priority queue

Merging k sorted sources is the canonical min-heap problem and a real data-engineering pattern (merging sorted shards/streams). The signal is the heap of k heads giving O(N log k). Here is the answer.

Dijkstra finds single-source shortest paths in O((V+E) log V) with a min-heap, the backbone of routing and network latency problems. The signal is why it needs non-negative weights and how lazy deletion keeps the heap simple. Here is the answer.