Sorting algorithms/Quicksort: Difference between revisions
(Replaced both versions of the Kotlin code: The first one did not even sort correctly, the second one did everything in a Java style.) |
m (Remove syntax error) |
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filter { it == first() } + |
filter { it == first() } + |
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filter { it > first() }.qsort() |
filter { it > first() }.qsort() |
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</lang> |
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A more efficient version that does only one comparison per element: |
A more efficient version that does only one comparison per element: |
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Revision as of 18:32, 9 March 2020
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.
360 Assembly
Structured version with ASM & ASSIST macros. <lang 360asm>* 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</lang>
- Output:
1 1 2 6 7 8 8 9 9 9 10 15 16 16 16 17 18 18 19 20
ABAP
This works for ABAP Version 7.40 and above <lang ABAP> 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. </lang>
- Output:
[ 31- 0 1 2 2 4 65 83 99 782 ]
ACL2
<lang Lisp>(defun partition (p xs)
(if (endp xs)
(mv nil nil)
(mv-let (less more)
(partition p (rest xs))
(if (< (first xs) p)
(mv (cons (first xs) less) more)
(mv less (cons (first xs) more))))))
(defun qsort (xs)
(if (endp xs)
nil
(mv-let (less more)
(partition (first xs) (rest xs))
(append (qsort less)
(list (first xs))
(qsort more)))))</lang>
Usage: <lang>> (qsort '(8 6 7 5 3 0 9)) (0 3 5 6 7 8 9)</lang>
ActionScript
The functional programming way <lang actionscript>function quickSort (array:Array):Array {
if (array.length <= 1)
return array;
var pivot:Number = array[Math.round(array.length / 2)];
return quickSort(array.filter(function (x:Number, index:int, array:Array):Boolean { return x < pivot; })).concat(
array.filter(function (x:Number, index:int, array:Array):Boolean { return x == pivot; })).concat(
quickSort(array.filter(function (x:Number, index:int, array:Array):Boolean { return x > pivot; })));
}</lang>
The faster way <lang actionscript>function quickSort (array:Array):Array {
if (array.length <= 1)
return array;
var pivot:Number = array[Math.round(array.length / 2)];
var less:Array = []; var equal:Array = []; var greater:Array = [];
for each (var x:Number in array) {
if (x < pivot)
less.push(x);
if (x == pivot)
equal.push(x);
if (x > pivot)
greater.push(x);
}
return quickSort(less).concat(
equal).concat(
quickSort(greater));
}</lang>
Ada
This example is implemented as a generic procedure.
The procedure specification is: <lang ada>----------------------------------------------------------------------- -- Generic 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);</lang> The procedure body deals with any discrete index type, either an integer type or an enumerated type. <lang ada>----------------------------------------------------------------------- -- 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;</lang> An example of how this procedure may be used is: <lang ada> with Ada.Text_Io; with Ada.Float_Text_IO; use Ada.Float_Text_IO;
procedure Sort_Test is
type Days is (Mon, Tue, Wed, Thu, Fri, Sat, Sun);
type Sales is array (Days range <>) of Float;
procedure Sort_Days is new Quick_Sort(Float, Days, Sales);
procedure Print (Item : Sales) is
begin
for I in Item'range loop
Put(Item => Item(I), Fore => 5, Aft => 2, Exp => 0);
end loop;
end Print;
Weekly_Sales : Sales := (Mon => 300.0,
Tue => 700.0,
Wed => 800.0,
Thu => 500.0,
Fri => 200.0,
Sat => 100.0,
Sun => 900.0);
begin
Print(Weekly_Sales); Ada.Text_Io.New_Line(2); Sort_Days(Weekly_Sales); Print(Weekly_Sales);
end Sort_Test;</lang>
ALGOL 68
<lang algol68>#--- Swap function ---# PROC swap = (REF []INT array, INT first, INT second) VOID: (
INT temp := array[first]; array[first] := array[second]; array[second]:= temp
);
- --- Quick sort 3 arg function ---#
PROC quick = (REF [] INT array, INT first, INT last) VOID: (
INT smaller := first + 1,
larger := last,
pivot := array[first];
WHILE smaller <= larger DO
WHILE array[smaller] < pivot AND smaller < last DO
smaller +:= 1
OD;
WHILE array[larger] > pivot AND larger > first DO
larger -:= 1
OD;
IF smaller < larger THEN
swap(array, smaller, larger);
smaller +:= 1;
larger -:= 1
ELSE
smaller +:= 1
FI
OD;
swap(array, first, larger);
IF first < larger-1 THEN
quick(array, first, larger-1)
FI;
IF last > larger +1 THEN
quick(array, larger+1, last)
FI
);
- --- Quick sort 1 arg function ---#
PROC quicksort = (REF []INT array) VOID: (
IF UPB array > 1 THEN quick(array, 1, UPB array) FI
);
main: (
[10]INT a;
FOR i FROM 1 TO UPB a DO
a[i] := ROUND(random*1000)
OD;
print(("Before:", a));
quicksort(a);
print((newline, newline));
print(("After: ", a))
) </lang>
- Output:
Before: +73 +921 +179 +961 +50 +324 +82 +178 +243 +458
After: +50 +73 +82 +178 +179 +243 +324 +458 +921 +961
ALGOL W
<lang algolw>% 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 ;</lang>
APL
<lang apl> qsort ← {1≥⍴⍵:⍵ ⋄ e←⍵[?⍴⍵] ⋄ (∇(⍵<e)/⍵) , ((⍵=e)/⍵) , (∇(⍵>e)/⍵)}
qsort 31 4 1 5 9 2 6 5 3 5 8
1 2 3 4 5 5 5 6 8 9 31</lang>
Of course, in real APL applications, one would use ⍋ to sort (which will pick a sorting algorithm suited to the argument).
AppleScript
Emphasising clarity and simplicity more than run-time performance. (Practical scripts will often delegate sorting to the OS X shell, or, since OS X Yosemite, to Foundation classes through the ObjC interface).
(Functional ES5 version)
<lang AppleScript>-- 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</lang>
- Output:
<lang AppleScript>{5.7, 8.5, 11.8, 14.1, 16.7, 21.3}</lang>
---
Emphasising clarity, simplicity, performance, and the non-use of list types which have never officially been part of AppleScript:
<lang applescript>(* Quicksort Algorithm: S.A.R. (Tony) Hoare, 1960. This is a basic in-place implementation.
Quicksort gets less efficient with recursion depth as the ratio of dividing-and-conquering to actual sorting increases. It's also pot luck whether or not the pivot values selected are the best ones in their partitions for optimal subpartitioning. Robert Sedgewick and others have suggested effective optimisations such as switching to insertion sorts for partitions below a certain length, using median-of-three pivot selection, three-way partitioning, tail-call elimination, etc. But the basic algorithm is still fast (depending on the language used and who writes the code) and elegant.
- )
on quicksort(theList)
-- This script object holds both the target list and the recursive process,
-- enabling the list's items to be accessed with faster specifiers (an AppleScript quirk)
-- and to save the list itself having to be passed as a parameter with the recursive calls.
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 leftValue to my lst's item i
repeat while (leftValue < pivot)
set i to i + 1
set leftValue to my lst's item i
end repeat
set rightValue to my lst's item j
repeat while (rightValue > pivot)
set j to j - 1
set rightValue to my lst's item j
end repeat
if (j > i) then
set my lst's item i to rightValue
set my lst's item j to leftValue
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
set listLength to (count theList)
if (listLength > 1) then tell o to qsrt(1, listLength)
return -- nothing. Either o's lst or theList can be returned if preferred. They and the input list are all the same object.
end quicksort
set aList to {28, 9, 95, 22, 67, 55, 20, 41, 60, 53, 100, 72, 19, 67, 14, 42, 29, 20, 74, 39} quicksort(aList) return aList --> {9, 14, 19, 20, 20, 22, 28, 29, 39, 41, 42, 53, 55, 60, 67, 67, 72, 74, 95, 100}</lang>
ARM Assembly
<lang 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 0xCCCCCCCD
</lang>
Arturo
<lang arturo>quickSort: @(items){ if [size items] < 2 { items } { [quickSort|filter [slice items 1] { & < items.0 }] + items.0 + [quickSort|filter [slice items 1] { & >= items.0 }] } }
print [quickSort #(3 1 2 8 5 7 9 4 6)]</lang>
- Output:
#(1 2 3 4 5 6 7 8 9)
AWK
<lang awk>
- the following qsort implementation extracted from:
- ftp://ftp.armory.com/pub/lib/awk/qsort
- Copyleft GPLv2 John DuBois
- @(#) qsort 1.2.1 2005-10-21
- 1990 john h. dubois iii (john@armory.com)
- qsortArbIndByValue(): Sort an array according to the values of its elements.
- Input variables:
- Arr[] is an array of values with arbitrary (associative) indices.
- Output variables:
- k[] is returned with numeric indices 1..n. The values assigned to these
- indices are the indices of Arr[], ordered so that if Arr[] is stepped
- through in the order Arr[k[1]] .. Arr[k[n]], it will be stepped through in
- order of the values of its elements.
- Return value: The number of elements in the arrays (n).
- NOTES:
- Full example for accessing results:
- foolist["second"] = 2;
- foolist["zero"] = 0;
- foolist["third"] = 3;
- foolist["first"] = 1;
- outlist[1] = 0;
- n = qsortArbIndByValue(foolist, outlist)
- for (i = 1; i <= n; i++) {
- printf("item at %s has value %d\n", outlist[i], foolist[outlist[i]]);
- }
- delete outlist;
function qsortArbIndByValue(Arr, k,
ArrInd, ElNum)
{
ElNum = 0;
for (ArrInd in Arr) {
k[++ElNum] = ArrInd;
}
qsortSegment(Arr, k, 1, ElNum);
return ElNum;
}
- qsortSegment(): Sort a segment of an array.
- Input variables:
- Arr[] contains data with arbitrary indices.
- k[] has indices 1..nelem, with the indices of Arr[] as values.
- Output variables:
- k[] is modified by this function. The elements of Arr[] that are pointed to
- by k[start..end] are sorted, with the values of elements of k[] swapped
- so that when this function returns, Arr[k[start..end]] will be in order.
- Return value: None.
function qsortSegment(Arr, k, start, end,
left, right, sepval, tmp, tmpe, tmps)
{
if ((end - start) < 1) { # 0 or 1 elements
return;
}
# handle two-element case explicitly for a tiny speedup
if ((end - start) == 1) {
if (Arr[tmps = k[start]] > Arr[tmpe = k[end]]) {
k[start] = tmpe;
k[end] = tmps;
}
return;
}
# Make sure comparisons act on these as numbers
left = start + 0;
right = end + 0;
sepval = Arr[k[int((left + right) / 2)]];
# Make every element <= sepval be to the left of every element > sepval
while (left < right) {
while (Arr[k[left]] < sepval) {
left++;
}
while (Arr[k[right]] > sepval) {
right--;
}
if (left < right) {
tmp = k[left];
k[left++] = k[right];
k[right--] = tmp;
}
}
if (left == right)
if (Arr[k[left]] < sepval) {
left++;
} else {
right--;
}
if (start < right) {
qsortSegment(Arr, k, start, right);
}
if (left < end) {
qsortSegment(Arr, k, left, end);
}
} </lang>
AutoHotkey
Translated from the python example: <lang AutoHotkey>a := [4, 65, 2, -31, 0, 99, 83, 782, 7] for k, v in QuickSort(a) Out .= "," v MsgBox, % SubStr(Out, 2) return
QuickSort(a) { if (a.MaxIndex() <= 1) return a Less := [], Same := [], More := [] Pivot := a[1] for k, v in a { if (v < Pivot) less.Insert(v) else if (v > Pivot) more.Insert(v) else same.Insert(v) } Less := QuickSort(Less) Out := QuickSort(More) if (Same.MaxIndex()) Out.Insert(1, Same*) ; insert all values of same at index 1 if (Less.MaxIndex()) Out.Insert(1, Less*) ; insert all values of less at index 1 return Out }</lang>
Old implementation for AutoHotkey 1.0: <lang AutoHotkey>MsgBox % quicksort("8,4,9,2,1")
quicksort(list) {
StringSplit, list, list, `,
If (list0 <= 1)
Return list
pivot := list1
Loop, Parse, list, `,
{
If (A_LoopField < pivot)
less = %less%,%A_LoopField%
Else If (A_LoopField > pivot)
more = %more%,%A_LoopField%
Else
pivotlist = %pivotlist%,%A_LoopField%
}
StringTrimLeft, less, less, 1
StringTrimLeft, more, more, 1
StringTrimLeft, pivotList, pivotList, 1
less := quicksort(less)
more := quicksort(more)
Return less . pivotList . more
}</lang>
BASIC
This is specifically for INTEGERs, but can be modified for any data type by changing arr()'s type.
<lang qbasic>DECLARE SUB quicksort (arr() AS INTEGER, leftN AS INTEGER, rightN AS INTEGER)
DIM q(99) AS INTEGER DIM n AS INTEGER
RANDOMIZE TIMER
FOR n = 0 TO 99
q(n) = INT(RND * 9999)
NEXT
OPEN "output.txt" FOR OUTPUT AS 1
FOR n = 0 TO 99
PRINT #1, q(n),
NEXT
PRINT #1,
quicksort q(), 0, 99
FOR n = 0 TO 99
PRINT #1, q(n),
NEXT
CLOSE
SUB quicksort (arr() AS INTEGER, leftN AS INTEGER, rightN AS INTEGER)
DIM pivot AS INTEGER, leftNIdx AS INTEGER, rightNIdx AS INTEGER
leftNIdx = leftN
rightNIdx = rightN
IF (rightN - leftN) > 0 THEN
pivot = (leftN + rightN) / 2
WHILE (leftNIdx <= pivot) AND (rightNIdx >= pivot)
WHILE (arr(leftNIdx) < arr(pivot)) AND (leftNIdx <= pivot)
leftNIdx = leftNIdx + 1
WEND
WHILE (arr(rightNIdx) > arr(pivot)) AND (rightNIdx >= pivot)
rightNIdx = rightNIdx - 1
WEND
SWAP arr(leftNIdx), arr(rightNIdx)
leftNIdx = leftNIdx + 1
rightNIdx = rightNIdx - 1
IF (leftNIdx - 1) = pivot THEN
rightNIdx = rightNIdx + 1
pivot = rightNIdx
ELSEIF (rightNIdx + 1) = pivot THEN
leftNIdx = leftNIdx - 1
pivot = leftNIdx
END IF
WEND
quicksort arr(), leftN, pivot - 1
quicksort arr(), pivot + 1, rightN
END IF
END SUB</lang>
BBC BASIC
<lang bbcbasic> DIM test(9)
test() = 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
PROCquicksort(test(), 0, 10)
FOR i% = 0 TO 9
PRINT test(i%) ;
NEXT
PRINT
END
DEF PROCquicksort(a(), s%, n%)
LOCAL l%, p, r%, t%
IF n% < 2 THEN ENDPROC
t% = s% + n% - 1
l% = s%
r% = t%
p = a((l% + r%) DIV 2)
REPEAT
WHILE a(l%) < p l% += 1 : ENDWHILE
WHILE a(r%) > p r% -= 1 : ENDWHILE
IF l% <= r% THEN
SWAP a(l%), a(r%)
l% += 1
r% -= 1
ENDIF
UNTIL l% > r%
IF s% < r% PROCquicksort(a(), s%, r% - s% + 1)
IF l% < t% PROCquicksort(a(), l%, t% - l% + 1 )
ENDPROC</lang>
- Output:
-31 0 1 2 2 4 65 83 99 782
IS-BASIC
<lang 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 EK 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 DEF</lang>
BCPL
<lang BCPL>// This can be run using Cintcode BCPL freely available from www.cl.cam.ac.uk/users/mr10.
GET "libhdr.h"
LET quicksort(v, n) BE qsort(v+1, v+n)
AND qsort(l, r) BE { WHILE l+8<r DO
{ LET midpt = (l+r)/2
// Select a good(ish) median value.
LET val = middle(!l, !midpt, !r)
LET i = partition(val, l, r)
// Only use recursion on the smaller partition.
TEST i>midpt THEN { qsort(i, r); r := i-1 }
ELSE { qsort(l, i-1); l := i }
}
FOR p = l+1 TO r DO // Now perform insertion sort.
FOR q = p-1 TO l BY -1 TEST q!0<=q!1 THEN BREAK
ELSE { LET t = q!0
q!0 := q!1
q!1 := t
}
}
AND middle(a, b, c) = a b<c -> b,
a<c -> c,
a,
b<c -> a<c -> a,
c,
b
AND partition(median, p, q) = VALOF { LET t = ?
WHILE !p < median DO p := p+1 WHILE !q > median DO q := q-1 IF p>=q RESULTIS p t := !p !p := !q !q := t p, q := p+1, q-1
} REPEAT
LET start() = VALOF {
LET v = VEC 1000
FOR i = 1 TO 1000 DO v!i := randno(1_000_000)
quicksort(v, 1000)
FOR i = 1 TO 1000 DO
{ IF i MOD 10 = 0 DO newline()
writef(" %i6", v!i)
}
newline()
}</lang>
Bracmat
Instead of comparing elements explicitly, this solution puts the two elements-to-compare in a sum. After evaluating the sum its terms are sorted. Numbers are sorted numerically, strings alphabetically and compound expressions by comparing nodes and leafs in a left-to right order. Now there are three cases: either the terms stayed put, or they were swapped, or they were equal and were combined into one term with a factor 2 in front. To not let the evaluator add numbers together, each term is constructed as a dotted list.
<lang bracmat>( ( Q
= Less Greater Equal pivot element
. !arg:%(?pivot:?Equal) %?arg
& :?Less:?Greater
& whl
' ( !arg:%?element ?arg
& (.!element)+(.!pivot) { BAD: 1900+90 adds to 1990, GOOD: (.1900)+(.90) is sorted to (.90)+(.1900) }
: ( (.!element)+(.!pivot)
& !element !Less:?Less
| (.!pivot)+(.!element)
& !element !Greater:?Greater
| ?&!element !Equal:?Equal
)
)
& Q$!Less !Equal Q$!Greater
| !arg
)
& out$Q$(1900 optimized variants of 4001/2 Quicksort (quick,sort) are (quick,sober) features of 90 languages) );</lang>
- Output:
90 1900 4001/2 Quicksort are features languages of of optimized variants (quick,sober) (quick,sort)
C
<lang c>
- include <stdio.h>
void 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);
} </lang>
- 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.
