First Journal

Cuneyt Yildirim | Nov 16, 2025 min read

Heap Sort

Posted 2025-11-16 | *By : Cuneyt Yildirim *# Heap Sort

Problem Statement

Given an unsorted array of n elements, write a function to sort the array

Approach

  • Build a max heap from the input data.
  • At this point, the largest item is stored at the root of the heap. Replace it with the last item of the heap followed by reducing the size of heap by 1. Finally, heapify the root of tree.
  • Repeat above steps while size of heap is greater than 1.

Time Complexity

O(n log n) Worst case performance

O(n log n) (distinct keys) or O(n) (equal keys) Best-case performance

O(n log n) Average performance

Space Complexity

O(1) Worst case auxiliary

Example

Input data: 4, 10, 3, 5, 1
        4(0)
       /   \
    10(1)   3(2)
   /   \
5(3)    1(4)

The numbers in bracket represent the indices in the array
representation of data.

Applying heapify procedure to index 1:
        4(0)
       /   \
   10(1)    3(2)
   /   \
5(3)    1(4)

Applying heapify procedure to index 0:
       10(0)
       /  \
    5(1)  3(2)
   /   \
4(3)    1(4)
The heapify procedure calls itself recursively to build heap
in top down manner.

heap-image

Video Explanation

A video explaining the Heap Sort Algorithm