The single-listing case is easy enough, just check if the listing's availability set is a superset of every day in the range.
Clarify the problem constraints and edge cases, then propose an efficient algorithm using hash maps and interval coverage. Discuss trade-offs between preprocessing and on-the-fly computation, and analyze time/space complexity.
Pro tip: Mention that you would preprocess each listing's available days into sorted intervals to enable O(log n) range queries, and handle the split by checking for a day where the first listing's coverage ends and the second begins.
Confirm the definition of 'available day numbers' (e.g., discrete days), whether the range is inclusive, and if listings can have gaps. Ask about input size and performance expectations.
For each listing, convert its available days into sorted intervals of consecutive days. This allows efficient checks for covering a subrange.
For each listing, check if its intervals cover the entire requested range. If so, add it as a valid single stay.
For each possible split day within the range, check if there exists a listing covering [start, split] and a different listing covering [split+1, end]. Use interval queries to do this efficiently.
Discuss time and space complexity of the approach. Consider optimizations like early termination or indexing listings by coverage to reduce redundant checks.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.