Sorting algorithms/Heapsort: Difference between revisions
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Revision as of 21:37, 13 March 2021
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 Heapsort. 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) |
Heapsort is an in-place sorting algorithm with worst case and average complexity of O(n logn).
The basic idea is to turn the array into a binary heap structure, which has the property that it allows efficient retrieval and removal of the maximal element.
We repeatedly "remove" the maximal element from the heap, thus building the sorted list from back to front.
A heap sort requires random access, so can only be used on an array-like data structure.
Pseudocode:
function heapSort(a, count) is input: an unordered array a of length count (first place a in max-heap order) heapify(a, count) end := count - 1 while end > 0 do (swap the root(maximum value) of the heap with the last element of the heap) swap(a[end], a[0]) (decrement the size of the heap so that the previous max value will stay in its proper place) end := end - 1 (put the heap back in max-heap order) siftDown(a, 0, end)
function heapify(a,count) is (start is assigned the index in a of the last parent node) start := (count - 2) / 2 while start ≥ 0 do (sift down the node at index start to the proper place such that all nodes below the start index are in heap order) siftDown(a, start, count-1) start := start - 1 (after sifting down the root all nodes/elements are in heap order) function siftDown(a, start, end) is (end represents the limit of how far down the heap to sift) root := start while root * 2 + 1 ≤ end do (While the root has at least one child) child := root * 2 + 1 (root*2+1 points to the left child) (If the child has a sibling and the child's value is less than its sibling's...) if child + 1 ≤ end and a[child] < a[child + 1] then child := child + 1 (... then point to the right child instead) if a[root] < a[child] then (out of max-heap order) swap(a[root], a[child]) root := child (repeat to continue sifting down the child now) else return
Write a function to sort a collection of integers using heapsort.
360 Assembly
The program uses ASM structured macros and two ASSIST macros (XDECO, XPRNT) to keep the code as short as possible. <lang 360asm>* Heap sort 22/06/2016 HEAPS CSECT
USING HEAPS,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 "
L R1,N n
BAL R14,HEAPSORT call heapsort(n)
LA R3,PG pgi=0
LA R6,1 i=1
DO WHILE=(C,R6,LE,N) for i=1 to n
LR R1,R6 i
SLA R1,2 .
L R2,A-4(R1) a(i)
XDECO R2,XDEC edit a(i)
MVC 0(4,R3),XDEC+8 output a(i)
LA R3,4(R3) pgi=pgi+4
LA R6,1(R6) i=i+1
ENDDO , end for
XPRNT PG,80 print buffer
L R13,4(0,R13) epilog
LM R14,R12,12(R13) "
XR R15,R15 "
BR R14 exit
PG DC CL80' ' local data XDEC DS CL12 "
- ------- heapsort(icount)----------------------------------------------
HEAPSORT ST R14,SAVEHPSR save return addr
ST R1,ICOUNT icount
BAL R14,HEAPIFY call heapify(icount)
MVC IEND,ICOUNT iend=icount
DO WHILE=(CLC,IEND,GT,=F'1') while iend>1
L R1,IEND iend
LA R2,1 1
BAL R14,SWAP call swap(iend,1)
LA R1,1 1
L R2,IEND iend
BCTR R2,0 -1
ST R2,IEND iend=iend-1
BAL R14,SIFTDOWN call siftdown(1,iend)
ENDDO , end while
L R14,SAVEHPSR restore return addr
BR R14 return to caller
SAVEHPSR DS A local data ICOUNT DS F " IEND DS F "
- ------- heapify(count)------------------------------------------------
HEAPIFY ST R14,SAVEHPFY save return addr
ST R1,COUNT count
SRA R1,1 /2
ST R1,ISTART istart=count/2
DO WHILE=(C,R1,GE,=F'1') while istart>=1
L R1,ISTART istart
L R2,COUNT count
BAL R14,SIFTDOWN call siftdown(istart,count)
L R1,ISTART istart
BCTR R1,0 -1
ST R1,ISTART istart=istart-1
ENDDO , end while
L R14,SAVEHPFY restore return addr
BR R14 return to caller
SAVEHPFY DS A local data COUNT DS F " ISTART DS F "
- ------- siftdown(jstart,jend)-----------------------------------------
SIFTDOWN ST R14,SAVESFDW save return addr
ST R1,JSTART jstart
ST R2,JEND jend
ST R1,ROOT root=jstart
LR R3,R1 root
SLA R3,1 root*2
DO WHILE=(C,R3,LE,JEND) while root*2<=jend
ST R3,CHILD child=root*2
MVC SW,ROOT sw=root
L R1,SW sw
SLA R1,2 .
L R2,A-4(R1) a(sw)
L R1,CHILD child
SLA R1,2 .
L R3,A-4(R1) a(child)
IF CR,R2,LT,R3 THEN if a(sw)<a(child) then
MVC SW,CHILD sw=child
ENDIF , end if
L R2,CHILD child
LA R2,1(R2) +1
L R1,SW sw
SLA R1,2 .
L R3,A-4(R1) a(sw)
L R1,CHILD child
LA R1,1(R1) +1
SLA R1,2 .
L R4,A-4(R1) a(child+1)
IF C,R2,LE,JEND,AND, if child+1<=jend and X
CR,R3,LT,R4 THEN a(sw)<a(child+1) then
L R2,CHILD child
LA R2,1(R2) +1
ST R2,SW sw=child+1
ENDIF , end if
IF CLC,SW,NE,ROOT THEN if sw^=root then
L R1,ROOT root
L R2,SW sw
BAL R14,SWAP call swap(root,sw)
MVC ROOT,SW root=sw
ELSE , else
B RETSFDW return
ENDIF , end if
L R3,ROOT root
SLA R3,1 root*2
ENDDO , end while
RETSFDW L R14,SAVESFDW restore return addr
BR R14 return to caller
SAVESFDW DS A local data JSTART DS F " ROOT DS F " JEND DS F " CHILD DS F " SW DS F "
- ------- swap(x,y)-----------------------------------------------------
SWAP SLA R1,2 x
LA R1,A-4(R1) @a(x)
SLA R2,2 y
LA R2,A-4(R2) @a(y)
L R3,0(R1) temp=a(x)
MVC 0(4,R1),0(R2) a(x)=a(y)
ST R3,0(R2) a(y)=temp
BR R14 return to caller
- ------- ------ -------------------------------------------------------
A DC F'4',F'65',F'2',F'-31',F'0',F'99',F'2',F'83',F'782',F'1'
DC F'45',F'82',F'69',F'82',F'104',F'58',F'88',F'112',F'89',F'74'
N DC A((N-A)/L'A) number of items
YREGS
END HEAPS</lang>
- Output:
-31 0 1 2 2 4 45 58 65 69 74 82 82 83 88 89 99 104 112 782
AArch64 Assembly
<lang AArch64 Assembly> /* ARM assembly AARCH64 Raspberry PI 3B */ /* program heapSort64.s */ /* look Pseudocode begin this task */
/*******************************************/ /* Constantes file */ /*******************************************/ /* for this file see task include a file in language AArch64 assembly */ .include "../includeConstantesARM64.inc"
/*********************************/ /* Initialized data */ /*********************************/ .data szMessSortOk: .asciz "Table sorted.\n" szMessSortNok: .asciz "Table not sorted !!!!!.\n" sMessResult: .asciz "Value : @ \n" szCarriageReturn: .asciz "\n"
.align 4 //TableNumber: .quad 1,3,6,2,5,9,10,8,4,7 TableNumber: .quad 10,9,8,7,6,-5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 8
/*********************************/ /* UnInitialized data */ /*********************************/ .bss sZoneConv: .skip 24 /*********************************/ /* code section */ /*********************************/ .text .global main main: // entry of program
1:
ldr x0,qAdrTableNumber // address number table mov x1,#NBELEMENTS // number of élements bl heapSort ldr x0,qAdrTableNumber // address number table bl displayTable ldr x0,qAdrTableNumber // address number table mov x1,#NBELEMENTS // number of élements bl isSorted // control sort cmp x0,#1 // sorted ? beq 2f ldr x0,qAdrszMessSortNok // no !! error sort bl affichageMess b 100f
2: // yes
ldr x0,qAdrszMessSortOk bl affichageMess
100: // standard end of the program
mov x0, #0 // return code mov x8, #EXIT // request to exit program svc #0 // perform the system call
qAdrszCarriageReturn: .quad szCarriageReturn qAdrsMessResult: .quad sMessResult qAdrTableNumber: .quad TableNumber qAdrszMessSortOk: .quad szMessSortOk qAdrszMessSortNok: .quad szMessSortNok /******************************************************************/ /* control sorted table */ /******************************************************************/ /* x0 contains the address of table */ /* x1 contains the number of elements > 0 */ /* x0 return 0 if not sorted 1 if sorted */ isSorted:
stp x2,lr,[sp,-16]! // save registers stp x3,x4,[sp,-16]! // save registers mov x2,#0 ldr x4,[x0,x2,lsl 3]
1:
add x2,x2,1 cmp x2,x1 bge 99f ldr x3,[x0,x2, lsl 3] cmp x3,x4 blt 98f mov x4,x3 b 1b
98:
mov x0,0 // not sorted b 100f
99:
mov x0,1 // sorted
100:
ldp x3,x4,[sp],16 // restaur 2 registers ldp x2,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* heap sort */ /******************************************************************/ /* x0 contains the address of table */ /* x1 contains the number of element */ heapSort:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers bl heapify // first place table in max-heap order sub x3,x1,1
1:
cmp x3,0 ble 100f mov x1,0 // swap the root(maximum value) of the heap with the last element of the heap) mov x2,x3 bl swapElement sub x3,x3,1 mov x1,0 mov x2,x3 // put the heap back in max-heap order bl siftDown b 1b
100:
ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* place table in max-heap order */ /******************************************************************/ /* x0 contains the address of table */ /* x1 contains the number of element */ heapify:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers str x4,[sp,-16]! // save registers mov x4,x1 sub x3,x1,2 lsr x3,x3,1
1:
cmp x3,0 blt 100f mov x1,x3 sub x2,x4,1 bl siftDown sub x3,x3,1 b 1b
100:
ldr x4,[sp],16 // restaur 1 registers ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* swap two elements of table */ /******************************************************************/ /* x0 contains the address of table */ /* x1 contains the first index */ /* x2 contains the second index */ swapElement:
stp x2,lr,[sp,-16]! // save registers stp x3,x4,[sp,-16]! // save registers ldr x3,[x0,x1,lsl #3] // swap number on the table ldr x4,[x0,x2,lsl #3] str x4,[x0,x1,lsl #3] str x3,[x0,x2,lsl #3]
100:
ldp x3,x4,[sp],16 // restaur 2 registers ldp x2,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* put the heap back in max-heap order */ /******************************************************************/ /* x0 contains the address of table */ /* x1 contains the first index */ /* x2 contains the last index */ siftDown:
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
// x1 = root = start
mov x3,x2 // save last index
1:
lsl x4,x1,1 add x4,x4,1 cmp x4,x3 bgt 100f add x5,x4,1 cmp x5,x3 bgt 2f ldr x6,[x0,x4,lsl 3] // compare elements on the table ldr x7,[x0,x5,lsl 3] cmp x6,x7 csel x4,x5,x4,lt //movlt x4,x5
2:
ldr x7,[x0,x4,lsl 3] // compare elements on the table ldr x6,[x0,x1,lsl 3] // root cmp x6,x7 bge 100f mov x2,x4 // and x1 is root bl swapElement mov x1,x4 // root = child b 1b
100:
ldp x6,x7,[sp],16 // restaur 2 registers ldp x4,x5,[sp],16 // restaur 2 registers ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* Display table elements */ /******************************************************************/ /* x0 contains the address of table */ displayTable:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers mov x2,x0 // table address mov x3,0
1: // loop display table
ldr x0,[x2,x3,lsl 3] ldr x1,qAdrsZoneConv bl conversion10S // décimal conversion ldr x0,qAdrsMessResult ldr x1,qAdrsZoneConv bl strInsertAtCharInc // insert result at @ character bl affichageMess // display message add x3,x3,1 cmp x3,NBELEMENTS - 1 ble 1b ldr x0,qAdrszCarriageReturn bl affichageMess mov x0,x2
100:
ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
qAdrsZoneConv: .quad sZoneConv /********************************************************/ /* File Include fonctions */ /********************************************************/ /* for this file see task include a file in language AArch64 assembly */ .include "../includeARM64.inc" </lang>
ActionScript
<lang ActionScript>function heapSort(data:Vector.<int>):Vector.<int> { for (var start:int = (data.length-2)/2; start >= 0; start--) { siftDown(data, start, data.length); } for (var end:int = data.length - 1; end > 0; end--) { var tmp:int=data[0]; data[0]=data[end]; data[end]=tmp; siftDown(data, 0, end); } return data; } function siftDown(data:Vector.<int>, start:int, end:int):void { var heapRoot:int=start; while (heapRoot * 2+1 < end) { var child:int=heapRoot*2+1; if (child+1<end&&data[child]<data[child+1]) { child++; } if (data[heapRoot]<data[child]) { var tmp:int=data[heapRoot]; data[heapRoot]=data[child]; data[child]=tmp; heapRoot=child; } else { return; } } }</lang>
Ada
This implementation is a generic heapsort for unconstrained arrays. <lang Ada>generic
type Element_Type is private; type Index_Type is (<>); type Collection is array(Index_Type range <>) of Element_Type; with function "<" (Left, right : element_type) return boolean is <>;
procedure Generic_Heapsort(Item : in out Collection);</lang> <lang Ada>procedure Generic_Heapsort(Item : in out Collection) is
procedure Swap(Left : in out Element_Type; Right : in out Element_Type) is
Temp : Element_Type := Left;
begin
Left := Right;
Right := Temp;
end Swap;
procedure Sift_Down(Item : in out Collection) is
Root : Integer := Index_Type'Pos(Item'First);
Child : Integer := Index_Type'Pos(Item'Last);
Last : Integer := Index_Type'Pos(Item'Last);
begin
while Root * 2 + 1 <= Last loop
Child := Root * 2 + 1;
if Child + 1 <= Last and then Item(index_Type'Val(Child)) < Item(Index_Type'Val(Child + 1)) then
Child := Child + 1;
end if;
if Item(Index_Type'Val(Root)) < Item(Index_Type'Val(Child)) then
Swap(Item(Index_Type'Val(Root)), Item(Index_Type'Val(Child)));
Root := Child;
else
exit;
end if;
end loop;
end Sift_Down;
procedure Heapify(Item : in out Collection) is
First_Pos : Integer := Index_Type'Pos(Index_Type'First);
Last_Pos : Integer := Index_Type'Pos(Index_type'Last);
Start : Index_type := Index_Type'Val((Last_Pos - First_Pos + 1) / 2);
begin
loop
Sift_Down(Item(Start..Item'Last));
if Start > Index_Type'First then
Start := Index_Type'Pred(Start);
else
exit;
end if;
end loop;
end Heapify;
Last_Index : Index_Type := Index_Type'Last;
begin
Heapify(Item);
while Last_Index > Index_Type'First loop
Swap(Item(Last_Index), Item(Item'First));
Last_Index := Index_Type'Pred(Last_Index);
Sift_Down(Item(Item'First..Last_Index));
end loop;
end Generic_Heapsort;</lang> Demo code: <lang Ada>with Generic_Heapsort; with Ada.Text_Io; use Ada.Text_Io;
procedure Test_Generic_Heapsort is
type Days is (Sun, Mon, Tue, Wed, Thu, Fri, Sat); type Days_Col is array(Days range <>) of Natural; procedure Sort is new Generic_Heapsort(Natural, Days, Days_Col); Week : Days_Col := (5, 2, 7, 3, 4, 9, 1);
begin
for I in Week'range loop
Put(Days'Image(I) & ":" & Natural'Image(Week(I)) & " ");
end loop;
New_Line;
Sort(Week);
for I in Week'range loop
Put(Days'Image(I) & ":" & Natural'Image(Week(I))& " ");
end loop;
New_Line;
end Test_Generic_Heapsort;</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
);
- --- Heap sort Move Down ---#
PROC heapmove = (REF []INT array, INT i, INT last) VOID: (
INT index := i;
INT larger := (index*2);
WHILE larger <= last DO
IF larger < last THEN IF array[larger] < array[larger+1] THEN
larger +:= 1
FI FI;
IF array[index] < array[larger] THEN
swap(array, index, larger)
FI;
index := larger;
larger := (index*2)
OD
);
- --- Heap sort ---#
PROC heapsort = (REF []INT array) VOID: (
FOR i FROM ENTIER((UPB array) / 2) BY -1 WHILE
heapmove(array, i, UPB array);
i > 1 DO SKIP OD;
FOR i FROM UPB array BY -1 WHILE
swap(array, 1, i);
heapmove(array, 1, i-1);
i > 1 DO SKIP OD
);
main: (
[10]INT a;
FOR i FROM 1 TO UPB a DO
a[i] := ROUND(random*100)
OD;
print(("Before:", a));
print((newline, newline));
heapsort(a);
print(("After: ", a))
)</lang>
- Output:
Before: +633 +972 +136 +494 +720 +326 +813 +980 +784 +760
After: +136 +326 +494 +633 +720 +760 +784 +813 +972 +980
AppleScript
<lang applescript>-- In-place binary heap sort. -- Heap sort algorithm: J.W.J. Williams. on heapSort(theList, l, r) -- Sort items l thru r of theList.
script o
-- The list index of each heap node's first child is calculated as l + (n - l) * c + 1,
-- where l is the left index of the sort range (top of heap), n the node index, and c the number of children per node.