<lang c>
- 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); }
} </lang>
C++
The following implements quicksort with a median-of-three pivot. As idiomatic in C++, the argument last is a one-past-end iterator. Note that this code takes advantage of std::partition, which is O(n). Also note that it needs a random-access iterator for efficient calculation of the median-of-three pivot (more exactly, for O(1) calculation of the iterator mid). <lang cpp>#include <iterator>
- include <algorithm> // for std::partition
- include <functional> // for std::less
// helper function for median of three template<typename T>
T median(T t1, T t2, T t3)
{
if (t1 < t2)
{
if (t2 < t3)
return t2;
else if (t1 < t3)
return t3;
else
return t1;
}
else
{
if (t1 < t3)
return t1;
else if (t2 < t3)
return t3;
else
return t2;
}
}
// helper object to get <= from < template<typename Order> struct non_strict_op:
public std::binary_function<typename Order::second_argument_type,
typename Order::first_argument_type,
bool>
{
non_strict_op(Order o): order(o) {}
bool operator()(typename Order::second_argument_type arg1,
typename Order::first_argument_type arg2) const
{
return !order(arg2, arg1);
}
private:
Order order;
};
template<typename Order> non_strict_op<Order> non_strict(Order o) {
return non_strict_op<Order>(o);
}
template<typename RandomAccessIterator,
typename Order> void quicksort(RandomAccessIterator first, RandomAccessIterator last, Order order)
{
if (first != last && first+1 != last)
{
typedef typename std::iterator_traits<RandomAccessIterator>::value_type value_type;
RandomAccessIterator mid = first + (last - first)/2;
value_type pivot = median(*first, *mid, *(last-1));
RandomAccessIterator split1 = std::partition(first, last, std::bind2nd(order, pivot));
RandomAccessIterator split2 = std::partition(split1, last, std::bind2nd(non_strict(order), pivot));
quicksort(first, split1, order);
quicksort(split2, last, order);
}
}
template<typename RandomAccessIterator>
void quicksort(RandomAccessIterator first, RandomAccessIterator last)
{
quicksort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());
}</lang>
A simpler version of the above that just uses the first element as the pivot and only does one "partition". <lang cpp>#include <iterator>
- include <algorithm> // for std::partition
- include <functional> // for std::less
template<typename RandomAccessIterator,
typename Order> void quicksort(RandomAccessIterator first, RandomAccessIterator last, Order order)
{
if (last - first > 1)
{
RandomAccessIterator split = std::partition(first+1, last, std::bind2nd(order, *first));
std::iter_swap(first, split-1);
quicksort(first, split-1, order);
quicksort(split, last, order);
}
}
template<typename RandomAccessIterator>
void quicksort(RandomAccessIterator first, RandomAccessIterator last)
{
quicksort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());
}</lang>
C#
Note that Array.Sort and ArrayList.Sort both use an unstable implementation of the quicksort algorithm. <lang csharp>// // The Tripartite conditional enables Bentley-McIlroy 3-way Partitioning. // This performs additional compares to isolate islands of keys equal to // the pivot value. Use unless key-equivalent classes are of small size. //
- define Tripartite
namespace Sort {
using System; using System.Diagnostics;
class QuickSort<T> where T : IComparable {
#region Constants
private const Int32 INSERTION_LIMIT_DEFAULT = 12;
#endregion
#region Properties
public Int32 InsertionLimit { get; set; }
private Random Random { get; set; }
private T Median { get; set; }
private Int32 Left { get; set; }
private Int32 Right { get; set; }
private Int32 LeftMedian { get; set; }
private Int32 RightMedian { get; set; }
#endregion
#region Constructors
public QuickSort(Int32 insertionLimit, Random random) {
this.InsertionLimit = insertionLimit;
this.Random = random;
}
public QuickSort(Int32 insertionLimit)
: this(insertionLimit, new Random()) {
}
public QuickSort()
: this(INSERTION_LIMIT_DEFAULT) {
}
#endregion
#region Sort Methods
public void Sort(T[] entries) {
Sort(entries, 0, entries.Length - 1);
}
public void Sort(T[] entries, Int32 first, Int32 last) {
var length = last + 1 - first;
while (length > 1) {
if (length < InsertionLimit) {
InsertionSort<T>.Sort(entries, first, last);
return;
}
Left = first;
Right = last;
pivot(entries);
partition(entries);
//[Note]Right < Left
var leftLength = Right + 1 - first;
var rightLength = last + 1 - Left;
//
// First recurse over shorter partition, then loop
// on the longer partition to elide tail recursion.
//
if (leftLength < rightLength) {
Sort(entries, first, Right);
first = Left;
length = rightLength;
}
else {
Sort(entries, Left, last);
last = Right;
length = leftLength;
}
}
}
private void pivot(T[] entries) {
//
// An odd sample size is chosen based on the log of the interval size.
// The median of a randomly chosen set of samples is then returned as
// an estimate of the true median.
//
var length = Right + 1 - Left;
var logLen = (Int32)Math.Log10(length);
var pivotSamples = 2 * logLen + 1;
var sampleSize = Math.Min(pivotSamples, length);
var last = Left + sampleSize - 1;
// Sample without replacement
for (var first = Left; first <= last; first++) {
// Random sampling avoids pathological cases
var random = Random.Next(first, Right + 1);
Swap(entries, first, random);
}
InsertionSort<T>.Sort(entries, Left, last);
Median = entries[Left + sampleSize / 2];
}
private void partition(T[] entries) {
var first = Left;
var last = Right;
- if Tripartite
LeftMedian = first;
RightMedian = last;
- endif
while (true) {
//[Assert]There exists some index >= Left where entries[index] >= Median
//[Assert]There exists some index <= Right where entries[index] <= Median
// So, there is no need for Left or Right bound checks
while (Median.CompareTo(entries[Left]) > 0) Left++;
while (Median.CompareTo(entries[Right]) < 0) Right--;
//[Assert]entries[Right] <= Median <= entries[Left]
if (Right <= Left) break;
Swap(entries, Left, Right);
swapOut(entries);
Left++;
Right--;
//[Assert]entries[first:Left - 1] <= Median <= entries[Right + 1:last]
}
if (Left == Right) {
Left++;
Right--;
}
//[Assert]Right < Left
swapIn(entries, first, last);
//[Assert]entries[first:Right] <= Median <= entries[Left:last]
//[Assert]entries[Right + 1:Left - 1] == Median when non-empty
}
#endregion
#region Swap Methods
[Conditional("Tripartite")]
private void swapOut(T[] entries) {
if (Median.CompareTo(entries[Left]) == 0) Swap(entries, LeftMedian++, Left);
if (Median.CompareTo(entries[Right]) == 0) Swap(entries, Right, RightMedian--);
}
[Conditional("Tripartite")]
private void swapIn(T[] entries, Int32 first, Int32 last) {
// Restore Median entries
while (first < LeftMedian) Swap(entries, first++, Right--);
while (RightMedian < last) Swap(entries, Left++, last--);
}
public static void Swap(T[] entries, Int32 index1, Int32 index2) {
if (index1 != index2) {
var entry = entries[index1];
entries[index1] = entries[index2];
entries[index2] = entry;
}
}
#endregion
}
#region Insertion Sort
static class InsertionSort<T> where T : IComparable {
public static void Sort(T[] entries, Int32 first, Int32 last) {
for (var index = first + 1; index <= last; index++)
insert(entries, first, index);
}
private static void insert(T[] entries, Int32 first, Int32 index) {
var entry = entries[index];
while (index > first && entries[index - 1].CompareTo(entry) > 0)
entries[index] = entries[--index];
entries[index] = entry;
}
}
#endregion
}</lang> Example: <lang csharp> using Sort;
using System;
class Program {
static void Main(String[] args) {
var entries = new Int32[] { 1, 3, 5, 7, 9, 8, 6, 4, 2 };
var sorter = new QuickSort<Int32>();
sorter.Sort(entries);
Console.WriteLine(String.Join(" ", entries));
}
}</lang>
- Output:
1 2 3 4 5 6 7 8 9
A very inefficient way to do qsort in C# to prove C# code can be just as compact and readable as any dynamic code
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
namespace QSort {
class QSorter
{
private static IEnumerable<IComparable> empty = new List<IComparable>();
public static IEnumerable<IComparable> QSort(IEnumerable<IComparable> iEnumerable)
{
if(iEnumerable.Any())
{
var pivot = iEnumerable.First();
return QSort(iEnumerable.Where((anItem) => pivot.CompareTo(anItem) > 0)).
Concat(iEnumerable.Where((anItem) => pivot.CompareTo(anItem) == 0)).
Concat(QSort(iEnumerable.Where((anItem) => pivot.CompareTo(anItem) < 0)));
}
return empty;
}
}
}</lang>
Clojure
A very Haskell-like solution using list comprehensions and lazy evaluation. <lang lisp>(defn qsort [L]
(if (empty? L)
'()
(let [[pivot & L2] L]
(lazy-cat (qsort (for [y L2 :when (< y pivot)] y))
(list pivot)
(qsort (for [y L2 :when (>= y pivot)] y))))))</lang>
Another short version (using quasiquote):
<lang lisp>(defn qsort pvt & rs
(if pvt
`(~@(qsort (filter #(< % pvt) rs))
~pvt
~@(qsort (filter #(>= % pvt) rs)))))</lang>
Another, more readable version (no macros):
<lang lisp>(defn qsort pivot & xs
(when pivot
(let [smaller #(< % pivot)]
(lazy-cat (qsort (filter smaller xs))
[pivot] (qsort (remove smaller xs))))))</lang>
A 3-group quicksort (fast when many values are equal): <lang lisp>(defn qsort3 pvt :as coll
(when pvt
(let [{left -1 mid 0 right 1} (group-by #(compare % pvt) coll)]
(lazy-cat (qsort3 left) mid (qsort3 right)))))</lang>
A lazier version of above (unlike group-by, filter returns (and reads) a lazy sequence) <lang lisp>(defn qsort3 pivot :as coll
(when pivot
(lazy-cat (qsort (filter #(< % pivot) coll))
(filter #{pivot} coll)
(qsort (filter #(> % pivot) coll)))))</lang>
COBOL
<lang cobol> IDENTIFICATION DIVISION.
PROGRAM-ID. quicksort RECURSIVE.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01 temp PIC S9(8).
01 pivot PIC S9(8).
01 left-most-idx PIC 9(5).
01 right-most-idx PIC 9(5).
01 left-idx PIC 9(5).
01 right-idx PIC 9(5).
LINKAGE SECTION.
78 Arr-Length VALUE 50.
01 arr-area.
03 arr PIC S9(8) OCCURS Arr-Length TIMES.
01 left-val PIC 9(5).
01 right-val PIC 9(5).
PROCEDURE DIVISION USING REFERENCE arr-area, OPTIONAL left-val,
OPTIONAL right-val.
IF left-val IS OMITTED OR right-val IS OMITTED
MOVE 1 TO left-most-idx, left-idx
MOVE Arr-Length TO right-most-idx, right-idx
ELSE
MOVE left-val TO left-most-idx, left-idx
MOVE right-val TO right-most-idx, right-idx
END-IF
IF right-most-idx - left-most-idx < 1
GOBACK
END-IF
COMPUTE pivot = arr ((left-most-idx + right-most-idx) / 2)
PERFORM UNTIL left-idx > right-idx
PERFORM VARYING left-idx FROM left-idx BY 1
UNTIL arr (left-idx) >= pivot
END-PERFORM
PERFORM VARYING right-idx FROM right-idx BY -1
UNTIL arr (right-idx) <= pivot
END-PERFORM
IF left-idx <= right-idx
MOVE arr (left-idx) TO temp
MOVE arr (right-idx) TO arr (left-idx)
MOVE temp TO arr (right-idx)
ADD 1 TO left-idx
SUBTRACT 1 FROM right-idx
END-IF
END-PERFORM
CALL "quicksort" USING REFERENCE arr-area,
CONTENT left-most-idx, right-idx
CALL "quicksort" USING REFERENCE arr-area, CONTENT left-idx,
right-most-idx
GOBACK
.</lang>
CoffeeScript
<lang coffeescript> quicksort = ([x, xs...]) ->
return [] unless x? smallerOrEqual = (a for a in xs when a <= x) larger = (a for a in xs when a > x) (quicksort smallerOrEqual).concat(x).concat(quicksort larger)
</lang>
Common Lisp
The functional programming way
<lang lisp>(defun quicksort (list &aux (pivot (car list)) )
(if (cdr list)
(nconc (quicksort (remove-if-not #'(lambda (x) (< x pivot)) list))
(remove-if-not #'(lambda (x) (= x pivot)) list)
(quicksort (remove-if-not #'(lambda (x) (> x pivot)) list)))
list))</lang>
With flet
<lang lisp>(defun qs (list)
(if (cdr list)
(flet ((pivot (test)
(remove (car list) list :test-not test)))
(nconc (qs (pivot #'>)) (pivot #'=) (qs (pivot #'<))))
list))</lang>
In-place non-functional
<lang lisp>(defun quicksort (sequence)
(labels ((swap (a b) (rotatef (elt sequence a) (elt sequence b)))
(sub-sort (left right)
(when (< left right)
(let ((pivot (elt sequence right))
(index left))
(loop for i from left below right
when (<= (elt sequence i) pivot)
do (swap i (prog1 index (incf index))))
(swap right index)
(sub-sort left (1- index))
(sub-sort (1+ index) right)))))
(sub-sort 0 (1- (length sequence)))
sequence))</lang>
Functional with destructuring
<lang lisp> (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))))))</lang>
Crystal
<lang ruby>def quick_sort(a : Array(Int32)) : Array(Int32)
return a if a.size <= 1
p = a[0]
lt, rt = a[1 .. -1].partition { |x| x < p }
return quick_sort(lt) + [p] + quick_sort(rt)
end
a = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0] puts quick_sort(a) # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]</lang>
Curry
Copied from Curry: Example Programs. <lang curry>-- quicksort using higher-order functions:
qsort :: [Int] -> [Int] qsort [] = [] qsort (x:l) = qsort (filter (<x) l) ++ x : qsort (filter (>=x) l)
goal = qsort [2,3,1,0]</lang>
D
A functional version: <lang d>import std.stdio, std.algorithm, std.range, std.array;
auto quickSort(T)(T[] items) pure nothrow @safe {
if (items.length < 2)
return items;
immutable pivot = items[0];
return items[1 .. $].filter!(x => x < pivot).array.quickSort ~
pivot ~
items[1 .. $].filter!(x => x >= pivot).array.quickSort;
}
void main() {
[4, 65, 2, -31, 0, 99, 2, 83, 782, 1].quickSort.writeln;
}</lang>
- Output:
[-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]
A simple high-level version (same output): <lang d>import std.stdio, std.array;
T[] quickSort(T)(T[] items) pure nothrow {
if (items.empty)
return items;
T[] less, notLess;
foreach (x; items[1 .. $])
(x < items[0] ? less : notLess) ~= x;
return less.quickSort ~ items[0] ~ notLess.quickSort;
}
void main() {
[4, 65, 2, -31, 0, 99, 2, 83, 782, 1].quickSort.writeln;
}</lang>
Often short functional sieves are not a true implementations of the Sieve of Eratosthenes: http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf
Similarly, one could argue that a true QuickSort is in-place, as this more efficient version (same output): <lang d>import std.stdio, std.algorithm;
void quickSort(T)(T[] items) pure nothrow @safe @nogc {
if (items.length >= 2) {
auto parts = partition3(items, items[$ / 2]);
parts[0].quickSort;
parts[2].quickSort;
}
}
void main() {
auto items = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]; items.quickSort; items.writeln;
}</lang>
Dart
<lang dart>quickSort(List a) {
if (a.length <= 1) {
return a;
}
var pivot = a[0];
var less = [];
var more = [];
var pivotList = [];
// Partition
a.forEach((var i){
if (i.compareTo(pivot) < 0) {
less.add(i);
} else if (i.compareTo(pivot) > 0) {
more.add(i);
} else {
pivotList.add(i);
}
});
// Recursively sort sublists
less = quickSort(less);
more = quickSort(more);
// Concatenate results
less.addAll(pivotList);
less.addAll(more);
return less;
}
void main() {
var arr=[1,5,2,7,3,9,4,6,8];
print("Before sort");
arr.forEach((var i)=>print("$i"));
arr = quickSort(arr);
print("After sort");
arr.forEach((var i)=>print("$i"));
}</lang>
E
<lang e>def quicksort := {
def swap(container, ixA, ixB) {
def temp := container[ixA]
container[ixA] := container[ixB]
container[ixB] := temp
}
def partition(array, var first :int, var last :int) {
if (last <= first) { return }
# Choose a pivot
def pivot := array[def pivotIndex := (first + last) // 2]
# Move pivot to end temporarily
swap(array, pivotIndex, last)
var swapWith := first
# Scan array except for pivot, and...
for i in first..!last {
if (array[i] <= pivot) { # items ≤ the pivot
swap(array, i, swapWith) # are moved to consecutive positions on the left
swapWith += 1
}
}
# Swap pivot into between-partition position.
# Because of the swapping we know that everything before swapWith is less
# than or equal to the pivot, and the item at swapWith (since it was not
# swapped) is greater than the pivot, so inserting the pivot at swapWith
# will preserve the partition.
swap(array, swapWith, last)
return swapWith
}
def quicksortR(array, first :int, last :int) {
if (last <= first) { return }
def pivot := partition(array, first, last)
quicksortR(array, first, pivot - 1)
quicksortR(array, pivot + 1, last)
}
def quicksort(array) { # returned from block
quicksortR(array, 0, array.size() - 1)
}
}</lang>
EasyLang
<lang>data[] = [ 29 4 72 44 55 26 27 77 92 5 ]
func qsort left right . .
while left < right
swap data[(left + right) / 2] data[left]
mid = left
for i = left + 1 to right
if data[i] < data[left]
mid += 1
swap data[i] data[mid]
.
.
swap data[left] data[mid]
call qsort left mid - 1
left = mid + 1
.
