Insert Interval
Given a set of non-overlapping intervals, insert a new interval into the intervals, merging if necessary.
Why Interviewers Ask This
Stripe values engineers who can handle complex state transitions and data integrity. This question tests your ability to manage edge cases in interval logic, such as merging overlapping ranges or handling non-overlapping insertions without creating duplicates. It evaluates your precision in algorithmic thinking and your capacity to write clean, bug-free code under pressure.
How to Answer This Question
1. Clarify Requirements: Confirm if intervals are sorted and if the new interval might overlap with multiple existing ones. Stripe often expects you to assume sorted input but verify it.
2. Define Logic States: Identify three distinct phases: intervals ending before the new one starts (add as-is), intervals overlapping the new one (merge by updating start/end), and intervals starting after the new one ends (add as-is).
3. Handle Edge Cases: Explicitly discuss scenarios where the new interval is entirely before, entirely after, or completely encompasses an existing range.
4. Implement Linear Scan: Iterate through the list once, using pointers to track current position. Avoid nested loops to maintain O(n) time complexity.
5. Validate Output: Briefly explain how you would test boundary conditions, ensuring no gaps or overlaps remain in the final merged array.
Key Points to Cover
- Demonstrate understanding of O(n) time complexity for a single-pass solution
- Explicitly define the three logical states for interval comparison
- Show awareness of sorting assumptions and how to handle unsorted inputs
- Clearly articulate the logic for calculating merged start and end points
- Provide a concrete trace of the algorithm with specific numerical examples
Sample Answer
To solve the Insert Interval problem efficiently, I would first verify that the input intervals are sorted by their start times, as this simplifies the merging logic significantly. My approach relies on a single pass linear scan with O(n) time complexity and O(1) extra space excluding the output array.
I will initialize a result list and iterate through the existing intervals. For each interval, I check its relationship with the new interval. If the current interval ends before the new interval starts, it cannot overlap, so I add it directly to the result. Conversely, if the current interval starts after the new interval ends, all remaining intervals will also be non-overlapping, so I add the new interval first, then the current one, and append the rest of the list.
The critical part is handling overlaps. If the current interval overlaps with the new one, I update the new interval's start to be the minimum of both starts and the end to be the maximum of both ends. This effectively merges them. Once I've processed all potential overlaps, I add the merged new interval to the result.
For example, if we have [[1,3], [6,9]] and insert [2,5], the first interval [1,3] overlaps because 3 >= 2. We merge them to get [1,5]. The next interval [6,9] starts after 5, so we add [1,5] then [6,9]. This ensures the final list remains non-overlapping and sorted, satisfying the core requirement while maintaining optimal performance.
Common Mistakes to Avoid
- Using nested loops which results in inefficient O(n^2) time complexity
- Failing to update the start point correctly when the new interval starts earlier than the current one
- Ignoring edge cases where the new interval is completely contained within an existing one
- Not verifying if the input array is already sorted before applying the standard merge logic
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