Explain the heap sort algorithm.

Heap sort is a comparison-based sorting algorithm that utilizes the concept of a binary heap data structure to sort elements in an array. It is an efficient and in-place sorting algorithm with a time complexity of O(n log n), making it suitable for large datasets.

The heap sort algorithm consists of two main steps: building a heap and extracting the maximum element repeatedly.

1. Building a Heap:
- Initially, the array is considered as a complete binary tree.
- Starting from the last non-leaf node (n/2 - 1), where n is the total number of elements in the array, we perform a heapify operation.
- Heapify operation ensures that the parent node is greater than its children in a max heap or smaller in a min heap.
- We repeat the heapify operation for each non-leaf node in a bottom-up manner until the entire array is transformed into a heap.

2. Extracting the Maximum Element:
- The maximum element in the heap is always at the root node (index 0).
- We swap this element with the last element in the heap and reduce the heap size by one.
- After the swap, the maximum element is at the end of the array, and the heap property is violated.
- To restore the heap property, we perform a heapify operation on the reduced heap (excluding the last element).
- We repeat this process until all elements are extracted and the array is sorted in ascending order.

The key idea behind heap sort is that the largest (or smallest) element is always at the root of the heap. By repeatedly extracting the maximum element and heapifying the remaining elements, we can efficiently sort the array.

Heap sort has several advantages:
- It has a guaranteed worst-case time complexity of O(n log n), making it efficient for large datasets.
- It is an in-place sorting algorithm, meaning it does not require additional memory apart from the input array.
- It is not sensitive to the initial order of elements, making it suitable for a wide range of scenarios.

However, heap sort also has some limitations:
- It is not a stable sorting algorithm, meaning it may change the relative order of equal elements.
- The constant factors involved in heap sort are typically larger than other efficient sorting algorithms like quicksort or mergesort.

In conclusion, heap sort is a comparison-based sorting algorithm that utilizes the binary heap data structure to efficiently sort elements in an array. It offers a guaranteed worst-case time complexity of O(n log n) and is suitable for large datasets.