Sorting algorithms/Heapsort: Difference between revisions

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siftDown(seq, 0, end - 1);
siftDown(seq, 0, end - 1);
}
}
}

void main() {
auto arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0];
inplaceHeapSort(arr);
writeln(arr);
}</lang>
===Using Standard Functions===
<lang d>import std.stdio, std.container;

void inplaceHeapSort(T)(T[] data) {
auto h = heapify(data);
while (!h.empty)
h.removeFront();
}
}


Revision as of 14:18, 16 June 2012

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

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

O(n logn) sorts

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. Heapsort 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.

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>

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>

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>

  1. include <stdlib.h>
  1. define ValType double
  2. define IS_LESS(v1, v2) (v1 < v2)

void siftDown( ValType *a, int start, int count);

  1. define SWAP(r,s) do{ValType t=r; r=s; s=t; } while(0)

void heapsort( ValType *a, int count) { 

   int start, end;

   /* heapify */
   for (start = (count-2)/2; start >=0; start--) {
       siftDown( a, start, count);
   }

   for (end=count-1; end > 0; end--) {
       SWAP(a[end],a[0]);
       siftDown(a, 0, end);
   }

}

void siftDown( ValType *a, int start, int end) { 

   int root = start;

   while ( root*2+1 < end ) {
       int child = 2*root + 1;
       if ((child + 1 < end) && IS_LESS(a[child],a[child+1])) {
           child += 1;
       }
       if (IS_LESS(a[root], a[child])) {
           SWAP( a[child], a[root] );
           root = child;
       }
       else
           return;
   }

}


int main() { 

   int ix;
   double valsToSort[] = {
       1.4, 50.2, 5.11, -1.55, 301.521, 0.3301, 40.17,
       -18.0, 88.1, 30.44, -37.2, 3012.0, 49.2};
  1. define VSIZE (sizeof(valsToSort)/sizeof(valsToSort[0]))
   heapsort(valsToSort, VSIZE);
   printf("{");
   for (ix=0; ix<VSIZE; ix++) printf(" %.3f ", valsToSort[ix]);
   printf("}\n");
   return 0;

}</lang>

C++

The easiest way is to use the make_heap and sort_heap standard library functions. <lang cpp>#include <iostream>

  1. include <algorithm> // for std::make_heap, std::sort_heap

template <typename Iterator> void heapsort(Iterator begin, Iterator end) { 

   std::make_heap(begin, end);
   std::sort_heap(begin, end);

}

int main() { 

   double valsToSort[] = {
       1.4, 50.2, 5.11, -1.55, 301.521, 0.3301, 40.17,
       -18.0, 88.1, 30.44, -37.2, 3012.0, 49.2};
   const int VSIZE = sizeof(valsToSort)/sizeof(*valsToSort);

   heapsort(valsToSort, valsToSort+VSIZE);
   for (int ix=0; ix<VSIZE; ix++) std::cout << valsToSort[ix] << std::endl;
   return 0;

}</lang> If you want to be slightly more verbose <lang cpp>#include <iostream>

  1. include <algorithm> // for std::make_heap, std::pop_heap

template <typename Iterator> void heapsort(Iterator begin, Iterator end) { 

   std::make_heap(begin, end);
   while (begin != end)
       std::pop_heap(begin, end--);

}</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>

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>

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.algorithm;

void inplaceHeapSort(R)(R seq) pure nothrow { 

  static void siftDown(R seq, in size_t start,
                       in size_t end) pure nothrow {
     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 (start; 1 .. (seq.length - 2) / 2 + 2)
        siftDown(seq, start - 1, seq.length - 1);

  foreach_reverse (end; 1 .. seq.length) {
     swap(seq[end], seq[0]);
     siftDown(seq, 0, end - 1);
  }

}

void main() { 

  auto arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0];
  inplaceHeapSort(arr);
  writeln(arr);

}</lang>

Using Standard Functions

<lang d>import std.stdio, std.container;

void inplaceHeapSort(T)(T[] data) { 

   auto h = heapify(data);
   while (!h.empty)
       h.removeFront();

}

void main() { 

  auto arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0];
  inplaceHeapSort(arr);
  writeln(arr);

}</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>

E

Translation of: Python

<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>

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>

Fortran

Works with: Fortran version 90 and later

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) .and. (a(child) < a(child+1))) then
     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>

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>

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

Generally, this task should be accomplished in J using /:~. Here we take an approach that's more comparable with the other examples on this page.

