Introduction to Heaps in Data structure

Heap: What is it?

A binary tree with all levels filled up except for the leaf node, which is the final level, is said to be complete.

Heap Sort Algorithm: What Is It?

 The "heap sort" sorting method creates a min- or max-heap for each element using the given array. The root element's value will correspond to the minimum or maximum element of the array depending on how the array is ordered, as shown by the min-heap or max-heap.

A heap sort's basic principle is to take each element out of the heap one at a time before re-inserting them in a heap in the appropriate order.

How can a tree be "heapified"?

Therefore, we can change the tree to either the maximum or minimum heap. In other words, the heapify process involves converting a binary tree into a heap tree.

Working of Heap sort:

In the heap sort procedure, the elements are sorted twice. Here are a few examples:

We'll create a heap by changing the elements of the array in the first step.

Create the heap, then repeatedly delete the root element by trading it with the last element of the array.

Heap sort is typically used to teach heap data structures. Since quicksort outperforms heap sort in most situations, the heap sort algorithm is used less frequently. Several uses for the heap include the following:

Priority Queue: The priority queue is effectively built using a heap. Either insert and extract the element with priority in the O time complexity, or it is simple to insert, remove, and identify priority items (log n).

Algorithms for Graphs: Heap Graph algorithms like Dijkstra's and prim's algorithms also employ implemented priority queues.

Order Statistics: Finding the kth largest/smallest element in the array is simple using heap data structures. Visit the data structure course to gain in-depth understanding of the Heap concepts in a practical way. 

Embedded System: In embedded systems like the Linux kernel and security-related systems, we can employ the heap data structure effectively. 

Heap Structure

A complete binary tree with some properties is called a heap. On the basis of the property, there are two different sorts of heaps.

Max-Heap: Any node's key must be bigger than the keys found at both of its children. The root node contains the biggest key.

Min-Heap: Any node's key must be less powerful than the keys at both of its descendants. The root node contains the smallest key.

Complete Binary Tree - A tree with all keys still present but perhaps the last level and the last level being totally filled.

Array Representation

An array is used to represent a binary heap. The representation follows some properties.

At Arr[0], the tree's root will be located.

The left and right children of any node at Arr[i] will be at Arr[2*i + 1] and Arr[2*i+2], respectively.

Any node at Arr[i] will have an associated parent node at Arr[(i-1)/2].

Why Array?

A Binary Heap can be easily represented as an array because it is a Complete Binary Tree, and array-based representation saves space.

Rank Order -  The order in which the elements are added to the array will be revealed by traversing the heap.

Applications of Heap in Data Structures

Heap Sort: Heap Sort sorts an array in O using Binary Heap (nlogn).

Priority Queue: It efficiently implements insert(), delete(), extract max(), and update() operations in O(logn) time by using a binary heap.

Graph algorithms: Dijkstra's algorithm and minimum spanning tree are two examples of graph algorithms that use heaps to cut down on their time complexity.

The K-way merge: To combine numerous input streams that have already been sorted into a single sorted output stream, a heap data structure is helpful.

Order information: To quickly get the kth smallest (or largest) member in an array, utilize the Heap data structure.

I hope you got the complete overview of the heap and how it's used. If you want to master the data structure concepts, sign up for the best course for data structure and algorithms offered by Learnbay.