Difference between Min Heap and Max Heap (original) (raw)

Last Updated : 2 Oct, 2025

A Heap is a special Tree-based data structure in which the tree is a complete binary tree. Since a heap is a complete binary tree, a heap with **N nodes has **log N height. It is useful to remove the highest or lowest priority element. It is typically represented as an array. There are two types of Heaps in the data structure.

Min-Heap

In a Min-Heap the key present at every node node node must be less than all of its children. In a Min-Heap the minimum key element present at the root. Below is the Binary Tree that satisfies all the property of Min Heap.

Max Heap

In a Max-Heap the key present at every node node must be greater than at all of its children. In a Max-Heap the maximum key element present at the root. Below is the Binary Tree that satisfies all the property of Max Heap.

Difference between Min Heap and Max Heap

| | **Min Heap | **Max Heap | | | ---------------- | ------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------- | | 1. | In a Min-Heap the key present at the root node must be less than all of its descendants and same thing must be true for all subtrees, | In a Max-Heap the key present at the root node must be more than all of its descendants and same thing must be true for all subtrees, | | 2. | In a Min-Heap the minimum key element present at the root. | In a Max-Heap the maximum key element present at the root. | | 3. | A Min-Heap uses the ascending priority. | A Max-Heap uses the descending priority. | | 4. | In the construction of a Min-Heap, the smallest element has priority. | In the construction of a Max-Heap, the largest element has priority. | | 5. | In a Min-Heap, the smallest element is the first to be popped from the heap. | In a Max-Heap, the largest element is the first to be popped from the heap. |

**Applications of Heaps :

  1. Heap Sort: Heap Sort is one of the best sorting algorithms that use Binary Heap to sort an array in **O(N*log N) time.
  2. Priority Queue: A priority queue can be implemented by using a heap because it supports **insert(), **delete(), **extractMax(), **decreaseKey() operations in **O(log N) time.
  3. Graph Algorithms: The heaps are especially used in Graph Algorithms like Dijkstra’s Shortest Path and Prim’s Minimum Spanning Tree.

**Performance Analysis of Min-Heap and Max-Heap :