First thing I fumbled was the inclusive endpoint part.
Clarify the problem and edge cases, then propose an efficient algorithm such as sorting intervals by start time and merging overlapping intervals while tracking total covered length. Discuss time and space complexity, and consider trade-offs between sorting-based and sweep-line approaches.
Pro tip: Explicitly handle the inclusive endpoints by treating intervals as half-open [start, end+1) or by carefully merging when next.start <= current.end. Mentioning this detail shows attention to problem constraints and prevents off-by-one errors.
Ask about input size, whether intervals can be unsorted, if endpoints are integers, and if zero-length intervals are possible. Confirm that overlapping intervals should be merged and that total time is the union length.
Propose sorting intervals by start time, then iterating to merge overlaps. Alternatively, mention a sweep-line approach using events (start +1, end+1 -1) if the problem scale or constraints favor it.
Explain how to maintain a current merged interval and accumulate total time when a non-overlapping interval is found. Emphasize the inclusive endpoint condition: merge if next.start <= current.end.
State that sorting takes O(n log n) time and O(1) or O(n) extra space depending on implementation. Compare with sweep-line which may be O(n log n) due to sorting events but can handle streaming data.
Validate the approach with simple cases (single interval, disjoint intervals, fully overlapping, touching intervals) and a complex case to ensure correctness.
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