-- c is 2 in a binary heap, so we get (n * 2) - (l - 1). Preset the constant part here.
property const : l - 1
property lst : theList
on hsrt(l, r)
-- Arrange the sort range into a "heap" with its "top" at the leftmost position.
repeat with i from (l + r) div 2 to l by -1
siftDown(item i of my lst, i, r)
end repeat
-- Sort the heap.
repeat with endOfHeap from r to (l + 1) by -1
-- Remove the value at the end.
set removedValue to item endOfHeap of my lst
-- Move the highest value in the heap from the top to the vacated slot.
set item endOfHeap of my lst to item l of my lst
-- Sift the removed value back into the reduced heap from the top.
siftDown(removedValue, l, endOfHeap - 1)
end repeat
end hsrt
-- Sift a value down into the heap from a given root node.
on siftDown(siftValue, root, endOfHeap)
set child to root * 2 - const
repeat until (child comes after endOfHeap)
-- Determine the higher-valued child of this root (if more than one).
set childValue to item child of my lst
if (child comes before endOfHeap) then
set child2 to child + 1
set child2Value to item child2 of my lst
if (child2Value > childValue) then
set child to child2
set childValue to child2Value
end if
end if
-- If the higher child value's greater than the one being sifted down, advance it to this node
-- and prepare to repeat the above with the node from which it came. Otherwise stop sifting.
if (childValue > siftValue) then
set item root of my lst to childValue
set root to child
set child to root * 2 - const
else
exit repeat
end if
end repeat
-- Insert the sifted-down value at the node reached.
set item root of my lst to siftValue
end siftDown
end script
set listLen to (count theList)
if (listLen > 1) then
-- Convert negative and/or transposed range indices.
if (l < 0) then set l to listLen + l + 1
if (r < 0) then set r to listLen + r + 1
if (l > r) then set {l, r} to {r, l}
-- Do the sort.
o's hsrt(l, r)
end if
return -- nothing
end heapSort
set aList to {} repeat with i from 1 to 25
set end of aList to (random number 100)
end repeat
-- Sort items 1 thru -1 of a copy. set sortedCopy to aList's items heapSort(sortedCopy, 1, -1)
set astid to AppleScript's text item delimiters set AppleScript's text item delimiters to ", " set output to "Original: {" & aList & "} Sorted: {" & sortedCopy & "}" set AppleScript's text item delimiters to astid
return output</lang>
- Output:
"Original: {28, 39, 41, 27, 78, 13, 11, 88, 10, 63, 13, 24, 51, 84, 47, 22, 0, 75, 66, 93, 22, 54, 44, 22, 53}
Sorted: {0, 10, 11, 13, 13, 22, 22, 22, 24, 27, 28, 39, 41, 44, 47, 51, 53, 54, 63, 66, 75, 78, 84, 88, 93}"
ARM Assembly
<lang ARM Assembly>
/* ARM assembly Raspberry PI */ /* program heapSort.s */ /* look Pseudocode begin this task */
/************************************/ /* 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 1,3,6,2,5,9,10,8,4,7
- TableNumber: .int 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,#NBELEMENTS @ number of élements bl heapSort 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
/******************************************************************/ /* heap sort */ /******************************************************************/ /* r0 contains the address of table */ /* r1 contains the number of element */ heapSort:
push {r2,r3,r4,lr} @ save registers
bl heapify @ first place table in max-heap order
sub r3,r1,#1
1:
cmp r3,#0 ble 100f mov r1,#0 @ swap the root(maximum value) of the heap with the last element of the heap) mov r2,r3 bl swapElement sub r3,#1 mov r1,#0 mov r2,r3 @ put the heap back in max-heap order bl siftDown b 1b
100:
pop {r2,r3,r4,lr}
bx lr @ return
/******************************************************************/ /* place table in max-heap order */ /******************************************************************/ /* r0 contains the address of table */ /* r1 contains the number of element */ heapify:
push {r1,r2,r3,r4,lr} @ save registers
mov r4,r1
sub r3,r1,#2
lsr r3,#1
1:
cmp r3,#0 blt 100f mov r1,r3 sub r2,r4,#1 bl siftDown sub r3,#1 b 1b
100:
pop {r1,r2,r3,r4,lr}
bx lr @ return
/******************************************************************/ /* swap two elements of table */ /******************************************************************/ /* r0 contains the address of table */ /* r1 contains the first index */ /* r2 contains the second index */ swapElement:
push {r3,r4,lr} @ save registers
ldr r3,[r0,r1,lsl #2] @ swap number on the table
ldr r4,[r0,r2,lsl #2]
str r4,[r0,r1,lsl #2]
str r3,[r0,r2,lsl #2]
100:
pop {r3,r4,lr}
bx lr @ return
/******************************************************************/ /* put the heap back in max-heap order */ /******************************************************************/ /* r0 contains the address of table */ /* r1 contains the first index */ /* r2 contains the last index */ siftDown:
push {r1-r7,lr} @ save registers
@ r1 = root = start
mov r3,r2 @ save last index
1:
lsl r4,r1,#1 add r4,#1 cmp r4,r3 bgt 100f add r5,r4,#1 cmp r5,r3 bgt 2f ldr r6,[r0,r4,lsl #2] @ compare elements on the table ldr r7,[r0,r5,lsl #2] cmp r6,r7 movlt r4,r5
2:
ldr r7,[r0,r4,lsl #2] @ compare elements on the table ldr r6,[r0,r1,lsl #2] @ root cmp r6,r7 bge 100f mov r2,r4 @ and r1 is root bl swapElement mov r1,r4 @ root = child b 1b
100:
pop {r1-r7,lr}
bx lr @ return
/******************************************************************/ /* 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>
AutoHotkey
<lang AutoHotkey>heapSort(a) {
Local end
end := %a%0
heapify(a,end)
While end > 1
%a%%end% := (%a%1 "", %a%1 := %a%%end%)
,siftDown(a, 1, --end)
}
heapify(a, count) {
Local start
start := count // 2
While start
siftDown(a, start--, count)
}
siftDown(a, start, end) {
Local child, c1
While start*2 <= end {
c1 := 1 + child := start*2
If (c1 <= end && %a%%child% < %a%%c1%)
child := c1
If (%a%%start% < %a%%child%)
%a%%start% := (%a%%child% "", %a%%child% := %a%%start%)
,start := child
Else Return
}
}
a = 1,5,2,7,3,4,6,8,1 ; ----- test ----- StringSplit a, a, `, heapSort("a") ListVars MsgBox</lang>
BBC BASIC
<lang bbcbasic> DIM test(9)
test() = 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
PROCheapsort(test())
FOR i% = 0 TO 9
PRINT test(i%) ;
NEXT
PRINT
END
DEF PROCheapsort(a())
LOCAL e%
PROCheapify(a())
FOR e% = DIM(a(),1) TO 1 STEP -1
SWAP a(e%), a(0)
PROCsiftdown(a(), 0, e%-1)
NEXT
ENDPROC
DEF PROCheapify(a())
LOCAL s%, m%
m% = DIM(a(),1)
FOR s% = (m% - 1) / 2 TO 0 STEP -1
PROCsiftdown(a(), s%, m%)
NEXT
ENDPROC
DEF PROCsiftdown(a(), s%, e%)
LOCAL c%, r%
r% = s%
WHILE r% * 2 + 1 <= e%
c% = r% * 2 + 1
IF c% + 1 <= e% IF a(c%) < a(c% + 1) c% += 1
IF a(r%) < a(c%) SWAP a(r%), a(c%) : r% = c% ELSE ENDPROC
ENDWHILE
ENDPROC</lang>
- Output:
-31 0 1 2 2 4 65 83 99 782
BCPL
<lang BCPL>// This can be run using Cintcode BCPL freely available from www.cl.cam.ac.uk/users/mr10.
GET "libhdr.h"
LET heapify(v, k, i, last) BE { LET j = i+i // If there is a son (or two), j = subscript of first.
AND x = k // x will hold the larger of the sons if any.
IF j<=last DO x := v!j // j, x = subscript and key of first son.
IF j< last DO
{ LET y = v!(j+1) // y = key of the other son.
IF x<y DO x,j := y, j+1 // j, x = subscript and key of larger son.
}
IF k>=x DO
{ v!i := k // k is not lower than larger son if any.
RETURN
}
v!i := x
i := j
} REPEAT
AND heapsort(v, upb) BE { FOR i = upb/2 TO 1 BY -1 DO heapify(v, v!i, i, upb)
FOR i = upb TO 2 BY -1 DO
{ LET k = v!i
v!i := v!1
heapify(v, k, 1, i-1)
}
}
LET start() = VALOF {
LET v = VEC 1000
FOR i = 1 TO 1000 DO v!i := randno(1_000_000)
heapsort(v, 1000)
FOR i = 1 TO 1000 DO
{ IF i MOD 10 = 0 DO newline()
writef(" %i6", v!i)
}
newline()
}</lang>
C
<lang c>#include <stdio.h>
int max (int *a, int n, int i, int j, int k) {
int m = i;
if (j < n && a[j] > a[m]) {
m = j;
}
if (k < n && a[k] > a[m]) {
m = k;
}
return m;
}
void downheap (int *a, int n, int i) {
while (1) {
int j = max(a, n, i, 2 * i + 1, 2 * i + 2);
if (j == i) {
break;
}
int t = a[i];
a[i] = a[j];
a[j] = t;
i = j;
}
}
void heapsort (int *a, int n) {
int i;
for (i = (n - 2) / 2; i >= 0; i--) {
downheap(a, n, i);
}
for (i = 0; i < n; i++) {
int t = a[n - i - 1];
a[n - i - 1] = a[0];
a[0] = t;
downheap(a, n - i - 1, 0);
}
}
int main () {
int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
int n = sizeof a / sizeof a[0];
int i;
for (i = 0; i < n; i++)
printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
heapsort(a, n);
for (i = 0; i < n; i++)
printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
return 0;
} </lang>
C#
<lang csharp>using System; using System.Collections.Generic; using System.Text;
public class HeapSortClass {
public static void HeapSort<T>(T[] array)
{
HeapSort<T>(array, 0, array.Length, Comparer<T>.Default);
}
public static void HeapSort<T>(T[] array, int offset, int length, IComparer<T> comparer)
{
HeapSort<T>(array, offset, length, comparer.Compare);
}
public static void HeapSort<T>(T[] array, int offset, int length, Comparison<T> comparison)
{
// build binary heap from all items
for (int i = 0; i < length; i++)
{
int index = i;
T item = array[offset + i]; // use next item
// and move it on top, if greater than parent
while (index > 0 &&
comparison(array[offset + (index - 1) / 2], item) < 0)
{
int top = (index - 1) / 2;
array[offset + index] = array[offset + top];
index = top;
}
array[offset + index] = item;
}
for (int i = length - 1; i > 0; i--)
{
// delete max and place it as last
T last = array[offset + i];
array[offset + i] = array[offset];
int index = 0;
// the last one positioned in the heap
while (index * 2 + 1 < i)
{
int left = index * 2 + 1, right = left + 1;
if (right < i && comparison(array[offset + left], array[offset + right]) < 0)
{
if (comparison(last, array[offset + right]) > 0) break;
array[offset + index] = array[offset + right];
index = right;
}
else
{
if (comparison(last, array[offset + left]) > 0) break;
array[offset + index] = array[offset + left];
index = left;
}
}
array[offset + index] = last;
}
}
static void Main()
{
// usage
byte[] r = {5, 4, 1, 2};
HeapSort(r);
string[] s = { "-", "D", "a", "33" };
HeapSort(s, 0, s.Length, StringComparer.CurrentCultureIgnoreCase);
}
}</lang>
C++
Uses C++11. Compile with
g++ -std=c++11 heap.cpp
<lang cpp>#include <algorithm>
- include <iterator>
- include <iostream>
template<typename RandomAccessIterator> void heap_sort(RandomAccessIterator begin, RandomAccessIterator end) {
std::make_heap(begin, end); std::sort_heap(begin, end);
}
int main() {
int a[] = {100, 2, 56, 200, -52, 3, 99, 33, 177, -199};
heap_sort(std::begin(a), std::end(a));
copy(std::begin(a), std::end(a), std::ostream_iterator<int>(std::cout, " "));
std::cout << "\n";
}</lang>
- Output:
-199 -52 2 3 33 56 99 100 177 200
Uses C++11. Compile with
g++ -std=c++11
<lang cpp>
- include <iostream>
- include <vector>
using namespace std;
void shift_down(vector<int>& heap,int i, int max) {
int i_big, c1, c2;
while(i < max) {
i_big = i;
c1 = (2*i) + 1;
c2 = c1 + 1;
if( c1<max && heap[c1]>heap[i_big] )
i_big = c1;
if( c2<max && heap[c2]>heap[i_big] )
i_big = c2;
if(i_big == i) return;
swap(heap[i],heap[i_big]);
i = i_big;
}
}
void to_heap(vector<int>& arr) {
int i = (arr.size()/2) - 1;
while(i >= 0) {
shift_down(arr, i, arr.size());
--i;
}
}
void heap_sort(vector<int>& arr) {
to_heap(arr);
int end = arr.size() - 1;
while (end > 0) {
swap(arr[0], arr[end]);
shift_down(arr, 0, end);
--end;
}
}
int main() {
vector<int> data = {
12, 11, 15, 10, 9, 1, 2,
3, 13, 14, 4, 5, 6, 7, 8
};
heap_sort(data);
for(int i : data) cout << i << " ";
}</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Clojure
<lang lisp>(defn- swap [a i j]
(assoc a i (nth a j) j (nth a i)))
(defn- sift [a pred k l]
(loop [a a x k y (inc (* 2 k))]
(if (< (inc (* 2 x)) l)
(let [ch (if (and (< y (dec l)) (pred (nth a y) (nth a (inc y))))
(inc y)
y)]
(if (pred (nth a x) (nth a ch))
(recur (swap a x ch) ch (inc (* 2 ch)))
a))
a)))
(defn- heapify[pred a len]
(reduce (fn [c term] (sift (swap c term 0) pred 0 term))
(reduce (fn [c i] (sift c pred i len))
(vec a)
(range (dec (int (/ len 2))) -1 -1))
(range (dec len) 0 -1)))
(defn heap-sort
([a pred]
(let [len (count a)]
(heapify pred a len)))
([a]
(heap-sort a <)))
</lang> Example usage: <lang lisp>user> (heapsort [1 2 4 6 2 3 6]) [1 2 2 3 4 6 6] user> (heapsort [1 2 4 6 2 3 6] >) [6 6 4 3 2 2 1] user> (heapsort (list 1 2 4 6 2 3 6)) [1 2 2 3 4 6 6]</lang>
COBOL
<lang cobol> >>SOURCE FORMAT FREE
- > This code is dedicated to the public domain
- > This is GNUCOBOL 2.0
identification division. program-id. heapsort. environment division. configuration section. repository. function all intrinsic. data division. working-storage section. 01 filler.
