Sorting algorithms/Heapsort

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

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
     input:  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.

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