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# Heap Sort Algorithm

Heap sort is one of the sorting algorithms used to arrange a list of elements in order. Heapsort algorithm uses one of the tree concepts called Heap Tree. In this sorting algorithm, we use Max Heap to arrange list of elements in Descending order and Min Heap to arrange list elements in Ascending order.

Step by Step Process

The Heap sort algorithm to arrange a list of elements in ascending order is performed using following steps...

• Step 1 - Construct a Binary Tree with given list of Elements.
• Step 2 - Transform the Binary Tree into Min Heap.
• Step 3 - Delete the root element from Min Heap using Heapify method.
• Step 4 - Put the deleted element into the Sorted list.
• Step 5 - Repeat the same until Min Heap becomes empty.
• Step 6 - Display the sorted list.

Example

Complexity of the Heap Sort Algorithm

To sort an unsorted list with 'n' number of elements, following are the complexities...

Worst Case : O(n log n)
Best Case : O(n log n)
Average Case : O(n log n)

# Implementaion of Heap Sort Algorithm using C++ Programming Language

``````#include<iostream>
#include<cmath>

using namespace std;

int find_min_element_index(int a[] , int element , int left_child , int right_child){
if(a[element] <= a[left_child] && a[element] <= a[right_child])
return element;

if(a[left_child] <= a[element] && a[left_child] <= a[right_child])
return left_child;

if(a[right_child] <= a[element] && a[right_child] <= a[left_child])
return right_child;
}

int check_heap(int a[] , int n){

int second_last_level = (int)log2(n);

int check_elements_upto_index = pow( 2 , second_last_level+1)-2;
for(int i=0; i<=check_elements_upto_index; i++){

if(2*i+1 <= n-1 || 2*i+2 <= n-1){
if(2*i+1 <= n-1 && 2*i+2 <= n-1){
if(a[i] <= a[2*i+1] && a[i] <= a[2*i+2])
continue;
else
return 0;
}
else if(2*i+1 <= n-1){
if(a[i] <= a[2*i+1])
continue;
else
return 0;
}
else{
if(a[i] <= a[2*i+2])
continue;
else
return 0;
}
}
else{
break;
}
}
return 1;
}

void heapify(int a[] , int n){
int heap_flag = 0;
while(heap_flag == 0){
int level = (int)log2(n);
int ending_index_at_corresponding_level = pow(2 ,level+1)-2;
for(int i = ending_index_at_corresponding_level;i >= 0 ;i--){
if(2*i+1 <= n-1 || 2*i+2 <= n-1){
if(2*i+1 <= n-1 && 2*i+2 <= n-1){
int min_index = find_min_element_index(a , i , 2*i+1 , 2*i+2);
if(min_index == i){
continue;
}
else{
int temp = a[min_index];
a[min_index] = a[i];
a[i] = temp;
}
}
else if( 2*i+1 <= n-1){
if(a[i] <= a[2*i+1])
continue;
else{
int temp = a[i];
a[i] = a[2*i+1];
a[2*i+1] = temp;
}
}
else{
if(a[i] <= a[2*i+2])
continue;
else{
int temp = a[i];
a[i] = a[2*i+2];
a[2*i+2] = temp;
}
}
}
}

heap_flag = check_heap(a , n);
if(heap_flag == 1){
cout << a[0] <<", ";
int temp = a[0];
a[0] = a[n-1];
a[n-1] = temp;
n = n-1;
}
if(n==1){
cout <<a[0] <<", ";
break;
}

heap_flag = check_heap(a , n);
}
}

int main(){
int list[] = {6,8,7,9,1,4,3,2,5,0};
cout<<endl<<"List of Elements before sort: ";
for(int i = 0; i<10; i++)
cout<<list[i]<<", ";
cout <<endl<<endl<<"Sorted Output as Follows : ";
heapify(list , 10);
cout<<endl;
}```
```

Output