Heap Sort in Data Structure

Heap Sort

  • Heap sort is a comparison based sorting algorithm.
  • It is a special tree-based data structure.
  • Heap sort is similar to selection sort. The only difference is, it finds largest element and places the it at the end.
  • This sort is not a stable sort. It requires a constant space for sorting a list.
  • It is very fast and widely used for sorting.
It has following two properties:

1. Shape Property
2. Heap Property

1. Shape property represents all the nodes or levels of the tree are fully filled. Heap data structure is a complete binary tree.

sheap property

2. Heap property is a binary tree with special characteristics. It can be classified into two types:

I. Max-Heap
II. Min Heap

I. Max Heap: If the parent nodes are greater than their child nodes, it is called a Max-Heap.

II. Min Heap: If the parent nodes are smaller than their child nodes, it is called a Min-Heap.

heap property

Example: Program for Heap Sort

#include <stdio.h>
void main()
{
    int heap[10], no, i, j, c, root, temp;  
    printf("\n Enter no of elements :");
    scanf("%d", &no);
    printf("\n Enter the nos : ");
    for (i = 0; i < no; i++)
       scanf("%d", &heap[i]);
    for (i = 1; i < no; i++)
    {
        c = i;
        do
        {
            root = (c - 1) / 2;             
            if (heap[root] < heap[c])   /* to create MAX heap array */
            {
                temp = heap[root];
                heap[root] = heap[c];
                heap[c] = temp;
            }
            c = root;
        } while (c != 0);
    }  
    printf("Heap array : ");
    for (i = 0; i < no; i++)
        printf("%d\t ", heap[i]);
    for (j = no - 1; j >= 0; j--)
    {
        temp = heap[0];
        heap[0] = heap[j];    /* swap max element with rightmost leaf element */
        heap[j] = temp;
        root = 0;
        do
        {
            c = 2 * root + 1;    /* left node of root element */
            if ((heap[c] < heap[c + 1]) && c < j-1)
                c++;
            if (heap[root]<heap[c] && c<j)    /* again rearrange to max heap array */
            {
                temp = heap[root];
                heap[root] = heap[c];
                heap[c] = temp;
            }
            root = c;
        } while (c < j);
    }
    printf("\n The sorted array is : ");
    for (i = 0; i < no; i++)
       printf("\t %d", heap[i]);
    printf("\n Complexity : \n Best case = Avg case = Worst case = O(n logn) \n");
}


Output:

heap sort
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