The core idea clicks fast: sweep line, collect all the events, sort them, walk through.
Use a sweep-line algorithm: create events for each interval start (+1) and end (-1), sort them by time, and then process events in order while maintaining a running count of active couriers. Group events with the same timestamp to handle simultaneous changes atomically, and emit segments only when the active count is positive.
Pro tip: Emphasize the atomic handling of simultaneous events: if one courier ends and another starts at the same time, the active count should not drop to zero between them. This shows attention to edge cases and real-world correctness.
Confirm that intervals are half-open [start, end), may overlap, and that all changes at the same timestamp are processed together. Discuss handling of empty input, zero-length intervals, and large datasets.
For each interval, create a start event with delta +1 and an end event with delta -1. Store events as tuples (time, delta).
Sort events by time. Then iterate through the sorted events, grouping all events with the same timestamp to compute the net change in active couriers atomically.
Maintain a running active count. For each group of events at time t, first apply the net delta, then if the active count is positive, emit a segment from t to the next event time with the current active count.
State that time complexity is O(n log n) due to sorting, and space is O(n). Walk through a small example to verify correctness, including simultaneous events.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.