.
call qsort 0 len data[] - 1 print data[]</lang>
EchoLisp
<lang scheme> (lib 'list) ;; list-partition
(define compare 0) ;; counter
(define (quicksort L compare-predicate: proc aux: (part null)) (if (<= (length L) 1) L
(begin
;; counting the number of comparisons
(set! compare (+ compare (length (rest L))))
;; pivot = first element of list
(set! part (list-partition (rest L) proc (first L)))
(append (quicksort (first part) proc )
(list (first L))
(quicksort (second part) proc)))))
</lang>
- Output:
<lang scheme> (shuffle (iota 15))
→ (10 0 14 11 13 9 2 5 4 8 1 7 12 3 6)
(quicksort (shuffle (iota 15)) <)
→ (0 1 2 3 4 5 6 7 8 9 10 11 12 13 14)
- random list of numbers in [0 .. n[
- count number of comparisons
(define (qtest (n 10000)) (set! compare 0) (quicksort (shuffle (iota n)) >) (writeln 'n n 'compare# compare ))
(qtest 1000)
n 1000 compare# 12764
(qtest 10000)
n 10000 compare# 277868
(qtest 100000)
n 100000 compare# 6198601
</lang>
Eero
Translated from Objective-C example on this page. <lang objc>#import <Foundation/Foundation.h>
void quicksortInPlace(MutableArray array, const long first, const long last)
if first >= last
return
Value pivot = array[(first + last) / 2]
left := first
right := last
while left <= right
while array[left] < pivot
left++
while array[right] > pivot
right--
if left <= right
array.exchangeObjectAtIndex: left++, withObjectAtIndex: right--
quicksortInPlace(array, first, right) quicksortInPlace(array, left, last)
Array quicksort(Array unsorted)
a := [] a.addObjectsFromArray: unsorted quicksortInPlace(a, 0, a.count - 1) return a
int main(int argc, const char * argv[])
autoreleasepool a := [1, 3, 5, 7, 9, 8, 6, 4, 2] Log( 'Unsorted: %@', a) Log( 'Sorted: %@', quicksort(a) ) b := ['Emil', 'Peg', 'Helen', 'Juergen', 'David', 'Rick', 'Barb', 'Mike', 'Tom'] Log( 'Unsorted: %@', b) Log( 'Sorted: %@', quicksort(b) )
return 0</lang>
Alternative implementation (not necessarily as efficient, but very readable)
<lang objc>#import <Foundation/Foundation.h>
implementation Array (Quicksort)
plus: Array array, return Array = self.arrayByAddingObjectsFromArray: array
filter: BOOL (^)(id) predicate, return Array
array := []
for id item in self
if predicate(item)
array.addObject: item
return array.copy
quicksort, return Array = self
if self.count > 1
id x = self[self.count / 2]
lesser := self.filter: (id y | return y < x)
greater := self.filter: (id y | return y > x)
return lesser.quicksort + [x] + greater.quicksort
end
int main()
autoreleasepool a := [1, 3, 5, 7, 9, 8, 6, 4, 2] Log( 'Unsorted: %@', a) Log( 'Sorted: %@', a.quicksort ) b := ['Emil', 'Peg', 'Helen', 'Juergen', 'David', 'Rick', 'Barb', 'Mike', 'Tom'] Log( 'Unsorted: %@', b) Log( 'Sorted: %@', b.quicksort )
return 0</lang>
- Output:
2013-09-04 16:54:31.780 a.out[2201:507] Unsorted: (
1,
3,
5,
7,
9,
8,
6,
4,
2
)
2013-09-04 16:54:31.781 a.out[2201:507] Sorted: (
1,
2,
3,
4,
5,
6,
7,
8,
9
)
2013-09-04 16:54:31.781 a.out[2201:507] Unsorted: (
Emil,
Peg,
Helen,
Juergen,
David,
Rick,
Barb,
Mike,
Tom
)
2013-09-04 16:54:31.782 a.out[2201:507] Sorted: (
Barb,
David,
Emil,
Helen,
Juergen,
Mike,
Peg,
Rick,
Tom
)
Eiffel
The <lang eiffel>QUICKSORT</lang> class: <lang eiffel> class QUICKSORT [G -> COMPARABLE]
create make
feature {NONE} --Implementation
is_sorted (list: ARRAY [G]): BOOLEAN require not_void: list /= Void local i: INTEGER do Result := True from i := list.lower + 1 invariant i >= list.lower + 1 and i <= list.upper + 1 until i > list.upper loop Result := Result and list [i - 1] <= list [i] i := i + 1 variant list.upper + 1 - i end end
concatenate_array (a: ARRAY [G] b: ARRAY [G]): ARRAY [G] require not_void: a /= Void and b /= Void do create Result.make_from_array (a) across b as t loop Result.force (t.item, Result.upper + 1) end ensure same_size: a.count + b.count = Result.count end
quicksort_array (list: ARRAY [G]): ARRAY [G] require not_void: list /= Void local less_a: ARRAY [G] equal_a: ARRAY [G] more_a: ARRAY [G] pivot: G do create less_a.make_empty create more_a.make_empty create equal_a.make_empty create Result.make_empty if list.count <= 1 then Result := list else pivot := list [list.lower] across list as li invariant less_a.count + equal_a.count + more_a.count <= list.count loop if li.item < pivot then less_a.force (li.item, less_a.upper + 1) elseif li.item = pivot then equal_a.force (li.item, equal_a.upper + 1) elseif li.item > pivot then more_a.force (li.item, more_a.upper + 1) end end Result := concatenate_array (Result, quicksort_array (less_a)) Result := concatenate_array (Result, equal_a) Result := concatenate_array (Result, quicksort_array (more_a)) end ensure same_size: list.count = Result.count sorted: is_sorted (Result) end
feature -- Initialization
make do end
quicksort (a: ARRAY [G]): ARRAY [G] do Result := quicksort_array (a) end
end </lang> A test application: <lang eiffel> class APPLICATION
create make
feature {NONE} -- Initialization
make -- Run application. local test: ARRAY [INTEGER] sorted: ARRAY [INTEGER] sorter: QUICKSORT [INTEGER] do create sorter.make test := <<1, 3, 2, 4, 5, 5, 7, -1>> sorted := sorter.quicksort (test) across sorted as s loop print (s.item) print (" ") end print ("%N") end
end </lang>
Elena
ELENA 4.1 : <lang elena>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());
}</lang>
- Output:
before:3,14,1,5,9,2,6,3 after :1,2,3,3,5,6,9,14
Elixir
<lang 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</lang>
Erlang
like haskell. Used by Measure_relative_performance_of_sorting_algorithms_implementations. If changed keep the interface or change Measure_relative_performance_of_sorting_algorithms_implementations <lang erlang> -module( quicksort ).
-export( [qsort/1] ).
qsort([]) -> []; qsort([X|Xs]) ->
qsort([ Y || Y <- Xs, Y < X]) ++ [X] ++ qsort([ Y || Y <- Xs, Y >= X]).
</lang>
multi-process implementation (number processes = number of processor cores): <lang erlang> 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.
</lang>
ERRE
<lang ERRE> PROGRAM QUICKSORT_DEMO
DIM ARRAY[21]
!$DYNAMIC DIM QSTACK[0]
!$INCLUDE="PC.LIB"
PROCEDURE QSORT(ARRAY[],START,NUM)
FIRST=START ! initialize work variables
LAST=START+NUM-1
LOOP
REPEAT
TEMP=ARRAY[(LAST+FIRST) DIV 2] ! seek midpoint
I=FIRST
J=LAST
REPEAT ! reverse both < and > below to sort descending
WHILE ARRAY[I]<TEMP DO
I=I+1
END WHILE
WHILE ARRAY[J]>TEMP DO
J=J-1
END WHILE
EXIT IF I>J
IF I<J THEN SWAP(ARRAY[I],ARRAY[J]) END IF
I=I+1
J=J-1
UNTIL NOT(I<=J)
IF I<LAST THEN ! Done
QSTACK[SP]=I ! Push I
QSTACK[SP+1]=LAST ! Push Last
SP=SP+2
END IF
LAST=J
UNTIL NOT(FIRST<LAST)
EXIT IF SP=0 SP=SP-2 FIRST=QSTACK[SP] ! Pop First LAST=QSTACK[SP+1] ! Pop Last END LOOP
END PROCEDURE
BEGIN
RANDOMIZE(TIMER) ! generate a new series each run
! create an array
FOR X=1 TO 21 DO ! fill with random numbers
ARRAY[X]=RND(1)*500 ! between 0 and 500
END FOR
PRIMO=6 ! sort starting here
NUM=10 ! sort this many elements
CLS
PRINT("Before Sorting:";TAB(31);"After sorting:")
PRINT("===============";TAB(31);"==============")
FOR X=1 TO 21 DO ! show them before sorting
IF X>=PRIMO AND X<=PRIMO+NUM-1 THEN
PRINT("==>";)
END IF
PRINT(TAB(5);)
WRITE("###.##";ARRAY[X])
END FOR
! create a stack !$DIM QSTACK[INT(NUM/5)+10]
QSORT(ARRAY[],PRIMO,NUM)
!$ERASE QSTACK
LOCATE(2,1)
FOR X=1 TO 21 DO ! print them after sorting
LOCATE(2+X,30)
IF X>=PRIMO AND X<=PRIMO+NUM-1 THEN
PRINT("==>";) ! point to sorted items
END IF
LOCATE(2+X,35)
WRITE("###.##";ARRAY[X])
END FOR
END PROGRAM </lang>
F#
<lang fsharp> let rec qsort = function
hd :: tl ->
let less, greater = List.partition ((>=) hd) tl
List.concat [qsort less; [hd]; qsort greater]
| _ -> []
</lang>
Factor
<lang factor>: qsort ( seq -- seq )
dup empty? [
unclip [ [ < ] curry partition [ qsort ] bi@ ] keep
prefix append
] unless ;</lang>
Fexl
<lang Fexl># (sort xs) is the ordered list of all elements in list xs.
- This version preserves duplicates.
\sort==
(\xs xs [] \x\xs append (sort; filter (gt x) xs); # all the items less than x cons x; append (filter (eq x) xs); # all the items equal to x sort; filter (lt x) xs # all the items greater than x )
- (unique xs) is the ordered list of unique elements in list xs.
\unique==
(\xs xs [] \x\xs append (unique; filter (gt x) xs); # all the items less than x cons x; # x itself unique; filter (lt x) xs # all the items greater than x )
</lang>
Forth
<lang forth>: mid ( l r -- mid ) over - 2/ -cell and + ;
- exch ( addr1 addr2 -- ) dup @ >r over @ swap ! r> swap ! ;
- partition ( l r -- l r r2 l2 )
2dup mid @ >r ( r: pivot ) 2dup begin swap begin dup @ r@ < while cell+ repeat swap begin r@ over @ < while cell- repeat 2dup <= if 2dup exch >r cell+ r> cell- then 2dup > until r> drop ;
- qsort ( l r -- )
partition swap rot \ 2over 2over - + < if 2swap then 2dup < if recurse else 2drop then 2dup < if recurse else 2drop then ;
- sort ( array len -- )
dup 2 < if 2drop exit then 1- cells over + qsort ;</lang>
Fortran
<lang fortran>module qsort_mod
implicit none
type group
integer :: order ! original order of unsorted data real :: value ! values to be sorted by
end type group
contains
recursive subroutine QSort(a,na)
! DUMMY ARGUMENTS integer, intent(in) :: nA type (group), dimension(nA), intent(in out) :: A
! LOCAL VARIABLES integer :: left, right real :: random real :: pivot type (group) :: temp integer :: marker
if (nA > 1) then
call random_number(random)
pivot = A(int(random*real(nA-1))+1)%value ! random pivor (not best performance, but avoids worst-case)
left = 0
right = nA + 1
do while (left < right)
right = right - 1
do while (A(right)%value > pivot)
right = right - 1
end do
left = left + 1
do while (A(left)%value < pivot)
left = left + 1
end do
if (left < right) then
temp = A(left)
A(left) = A(right)
A(right) = temp
end if
end do
if (left == right) then
marker = left + 1
else
marker = left
end if
call QSort(A(:marker-1),marker-1)
call QSort(A(marker:),nA-marker+1)
end if
end subroutine QSort
end module qsort_mod
! Test Qsort Module program qsort_test use qsort_mod implicit none
integer, parameter :: l = 8 type (group), dimension(l) :: A integer, dimension(12) :: seed = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] integer :: i real :: random
write (*,*) "Unsorted Values:"
call random_seed(put = seed)
do i = 1, l
call random_number(random)
A(i)%value = random
A(i)%order = i
if (mod(i,4) == 0) write (*,"(4(I5,1X,F8.6))") A(i-3:i)
end do
call QSort(A,l)
write (*,*) "Sorted Values:"
do i = 4, l, 4
if (mod(i,4) == 0) write (*,"(4(I5,1X,F8.6))") A(i-3:i)
end do
end program qsort_test</lang>
- Output:
Compiled with GNU Fortran 4.6.3
Unsorted Values:
1 0.228570 2 0.352733 3 0.167898 4 0.883237
5 0.968189 6 0.806234 7 0.117714 8 0.487401
Sorted Values:
7 0.117714 3 0.167898 1 0.228570 2 0.352733
8 0.487401 6 0.806234 4 0.883237 5 0.968189
A discussion about Quicksort pivot options, free source code for an optimized quicksort using insertion sort as a finisher, and an OpenMP multi-threaded quicksort is found at balfortran.org
FreeBASIC
<lang 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</lang>
- 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
FunL
<lang funl>def
qsort( [] ) = [] qsort( p:xs ) = qsort( xs.filter((< p)) ) + [p] + qsort( xs.filter((>= p)) )</lang>
Here is a more efficient version using the partition function.
<lang funl>def
qsort( [] ) = [] qsort( x:xs ) = val (ys, zs) = xs.partition( (< x) ) qsort( ys ) + (x : qsort( zs ))
println( qsort([4, 2, 1, 3, 0, 2]) ) println( qsort(["Juan", "Daniel", "Miguel", "William", "Liam", "Ethan", "Jacob"]) )</lang>
- Output:
[0, 1, 2, 2, 3, 4] [Daniel, Ethan, Jacob, Juan, Liam, Miguel, William]
Go
Note that Go's sort.Sort function is a Quicksort so in practice it would be just be used.
It's actually a combination of quick sort, heap sort, and insertion sort.
It starts with a quick sort, after a depth of 2*ceil(lg(n+1)) it switches to heap sort, or once a partition becomes small (less than eight items) it switches to insertion sort.
Old school, following Hoare's 1962 paper.
As a nod to the task request to work for all types with weak strict ordering, code below uses the < operator when comparing key values. The three points are noted in the code below.
Actually supporting arbitrary types would then require at a minimum a user supplied less-than function, and values referenced from an array of interface{} types. More efficient and flexible though is the sort interface of the Go sort package. Replicating that here seemed beyond the scope of the task so code was left written to sort an array of ints.
Go has no language support for indexing with discrete types other than integer types, so this was not coded.
Finally, the choice of a recursive closure over passing slices to a recursive function is really just a very small optimization. Slices are cheap because they do not copy the underlying array, but there's still a tiny bit of overhead in constructing the slice object. Passing just the two numbers is in the interest of avoiding that overhead. <lang go>package main
import "fmt"
func main() {
list := []int{31, 41, 59, 26, 53, 58, 97, 93, 23, 84}
fmt.Println("unsorted:", list)
quicksort(list)
fmt.Println("sorted! ", list)
}
func quicksort(a []int) {
var pex func(int, int)
pex = func(lower, upper int) {
for {
switch upper - lower {
case -1, 0: // 0 or 1 item in segment. nothing to do here!
return
case 1: // 2 items in segment
// < operator respects strict weak order
if a[upper] < a[lower] {
// a quick exchange and we're done.
a[upper], a[lower] = a[lower], a[upper]
}
return
// Hoare suggests optimized sort-3 or sort-4 algorithms here,
// but does not provide an algorithm.
}
// Hoare stresses picking a bound in a way to avoid worst case
// behavior, but offers no suggestions other than picking a
// random element. A function call to get a random number is
// relatively expensive, so the method used here is to simply
// choose the middle element. This at least avoids worst case
// behavior for the obvious common case of an already sorted list.
bx := (upper + lower) / 2
b := a[bx] // b = Hoare's "bound" (aka "pivot")
lp := lower // lp = Hoare's "lower pointer"
up := upper // up = Hoare's "upper pointer"
outer:
for {
// use < operator to respect strict weak order
for lp < upper && !(b < a[lp]) {
lp++
}
for {
if lp > up {
// "pointers crossed!"
break outer
}
// < operator for strict weak order
if a[up] < b {
break // inner
}
up--
}
// exchange
a[lp], a[up] = a[up], a[lp]
lp++
up--
}
// segment boundary is between up and lp, but lp-up might be
// 1 or 2, so just call segment boundary between lp-1 and lp.
if bx < lp {
// bound was in lower segment
if bx < lp-1 {
// exchange bx with lp-1
a[bx], a[lp-1] = a[lp-1], b
}
up = lp - 2
} else {
// bound was in upper segment
if bx > lp {
// exchange
a[bx], a[lp] = a[lp], b
}
up = lp - 1
lp++
}
// "postpone the larger of the two segments" = recurse on
// the smaller segment, then iterate on the remaining one.
if up-lower < upper-lp {
pex(lower, up)
lower = lp
} else {
pex(lp, upper)
upper = up
}
}
}
pex(0, len(a)-1)
}</lang>
- Output:
unsorted: [31 41 59 26 53 58 97 93 23 84] sorted! [23 26 31 41 53 58 59 84 93 97]
More traditional version of quicksort. It work generically with any container that conforms to sort.Interface.
<lang go>package main
import (
"fmt" "sort" "math/rand"
)
func partition(a sort.Interface, first int, last int, pivotIndex int) int {
a.Swap(first, pivotIndex) // move it to beginning
left := first+1
right := last
for left <= right {
for left <= last && a.Less(left, first) {
left++
}
for right >= first && a.Less(first, right) {
right--
}
if left <= right {
a.Swap(left, right)
left++
right--
}
}
a.Swap(first, right) // swap into right place
return right
}
func quicksortHelper(a sort.Interface, first int, last int) {
if first >= last {
return
}
pivotIndex := partition(a, first, last, rand.Intn(last - first + 1) + first)
quicksortHelper(a, first, pivotIndex-1)
quicksortHelper(a, pivotIndex+1, last)
}
func quicksort(a sort.Interface) {
quicksortHelper(a, 0, a.Len()-1)
}
func main() {
a := []int{1, 3, 5, 7, 9, 8, 6, 4, 2}
fmt.Printf("Unsorted: %v\n", a)
quicksort(sort.IntSlice(a))
fmt.Printf("Sorted: %v\n", a)
b := []string{"Emil", "Peg", "Helen", "Juergen", "David", "Rick", "Barb", "Mike", "Tom"}
fmt.Printf("Unsorted: %v\n", b)
quicksort(sort.StringSlice(b))
fmt.Printf("Sorted: %v\n", b)
}</lang>
- Output:
Unsorted: [1 3 5 7 9 8 6 4 2] Sorted: [1 2 3 4 5 6 7 8 9] Unsorted: [Emil Peg Helen Juergen David Rick Barb Mike Tom] Sorted: [Barb David Emil Helen Juergen Mike Peg Rick Tom]
Haskell
The famous two-liner, reflecting the underlying algorithm directly: <lang haskell>qsort [] = [] qsort (x:xs) = qsort [y | y <- xs, y < x] ++ [x] ++ qsort [y | y <- xs, y >= x]</lang> A more efficient version, doing only one comparison per element: <lang haskell>import Data.List (partition)
qsort :: Ord a => [a] -> [a] qsort [] = [] qsort (x:xs) = qsort ys ++ x : qsort zs
where (ys, zs) = partition (< x) xs</lang>
IDL
IDL has a powerful optimized sort() built-in. The following is thus merely for demonstration. <lang idl>function qs, arr
if (count = n_elements(arr)) lt 2 then return,arr pivot = total(arr) / count ; use the average for want of a better choice return,[qs(arr[where(arr le pivot)]),qs(arr[where(arr gt pivot)])] end</lang>
Example:
IDL> print,qs([3,17,-5,12,99])
-5 3 12 17 99
Icon and Unicon
<lang Icon>procedure main() #: demonstrate various ways to sort a list and string
demosort(quicksort,[3, 14, 1, 5, 9, 2, 6, 3],"qwerty")
end
procedure quicksort(X,op,lower,upper) #: return sorted list local pivot,x
if /lower := 1 then { # top level call setup
upper := *X
op := sortop(op,X) # select how and what we sort
}
if upper - lower > 0 then {
every x := quickpartition(X,op,lower,upper) do # find a pivot and sort ...
