sweep line

The minimum number of meeting rooms equals the peak number of meetings running at once. The reframing is the whole interview; two O(n log n) solutions fall out of it, and the tie-handling trips up the careless.

Merging intervals is the gateway to the whole interval family. The trick is sorting by start so overlaps land next to each other, then collapsing them in one linear sweep. Here is the pattern and the sweep-line generalization behind it.