External Sort: Same Top-K, Bounded RAM Diagram

Disk Is the Memory

RAM holds one bounded chunk; disk holds every sorted run
A chunk that fits is sorted in memory, written out, forgotten
Total disk traffic is linear in input: read, write runs, merge

Merge Streams, Never Stores

The k-way merge keeps one line per run in RAM: O(runs), not O(urls)
Equal neighbours arrive adjacent, so counting streams without a table
The job always finishes: it degrades with I/O instead of dying

Bottleneck Moves to I/O

The bottleneck moves to sequential disk read and write rates
Bigger chunks mean fewer runs and a cheaper merge: tune, do not guess
Teaching numbers only: report your disk, your cap, your threshold