Sort by start time first, that's the whole trick.
Start by clarifying assumptions (e.g., intervals are closed, input may be unsorted). Then propose sorting intervals by start time and merging in a single pass, explaining the logic and edge cases. Finally, analyze time and space complexity and discuss potential optimizations or variations.
Pro tip: Mention that sorting is the key to achieving O(n log n) time, and that the merge step is O(n) after sorting. Also, proactively discuss how to handle edge cases like empty input, single interval, and intervals that touch at endpoints (e.g., [1,2] and [2,3] should merge if closed).
Ask about interval inclusivity (closed vs. open), input size, whether intervals are sorted, and expected output format. Confirm that overlapping includes touching endpoints if closed.
Propose sorting intervals by start time. Then iterate through sorted intervals, merging with the last interval in the result if they overlap; otherwise, add the current interval to the result.
Use a small example like [[1,3],[2,6],[8,10],[15,18]] to demonstrate the merging process step by step, showing how the result is built.
State that sorting takes O(n log n) time and the merge pass takes O(n) time, leading to O(n log n) overall. Space complexity is O(n) for the output (or O(log n) to O(n) for sorting, depending on implementation).
Cover edge cases: empty input, single interval, all overlapping, none overlapping, and intervals with same start. Mention that if input is already sorted, we can skip sorting and achieve O(n) time.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.