0.186 seconds Stack2Stem 0.001 seconds Quicksort: Timing Version 3 for 10000 random numbers Elegant 0.061 seconds Quicksort: Timing Version 4 for 10000 random numbers Recursive 0.064 seconds Quicksort: Timing Version 5 for 10000 random numbers Optimized 0.051 seconds Quicksort: Timing Version 1 for 100000 random numbers Qsort 0.667 seconds Quicksort: Timing Version 2 for 100000 random numbers Save2Stack 0.013 seconds Quicksort 2.648 seconds Stack2Stem 0.016 seconds Quicksort: Timing Version 3 for 100000 random numbers Elegant 0.772 seconds Quicksort: Timing Version 4 for 100000 random numbers Recursive 0.768 seconds Quicksort: Timing Version 5 for 100000 random numbers Optimized 0.596 seconds Quicksort: Timing Version 1 for 1000000 random numbers Qsort 8.827 seconds Quicksort: Timing Version 2 for 1000000 random numbers Save2Stack 0.123 seconds Quicksort 154.509 seconds Stack2Stem 0.775 seconds Quicksort: Timing Version 3 for 1000000 random numbers Elegant 10.800 seconds Quicksort: Timing Version 4 for 1000000 random numbers Recursive 9.927 seconds Quicksort: Timing Version 5 for 1000000 random numbers Optimized 8.403 seconds
And the same for ooRexx.
- Output:
REXX-ooRexx_5.0.0(MT)_64-bit 6.05 23 Dec 2022 9 digits Quicksort: Timing Version 1 for 1000 random numbers Qsort 0.005 seconds Quicksort: Timing Version 2 for 1000 random numbers Save2Stack 0.020 seconds Quicksort 0.812 seconds Stack2Stem 0.017 seconds Quicksort: Timing Version 3 for 1000 random numbers Elegant 0.109 seconds Quicksort: Timing Version 4 for 1000 random numbers Recursive 0.007 seconds Quicksort: Timing Version 5 for 1000 random numbers Optimized 0.005 seconds Quicksort: Timing Version 1 for 10000 random numbers Qsort 0.079 seconds Quicksort: Timing Version 2 for 10000 random numbers Save2Stack 0.182 seconds Quicksort 11.317 seconds Stack2Stem 0.168 seconds Quicksort: Timing Version 3 for 10000 random numbers Elegant 1.109 seconds Quicksort: Timing Version 4 for 10000 random numbers Recursive 0.085 seconds Quicksort: Timing Version 5 for 10000 random numbers Optimized 0.068 seconds Quicksort: Timing Version 1 for 100000 random numbers Qsort 1.421 seconds Quicksort: Timing Version 2 for 100000 random numbers Save2Stack 1.824 seconds Quicksort 221.823 seconds Stack2Stem 1.766 seconds Quicksort: Timing Version 3 for 100000 random numbers Elegant 12.908 seconds Quicksort: Timing Version 4 for 100000 random numbers Recursive 2.372 seconds Quicksort: Timing Version 5 for 100000 random numbers Optimized 1.253 seconds Quicksort: Timing Version 1 for 1000000 random numbers Qsort 18.017 seconds Quicksort: Timing Version 2 for 1000000 random numbers Took >> 1000 seconds Quicksort: Timing Version 3 for 1000000 random numbers Elegant 124.153 seconds Quicksort: Timing Version 4 for 1000000 random numbers Recursive 21.370 seconds Quicksort: Timing Version 5 for 1000000 random numbers Optimized 17.803 seconds
- Overall Regina is about 2 times faster with big stems
- Both interpreters aren't really fond of stack operations
- But ooRexx underperforms in this area
- Straithforward coding (no stack, no recursion) showed to be fastest
- However, the fast versions require 'expose stem.' and thus are not generic anymore
Refal
$ENTRY Go {
, 7 6 5 9 8 4 3 1 2 0: e.Arr
= <Prout e.Arr>
<Prout <Sort e.Arr>>;
};
Sort {
= ;
s.N = s.N;
s.Pivot e.X =
<Sort <Filter s.Pivot '-' e.X>>
<Filter s.Pivot '=' e.X>
s.Pivot
<Sort <Filter s.Pivot '+' e.X>>;
};
Filter {
s.N s.Comp = ;
s.N s.Comp s.I e.List, <Compare s.I s.N>: {
s.Comp = s.I <Filter s.N s.Comp e.List>;
s.X = <Filter s.N s.Comp e.List>;
};
};- Output:
7 6 5 9 8 4 3 1 2 0 0 1 2 3 4 5 6 7 8 9
