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