My first instinct was to just sort and merge like a standard interval problem, but that breaks down the second you have overlapping people.
Use a sweep-line algorithm: create events for each interval start and end, sort them by time, and maintain a set of active people. At each event, output the previous time segment with the current active set if non-empty, then update the active set and continue.
Pro tip: Clarify the half-open interval semantics (e.g., [start, end)) to avoid off-by-one errors, and discuss how to handle simultaneous events (e.g., process ends before starts at the same timestamp to avoid empty segments).
Confirm interval semantics (half-open), input format, and expected output. Discuss edge cases like overlapping intervals, zero-length intervals, and simultaneous events.
Create events for each interval start and end, each with a timestamp and type (start/end). Sort events by time, with ends processed before starts at the same time to avoid empty segments.
Iterate through sorted events, keeping a set of active people. When the active set changes, if the previous segment had a non-empty set, output it with its start and end times.
Explain that sorting takes O(n log n) time, and the sweep is O(n). Discuss space complexity O(n) for events and active set. Mention alternative approaches like interval trees if needed.
Walk through a sample input, verifying correct merging and omission of gaps. Test cases with no overlaps, full overlaps, and simultaneous start/end events.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.