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Pretty standard stuff if you've done any interval problems before.
Start by clarifying the problem constraints (e.g., whether intervals are sorted, if they are inclusive/exclusive, and expected input size). Then propose sorting intervals by start time and merging overlapping ones in a single pass, explaining the logic and edge cases. Finally, analyze time and space complexity and discuss potential optimizations or alternative approaches.
Pro tip: Mention that sorting is the key insight and that you can merge in-place or use a result list; also discuss how you would handle edge cases like empty input or intervals that touch exactly (e.g., [1,2] and [2,3]).
Ask about input format, whether intervals are sorted, if they are inclusive/exclusive, and expected size. This shows attention to detail and avoids assumptions.
Explain that sorting by start time allows a linear scan to merge overlapping intervals. Describe how to compare the current interval's start with the last merged interval's end.
Use a small example like [[1,3],[2,6],[8,10],[15,18]] to demonstrate the merging process step by step, highlighting how overlaps are detected and merged.
State that time complexity is O(n log n) due to sorting, and space is O(n) for the output (or O(1) extra if merging in-place). Discuss edge cases: empty list, single interval, intervals that touch exactly, and unsorted input.
Mention that if intervals are already sorted, we can skip sorting and achieve O(n). Also note that for very large data, external sorting might be needed, but for interviews, the standard approach suffices.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify that available intervals override busy ones, then model the timeline as a sweep over sorted endpoints, tracking the current state (busy/available) with a counter or flag. Merge overlapping busy intervals and subtract any available intervals that overlap them, outputting only the remaining busy portions.
Pro tip: Explicitly discuss how you handle edge cases like adjacent intervals, zero-length intervals, and multiple overlapping available intervals—interviewers at Bloomberg value robustness and clear reasoning about boundary conditions.
Confirm that available intervals override busy ones wherever they overlap, and that the output should be the busy portions after removing any overlap with available intervals. Ask about input format, interval inclusivity, and whether intervals can be zero-length or unsorted.
Decide between a sweep-line approach (sort all endpoints, track state) or a merge-and-subtract approach (merge busy intervals, then subtract available intervals). Consider time/space complexity and explain your choice.
For sweep-line: create events for start/end of busy and available intervals, sort by time, and maintain a counter of active busy and available intervals. For merge-and-subtract: merge busy intervals, then for each available interval, split overlapping busy intervals.
Test with adjacent intervals, fully covered busy intervals, multiple available intervals overlapping the same busy interval, and unsorted input. Ensure the output intervals are non-overlapping and sorted.
State the time complexity (e.g., O(n log n) due to sorting) and space complexity. Discuss trade-offs between the sweep-line and merge-subtract approaches in terms of code simplicity and performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.