A heap sort is a sorting algorithm that utilizes a special type of data structure called a heap. In this article, we will explore the various data structures that can be built using a heap sort.

## What is a Heap Sort?

A heap sort is an efficient comparison-based sorting algorithm that divides the input array into two regions: the sorted region and the unsorted region. The algorithm repeatedly selects the maximum (or minimum) element from the unsorted region and places it at the end of the sorted region. This process continues until the entire array is sorted.

## The Heap Data Structure

A heap is a complete binary tree where each node satisfies the heap property. The heap property states that for every node, its value must be greater (or smaller) than its children’s values, depending on whether it’s a max-heap or a min-heap.

### Max-Heap

In a max-heap, each parent node has a value greater than or equal to its children’s values. This means that the root node of a max-heap contains the maximum element in the tree.

### Min-Heap

In contrast, in a min-heap, each parent node has a value less than or equal to its children’s values. Therefore, the root node of a min-heap contains the minimum element in the tree.

## Data Structures Built with Heap Sort

### 1. Priority Queue

A priority queue is an abstract data type that allows efficient access to and removal of elements based on their priority. A common implementation of priority queue uses a min-heap or max-heap to prioritize elements based on their values.

**Max-Priority Queue:**A max-heap can be used to implement a max-priority queue, where the element with the highest priority (largest value) is always at the front of the queue.**Min-Priority Queue:**Conversely, a min-heap can be used to implement a min-priority queue, where the element with the lowest priority (smallest value) is always at the front of the queue.

### 2. Heap-Based Sorting Algorithms

Heap sort itself is an example of a sorting algorithm that can be built using a heap. By constructing a max-heap from the input array and repeatedly extracting the maximum element, we achieve an efficient sorting mechanism with a time complexity of O(n log n).

## Conclusion

A heap sort utilizes a heap data structure to efficiently sort an array. Additionally, heaps can be used to build other data structures such as priority queues. Understanding how heap sort works and its relationship to heaps can greatly enhance your understanding of sorting algorithms and data structures.

In summary, heap sort can be used to build data structures like priority queues and is itself an efficient sorting algorithm. By incorporating elements such as max-heaps and min-heaps, you can optimize your code for specific use cases.