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 + nlOutput:
before sort: 4 65 2 -31 0 99 2 83 782 1 after sort: -31 0 1 2 2 4 65 83 99 782
RPL
≪ DUP SIZE → size
≪ IF size 1 > THEN
DUP size 2 / CEIL GET { } DUP DUP → pivot less equal greater
≪ 1 size FOR j
DUP j GET pivot
CASE
DUP2 < THEN DROP 'less' STO+ END
DUP2 == THEN DROP 'equal' STO+ END
DROP 'greater' STO+ END
NEXT DROP
less QSORT
greater QSORT
equal SWAP + +
≫
END
≫ ≫ 'QSORT' STO
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
endor
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
endor functionally
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
endRust
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<T,F>(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<T,F>(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
}- Output:
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"]
Or, using functional style (slower than the imperative style but faster than functional style in other languages):
fn main() {
let numbers = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1];
println!("{:?}\n", quick_sort(numbers.iter()));
}
fn quick_sort<T, E>(mut v: T) -> Vec<E>
where
T: Iterator<Item = E>,
E: PartialOrd,
{
match v.next() {
None => Vec::new(),
Some(pivot) => {
let (lower, higher): (Vec<_>, Vec<_>) = v.partition(|it| it < &pivot);
let lower = quick_sort(lower.into_iter());
let higher = quick_sort(higher.into_iter());
lower.into_iter()
.chain(core::iter::once(pivot))
.chain(higher.into_iter())
.collect()
}
}
}By the way this implementation needs only O(n) memory because the partition(...) call already "consumes" v. This means that the memory of v will be freed here, before the recursive calls to quick_sort(...). If we tried to use v later, we would get a compilation error.
SASL
Copied from SASL manual, Appendix II, solution (2)(b)
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
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;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:
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:
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]:
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.
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:
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
List quicksort
(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:
(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) >)
Vector quicksort (in place)
For CHICKEN:
;;;-------------------------------------------------------------------
;;;
;;; Quicksort in R7RS Scheme, working in-place on vectors (that is,
;;; arrays). I closely follow the "better quicksort algorithm"
;;; pseudocode, and thus the code is more "procedural" than
;;; "functional".
;;;
;;; I use a random pivot. If you can generate a random number quickly,
;;; this is a good method, but for this demonstration I have taken a
;;; fast linear congruential generator and made it brutally slow. It's
;;; just a demonstration. :)
;;;
(import (scheme base))
(import (scheme case-lambda))
(import (scheme write))
;;;-------------------------------------------------------------------
;;;
;;; Add "while" loops to the language.
;;;
(define-syntax while
(syntax-rules ()
((_ pred? body ...)
(let loop ()
(when pred?
(begin body ...)
(loop))))))
;;;-------------------------------------------------------------------
;;;
;;; In-place quicksort.
;;;
(define vector-quicksort!
(case-lambda
;; Use a default pivot selector.
((<? vec)
;; Random pivot.
(vector-quicksort! (lambda (vec i-first i-last)
(vector-ref vec (randint i-first i-last)))
<? vec))
;; Specify a pivot selector.
