My first instinct was just iterate every pair and check coverage.
First, clarify the problem constraints and edge cases, then propose an efficient algorithm that avoids brute-force O(n^2) comparison. For each listing, compute the gaps in its availability relative to the desired range, and use a hash map to find complementary listings that cover those gaps.
Pro tip: Mention that in production, availability data is often large and dynamic, so you'd consider indexing or precomputing coverage patterns to enable fast lookups, and discuss trade-offs between preprocessing time and query latency.
Ask about the size of the input, whether dates are discrete or continuous, if listings can have overlapping availability, and if the stay must be split into exactly two contiguous segments.
For each listing, determine which parts of the desired range it covers and which parts it doesn't. The complement is the set of dates that must be covered by the other listing.
Use a hash map to store listings keyed by their coverage pattern (e.g., a bitmask or interval representation). For each listing, look up its complement in the map to find valid pairs.
Consider cases where one listing covers the entire range, where availability is non-contiguous, and where multiple listings share the same pattern. Validate with small examples.
Compare time and space complexity of the proposed solution versus brute force. Mention potential optimizations like interval trees or precomputed indexes for large-scale systems.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.