03 a pic 99. 03 a-start pic 99. 03 a-end pic 99. 03 a-parent pic 99. 03 a-child pic 99. 03 a-sibling pic 99. 03 a-lim pic 99 value 10. 03 array-swap pic 99. 03 array occurs 10 pic 99.
procedure division. start-heapsort.
*> fill the array
compute a = random(seconds-past-midnight)
perform varying a from 1 by 1 until a > a-lim
compute array(a) = random() * 100
end-perform
perform display-array display space 'initial array'
*>heapify the array move a-lim to a-end compute a-start = (a-lim + 1) / 2 perform sift-down varying a-start from a-start by -1 until a-start = 0
perform display-array display space 'heapified'
*> sort the array
move 1 to a-start
move a-lim to a-end
perform until a-end = a-start
move array(a-end) to array-swap
move array(a-start) to array(a-end)
move array-swap to array(a-start)
subtract 1 from a-end
perform sift-down
end-perform
perform display-array display space 'sorted'
stop run .
sift-down.
move a-start to a-parent
perform until a-parent * 2 > a-end
compute a-child = a-parent * 2
compute a-sibling = a-child + 1
if a-sibling <= a-end and array(a-child) < array(a-sibling)
*> take the greater of the two
move a-sibling to a-child
end-if
if a-child <= a-end and array(a-parent) < array(a-child)
*> the child is greater than the parent
move array(a-child) to array-swap
move array(a-parent) to array(a-child)
move array-swap to array(a-parent)
end-if
*> continue down the tree
move a-child to a-parent
end-perform
.
display-array.
perform varying a from 1 by 1 until a > a-lim
display space array(a) with no advancing
end-perform
.
end program heapsort.</lang>
- Output:
prompt$ cobc -xj heapsort.cob 20 26 47 88 97 39 07 77 35 98 initial array 98 97 47 88 26 39 07 77 35 20 heapified 07 20 26 35 39 47 77 88 97 98 sorted
CoffeeScript
<lang coffeescript># Do an in-place heap sort. heap_sort = (arr) ->
put_array_in_heap_order(arr) end = arr.length - 1 while end > 0 [arr[0], arr[end]] = [arr[end], arr[0]] sift_element_down_heap arr, 0, end end -= 1
put_array_in_heap_order = (arr) ->
i = arr.length / 2 - 1 i = Math.floor i while i >= 0 sift_element_down_heap arr, i, arr.length i -= 1
sift_element_down_heap = (heap, i, max) ->
while i < max
i_big = i
c1 = 2*i + 1
c2 = c1 + 1
if c1 < max and heap[c1] > heap[i_big]
i_big = c1
if c2 < max and heap[c2] > heap[i_big]
i_big = c2
return if i_big is i
[heap[i], heap[i_big]] = [heap[i_big], heap[i]]
i = i_big
do ->
arr = [12, 11, 15, 10, 9, 1, 2, 3, 13, 14, 4, 5, 6, 7, 8] heap_sort arr console.log arr</lang>
- Output:
> coffee heap.coffee [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
Common Lisp
<lang lisp>(defun make-heap (&optional (length 7))
(make-array length :adjustable t :fill-pointer 0))
(defun left-index (index)
(1- (* 2 (1+ index))))
(defun right-index (index)
(* 2 (1+ index)))
(defun parent-index (index)
(floor (1- index) 2))
(defun percolate-up (heap index predicate)
(if (zerop index) heap
(do* ((element (aref heap index))
(index index pindex)
(pindex (parent-index index)
(parent-index index)))
((zerop index) heap)
(if (funcall predicate element (aref heap pindex))
(rotatef (aref heap index) (aref heap pindex))
(return-from percolate-up heap)))))
(defun heap-insert (heap element predicate)
(let ((index (vector-push-extend element heap 2))) (percolate-up heap index predicate)))
(defun percolate-down (heap index predicate)
(let ((length (length heap))
(element (aref heap index)))
(flet ((maybe-element (index)
"return the element at index or nil, and a boolean
indicating whether there was an element."
(if (< index length)
(values (aref heap index) t)
(values nil nil))))
(do ((index index swap-index)
(lindex (left-index index) (left-index index))
(rindex (right-index index) (right-index index))
(swap-index nil) (swap-child nil))
(nil)
;; Extact the left child if there is one. If there is not,
;; return the heap. Set the left child as the swap-child.
(multiple-value-bind (lchild lp) (maybe-element lindex)
(if (not lp) (return-from percolate-down heap)
(setf swap-child lchild
swap-index lindex))
;; Extract the right child, if any, and when better than the
;; current swap-child, update the swap-child.
(multiple-value-bind (rchild rp) (maybe-element rindex)
(when (and rp (funcall predicate rchild lchild))
(setf swap-child rchild
swap-index rindex))
;; If the swap-child is better than element, rotate them,
;; and continue percolating down, else return heap.
(if (not (funcall predicate swap-child element))
(return-from percolate-down heap)
(rotatef (aref heap index) (aref heap swap-index)))))))))
(defun heap-empty-p (heap)
(eql (length heap) 0))
(defun heap-delete-min (heap predicate)
(assert (not (heap-empty-p heap)) () "Can't pop from empty heap.")
(prog1 (aref heap 0)
(setf (aref heap 0) (vector-pop heap))
(unless (heap-empty-p heap)
(percolate-down heap 0 predicate))))
(defun heapsort (sequence predicate)
(let ((h (make-heap (length sequence)))) (map nil #'(lambda (e) (heap-insert h e predicate)) sequence) (map-into sequence #'(lambda () (heap-delete-min h predicate)))))</lang>
Example usage:
(heapsort (vector 1 9 2 8 3 7 4 6 5) '<) ; #(1 2 3 4 5 6 7 8 9) (heapsort (list 9 8 1 2 7 6 3 4 5) '<) ; (1 2 3 4 5 6 7 8 9)
D
<lang d>import std.stdio, std.container;
void heapSort(T)(T[] data) /*pure nothrow @safe @nogc*/ {
for (auto h = data.heapify; !h.empty; h.removeFront) {}
}
void main() {
auto items = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]; items.heapSort; items.writeln;
}</lang>
A lower level implementation: <lang d>import std.stdio, std.algorithm;
void heapSort(R)(R seq) pure nothrow @safe @nogc {
static void siftDown(R seq, in size_t start,
in size_t end) pure nothrow @safe @nogc {
for (size_t root = start; root * 2 + 1 <= end; ) {
auto child = root * 2 + 1;
if (child + 1 <= end && seq[child] < seq[child + 1])
child++;
if (seq[root] < seq[child]) {
swap(seq[root], seq[child]);
root = child;
} else
break;
}
}
if (seq.length > 1)
foreach_reverse (immutable start; 1 .. (seq.length - 2) / 2 + 2)
siftDown(seq, start - 1, seq.length - 1);
foreach_reverse (immutable end; 1 .. seq.length) {
swap(seq[end], seq[0]);
siftDown(seq, 0, end - 1);
}
}
void main() {
auto data = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]; data.heapSort; data.writeln;
}</lang>
Dart
<lang dart> void heapSort(List a) {
int count = a.length;
// first place 'a' in max-heap order
heapify(a, count);
int end = count - 1;
while (end > 0) {
// swap the root (maximum value) of the heap with the
// last element of the heap
int tmp = a[end];
a[end] = a[0];
a[0] = tmp;
// put the heap back in max-heap order
siftDown(a, 0, end - 1);
// decrement the size of the heap so that the previous
// max value will stay in its proper place
end--;
}
}
void heapify(List a, int count) {
// start is assigned the index in 'a' of the last parent node
int start = ((count - 2)/2).toInt(); // binary heap
while (start >= 0) {
// sift down the node at index 'start' to the proper place
// such that all nodes below the 'start' index are in heap
// order
siftDown(a, start, count - 1);
start--;
}
}
void siftDown(List a, int start, int end) {
// end represents the limit of how far down the heap to shift
int root = start;
while ((root*2 + 1) <= end) { // While the root has at least one child
int child = root*2 + 1; // root*2+1 points to the left child
// if the child has a sibling and the child's value is less than its sibling's...
if (child + 1 <= end && a[child] < a[child + 1]) {
child = child+1; // .. then point to the right child instead
}
if (a[root] < a[child]) { // out of max-heap order
int tmp = a[root];
a[root] = a[child];
a[child] = tmp;
root = child; // repeat to continue shifting down the child now
} else {
return;
}
}
}
void main() {
var arr=[1,5,2,7,3,9,4,6,8];
print("Before sort");
arr.forEach((var i)=>print("$i"));
heapSort(arr);
print("After sort");
arr.forEach((var i)=>print("$i"));
}
</lang>
Delphi
See Pascal.
E
<lang e>def heapsort := {
def cswap(c, a, b) {
def t := c[a]
c[a] := c[b]
c[b] := t
# println(c)
}
def siftDown(array, start, finish) {
var root := start
while (var child := root * 2 + 1
child <= finish) {
if (child + 1 <= finish && array[child] < array[child + 1]) {
child += 1
}
if (array[root] < array[child]) {
cswap(array, root, child)
root := child
} else {
break
}
}
}
/** Heapsort (in-place). */
def heapsort(array) {
# in pseudo-code, heapify only called once, so inline it here
for start in (0..((array.size()-2)//2)).descending() {
siftDown(array, start, array.size()-1)
}
for finish in (0..(array.size()-1)).descending() {
cswap(array, 0, finish)
siftDown(array, 0, finish - 1)
}
}
}</lang>
EasyLang
<lang>subr make_heap
for i = 1 to n - 1
if data[i] > data[(i - 1) / 2]
j = i
while data[j] > data[(j - 1) / 2]
swap data[j] data[(j - 1) / 2]
j = (j - 1) / 2
.
.
.
. subr sort
n = len data[]
call make_heap
for i = n - 1 downto 1
swap data[0] data[i]
j = 0
ind = 1
while ind < i
if ind + 1 < i and data[ind + 1] > data[ind]
ind += 1
.
if data[j] < data[ind]
swap data[j] data[ind]
.
j = ind
ind = 2 * j + 1
.
.
. data[] = [ 29 4 72 44 55 26 27 77 92 5 ] call sort print data[]</lang>
EchoLisp
We use the heap library and the heap-pop primitive to implement heap-sort. <lang scheme> (lib 'heap)
(define (heap-sort list)
(define heap (make-heap < )) ;; make a min heap
(list->heap list heap)
(while (not (heap-empty? heap))
(push 'stack (heap-pop heap)))
(stack->list 'stack))
(define L (shuffle (iota 15)))
→ (9 4 0 12 8 3 10 7 11 2 5 6 14 13 1)
(heap-sort L)
→ (0 1 2 3 4 5 6 7 8 9 10 11 12 13 14)
</lang>
Eiffel
<lang Eiffel> class HEAPSORT
feature
sort_array (ar: ARRAY [INTEGER]) -- Sorts array 'ar' in ascending order. require not_empty: ar.count > 0 local i, j, r, l, m, n: INTEGER sorted: BOOLEAN do n := ar.count j := 0 i := 0 m := 0 r := n l := (n // 2)+1 from until sorted loop if l > 1 then l := l - 1 m := ar[l] else m := ar[r] ar[r] := ar[1] r := r - 1 if r = 1 then ar[1]:=m sorted := True end end if not sorted then i := l j := l * 2 from until j > r loop if (j < r) and (ar[j] < ar[j + 1]) then j := j + 1 end if m < ar[j] then ar[i]:= ar[j] i := j j := j + i else j := r + 1 end end ar[i]:= m end end ensure sorted: is_sorted(ar) end
feature{NONE}
is_sorted (ar: ARRAY [INTEGER]): BOOLEAN --- Is 'ar' sorted in ascending order? local i: INTEGER do Result := True from i := ar.lower until i >= ar.upper loop if ar [i] > ar [i + 1] then Result := False end i := i + 1 end end
end </lang> Test: <lang Eiffel> class APPLICATION
create make
feature
make local test: ARRAY [INTEGER] do create test.make_empty test := <<5, 91, 13, 99,7, 35>> io.put_string ("Unsorted: ") across test as t loop io.put_string (t.item.out + " ") end io.new_line create heap_sort heap_sort.sort_array (test) io.put_string ("Sorted: ") across test as t loop io.put_string (t.item.out + " ") end end
heap_sort: HEAPSORT
end </lang>
- Output:
Unsorted: 5 91 13 99 7 35 Sorted: 5 7 13 35 91 99
Elixir
<lang elixir>defmodule Sort do
def heapSort(list) do
len = length(list)
heapify(List.to_tuple(list), div(len - 2, 2))
|> heapSort(len-1)
|> Tuple.to_list
end
defp heapSort(a, finish) when finish > 0 do
swap(a, 0, finish)
|> siftDown(0, finish-1)
|> heapSort(finish-1)
end
defp heapSort(a, _), do: a
defp heapify(a, start) when start >= 0 do
siftDown(a, start, tuple_size(a)-1)
|> heapify(start-1)
end
defp heapify(a, _), do: a
defp siftDown(a, root, finish) when root * 2 + 1 <= finish do
child = root * 2 + 1
if child + 1 <= finish and elem(a,child) < elem(a,child + 1), do: child = child + 1
if elem(a,root) < elem(a,child),
do: swap(a, root, child) |> siftDown(child, finish),
else: a
end
defp siftDown(a, _root, _finish), do: a
defp swap(a, i, j) do
{vi, vj} = {elem(a,i), elem(a,j)}
a |> put_elem(i, vj) |> put_elem(j, vi)
end
end
(for _ <- 1..20, do: :rand.uniform(20)) |> IO.inspect |> Sort.heapSort |> IO.inspect</lang>
- Output:
[6, 1, 12, 3, 7, 7, 9, 20, 8, 15, 2, 10, 14, 5, 19, 7, 20, 9, 14, 19] [1, 2, 3, 5, 6, 7, 7, 7, 8, 9, 9, 10, 12, 14, 14, 15, 19, 19, 20, 20]
F#
<lang fsharp>let inline swap (a: _ []) i j =
let temp = a.[i] a.[i] <- a.[j] a.[j] <- temp
let inline sift cmp (a: _ []) start count =
let rec loop root child =
if root * 2 + 1 < count then
let p = child < count - 1 && cmp a.[child] a.[child + 1] < 0
let child = if p then child + 1 else child
if cmp a.[root] a.[child] < 0 then
swap a root child
loop child (child * 2 + 1)
loop start (start * 2 + 1)
let inline heapsort cmp (a: _ []) =
let n = a.Length for start = n/2 - 1 downto 0 do sift cmp a start n for term = n - 1 downto 1 do swap a term 0 sift cmp a 0 term</lang>
Forth
This program assumes that return addresses simply reside as a single cell on the Return Stack. Most Forth compilers fulfill this requirement. <lang forth>create example
70 , 61 , 63 , 37 , 63 , 25 , 46 , 92 , 38 , 87 ,
[UNDEFINED] r'@ [IF]
- r'@ r> r> r@ swap >r swap >r ;
[THEN]
defer precedes ( n1 n2 a -- f) defer exchange ( n1 n2 a --)
- siftDown ( a e s -- a e s)
swap >r swap >r dup ( s r)
begin ( s r)
dup 2* 1+ dup r'@ < ( s r c f)
while ( s r c)
dup 1+ dup r'@ < ( s r c c+1 f)
if ( s r c c+1)
over over r@ precedes if swap then
then drop ( s r c)
over over r@ precedes ( s r c f)
while ( s r c)
tuck r@ exchange ( s r)
repeat then ( s r)
drop drop r> swap r> swap ( a e s)
- heapsort ( a n --)
over >r ( a n) dup 1- 1- 2/ ( a c s) begin ( a c s) dup 0< 0= ( a c s f) while ( a c s) siftDown 1- ( a c s) repeat drop ( a c)
1- 0 ( a e 0) begin ( a e 0) over 0> ( a e 0 f) while ( a e 0) over over r@ exchange ( a e 0) siftDown swap 1- swap ( a e 0) repeat ( a e 0) drop drop drop r> drop
- noname >r cells r@ + @ swap cells r> + @ swap < ; is precedes
- noname >r cells r@ + swap cells r> + over @ over @ swap rot ! swap ! ; is exchange
- .array 10 0 do example i cells + ? loop cr ;
.array example 10 heapsort .array </lang>
<lang forth>
\ Written in ANS-Forth; tested under VFX.