((pivot-select <? vec)
;;
;; The recursion:
;;
(let quicksort! ((i-first 0)
(i-last (- (vector-length vec) 1)))
(let ((n (- i-last i-first -1)))
(when (> n 1)
(let* ((pivot (pivot-select vec i-first i-last)))
(let ((left i-first)
(right i-last))
(while (<= left right)
(while (< (vector-ref vec left) pivot)
(set! left (+ left 1)))
(while (> (vector-ref vec right) pivot)
(set! right (- right 1)))
(when (<= left right)
(let ((lft (vector-ref vec left))
(rgt (vector-ref vec right)))
(vector-set! vec left rgt)
(vector-set! vec right lft)
(set! left (+ left 1))
(set! right (- right 1)))))
(quicksort! i-first right)
(quicksort! left i-last)))))))))
;;;-------------------------------------------------------------------
;;;
;;; A simple linear congruential generator, attributed by
;;; https://en.wikipedia.org/w/index.php?title=Linear_congruential_generator&oldid=1083800601
;;; to glibc and GCC. No attempt has been made to optimize this code.
;;;
(define seed 1)
(define two**31 (expt 2 31))
(define (random-integer)
(let* ((s0 seed)
(s1 (truncate-remainder (+ (* 1103515245 s0) 12345)
two**31)))
(set! seed s1)
s0))
(define randint
(case-lambda
((n) (truncate-remainder (random-integer) n))
((i-first i-last) (+ i-first (randint (- i-last i-first -1))))))
;;;-------------------------------------------------------------------
;;;
;;; A demonstration of in-place vector quicksort.
;;;
(define vec1 (vector-copy #(60 53 100 72 19 67 14
31 4 1 5 9 2 6 5 3 5 8
28 9 95 22 67 55 20 41
42 29 20 74 39)))
(vector-quicksort! < vec1)
(write vec1)
(newline)
;;;-------------------------------------------------------------------- Output:
$ gosh vector-quicksort.scm #(1 2 3 4 5 5 5 6 8 9 9 14 19 20 20 22 28 29 31 39 41 42 53 55 60 67 67 72 74 95 100)
Seed7
const proc: quickSort (inout array elemType: arr, in integer: left, in integer: right) is func
local
var elemType: compare_elem is elemType.value;
var integer: less_idx is 0;
var integer: greater_idx is 0;
var elemType: help is elemType.value;
begin
if right > left then
compare_elem := arr[right];
less_idx := pred(left);
greater_idx := right;
repeat
repeat
incr(less_idx);
until arr[less_idx] >= compare_elem;
repeat
decr(greater_idx);
until arr[greater_idx] <= compare_elem or greater_idx = left;
if less_idx < greater_idx then
help := arr[less_idx];
arr[less_idx] := arr[greater_idx];
arr[greater_idx] := help;
end if;
until less_idx >= greater_idx;
arr[right] := arr[less_idx];
arr[less_idx] := compare_elem;
quickSort(arr, left, pred(less_idx));
quickSort(arr, succ(less_idx), right);
end if;
end func;
const proc: quickSort (inout array elemType: arr) is func
begin
quickSort(arr, 1, length(arr));
end func;Original source: [2]
SETL
In-place sort (looks much the same as the C version)
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:
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
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
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
fun quicksort [] = []
| quicksort (x::xs) =
let
val (left, right) = List.partition (fn y => y<x) xs
in
quicksort left @ [x] @ quicksort right
endSolution 2:
Without using List.partition
fun par_helper([], x, l, r) = (l, r)
| par_helper(h::t, x, l, r) =
if h <= x then
par_helper(t, x, l @ [h], r)
else
par_helper(t, x, l, r @ [h]);
fun par(l, x) = par_helper(l, x, [], []);
fun quicksort [] = []
| quicksort (h::t) =
let
val (left, right) = par(t, h)
in
quicksort left @ [h] @ quicksort right
end;Swift
func quicksort<T where T : Comparable>(inout elements: [T], range: Range<Int>) {
if (range.endIndex - range.startIndex > 1) {
let pivotIndex = partition(&elements, range)
quicksort(&elements, range.startIndex ..< pivotIndex)
quicksort(&elements, pivotIndex+1 ..< range.endIndex)
}
}
func quicksort<T where T : Comparable>(inout elements: [T]) {
quicksort(&elements, indices(elements))
}Symsyn
x : 23 : 15 : 99 : 146 : 3 : 66 : 71 : 5 : 23 : 73 : 19
quicksort param l r
l i
r j
((l+r) shr 1) k
x.k pivot
repeat
if pivot > x.i
+ cmp
+ i
goif
endif
if pivot < x.j
+ cmp
- j
goif
endif
if i <= j
swap x.i x.j
- j
+ i
endif
if i <= j
go repeat
endif
if l < j
save l r i j
call quicksort l j
restore l r i j
endif
if i < r
save l r i j
call quicksort i r
restore l r i j
endif
return
start
' original values : ' $r
call showvalues
call quicksort 0 10
' sorted values : ' $r
call showvalues
stop
showvalues
$s
i
if i <= 10
"$s ' ' x.i ' '" $s
+ i
goif
endif
" $r $s " []
returnTailspin
Simple recursive quicksort:
templates quicksort
@: [];
$ -> #
when <[](2..)> do
def pivot: $(1);
[ [ $(2..last)... -> \(
when <..$pivot> do
$ !
