The first part clicked fast, standard sweep with a sorted event list.
Start by clarifying the interval semantics (inclusive/exclusive, half-open) and edge cases like empty input or zero-length intervals. Then explain the line-sweep algorithm: create events for each interval start (+1) and end (-1), sort them, and sweep to track the running count and peak. For the extension, during the sweep, record the start and end times of each contiguous window where the count equals the peak, merging adjacent windows if needed.
Pro tip: Mention that using half-open intervals [start, end) avoids ambiguity at boundaries and simplifies merging adjacent peak windows. Also, discuss how to handle simultaneous events (e.g., process starts before ends) to correctly capture the peak.
Ask about interval inclusivity, input size, and whether intervals can be zero-length or unsorted. Confirm the output format for peak windows (e.g., list of [start, end) pairs).
Create events: for each interval, add (start, +1) and (end, -1). Sort events by time, with a tie-breaking rule (e.g., process +1 before -1 for half-open intervals). Sweep through events, maintaining a running count and updating the peak.
During the sweep, track when the count becomes equal to the peak and when it drops below. Record the start and end times of each contiguous window where count == peak. Merge windows that are adjacent (end of one equals start of next).
State time complexity O(n log n) due to sorting, and space O(n) for events. Discuss alternative approaches (e.g., difference array if time range is small) and why line-sweep is preferred for large or sparse intervals.
Walk through a simple example (e.g., [[1,3], [2,4], [3,5]]) to show peak count and windows. Test edge cases: no intervals, all non-overlapping, all overlapping, and intervals with same start/end times.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.