/pivot | X := x # ... how to return 2 values w/o a structure
X := quicksort(X,op,lower,pivot-1) # ... left
X := quicksort(X,op,pivot,upper) # ... right
}
return X
end
procedure quickpartition(X,op,lower,upper) #: quicksort partitioner helper local pivot static pivotL initial pivotL := list(3)
pivotL[1] := X[lower] # endpoints pivotL[2] := X[upper] # ... and pivotL[3] := X[lower+?(upper-lower)] # ... random midpoint if op(pivotL[2],pivotL[1]) then pivotL[2] :=: pivotL[1] # mini- if op(pivotL[3],pivotL[2]) then pivotL[3] :=: pivotL[2] # ... sort pivot := pivotL[2] # median is pivot
lower -:= 1
upper +:= 1
while lower < upper do { # find values on wrong side of pivot ...
while op(pivot,X[upper -:= 1]) # ... rightmost
while op(X[lower +:=1],pivot) # ... leftmost
if lower < upper then # not crossed yet
X[lower] :=: X[upper] # ... swap
}
suspend lower # 1st return pivot point suspend X # 2nd return modified X (in case immutable)
end</lang>
Implementation notes:
- Since this transparently sorts both string and list arguments the result must 'return' to bypass call by value (strings)
- The partition procedure must "return" two values - 'suspend' is used to accomplish this
Algorithm notes:
- The use of a type specific sorting operator meant that a general pivot choice need to be made. The median of the ends and random middle seemed reasonable. It turns out to have been suggested by Sedgewick.
- Sedgewick's suggestions for tail calling to recurse into the larger side and using insertion sort below a certain size were not implemented. (Q: does Icon/Unicon has tail calling optimizations?)
Note: This example relies on the supporting procedures 'sortop', and 'demosort' in Bubble Sort. The full demosort exercises the named sort of a list with op = "numeric", "string", ">>" (lexically gt, descending),">" (numerically gt, descending), a custom comparator, and also a string.
- Output:
Abbreviated
Sorting Demo using procedure quicksort
on list : [ 3 14 1 5 9 2 6 3 ]
with op = &null: [ 1 2 3 3 5 6 9 14 ] (0 ms)
...
on string : "qwerty"
with op = &null: "eqrtwy" (0 ms)Io
<lang io>List do(
quickSort := method(
if(size > 1) then(
pivot := at(size / 2 floor)
return select(x, x < pivot) quickSort appendSeq(
select(x, x == pivot) appendSeq(select(x, x > pivot) quickSort)
)
) else(return self)
)
quickSortInPlace := method(
copy(quickSort)
)
)
lst := list(5, -1, -4, 2, 9) lst quickSort println # ==> list(-4, -1, 2, 5, 9) lst quickSortInPlace println # ==> list(-4, -1, 2, 5, 9)</lang> Another more low-level Quicksort implementation can be found in Io's [github ] repository.
J
<lang j>sel=: 1 : 'x # ['
quicksort=: 3 : 0
if.
1 >: #y
do.
y
else.
e=. y{~?#y
(quicksort y <sel e),(y =sel e),quicksort y >sel e
end.
)</lang>
See the Quicksort essay in the J Wiki for additional explanations and examples.
Java
Imperative
<lang java5>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;
}
} </lang>
Functional
<lang java5>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());
}
}</lang>
JavaScript
Imperative
<lang javascript>function sort(array, less) {
function swap(i, j) {
var t = array[i];
array[i] = array[j];
array[j] = t;
}
function quicksort(left, right) {
if (left < right) {
var pivot = array[left + Math.floor((right - 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;
}</lang>
Example:<lang javascript>var test_array = [10, 3, 11, 15, 19, 1]; var sorted_array = sort(test_array, function(a,b) { return a<b; });</lang>
- Output:
<lang javascript>[ 1, 3, 10, 11, 15, 19 ]</lang>
Functional
ES5
Emphasising clarity more than run-time optimisation (for which Array.sort() would be a better option)
<lang JavaScript>(function () {
'use strict';
// quickSort :: (Ord a) => [a] -> [a]
function quickSort(xs) {
if (xs.length) {
var h = xs[0],
t = xs.slice(1),
lessMore = partition(function (x) {
return x <= h;
}, t),
less = lessMore[0],
more = lessMore[1];
return [].concat.apply(
[], [quickSort(less), h, quickSort(more)]
);
} else return []; }
// partition :: Predicate -> List -> (Matches, nonMatches)
// partition :: (a -> Bool) -> [a] -> ([a], [a])
function partition(p, xs) {
return xs.reduce(function (a, x) {
return (
a[p(x) ? 0 : 1].push(x),
a
);
}, [[], []]);
}
return quickSort([11.8, 14.1, 21.3, 8.5, 16.7, 5.7])
})();</lang>
- Output:
[5.7, 8.5, 11.8, 14.1, 16.7, 21.3]
ES6
<lang javascript>Array.prototype.quick_sort = function () {
if (this.length < 2) { return this; }
var pivot = this[Math.round(this.length / 2)];
return this.filter(x => x < pivot)
.quick_sort()
.concat(this.filter(x => x == pivot))
.concat(this.filter(x => x > pivot).quick_sort());
};</lang>
Or, expressed in terms of a single partition, rather than two consecutive filters:
<lang JavaScript>(() => {
'use strict';
// QUICKSORT --------------------------------------------------------------
// quickSort :: (Ord a) => [a] -> [a]
const quickSort = xs =>
xs.length > 1 ? (() => {
const
h = xs[0],
[less, more] = partition(x => x <= h, xs.slice(1));
return [].concat.apply(
[], [quickSort(less), h, quickSort(more)]
);
})() : xs;
// GENERIC ----------------------------------------------------------------
// partition :: Predicate -> List -> (Matches, nonMatches)
// partition :: (a -> Bool) -> [a] -> ([a], [a])
const partition = (p, xs) =>
xs.reduce((a, x) =>
p(x) ? [a[0].concat(x), a[1]] : [a[0], a[1].concat(x)], [
[],
[]
]);
// TEST ------------------------------------------------------------------- return quickSort([11.8, 14.1, 21.3, 8.5, 16.7, 5.7]);
})();</lang>
- Output:
[5.7, 8.5, 11.8, 14.1, 16.7, 21.3]
Joy
<lang joy> DEFINE qsort ==
[small] # termination condition: 0 or 1 element [] # do nothing [uncons [>] split] # pivot and two lists [enconcat] # insert the pivot after the recursion binrec. # recursion on the two lists
</lang>
jq
jq's built-in sort currently (version 1.4) uses the standard C qsort, a quicksort. sort can be used on any valid JSON array.
Example:<lang jq>[1, 1.1, [1,2], true, false, null, {"a":1}, null] | sort</lang>
- Output:
<lang jq>[null,null,false,true,1,1.1,[1,2],{"a"
Here is an implementation in jq of the pseudo-code (and comments :-) given at the head of this article:<lang jq>def quicksort:
if length < 2 then . # it is already sorted
else .[0] as $pivot
| reduce .[] as $x
# state: [less, equal, greater]
( [ [], [], [] ]; # three empty arrays:
if $x < $pivot then .[0] += [$x] # add x to less
elif $x == $pivot then .[1] += [$x] # add x to equal
else .[2] += [$x] # add x to greater
end
)
| (.[0] | quicksort ) + .[1] + (.[2] | quicksort )
end ;
</lang>Fortunately, the example input used above produces the same output, and so both are omitted here.
Julia
Built-in function for in-place sorting via quicksort (the code from the standard library is quite readable): <lang julia>sort!(A, alg=QuickSort)</lang> A simple polymorphic implementation of an in-place recursive quicksort (based on the pseudocode above): <lang julia>function quicksort!(A,i=1,j=length(A))
if j > i
pivot = A[rand(i:j)] # random element of A
left, right = i, j
while left <= right
while A[left] < pivot
left += 1
end
while A[right] > pivot
right -= 1
end
if left <= right
A[left], A[right] = A[right], A[left]
left += 1
right -= 1
end
end
quicksort!(A,i,right)
quicksort!(A,left,j)
end
return A
end</lang> A one-line (but rather inefficient) implementation based on the Haskell version, which operates out-of-place and allocates temporary arrays: <lang julia>qsort(L) = isempty(L) ? L : vcat(qsort(filter(x -> x < L[1], L[2:end])), L[1:1], qsort(filter(x -> x >= L[1], L[2:end])))</lang>
- Output:
julia> A = [84,77,20,60,47,20,18,97,41,49,31,39,73,68,65,52,1,92,15,9] julia> qsort(A) [1,9,15,18,20,20,31,39,41,47,49,52,60,65,68,73,77,84,92,97] julia> quicksort!(copy(A)) [1,9,15,18,20,20,31,39,41,47,49,52,60,65,68,73,77,84,92,97] julia> qsort(A) == quicksort!(copy(A)) == sort(A) == sort(A, alg=QuickSort) true
K
<lang K>quicksort:{f:*x@1?#x;:[0=#x;x;,/(_f x@&x<f;x@&x=f;_f x@&x>f)]}</lang>
Example: <lang K>
quicksort 1 3 5 7 9 8 6 4 2
</lang>
- Output:
1 2 3 4 5 6 7 8 9
Explanation:
<lang K>
_f()
</lang>
is the current function called recursively.
<lang K>
:[....]
</lang>
generally means :[condition1;then1;condition2;then2;....;else]. Though here it is used as :[if;then;else].
This construct
<lang K>
f:*x@1?#x
</lang>
assigns a random element in x (the argument) to f, as the pivot value.
And here is the full if/then/else clause:
<lang K>
:[
0=#x; / if length of x is zero
x; / then return x
/ else
,/( / join the results of:
_f x@&x<f / sort (recursively) elements less than f (pivot)
x@&x=f / element equal to f
_f x@&x>f) / sort (recursively) elements greater than f
]
</lang>
Though - as with APL and J - for larger arrays it's much faster to sort using "<" (grade up) which gives the indices of the list sorted ascending, i.e.
<lang K>
t@<t:1 3 5 7 9 8 6 4 2
</lang>
Kotlin
A version that reflects the algorithm directly:
<lang scala>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()
</lang>
A more efficient version that does only one comparison per element:
<lang scala>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()
}
</lang>
Lobster
<lang lobster>include "std.lobster"
def quicksort(xs, lt):
if xs.length <= 1:
xs
else:
pivot := xs[0]
tail := xs.slice(1, -1)
f1 := filter tail: lt(_, pivot)
f2 := filter tail: !lt(_, pivot)
append(append(quicksort(f1, lt), [ pivot ]),
quicksort(f2, lt))
sorted := [ 3, 9, 5, 4, 1, 3, 9, 5, 4, 1 ].quicksort(): _a < _b print sorted</lang>
Logo
<lang logo>; quicksort (lists, functional)
to small? :list
output or [empty? :list] [empty? butfirst :list]
end to quicksort :list
if small? :list [output :list]
localmake "pivot first :list
output (sentence
quicksort filter [? < :pivot] butfirst :list
filter [? = :pivot] :list
quicksort filter [? > :pivot] butfirst :list
)
end
show quicksort [1 3 5 7 9 8 6 4 2]</lang> <lang logo>; quicksort (arrays, in-place)
to incr :name
make :name (thing :name) + 1
end to decr :name
make :name (thing :name) - 1
end to swap :i :j :a
localmake "t item :i :a setitem :i :a item :j :a setitem :j :a :t
end
to quick :a :low :high
if :high <= :low [stop] localmake "l :low localmake "h :high localmake "pivot item ashift (:l + :h) -1 :a do.while [ while [(item :l :a) < :pivot] [incr "l] while [(item :h :a) > :pivot] [decr "h] if :l <= :h [swap :l :h :a incr "l decr "h] ] [:l <= :h] quick :a :low :h quick :a :l :high
end to sort :a
quick :a first :a count :a
end
make "test {1 3 5 7 9 8 6 4 2} sort :test show :test</lang>
Logtalk
<lang logtalk>quicksort(List, Sorted) :-
quicksort(List, [], Sorted).
quicksort([], Sorted, Sorted). quicksort([Pivot| Rest], Acc, Sorted) :-
partition(Rest, Pivot, Smaller0, Bigger0), quicksort(Smaller0, [Pivot| Bigger], Sorted), quicksort(Bigger0, Acc, Bigger).
partition([], _, [], []). partition([X| Xs], Pivot, Smalls, Bigs) :-
( X @< Pivot ->
Smalls = [X| Rest],
partition(Xs, Pivot, Rest, Bigs)
; Bigs = [X| Rest],
partition(Xs, Pivot, Smalls, Rest)
).</lang>
Lua
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
<lang lua>--in-place quicksort function quicksort(t, start, endi)
start, endi = start or 1, endi or #t
--partition w.r.t. first element
if(endi - start < 1) then return t end
local pivot = start
for i = start + 1, endi do
if t[i] <= t[pivot] then
if i == pivot + 1 then
t[pivot],t[pivot+1] = t[pivot+1],t[pivot]
else
t[pivot],t[pivot+1],t[i] = t[i],t[pivot],t[pivot+1]
end
pivot = pivot + 1
end
end
t = quicksort(t, start, pivot - 1)
return quicksort(t, pivot + 1, endi)
end
--example print(unpack(quicksort{5, 2, 7, 3, 4, 7, 1}))</lang>
non in-place
<lang lua>function quicksort(t)
if #t<2 then return t end
local pivot=t[1]
local a,b,c={},{},{}
for _,v in ipairs(t) do
if v<pivot then a[#a+1]=v
elseif v>pivot then c[#c+1]=v
else b[#b+1]=v
end
end
a=quicksort(a)
c=quicksort(c)
for _,v in ipairs(b) do a[#a+1]=v end
for _,v in ipairs(c) do a[#a+1]=v end
return a
end</lang>
Lucid
[1] <lang lucid>qsort(a) = if eof(first a) then a else follow(qsort(b0),qsort(b1)) fi
where
p = first a < a;
b0 = a whenever p;
b1 = a whenever not p;
follow(x,y) = if xdone then y upon xdone else x fi
where
xdone = iseod x fby xdone or iseod x;
end;
end</lang>
M2000 Interpreter
Recursive calling Functions
<lang M2000 Interpreter> Module Checkit1 {
Group Quick {
Private:
Function partition {
Read &A(), p, r
x = A(r)
i = p-1
For j=p to r-1 {
If .LE(A(j), x) Then {
i++
Swap A(i),A(j)
}
}
Swap A(i+1),A(r)
= i+1
}
Public:
LE=Lambda->Number<=Number
Function quicksort {
Read &A(), p, r
If p < r Then {
q = .partition(&A(), p, r)
Call .quicksort(&A(), p, q - 1)
Call .quicksort(&A(), q + 1, r)
}
}
}
Dim A(10)<<Random(50, 100)
Print A()
Call Quick.quicksort(&A(), 0, Len(A())-1)
Print A()
} Checkit1 </lang>
Recursive calling Subs
Variables p, r, q removed from quicksort function. we use stack for values. Also Partition push to stack now. Works for string arrays too. <lang M2000 Interpreter> Module Checkit2 {
Class Quick {
Private:
partition=lambda-> {
Read &A(), p, r : i = p-1 : x=A(r)
For j=p to r-1 {If .LE(A(j), x) Then i++:Swap A(i),A(j)
} : Swap A(i+1), A(r) : Push i+1
}
Public:
LE=Lambda->Number<=Number
Module ForStrings {
.partition<=lambda-> {
Read &A$(), p, r : i = p-1 : x$=A$(r)
For j=p to r-1 {If A$(j)<= x$ Then i++:Swap A$(i),A$(j)
} : Swap A$(i+1), A$(r) : Push i+1
}
}
Function quicksort (ref$) {
myQuick()
sub myQuick()
If Stackitem() >= stackitem(2) Then drop 2 : Exit Sub
Over 2, 2 : Call .partition(ref$) : Over : Shiftback 3, 2
myQuick(number, number - 1)
myQuick( number + 1, number)
End Sub
}
}
Quick=Quick()
Dim A(10)
A(0):=57, 83, 74, 98, 51, 73, 85, 76, 65, 92
Print A()
Call Quick.quicksort(&A(), 0, Len(A())-1)
Print A()
Quick=Quick()
Quick.ForStrings
Dim A$()
A$()=("one","two", "three","four", "five")
Print A$()
Call Quick.quicksort(&A$(), 0, Len(A$())-1)
Print A$()
} Checkit2 </lang>
Non Recursive
Partition function return two values (where we want q, and use it as q-1 an q+1 now Partition() return final q-1 and q+1_ Example include numeric array, array of arrays (we provide a lambda for comparison) and string array. <lang M2000 Interpreter> Module Checkit3 {
Class Quick {
Private:
partition=lambda-> {
Read &A(), p, r : i = p-1 : x=A(r)
For j=p to r-1 {If .LE(A(j), x) Then i++:Swap A(i),A(j)
} : Swap A(i+1), A(r) : Push i+2, i
}
Public:
LE=Lambda->Number<=Number
Module ForStrings {
.partition<=lambda-> {
Read &A$(), p, r : i = p-1 : x$=A$(r)
For j=p to r-1 {If A$(j)<= x$ Then i++:Swap A$(i),A$(j)
} : Swap A$(i+1), A$(r) : Push i+2, i
}
}
Function quicksort {
Read ref$
{
loop : If Stackitem() >= Stackitem(2) Then Drop 2 : if empty then {Break} else continue
over 2,2 : call .partition(ref$) :shift 3
}
}
}
Quick=Quick()
Dim A(10)<<Random(50, 100)
Print A()
Call Quick.quicksort(&A(), 0, Len(A())-1)
Print A()
Quick=Quick()
Function join$(a$()) {
n=each(a$(), 1, -2)
k$=""
while n {
overwrite k$, ".", n^:=array$(n)
}
=k$
}
Stack New {
Data "1.3.6.1.4.1.11.2.17.19.3.4.0.4" , "1.3.6.1.4.1.11.2.17.19.3.4.0.1", "1.3.6.1.4.1.11150.3.4.0.1"
Data "1.3.6.1.4.1.11.2.17.19.3.4.0.10", "1.3.6.1.4.1.11.2.17.5.2.0.79", "1.3.6.1.4.1.11150.3.4.0"
Dim Base 0, arr(Stack.Size)
Link arr() to arr$()
i=0 : While not Empty {arr$(i)=piece$(letter$+".", ".") : i++ }
}
\\ change comparison function
Quick.LE=lambda (a, b)->{
Link a, b to a$(), b$()
def i=-1
do {
i++
} until a$(i)="" or b$(i)="" or a$(i)<>b$(i)
if b$(i)="" then =a$(i)="":exit
if a$(i)="" then =true:exit
=val(a$(i))<=val(b$(i))
}
Call Quick.quicksort(&arr(), 0, Len(arr())-1)
For i=0 to len(arr())-1 {
Print join$(arr(i))
}
\\ Fresh load
Quick=Quick()
Quick.ForStrings
Dim A$()
A$()=("one","two", "three","four", "five")
Print A$()
Call Quick.quicksort(&A$(), 0, Len(A$())-1)
Print A$()
} Checkit3 </lang>
M4
<lang M4>dnl return the first element of a list when called in the funny way seen below define(`arg1', `$1')dnl dnl dnl append lists 1 and 2 define(`append',
`ifelse(`$1',`()',
`$2',
`ifelse(`$2',`()',
`$1',
`substr($1,0,decr(len($1))),substr($2,1)')')')dnl
dnl dnl separate list 2 based on pivot 1, appending to left 3 and right 4, dnl until 2 is empty, and then combine the sort of left with pivot with dnl sort of right define(`sep',
`ifelse(`$2', `()',
`append(append(quicksort($3),($1)),quicksort($4))',
`ifelse(eval(arg1$2<=$1),1,
`sep($1,(shift$2),append($3,(arg1$2)),$4)',
`sep($1,(shift$2),$3,append($4,(arg1$2)))')')')dnl
dnl dnl pick first element of list 1 as pivot and separate based on that define(`quicksort',
`ifelse(`$1', `()',
`()',
`sep(arg1$1,(shift$1),`()',`()')')')dnl
dnl quicksort((3,1,4,1,5,9))</lang>
- Output:
(1,1,3,4,5,9)
Maple
<lang 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;</lang>
- Output:
[0, 1, 2, 4, 12]
Mathematica
<lang Mathematica>QuickSort[x_List] := Module[{pivot},
If[Length@x <= 1, Return[x]];
pivot = RandomChoice@x;
Flatten@{QuickSort[Cases[x, j_ /; j < pivot]], Cases[x, j_ /; j == pivot], QuickSort[Cases[x, j_ /; j > pivot]]}
]</lang>
<lang Mathematica>qsort[{}] = {}; qsort[{x_, xs___}] := Join[qsort@Select[{xs}, # <= x &], {x}, qsort@Select[{xs}, # > x &]];</lang>
<lang Mathematica>QuickSort[{}] := {} QuickSort[list: {__}] := With[{pivot=RandomChoice[list]}, Join[ <|1->{}, -1->{}|>, GroupBy[list,Order[#,pivot]&] ] // Catenate[ {QuickSort@#[1], #[0], QuickSort@#[-1]} ]& ]</lang>
MATLAB
This implements the pseudo-code in the specification. The input can be either a row or column vector, but the returned vector will always be a row vector. This can be modified to operate on any built-in primitive or user defined class by replacing the "<=" and ">" comparisons with "le" and "gt" functions respectively. This is because operators can not be overloaded, but the functions that are equivalent to the operators can be overloaded in class definitions.
