## What Is Heap Tree in Data Structure?

In the realm of data structures, a heap tree is a specialized tree-based data structure that satisfies the heap property. A heap is commonly used to implement priority queues and provides efficient solutions for various applications, such as sorting algorithms like heapsort.

Let’s dive deeper into understanding the concept of a heap tree.

### The Heap Property

The heap property defines the ordering between elements in a heap. In a max heap, for example, every parent node has a value greater than or equal to its children.

On the other hand, in a min heap, every parent node has a value less than or equal to its children. This property ensures that the highest (or lowest) priority element is always at the root of the tree.

### Complete Binary Tree Structure

A heap tree is structured as a complete binary tree. This means that all levels of the tree are fully filled, except possibly for the last level which is filled from left to right.

The complete binary tree structure allows us to efficiently represent a heap using an array.

### Array Representation

The array representation of a heap utilizes the fact that we can compute the index of any node’s parent or children based on its own index. By storing elements in an array and following certain indexing rules, we can access and manipulate elements within the heap without explicitly defining pointers or references between nodes.

### Operations on Heap Trees

**Insertion:**To insert an element into a heap, we first add it at the last position of the array and then “bubble up” the element until the heap property is satisfied.**Deletion:**To remove an element from a heap, we typically want to remove the root node. After removal, we replace it with the last element in the array and “bubble down” this element until the heap property is restored.**Heapify:**Heapify is an operation that converts an unordered array into a heap.It rearranges elements in a way that satisfies the heap property.

**Extract Max (or Min):**This operation extracts and returns the maximum (or minimum) value from a max (or min) heap, respectively. It also ensures that the heap property is maintained after extraction.

### Applications of Heap Trees

Heap trees find applications in various scenarios where efficient handling of priority-based operations is required. Some notable applications include:

__Priority Queues:__A priority queue stores elements with associated priorities and provides access to the highest-priority element at any given time.__Heap Sort:__Heapsort is an in-place sorting algorithm that uses a heap to sort elements in ascending or descending order efficiently.__Dijkstra’s Algorithm:__Dijkstra’s algorithm uses a min heap to efficiently find the shortest path between nodes in a graph.

### In Conclusion

A heap tree is a powerful data structure that combines tree-like properties with efficient array representation. Its ability to efficiently manipulate priority-based elements makes it invaluable for various applications.

Understanding how heaps work and implementing them can greatly enhance your ability to solve problems that involve prioritization and sorting.