Heap interview questions

A heap is a specialized tree that keeps only the single most extreme item at the very top. In a min-heap, every parent node is smaller than its children, so the smallest element in the entire collection sits immediately at the root. Unlike a binary search tree, a heap does not keep all items in full sorted order. It maintains only a partial order, making it fast at giving you the single smallest or largest item without spending time sorting everything else.

When to reach for it

Reach for a heap when a problem asks for the top k largest elements, the kth smallest value, or a running median from a stream of numbers. Signals include phrases like continuously finding the cheapest item, merging k sorted linked lists, or scheduling tasks with priorities. Whenever you need repeated access to the minimum or maximum value while items are added and removed dynamically, a priority heap is the tool.

How to think about it

To find the k largest elements, keep a min-heap of fixed size k. Push incoming numbers into the heap; whenever the heap size grows past k, pop the top item, which is the smallest among them. After processing all elements, only the k largest remain. For a running median, balance two heaps: a max-heap holding the smaller half of numbers and a min-heap holding the larger half. In code, heaps are stored compactly as flat arrays where a node at index i has children at indices 2i plus 1 and 2i plus 2.

What each operation costs