Heap: Practice Problems and Interview Questions

Heap Data Structure

A heap is a specialized tree-based data structure that satisfies the heap property: If `A` is a parent node of `B`, then the key (the value) of a node `A` is ordered with respect to the key of node `B` with the same ordering applying across the heap. A heap can be classified further as either a “max-heap” or a “min-heap”. In a max-heap, the keys of parent nodes are always greater than or equal to those of the children and the highest key is in the root node. In a min-heap, the keys of parent nodes are less than or equal to those of the children and the lowest key is in the root node.

The heap is one maximally efficient implementation of an abstract data type called a priority queue, and in fact, priority queues are often referred to as “heaps”, regardless of how they may be implemented. A common implementation of a heap is the binary heap, in which the tree is a complete binary tree.

The heap data structure, specifically the binary heap, was introduced as a data structure for the heapsort sorting algorithm. Heaps are also crucial in several efficient graph algorithms such as Dijkstra’s algorithm. In a heap, the highest (or lowest) priority element is always stored at the root. A heap is not a sorted structure and can be regarded as partially ordered. There is no particular relationship among nodes on any given level, even among the siblings. When a heap is a complete binary tree, it has the smallest possible height — a heap with `N` nodes always has `log N` height. A heap is a useful data structure when you need to remove the object with the highest (or lowest) priority.

In this post, we have listed out commonly asked interview questions that use heap data structure:

1. Introduction to Priority Queues using Binary Heaps
2. Min Heap and Max Heap Implementation — C++, Java
3. Check if an array represents a min-heap or not
4. Convert max heap to min heap in linear time
5. Find k’th largest element in an array
6. Sort a k-sorted array
7. Merge `M` sorted lists of variable length
8. Find k’th smallest element in an array
9. Find the smallest range with at least one element from each of the given lists
10. Merge `M` sorted lists each containing `N` elements
11. Find first `k` non-repeating characters in a string in a single traversal
12. Connect `n` ropes with minimal cost
13. Return k’th largest element in a stream
14. Huffman Coding Compression Algorithm
15. Replace each array element by its corresponding rank
16. Single-Source Shortest Paths — Dijkstra’s Algorithm
17. Construct a Cartesian tree from an inorder traversal
18. Treap Data Structure
19. Implementation of Treap Data Structure (Insert, Search, and Delete)
20. Heap Sort Algorithm
21. Introsort Algorithm — Overview and C++ Implementation
22. External Merge Sort Algorithm
23. Efficiently merge `k` sorted linked lists
24. Check if a binary tree is a min-heap or not
25. Convert a Binary Search Tree into a Min Heap
26. Find first `k` maximum occurring words in a given set of strings

Thank you.