Heap cheatsheet for coding interviews
Introduction
A heap is a specialized tree-based data structure which is a complete tree that satisfies the heap property.
- Max heap - In a max heap the value of a node must be greatest among the node values in its entire subtree. The same property must be recursively true for all nodes in the tree.
- Min heap - In a min heap the value of a node must be smallest among the node values in its entire subtree. The same property must be recursively true for all nodes in the tree.
In the context of algorithm interviews, heaps and priority queues can be treated as the same data structure. A heap is a useful data structure when it is necessary to repeatedly remove the object with the highest (or lowest) priority, or when insertions need to be interspersed with removals of the root node.
Learning resources
- Learning to Love Heaps, basecs
- Heapify All The Things With Heap Sort, basecs
- Heaps, James Aspnes, Yale University
Implementations
| Language | API |
|---|---|
| C++ | std::priority_queue |
| Java | java.util.PriorityQueue |
| Python | heapq |
| JavaScript | N/A |
Time complexity
| Operation | Big-O |
|---|---|
| Find max/min | O(1) |
| Insert | O(log(n)) |
| Remove | O(log(n)) |
| Heapify (create a heap out of given array of elements) | O(n) |
Techniques
Mention of k
If you see a top or lowest k being mentioned in the question, it is usually a signal that a heap can be used to solve the problem, such as in Top K Frequent Elements.
If you require the top k elements use a Min Heap of size k. Iterate through each element, pushing it into the heap (for python heapq, invert the value before pushing to find the max). Whenever the heap size exceeds k, remove the minimum element, that will guarantee that you have the k largest elements.
Essential questions
These are essential questions to practice if you're studying for this topic.
Recommended practice questions
These are recommended questions to practice after you have studied for the topic and have practiced the essential questions.
Recommended courses
AlgoMonster
AlgoMonster aims to help you ace the technical interview in the shortest time possible. By Google engineers, AlgoMonster uses a data-driven approach to teach you the most useful key question patterns and has contents to help you quickly revise basic data structures and algorithms. Best of all, AlgoMonster is not subscription-based - pay a one-time fee and get lifetime access. Join today for a 70% discount →
Grokking the Coding Interview: Patterns for Coding Questions
This course on by Design Gurus expands upon the questions on the recommended practice questions but approaches the practicing from a questions pattern perspective, which is an approach I also agree with for learning and have personally used to get better at coding interviews. The course allows you to practice selected questions in Java, Python, C++, JavaScript and also provides sample solutions in those languages along with step-by-step visualizations. Learn and understand patterns, not memorize answers! Get lifetime access now →
Master the Coding Interview: Data Structures + Algorithms
This Udemy bestseller is one of the highest-rated interview preparation course (4.6 stars, 21.5k ratings, 135k students) and packs 19 hours worth of contents into it. Like Tech Interview Handbook, it goes beyond coding interviews and covers resume, non-technical interviews, negotiations. It's an all-in-one package! Note that JavaScript is being used for the coding demos. Check it out →