\ Requires the novice package: http://www.forth.org/novice.html
\ The following should already be done:
\ include novice.4th
\ This is already in the novice package, so it is not really necessary to compile the code provided here.
\ ****** \ ****** This is our array sort. We are using the heap-sort because it provides consistent times and it is not recursive. \ ****** This code was ported from C++ at: http://www.snippets.24bytes.com/2010/06/heap-sort.html \ ****** Our array record size must be a multiple of W. This is assured if FIELD is used for creating the record. \ ****** The easiest way to speed this up is to rewrite EXCHANGE in assembly language. \ ******
marker HeapSort.4th
macro: exchange ( adrX adrY size -- ) \ the size of the record must be a multiple of W
begin dup while \ -- adrX adrY remaining
over @ fourth @ \ -- adrX adrY remaining Y X
fourth ! fourth ! \ -- adrX adrY remaining
rot w + rot w + rot w -
repeat
3drop ;
\ All of these macros use the locals from SORT, and can only be called from SORT.
macro: adr ( index -- adr )
recsiz * array + ;
macro: left ( x -- y ) 2* 1+ ;
macro: right ( x -- y ) 2* 2 + ;
macro: heapify ( x -- )
dup >r begin \ r: -- great
dup left dup limit < if dup adr rover adr 'comparer execute if rdrop dup >r then then drop
dup right dup limit < if dup adr r@ adr 'comparer execute if rdrop dup >r then then drop
dup r@ <> while
adr r@ adr recsiz exchange
r@ repeat
drop rdrop ;
macro: build-max-heap ( -- )
limit 1- 2/ begin dup 0>= while dup heapify 1- repeat drop ;
- sort { array limit recsiz 'comparer -- }
recsiz [ w 1- ] literal and abort" *** SORT: record size must be a multiple of the cell size ***"
build-max-heap
begin limit while -1 +to limit
0 adr limit adr recsiz exchange
0 heapify repeat ;
\ The SORT locals: \ array \ the address of the 0th element \ limit \ the number of records in the array \ recsiz \ the size of a record in the array \ this must be a multiple of W (FIELD assures this) \ 'comparer \ adrX adrY -- X>Y?
\ Note for the novice: \ This code was originally written with colon words rather than macros, and using items rather than local variables. \ After it was debugged, it was changed to use macros and locals so that it would be fast and reentrant. \ One of the reasons why the heap-sort was chosen is because it is not recursive, which allows macros to be used. \ Using macros allows the data (array, limit, recsiz, 'comparer) to be held in locals rather than items, which is reentrant.
\ ******
\ ****** This tests SORT.
\ ******
create aaa 2 , 9 , 3 , 6 , 1 , 4 , 5 , 7 , 0 , 8 ,
- print-aaa ( limit -- )
cells aaa + aaa do I @ . w +loop ;
- int> ( adrX adrY -- X>Y? )
swap @ swap @ > ;
- test-sort ( limit -- )
cr dup print-aaa aaa over w ['] int> sort cr print-aaa ;
10 test-sort </lang>
- Output:
2 9 3 6 1 4 5 7 0 8 0 1 2 3 4 5 6 7 8 9
Fortran
Translation of the pseudocode <lang fortran>program Heapsort_Demo
implicit none integer, parameter :: num = 20 real :: array(num) call random_seed call random_number(array) write(*,*) "Unsorted array:-" write(*,*) array write(*,*) call heapsort(array) write(*,*) "Sorted array:-" write(*,*) array
contains
subroutine heapsort(a)
real, intent(in out) :: a(0:) integer :: start, n, bottom real :: temp
n = size(a)
do start = (n - 2) / 2, 0, -1
call siftdown(a, start, n);
end do
do bottom = n - 1, 1, -1
temp = a(0)
a(0) = a(bottom)
a(bottom) = temp;
call siftdown(a, 0, bottom)
end do
end subroutine heapsort
subroutine siftdown(a, start, bottom)
real, intent(in out) :: a(0:) integer, intent(in) :: start, bottom integer :: child, root real :: temp
root = start
do while(root*2 + 1 < bottom)
child = root * 2 + 1
if (child + 1 < bottom) then
if (a(child) < a(child+1)) child = child + 1
end if
if (a(root) < a(child)) then
temp = a(child)
a(child) = a (root)
a(root) = temp
root = child
else
return
end if
end do
end subroutine siftdown
end program Heapsort_Demo</lang>
FreeBASIC
<lang freebasic>' version 22-10-2016 ' compile with: fbc -s console ' for boundary checks on array's compile with: fbc -s console -exx
' sort from lower bound to the higher bound ' array's can have subscript range from -2147483648 to +2147483647
Sub siftdown(hs() As Long, start As ULong, end_ As ULong)
Dim As ULong root = start Dim As Long lb = LBound(hs)
While root * 2 + 1 <= end_
Dim As ULong child = root * 2 + 1
If (child + 1 <= end_) AndAlso (hs(lb + child) < hs(lb + child + 1)) Then
child = child + 1
End If
If hs(lb + root) < hs(lb + child) Then
Swap hs(lb + root), hs(lb + child)
root = child
Else
Return
End If
Wend
End Sub
Sub heapsort(hs() As Long)
Dim As Long lb = LBound(hs) Dim As ULong count = UBound(hs) - lb + 1 Dim As Long start = (count - 2) \ 2 Dim As ULong end_ = count - 1
While start >= 0
siftdown(hs(), start, end_)
start = start - 1
Wend
While end_ > 0
Swap hs(lb + end_), hs(lb)
end_ = end_ - 1
siftdown(hs(), 0, end_)
Wend
End Sub
' ------=< MAIN >=------
Dim As Long array(-7 To 7) Dim As Long i, lb = LBound(array), ub = UBound(array)
Randomize Timer For i = lb To ub : array(i) = i : Next For i = lb To ub
Swap array(i), array(Int(Rnd * (ub - lb + 1)) + lb)
Next
Print "Unsorted" For i = lb To ub
Print Using " ###"; array(i);
Next : Print : Print
heapsort(array())
Print "After heapsort" For i = lb To ub
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 0 3 -6 2 1 -4 7 5 6 -3 4 -7 -1 -5 -2 After heapsort -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
FunL
Direct translation of the pseudocode. The array object (using Scala's ArraySeq class) has built-in method length, so the count parameter is not needed.
<lang funl>def heapSort( a ) =
heapify( a ) end = a.length() - 1
while end > 0 a(end), a(0) = a(0), a(end) siftDown( a, 0, --end )
def heapify( a ) =
for i <- (a.length() - 2)\2..0 by -1 siftDown( a, i, a.length() - 1 )
def siftDown( a, start, end ) =
root = start
while root*2 + 1 <= end child = root*2 + 1
if child + 1 <= end and a(child) < a(child + 1)
child++
if a(root) < a(child)
a(root), a(child) = a(child), a(root)
root = child
else
break
a = array( [7, 2, 6, 1, 9, 5, 0, 3, 8, 4] ) heapSort( a ) println( a )</lang>
- Output:
ArraySeq(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Go
Here's an ingenious solution that makes use of the heap module. Although the heap module usually implements an independent heap with push/pop operations, we use a helper type where the "pop" operation does not actually change the size of the underlying container, but changes a "heap length" variable indicating the length of the prefix of the underlying container that is considered "the heap".
Since we want to implement a generic algorithm, we accept an argument of type sort.Interface, and thus do not have access to the actual elements of the container we're sorting. We can only swap elements. This causes a problem for us when implementing the Pop method, as we can't actually return an element. The ingenious step is realizing that heap.Pop() must move the value to pop to the "end" of the heap area, because its interface only has access to a "Swap" function, and a "Pop" function that pops from the end. (It does not have the ability to pop a value at the beginning.) This is perfect because we precisely want to move the thing popped to the end and shrink the "heap area" by 1. Our "Pop" function returns nothing since we can't get the value, but don't actually need it. (We only need the swapping that it does for us.)
<lang go>package main
import (
"sort" "container/heap" "fmt"
)
type HeapHelper struct {
container sort.Interface length int
}
func (self HeapHelper) Len() int { return self.length } // We want a max-heap, hence reverse the comparison func (self HeapHelper) Less(i, j int) bool { return self.container.Less(j, i) } func (self HeapHelper) Swap(i, j int) { self.container.Swap(i, j) } // this should not be called func (self *HeapHelper) Push(x interface{}) { panic("impossible") } func (self *HeapHelper) Pop() interface{} {
self.length-- return nil // return value not used
}
func heapSort(a sort.Interface) {
helper := HeapHelper{ a, a.Len() }
heap.Init(&helper)
for helper.length > 0 {
heap.Pop(&helper)
}
}
func main() {
a := []int{170, 45, 75, -90, -802, 24, 2, 66}
fmt.Println("before:", a)
heapSort(sort.IntSlice(a))
fmt.Println("after: ", a)
}</lang>
- Output:
before: [170 45 75 -90 -802 24 2 66] after: [-802 -90 2 24 45 66 75 170]
If you want to implement it manually: <lang go>package main
import (
"sort" "fmt"
)
func main() {
a := []int{170, 45, 75, -90, -802, 24, 2, 66}
fmt.Println("before:", a)
heapSort(sort.IntSlice(a))
fmt.Println("after: ", a)
}
func heapSort(a sort.Interface) {
for start := (a.Len() - 2) / 2; start >= 0; start-- {
siftDown(a, start, a.Len()-1)
}
for end := a.Len() - 1; end > 0; end-- {
a.Swap(0, end)
siftDown(a, 0, end-1)
}
}
func siftDown(a sort.Interface, start, end int) {
for root := start; root*2+1 <= end; {
child := root*2 + 1
if child+1 <= end && a.Less(child, child+1) {
child++
}
if !a.Less(root, child) {
return
}
a.Swap(root, child)
root = child
}
}</lang>
Groovy
Loose translation of the pseudocode: <lang groovy>def makeSwap = { a, i, j = i+1 -> print "."; aj,i = ai,j }
def checkSwap = { list, i, j = i+1 -> [(list[i] > list[j])].find{ it }.each { makeSwap(list, i, j) } }
def siftDown = { a, start, end ->
def p = start
while (p*2 < end) {
def c = p*2 + ((p*2 + 1 < end && a[p*2 + 2] > a[p*2 + 1]) ? 2 : 1)
if (checkSwap(a, c, p)) { p = c }
else { return }
}
}
def heapify = {
(((it.size()-2).intdiv(2))..0).each { start -> siftDown(it, start, it.size()-1) }
}
def heapSort = { list ->
heapify(list)
(0..<(list.size())).reverse().each { end ->
makeSwap(list, 0, end)
siftDown(list, 0, end-1)
}
list
}</lang> Test: <lang groovy>println (heapSort([23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4])) println (heapSort([88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))</lang>
- Output:
.......................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99] ..........................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
Haskell
Using package fgl from HackageDB <lang haskell>import Data.Graph.Inductive.Internal.Heap(
Heap(..),insert,findMin,deleteMin)
-- heapsort is added in this module as an example application
build :: Ord a => [(a,b)] -> Heap a b build = foldr insert Empty
toList :: Ord a => Heap a b -> [(a,b)] toList Empty = [] toList h = x:toList r
where (x,r) = (findMin h,deleteMin h)
heapsort :: Ord a => [a] -> [a] heapsort = (map fst) . toList . build . map (\x->(x,x))</lang> e.g. <lang haskell>*Main> heapsort [[6,9],[2,13],[6,8,14,9],[10,7],[5]] [[2,13],[5],[6,8,14,9],[6,9],[10,7]]</lang>
Haxe
<lang haxe>class HeapSort {
@:generic
private static function siftDown<T>(arr: Array<T>, start:Int, end:Int) {
var root = start;
while (root * 2 + 1 <= end) {
var child = root * 2 + 1;
if (child + 1 <= end && Reflect.compare(arr[child], arr[child + 1]) < 0)
child++;
if (Reflect.compare(arr[root], arr[child]) < 0) {
var temp = arr[root];
arr[root] = arr[child];
arr[child] = temp;
root = child;
} else {
break;
}
}
}
@:generic
public static function sort<T>(arr:Array<T>) {
if (arr.length > 1)
{
var start = (arr.length - 2) >> 1;
while (start > 0) {
siftDown(arr, start - 1, arr.length - 1);
start--;
}
}
var end = arr.length - 1;
while (end > 0) {
var temp = arr[end];
arr[end] = arr[0];
arr[0] = temp;
siftDown(arr, 0, end - 1);
end--;
}
}
}
class Main {
static function main() {
var integerArray = [1, 10, 2, 5, -1, 5, -19, 4, 23, 0];
var floatArray = [1.0, -3.2, 5.2, 10.8, -5.7, 7.3,
3.5, 0.0, -4.1, -9.5];
var stringArray = ['We', 'hold', 'these', 'truths', 'to',
'be', 'self-evident', 'that', 'all',
'men', 'are', 'created', 'equal'];
Sys.println('Unsorted Integers: ' + integerArray);
HeapSort.sort(integerArray);
Sys.println('Sorted Integers: ' + integerArray);
Sys.println('Unsorted Floats: ' + floatArray);
HeapSort.sort(floatArray);
Sys.println('Sorted Floats: ' + floatArray);
Sys.println('Unsorted Strings: ' + stringArray);
HeapSort.sort(stringArray);
Sys.println('Sorted Strings: ' + stringArray);
}
}</lang>
- Output:
Unsorted Integers: [1,10,2,5,-1,5,-19,4,23,0] Sorted Integers: [-19,-1,0,1,2,4,5,5,10,23] Unsorted Floats: [1,-3.2,5.2,10.8,-5.7,7.3,3.5,0,-4.1,-9.5] Sorted Floats: [-9.5,-5.7,-4.1,-3.2,0,1,3.5,5.2,7.3,10.8] Unsorted Strings: [We,hold,these,truths,to,be,self-evident,that,all,men,are,created,equal] Sorted Strings: [We,all,are,be,created,equal,hold,men,self-evident,that,these,to,truths]
Icon and Unicon
<lang Icon>procedure main() #: demonstrate various ways to sort a list and string
demosort(heapsort,[3, 14, 1, 5, 9, 2, 6, 3],"qwerty")
end
procedure heapsort(X,op) #: return sorted list ascending(or descending) local head,tail
op := sortop(op,X) # select how and what we sort
every head := (tail := *X) / 2 to 1 by -1 do # work back from from last parent node
X := siftdown(X,op,head,tail) # sift down from head to make the heap
every tail := *X to 2 by -1 do { # work between the beginning and the tail to final positions
X[1] :=: X[tail]
X := siftdown(X,op,1,tail-1) # re-sift next (previous) branch after shortening the heap
}
return X
end
procedure siftdown(X,op,root,tail) #: the value @root is moved "down" the path of max(min) value to its level local child
while (child := root * 2) <= tail do { # move down the branch from root to tail
if op(X[child],X[tail >= child + 1]) then # choose the larger(smaller)
child +:= 1 # ... child
if op(X[root],X[child]) then { # root out of order?
X[child] :=: X[root]
root := child # follow max(min) branch
}
else
return X
}
return X
end</lang> Algorithm notes:
- This is a fairly straight forward implementation of the pseudo-code with 'heapify' coded in-line.
Implementation notes:
- Since this transparently sorts both string and list arguments the result must 'return' to bypass call by value (strings)
- Beware missing trailing 'returns' when translating pseudo-code. For amusement try comment out the return at the end of 'shiftdown'
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.