otherwise
..|@quicksort: $;
\)] -> quicksort..., $pivot, $@ -> quicksort... ] !
otherwise
$ !
end quicksort
[4,5,3,8,1,2,6,7,9,8,5] -> quicksort -> !OUT::writeIn place:
templates quicksort
templates partial
def first: $(1);
def last: $(2);
def pivot: $@quicksort($first);
@: $(1) + 1;
$(2) -> #
when <..~$@> do
def limit: $;
@quicksort($first): $@quicksort($limit);
@quicksort($limit): $pivot;
[ $first, $limit - 1 ] !
[ $limit + 1, $last ] !
when <?($@quicksort($) <$pivot~..>)> do
$ - 1 -> #
when <?($@quicksort($@) <..$pivot>)> do
@: $@ + 1; $ -> #
otherwise
def temp: $@quicksort($@);
@quicksort($@): $@quicksort($);
@quicksort($): $temp;
@: $@ + 1; $ - 1 -> #
end partial
@: $;
[1, $@::length] -> #
$@ !
when <?($(1) <..~$(2)>)> do
$ -> partial -> #
end quicksort
[4,5,3,8,1,2,6,7,9,8,5] -> quicksort -> !OUT::writeTcl
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 9TypeScript
/**
Generic quicksort function using typescript generics.
Follows quicksort as done in CLRS.
*/
export type Comparator<T> = (o1: T, o2: T) => number;
export function quickSort<T>(array: T[], compare: Comparator<T>) {
if (array.length <= 1 || array == null) {
return;
}
sort(array, compare, 0, array.length - 1);
}
function sort<T>(
array: T[], compare: Comparator<T>, 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<T>(
array: T[], compare: Comparator<T>, 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<T>(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);
}
}UnixPipes
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 | qsortUrsala
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.
#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>- Output:
<367,381,475,506,694,1377,1580,1704,1872,3712>
V
[qsort
[joinparts [p [*l1] [*l2] : [*l1 p *l2]] view].
[split_on_first uncons [>] split].
[small?]
[]
[split_on_first [l1 l2 : [l1 qsort l2 qsort joinparts]] view i]
ifte].The way of joy (using binrec)
[qsort
[small?] []
[uncons [>] split]
[[p [*l] [*g] : [*l p *g]] view]
binrec].V (Vlang)
fn partition(mut arr []int, low int, high int) int {
pivot := arr[high]
mut i := (low - 1)
for j in low .. high {
if arr[j] < pivot {
i++
temp := arr[i]
arr[i] = arr[j]
arr[j] = temp
}
}
temp := arr[i + 1]
arr[i + 1] = arr[high]
arr[high] = temp
return i + 1
}
fn quick_sort(mut arr []int, low int, high int) {
if low < high {
pi := partition(mut arr, low, high)
quick_sort(mut arr, low, pi - 1)
quick_sort(mut arr, pi + 1, high)
}
}
fn main() {
mut arr := [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
n := arr.len - 1
println('Input: ' + arr.str())
quick_sort(mut arr, 0, n)
println('Output: ' + arr.str())
}- Output:
Input: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1] Output: [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]
Wart
def (qsort (pivot ... ns))
(+ (qsort+keep (fn(_) (_ < pivot)) ns)
list.pivot
(qsort+keep (fn(_) (_ > pivot)) ns))
def (qsort x) :case x=nil
nilWren
import "./sort" for Sort
var array = [
[4, 65, 2, -31, 0, 99, 2, 83, 782, 1],
[7, 5, 2, 6, 1, 4, 2, 6, 3],
["echo", "lima", "charlie", "whiskey", "golf", "papa", "alfa", "india", "foxtrot", "kilo"]
]
for (a in array) {
System.print("Before: %(a)")
Sort.quick(a)
System.print("After : %(a)")
System.print()
}- Output:
Before: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1] After : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782] Before: [7, 5, 2, 6, 1, 4, 2, 6, 3] After : [1, 2, 2, 3, 4, 5, 6, 6, 7] Before: [echo, lima, charlie, whiskey, golf, papa, alfa, india, foxtrot, kilo] After : [alfa, charlie, echo, foxtrot, golf, india, kilo, lima, papa, whiskey]
