Heap Problems (1)
Problems tagged with Heap. Start with the easy ones, then move to medium and hard.
Learn these first
Heaps are typically stored in a flat array, so you need to be comfortable with index math (2i+1, 2i+2) and random access before implementing heap operations.
Greedy algorithms often need the current minimum or maximum at each step, which is exactly what a priority queue provides.
Heap Sort is a classic comparison-based sort, and knowing how sorting algorithms trade off time and space makes heap-based top-K solutions more intuitive.
A heap is a complete binary tree, so understanding tree height, parent-child relationships, and level-order traversal helps you visualize sift-up and sift-down.
Many heap problems, like merge K sorted lists, combine divide-and-conquer thinking with a heap to efficiently merge partial results.
More about Heap
A Heap is a specialized tree-based data structure that satisfies the heap property: in a max-heap, every parent node is greater than or equal to its children, and in a min-heap, every parent is smaller than or equal to its children. It is most commonly implemented as a binary heap using an Array, where the root sits at index 0 and children of node i are at 2i+1 and 2i+2. Because heaps provide O(log n) insertion and deletion and O(1) access to the largest or smallest element, they are the engine behind priority queues, schedulers, and graph algorithms.
For coding interviews, heaps are one of the highest-yield topics. Companies like Google, Amazon, and Meta frequently ask heap problems to test your ability to reason about ordering, streaming data, and trade-offs. In fact, "Top K" and "Kth largest/smallest" problems are so common that many interviewers consider them mandatory practice. A strong grasp of heaps also unlocks efficient solutions to problems that otherwise seem to require O(n log n) sorting or repeated scans.
Common patterns and techniques include:
- Top K Elements: Use a min-heap of size K to keep the largest K elements, or a max-heap to keep the smallest K.
- K-way Merge: Push the head of each sorted list into a heap, then repeatedly pop the smallest and push its next element.
- Two Heaps: Maintain a max-heap for the lower half and a min-heap for the upper half to solve median-of-stream problems in O(log n) per insertion.
- Heapify: Build a heap from an unsorted array in O(n) instead of O(n log n) by sifting down from the last internal node.
- Dijkstra / Prim: Use a min-heap as a priority queue to process nodes in order of distance or edge weight.
Reach for a heap whenever you need repeated access to the smallest or largest element, or when you are dealing with streaming data, k-way merges, or scheduling. It pairs beautifully with Greedy algorithms, Divide and Conquer strategies, and Graph traversal. If you are already comfortable with Sorting, you will notice that heaps often give you a way to maintain sorted order dynamically without re-sorting the entire dataset. Start with the single practice problem on FleetCode, then move on to harder patterns to build interview-ready intuition.
Heap: common questions
Is Heap important for FAANG?
Yes, heap questions appear regularly at FAANG and other top tech companies. They are used to test problem-solving with streaming data, scheduling, and graph algorithms like Dijkstra. You should expect at least one heap-related problem in a typical interview loop, especially for mid-level and senior roles.
What are common Heap patterns?
The five most common patterns are Top K Elements, Kth Largest/Smallest, K-way Merge, Two Heaps for medians, and Heap-based Dijkstra/Prim. Each pattern has a recognizable trigger: repeated min/max access, streaming data, or merging sorted lists. Mastering these five covers the majority of heap interview questions.
What is the best way to learn Heap?
Start by implementing a binary heap from scratch in your favorite language to understand sift-up and sift-down operations. Then solve pattern-based problems, beginning with Top K Elements and Kth Largest Element. Finally, review solutions on FleetCode to see how heaps combine with arrays, graphs, and greedy algorithms.
How many Heap problems should I solve?
Spend extra time on Top K and Two Heaps patterns because they appear most frequently.
What are the best Heap problems for interviews?
Focus on Top K Frequent Elements, Kth Largest Element in an Array, Merge K Sorted Lists, Find Median from Data Stream, and Task Scheduler. These five problems cover the core heap patterns: top-K, k-way merge, two heaps, and greedy scheduling. On FleetCode, start with the Heap practice problem and then apply these patterns to similar questions.
What is the difference between a Heap and a Priority Queue?
A heap is a concrete data structure, usually a complete binary tree, while a priority queue is an abstract data type that supports insert and extract-min/max. In practice, most languages implement priority queues using heaps, so the terms are often used interchangeably. The key operations are O(log n) for insert/delete and O(1) for peek.