- Abbreviated sample output:
Sorting Demo using procedure heapsort
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)
J
Translation of the pseudocode <lang j>swap=: C.~ <
siftDown=: 4 : 0
'c e'=. x
while. e > c=.1+2*s=.c do.
before=. <&({&y)
if. e > 1+c do. c=.c+ c before c+1 end.
if. s before c do. y=. y swap c,s else. break. end.
end.
y
)
heapSort=: 3 : 0
if. 1>: c=. # y do. y return. end. z=. siftDown&.>/ (c,~each i.<.c%2),<y NB. heapify > ([ siftDown swap~)&.>/ (0,each}.i.c),z
)</lang> Examples <lang j> heapSort 1 5 2 7 3 9 4 6 8 1 1 1 2 3 4 5 6 7 8 9
heapSort &. (a.&i.) 'aqwcdhkij'
acdhijkqw</lang>
Java
Direct translation of the pseudocode. <lang java>public static void heapSort(int[] a){ int count = a.length;
//first place a in max-heap order heapify(a, count);
int end = count - 1; while(end > 0){ //swap the root(maximum value) of the heap with the //last element of the heap int tmp = a[end]; a[end] = a[0]; a[0] = tmp; //put the heap back in max-heap order siftDown(a, 0, end - 1); //decrement the size of the heap so that the previous //max value will stay in its proper place end--; } }
public static void heapify(int[] a, int count){ //start is assigned the index in a of the last parent node int start = (count - 2) / 2; //binary heap
while(start >= 0){ //sift down the node at index start to the proper place //such that all nodes below the start index are in heap //order siftDown(a, start, count - 1); start--; } //after sifting down the root all nodes/elements are in heap order }
public static void siftDown(int[] a, int start, int end){ //end represents the limit of how far down the heap to sift int root = start;
while((root * 2 + 1) <= end){ //While the root has at least one child int child = root * 2 + 1; //root*2+1 points to the left child //if the child has a sibling and the child's value is less than its sibling's... if(child + 1 <= end && a[child] < a[child + 1]) child = child + 1; //... then point to the right child instead if(a[root] < a[child]){ //out of max-heap order int tmp = a[root]; a[root] = a[child]; a[child] = tmp; root = child; //repeat to continue sifting down the child now }else return; } }</lang>
JavaScript
<lang Javascript> function swap(data, i, j) {
var tmp = data[i]; data[i] = data[j]; data[j] = tmp;
}
function heap_sort(arr) {
put_array_in_heap_order(arr);
var end = arr.length - 1;
while(end > 0) {
swap(arr, 0, end);
sift_element_down_heap(arr, 0, end);
end -= 1
}
}
function put_array_in_heap_order(arr) {
var i;
i = arr.length / 2 - 1;
i = Math.floor(i);
while (i >= 0) {
sift_element_down_heap(arr, i, arr.length);
i -= 1;
}
}
function sift_element_down_heap(heap, i, max) {
var i_big, c1, c2;
while(i < max) {
i_big = i;
c1 = 2*i + 1;
c2 = c1 + 1;
if (c1 < max && heap[c1] > heap[i_big])
i_big = c1;
if (c2 < max && heap[c2] > heap[i_big])
i_big = c2;
if (i_big == i) return;
swap(heap,i, i_big);
i = i_big;
}
}
arr = [12, 11, 15, 10, 9, 1, 2, 3, 13, 14, 4, 5, 6, 7, 8,]; heap_sort(arr); alert(arr);</lang>
- Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
Julia
<lang julia>function swap(a, i, j)
a[i], a[j] = a[j], a[i]
end
function pd!(a, first, last)
while (c = 2 * first - 1) < last
if c < last && a[c] < a[c + 1]
c += 1
end
if a[first] < a[c]
swap(a, c, first)
first = c
else
break
end
end
end
function heapify!(a, n)
f = div(n, 2)
while f >= 1
pd!(a, f, n)
f -= 1
end
end
function heapsort!(a)
n = length(a)
heapify!(a, n)
l = n
while l > 1
swap(a, 1, l)
l -= 1
pd!(a, 1, l)
end
return a
end
using Random: shuffle a = shuffle(collect(1:12)) println("Unsorted: $a") println("Heap sorted: ", heapsort!(a))
</lang>
- Output:
Unsorted: [3, 12, 11, 4, 2, 7, 5, 8, 9, 1, 10, 6] Heap sorted: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
Kotlin
<lang scala>// version 1.1.0
fun heapSort(a: IntArray) {
heapify(a)
var end = a.size - 1
while (end > 0) {
val temp = a[end]
a[end] = a[0]
a[0] = temp
end--
siftDown(a, 0, end)
}
}
fun heapify(a: IntArray) {
var start = (a.size - 2) / 2
while (start >= 0) {
siftDown(a, start, a.size - 1)
start--
}
}
fun siftDown(a: IntArray, start: Int, end: Int) {
var root = start
while (root * 2 + 1 <= end) {
var child = root * 2 + 1
if (child + 1 <= end && a[child] < a[child + 1]) child++
if (a[root] < a[child]) {
val temp = a[root]
a[root] = a[child]
a[child] = temp
root = child
}
else return
}
}
fun main(args: Array<String>) {
val aa = arrayOf(
intArrayOf(100, 2, 56, 200, -52, 3, 99, 33, 177, -199),
intArrayOf(4, 65, 2, -31, 0, 99, 2, 83, 782, 1),
intArrayOf(12, 11, 15, 10, 9, 1, 2, 3, 13, 14, 4, 5, 6, 7, 8)
)
for (a in aa) {
heapSort(a)
println(a.joinToString(", "))
}
}</lang>
- Output:
-199, -52, 2, 3, 33, 56, 99, 100, 177, 200 -31, 0, 1, 2, 2, 4, 65, 83, 99, 782 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
Liberty BASIC
<lang lb>wikiSample=1 'comment out for random array
data 6, 5, 3, 1, 8, 7, 2, 4
itemCount = 20
if wikiSample then itemCount = 8
dim A(itemCount)
for i = 1 to itemCount
A(i) = int(rnd(1) * 100)
if wikiSample then read tmp: A(i)=tmp
next i
print "Before Sort" call printArray itemCount
call heapSort itemCount
print "After Sort" call printArray itemCount
end
'------------------------------------------ sub heapSort count
call heapify count
print "the heap" call printArray count
theEnd = count
while theEnd > 1
call swap theEnd, 1
call siftDown 1, theEnd-1
theEnd = theEnd - 1
wend
end sub
sub heapify count
start = int(count / 2)
while start >= 1
call siftDown start, count
start = start - 1
wend
end sub
sub siftDown start, theEnd
root = start
while root * 2 <= theEnd
child = root * 2
swap = root
if A(swap) < A(child) then
swap = child
end if
if child+1 <= theEnd then
if A(swap) < A(child+1) then
swap = child + 1
end if
end if
if swap <> root then
call swap root, swap
root = swap
else
exit sub
end if
wend
end sub
sub swap a,b
tmp = A(a) A(a) = A(b) A(b) = tmp
end sub
'=========================================== sub printArray itemCount
for i = 1 to itemCount
print using("###", A(i));
next i
print
end sub</lang>
Lobster
<lang Lobster>def siftDown(a, start, end):
// (end represents the limit of how far down the heap to sift) var root = start
while root * 2 + 1 <= end: // (While the root has at least one child)
var child = root * 2 + 1 // (root*2+1 points to the left child)
// (If the child has a sibling and the child's value is less than its sibling's...)
if child + 1 <= end and a[child] < a[child + 1]:
child += 1 // (... then point to the right child instead)
if a[root] < a[child]: // (out of max-heap order)
let r = a[root] // swap(a[root], a[child])
a[root] = a[child]
a[child] = r
root = child // (repeat to continue sifting down the child now)
else:
return
def heapify(a, count):
//(start is assigned the index in a of the last parent node) var start = (count - 2) >> 1
while start >= 0:
// (sift down the node at index start to the proper place
// such that all nodes below the start index are in heap order)
siftDown(a, start, count-1)
start -= 1
// (after sifting down the root all nodes/elements are in heap order)
def heapSort(a):
// input: an unordered array a of length count let count = a.length // (first place a in max-heap order) heapify(a, count)
var end = count - 1
while end > 0:
//(swap the root(maximum value) of the heap with the last element of the heap)
let z = a[0]
a[0] = a[end]
a[end] = z
//(decrement the size of the heap so that the previous max value will stay in its proper place)
end -= 1
// (put the heap back in max-heap order)
siftDown(a, 0, end)
let inputi = [1,10,2,5,-1,5,-19,4,23,0] print ("input: " + inputi) heapSort(inputi) print ("sorted: " + inputi) let inputf = [1,-3.2,5.2,10.8,-5.7,7.3,3.5,0,-4.1,-9.5] print ("input: " + inputf) heapSort(inputf) print ("sorted: " + inputf) let inputs = ["We","hold","these","truths","to","be","self-evident","that","all","men","are","created","equal"] print ("input: " + inputs) heapSort(inputs) print ("sorted: " + inputs) </lang>
- Output:
input: [1, 10, 2, 5, -1, 5, -19, 4, 23, 0] sorted: [-19, -1, 0, 1, 2, 4, 5, 5, 10, 23] input: [1.0, -3.2, 5.2, 10.8, -5.7, 7.3, 3.5, 0.0, -4.1, -9.5] sorted: [-9.5, -5.7, -4.1, -3.2, 0.0, 1.0, 3.5, 5.2, 7.3, 10.8] input: ["We", "hold", "these", "truths", "to", "be", "self-evident", "that", "all", "men", "are", "created", "equal"] sorted: ["We", "all", "are", "be", "created", "equal", "hold", "men", "self-evident", "that", "these", "to", "truths"]
LotusScript
<lang LotusScript> Public Sub heapsort(pavIn As Variant)
Dim liCount As Integer, liEnd As Integer Dim lvTemp As Variant liCount = UBound(pavIn) + 1
heapify pavIn, liCount
liEnd = liCount - 1 While liEnd > 0 lvTemp = pavIn(liEnd) pavIn(liEnd) = pavIn(0) pavIn(0) = lvTemp liEnd = liEnd -1 siftDown pavIn,0, liEnd Wend
End Sub
Private Sub heapify(pavIn As Variant,piCount As Integer)
Dim liStart As Integer liStart = (piCount - 2) / 2 While liStart >=0 siftDown pavIn, liStart, piCount -1 liStart = liStart - 1 Wend
End Sub
Private Sub siftDown(pavIn As Variant, piStart As Integer, piEnd As Integer)
Dim liRoot As Integer, liChild As Integer
Dim lvTemp As Variant
liRoot = piStart
While liRoot *2 + 1 <= piEnd
liChild = liRoot *2 + 1
If liChild +1 <= piEnd And pavIn(liChild) < pavIn(liChild + 1) Then
liChild = liChild + 1
End If
If pavIn(liRoot) < pavIn(liChild) Then
lvTemp = pavIn(liRoot)
pavIn(liRoot) = pavIn(liChild)
pavIn(liChild) = lvTemp
liRoot = liChild
Else
Exit sub
End if
wend
End Sub </lang>
M4
<lang M4>divert(-1)
define(`randSeed',141592653) define(`setRand',
`define(`randSeed',ifelse(eval($1<10000),1,`eval(20000-$1)',`$1'))')
define(`rand_t',`eval(randSeed^(randSeed>>13))') define(`random',
`define(`randSeed',eval((rand_t^(rand_t<<18))&0x7fffffff))randSeed')
define(`set',`define(`$1[$2]',`$3')') define(`get',`defn(`$1[$2]')') define(`new',`set($1,size,0)') dnl for the heap calculations, it's easier if origin is 0, so set value first define(`append',
`set($1,get($1,size),$2)`'set($1,size,incr(get($1,size)))')
dnl swap(<name>,<j>,<name>[<j>],<k>) using arg stack for the temporary define(`swap',`set($1,$2,get($1,$4))`'set($1,$4,$3)')
define(`deck',
`new($1)for(`x',1,$2,
`append(`$1',eval(random%100))')')
define(`show',
`for(`x',0,decr(get($1,size)),`get($1,x) ')')
define(`for',
`ifelse($#,0,``$0, `ifelse(eval($2<=$3),1, `pushdef(`$1',$2)$4`'popdef(`$1')$0(`$1',incr($2),$3,`$4')')')')
define(`ifywork',
`ifelse(eval($2>=0),1,
`siftdown($1,$2,$3)`'ifywork($1,decr($2),$3)')')
define(`heapify',
`define(`start',eval((get($1,size)-2)/2))`'ifywork($1,start,
decr(get($1,size)))')
define(`siftdown',
`define(`child',eval($2*2+1))`'ifelse(eval(child<=$3),1,
`ifelse(eval(child+1<=$3),1,
`ifelse(eval(get($1,child)<get($1,incr(child))),1,
`define(`child',
incr(child))')')`'ifelse(eval(get($1,$2)<get($1,child)),1,
`swap($1,$2,get($1,$2),child)`'siftdown($1,child,$3)')')')
define(`sortwork',
`ifelse($2,0,
`',
`swap($1,0,get($1,0),$2)`'siftdown($1,0,decr($2))`'sortwork($1,
decr($2))')')
define(`heapsort',
`heapify($1)`'sortwork($1,decr(get($1,size)))')
divert deck(`a',10) show(`a') heapsort(`a') show(`a')</lang>
Maple
<lang>swap := proc(arr, a, b) local temp: temp := arr[a]: arr[a] := arr[b]: arr[b] := temp: end proc: heapify := proc(toSort, n, i) local largest, l, r, holder: largest := i: l := 2*i: r := 2*i+1: if (l <= n and toSort[l] > toSort[largest]) then largest := l: end if: if (r <= n and toSort[r] > toSort[largest]) then largest := r: end if: if (not largest = i) then swap(toSort, i, largest); heapify(toSort, n, largest): end if: end proc: heapsort := proc(arr) local n,i: n := numelems(arr): for i from trunc(n/2) to 1 by -1 do heapify(arr, n, i): end do: for i from n to 2 by -1 do swap(arr, 1, i): heapify(arr, i-1, 1): end do: end proc: arr := Array([17,3,72,0,36,2,3,8,40,0]); heapsort(arr); arr;</lang>
- Output:
[0,0,2,3,3,8,17,36,40,72]
Mathematica
<lang Mathematica>siftDown[list_,root_,theEnd_]:=
While[(root*2) <= theEnd, child = root*2; If[(child+1 <= theEnd)&&(listchild < listchild+1), child++;]; If[listroot < listchild, list[[{root,child}]] = list[[{child,root}]]; root = child;, Break[]; ] ]
heapSort[list_] := Module[{ count, start},
count = Length[list]; start = Floor[count/2];
While[start >= 1,list = siftDown[list,start,count];
start--;
]
While[count > 1, list[[{count,1}]] = list[[{1,count}]];
count--; list = siftDown[list,1,count];
]
]</lang>
- Output:
heapSort@{2,3,1,5,7,6}
{1,2,3,5,6,7}
MATLAB / Octave
This function definition is an almost exact translation of the pseudo-code into MATLAB, but I have chosen to make the heapify function inline because it is only called once in the pseudo-code. Also, MATLAB uses 1 based array indecies, therefore all of the pseudo-code has been translated to reflect that difference. <lang MATLAB>function list = heapSort(list)
function list = siftDown(list,root,theEnd)
while (root * 2) <= theEnd
child = root * 2;
if (child + 1 <= theEnd) && (list(child) < list(child+1))
child = child + 1;
end
if list(root) < list(child)
list([root child]) = list([child root]); %Swap
root = child;
else
return
end
end %while
end %siftDown
count = numel(list);
%Because heapify is called once in pseudo-code, it is inline here
start = floor(count/2);
while start >= 1
list = siftDown(list, start, count);
start = start - 1;
end
%End Heapify
while count > 1
list([count 1]) = list([1 count]); %Swap
count = count - 1;
list = siftDown(list,1,count);
end
end</lang> Sample Usage: <lang MATLAB>>> heapSort([4 3 1 5 6 2])
ans =
1 2 3 4 5 6</lang>
MAXScript