This should be placed in a file named quickSort.m. <lang Matlab>function sortedArray = quickSort(array)
if numel(array) <= 1 %If the array has 1 element then it can't be sorted
sortedArray = array;
return
end
pivot = array(end);
array(end) = [];
%Create two new arrays which contain the elements that are less than or
%equal to the pivot called "less" and greater than the pivot called
%"greater"
less = array( array <= pivot );
greater = array( array > pivot );
%The sorted array is the concatenation of the sorted "less" array, the
%pivot and the sorted "greater" array in that order
sortedArray = [quickSort(less) pivot quickSort(greater)];
end</lang>
A slightly more vectorized version of the above code that removes the need for the less and greater arrays: <lang Matlab>function sortedArray = quickSort(array)
if numel(array) <= 1 %If the array has 1 element then it can't be sorted
sortedArray = array;
return
end
pivot = array(end);
array(end) = [];
sortedArray = [quickSort( array(array <= pivot) ) pivot quickSort( array(array > pivot) )];
end</lang>
Sample usage: <lang MATLAB>quickSort([4,3,7,-2,9,1])
ans =
-2 1 3 4 7 9</lang>
MAXScript
<lang maxscript>fn quickSort arr = (
less = #()
pivotList = #()
more = #()
if arr.count <= 1 then
(
arr
)
else
(
pivot = arr[arr.count/2]
for i in arr do
(
case of
(
(i < pivot): (append less i)
(i == pivot): (append pivotList i)
(i > pivot): (append more i)
)
)
less = quickSort less
more = quickSort more
less + pivotList + more
)
) a = #(4, 89, -3, 42, 5, 0, 2, 889) a = quickSort a</lang>
Modula-2
The definition module exposes the interface. This one uses the procedure variable feature to pass a caller defined compare callback function so that it can sort various simple and structured record types.
This Quicksort assumes that you are working with an an array of pointers to an arbitrary type and are not moving the record data itself but only the pointers. The M2 type "ADDRESS" is considered compatible with any pointer type.
The use of type ADDRESS here to achieve genericity is something of a chink the the normal strongly typed flavor of Modula-2. Unlike the other language types, "system" types such as ADDRESS or WORD must be imported explicity from the SYSTEM MODULE. The ISO standard for the "Generic Modula-2" language extension provides genericity without the chink, but most compilers have not implemented this extension.
<lang Modula2>(*#####################*)
DEFINITION MODULE QSORT;
(*#####################*)
FROM SYSTEM IMPORT ADDRESS;
TYPE CmpFuncPtrs = PROCEDURE(ADDRESS, ADDRESS):INTEGER;
PROCEDURE QuickSortPtrs(VAR Array:ARRAY OF ADDRESS; N:CARDINAL;
Compare:CmpFuncPtrs);
END QSORT.
</lang>
The implementation module is not visible to clients, so it may be changed without worry so long as it still implements the definition.
Sedgewick suggests that faster sorting will be achieved if you drop back to an insertion sort once the partitions get small.
<lang Modula2>(*##########################*)
IMPLEMENTATION MODULE QSORT;
(*##########################*)
FROM SYSTEM IMPORT ADDRESS;
CONST SmallPartition = 9;
(* NOTE
1.Reference on QuickSort: "Implementing Quicksort Programs", Robert
Sedgewick, Communications of the ACM, Oct 78, v21 #10.
- )
(*==============================================================*)
PROCEDURE QuickSortPtrs(VAR Array:ARRAY OF ADDRESS; N:CARDINAL;
Compare:CmpFuncPtrs);
(*==============================================================*)
(*-----------------------------*)
PROCEDURE Swap(VAR A,B:ADDRESS);
(*-----------------------------*)
VAR temp :ADDRESS;
BEGIN
temp := A; A := B; B := temp;
END Swap;
(*-------------------------------*)
PROCEDURE TstSwap(VAR A,B:ADDRESS);
(*-------------------------------*)
VAR temp :ADDRESS;
BEGIN
IF Compare(A,B) > 0 THEN
temp := A; A := B; B := temp;
END;
END TstSwap;
(*--------------*)
PROCEDURE Isort;
(*--------------*)
(*
Insertion sort.
*)
VAR i,j :CARDINAL;
temp :ADDRESS;
BEGIN
IF N < 2 THEN RETURN END;
FOR i := N-2 TO 0 BY -1 DO
IF Compare(Array[i],Array[i+1]) > 0 THEN
temp := Array[i];
j := i+1;
REPEAT
Array[j-1] := Array[j];
INC(j);
UNTIL (j = N) OR (Compare(Array[j],temp) >= 0);
Array[j-1] := temp;
END;
END;
END Isort;
(*----------------------------------*)
PROCEDURE Quick(left,right:CARDINAL);
(*----------------------------------*)
VAR
i,j,
second :CARDINAL;
Partition :ADDRESS;
BEGIN
IF right > left THEN
i := left; j := right;
Swap(Array[left],Array[(left+right) DIV 2]);
second := left+1; (* insure 2nd element is in *)
TstSwap(Array[second], Array[right]); (* the lower part, last elem *)
TstSwap(Array[left], Array[right]); (* in the upper part *)
TstSwap(Array[second], Array[left]); (* THUS, only one test is *)
(* needed in repeat loops *)
Partition := Array[left];
LOOP
REPEAT INC(i) UNTIL Compare(Array[i],Partition) >= 0;
REPEAT DEC(j) UNTIL Compare(Array[j],Partition) <= 0;
IF j < i THEN
EXIT
END;
Swap(Array[i],Array[j]);
END; (*loop*)
Swap(Array[left],Array[j]);
IF (j > 0) AND (j-1-left >= SmallPartition) THEN
Quick(left,j-1);
END;
IF right-i >= SmallPartition THEN
Quick(i,right);
END;
END;
END Quick;
BEGIN (* QuickSortPtrs --------------------------------------------------*)
IF N > SmallPartition THEN (* won't work for 2 elements *)
Quick(0,N-1);
END;
Isort;
END QuickSortPtrs;
END QSORT. </lang>
Modula-3
This code is taken from libm3, which is basically Modula-3's "standard library". Note that this code uses Insertion sort when the array is less than 9 elements long.
<lang modula3>GENERIC INTERFACE ArraySort(Elem);
PROCEDURE Sort(VAR a: ARRAY OF Elem.T; cmp := Elem.Compare);
END ArraySort.</lang>
<lang modula3>GENERIC MODULE ArraySort (Elem);
PROCEDURE Sort (VAR a: ARRAY OF Elem.T; cmp := Elem.Compare) =
BEGIN QuickSort (a, 0, NUMBER (a), cmp); InsertionSort (a, 0, NUMBER (a), cmp); END Sort;
PROCEDURE QuickSort (VAR a: ARRAY OF Elem.T; lo, hi: INTEGER;
cmp := Elem.Compare) = CONST CutOff = 9; VAR i, j: INTEGER; key, tmp: Elem.T; BEGIN WHILE (hi - lo > CutOff) DO (* sort a[lo..hi) *)
(* use median-of-3 to select a key *)
i := (hi + lo) DIV 2;
IF cmp (a[lo], a[i]) < 0 THEN
IF cmp (a[i], a[hi-1]) < 0 THEN
key := a[i];
ELSIF cmp (a[lo], a[hi-1]) < 0 THEN
key := a[hi-1]; a[hi-1] := a[i]; a[i] := key;
ELSE
key := a[lo]; a[lo] := a[hi-1]; a[hi-1] := a[i]; a[i] := key;
END;
ELSE (* a[lo] >= a[i] *)
IF cmp (a[hi-1], a[i]) < 0 THEN
key := a[i]; tmp := a[hi-1]; a[hi-1] := a[lo]; a[lo] := tmp;
ELSIF cmp (a[lo], a[hi-1]) < 0 THEN
key := a[lo]; a[lo] := a[i]; a[i] := key;
ELSE
key := a[hi-1]; a[hi-1] := a[lo]; a[lo] := a[i]; a[i] := key;
END;
END;
(* partition the array *)
i := lo+1; j := hi-2;
(* find the first hole *)
WHILE cmp (a[j], key) > 0 DO DEC (j) END;
tmp := a[j];
DEC (j);
LOOP
IF (i > j) THEN EXIT END;
WHILE i < hi AND cmp (a[i], key) < 0 DO INC (i) END;
IF (i > j) THEN EXIT END;
a[j+1] := a[i];
INC (i);
WHILE j > lo AND cmp (a[j], key) > 0 DO DEC (j) END;
IF (i > j) THEN IF (j = i-1) THEN DEC (j) END; EXIT END;
a[i-1] := a[j];
DEC (j);
END;
(* fill in the last hole *)
a[j+1] := tmp;
i := j+2;
(* then, recursively sort the smaller subfile *)
IF (i - lo < hi - i)
THEN QuickSort (a, lo, i-1, cmp); lo := i;
ELSE QuickSort (a, i, hi, cmp); hi := i-1;
END;
END; (* WHILE (hi-lo > CutOff) *) END QuickSort;
PROCEDURE InsertionSort (VAR a: ARRAY OF Elem.T; lo, hi: INTEGER;
cmp := Elem.Compare) =
VAR j: INTEGER; key: Elem.T;
BEGIN
FOR i := lo+1 TO hi-1 DO
key := a[i];
j := i-1;
WHILE (j >= lo) AND cmp (key, a[j]) < 0 DO
a[j+1] := a[j];
DEC (j);
END;
a[j+1] := key;
END;
END InsertionSort;
BEGIN END ArraySort.</lang>
To use this generic code to sort an array of text, we create two files called TextSort.i3 and TextSort.m3, respectively.
<lang modula3>INTERFACE TextSort = ArraySort(Text) END TextSort.</lang> <lang modula3>MODULE TextSort = ArraySort(Text) END TextSort.</lang>
Then, as an example: <lang modula3>MODULE Main;
IMPORT IO, TextSort;
VAR arr := ARRAY [1..10] OF TEXT {"Foo", "bar", "!ooF", "Modula-3", "hickup",
"baz", "quuz", "Zeepf", "woo", "Rosetta Code"};
BEGIN
TextSort.Sort(arr); FOR i := FIRST(arr) TO LAST(arr) DO IO.Put(arr[i] & "\n"); END;
END Main.</lang>
Mond
Implements the simple quicksort algorithm.
<lang Mond>fun quicksort( arr, cmp ) {
if( arr.length() < 2 )
return arr;
if( !cmp )
cmp = ( a, b ) -> a - b;
var a = [ ], b = [ ];
var pivot = arr[0];
var len = arr.length();
for( var i = 1; i < len; ++i )
{
var item = arr[i];
if( cmp( item, pivot ) < cmp( pivot, item ) )
a.add( item );
else
b.add( item );
}
a = quicksort( a, cmp );
b = quicksort( b, cmp );
a.add( pivot );
foreach( var item in b )
a.add( item );
return a;
}</lang>
- Usage
<lang Mond>var array = [ 532, 16, 153, 3, 63.60, 925, 0.214 ]; var sorted = quicksort( array );
printLn( sorted );</lang>
- Output:
[ 0.214, 3, 16, 63.6, 153, 532, 925 ]
MUMPS
Shows quicksort on a 16-element array.
<lang MUMPS> 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
</lang>
- Usage
<lang MUMPS> do main()</lang>
- 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
<lang 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 end</lang>
Nemerle
A little less clean and concise than Haskell, but essentially the same. <lang Nemerle>using System; using System.Console; using Nemerle.Collections.NList;
module Quicksort {
Qsort[T] (x : list[T]) : list[T]
where T : IComparable
{
|[] => []
|x::xs => Qsort($[y|y in xs, (y.CompareTo(x) < 0)]) + [x] + Qsort($[y|y in xs, (y.CompareTo(x) > 0)])
}
Main() : void
{
def empty = [];
def single = [2];
def several = [2, 6, 1, 7, 3, 9, 4];
WriteLine(Qsort(empty));
WriteLine(Qsort(single));
WriteLine(Qsort(several));
}
}</lang>
NetRexx
This sample implements both the simple and in place algorithms as described in the task's description: <lang NetRexx>/* NetRexx */ options replace format comments java crossref savelog symbols binary
import java.util.List
placesList = [String -
"UK London", "US New York", "US Boston", "US Washington" - , "UK Washington", "US Birmingham", "UK Birmingham", "UK Boston" -
] lists = [ -
placesList - , quickSortSimple(String[] Arrays.copyOf(placesList, placesList.length)) - , quickSortInplace(String[] Arrays.copyOf(placesList, placesList.length)) -
]
loop ln = 0 to lists.length - 1
cl = lists[ln] loop ct = 0 to cl.length - 1 say cl[ct] end ct say end ln
return
method quickSortSimple(array = String[]) public constant binary returns String[]
rl = String[array.length] al = List quickSortSimple(Arrays.asList(array)) al.toArray(rl)
return rl
method quickSortSimple(array = List) public constant binary returns ArrayList
if array.size > 1 then do less = ArrayList() equal = ArrayList() greater = ArrayList()
pivot = array.get(Random().nextInt(array.size - 1))
loop x_ = 0 to array.size - 1
if (Comparable array.get(x_)).compareTo(Comparable pivot) < 0 then less.add(array.get(x_))
if (Comparable array.get(x_)).compareTo(Comparable pivot) = 0 then equal.add(array.get(x_))
if (Comparable array.get(x_)).compareTo(Comparable pivot) > 0 then greater.add(array.get(x_))
end x_
less = quickSortSimple(less)
greater = quickSortSimple(greater)
out = ArrayList(array.size)
out.addAll(less)
out.addAll(equal)
out.addAll(greater)
array = out end
return ArrayList array
method quickSortInplace(array = String[]) public constant binary returns String[]
rl = String[array.length] al = List quickSortInplace(Arrays.asList(array)) al.toArray(rl)
return rl
method quickSortInplace(array = List, ixL = int 0, ixR = int array.size - 1) public constant binary returns ArrayList
if ixL < ixR then do ixP = int ixL + (ixR - ixL) % 2 ixP = quickSortInplacePartition(array, ixL, ixR, ixP) quickSortInplace(array, ixL, ixP - 1) quickSortInplace(array, ixP + 1, ixR) end
array = ArrayList(array) return ArrayList array
method quickSortInplacePartition(array = List, ixL = int, ixR = int, ixP = int) public constant binary returns int
pivotValue = array.get(ixP)
rValue = array.get(ixR)
array.set(ixP, rValue)
array.set(ixR, pivotValue)
ixStore = ixL
loop i_ = ixL to ixR - 1
iValue = array.get(i_)
if (Comparable iValue).compareTo(Comparable pivotValue) < 0 then do
storeValue = array.get(ixStore)
array.set(i_, storeValue)
array.set(ixStore, iValue)
ixStore = ixStore + 1
end
end i_
storeValue = array.get(ixStore)
rValue = array.get(ixR)
array.set(ixStore, rValue)
array.set(ixR, storeValue)
return ixStore
</lang>
- Output:
UK London US New York US Boston US Washington UK Washington US Birmingham UK Birmingham UK Boston UK Birmingham UK Boston UK London UK Washington US Birmingham US Boston US New York US Washington UK Birmingham UK Boston UK London UK Washington US Birmingham US Boston US New York US Washington
Nial
<lang nial>quicksort is fork [ >= [1 first,tally],
pass,
link [
quicksort sublist [ < [pass, first], pass ],
sublist [ match [pass,first],pass ],
quicksort sublist [ > [pass,first], pass ]
]
]</lang>
Using it. <lang nial>|quicksort [5, 8, 7, 4, 3] =3 4 5 7 8</lang>
Nim
<lang nim> proc quickSort[T](a: var openarray[T], inl = 0, inr = -1) =
var r = if inr >= 0: inr else: a.high
var l = inl
let n = r - l + 1
if n < 2: return
let p = a[l + 3 * n div 4]
while l <= r:
if a[l] < p:
inc l
continue
if a[r] > p:
dec r
continue
if l <= r:
swap a[l], a[r]
inc l
dec r
quickSort(a, inl, r)
quickSort(a, l, inr)
var a = @[4, 65, 2, -31, 0, 99, 2, 83, 782] quickSort a echo a</lang>
- Output:
@[-31, 0, 2, 2, 4, 65, 83, 99, 782]
Nix
<lang 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]
</lang>
- Output:
[ -31 0 2 4 65 83 99 782 ]
Objeck
<lang objeck> class QuickSort {
function : Main(args : String[]) ~ Nil {
array := [1, 3, 5, 7, 9, 8, 6, 4, 2];
Sort(array);
each(i : array) {
array[i]->PrintLine();
};
}
function : Sort(array : Int[]) ~ Nil {
size := array->Size();
if(size <= 1) {
return;
};
Sort(array, 0, size - 1);
}
function : native : Sort(array : Int[], low : Int, high : Int) ~ Nil {
i := low; j := high;
pivot := array[low + (high-low)/2];
while(i <= j) {
while(array[i] < pivot) {
i+=1;
};
while(array[j] > pivot) {
j-=1;
};
if (i <= j) {
temp := array[i];
array[i] := array[j];
array[j] := temp;
i+=1; j-=1;
};
};
if(low < j) {
Sort(array, low, j);
};
if(i < high) {
Sort(array, i, high);
};
}
} </lang>
Objective-C
The latest XCode compiler is assumed with ARC enabled. <lang objc>void quicksortInPlace(NSMutableArray *array, NSInteger first, NSInteger last, NSComparator comparator) {
if (first >= last) return;
id pivot = array[(first + last) / 2];
NSInteger left = first;
NSInteger right = last;
while (left <= right) {
while (comparator(array[left], pivot) == NSOrderedAscending)
left++;
while (comparator(array[right], pivot) == NSOrderedDescending)
right--;
if (left <= right)
[array exchangeObjectAtIndex:left++ withObjectAtIndex:right--];
}
quicksortInPlace(array, first, right, comparator);
quicksortInPlace(array, left, last, comparator);
}
NSArray* quicksort(NSArray *unsorted, NSComparator comparator) {
NSMutableArray *a = [NSMutableArray arrayWithArray:unsorted]; quicksortInPlace(a, 0, a.count - 1, comparator); return a;
}
int main(int argc, const char * argv[]) {
@autoreleasepool {
NSArray *a = @[ @1, @3, @5, @7, @9, @8, @6, @4, @2 ];
NSLog(@"Unsorted: %@", a);
NSLog(@"Sorted: %@", quicksort(a, ^(id x, id y) { return [x compare:y]; }));
NSArray *b = @[ @"Emil", @"Peg", @"Helen", @"Juergen", @"David", @"Rick", @"Barb", @"Mike", @"Tom" ];
NSLog(@"Unsorted: %@", b);
NSLog(@"Sorted: %@", quicksort(b, ^(id x, id y) { return [x compare:y]; }));
}
return 0;
}</lang>
- Output:
Unsorted: (
1,
3,
5,
7,
9,
8,
6,
4,
2
)
Sorted: (
1,
2,
3,
4,
5,
6,
7,
8,
9
)
Unsorted: (
Emil,
Peg,
Helen,
Juergen,
David,
Rick,
Barb,
Mike,
Tom
)
Sorted: (
Barb,
David,
Emil,
Helen,
Juergen,
Mike,
Peg,
Rick,
Tom
)OCaml
Declarative and purely functional
<lang ocaml>let rec quicksort gt = function
| [] -> []
| x::xs ->
let ys, zs = List.partition (gt x) xs in
(quicksort gt ys) @ (x :: (quicksort gt zs))
let _ =
quicksort (>) [4; 65; 2; -31; 0; 99; 83; 782; 1]</lang>
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.
