My first instinct was to sort by start time and then just walk through comparing neighbors.
First, clarify the problem: whether intervals are closed/open, if input is sorted, and what 'all pairs' means (all overlapping pairs or all overlaps among any intervals). Then, propose sorting intervals by start time and using a sweep line or two-pointer technique to efficiently find overlaps, or if the number of intervals is small, a brute-force O(n^2) approach may suffice. Discuss trade-offs and edge cases before coding.
Pro tip: Demonstrate awareness of interval inclusivity (e.g., [1,3] and [3,5] may or may not overlap) and ask clarifying questions; this shows attention to detail and prevents incorrect assumptions.
Ask about interval inclusivity, input size, sortedness, and whether to return unique overlaps or all pairs. Confirm output format (set of intervals).
If n is small, brute-force O(n^2) is acceptable; if large, sort by start and use a sweep line or two-pointer to achieve O(n log n).
For sorted intervals, iterate and compare current with next; compute overlap as [max(start1, start2), min(end1, end2)] if max(start) <= min(end).
State time and space complexity. Discuss potential optimizations like early termination or using a heap for active intervals.
Walk through examples including no overlaps, touching intervals, nested intervals, and duplicates. Verify output as a set.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.