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);
]- Output:
.Pabcdeefghiiijklmnoooqrstuuvwxyz
Z80 Assembly
sjasmplus syntax
;--------------------------------------------------------------------------------------------------------------------
; Quicksort, inputs (__sdcccall(1) calling convention):
; HL = uint16_t* A (pointer to beginning of array)
; DE = uint16_t len (number of word elements in array)
; modifies: AF, A'F', BC, DE, HL
; WARNING: array can't be aligned to start/end of 64ki address space, like HL == 0x0000, or having last value at 0xFFFE
; WARNING: stack space required is on average about 6*log(len) (depending on the data, in extreme case it may be more)
quicksort_a:
; convert arguments to HL=A.begin(), DE=A.end() and continue with quicksort_a_impl
ex de,hl
add hl,hl
add hl,de
ex de,hl
; |
; fallthrough into implementation
; |
; v
;--------------------------------------------------------------------------------------------------------------------
; Quicksort implementation, inputs:
; HL = uint16_t* A.begin() (pointer to beginning of array)
; DE = uint16_t* A.end() (pointer beyond array)
; modifies: AF, A'F', BC, HL (DE is preserved)
quicksort_a_impl:
; array must be located within 0x0002..0xFFFD
ld c,l
ld b,h ; BC = A.begin()
; if (len < 2) return; -> if (end <= begin+2) return;
inc hl
inc hl
or a
sbc hl,de ; HL = -(2*len-2), len = (2-HL)/2
ret nc ; case: begin+2 >= end <=> (len < 2)
push de ; preserve A.end() for recursion
push bc ; preserve A.begin() for recursion
; uint16_t pivot = A[len / 2];
rr h
rr l
dec hl
res 0,l
add hl,de
ld a,(hl)
inc hl
ld l,(hl)
ld h,b
ld b,l
ld l,c
ld c,a ; HL = A.begin(), DE = A.end(), BC = pivot
; flip HL/DE meaning, it makes simpler the recursive tail and (A[j] > pivot) test
ex de,hl ; DE = A.begin(), HL = A.end(), BC = pivot
dec de ; but keep "from" address (related to A[i]) at -1 as "default" state
; for (i = 0, j = len - 1; ; i++, j--) { ; DE = (A+i-1).hi, HL = A+j+1
.find_next_swap:
; while (A[j] > pivot) j--;
.find_j:
dec hl
ld a,b
sub (hl)
dec hl ; HL = A+j (finally)
jr c,.find_j ; if cf=1, A[j].hi > pivot.hi
jr nz,.j_found ; if zf=0, A[j].hi < pivot.hi
ld a,c ; if (A[j].hi == pivot.hi) then A[j].lo vs pivot.lo is checked
sub (hl)
jr c,.find_j
.j_found:
; while (A[i] < pivot) i++;
.find_i:
inc de
ld a,(de)
inc de ; DE = (A+i).hi (ahead +0.5 for swap)
sub c
ld a,(de)
sbc a,b
jr c,.find_i ; cf=1 -> A[i] < pivot
; if (i >= j) break; // DE = (A+i).hi, HL = A+j, BC=pivot
sbc hl,de ; cf=0 since `jr c,.find_i`
jr c,.swaps_done
add hl,de ; DE = (A+i).hi, HL = A+j
; swap(A[i], A[j]);
inc hl
ld a,(de)
ldd
ex af,af
ld a,(de)
ldi
ex af,af
ld (hl),a ; Swap(A[i].hi, A[j].hi) done
dec hl
ex af,af
ld (hl),a ; Swap(A[i].lo, A[j].lo) done
inc bc
inc bc ; pivot value restored (was -=2 by ldd+ldi)
; --j; HL = A+j is A+j+1 for next loop (ready)
; ++i; DE = (A+i).hi is (A+i-1).hi for next loop (ready)
jp .find_next_swap
.swaps_done:
; i >= j, all elements were already swapped WRT pivot, call recursively for the two sub-parts
dec de ; DE = A+i
; quicksort_c(A, i);
pop hl ; HL = A
call quicksort_a_impl
; quicksort_c(A + i, len - i);
ex de,hl ; HL = A+i
pop de ; DE = end() (and return it preserved)
jp quicksort_a_implFull example with test/debug data for ZX Spectrum is at [github].