<lang ocaml> 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'
</lang>
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)
<lang octave>function f=quicksort(v) % v must be a column vector
f = v; n=length(v);
if(n > 1)
vl = min(f); vh = max(f); % min, max
p = (vl+vh)*0.5; % pivot
ia = find(f < p); ib = find(f == p); ic=find(f > p);
f = [quicksort(f(ia)); f(ib); quicksort(f(ic))];
end
endfunction
N=30; v=rand(N,1); tic,u=quicksort(v); toc u</lang>
Oforth
Oforth built-in sort uses quick sort algorithm (see lang/collect/ListBuffer.of for implementation) :
<lang Oforth>[ 5, 8, 2, 3, 4, 1 ] sort</lang>
ooRexx
<lang ooRexx> a = .array~Of(4, 65, 2, -31, 0, 99, 83, 782, 1)
say 'before:' a~toString( ,', ') a = quickSort(a) say ' after:' a~toString( ,', ') exit
- routine quickSort
use arg arr -- the array to be sorted
less = .array~new
pivotList = .array~new
more = .array~new
if arr~items <= 1 then
return arr
else do
pivot = arr[1]
do i over arr
if i < pivot then
less~append(i)
else if i > pivot then
more~append(i)
else
pivotList~append(i)
end
less = quickSort(less)
more = quickSort(more)
return less~~appendAll(pivotList)~~appendAll(more)
end</lang>
- Output:
before: 4, 65, 2, -31, 0, 99, 83, 782, 1 after: -31, 0, 1, 2, 4, 65, 83, 99, 782
Oz
<lang oz>declare
fun {QuickSort Xs}
case Xs of nil then nil
[] Pivot|Xr then
fun {IsSmaller X} X < Pivot end
Smaller Larger
in
{List.partition Xr IsSmaller ?Smaller ?Larger}
{Append {QuickSort Smaller} Pivot|{QuickSort Larger}}
end
end
in
{Show {QuickSort [3 1 4 1 5 9 2 6 5]}}</lang>
PARI/GP
<lang parigp>quickSort(v)={
if(#v<2, return(v));
my(less=List(),more=List(),same=List(),pivot);
pivot=median([v[random(#v)+1],v[random(#v)+1],v[random(#v)+1]]); \\ Middle-of-three
for(i=1,#v,
if(v[i]<pivot,
listput(less, v[i]),
if(v[i]==pivot, listput(same, v[i]), listput(more, v[i]))
)
);
concat(quickSort(Vec(less)), concat(Vec(same), quickSort(Vec(more))))
}; median(v)={
vecsort(v)[#v>>1]
};</lang>
Pascal
<lang pascal> { X is array of LongInt } Procedure QuickSort ( Left, Right : LongInt ); Var
i, j,
tmp, pivot : LongInt; { tmp & pivot are the same type as the elements of array }
Begin
i:=Left;
j:=Right;
pivot := X[(Left + Right) shr 1]; // pivot := X[(Left + Rigth) div 2]
Repeat
While pivot > X[i] Do inc(i); // i:=i+1;
While pivot < X[j] Do dec(j); // j:=j-1;
If i<=j Then Begin
tmp:=X[i];
X[i]:=X[j];
X[j]:=tmp;
dec(j); // j:=j-1;
inc(i); // i:=i+1;
End;
Until i>j;
If Left<j Then QuickSort(Left,j);
If i<Right Then QuickSort(i,Right);
End; </lang>
Perl
<lang perl> sub quick_sort {
return @_ if @_ < 2; my $p = splice @_, int rand @_, 1; quick_sort(grep $_ < $p, @_), $p, quick_sort(grep $_ >= $p, @_);
}
my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1); @a = quick_sort @a; print "@a\n"; </lang>
Perl 6
<lang perl6># Empty list sorts to the empty list
multi quicksort([]) { () }
# Otherwise, extract first item as pivot...
multi quicksort([$pivot, *@rest]) {
# Partition.
my $before := @rest.grep(* before $pivot);
my $after := @rest.grep(* !before $pivot);
# Sort the partitions.
flat quicksort($before), $pivot, quicksort($after)
}</lang>
Note that $before and $after are bound to lazy lists, so the partitions can (at least in theory) be sorted in parallel.
Phix
<lang Phix>function quick_sort(sequence x) -- -- put x into ascending order using recursive quick sort -- integer n, last, mid object xi, midval
n = length(x)
if n<2 then
return x -- already sorted (trivial case)
end if
mid = floor((n+1)/2) midval = x[mid] x[mid] = x[1]
last = 1
for i=2 to n do
xi = x[i]
if xi<midval then
last += 1
x[i] = x[last]
x[last] = xi
end if
end for
return quick_sort(x[2..last]) & {midval} & quick_sort(x[last+1..n])
end function
?quick_sort({5,"oranges","and",3,"apples"})</lang>
- Output:
{3,5,"and","apples","oranges"}
PHP
<lang php>function quicksort($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);</lang>
1,2,3,4,5,6,7,8,9
<lang php> 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)); </lang>
[1, 4, 8, 2, 8, 0, 2, 8] ==> [0, 1, 2, 2, 4, 8, 8, 8]
PicoLisp
<lang lisp>(de quicksort (L)
(if (cdr L)
(let Pivot (car L)
(append (quicksort (filter '((A) (< A Pivot)) (cdr L)))
(filter '((A) (= A Pivot)) L )
(quicksort (filter '((A) (> A Pivot)) (cdr L)))) )
L) )</lang>
PL/I
<lang pli>DCL (T(20)) FIXED BIN(31); /* scratch space of length N */
QUICKSORT: PROCEDURE (A,AMIN,AMAX,N) RECURSIVE ;
DECLARE (A(*)) FIXED BIN(31);
DECLARE (N,AMIN,AMAX) FIXED BIN(31) NONASGN;
DECLARE (I,J,IA,IB,IC,PIV) FIXED BIN(31);
DECLARE (P,Q) POINTER;
DECLARE (AP(1)) FIXED BIN(31) BASED(P);
IF(N <= 1)THEN RETURN;
IA=0; IB=0; IC=N+1;
PIV=(AMIN+AMAX)/2;
DO I=1 TO N;
IF(A(I) < PIV)THEN DO;
IA+=1; A(IA)=A(I);
END; ELSE IF(A(I) > PIV) THEN DO;
IC-=1; T(IC)=A(I);
END; ELSE DO;
IB+=1; T(IB)=A(I);
END;
END;
DO I=1 TO IB; A(I+IA)=T(I); END;
DO I=IC TO N; A(I)=T(N+IC-I); END;
P=ADDR(A(IC));
IC=N+1-IC;
IF(IA > 1) THEN CALL QUICKSORT(A, AMIN, PIV-1,IA);
IF(IC > 1) THEN CALL QUICKSORT(AP,PIV+1,AMAX, IC);
RETURN;
END QUICKSORT;
MINMAX: PROC(A,AMIN,AMAX,N);
DCL (AMIN,AMAX) FIXED BIN(31),
(N,A(*)) FIXED BIN(31) NONASGN ;
DCL (I,X,Y) FIXED BIN(31);
AMIN=A(N); AMAX=AMIN;
DO I=1 TO N-1;
X=A(I); Y=A(I+1);
IF (X < Y)THEN DO;
IF (X < AMIN) THEN AMIN=X;
IF (Y > AMAX) THEN AMAX=Y;
END; ELSE DO;
IF (X > AMAX) THEN AMAX=X;
IF (Y < AMIN) THEN AMIN=Y;
END;
END;
RETURN;
END MINMAX; CALL MINMAX(A,AMIN,AMAX,N); CALL QUICKSORT(A,AMIN,AMAX,N);</lang>
PowerShell
First solution
<lang PowerShell>Function SortThree( [Array] $data ) { if( $data[ 0 ] -gt $data[ 1 ] ) { if( $data[ 0 ] -lt $data[ 2 ] ) { $data = $data[ 1, 0, 2 ] } elseif ( $data[ 1 ] -lt $data[ 2 ] ){ $data = $data[ 1, 2, 0 ] } else { $data = $data[ 2, 1, 0 ] } } else { if( $data[ 0 ] -gt $data[ 2 ] ) { $data = $data[ 2, 0, 1 ] } elseif( $data[ 1 ] -gt $data[ 2 ] ) { $data = $data[ 0, 2, 1 ] } } $data }
Function QuickSort( [Array] $data, $rand = ( New-Object Random ) ) { $datal = $data.length if( $datal -gt 3 ) { [void] $datal-- $median = ( SortThree $data[ 0, ( $rand.Next( 1, $datal - 1 ) ), -1 ] )[ 1 ] $lt = @() $eq = @() $gt = @() $data | ForEach-Object { if( $_ -lt $median ) { $lt += $_ } elseif( $_ -eq $median ) { $eq += $_ } else { $gt += $_ } } $lt = ( QuickSort $lt $rand ) $gt = ( QuickSort $gt $rand ) $data = @($lt) + $eq + $gt } elseif( $datal -eq 3 ) { $data = SortThree( $data ) } elseif( $datal -eq 2 ) { if( $data[ 0 ] -gt $data[ 1 ] ) { $data = $data[ 1, 0 ] } } $data }
QuickSort 5,3,1,2,4 QuickSort 'e','c','a','b','d' QuickSort 0.5,0.3,0.1,0.2,0.4 $l = 100; QuickSort ( 1..$l | ForEach-Object { $Rand = New-Object Random }{ $Rand.Next( 0, $l - 1 ) } )</lang>
Another solution
<lang powershell> function quicksort($array) {
$less, $equal, $greater = @(), @(), @()
if( $array.Count -gt 1 ) {
$pivot = $array[0]
foreach( $x in $array) {
if($x -lt $pivot) { $less += @($x) }
elseif ($x -eq $pivot) { $equal += @($x)}
else { $greater += @($x) }
}
$array = (@(quicksort $less) + @($equal) + @(quicksort $greater))
}
$array
} $array = @(60, 21, 19, 36, 63, 8, 100, 80, 3, 87, 11) "$(quicksort $array)" </lang>
The output is: 3 8 11 19 21 36 60 63 80 87 100
Yet another solution
<lang powershell> function quicksort($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)
}
}
} </lang>
Prolog
<lang prolog>qsort( [], [] ). qsort( [H|U], S ) :- splitBy(H, U, L, R), qsort(L, SL), qsort(R, SR), append(SL, [H|SR], S).
