Binary Heap

A Binary Heap is a special type of complete binary tree, meaning all levels are filled except possibly the last, which is filled from left to right.

• It allows fast access to the minimum or maximum element. There are two types of binary heaps: Min Heap and Max Heap.
• Min Heap: The value of the root node is the smallest, and this property is true for all subtrees.
• Max Heap: The value of the root node is the largest, and this rule also applies to all subtrees.
• Binary heaps are commonly used in priority queues and heap sort algorithms because of their efficient insertion and deletion operations.

Valid and Invalid examples of heaps

How is Binary Heap represented? 

A Binary Heap is a Complete Binary Tree. A binary heap is typically represented as an array.

• The root element will be at arr[0].
• The below table shows indices of other nodes for the i^th node, i.e., arr[i]:

The traversal method use to achieve Array representation is Level Order Traversal. Please refer to Array Representation Of Binary Heap for details.

Operations on Heap

2 4 1

Applications of Heaps

• Heap Sort: Heap Sort uses Binary Heap to sort an array in O(nLogn) time.
• Priority Queue: Priority queues are efficiently implemented using Binary Heaps, which allow operations like insert, delete, extractMax, and decreaseKey in O(log N) time. Binomial and Fibonacci Heaps are advanced types that also support fast union operations.
• Graph Algorithms: The priority queues are especially used in Graph Algorithms like Dijkstra's Shortest Path and Prim's Minimum Spanning Tree.
• Many problems can be efficiently solved using Heaps.
  See following for example. a) K'th Largest Element in an array. b) Sort an almost sorted array/ c) Merge K Sorted Arrays.

Related Links:

• Coding Practice on Heap
• All Articles on Heap
• Quiz on Heap