Zig
Works with: 0.10.x, 0.11.x, 0.12.0-dev.1390+94cee4fb2
const std = @import("std");
pub fn quickSort(comptime T: type, arr: []T, comptime compareFn: fn (T, T) bool) void {
if (arr.len < 2) return;
const pivot_index = partition(T, arr, compareFn);
quickSort(T, arr[0..pivot_index], compareFn);
quickSort(T, arr[pivot_index + 1 .. arr.len], compareFn);
}
fn partition(comptime T: type, arr: []T, comptime compareFn: fn (T, T) bool) usize {
const pivot_index = arr.len / 2;
const last_index = arr.len - 1;
std.mem.swap(T, &arr[pivot_index], &arr[last_index]);
var store_index: usize = 0;
for (arr[0 .. arr.len - 1]) |*elem_ptr| {
if (compareFn(elem_ptr.*, arr[last_index])) {
std.mem.swap(T, elem_ptr, &arr[store_index]);
store_index += 1;
}
}
std.mem.swap(T, &arr[store_index], &arr[last_index]);
return store_index;
}const std = @import("std");
pub fn main() void {
const print = std.debug.print;
var arr = [_]i16{ 4, 65, 2, -31, 0, 99, 2, 83, 782, 1 };
print("Before: {any}\n\n", .{arr});
print("Sort numbers in ascending order.\n", .{});
quickSort(i16, &arr, struct {
fn sortFn(left: i16, right: i16) bool {
return left < right;
}
}.sortFn);
print("After: {any}\n\n", .{arr});
print("Sort numbers in descending order.\n", .{});
quickSort(i16, &arr, struct {
fn sortFn(left: i16, right: i16) bool {
return left > right;
}
}.sortFn);
print("After: {any}\n\n", .{arr});
}- Output:
Before: { 4, 65, 2, -31, 0, 99, 2, 83, 782, 1 }
Sort numbers in ascending order.
After: { -31, 0, 1, 2, 2, 4, 65, 83, 99, 782 }
Sort numbers in descending order.
After: { 782, 99, 83, 65, 4, 2, 2, 1, 0, -31 }
zkl
These are the Wikipedia algorithms.
Quick sort immutable sequence using crappy pivot choice:
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:
fcn qiSort(list,cmp='<){ // in place quick sort
fcn(list,left,right,cmp){
if (left<right){
// partition list
pivotIndex:=(left+right)/2; // or median of first,middle,last
pivot:=list[pivotIndex];
list.swap(pivotIndex,right); // move pivot to end
pivotIndex:=left;
i:=left; do(right-left){ // foreach i in ([left..right-1])
if(cmp(list[i],pivot)){ // not cheap
list.swap(i,pivotIndex);
pivotIndex+=1;
}
i+=1;
}
list.swap(pivotIndex,right); // move pivot to final place
// sort the partitions
self.fcn(list,left,pivotIndex-1,cmp);
return(self.fcn(list,pivotIndex+1,right,cmp));
}
}(list,0,list.len()-1,cmp);
list;
}Categories:
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