Heaps and Priority Queues Questions

Binary heaps and priority queues as data structures: min-heap and max-heap, array layout, sift-up and sift-down, push/pop/peek costs, build-heap (heapify) in O(n), and indexed heaps with decrease-key versus lazy deletion of stale entries. Covers the problems where a heap is the intended tool: top-K and kth largest or smallest selection (including over a one-pass stream and under inserts and deletes), sorting an array whose elements are at most k places out of order with a window heap, the two-heap pattern for running and sliding-window medians (invariants, rebalancing, lazy deletion, testing, and extensions to percentiles, weighted medians, custom orderings and merging structures), k-way merge of sorted lists, arrays, files or streams with bounded memory, scheduling by priority with cancellation and reprioritisation, stable priority queues with tie-breaking, and implementing a heap or priority queue with a language library such as heapq or PriorityQueue (including max-heap behaviour from a min-heap). Boundary: graph shortest-path algorithms, approximate quantile sketches, production streaming-system design, and heapsort and quickselect as sorting and selection algorithms are covered elsewhere.