Heap Sort is a comparison-based sorting algorithm that uses a binary heap data structure to efficiently sort a given list or array of elements. The algorithm works in two major steps: building the heap and extracting elements from the heap. Here's a step-by-step description of how Heap Sort works:

    Building the Heap:
    a. Convert the input array into a binary max-heap. A max-heap is a binary tree in which each parent node has a value greater than or equal to the values of its children.
    b. Start from the middle of the array and move towards the first element. For each element, apply the 'heapify' procedure to ensure the subtree rooted at that element follows the max-heap property.
    c. Repeat the heapify process until the entire array forms a max-heap.

    Extracting Elements from the Heap:
    a. Swap the first element (which is the maximum value) of the heap with the last element of the unsorted part of the array.
    b. Decrease the size of the unsorted part of the array by one.
    c. Apply the heapify procedure to the first element, ensuring that the remaining unsorted elements still form a max-heap.
    d. Repeat steps a-c until the unsorted part of the array becomes empty.

At the end of this process, the input array will be sorted in ascending order. Heap Sort has a time complexity of O(n log n) for both the average and worst-case scenarios, which makes it an efficient sorting algorithm for large datasets. However, due to its relatively lower cache performance compared to other sorting algorithms like Quick Sort, Heap Sort may not be the most suitable choice for smaller datasets or when cache performance is a priority.
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