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Sort by start time then sweep through, merging as you go.
Sort the intervals by their start times, then iterate through them while maintaining a 'current' merged interval, extending it whenever the next interval overlaps. This greedy approach ensures a single linear pass after sorting, yielding an O(n log n) overall solution dominated by the sort step.
Pro tip: Proactively mention edge cases like an empty input array, a single interval, or intervals that are only touching (e.g., [1,2] and [2,3]) and clarify with your interviewer whether touching intervals should be merged — this signals production-level thinking that Meta values.
Confirm input format (e.g., list of [start, end] pairs), whether intervals can be unsorted, and edge cases like empty arrays or touching intervals. Ask if in-place modification is preferred or a new list is acceptable.
Sort the array of intervals based on the start value of each interval. This guarantees that any overlapping interval with the current one can only appear immediately after it in the sorted order.
Initialize a result list with the first interval, then for each subsequent interval check if its start is less than or equal to the current interval's end. If so, extend the end to the maximum of both ends; otherwise, push the current interval to results and start a new one.
After the loop, ensure the last active interval is appended to the result list, as it won't be pushed inside the loop iteration.
State the time complexity as O(n log n) due to sorting and O(n) space for the output. Walk through 2-3 test cases including normal overlap, no overlap, and fully contained intervals to validate correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the requirements: what types of queries (e.g., point stabbing, range overlap, total coverage), expected throughput, and whether intervals can be deleted or updated. Then propose a data structure that maintains the merged set incrementally, such as a balanced BST of disjoint intervals, and discuss trade-offs between update and query costs. Finally, outline how you would handle concurrency and persistence if needed.
Pro tip: Mention that you would keep the merged set as a sorted list of disjoint intervals and use binary search for queries, but also consider a segment tree or interval tree if queries are more complex. Showing awareness of real-world constraints like memory and latency will impress.
Ask about query types, update frequency, latency requirements, and whether intervals can be removed or modified. This ensures you design the right solution.
Propose maintaining a dynamic set of disjoint intervals, e.g., using a balanced BST (like a red-black tree) keyed by start point, or a skip list for simpler concurrency.
Describe how to insert a new interval: find overlapping intervals, merge them, and update the set. Discuss time complexity (O(log n + k) where k is number of overlaps).
Explain how to answer queries efficiently, e.g., point stabbing via binary search, range overlap by finding intervals intersecting a query range.
Address concurrency (locking, lock-free), persistence, and alternative structures (segment trees, interval trees) with their pros and cons.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Binary search to find where the new interval fits, then walk left and right to absorb any overlaps.
Start by clarifying that the input list is sorted and non-overlapping, then describe a linear scan approach that adds all intervals ending before the new interval, merges all overlapping intervals, and finally adds the remaining intervals. Emphasize that this achieves O(n) time and O(n) space, which is optimal since the output may require copying all intervals.
Pro tip: Mention that if the list is stored in a data structure allowing in-place modification (like an array with extra capacity), you can merge in O(k) extra space where k is the number of overlapping intervals, but in the worst case it's still O(n). Also, note that binary search can find the insertion point in O(log n) but merging still requires O(n) due to shifting elements.
Confirm that the existing list is sorted by start time and contains no overlapping intervals. Ask about the expected size of the list and whether in-place modification is allowed.
Explain that you will iterate through the intervals, adding all intervals that end before the new interval starts, then merge all intervals that overlap with the new interval, and finally add the remaining intervals.
Describe how to update the new interval's start and end when overlapping: new_start = min(new_start, current_start), new_end = max(new_end, current_end). Continue until an interval starts after the new interval ends.
State that the time complexity is O(n) because each interval is visited once, and space complexity is O(n) for the output list. Mention that binary search for the insertion point doesn't improve overall complexity due to shifting/merging.
Cover edge cases: new interval before all, after all, overlapping multiple, or contained within one. Mention that if the list is empty, just return the new interval. If in-place is allowed and there's extra capacity, you can merge without allocating a new list.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.