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:
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 Sorting algorithms/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]) (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 := end - 1 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.
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>
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>
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)
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>
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>
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>
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
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]
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]
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:
<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