% splitBy( H, U, LS, RS ) % True if LS = { L in U | L <= H }; RS = { R in U | R > H } splitBy( _, [], [], []). splitBy( H, [U|T], [U|LS], RS ) :- U =< H, splitBy(H, T, LS, RS). splitBy( H, [U|T], LS, [U|RS] ) :- U > H, splitBy(H, T, LS, RS). </lang>
PureBasic
<lang PureBasic>Procedure qSort(Array a(1), firstIndex, lastIndex)
Protected low, high, pivotValue
low = firstIndex
high = lastIndex
pivotValue = a((firstIndex + lastIndex) / 2)
Repeat
While a(low) < pivotValue
low + 1
Wend
While a(high) > pivotValue
high - 1
Wend
If low <= high
Swap a(low), a(high)
low + 1
high - 1
EndIf
Until low > high
If firstIndex < high
qSort(a(), firstIndex, high)
EndIf
If low < lastIndex
qSort(a(), low, lastIndex)
EndIf
EndProcedure
Procedure quickSort(Array a(1))
qSort(a(),0,ArraySize(a()))
EndProcedure</lang>
Python
<lang python>def quickSort(arr):
less = []
pivotList = []
more = []
if len(arr) <= 1:
return arr
else:
pivot = arr[0]
for i in arr:
if i < pivot:
less.append(i)
elif i > pivot:
more.append(i)
else:
pivotList.append(i)
less = quickSort(less)
more = quickSort(more)
return less + pivotList + more
a = [4, 65, 2, -31, 0, 99, 83, 782, 1] a = quickSort(a)</lang>
In a Haskell fashion -- <lang python>def qsort(L):
return (qsort([y for y in L[1:] if y < L[0]]) +
L[:1] +
qsort([y for y in L[1:] if y >= L[0]])) if len(L) > 1 else L</lang>
More readable, but still using list comprehensions: <lang python>def qsort(list):
if not list:
return []
else:
pivot = list[0]
less = [x for x in list if x < pivot]
more = [x for x in list[1:] if x >= pivot]
return qsort(less) + [pivot] + qsort(more)</lang>
More correctly in some tests: <lang python>from random import *
def qSort(a):
if len(a) <= 1:
return a
else:
q = choice(a)
return qSort([elem for elem in a if elem < q]) + [q] * a.count(q) + qSort([elem for elem in a if elem > q])</lang>
<lang python>def quickSort(a):
if len(a) <= 1:
return a
else:
less = []
more = []
pivot = choice(a)
for i in a:
if i < pivot:
less.append(i)
if i > pivot:
more.append(i)
less = quickSort(less)
more = quickSort(more)
return less + [pivot] * a.count(pivot) + more</lang>
Returning a new list:
<lang python>def qsort(array):
if len(array) < 2:
return array
head, *tail = array
less = qsort([i for i in tail if i < head])
more = qsort([i for i in tail if i >= head])
return less + [head] + more</lang>
Sorting a list in place:
<lang python>def quicksort(array):
_quicksort(array, 0, len(array) - 1)
def _quicksort(array, start, stop):
if stop - start > 0:
pivot, left, right = array[start], start, stop
while left <= right:
while array[left] < pivot:
left += 1
while array[right] > pivot:
right -= 1
if left <= right:
array[left], array[right] = array[right], array[left]
left += 1
right -= 1
_quicksort(array, start, right)
_quicksort(array, left, stop)</lang>
Qi
<lang Qi>(define keep
_ [] -> [] Pred [A|Rest] -> [A | (keep Pred Rest)] where (Pred A) Pred [_|Rest] -> (keep Pred Rest))
(define quicksort
[] -> []
[A|R] -> (append (quicksort (keep (>= A) R))
[A]
(quicksort (keep (< A) R))))
(quicksort [6 8 5 9 3 2 2 1 4 7]) </lang>
R
<lang R>qsort <- function(v) {
if ( length(v) > 1 )
{
pivot <- (min(v) + max(v))/2.0 # Could also use pivot <- median(v)
c(qsort(v[v < pivot]), v[v == pivot], qsort(v[v > pivot]))
} else v
}
N <- 100 vs <- runif(N) system.time(u <- qsort(vs)) print(u)</lang>
Racket
<lang Racket>#lang racket (define (quicksort < l)
(match l
['() '()]
[(cons x xs)
(let-values ([(xs-gte xs-lt) (partition (curry < x) xs)])
(append (quicksort < xs-lt)
(list x)
(quicksort < xs-gte)))]))</lang>
Examples
<lang Racket>(quicksort < '(8 7 3 6 4 5 2))
- returns '(2 3 4 5 6 7 8)
(quicksort string<? '("Mergesort" "Quicksort" "Bubblesort"))
- returns '("Bubblesort" "Mergesort" "Quicksort")</lang>
Red
<lang 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] </lang>
REXX
version 1
<lang rexx>/*REXX program sorts a stemmed array using the quicksort algorithm. */ call gen@ /*generate the elements for the array. */ call show@ 'before sort' /*show the before array elements. */ call qSort # /*invoke the quicksort subroutine. */ call show@ ' after sort' /*show the after array elements. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ qSort: procedure expose @.; a.1=1; parse arg b.1 /*access the caller's local variable. */
$=1
do while $\==0; L=a.$; t=b.$; $=$-1; if t<2 then iterate
H=L+t-1; ?=L+t%2
if @.H<@.L then if @.?<@.H then do; p=@.H; @.H=@.L; end
else if @.?>@.L then p=@.L
else do; p=@.?; @.?=@.L; end
else if @.?<@.L then p=@.L
else if @.?>@.H then do; p=@.H; @.H=@.L; end
else do; p=@.?; @.?=@.L; end
j=L+1; k=h
do forever
do j=j while j<=k & @.j<=p; end /*a tinie─tiny loop.*/
do k=k by -1 while j <k & @.k>=p; end /*another " " */
if j>=k then leave /*segment finished? */
_=@.j; @.j=@.k; @.k=_ /*swap J&K elements.*/
end /*forever*/
$=$+1
k=j-1; @.L=@.k; @.k=p
if j<=? then do; a.$=j; b.$=H-j+1; $=$+1; a.$=L; b.$=k-L; end
else do; a.$=L; b.$=k-L; $=$+1; a.$=j; b.$=H-j+1; end
end /*while $¬==0*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/ show@: w=length(#); do j=1 for #; say 'element' right(j,w) arg(1)":" @.j; end
say copies('▒', maxL + w + 22) /*display a separator (between outputs)*/
return
/*───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/ gen@: @.=; maxL=0 /*assign a default value for the array.*/ @.1 = " Rivers that form part of a (USA) state's border " /*this value is adjusted later to include a prefix & suffix.*/ @.2 = '=' /*this value is expanded later. */ @.3 = "Perdido River Alabama, Florida" @.4 = "Chattahoochee River Alabama, Georgia" @.5 = "Tennessee River Alabama, Kentucky, Mississippi, Tennessee" @.6 = "Colorado River Arizona, California, Nevada, Baja California (Mexico)" @.7 = "Mississippi River Arkansas, Illinois, Iowa, Kentucky, Minnesota, Mississippi, Missouri, Tennessee, Louisiana, Wisconsin" @.8 = "St. Francis River Arkansas, Missouri" @.9 = "Poteau River Arkansas, Oklahoma" @.10 = "Arkansas River Arkansas, Oklahoma" @.11 = "Red River (Mississippi watershed) Arkansas, Oklahoma, Texas" @.12 = "Byram River Connecticut, New York" @.13 = "Pawcatuck River Connecticut, Rhode Island and Providence Plantations" @.14 = "Delaware River Delaware, New Jersey, New York, Pennsylvania" @.15 = "Potomac River District of Columbia, Maryland, Virginia, West Virginia" @.16 = "St. Marys River Florida, Georgia" @.17 = "Chattooga River Georgia, South Carolina" @.18 = "Tugaloo River Georgia, South Carolina" @.19 = "Savannah River Georgia, South Carolina" @.20 = "Snake River Idaho, Oregon, Washington" @.21 = "Wabash River Illinois, Indiana" @.22 = "Ohio River Illinois, Indiana, Kentucky, Ohio, West Virginia" @.23 = "Great Miami River (mouth only) Indiana, Ohio" @.24 = "Des Moines River Iowa, Missouri" @.25 = "Big Sioux River Iowa, South Dakota" @.26 = "Missouri River Kansas, Iowa, Missouri, Nebraska, South Dakota" @.27 = "Tug Fork River Kentucky, Virginia, West Virginia" @.28 = "Big Sandy River Kentucky, West Virginia" @.29 = "Pearl River Louisiana, Mississippi" @.30 = "Sabine River Louisiana, Texas" @.31 = "Monument Creek Maine, New Brunswick (Canada)" @.32 = "St. Croix River Maine, New Brunswick (Canada)" @.33 = "Piscataqua River Maine, New Hampshire" @.34 = "St. Francis River Maine, Quebec (Canada)" @.35 = "St. John River Maine, Quebec (Canada)" @.36 = "Pocomoke River Maryland, Virginia" @.37 = "Palmer River Massachusetts, Rhode Island and Providence Plantations" @.38 = "Runnins River Massachusetts, Rhode Island and Providence Plantations" @.39 = "Montreal River Michigan (upper peninsula), Wisconsin" @.40 = "Detroit River Michigan, Ontario (Canada)" @.41 = "St. Clair River Michigan, Ontario (Canada)" @.42 = "St. Marys River Michigan, Ontario (Canada)" @.43 = "Brule River Michigan, Wisconsin" @.44 = "Menominee River Michigan, Wisconsin" @.45 = "Red River of the North Minnesota, North Dakota" @.46 = "Bois de Sioux River Minnesota, North Dakota, South Dakota" @.47 = "Pigeon River Minnesota, Ontario (Canada)" @.48 = "Rainy River Minnesota, Ontario (Canada)" @.49 = "St. Croix River Minnesota, Wisconsin" @.50 = "St. Louis River Minnesota, Wisconsin" @.51 = "Halls Stream New Hampshire, Canada" @.52 = "Salmon Falls River New Hampshire, Maine" @.53 = "Connecticut River New Hampshire, Vermont" @.54 = "Arthur Kill New Jersey, New York (tidal strait)" @.55 = "Kill Van Kull New Jersey, New York (tidal strait)" @.56 = "Hudson River (lower part only) New Jersey, New York" @.57 = "Rio Grande New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila de Zaragoza (Mexico), Chihuahua (Mexico)" @.58 = "Niagara River New York, Ontario (Canada)" @.59 = "St. Lawrence River New York, Ontario (Canada)" @.60 = "Poultney River New York, Vermont" @.61 = "Catawba River North Carolina, South Carolina" @.62 = "Blackwater River North Carolina, Virginia" @.63 = "Columbia River Oregon, Washington"
do #=1 until @.#== /*find how many entries in array, and */
maxL=max(maxL, length(@.#)) /* also find the maximum width entry.*/
end /*#*/
- =#-1 /*adjust the highest element number. */
@.1=center(@.1, maxL, '-') /* " " header information. */ @.2=copies(@.2, maxL) /* " " " separator. */ return</lang> output
element 1 before sort: ------------------------------------------------ Rivers that form part of a (USA) state's border ------------------------------------------------- element 2 before sort: ================================================================================================================================================== element 3 before sort: Perdido River Alabama, Florida element 4 before sort: Chattahoochee River Alabama, Georgia element 5 before sort: Tennessee River Alabama, Kentucky, Mississippi, Tennessee element 6 before sort: Colorado River Arizona, California, Nevada, Baja California (Mexico) element 7 before sort: Mississippi River Arkansas, Illinois, Iowa, Kentucky, Minnesota, Mississippi, Missouri, Tennessee, Louisiana, Wisconsin element 8 before sort: St. Francis River Arkansas, Missouri element 9 before sort: Poteau River Arkansas, Oklahoma element 10 before sort: Arkansas River Arkansas, Oklahoma element 11 before sort: Red River (Mississippi watershed) Arkansas, Oklahoma, Texas element 12 before sort: Byram River Connecticut, New York element 13 before sort: Pawcatuck River Connecticut, Rhode Island and Providence Plantations element 14 before sort: Delaware River Delaware, New Jersey, New York, Pennsylvania element 15 before sort: Potomac River District of Columbia, Maryland, Virginia, West Virginia element 16 before sort: St. Marys River Florida, Georgia element 17 before sort: Chattooga River Georgia, South Carolina element 18 before sort: Tugaloo River Georgia, South Carolina element 19 before sort: Savannah River Georgia, South Carolina element 20 before sort: Snake River Idaho, Oregon, Washington element 21 before sort: Wabash River Illinois, Indiana element 22 before sort: Ohio River Illinois, Indiana, Kentucky, Ohio, West Virginia element 23 before sort: Great Miami River (mouth only) Indiana, Ohio element 24 before sort: Des Moines River Iowa, Missouri element 25 before sort: Big Sioux River Iowa, South Dakota element 26 before sort: Missouri River Kansas, Iowa, Missouri, Nebraska, South Dakota element 27 before sort: Tug Fork River Kentucky, Virginia, West Virginia element 28 before sort: Big Sandy River Kentucky, West Virginia element 29 before sort: Pearl River Louisiana, Mississippi element 30 before sort: Sabine River Louisiana, Texas element 31 before sort: Monument Creek Maine, New Brunswick (Canada) element 32 before sort: St. Croix River Maine, New Brunswick (Canada) element 33 before sort: Piscataqua River Maine, New Hampshire element 34 before sort: St. Francis River Maine, Quebec (Canada) element 35 before sort: St. John River Maine, Quebec (Canada) element 36 before sort: Pocomoke River Maryland, Virginia element 37 before sort: Palmer River Massachusetts, Rhode Island and Providence Plantations element 38 before sort: Runnins River Massachusetts, Rhode Island and Providence Plantations element 39 before sort: Montreal River Michigan (upper peninsula), Wisconsin element 40 before sort: Detroit River Michigan, Ontario (Canada) element 41 before sort: St. Clair River Michigan, Ontario (Canada) element 42 before sort: St. Marys River Michigan, Ontario (Canada) element 43 before sort: Brule River Michigan, Wisconsin element 44 before sort: Menominee River Michigan, Wisconsin element 45 before sort: Red River of the North Minnesota, North Dakota element 46 before sort: Bois de Sioux River Minnesota, North Dakota, South Dakota element 47 before sort: Pigeon River Minnesota, Ontario (Canada) element 48 before sort: Rainy River Minnesota, Ontario (Canada) element 49 before sort: St. Croix River Minnesota, Wisconsin element 50 before sort: St. Louis River Minnesota, Wisconsin element 51 before sort: Halls Stream New Hampshire, Canada element 52 before sort: Salmon Falls River New Hampshire, Maine element 53 before sort: Connecticut River New Hampshire, Vermont element 54 before sort: Arthur Kill New Jersey, New York (tidal strait) element 55 before sort: Kill Van Kull New Jersey, New York (tidal strait) element 56 before sort: Hudson River (lower part only) New Jersey, New York element 57 before sort: Rio Grande New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila De Zaragoza (Mexico), Chihuahua (Mexico) element 58 before sort: Niagara River New York, Ontario (Canada) element 59 before sort: St. Lawrence River New York, Ontario (Canada) element 60 before sort: Poultney River New York, Vermont element 61 before sort: Catawba River North Carolina, South Carolina element 62 before sort: Blackwater River North Carolina, Virginia element 63 before sort: Columbia River Oregon, Washington ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ element 1 after sort: ------------------------------------------------ Rivers that form part of a (USA) state's border ------------------------------------------------- element 2 after sort: ================================================================================================================================================== element 3 after sort: Arkansas River Arkansas, Oklahoma element 4 after sort: Arthur Kill New Jersey, New York (tidal strait) element 5 after sort: Big Sandy River Kentucky, West Virginia element 6 after sort: Big Sioux River Iowa, South Dakota element 7 after sort: Blackwater River North Carolina, Virginia element 8 after sort: Bois de Sioux River Minnesota, North Dakota, South Dakota element 9 after sort: Brule River Michigan, Wisconsin element 10 after sort: Byram River Connecticut, New York element 11 after sort: Catawba River North Carolina, South Carolina element 12 after sort: Chattahoochee River Alabama, Georgia element 13 after sort: Chattooga River Georgia, South Carolina element 14 after sort: Colorado River Arizona, California, Nevada, Baja California (Mexico) element 15 after sort: Columbia River Oregon, Washington element 16 after sort: Connecticut River New Hampshire, Vermont element 17 after sort: Delaware River Delaware, New Jersey, New York, Pennsylvania element 18 after sort: Des Moines River Iowa, Missouri element 19 after sort: Detroit River Michigan, Ontario (Canada) element 20 after sort: Great Miami River (mouth only) Indiana, Ohio element 21 after sort: Halls Stream New Hampshire, Canada element 22 after sort: Hudson River (lower part only) New Jersey, New York element 23 after sort: Kill Van Kull New Jersey, New York (tidal strait) element 24 after sort: Menominee River Michigan, Wisconsin element 25 after sort: Mississippi River Arkansas, Illinois, Iowa, Kentucky, Minnesota, Mississippi, Missouri, Tennessee, Louisiana, Wisconsin element 26 after sort: Missouri River Kansas, Iowa, Missouri, Nebraska, South Dakota element 27 after sort: Montreal River Michigan (upper peninsula), Wisconsin element 28 after sort: Monument Creek Maine, New Brunswick (Canada) element 29 after sort: Niagara River New York, Ontario (Canada) element 30 after sort: Ohio River Illinois, Indiana, Kentucky, Ohio, West Virginia element 31 after sort: Palmer River Massachusetts, Rhode Island and Providence Plantations element 32 after sort: Pawcatuck River Connecticut, Rhode Island and Providence Plantations element 33 after sort: Pearl River Louisiana, Mississippi element 34 after sort: Perdido River Alabama, Florida element 35 after sort: Pigeon River Minnesota, Ontario (Canada) element 36 after sort: Piscataqua River Maine, New Hampshire element 37 after sort: Pocomoke River Maryland, Virginia element 38 after sort: Poteau River Arkansas, Oklahoma element 39 after sort: Potomac River District of Columbia, Maryland, Virginia, West Virginia element 40 after sort: Poultney River New York, Vermont element 41 after sort: Rainy River Minnesota, Ontario (Canada) element 42 after sort: Red River (Mississippi watershed) Arkansas, Oklahoma, Texas element 43 after sort: Red River of the North Minnesota, North Dakota element 44 after sort: Rio Grande New Mexico, Texas, Tamaulipas (Mexico), Nuevo Leon (Mexico), Coahuila De Zaragoza (Mexico), Chihuahua (Mexico) element 45 after sort: Runnins River Massachusetts, Rhode Island and Providence Plantations element 46 after sort: Sabine River Louisiana, Texas element 47 after sort: Salmon Falls River New Hampshire, Maine element 48 after sort: Savannah River Georgia, South Carolina element 49 after sort: Snake River Idaho, Oregon, Washington element 50 after sort: St. Clair River Michigan, Ontario (Canada) element 51 after sort: St. Croix River Maine, New Brunswick (Canada) element 52 after sort: St. Croix River Minnesota, Wisconsin element 53 after sort: St. Francis River Arkansas, Missouri element 54 after sort: St. Francis River Maine, Quebec (Canada) element 55 after sort: St. John River Maine, Quebec (Canada) element 56 after sort: St. Lawrence River New York, Ontario (Canada) element 57 after sort: St. Louis River Minnesota, Wisconsin element 58 after sort: St. Marys River Florida, Georgia element 59 after sort: St. Marys River Michigan, Ontario (Canada) element 60 after sort: Tennessee River Alabama, Kentucky, Mississippi, Tennessee element 61 after sort: Tug Fork River Kentucky, Virginia, West Virginia element 62 after sort: Tugaloo River Georgia, South Carolina element 63 after sort: Wabash River Illinois, Indiana ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
version 2
The Python code translates very well to ooRexx but here is a way to implement it in classic REXX as well.
<lang Rexx> a = '4 65 2 -31 0 99 83 782 1'
do i = 1 to words(a)
queue word(a, i)
end
call quickSort
parse pull item
do queued()
call charout ,item', '
parse pull item
end
say item
exit
quickSort: procedure /* In classic Rexx, arguments are passed by value, not by reference so stems
cannot be passed as arguments nor used as return values. Putting their contents on the external data queue is a way to bypass this issue. */
/* construct the input stem */
arr.0 = queued()
do i = 1 to arr.0
parse pull arr.i
end
less.0 = 0
pivotList.0 = 0
more.0 = 0
if arr.0 <= 1 then do
if arr.0 = 1 then
queue arr.1
return
end
else do
pivot = arr.1
do i = 1 to arr.0
item = arr.i
select
when item < pivot then do
j = less.0 + 1
less.j = item
less.0 = j
end
when item > pivot then do
j = more.0 + 1
more.j = item
more.0 = j
end
otherwise
j = pivotList.0 + 1
pivotList.j = item
pivotList.0 = j
end
end
end
/* recursive call to sort the less. stem */
do i = 1 to less.0
queue less.i
end
if queued() > 0 then do
call quickSort
less.0 = queued()
do i = 1 to less.0
parse pull less.i
end
end
/* recursive call to sort the more. stem */
do i = 1 to more.0
queue more.i
end
if queued() > 0 then do
call quickSort
more.0 = queued()
do i = 1 to more.0
parse pull more.i
end
end
/* put the contents of all 3 stems on the queue in order */
do i = 1 to less.0
queue less.i
end
do i = 1 to pivotList.0
queue pivotList.i
end
do i = 1 to more.0
queue more.i
end
return</lang>
Ring
<lang ring>
- Project : Sorting algorithms/Quicksort
test = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1] see "before sort:" + nl showarray(test) quicksort(test, 1, 10) see "after sort:" + nl showarray(test)
func quicksort(a, s, n)
if n < 2
return
ok
t = s + n - 1
l = s
r = t
p = a[floor((l + r) / 2)]
while l <= r
while a[l] < p
l = l + 1
end
while a[r] > p
r = r - 1
end
if l <= r
temp = a[l]
a[l] = a[r]
a[r] = temp
l = l + 1
r = r - 1
ok
end
if s < r
quicksort(a, s, r - s + 1)
ok
if l < t
quicksort(a, l, t - l + 1 )
ok
func showarray(vect)
svect = ""
for n = 1 to len(vect)
svect = svect + vect[n] + " "
next
svect = left(svect, len(svect) - 1)
see svect + nl
</lang> Output:
before sort: 4 65 2 -31 0 99 2 83 782 1 after sort: -31 0 1 2 2 4 65 83 99 782
Ruby
<lang ruby>class Array
def quick_sort
return self if length <= 1
pivot = self[0]
less, greatereq = self[1..-1].partition { |x| x < pivot }
less.quick_sort + [pivot] + greatereq.quick_sort
end
end</lang> or <lang ruby>class Array
def quick_sort
return self if length <= 1
pivot = sample
group = group_by{ |x| x <=> pivot }
group.default = []
group[-1].quick_sort + group[0] + group[1].quick_sort
end
end</lang> or functionally <lang ruby>class Array
def quick_sort
h, *t = self
h ? t.partition { |e| e < h }.inject { |l, r| l.quick_sort + [h] + r.quick_sort } : []
end
end</lang>
Run BASIC
<lang runbasic>' ------------------------------- ' quick sort ' ------------------------------- size = 50 dim s(size) ' array to sort for i = 1 to size ' fill it with some random numbers
s(i) = rnd(0) * 100
next i
lft = 1 rht = size
[qSort]
lftHold = lft
rhtHold = rht
pivot = s(lft)
while lft < rht
while (s(rht) >= pivot) and (lft < rht) : rht = rht - 1 :wend
if lft <> rht then
s(lft) = s(rht)
lft = lft + 1
end if
while (s(lft) <= pivot) and (lft < rht) : lft = lft + 1 :wend
if lft <> rht then
s(rht) = s(lft)
rht = rht - 1
end if
wend
s(lft) = pivot pivot = lft lft = lftHold rht = rhtHold if lft < pivot then rht = pivot - 1 goto [qSort] end if if rht > pivot then lft = pivot + 1 goto [qSort] end if
for i = 1 to size
print i;"-->";s(i)
next i</lang>
Rust
<lang rust>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
}</lang>
- 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"]
SASL
Copied from SASL manual, Appendix II, solution (2)(b) <lang SASL>DEF || this rather nice solution is due to Silvio Meira sort () = () sort (a : x) = sort {b <- x; b <= a } ++ a : sort { b <- x; b>a} ?</lang>
Sather
<lang sather>class SORT{T < $IS_LT{T}} is
private afilter(a:ARRAY{T}, cmp:ROUT{T,T}:BOOL, p:T):ARRAY{T} is
filtered ::= #ARRAY{T};
loop v ::= a.elt!;
if cmp.call(v, p) then
filtered := filtered.append(|v|);
end;
end;
return filtered;
end;
private mlt(a, b:T):BOOL is return a < b; end;
private mgt(a, b:T):BOOL is return a > b; end;
quick_sort(inout a:ARRAY{T}) is
if a.size < 2 then return; end;
pivot ::= a.median;
left:ARRAY{T} := afilter(a, bind(mlt(_,_)), pivot);
right:ARRAY{T} := afilter(a, bind(mgt(_,_)), pivot);
quick_sort(inout left);
quick_sort(inout right);
res ::= #ARRAY{T};
res := res.append(left, |pivot|, right);
a := res;
end;
end;</lang>
<lang sather>class MAIN is
main is
a:ARRAY{INT} := |10, 9, 8, 7, 6, -10, 5, 4, 656, -11|;
b ::= a.copy;
SORT{INT}::quick_sort(inout a);
#OUT + a + "\n" + b.sort + "\n";
end;
end;</lang>
The ARRAY class has a builtin sorting method, which is quicksort (but under certain condition an insertion sort is used instead), exactly quicksort_range; this implementation is original.
