The base problem wasn't too bad once I realized it was really just about how the override punches a hole in the existing intervals and replaces that range.
Clarify the input format and the meaning of 'override' (e.g., replace or merge) before designing the algorithm. Then choose a sweep-line or interval merging approach that processes all intervals sorted by start day, applying the override with higher priority. Finally, handle edge cases like overlapping intervals and boundaries (day 1 and 31) to produce a clean merged timeline.
Pro tip: Explicitly state your assumptions about the override semantics (e.g., does it replace overlapping base intervals entirely or just take precedence?) and confirm with the interviewer. This shows you think about ambiguity and real-world data merging, which is crucial for production systems.
Ask questions to understand the exact representation of intervals (inclusive/exclusive, start/end days), the meaning of 'override' (replace vs. merge), and expected output format. Confirm edge cases like intervals spanning the entire range or touching boundaries.
Decide between a sweep-line approach (events sorted by day) or an interval merging approach (sort intervals by start, then merge). For a single override, you can also split the base timeline into segments before, during, and after the override.
Process intervals in order of priority (override first, then base) or use a sweep-line that tracks the active interval with highest priority. Ensure that overlapping intervals are correctly combined or replaced according to the override semantics.
Test with intervals that overlap the override partially, fully, or not at all. Check boundaries (day 1 and 31) and ensure no gaps or overlaps in the output. Validate that the override truly takes precedence.
Discuss time and space complexity (e.g., O(n log n) for sorting). If needed, propose optimizations like using a balanced tree for dynamic updates or a difference array for fixed ranges.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The non-overlapping guarantee on the overrides is doing a lot of work here and I almost missed it.
First, clarify the problem: we need to extend a solution that likely handles a single override interval to support multiple non-overlapping intervals. Then, propose a data structure like an interval tree or sorted list of intervals, and discuss how to efficiently apply overrides, considering time and space complexity. Finally, walk through an example and edge cases to validate the approach.
Pro tip: Mention that since overrides are guaranteed non-overlapping, we can simplify by sorting intervals and using binary search for point queries or merging for range updates, which shows you leverage constraints for efficiency.
Restate the problem to ensure understanding: we have a base solution and need to support multiple override intervals that do not overlap. Ask about expected operations (e.g., point queries, range updates) and input sizes.
Select a data structure that efficiently handles non-overlapping intervals, such as a sorted array of intervals with binary search, an interval tree, or a segment tree with lazy propagation, depending on the operations.
Describe how to insert, delete, or query overrides. For example, for point queries, binary search to find the interval containing the point; for range updates, merge intervals if needed.
Discuss time and space complexity of the chosen approach and compare with alternatives. Mention that non-overlapping property allows simpler merging and faster queries.
Walk through a concrete example, including edge cases like empty overrides, queries outside intervals, and intervals touching boundaries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.