Putting It All Together

Heaps are EVERYWHERE:

• Priority queues: OS schedulers, event simulation, network packet queues
• Graph algorithms: Dijkstra, Prim's MST, A*
• Compression: Huffman tree construction
• Top-K: stream analytics, search ranking
• Heapsort: in-place O(n log n) sort
• Median finding: two heaps (max + min)

Beyond binary heaps:

• d-ary heaps: each node has d children. Better for decrease-key heavy use (Dijkstra).
• Fibonacci heap: amortized O(1) decrease-key. Theoretical interest; bad constants.
• Pairing heap: simpler than Fibonacci, similar bounds in practice.
• Skew heap / Leftist heap: meld two heaps in O(log n).
• Soft heap: relaxes the property to enable corruption — used in MST algorithms.
• Treap: random-priority BST that's effectively a heap.

For 99% of real code, a plain binary heap is what you want. Python's heapq, Java's PriorityQueue, C++'s std::priority_queue — all binary heaps.