**What Is Heapsort in Data Structure?**

Heapsort is a comparison-based sorting algorithm that falls under the category of in-place sorting algorithms. It was first introduced by J. W. J. Williams in 1964. Heapsort is known for its efficiency and stability, making it a popular choice for sorting large datasets.

## How does Heapsort work?

Heapsort operates by first building a binary heap from the input array and then repeatedly extracting the maximum element from the heap and placing it at the end of the sorted array. The process continues until all elements are extracted and placed in their correct order.

### Building a Heap

To build a heap, we start with an unsorted array of elements and convert it into a binary heap. A binary heap is a complete binary tree where each parent node is greater than or equal to its child nodes (in case of a max heap) or lesser than or equal to its child nodes (in case of a min heap).

The process of building a max heap involves iterating through the array from right to left and performing “heapify” operations on each element. Heapify operation compares the parent node with its children and swaps them if necessary to maintain the heap property.

<ul><li>Start with an unsorted array.</li><li>Convert it into a binary heap by applying "heapify" operations.</li><li>Repeat until all elements have been processed.</li></ul>

### Sorting the Heap

Once the binary heap is built, the sorting process begins. The maximum element (root) is extracted from the heap and placed at the end of the array. This step is repeated for each remaining element in the heap, resulting in a sorted array.

<ul><li>Extract the maximum element (root) from the heap.</li><li>Swap it with the last element in the array.</li><li>Reduce the size of the heap by one.</li><li>Perform "heapify" operation on the root to maintain heap property.</li><li>Repeat until all elements have been extracted and sorted.</li></ul>

## Advantages of Heapsort

__Efficient:__

Heapsort has an average and worst-case time complexity of O(n log n), making it efficient for sorting large datasets. Additionally, Heapsort requires only a constant amount of additional memory space, making it an in-place sorting algorithm.

__Stable:__

In comparison to other sorting algorithms like Quicksort or Mergesort, Heapsort is a stable sorting algorithm. This means that elements with equal keys maintain their relative order after sorting.

## Conclusion

Heapsort is a powerful sorting algorithm that efficiently sorts large datasets. Its stability and in-place nature make it a popular choice among programmers for various applications. By understanding the process of building a heap and sorting it, you can leverage Heapsort to efficiently sort your own datasets.