streams

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.

Sampling uniformly from a stream you cannot fit in memory (or whose length you never learn) is a real data-engineering problem. The signal is the replace-with-decreasing-probability trick and a proof that telescopes. Here is the answer.