# Heap Sort

Heap sort is performed on the heap data structure. We know that heap is a complete binary tree. Heap tree can be of two types. Min-heap or max heap. For min heap the root element is minimum and for max heap the root is maximum. After forming a heap, we can delete an element from the root and send the last element to the root. After these swapping procedure, we need to re-heap the whole array. By deleting elements from root we can sort the whole array.

## The complexity of Heap Sort Technique

• Time Complexity: O(n log n)
• Space Complexity: O(1)

## Input and Output

Input:
A list of unsorted data: 30 8 99 11 24 39
Output:
Array before Sorting: 30 8 99 11 24 39
Array after Sorting: 8 11 24 30 39 99

## Algorithm

heapify(array, size)

Input − An array of data, and the total number in the array

Output − The max heap using an array element

Begin
for i := 1 to size do
node := i
par := floor (node / 2)
while par >= 1 do
if array[par] < array[node] then
swap array[par] with array[node]
node := par
par := floor (node / 2)
done
done
End

heapSort(array, size)

## Input: An array of data, and the total number in the array

Output −nbsp;sorted array

Begin
for i := n to 1 decrease by 1 do
heapify(array, i)
swap array[1] with array[i]
done
End

## Example

#include<iostream>
using namespace std;

void display(int *array, int size) {
for(int i = 1; i<=size; i++)
cout << array[i] << " ";
cout << endl;
}

void heapify(int *array, int n) {
int i, par, l, r, node;
// create max heap

for(i = 1; i<= n; i++) {
node = i; par = (int)node/2;
while(par >= 1) {
//if new node bigger than parent, then swap
if(array[par] < array[node])
swap(array[par], array[node]);
node = par;
par = (int)node/2;//update parent to check
}
}
}

void heapSort(int *array, int n) {
int i;

for(i = n; i>= 1; i--) {
heapify(array, i);//heapify each time
swap(array[1], array[i]);//swap last element with first
}
}

int main() {
int n;
cout << "Enter the number of elements: ";
cin >> n;
int arr[n+1]; //effective index starts from i = 1.
cout << "Enter elements:" << endl;

for(int i = 1; i<=n; i++) {
cin >> arr[i];
}

cout << "Array before Sorting: ";
display(arr, n);
heapSort(arr, n);
cout << "Array after Sorting: ";
display(arr, n);
}

## Output

Enter the number of elements: 6
Enter elements:
30 8 99 11 24 39
Array before Sorting: 30 8 99 11 24 39
Array after Sorting: 8 11 24 30 39 99

Updated on: 15-Jun-2020

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