Heap / Priority Queue

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## TL;DR

A heap is a complete binary tree with the heap property (parent ≤ children for min-heap). O(1) peek, O(log n) insert/extract. Array-based representation: children of i are 2i+1, 2i+2.

## Core Explanation

Binary heap is the most common implementation. Heapify (construction): O(n) bottom-up. Heapsort: build heap + n extractions = O(n log n) in-place. Priority queues in Dijkstra, job scheduling, event simulation. Fibonacci heap achieves O(1) insert, amortized O(log n) extract.

## Further Reading

- [Introduction to Algorithms (CLRS)](undefined)

## Related Articles

- [NATS and Message Brokers: Pub-Sub, Request-Reply, and Queue Groups](../nats-and-message-brokers-pub-sub-request-reply-and-queue-groups.md)