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Airbnb·Software Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say
Jun 2026Remote

Summary

Airbnb software engineer interview with a pretty gnarly algorithmic problem involving bitmask DP and set cover. One question, lots of depth expected, and they wanted full complexity analysis plus test cases on top of working code.

Questions Asked (1)

Q1

You're given a list of rental service packages, each with a set of services and a price, plus a list of required services. Design an algorithm that returns the minimum total cost to cover all required services (case-insensitive), and all combinations of package indices that achieve that minimum. If coverage is impossible, return (-1, []). Walk through your approach, time and space complexity in terms of N packages and S distinct required services, how you reconstruct optimal combinations from your DP state, and how you handle ties without duplicate combinations. Include tests for the provided example and at least one infeasible case.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

This is basically weighted set cover which is NP-hard in general, so the bitmask DP angle makes sense when S is small.

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Suggested Approach

Model the problem as a set cover DP over bitmasks of required services, where each package is an item with a cost and a coverage mask. Compute the minimum cost to cover each subset, then backtrack from the full mask to reconstruct all optimal package index combinations, deduplicating by sorting indices. Handle infeasibility by checking if the full mask is reachable.

Pro tip: Emphasize that the DP state should be the set of covered services, not the packages considered, and that you can iterate over packages in any order to avoid duplicate combinations. Also, mention that you can prune dominated packages (those with higher cost and subset coverage) to improve performance.

1. Clarify and preprocess

Confirm that services are case-insensitive and that packages can be used at most once (or unlimited? clarify). Map each distinct required service to a bit position, and convert each package's services to a bitmask. Remove packages that cover no required services or are dominated (higher cost and subset coverage of another package).

2. Define DP state and transition

Let dp[mask] = minimum cost to cover exactly the services in mask. Initialize dp[0] = 0, others infinity. For each package with mask p and cost c, update dp[mask | p] = min(dp[mask | p], dp[mask] + c) for all masks. This is a standard 0/1 knapsack over subsets.

3. Reconstruct optimal combinations

After filling dp, if dp[full] is infinity, return (-1, []). Otherwise, backtrack from full mask: for each package, if dp[mask] == dp[mask ^ p] + c (and mask contains p), include it and recurse on mask ^ p. Collect all combinations, sort indices within each combination, and deduplicate using a set.

4. Analyze complexity and handle ties

Time: O(N * 2^S) for DP, plus O(2^S * N) for backtracking in worst case. Space: O(2^S) for dp and O(2^S * N) for storing combinations if many ties. Ties are handled by exploring all valid predecessors and deduplicating sorted index lists.

5. Test with examples

Walk through the provided example: packages and required services, compute DP, show optimal combinations. Also test an infeasible case where some required service is not covered by any package, returning (-1, []).

Key Points to Mention

  • Bitmask DP over subsets of required services, with state dp[mask] = min cost.
  • Case-insensitive normalization: convert all service names to lowercase before mapping to bits.
  • Reconstruction via backtracking from the full mask, checking if dp[mask] == dp[mask ^ package_mask] + cost.
  • Deduplication of combinations by sorting package indices and using a set to avoid duplicates.
  • Time complexity O(N * 2^S) and space O(2^S) for DP, plus output-sensitive space for combinations.
  • Handling infeasibility: if dp[full] remains infinity, return (-1, []).

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.