<lang MAXScript>fn heapify arr count = ( local s = count /2 while s > 0 do ( arr = siftDown arr s count s -= 1 ) return arr ) fn siftDown arr s end = ( local root = s while root * 2 <= end do ( local child = root * 2 if child < end and arr[child] < arr[child+1] do ( child += 1 ) if arr[root] < arr[child] then ( swap arr[root] arr[child] root = child ) else return arr ) return arr ) fn heapSort arr = ( local count = arr.count arr = heapify arr count local end = count while end >= 1 do ( swap arr[1] arr[end]
end -= 1 arr = siftDown arr 1 end )
)</lang> Output: <lang MAXScript> a = for i in 1 to 10 collect random 0 9
- (7, 2, 5, 6, 1, 5, 4, 0, 1, 6)
heapSort a
- (0, 1, 1, 2, 4, 5, 5, 6, 6, 7)
</lang>
NetRexx
<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 - , heapSort(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 heapSort(a = String[], count = a.length) public constant binary returns String[]
rl = String[a.length] al = List heapSort(Arrays.asList(a), count) al.toArray(rl)
return rl
method heapSort(a = List, count = a.size) public constant binary returns ArrayList
a = heapify(a, count)
iend = count - 1 loop label iend while iend > 0 swap = a.get(0) a.set(0, a.get(iend)) a.set(iend, swap) a = siftDown(a, 0, iend - 1) iend = iend - 1 end iend
return ArrayList(a)
method heapify(a = List, count = int) public constant binary returns List
start = (count - 2) % 2
loop label strt while start >= 0 a = siftDown(a, start, count - 1) start = start - 1 end strt
return a
method siftDown(a = List, istart = int, iend = int) public constant binary returns List
root = istart
loop label root while root * 2 + 1 <= iend
child = root * 2 + 1
if child + 1 <= iend then do
if (Comparable a.get(child)).compareTo(Comparable a.get(child + 1)) < 0 then do
child = child + 1
end
end
if (Comparable a.get(root)).compareTo(Comparable a.get(child)) < 0 then do
swap = a.get(root)
a.set(root, a.get(child))
a.set(child, swap)
root = child
end
else do
leave root
end
end root
return a</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
Nim
<lang nim>proc siftDown[T](a: var openarray[T]; start, ending: int) =
var root = start
while root * 2 + 1 < ending:
var child = 2 * root + 1
if child + 1 < ending and a[child] < a[child+1]:
inc child
if a[root] < a[child]:
swap a[child], a[root]
root = child
else:
return
proc heapSort[T](a: var openarray[T]) =
let count = a.len for start in countdown((count - 2) div 2, 0): siftDown(a, start, count) for ending in countdown(count - 1, 1): swap a[ending], a[0] siftDown(a, 0, ending)
var a = @[4, 65, 2, -31, 0, 99, 2, 83, 782] heapSort a echo a</lang>
- Output:
@[-31, 0, 2, 2, 4, 65, 83, 99, 782]
Objeck
<lang objeck>bundle Default {
class HeapSort {
function : Main(args : String[]) ~ Nil {
values := [4, 3, 1, 5, 6, 2];
HeapSort(values);
each(i : values) {
values[i]->PrintLine();
};
}
function : HeapSort(a : Int[]) ~ Nil {
count := a->Size();
Heapify(a, count);
end := count - 1;
while(end > 0) {
tmp := a[end];
a[end] := a[0];
a[0] := tmp;
SiftDown(a, 0, end - 1);
end -= 1;
};
}
function : Heapify(a : Int[], count : Int) ~ Nil {
start := (count - 2) / 2;
while(start >= 0) {
SiftDown(a, start, count - 1);
start -= 1;
};
}
function : SiftDown(a : Int[], start : Int, end : Int) ~ Nil {
root := start;
while((root * 2 + 1) <= end) {
child := root * 2 + 1;
if(child + 1 <= end & a[child] < a[child + 1]) {
child := child + 1;
};
if(a[root] < a[child]) {
tmp := a[root];
a[root] := a[child];
a[child] := tmp;
root := child;
}
else {
return;
};
};
}
}
}</lang>
OCaml
<lang ocaml>let heapsort a =
let swap i j = let t = a.(i) in a.(i) <- a.(j); a.(j) <- t in
let sift k l =
let rec check x y =
if 2*x+1 < l then
let ch =
if y < l-1 && a.(y) < a.(y+1) then y+1 else y in
if a.(x) < a.(ch) then (swap x ch; check ch (2*ch+1)) in
check k (2*k+1) in
let len = Array.length a in
for start = (len/2)-1 downto 0 do sift start len; done;
for term = len-1 downto 1 do swap term 0; sift 0 term; done;;</lang>
Usage: <lang ocaml>let a = [|3;1;4;1;5;9;2;6;5;3;5;8;97;93;23;84;62;64;33;83;27;95|] in
heapsort a; Array.iter (Printf.printf "%d ") a;;
print_newline ();;
let s = "Just to show this is a type-checked polymorphic function" in let b = Array.init (String.length s) (String.get s) in
heapsort b; Array.iter print_char b;;
print_newline ();;</lang>
- Output:
1 1 2 3 3 4 5 5 5 6 8 9 23 27 33 62 64 83 84 93 95 97
-Jaccccdeeefhhhhiiiiklmnnoooooppprsssstttttuuwyy
Oz
A faithful translation of the pseudocode, adjusted to the fact that Oz arrays can start with an arbitrary index, not just 0 or 1. <lang oz>declare
proc {HeapSort A}
Low = {Array.low A}
High = {Array.high A}
Count = High-Low+1
%% heapify
LastParent = Low + (Count-2) div 2
in
for Start in LastParent..Low;~1 do
{Siftdown A Start High}
end
%% repeatedly put the maximum element to the end
%% and re-heapify the rest
for End in High..Low+1;~1 do
{Swap A End Low}
{Siftdown A Low End-1}
end
end
proc {Siftdown A Start End}
Low = {Array.low A}
fun {FirstChildOf I} Low+(I-Low)*2+1 end
Root = {NewCell Start}
in
for while:{FirstChildOf @Root} =< End
break:Break
do
Child = {NewCell {FirstChildOf @Root}}
in
if @Child + 1 =< End andthen A.@Child < A.(@Child + 1) then
Child := @Child + 1
end
if A.@Root < A.@Child then
{Swap A @Root @Child}
Root := @Child
else
{Break}
end
end
end
proc {Swap A I J}
A.J := (A.I := A.J)
end
%% create array with indices ~1..7 and fill it
Arr = {Array.new ~1 7 0}
{Record.forAllInd unit(~1:3 0:1 4 1 5 9 2 6 5)
proc {$ I V}
Arr.I := V
end}
in
{HeapSort Arr}
{Show {Array.toRecord unit Arr}}</lang>
Pascal
An example, which works on arrays with arbitrary bounds :-) <lang pascal>program HeapSortDemo;
type
TIntArray = array[4..15] of integer;
var
data: TIntArray; i: integer;
procedure siftDown(var a: TIntArray; start, ende: integer);
var
root, child, swap: integer;
begin
root := start;
while root * 2 - start + 1 <= ende do
begin
child := root * 2 - start + 1;
if (child + 1 <= ende) and (a[child] < a[child + 1]) then
inc(child);
if a[root] < a[child] then
begin
swap := a[root];
a[root] := a[child];
a[child] := swap;
root := child;
end
else
exit;
end;
end;
procedure heapify(var a: TIntArray);
var
start, count: integer;
begin
count := length(a);
start := low(a) + count div 2 - 1;
while start >= low(a) do
begin
siftdown(a, start, high(a));
dec(start);
end;
end;
procedure heapSort(var a: TIntArray);
var
ende, swap: integer;
begin
heapify(a);
ende := high(a);
while ende > low(a) do
begin
swap := a[low(a)];
a[low(a)] := a[ende];
a[ende] := swap;
dec(ende);
siftdown(a, low(a), ende);
end;
end;
begin
Randomize;
writeln('The data before sorting:');
for i := low(data) to high(data) do
begin
data[i] := Random(high(data));
write(data[i]:4);
end;
writeln;
heapSort(data);
writeln('The data after sorting:');
for i := low(data) to high(data) do
begin
write(data[i]:4);
end;
writeln;
end.</lang>
- Output:
The data before sorting: 12 13 0 1 0 14 13 10 1 10 9 2 The data after sorting: 0 0 1 1 2 9 10 10 12 13 13 14
Perl
<lang perl>#!/usr/bin/perl
my @a = (4, 65, 2, -31, 0, 99, 2, 83, 782, 1); print "@a\n"; heap_sort(\@a); print "@a\n";
sub heap_sort {
my ($a) = @_;
my $n = @$a;
for (my $i = ($n - 2) / 2; $i >= 0; $i--) {
down_heap($a, $n, $i);
}
for (my $i = 0; $i < $n; $i++) {
my $t = $a->[$n - $i - 1];
$a->[$n - $i - 1] = $a->[0];
$a->[0] = $t;
down_heap($a, $n - $i - 1, 0);
}
}
sub down_heap {
my ($a, $n, $i) = @_;
while (1) {
my $j = max($a, $n, $i, 2 * $i + 1, 2 * $i + 2);
last if $j == $i;
my $t = $a->[$i];
$a->[$i] = $a->[$j];
$a->[$j] = $t;
$i = $j;
}
}
sub max {
my ($a, $n, $i, $j, $k) = @_; my $m = $i; $m = $j if $j < $n && $a->[$j] > $a->[$m]; $m = $k if $k < $n && $a->[$k] > $a->[$m]; return $m;
} </lang>
Phix
<lang Phix>function siftDown(sequence arr, integer s, integer last) integer root = s
while root*2<=last do
integer child = root*2
if child<last and arr[child]<arr[child+1] then
child += 1
end if
if arr[root]>=arr[child] then exit end if
object tmp = arr[root]
arr[root] = arr[child]
arr[child] = tmp
root = child
end while
return arr
end function
function heapify(sequence arr, integer count) integer s = floor(count/2)
while s>0 do
arr = siftDown(arr,s,count)
s -= 1
end while
return arr
end function
function heap_sort(sequence arr) integer last = length(arr)
arr = heapify(arr,last)
while last>1 do
object tmp = arr[1]
arr[1] = arr[last]
arr[last] = tmp
last -= 1
arr = siftDown(arr,1,last)
end while
return arr
end function
?heap_sort({5,"oranges","and",3,"apples"})</lang>
- Output:
{3,5,"and","apples","oranges"}
PicoLisp
<lang PicoLisp>(de heapSort (A Cnt)
(let Cnt (length A)
(for (Start (/ Cnt 2) (gt0 Start) (dec Start))
(siftDown A Start (inc Cnt)) )
(for (End Cnt (> End 1) (dec End))
(xchg (nth A End) A)
(siftDown A 1 End) ) )
A )
(de siftDown (A Start End)
(use Child
(for (Root Start (> End (setq Child (* 2 Root))))
(and
(> End (inc Child))
(> (get A (inc Child)) (get A Child))
(inc 'Child) )
(NIL (> (get A Child) (get A Root)))
(xchg (nth A Root) (nth A Child))
(setq Root Child) ) ) )</lang>
- Output:
: (heapSort (make (do 9 (link (rand 1 999))))) -> (1 167 183 282 524 556 638 891 902)
PL/I
<lang pli>*process source xref attributes or(!);
/********************************************************************* * Pseudocode found here: * http://en.wikipedia.org/wiki/Heapsort#Pseudocode * Sample data from REXX * 27.07.2013 Walter Pachl *********************************************************************/ heaps: Proc Options(main); Dcl a(0:25) Char(50) Var Init( '---letters of the modern Greek Alphabet---', '==========================================', 'alpha','beta','gamma','delta','epsilon','zeta','eta','theta', 'iota','kappa','lambda','mu','nu','xi','omicron','pi', 'rho','sigma','tau','upsilon','phi','chi','psi','omega'); Dcl n Bin Fixed(31) Init((hbound(a)+1));
Call showa('before sort');
Call heapsort((n));
Call showa(' after sort');
heapSort: Proc(count);
Dcl (count,end) Bin Fixed(31);
Call heapify((count));
end=count-1;
do while(end>0);
Call swap(end,0);
end=end-1;
Call siftDown(0,(end));
End;
End;
heapify: Proc(count);
Dcl (count,start) Bin Fixed(31);
start=(count-2)/2;
Do while (start>=0);
Call siftDown((start),count-1);
start=start-1;
End;
End;
siftDown: Proc(start,end);
Dcl (count,start,root,end,child,sw) Bin Fixed(31);
root=start;
Do while(root*2+1<= end);
child=root*2+1;
sw=root;
if a(sw)<a(child) Then
sw=child;
if child+1<=end & a(sw)<a(child+1) Then
sw=child+1;
if sw^=root Then Do;
Call swap(root,sw);
root=sw;
End;
else
return;
End;
End;
swap: Proc(x,y); Dcl (x,y) Bin Fixed(31); Dcl temp Char(50) Var; temp=a(x); a(x)=a(y); a(y)=temp; End;
showa: Proc(txt);
Dcl txt Char(*);
Dcl j Bin Fixed(31);
Do j=0 To hbound(a);
Put Edit('element',j,txt,a(j))(skip,a,f(3),x(1),a,x(1),a);
End;
End;
End;</lang>
- Output:
element 0 before sort ---letters of the modern Greek Alphabet--- element 1 before sort ========================================== element 2 before sort alpha element 3 before sort beta element 4 before sort gamma element 5 before sort delta element 6 before sort epsilon element 7 before sort zeta element 8 before sort eta element 9 before sort theta element 10 before sort iota element 11 before sort kappa element 12 before sort lambda element 13 before sort mu element 14 before sort nu element 15 before sort xi element 16 before sort omicron element 17 before sort pi element 18 before sort rho element 19 before sort sigma element 20 before sort tau element 21 before sort upsilon element 22 before sort phi element 23 before sort chi element 24 before sort psi element 25 before sort omega element 0 after sort ---letters of the modern Greek Alphabet--- element 1 after sort ========================================== element 2 after sort alpha element 3 after sort beta element 4 after sort chi element 5 after sort delta element 6 after sort epsilon element 7 after sort eta element 8 after sort gamma element 9 after sort iota element 10 after sort kappa element 11 after sort lambda element 12 after sort mu element 13 after sort nu element 14 after sort omega element 15 after sort omicron element 16 after sort phi element 17 after sort pi element 18 after sort psi element 19 after sort rho element 20 after sort sigma element 21 after sort tau element 22 after sort theta element 23 after sort upsilon element 24 after sort xi element 25 after sort zeta
PowerShell
<lang PowerShell> function heapsort($a, $count) {
$a = heapify $a $count
$end = $count - 1
while( $end -gt 0) {
$a[$end], $a[0] = $a[0], $a[$end]
$end--
$a = siftDown $a 0 $end
}
$a
} function heapify($a, $count) {
$start = [Math]::Floor(($count - 2) / 2)
while($start -ge 0) {
$a = siftDown $a $start ($count-1)
$start--
}
$a
} function siftdown($a, $start, $end) {
$b, $root = $true, $start
while(( ($root * 2 + 1) -le $end) -and $b) {
$child = $root * 2 + 1
if( ($child + 1 -le $end) -and ($a[$child] -lt $a[$child + 1]) ) {
$child++
}
if($a[$root] -lt $a[$child]) {
$a[$root], $a[$child] = $a[$child], $a[$root]
$root = $child
}
else { $b = $false}
}
$a
} $array = @(60, 21, 19, 36, 63, 8, 100, 80, 3, 87, 11) "$(heapsort $array $array.Count)" </lang> Output:
3 8 11 19 21 36 60 63 80 87 100
PureBasic
<lang PureBasic>Declare heapify(Array a(1), count) Declare siftDown(Array a(1), start, ending)
Procedure heapSort(Array a(1), count)
Protected ending=count-1 heapify(a(), count) While ending>0 Swap a(ending),a(0) siftDown(a(), 0, ending-1) ending-1 Wend
EndProcedure
Procedure heapify(Array a(1), count)
Protected start=(count-2)/2 While start>=0 siftDown(a(),start,count-1) start-1 Wend
EndProcedure
Procedure siftDown(Array a(1), start, ending)
Protected root=start, child
While (root*2+1)<=ending
child=root*2+1
If child+1<=ending And a(child)<a(child+1)
child+1
EndIf
If a(root)<a(child)
Swap a(root), a(child)
root=child
Else
Break
EndIf
Wend
EndProcedure</lang>
Python
<lang python>def heapsort(lst):
Heapsort. Note: this function sorts in-place (it mutates the list).
