intervals

Merging intervals is a staple that probes the sort-then-sweep idea. The tell is sorting by start and merging in a single pass, O(n log n). Below is the pattern along with the family of problems it opens up.

The fewest meeting rooms you need equals the highest number of meetings active simultaneously. That reframing is the entire interview; two O(n log n) solutions drop out of it, and the tie-handling catches careless candidates.

Merging intervals is the entry point to the whole interval family. The trick is sorting by start so overlaps end up 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 runs through all of analytics, and time zones and bucketing are the usual traps. The signal is DATE_TRUNC for bucketing, interval math, and storing UTC.

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