Start by clarifying the problem constraints (e.g., whether intervals are sorted, inclusive/exclusive endpoints, and expected output format). Then propose a sort-based approach: sort intervals by start time, iterate through them, and merge overlapping intervals by comparing the current interval's start with the previous merged interval's end. Finally, analyze time and space complexity and discuss edge cases.
Pro tip: Mention that sorting is the key to achieving O(n log n) time, and that without sorting, the problem would require O(n^2) comparisons. Also, proactively discuss how you would handle edge cases like empty input or intervals that touch at endpoints.
Ask about input format, whether intervals are sorted, endpoint inclusivity, and expected output. Confirm if intervals are given as pairs [start, end] and if merging touching intervals (e.g., [1,2] and [2,3]) is required.
Propose sorting intervals by start time, then merging in a single pass. Explain why this yields O(n log n) time due to sorting, and O(n) space for the output.
Describe iterating through sorted intervals: if the current interval's start <= last merged interval's end, update the end to max of both ends; otherwise, add the last merged interval to the result and start a new one.
State time and space complexity. Discuss edge cases: empty list, single interval, all overlapping, none overlapping, and intervals with same start times.
Walk through a concrete example, such as [[1,3],[2,6],[8,10],[15,18]] -> [[1,6],[8,10],[15,18]], to verify correctness and demonstrate understanding.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.