Sorting first was obvious enough, but I fumbled the text concatenation part initially.
First, clarify the problem constraints and edge cases, then propose a sort-then-merge algorithm: sort intervals by start time, iterate through them, and merge overlapping intervals while concatenating labels. Discuss time and space complexity, and consider trade-offs such as whether to modify the input or create a new list.
Pro tip: Mention that sorting by start time ensures chronological order for label concatenation, and explicitly handle edge cases like empty input, single interval, and intervals that touch (e.g., end == start) to show attention to detail.
Ask about input format, whether intervals are inclusive/exclusive, and how to handle empty lists, single intervals, and intervals that touch. Confirm that labels should be concatenated in chronological order.
Propose sorting intervals by start time, then iterating and merging overlapping intervals. Explain that overlapping means the next interval's start is less than or equal to the current merged interval's end.
Describe maintaining a current merged interval; when overlap occurs, update the end to the max of both ends and append the label. When no overlap, add the current merged interval to the result and start a new one.
State that sorting takes O(n log n) time and merging takes O(n), so overall O(n log n) time and O(n) space for the output. Discuss whether to sort in-place or create a copy, and if labels should be concatenated with a delimiter.
Walk through a few test cases: non-overlapping intervals, overlapping intervals, nested intervals, and intervals that touch. Verify that labels are concatenated correctly and in order.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The overlap check felt like a natural extension of task one since you're already sorting.
First, clarify that the intervals are unmerged and may be unsorted. Then, for overlap detection, sort intervals by start time and check adjacent intervals for overlap; for gap detection, find the global start (minimum start) and global end (maximum end), then check if the union of intervals covers the entire range without gaps. Explain that both can be done in O(n log n) time due to sorting, with O(1) extra space if sorting in-place or O(n) if not.
Pro tip: Mention that if the intervals are already sorted, both checks can be done in O(n) time, and that gap detection can be integrated with overlap detection in a single pass after sorting. Also, clarify that 'gap' means a point not covered by any interval between the global start and global end.
Confirm what 'overlap' means (e.g., sharing at least one point) and what 'gap' means (a point between global start and global end not covered by any interval). Also, ask if intervals are sorted or if we can sort them.
Sort intervals by start time. Then iterate through the sorted list, checking if the current interval's start is less than or equal to the previous interval's end. If so, an overlap exists.
After sorting, find the global start (first interval's start) and global end (maximum end seen so far). Iterate through intervals, keeping track of the maximum end seen. If the next interval's start is greater than the current maximum end, there is a gap.
Sorting takes O(n log n) time. The subsequent scans take O(n) time. Space complexity is O(1) if sorting in-place, otherwise O(n) for the sorted copy. If intervals are already sorted, time is O(n).
Consider empty input, single interval, intervals that touch at endpoints (e.g., [1,2] and [2,3] — does that count as overlap? Usually not, but clarify), and intervals that are completely contained within others.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.