Sort first, then sweep through and extend the current interval's end if the next one overlaps or touches.
Start by sorting the intervals by their start times, which enables a single linear scan to merge overlapping or touching intervals. Then iterate through the sorted list, comparing each interval with the last one in the result; if they overlap or touch, merge them by updating the end time, otherwise append the new interval. This yields O(n log n) time due to sorting and O(n) space for the output (or O(1) extra if merging in-place).
Pro tip: Clarify the definition of 'touching' (e.g., [1,2] and [2,3] should merge) and mention that you can merge in-place by reusing the input array to minimize extra space, which shows awareness of memory constraints.
Ask clarifying questions about interval inclusivity, touching behavior, input format, and whether the input can be modified. Confirm the expected output format and any constraints.
Sort the intervals by their start times. If start times are equal, sort by end times to ensure consistent merging.
Iterate through the sorted intervals, maintaining a result list. For each interval, if it overlaps or touches the last interval in the result, merge them by updating the end time; otherwise, append it.
If allowed, merge in-place by writing the merged intervals back into the input array to achieve O(1) extra space beyond the output. Otherwise, use a separate result list.
State that sorting takes O(n log n) time and the linear scan takes O(n) time, resulting in O(n log n) overall. Space is O(n) for the output, or O(1) extra if in-place.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
They asked this as a follow-up and I think I handled the touching endpoints part fine but glossed over invalid inputs too quickly.
Start by clarifying the problem constraints and defining what constitutes an edge case for interval merging. Then systematically address each edge case (touching endpoints, zero-length intervals, invalid inputs) by explaining how your algorithm handles them, including any necessary input validation and normalization. Emphasize robustness and testability.
Pro tip: Mention that you would write unit tests for each edge case to ensure correctness, and discuss trade-offs between strict validation and performance. This shows you think about production-quality code.
Ask clarifying questions about input format, expected behavior for invalid inputs, and whether intervals are inclusive/exclusive. Define what 'touching endpoints' means (e.g., [1,2] and [2,3] should merge if inclusive).
Decide on validation strategy: reject invalid intervals (e.g., start > end) with exceptions or filter them out. Discuss whether to sanitize or fail fast, and how to communicate errors.
Treat zero-length intervals (e.g., [1,1]) as valid points. Decide if they should be merged with overlapping intervals or kept separate; typically they merge if they touch or overlap.
Ensure the merge condition uses <= for the start of the next interval compared to the current end, so that touching intervals merge. Explain how this affects sorting and merging logic.
Outline a testing plan: unit tests for each edge case, including empty input, single interval, all touching, zero-length, and invalid inputs. Mention property-based testing if relevant.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Structure your answer by first outlining a systematic test plan that covers functional correctness, edge cases, and performance. Then, for each category (nested intervals, duplicates, sorted inputs, large inputs), describe specific test cases and expected outcomes, emphasizing how they validate the merging logic. Conclude by mentioning how you would automate and run these tests to ensure robustness.
Pro tip: Demonstrate awareness of production concerns by discussing how you'd handle large inputs efficiently (e.g., streaming or in-place merging) and how you'd test for stability and idempotency. Also, mention property-based testing to catch unexpected edge cases.
Confirm the definition of interval merging, input format (e.g., list of [start, end]), and expected output (e.g., sorted, non-overlapping intervals). Discuss assumptions like whether intervals are inclusive, and if input can be modified.
Break down tests into functional cases (normal, nested, duplicates), edge cases (empty input, single interval, touching intervals), and non-functional cases (large inputs, performance).
For each category, list concrete examples with input and expected output. For instance, nested intervals: [[1,10],[2,3]] -> [[1,10]]; duplicates: [[1,2],[1,2]] -> [[1,2]]; already-sorted: [[1,2],[3,4]] -> same; reverse-sorted: [[3,4],[1,2]] -> [[1,2],[3,4]].
Describe how you would test large inputs (e.g., millions of intervals) to ensure the algorithm runs in O(n log n) time and doesn't crash due to memory. Mention using generated data and measuring runtime.
Explain how you would write these as unit tests (e.g., using JUnit, pytest) and possibly property-based tests (e.g., Hypothesis) to validate invariants like non-overlapping and sorted output.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.