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>

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>

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>

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>

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

Objeck

Translation of: Java

<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

Translation of the pseudocode. <lang perl>my @my_list = (2,3,6,23,13,5,7,3,4,5); heap_sort(\@my_list); print "@my_list\n"; exit;

sub heap_sort { 

       my($list) = @_;
       my $count = scalar @$list;
       heapify($count,$list);

       my $end = $count - 1;
       while($end > 0)
       {
               @$list[0,$end] = @$list[$end,0];
               sift_down(0,$end-1,$list);
               $end--;
       }

} sub heapify { 

       my ($count,$list) = @_;
       my $start = ($count - 2) / 2;
       while($start >= 0)
       {
               sift_down($start,$count-1,$list);
               $start--;
       }

} sub sift_down { 

       my($start,$end,$list) = @_;

       my $root = $start;
       while($root * 2 + 1 <= $end)
       {
               my $child = $root * 2 + 1;
               $child++ if($child + 1 <= $end && $list->[$child] < $list->[$child+1]);
               if($list->[$root] < $list->[$child])
               {
                       @$list[$root,$child] = @$list[$child,$root];
                       $root = $child;
               }else{ return }
       }

}</lang>

Perl 6

<lang perl6>sub heap_sort ( @list is rw ) { 

   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 is rw ) { 

   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

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)

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]

REXX

<lang rexx>/*REXX program sorts an array using the heapsort method. */ call gen@ /*generate array elements. */ call show@ 'before sort' /*show before array elements*/ call heapSort highItem /*invoke the heap sort. */ call show@ ' after sort' /*show after array elements*/ exit /*─────────────────────────────────────HEAPSORT subroutine─────────*/ heapSort: procedure expose @.; parse arg n 

       do j=n%2 by -1 to 1
       call shuffle j,n
       end

 do n=n by -1 to 2
 _=@.1;  @.1=@.n;  @.n=_;  call shuffle 1,n
 end

return /*─────────────────────────────────────SHUFFLE subroutine──────────*/ shuffle: procedure expose @.; parse arg i,n; _=@.i 

 do while i+i<=n
 j=i+i;  k=j+1
 if k<=n & @.k>@.j then j=k
 if _>=@.j then leave
 @.i=@.j;  i=j
 end

@.i=_ return /*─────────────────────────────────────GEN@ subroutine─────────────*/ gen@: @.= /*assign default value. */ @.1 ='---letters of the modern Greek Alphabet---' @.2 ='==========================================' @.3 ='alpha' @.4 ='beta' @.5 ='gamma' @.6 ='delta' @.7 ='epsilon' @.8 ='zeta' @.9 ='eta' @.10='theta' @.11='iota' @.12='kappa' @.13='lambda' @.14='mu' @.15='nu' @.16='xi' @.17='omicron' @.18='pi' @.19='rho' @.20='sigma' @.21='tau' @.22='upsilon' @.23='phi' @.24='chi' @.25='psi' @.26='omega' 

 do highItem=1 while @.highItem\==  /*find how many entries.    */
 end

highItem=highItem-1 /*adjust highItem slightly. */ return /*─────────────────────────────────────SHOW@ subroutine────────────*/ show@: widthH=length(highItem) /*maximum width of any line.*/ 

 do j=1 for highItem
 say 'element' right(j,widthH) arg(1)':' @.j
 end

say copies('─',80) /*show a separator line. */ return</lang>

Output:
element  1 before sort: ---letters of the modern Greek Alphabet---
element  2 before sort: ==========================================
element  3 before sort: alpha
element  4 before sort: beta
element  5 before sort: gamma
element  6 before sort: delta
element  7 before sort: epsilon
element  8 before sort: zeta
element  9 before sort: eta
element 10 before sort: theta
element 11 before sort: iota
element 12 before sort: kappa
element 13 before sort: lambda
element 14 before sort: mu
element 15 before sort: nu
element 16 before sort: xi
element 17 before sort: omicron
element 18 before sort: pi
element 19 before sort: rho
element 20 before sort: sigma
element 21 before sort: tau
element 22 before sort: upsilon
element 23 before sort: phi
element 24 before sort: chi
element 25 before sort: psi
element 26 before sort: omega
────────────────────────────────────────────────────────────────────────────────
element  1  after sort: eta
element  2  after sort: ==========================================
element  3  after sort: chi
element  4  after sort: beta
element  5  after sort: delta
element  6  after sort: ---letters of the modern Greek Alphabet---
element  7  after sort: theta
element  8  after sort: iota
element  9  after sort: omicron
element 10  after sort: lambda
element 11  after sort: omega
element 12  after sort: kappa
element 13  after sort: nu
element 14  after sort: mu
element 15  after sort: epsilon
element 16  after sort: alpha
element 17  after sort: phi
element 18  after sort: pi
element 19  after sort: psi
element 20  after sort: rho
element 21  after sort: sigma
element 22  after sort: tau
element 23  after sort: gamma
element 24  after sort: upsilon
element 25  after sort: xi
element 26  after sort: zeta
────────────────────────────────────────────────────────────────────────────────

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]

Scala

Works with: Scala version 2.8

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

Works with: Scheme version RRS

<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]

Tcl

Based on the algorithm from Wikipedia:

Works with: Tcl version 8.5

<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), but I coded this when I was paying attention to a math lecture. Could you make a better version that accepts any input, without having to use my clunky If structure? Could you make it 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
Retrieved from "https://rosettacode.org/wiki/Sorting_algorithms/Heapsort?oldid=120600"