# in pseudo-code, heapify only called once, so inline it here for start in range((len(lst)-2)/2, -1, -1): siftdown(lst, start, len(lst)-1)
for end in range(len(lst)-1, 0, -1): lst[end], lst[0] = lst[0], lst[end] siftdown(lst, 0, end - 1) return lst
def siftdown(lst, start, end):
root = start
while True:
child = root * 2 + 1
if child > end: break
if child + 1 <= end and lst[child] < lst[child + 1]:
child += 1
if lst[root] < lst[child]:
lst[root], lst[child] = lst[child], lst[root]
root = child
else:
break</lang>
Testing:
>>> ary = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0] >>> heapsort(ary) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Quackery
<lang Quackery>
[ stack ] is pq ( [ --> [ )
[ pq share swap peek ] is pq.peek ( n --> x )
[ pq take swap poke pq put ] is pq.poke ( n x --> )
[ 1+ 2 / 1 - ] is parent ( n --> n )
[ 0 > ] is has-parent ( n --> b )
[ 2 * 1+ ] is child ( n --> n )
[ child pq share size < ] is has-child ( n --> b )
[ 1+ ] is sibling ( n --> n )
[ sibling pq share size < ] is has-sibling ( n --> b )
[ stack ] is comparison ( [ --> [ )
[ comparison share do ] is pq.compare ( x x --> b )
[ over size
rot 0 join pq put
[ dup has-parent while
dup parent
rot over pq.peek
2dup pq.compare iff
[ 2swap unrot pq.poke ]
again
rot 2drop swap ]
pq.poke pq take ] is toheap ( h x --> h )
( toheap is not used in the heapsort, but
completes the set of heap operations )
[ dup pq.peek swap
[ dup has-child while
dup child
dup has-sibling if
[ dup sibling pq.peek
over pq.peek
pq.compare if sibling ]
dip over dup pq.peek
rot dip dup pq.compare iff
[ rot pq.poke ]
again
2drop ]
pq.poke ] is pq.heapify ( n --> )
[ behead over [] = if done swap -1 split swap join pq put 0 pq.heapify pq take swap ] is fromheap ( h --> h v )
[ dup pq put
size 2 / times
[ i pq.heapify ]
pq take ] is makeheap ( [ --> h )
[ ]'[ comparison put
[] swap makeheap
dup size times
[ fromheap
nested rot join
swap ]
drop
comparison release ] is hsortwith ( [ --> [ )
[ hsortwith > ] is hsort ( [ --> [ )
[] 23 times [ 90 random 10 + join ] say " " dup echo cr say " --> " hsort echo </lang>
Output:
[ 71 62 11 25 15 19 87 91 62 73 89 81 39 12 35 20 25 72 76 20 88 73 82 ] --> [ 11 12 15 19 20 20 25 25 35 39 62 62 71 72 73 73 76 81 82 87 88 89 91 ]
Racket
<lang racket>
- lang racket
(require (only-in srfi/43 vector-swap!))
(define (heap-sort! xs)
(define (ref i) (vector-ref xs i))
(define (swap! i j) (vector-swap! xs i j))
(define size (vector-length xs))
(define (sift-down! r end)
(define c (+ (* 2 r) 1))
(define c+1 (+ c 1))
(when (<= c end)
(define child
(if (and (<= c+1 end) (< (ref c) (ref c+1)))
c+1 c))
(when (< (ref r) (ref child))
(swap! r child))
(sift-down! child end)))
(for ([i (in-range (quotient (- size 2) 2) -1 -1)])
(sift-down! i (- size 1)))
(for ([end (in-range (- size 1) 0 -1)])
(swap! 0 end)
(sift-down! 0 (- end 1)))
xs)
</lang>
Raku
(formerly Perl 6) <lang perl6>sub heap_sort ( @list ) {
for ( 0 ..^ +@list div 2 ).reverse -> $start {
_sift_down $start, @list.end, @list;
}
for ( 1 ..^ +@list ).reverse -> $end {
@list[ 0, $end ] .= reverse;
_sift_down 0, $end-1, @list;
}
}
sub _sift_down ( $start, $end, @list ) {
my $root = $start;
while ( my $child = $root * 2 + 1 ) <= $end {
$child++ if $child + 1 <= $end and [<] @list[ $child, $child+1 ];
return if @list[$root] >= @list[$child];
@list[ $root, $child ] .= reverse;
$root = $child;
}
}
my @data = 6, 7, 2, 1, 8, 9, 5, 3, 4; say 'Input = ' ~ @data; @data.&heap_sort; say 'Output = ' ~ @data;</lang>
- Output:
Input = 6 7 2 1 8 9 5 3 4 Output = 1 2 3 4 5 6 7 8 9
REXX
version 1, elements of an array
This REXX version uses a heapsort to sort elements of an array which is constructed from a list of words or numbers,
or a mixture of both.
Indexing of the array starts with 1 (one), but can be programmed to start with zero. <lang rexx>/*REXX pgm sorts an array (names of epichoric Greek letters) using a heapsort algorithm.*/ parse arg x; call init /*use args or default, define @ array.*/ call show "before sort:" /*#: the number of elements in array*/ call heapSort #; say copies('▒', 40) /*sort; then after sort, show separator*/ call show " after sort:" exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ init: _= 'alpha beta gamma delta digamma epsilon zeta eta theta iota kappa lambda mu nu' ,
"xi omicron pi san qoppa rho sigma tau upsilon phi chi psi omega"
if x= then x= _; #= words(x) /*#: number of words in X*/
do j=1 for #; @.j= word(x, j); end; return /*assign letters to array*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ heapSort: procedure expose @.; arg n; do j=n%2 by -1 to 1; call shuffle j,n; end /*j*/
do n=n by -1 to 2; _= @.1; @.1= @.n; @.n= _; call shuffle 1, n-1
end /*n*/; return /* [↑] swap two elements; and shuffle.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ shuffle: procedure expose @.; parse arg i,n; $= @.i /*obtain parent.*/
do while i+i<=n; j= i+i; k= j+1; if k<=n then if @.k>@.j then j= k
if $>=@.j then leave; @.i= @.j; i= j
end /*while*/; @.i= $; return /*define lowest.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ show: do s=1 for #; say ' element' right(s, length(#)) arg(1) @.s; end; return</lang>
- output when using the default (epichoric Greek alphabet) for input:
(Shown at three-quarter size.)
element 1 before sort: alpha
element 2 before sort: beta
element 3 before sort: gamma
element 4 before sort: delta
element 5 before sort: digamma
element 6 before sort: epsilon
element 7 before sort: zeta
element 8 before sort: eta
element 9 before sort: theta
element 10 before sort: iota
element 11 before sort: kappa
element 12 before sort: lambda
element 13 before sort: mu
element 14 before sort: nu
element 15 before sort: xi
element 16 before sort: omicron
element 17 before sort: pi
element 18 before sort: san
element 19 before sort: qoppa
element 20 before sort: rho
element 21 before sort: sigma
element 22 before sort: tau
element 23 before sort: upsilon
element 24 before sort: phi
element 25 before sort: chi
element 26 before sort: psi
element 27 before sort: omega
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
element 1 after sort: alpha
element 2 after sort: beta
element 3 after sort: chi
element 4 after sort: delta
element 5 after sort: digamma
element 6 after sort: epsilon
element 7 after sort: eta
element 8 after sort: gamma
element 9 after sort: iota
element 10 after sort: kappa
element 11 after sort: lambda
element 12 after sort: mu
element 13 after sort: nu
element 14 after sort: omega
element 15 after sort: omicron
element 16 after sort: phi
element 17 after sort: pi
element 18 after sort: psi
element 19 after sort: qoppa
element 20 after sort: rho
element 21 after sort: san
element 22 after sort: sigma
element 23 after sort: tau
element 24 after sort: theta
element 25 after sort: upsilon
element 26 after sort: xi
element 27 after sort: zeta
- output when using the following for input: 19 0 -.2 .1 1e5 19 17 -6 789 11 37
(Shown at three-quarter size.)
element 1 before sort: 19
element 2 before sort: 0
element 3 before sort: -.2
element 4 before sort: .1
element 5 before sort: 1e5
element 6 before sort: 19
element 7 before sort: 17
element 8 before sort: -6
element 9 before sort: 789
element 10 before sort: 11
element 11 before sort: 37
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
element 1 after sort: -6
element 2 after sort: -.2
element 3 after sort: 0
element 4 after sort: .1
element 5 after sort: 11
element 6 after sort: 17
element 7 after sort: 19
element 8 after sort: 19
element 9 after sort: 37
element 10 after sort: 789
element 11 after sort: 1e5
On an ASCII system, numbers are sorted before letters.
- output when executing on an ASCII system using the following for input: 11 33 22 scotoma pareidolia
element 1 before sort: 11
element 2 before sort: 33
element 3 before sort: 22
element 4 before sort: scotoma
element 5 before sort: pareidolia
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
element 1 after sort: 11
element 2 after sort: 22
element 3 after sort: 33
element 4 after sort: pareidolia
element 5 after sort: scotoma
On an EBCDIC system, numbers are sorted after letters.
- output when executing on an EBCDIC system using the following for input: 11 33 22 scotoma pareidolia
element 1 before sort: 11
element 2 before sort: 33
element 3 before sort: 22
element 4 before sort: scotoma
element 5 before sort: pareidolia
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
element 1 after sort: pareidolia
element 2 after sort: scotoma
element 3 after sort: 11
element 4 after sort: 22
element 5 after sort: 33
version 2
<lang rexx>/* REXX ***************************************************************
- Translated from PL/I
- 27.07.2013 Walter Pachl
- /
list='---letters of the modern Greek Alphabet---|'||,
'==========================================|'||,
'alpha|beta|gamma|delta|epsilon|zeta|eta|theta|'||,
'iota|kappa|lambda|mu|nu|xi|omicron|pi|'||,
'rho|sigma|tau|upsilon|phi|chi|psi|omega'
Do i=0 By 1 While list<>
Parse Var list a.i '|' list
End
n=i-1
Call showa 'before sort' Call heapsort n Call showa ' after sort' Exit
heapSort: Procedure Expose a. Parse Arg count Call heapify count end=count-1 do while end>0 Call swap end,0 end=end-1 Call siftDown 0,end End Return
heapify: Procedure Expose a. Parse Arg count start=(count-2)%2 Do while start>=0 Call siftDown start,count-1 start=start-1 End Return
siftDown: Procedure Expose a.
Parse Arg start,end
root=start
Do while root*2+1<= end
child=root*2+1
sw=root
if a.sw<a.child Then
sw=child
child_1=child+1
if child+1<=end & a.sw<a.child_1 Then
sw=child+1
if sw<>root Then Do
Call swap root,sw
root=sw
End
else
return
End
Return
swap: Procedure Expose a. Parse arg x,y temp=a.x a.x=a.y a.y=temp Return
showa: Procedure Expose a. n Parse Arg txt Do j=0 To n-1 Say 'element' format(j,2) txt a.j End Return</lang>
Output: see PL/I
Ring
<lang ring>
- Project : Sorting algorithms/Heapsort
test = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1] see "before sort:" + nl showarray(test) heapsort(test) see "after sort:" + nl showarray(test)
func heapsort(a) cheapify(a) for e = len(a) to 1 step -1
temp = a[e]
a[e] = a[1]
a[1] = temp
siftdown(a, 1, e-1)
next
func cheapify(a) m = len(a) for s = floor((m - 1) / 2) to 1 step -1
siftdown(a,s,m)
next
func siftdown(a,s,e) r = s while r * 2 + 1 <= e
c = r * 2
if c + 1 <= e
if a[c] < a[c + 1]
c = c + 1
ok
ok
if a[r] < a[c]
temp = a[r]
a[r] = a[c]
a[c] = temp
r = c
else
exit
ok
end
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 heapsort self.dup.heapsort! end
def heapsort!
# in pseudo-code, heapify only called once, so inline it here
((length - 2) / 2).downto(0) {|start| siftdown(start, length - 1)}
# "end" is a ruby keyword
(length - 1).downto(1) do |end_|
self[end_], self[0] = self[0], self[end_]
siftdown(0, end_ - 1)
end
self
end
def siftdown(start, end_)
root = start
loop do
child = root * 2 + 1
break if child > end_
if child + 1 <= end_ and self[child] < self[child + 1]
child += 1
end
if self[root] < self[child]
self[root], self[child] = self[child], self[root]
root = child
else
break
end
end
end
end</lang> Testing:
irb(main):035:0> ary = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0] => [7, 6, 5, 9, 8, 4, 3, 1, 2, 0] irb(main):036:0> ary.heapsort => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Rust
This program allows the caller to specify an arbitrary function by which an order is determined. <lang rust>fn main() {
let mut v = [4, 6, 8, 1, 0, 3, 2, 2, 9, 5];
heap_sort(&mut v, |x, y| x < y);
println!("{:?}", v);
}
fn heap_sort<T, F>(array: &mut [T], order: F) where
F: Fn(&T, &T) -> bool,
{
let len = array.len();
// Create heap
for start in (0..len / 2).rev() {
shift_down(array, &order, start, len - 1)
}
for end in (1..len).rev() {
array.swap(0, end);
shift_down(array, &order, 0, end - 1)
}
}
fn shift_down<T, F>(array: &mut [T], order: &F, start: usize, end: usize) where
F: Fn(&T, &T) -> bool,
{
let mut root = start;
loop {
let mut child = root * 2 + 1;
if child > end {
break;
}
if child + 1 <= end && order(&array[child], &array[child + 1]) {
child += 1;
}
if order(&array[root], &array[child]) {
array.swap(root, child);
root = child
} else {
break;
}
}
}</lang>
Of course, you could also simply use BinaryHeap in the standard library.
<lang rust>use std::collections::BinaryHeap;
fn main() {
let src = vec![6, 2, 3, 6, 1, 2, 7, 8, 3, 2];
let sorted = BinaryHeap::from(src).into_sorted_vec();
println!("{:?}", sorted);
}</lang>
Scala
This code is not written for maximum performance, though, of course, it preserves the O(n log n) characteristic of heap sort. <lang scala>def heapSort[T](a: Array[T])(implicit ord: Ordering[T]) {
import scala.annotation.tailrec // Ensure functions are tail-recursive import ord._ val indexOrdering = Ordering by a.apply
def numberOfLeaves(heapSize: Int) = (heapSize + 1) / 2
def children(i: Int, heapSize: Int) = {
val leftChild = i * 2 + 1
leftChild to leftChild + 1 takeWhile (_ < heapSize)
}
def swap(i: Int, j: Int) = {
val tmp = a(i)
a(i) = a(j)
a(j) = tmp
}
// Maintain partial ordering by bubbling down elements
@tailrec
def siftDown(i: Int, heapSize: Int) {
val childrenOfI = children(i, heapSize)
if (childrenOfI nonEmpty) {
val biggestChild = childrenOfI max indexOrdering
if (a(i) < a(biggestChild)) {
swap(i, biggestChild)
siftDown(biggestChild, heapSize)
}
}
}
// Prepare heap by sifting down all non-leaf elements
for (i <- a.indices.reverse drop numberOfLeaves(a.size)) siftDown(i, a.size)
// Sort from the end of the array forward, by swapping the highest element,
// which is always the top of the heap, to the end of the unsorted array
for (i <- a.indices.reverse) {
swap(0, i)
siftDown(0, i)
}
}</lang>
Scheme
<lang scheme>; swap two elements of a vector (define (swap! v i j)
(define temp (vector-ref v i)) (vector-set! v i (vector-ref v j)) (vector-set! v j temp))
- sift element at node start into place
(define (sift-down! v start end)
(let ((child (+ (* start 2) 1)))
(cond
((> child end) 'done) ; start has no children
(else
(begin
; if child has a sibling node whose value is greater ...
