The partial overlap part tripped me up more than I expected.
Clarify the problem constraints and data representation first, then propose a sweep-line algorithm that processes interval endpoints in sorted order. For each segment between consecutive endpoints, determine the active intervals and whether the override applies, compute the cost for that segment, and sum. Emphasize O(n log n) complexity and handling of partial overlaps by splitting intervals at boundaries.
Pro tip: Mention that you would handle edge cases like zero-duration intervals, multiple overrides (if allowed), and floating-point precision by using exact arithmetic or epsilon comparisons. Also, discuss how to extend the solution if the override applies to only a subset of intervals or if there are multiple overrides.
Ask about input format, interval inclusivity, whether durations are fixed or variable, and if multiple overrides are possible. Confirm that the override applies to all intervals overlapping its time range.
Propose a sweep-line approach: collect all interval start and end points, sort them, and process segments between consecutive points. Alternatively, use an interval tree if queries are frequent.
For each segment, identify which usage intervals are active and whether the override interval covers it. Compute the cost per unit time for that segment, multiply by segment length, and accumulate.
Write pseudocode or code, ensuring correct handling of boundaries (e.g., half-open intervals). Test with cases like no overlap, full overlap, partial overlap, and multiple intervals.
State time complexity O(n log n) due to sorting, and space O(n). Discuss potential optimizations like early termination or using a priority queue for active intervals.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the semantics of overlapping overrides: do they stack, or does the most recent or highest-priority override win? Then, adapt your data structure to efficiently resolve conflicts, likely using interval trees or sweep-line algorithms, and discuss trade-offs between preprocessing and query time.
Pro tip: Mention that overlapping overrides often require a deterministic tie-breaking rule (e.g., latest timestamp or highest priority) and that you would confirm this with the interviewer before coding, showing you think about real-world ambiguity.
Ask whether overlapping overrides should be merged, stacked, or resolved by priority. Confirm if overrides are static or dynamic, and what operations (insert, delete, query) are needed.
Select an interval tree, segment tree, or sweep-line approach to handle overlaps efficiently. Consider if overrides are known in advance (offline) or streaming (online).
Specify how to resolve overlaps: e.g., latest timestamp wins, highest priority wins, or combine values. Implement a comparator or merge function.
Compare time/space complexity of your approach versus naive methods. Discuss preprocessing vs. query time, and scalability with many overrides.
Walk through examples with nested, partially overlapping, and identical intervals. Verify correctness and performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.