My first instinct was to sort by start time and merge greedily, which is wrong because overlapping intervals can end at different points and you need to split on every boundary, not just starts.
Use a sweep-line algorithm: create events for each interval start and end, sort them by time, and process in order while maintaining a set of active on-call people. At each event, output the previous segment if the active set is non-empty and the time has advanced, then update the active set.
Pro tip: Clarify the half-open interval semantics and how to handle simultaneous events (e.g., process all events at the same timestamp before emitting a segment) to avoid zero-length or incorrect segments.
Confirm that intervals are half-open [start, end), that output segments should be maximal and omit gaps, and discuss handling of zero-length intervals and simultaneous events.
Create events for each interval start (add name) and end (remove name). Sort events by time, ensuring that at the same timestamp, ends are processed before starts (or group all events at the same time).
Iterate through sorted events, maintaining the current active set and the start time of the current segment. When the active set changes, if the set was non-empty and time has advanced, emit a segment from the previous start time to the current time.
After processing all events, if the active set is non-empty, emit a final segment from the last start time to the last event time. Ensure gaps (where active set is empty) are skipped.
State that the algorithm runs in O(n log n) time due to sorting and O(n) space. Walk through a small example to verify correctness, including overlapping intervals and gaps.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.