(and (and (<= (+ child 1) end)
(< (vector-ref v child) (vector-ref v (+ child 1))))
; ... then we'll look at the sibling instead
(set! child (+ child 1)))
(if (< (vector-ref v start) (vector-ref v child))
(begin
(swap! v start child)
(sift-down! v child end))
'done))))))
- transform v into a binary max-heap
(define (heapify v)
(define (iter v start)
(if (>= start 0)
(begin (sift-down! v start (- (vector-length v) 1))
(iter v (- start 1)))
'done))
; start sifting with final parent node of v
(iter v (quotient (- (vector-length v) 2) 2)))
(define (heapsort v)
; swap root and end node values,
; sift the first element into place
; and recurse with new root and next-to-end node
(define (iter v end)
(if (zero? end)
'done
(begin
(swap! v 0 end)
(sift-down! v 0 (- end 1))
(iter v (- end 1)))))
(begin
(heapify v)
; start swapping with root and final node
(iter v (- (vector-length v) 1))))
- testing
(define uriah (list->vector '(3 5 7 9 0 8 1 4 2 6))) (heapsort uriah) uriah</lang>
- Output:
done #(0 1 2 3 4 5 6 7 8 9)
Seed7
<lang seed7>const proc: downheap (inout array elemType: arr, in var integer: k, in integer: n) is func
local
var elemType: help is elemType.value;
var integer: j is 0;
begin
if k <= n div 2 then
help := arr[k];
repeat
j := 2 * k;
if j < n and arr[j] < arr[succ(j)] then
incr(j);
end if;
if help < arr[j] then
arr[k] := arr[j];
k := j;
end if;
until help >= arr[j] or k > n div 2;
arr[k] := help;
end if;
end func;
const proc: heapSort (inout array elemType: arr) is func
local
var integer: n is 0;
var integer: k is 0;
var elemType: help is elemType.value;
begin
n := length(arr);
for k range n div 2 downto 1 do
downheap(arr, k, n);
end for;
repeat
help := arr[1];
arr[1] := arr[n];
arr[n] := help;
decr(n);
downheap(arr, 1, n);
until n <= 1;
end func;</lang>
Original source: [1]
SequenceL
<lang sequenceL> import <Utilities/Sequence.sl>;
TUPLE<T> ::= (A: T, B: T);
heapSort(x(1)) := let heapified := heapify(x, (size(x) - 2) / 2 + 1); in sortLoop(heapified, size(heapified));
heapify(x(1), i) := x when i <= 0 else heapify(siftDown(x, i, size(x)), i - 1);
sortLoop(x(1), i) := x when i <= 2 else sortLoop( siftDown(swap(x, 1, i), 1, i - 1), i - 1);
siftDown(x(1), start, end) := let child := start * 2; child1 := child + 1 when child + 1 <= end and x[child] < x[child + 1] else child; in x when child >= end else x when x[start] >= x[child1] else siftDown(swap(x, child1, start), child1, end);
swap(list(1), i, j) := let vals := (A: list[i], B: list[j]); in setElementAt(setElementAt(list, i, vals.B), j, vals.A); </lang>
Sidef
<lang ruby>func sift_down(a, start, end) {
var root = start;
while ((2*root + 1) <= end) {
var child = (2*root + 1);
if ((child+1 <= end) && (a[child] < a[child + 1])) {
child += 1;
}
if (a[root] < a[child]) {
a[child, root] = a[root, child];
root = child;
} else {
return;
}
}
}
func heapify(a, count) {
var start = ((count - 2) / 2);
while (start >= 0) {
sift_down(a, start, count-1);
start -= 1;
}
}
func heap_sort(a, count) {
heapify(a, count);
var end = (count - 1);
while (end > 0) {
a[0, end] = a[end, 0];
end -= 1;
sift_down(a, 0, end)
}
return a
}
var arr = (1..10 -> shuffle); # creates a shuffled array say arr; # prints the unsorted array heap_sort(arr, arr.len); # sorts the array in-place say arr; # prints the sorted array</lang>
- Output:
[10, 5, 2, 1, 7, 6, 4, 8, 3, 9] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Standard ML
Since Standard ML is a functional language, a pairing heap is used instead of a standard binary heap.
<lang sml>(* Pairing heap - http://en.wikipedia.org/wiki/Pairing_heap *) functor PairingHeap(type t
val cmp : t * t -> order) =
struct
datatype 'a heap = Empty
| Heap of 'a * 'a heap list;
(* merge, O(1)
* Merges two heaps *)
fun merge (Empty, h) = h
| merge (h, Empty) = h
| merge (h1 as Heap(e1, s1), h2 as Heap(e2, s2)) =
case cmp (e1, e2) of LESS => Heap(e1, h2 :: s1)
| _ => Heap(e2, h1 :: s2)
(* insert, O(1) * Inserts an element into the heap *) fun insert (e, h) = merge (Heap (e, []), h)
(* findMin, O(1) * Returns the smallest element of the heap *) fun findMin Empty = raise Domain | findMin (Heap(e, _)) = e
(* deleteMin, O(lg n) amortized
* Deletes the smallest element of the heap *)
local
fun mergePairs [] = Empty
| mergePairs [h] = h
| mergePairs (h1::h2::hs) = merge (merge(h1, h2), mergePairs hs)
in
fun deleteMin Empty = raise Domain
| deleteMin (Heap(_, s)) = mergePairs s
end
(* build, O(n) * Builds a heap from a list *) fun build es = foldl insert Empty es;
end
local
structure IntHeap = PairingHeap(type t = int; val cmp = Int.compare); open IntHeap
fun heapsort' Empty = [] | heapsort' h = findMin h :: (heapsort' o deleteMin) h;
in
fun heapsort ls = (heapsort' o build) ls
val test_0 = heapsort [] = [] val test_1 = heapsort [1,2,3] = [1, 2, 3] val test_2 = heapsort [1,3,2] = [1, 2, 3] val test_3 = heapsort [6,2,7,5,8,1,3,4] = [1, 2, 3, 4, 5, 6, 7, 8]
end; </lang>
Stata
Variant with siftup and siftdown, using Mata.
<lang mata>function siftup(a, i) { k = i while (k > 1) { p = floor(k/2) if (a[k] > a[p]) { s = a[p] a[p] = a[k] a[k] = s k = p } else break } }
function siftdown(a, i) { k = 1 while (1) { l = k+k if (l > i) break if (l+1 <= i) { if (a[l+1] > a[l]) l++ } if (a[k] < a[l]) { s = a[k] a[k] = a[l] a[l] = s k = l } else break } }
function heapsort(a) { n = length(a) for (i = 2; i <= n; i++) { siftup(a, i) } for (i = n; i >= 2; i--) { s = a[i] a[i] = a[1] a[1] = s siftdown(a, i-1) } }</lang>
Swift
<lang Swift>func heapsort<T:Comparable>(inout list:[T]) {
var count = list.count
func shiftDown(inout list:[T], start:Int, end:Int) {
var root = start
while root * 2 + 1 <= end {
var child = root * 2 + 1
var swap = root
if list[swap] < list[child] {
swap = child
}
if child + 1 <= end && list[swap] < list[child + 1] {
swap = child + 1
}
if swap == root {
return
} else {
(list[root], list[swap]) = (list[swap], list[root])
root = swap
}
}
}
func heapify(inout list:[T], count:Int) {
var start = (count - 2) / 2
while start >= 0 {
shiftDown(&list, start, count - 1)
start--
}
}
heapify(&list, count)
var end = count - 1
while end > 0 {
(list[end], list[0]) = (list[0], list[end])
end--
shiftDown(&list, 0, end)
}
}</lang>
Tcl
Based on the algorithm from Wikipedia:
<lang tcl>package require Tcl 8.5
proc heapsort {list {count ""}} {
if {$count eq ""} {
set count [llength $list]
}
for {set i [expr {$count/2 - 1}]} {$i >= 0} {incr i -1} {
siftDown list $i [expr {$count - 1}]
}
for {set i [expr {$count - 1}]} {$i > 0} {} {
swap list $i 0 incr i -1 siftDown list 0 $i
} return $list
} proc siftDown {varName i j} {
upvar 1 $varName a
while true {
set child [expr {$i*2 + 1}] if {$child > $j} { break } if {$child+1 <= $j && [lindex $a $child] < [lindex $a $child+1]} { incr child } if {[lindex $a $i] >= [lindex $a $child]} { break } swap a $i $child set i $child
}
} proc swap {varName x y} {
upvar 1 $varName a set tmp [lindex $a $x] lset a $x [lindex $a $y] lset a $y $tmp
}</lang> Demo code: <lang tcl>puts [heapsort {1 5 3 7 9 2 8 4 6 0}]</lang>
- Output:
0 1 2 3 4 5 6 7 8 9
TI-83 BASIC
Store list with a dimension of 7 or less into L1 (if less input will be padded with zeros), run prgmSORTHEAP, look into L2 for the sorted version of L1. It is possible to do this without L3 (thus, in place).
:If dim(L1)>7
:Then
:Disp "ERR:7"
:Stop
:End
:If dim(L1)<7
:Then
:For(A,1,7)
:If A>dim(L1)
:0→L1(A)
:End
:End
:{0}→L2
:For(B,2,7)
:0→L2(B)
:End
:L1→L3
:For(B,0,6)
:If L3(4)>L3(2)
:Then
:L3(2)→A
:L3(4)→L3(2)
:A→L3(4)
:End
:If L3(5)>L3(2)
:Then
:L3(2)→A
:L3(5)→L3(2)
:A→L3(5)
:End
:If L3(6)>L3(3)
:Then
:L3(3)→A
:L3(6)→L3(3)
:A→L3(6)
:End
:If L3(7)>L3(3)
:Then
:L3(3)→A
:L3(7)→L3(3)
:A→L3(7)
:End
:If L3(2)>L3(1)
:Then
:L3(1)→A
:L3(2)→L3(1)
:A→L3(2)
:End
:If L3(3)>L3(1)
:Then
:L3(1)→A
:L3(3)→L3(1)
:A→L3(3)
:End
:L3(1)→L2(7-B)
:If L3(2)>L3(3)
:Then
:L3(2)→L3(1)
:0→L3(2)
:Else
:L3(3)→L3(1)
:0→L3(3)
:End
:End
:DelVar A
:DelVar B
:DelVar L3
:Return
uBasic/4tH
<lang>PRINT "Heap sort:"
n = FUNC (_InitArray) PROC _ShowArray (n) PROC _Heapsort (n) PROC _ShowArray (n)
END
_Heapsort PARAM(1) ' Heapsort
LOCAL(1) PROC _Heapify (a@)
b@ = a@ - 1
DO WHILE b@ > 0
PROC _Swap (b@, 0)
PROC _Siftdown (0, b@)
b@ = b@ - 1
LOOP
RETURN
_Heapify PARAM(1)
LOCAL(1)
b@ = (a@ - 2) / 2
DO WHILE b@ > -1
PROC _Siftdown (b@, a@)
b@ = b@ - 1
LOOP
RETURN
_Siftdown PARAM(2)
LOCAL(2) c@ = a@
DO WHILE ((c@ * 2) + 1) < (b@) d@ = c@ * 2 + 1 IF d@+1 < b@ IF @(d@) < @(d@+1) THEN d@ = d@ + 1 WHILE @(c@) < @(d@) PROC _Swap (d@, c@) c@ = d@ LOOP
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
RETURN</lang>
Vala
<lang vala>void swap(int[] array, int i1, int i2) {
if (array[i1] == array[i2]) return; var tmp = array[i1]; array[i1] = array[i2]; array[i2] = tmp;
}
void shift_down(int[] heap, int i, int max) {
int i_big, c1, c2;
while (i < max) {
i_big = i;
c1 = (2 * i) + 1;
c2 = c1 + 1;
if (c1 < max && heap[c1] > heap[i_big])
i_big = c1;
if (c2 < max && heap[c2] > heap[i_big])
i_big = c2;
if (i_big == i) return;
swap(heap, i, i_big);
i = i_big;
}
}
void to_heap(int[] array) {
int i = (array.length / 2) - 1;
while (i >= 0) {
shift_down(array, i, array.length);
--i;
}
}
void heap_sort(int[] array) {
to_heap(array);
int end = array.length - 1;
while (end > 0) {
swap(array, 0, end);
shift_down(array, 0, end);
--end;
}
}
void main() {
int[] data = {
12, 11, 15, 10, 9,
1, 2, 13, 3, 14,
4, 5, 6, 7, 8
};
heap_sort(data);
foreach (int i in data) {
stdout.printf("%d ", i);
}
}</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
VBA
<lang VBA>Sub SiftDown(list() As Integer, start As Long, eend As Long) Dim root As Long : root = start Dim lb As Long : lb = LBound(list) Dim temp As Integer
While root * 2 + 1 <= eend Dim child As Long : child = root * 2 + 1 If child + 1 <= eend Then If list(lb + child) < list(lb + child + 1) Then child = child + 1 End If End If If list(lb + root) < list(lb + child) Then temp = list(lb + root) list(lb + root) = list(lb + child) list(lb + child) = temp
root = child Else Exit Sub End If Wend End Sub
Sub HeapSort(list() As Integer) Dim lb As Long : lb = LBound(list) Dim count As Long : count = UBound(list) - lb + 1 Dim start As Long : start = (count - 2) \ 2 Dim eend As Long : eend = count - 1
While start >= 0 SiftDown list(), start, eend start = start - 1 Wend
Dim temp As Integer
While eend > 0 temp = list(lb + eend) list(lb + eend) = list(lb) list(lb) = temp
eend = eend - 1
SiftDown list(), 0, eend Wend End Sub</lang>
Wren
<lang ecmascript>var siftDown = Fn.new { |a, start, end|
var root = start
while (root*2 + 1 <= end) {
var child = root*2 + 1
if (child + 1 <= end && a[child] < a[child+1]) child = child + 1
if (a[root] < a[child]) {
var t = a[root]
a[root] = a[child]
a[child] = t
root = child
} else {
return
}
}
}
var heapify = Fn.new { |a, count|
var start = ((count - 2)/2).floor
while (start >= 0) {
siftDown.call(a, start, count - 1)
start = start - 1
}
}
var heapSort = Fn.new { |a|
var count = a.count
heapify.call(a, count)
var end = count - 1
while (end > 0) {
var t = a[end]
a[end] = a[0]
a[0] = t
end = end - 1
siftDown.call(a, 0, end)
}
}
var as = [ [4, 65, 2, -31, 0, 99, 2, 83, 782, 1], [7, 5, 2, 6, 1, 4, 2, 6, 3] ] for (a in as) {
System.print("Before: %(a)")
heapSort.call(a)
System.print("After : %(a)")
System.print()
}</lang>
- Output:
Before: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1] After : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782] Before: [7, 5, 2, 6, 1, 4, 2, 6, 3] After : [1, 2, 2, 3, 4, 5, 6, 6, 7]
Alternatively, we can just call a library method.
<lang ecmascript>import "/sort" for Sort
var as = [ [4, 65, 2, -31, 0, 99, 2, 83, 782, 1], [7, 5, 2, 6, 1, 4, 2, 6, 3] ] for (a in as) {
System.print("Before: %(a)")
Sort.heap(a)
System.print("After : %(a)")
System.print()
}</lang>
- Output:
As above.
zkl
<lang zkl>fcn heapSort(a){ // in place
n := a.len();
foreach start in ([(n-2)/2 .. 0,-1])
{ siftDown(a, start, n-1) }
foreach end in ([n-1 .. 1,-1]){
a.swap(0, end);
siftDown(a, 0, end-1);
}
a
}
fcn siftDown(a, start, end){
while((child := start*2 + 1) <= end){
if(child < end and a[child]<a[child+1]) child+=1;
if(a[start] >= a[child]) return();
a.swap(start, child);
start = child;
}
}</lang> <lang zkl>heapSort(L(170, 45, 75, -90, -802, 24, 2, 66)).println(); heapSort("this is a test".split("")).println();</lang>
- Output:
L(-802,-90,2,24,45,66,75,170)
L(" "," "," ","a","e","h","i","i","s","s","s","t","t","t")
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