intervals

Interval merging is a classic that tests the sort-then-sweep insight. The signal is sorting by start, then merging in one pass, O(n log n). Here is the pattern and the family of problems it unlocks.

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.

Time-based analysis is everywhere in analytics, and time zones and bucketing are the common traps. The signal is DATE_TRUNC for bucketing, interval math, and storing UTC.

Overlapping subscription or session windows need collapsing into clean periods, and a naive self-join is quadratic. The signal is the gaps-and-islands trick: a running max end-time to mark where each new island begins.