Heap Data Structure

A Heap is a complete binary tree data structure that satisfies the heap property: in a min-heap, the value of each child is greater than or equal to its parent, and in a max-heap, the value of each child is less than or equal to its parent. Heaps are commonly used to implement priority queues, where the smallest (or largest) element is always at the root.

Basics

• Binary Heap
• Applications

Library Implementations

• Heap in C++ STL
• priority_queue in C++
• PriorityQueue in Java
• PriorityQueue in C#
• heapq in Python
• Heap in JavaScript

Easy Problems

• Check if an array is Heap?
• K’th Smallest & K'th Largest
• Heap Sort
• Heap Sort for Decreasing Order
• Height of a Heap with N Nodes

Medium Problems

• Nearly Sorted Array
• K Largest Elements & K Smallest
• k Closest Elements
• Max diff between two m Sized Subsets
• Check if Binary Tree is Heap
• Huffman Coding
• Nodes less than a value in a Min Heap.
• Connect n ropes with minimum cost
• K maximum sum combinations from two arrays
• K’th largest in a stream
• Largest triplet product in a stream
• k most frequent
• Min Heap to Max Heap
• Check for Min-Heap from Level Order
• BST to Min Heap
• K Closest Points to the Origin

Hard Problems

• The Skyline Problem
• Median in a stream
• K-th Largest Sum Subarray
• Sort by Frequency
• Merge k sorted arrays & Linked Lists
• Range Covering K Sorted Lists
• Prim's Minimum Spanning Tree
• Dijkstra's Shortest Path
• Sort from different machines
• Largest Derangement of a Sequence
• Merge two binary Max Heaps
• Sum of all between k1’th and k2’th smallest
• A data structure with min and max

Other Types of Heaps

• Binomial Heap
• Fibonacci Heap
• Leftist Heap
• K-ary Heap

Quick Links:

• Interview Questions on Heap
• Practice Problems on Heap
• Quiz on Heap
• DSA Tutorial