The singleton case tripped me up at first.
Clarify the problem constraints and edge cases, then propose an efficient algorithm using bitmasks or sets to represent availability. Precompute coverage for each listing, then check singles and pairs for full coverage, discussing time/space trade-offs.
Pro tip: Mention that using bitmasks allows O(1) coverage checks and fast intersections, but be prepared to discuss memory trade-offs for large ranges. Also, consider sorting or hashing to avoid redundant pair checks.
Ask about input size, date range representation (inclusive/exclusive), and whether listings can have overlapping availability. Confirm output format and if order matters.
Decide between sets, bitmasks, or interval lists based on range size and density. Bitmasks are efficient for small ranges; sets or interval trees for large sparse ranges.
For each listing, compute its coverage as a bitmask or set, and filter out those with no overlap with the target range. Identify singles that fully cover the range.
Iterate over pairs of listings, checking if the union of their coverage equals the target range. Use bitwise OR for bitmasks or set union for sets, and optimize by skipping pairs that cannot cover.
Discuss time complexity (O(n^2) for pairs, but can be optimized with indexing) and space complexity. Mention alternative approaches like interval merging or using a hash map of missing days.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.