Scala
What follows is a progression on genericity here.
First, a quick sort of a list of integers:
<lang scala> def sort(xs: List[Int]): List[Int] = xs match {
case Nil => Nil
case head :: tail =>
val (less, notLess) = tail.partition(_ < head) // Arbitrarily partition list in two
sort(less) ++ (head :: sort(notLess)) // Sort each half
}</lang>
Next, a quick sort of a list of some type T, given a lessThan function:
<lang scala> def sort[T](xs: List[T], lessThan: (T, T) => Boolean): List[T] = xs match {
case Nil => Nil
case x :: xx =>
val (lo, hi) = xx.partition(lessThan(_, x))
sort(lo, lessThan) ++ (x :: sort(hi, lessThan))
}</lang>
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]:
<lang scala> def sort[T](xs: List[T])(implicit ord: Ordering[T]): List[T] = xs match {
case Nil => Nil
case x :: xx =>
val (lo, hi) = xx.partition(ord.lt(_, x))
sort[T](lo) ++ (x :: sort[T](hi))
}</lang>
That last one could have worked with Ordering, but Ordering is Java, and doesn't have the less than operator. Ordered is Scala-specific, and provides it.
<lang scala> def sort[T <: Ordered[T]](xs: List[T]): List[T] = xs match {
case Nil => Nil
case x :: xx =>
val (lo, hi) = xx.partition(_ < x)
sort(lo) ++ (x :: sort(hi))
}</lang>
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:
<lang scala> def sort[T, C[T] <: scala.collection.TraversableLike[T, C[T]]]
(xs: C[T])
(implicit ord: scala.math.Ordering[T],
cbf: scala.collection.generic.CanBuildFrom[C[T], T, C[T]]): C[T] = {
// Some collection types can't pattern match
if (xs.isEmpty) {
xs
} else {
val (lo, hi) = xs.tail.partition(ord.lt(_, xs.head))
val b = cbf()
b.sizeHint(xs.size)
b ++= sort(lo)
b += xs.head
b ++= sort(hi)
b.result()
}
}</lang>
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
<lang scheme>(define (split-by l p k)
(let loop ((low '())
(high '())
(l l))
(cond ((null? l)
(k low high))
((p (car l))
(loop low (cons (car l) high) (cdr l)))
(else
(loop (cons (car l) low) high (cdr l))))))
(define (quicksort l gt?)
(if (null? l)
'()
(split-by (cdr l)
(lambda (x) (gt? x (car l)))
(lambda (low high)
(append (quicksort low gt?)
(list (car l))
(quicksort high gt?))))))
(quicksort '(1 3 5 7 9 8 6 4 2) >)</lang>
With srfi-1: <lang scheme>(define (quicksort l gt?)
(if (null? l)
'()
(append (quicksort (filter (lambda (x) (gt? (car l) x)) (cdr l)) gt?)
(list (car l))
(quicksort (filter (lambda (x) (not (gt? (car l) x))) (cdr l)) gt?))))
(quicksort '(1 3 5 7 9 8 6 4 2) >) </lang>
Seed7
<lang seed7>const proc: quickSort (inout array elemType: arr, in integer: left, in integer: right) is func
local
var elemType: compare_elem is elemType.value;
var integer: less_idx is 0;
var integer: greater_idx is 0;
var elemType: help is elemType.value;
begin
if right > left then
compare_elem := arr[right];
less_idx := pred(left);
greater_idx := right;
repeat
repeat
incr(less_idx);
until arr[less_idx] >= compare_elem;
repeat
decr(greater_idx);
until arr[greater_idx] <= compare_elem or greater_idx = left;
if less_idx < greater_idx then
help := arr[less_idx];
arr[less_idx] := arr[greater_idx];
arr[greater_idx] := help;
end if;
until less_idx >= greater_idx;
arr[right] := arr[less_idx];
arr[less_idx] := compare_elem;
quickSort(arr, left, pred(less_idx));
quickSort(arr, succ(less_idx), right);
end if;
end func;
const proc: quickSort (inout array elemType: arr) is func
begin quickSort(arr, 1, length(arr)); end func;</lang>
Original source: [2]
SETL
In-place sort (looks much the same as the C version) <lang SETL>a := [2,5,8,7,0,9,1,3,6,4]; qsort(a); print(a);
proc qsort(rw a);
if #a > 1 then
pivot := a(#a div 2 + 1);
l := 1;
r := #a;
(while l < r)
(while a(l) < pivot) l +:= 1; end;
(while a(r) > pivot) r -:= 1; end;
swap(a(l), a(r));
end;
qsort(a(1..l-1));
qsort(a(r+1..#a));
end if;
end proc;
proc swap(rw x, rw y);
[y,x] := [x,y];
end proc;</lang>
Copying sort using comprehensions:
<lang SETL>a := [2,5,8,7,0,9,1,3,6,4]; print(qsort(a));
proc qsort(a);
if #a > 1 then
pivot := a(#a div 2 + 1);
a := qsort([x in a | x < pivot]) +
[x in a | x = pivot] +
qsort([x in a | x > pivot]);
end if;
return a;
end proc;</lang>
Sidef
<lang ruby>func quicksort (a) {
a.len < 2 && return(a);
var p = a.pop_rand; # to avoid the worst cases
__FUNC__(a.grep{ .< p}) + [p] + __FUNC__(a.grep{ .>= p});
}</lang>
Simula
<lang 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; </lang>
Standard ML
<lang sml>fun quicksort [] = []
| quicksort (x::xs) =
let
val (left, right) = List.partition (fn y => y<x) xs
in
quicksort left @ [x] @ quicksort right
end
</lang>
Solution 2:
Without using List.partition <lang sml> 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;</lang>
Swift
<lang swift>func quicksort<T where T : Comparable>(inout elements: [T], range: Range<Int>) {
if (range.endIndex - range.startIndex > 1) {
let pivotIndex = partition(&elements, range)
quicksort(&elements, range.startIndex ..< pivotIndex)
quicksort(&elements, pivotIndex+1 ..< range.endIndex)
}
}
func quicksort<T where T : Comparable>(inout elements: [T]) {
quicksort(&elements, indices(elements))
}</lang>
Tailspin
Simple recursive quicksort: <lang tailspin> templates quicksort
@: [];
$ -> #
<[](2..)>
def pivot: $(1);
[ [ $(2..last)... -> \(
<..$pivot>
$ !
<>
..|@quicksort: $;
\)] -> quicksort..., $pivot, $@ -> quicksort... ] !
<>
$ !
end quicksort
[4,5,3,8,1,2,6,7,9,8,5] -> quicksort -> !OUT::write </lang>
In place: <lang tailspin> templates quicksort
templates partial def first: $(1); def last: $(2); def pivot: $@quicksort($first); [ $(1) + 1, $(2) ] -> #
<?($(2) <..~$(1)>)>
def limit: $(2);
@quicksort($first): $@quicksort($limit);
@quicksort($limit): $pivot;
[ $first, $limit - 1 ] !
[ $limit + 1, $last ] !
<?($@quicksort($(2)) <$pivot~..>)>
[ $(1), $(2) - 1] -> #
<?($@quicksort($(1)) <..$pivot>)>
[ $(1) + 1, $(2)] -> #
<>
def temp: $@quicksort($(1));
@quicksort($(1)): $@quicksort($(2));
@quicksort($(2)): $temp;
[ $(1) + 1, $(2) - 1] -> #
end partial
@: $;
[1, $@::length] -> #
$@ !
<?($(1) <..~$(2)>)> $ -> partial -> #
end quicksort
[4,5,3,8,1,2,6,7,9,8,5] -> quicksort -> !OUT::write </lang>
Tcl
<lang tcl>package require Tcl 8.5
proc quicksort {m} {
if {[llength $m] <= 1} {
return $m
}
set pivot [lindex $m 0]
set less [set equal [set greater [list]]]
foreach x $m {
lappend [expr {$x < $pivot ? "less" : $x > $pivot ? "greater" : "equal"}] $x
}
return [concat [quicksort $less] $equal [quicksort $greater]]
}
puts [quicksort {8 6 4 2 1 3 5 7 9}] ;# => 1 2 3 4 5 6 7 8 9</lang>
TypeScript
<lang> /**
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);
}
} </lang>
uBasic/4tH
<lang>PRINT "Quick sort:"
n = FUNC (_InitArray) PROC _ShowArray (n) PROC _Quicksort (n) PROC _ShowArray (n)
END
_InnerQuick PARAM(2)
LOCAL(4)
IF b@ < 2 THEN RETURN f@ = a@ + b@ - 1 c@ = a@ e@ = f@ d@ = @((c@ + e@) / 2)
DO
DO WHILE @(c@) < d@
c@ = c@ + 1
LOOP
DO WHILE @(e@) > d@
e@ = e@ - 1
LOOP
IF c@ - 1 < e@ THEN
PROC _Swap (c@, e@)
c@ = c@ + 1
e@ = e@ - 1
ENDIF
UNTIL c@ > e@ LOOP
IF a@ < e@ THEN PROC _InnerQuick (a@, e@ - a@ + 1) IF c@ < f@ THEN PROC _InnerQuick (c@, f@ - c@ + 1)
RETURN
_Quicksort PARAM(1) ' Quick sort
PROC _InnerQuick (0, a@)
RETURN
_Swap PARAM(2) ' Swap two array elements
PUSH @(a@) @(a@) = @(b@) @(b@) = POP()
RETURN
_InitArray ' Init example array
PUSH 4, 65, 2, -31, 0, 99, 2, 83, 782, 1 FOR i = 0 TO 9 @(i) = POP() NEXT
RETURN (i)
_ShowArray PARAM (1) ' Show array subroutine
FOR i = 0 TO a@-1 PRINT @(i), NEXT PRINT
RETURN</lang>
UnixPipes
<lang bash>split() {
(while read n ; do
test $1 -gt $n && echo $n > $2 || echo $n > $3
done)
}
qsort() {
(read p; test -n "$p" && (
lc="1.$1" ; gc="2.$1"
split $p >(qsort $lc >$lc) >(qsort $gc >$gc);
cat $lc <(echo $p) $gc
rm -f $lc $gc;
))
}
cat to.sort | qsort</lang>
Ursala
The distributing bipartition operator, *|, is useful for this algorithm. The pivot is chosen as the greater of the first two items, this being the least sophisticated method sufficient to ensure termination. The quicksort function is a higher order function parameterized by the relational predicate p, which can be chosen appropriately for the type of items in the list being sorted. This example demonstrates sorting a list of natural numbers.
<lang Ursala>#import nat
quicksort "p" = ~&itB^?a\~&a ^|WrlT/~& "p"*|^\~& "p"?hthPX/~&th ~&h
- cast %nL
example = quicksort(nleq) <694,1377,367,506,3712,381,1704,1580,475,1872></lang>
- Output:
<367,381,475,506,694,1377,1580,1704,1872,3712>
V
<lang v>[qsort
[joinparts [p [*l1] [*l2] : [*l1 p *l2]] view]. [split_on_first uncons [>] split]. [small?] [] [split_on_first [l1 l2 : [l1 qsort l2 qsort joinparts]] view i] ifte].</lang>
The way of joy (using binrec) <lang v>[qsort
[small?] []
[uncons [>] split]
[[p [*l] [*g] : [*l p *g]] view]
binrec].</lang>
VBA
This is the "simple" quicksort, using temporary arrays. <lang vb>Public Sub Quick(a() As Variant, last As Integer) ' quicksort a Variant array (1-based, numbers or strings) Dim aLess() As Variant Dim aEq() As Variant Dim aGreater() As Variant Dim pivot As Variant Dim naLess As Integer Dim naEq As Integer Dim naGreater As Integer
If last > 1 Then
'choose pivot in the middle of the array
pivot = a(Int((last + 1) / 2))
'construct arrays
naLess = 0
naEq = 0
naGreater = 0
For Each el In a()
If el > pivot Then
naGreater = naGreater + 1
ReDim Preserve aGreater(1 To naGreater)
aGreater(naGreater) = el
ElseIf el < pivot Then
naLess = naLess + 1
ReDim Preserve aLess(1 To naLess)
aLess(naLess) = el
Else
naEq = naEq + 1
ReDim Preserve aEq(1 To naEq)
aEq(naEq) = el
End If
Next
'sort arrays "less" and "greater"
Quick aLess(), naLess
Quick aGreater(), naGreater
'concatenate
P = 1
For i = 1 To naLess
a(P) = aLess(i): P = P + 1
Next
For i = 1 To naEq
a(P) = aEq(i): P = P + 1
Next
For i = 1 To naGreater
a(P) = aGreater(i): P = P + 1
Next
End If End Sub
Public Sub QuicksortTest() Dim a(1 To 26) As Variant
'populate a with numbers in descending order, then sort
For i = 1 To 26: a(i) = 26 - i: Next
Quick a(), 26
For i = 1 To 26: Debug.Print a(i);: Next
Debug.Print
'now populate a with strings in descending order, then sort
For i = 1 To 26: a(i) = Chr$(Asc("z") + 1 - i) & "-stuff": Next
Quick a(), 26
For i = 1 To 26: Debug.Print a(i); " ";: Next
Debug.Print
End Sub</lang>
- Output:
quicksorttest 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 a-stuff b-stuff c-stuff d-stuff e-stuff f-stuff g-stuff h-stuff i-stuff j-stuff k-stuff l-stuff m-stuff n-stuff o-stuff p-stuff q-stuff r-stuff s-stuff t-stuff u-stuff v-stuff w-stuff x-stuff y-stuff z-stuff
Note: the "quicksort in place"
VBScript
<lang vb>Function quicksort(arr,s,n) l = s r = s + n - 1 p = arr(Int((l + r)/2)) Do Until l > r Do While arr(l) < p l = l + 1 Loop Do While arr(r) > p r = r -1 Loop If l <= r Then tmp = arr(l) arr(l) = arr(r) arr(r) = tmp l = l + 1 r = r - 1 End If Loop If s < r Then Call quicksort(arr,s,r-s+1) End If If l < t Then Call quicksort(arr,l,t-l+1) End If quicksort = arr End Function
myarray=Array(9,8,7,6,5,5,4,3,2,1,0,-1) m = quicksort(myarray,0,12) WScript.Echo Join(m,",")</lang>
- Output:
-1,0,1,2,3,4,5,5,6,7,8,9
Vlang
<lang vlang>fn partition(arr mut []int, low, 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(arr mut []int, low, 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()) }</lang>
- Output:
Input: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1] Output: [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]
Wart
<lang python>def (qsort (pivot ... ns))
(+ (qsort+keep (fn(_) (_ < pivot)) ns)
list.pivot
(qsort+keep (fn(_) (_ > pivot)) ns))
def (qsort x) :case x=nil
nil</lang>
XPL0
<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations string 0; \use zero-terminated strings
proc QSort(Array, Num); \Quicksort Array into ascending order char Array; \address of array to sort int Num; \number of elements in the array int I, J, Mid, Temp; [I:= 0; J:= Num-1; Mid:= Array(J>>1); while I <= J do
[while Array(I) < Mid do I:= I+1;
while Array(J) > Mid do J:= J-1;
if I <= J then
[Temp:= Array(I); Array(I):= Array(J); Array(J):= Temp;
I:= I+1;
J:= J-1;
];
];
if I < Num-1 then QSort(@Array(I), Num-I); if J > 0 then QSort(Array, J+1); ]; \QSort
func StrLen(Str); \Return number of characters in an ASCIIZ string char Str; int I; for I:= 0 to -1>>1-1 do
if Str(I) = 0 then return I;
char Str; [Str:= "Pack my box with five dozen liquor jugs."; QSort(Str, StrLen(Str), 1); Text(0, Str); CrLf(0); ]</lang>
- Output:
.Pabcdeefghiiijklmnoooqrstuuvwxyz
zkl
These are the Wikipedia algorithms.
Quick sort immutable sequence using crappy pivot choice: <lang zkl>fcn qtSort(list,cmp=Op("<")){ // sort immutable lists
fcn(list,cmp,N){ // spendy to keep recreating cmp
reg pivot=list[0], rest=list[1,*];
left,right:=rest.filter22(cmp,pivot);
N+=1;
T.extend(self.fcn(left,cmp,N),T(pivot),self.fcn(right,cmp,N));
}(list,cmp,0);
}</lang> In place quick sort: <lang zkl>fcn qiSort(list,cmp='<){ // in place quick sort
fcn(list,left,right,cmp){
if (left<right){
// partition list pivotIndex:=(left+right)/2; // or median of first,middle,last pivot:=list[pivotIndex]; list.swap(pivotIndex,right); // move pivot to end pivotIndex:=left; i:=left; do(right-left){ // foreach i in ([left..right-1]) if(cmp(list[i],pivot)){ // not cheap list.swap(i,pivotIndex); pivotIndex+=1; } i+=1; } list.swap(pivotIndex,right); // move pivot to final place
// sort the partitions
self.fcn(list,left,pivotIndex-1,cmp);
return(self.fcn(list,pivotIndex+1,right,cmp));
} }(list,0,list.len()-1,cmp); list;
}</lang>
- Programming Tasks
- Sorting Algorithms
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