The problem is product-flavored which threw me a bit because I kept thinking about it from a UI angle instead of just treating it as a set coverage problem.
First, clarify the problem constraints and edge cases (e.g., date format, inclusivity, hotel availability). Then, propose an efficient algorithm: for each hotel, compute the maximal contiguous coverage from start and to end, then find valid split points by intersecting coverage intervals from different hotels. Finally, discuss trade-offs between time and space complexity and potential optimizations.
Pro tip: Demonstrate product thinking by relating the solution to Airbnb's business needs: split stays increase booking options and revenue, so efficiency and correctness are critical. Also, mention how you would handle large datasets with many hotels and dates.
Ask about date format, inclusivity of start/end, whether hotels can have overlapping availability, and if the output should be sorted or deduplicated.
For each hotel, sort its available dates and compute the longest contiguous coverage from the start date and the longest coverage ending at the end date.
For each hotel A, determine the furthest date s it can cover from start; then for each other hotel B, check if B covers from s+1 to end. Collect all valid (A, B, s) triples.
Discuss time and space complexity, and propose optimizations like using hash maps for coverage intervals or two-pointer techniques to avoid O(n^2) comparisons.
Walk through examples including no valid splits, single hotel, overlapping coverage, and dates at boundaries to ensure correctness.
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