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Microsoft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Microsoft SWE interview with a DP problem that sounds deceptively clean on paper. The core challenge was trickier to model than I expected.

Questions Asked (1)

Q1

A founder wants to meet as many investors as possible. Each investor has a set of available days. The founder can choose at most k days total, meets at most one investor per day, and each investor can only be met once. Find the maximum number of investors the founder can meet. Solve this using dynamic programming.

Algorithms & Data Structures
Author's notes

I spent way too long trying to think of it as a greedy problem before the interviewer nudged me toward DP.

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AI HintsAI Generated

Suggested Approach

Model the problem as a maximum bipartite matching with a cardinality constraint on the number of days used. Use dynamic programming over days and investors, where the state captures the number of days chosen so far and the set of investors already met, but optimize by sorting investors by availability and using bitmask DP if the number of investors is small, or a min-cost max-flow formulation for larger inputs.

Pro tip: Clarify the constraints first: if the number of investors is small (≤20), bitmask DP is ideal; if large, a flow-based approach with binary search on the number of investors is more scalable. Always discuss trade-offs between DP and flow.

1. Clarify constraints and assumptions

Ask about the maximum number of investors, days, and k. Determine if days are discrete and if investors have arbitrary availability sets.

2. Define the DP state

For small investor count, use dp[mask][d] = max investors met using d days and a subset mask of investors. For larger, consider dp over days with a bitmask of investors or a flow network.

3. Formulate transitions

For each day, either skip it or assign it to an available investor not yet met, updating the mask and day count. Ensure at most k days are used.

4. Optimize and handle large inputs

If investors > 20, use a max-flow formulation: source to investors (capacity 1), investors to days (capacity 1 if available), days to sink (capacity 1), and add a super sink with capacity k. Then binary search or use min-cost max-flow to maximize investors.

5. Analyze complexity and edge cases

Discuss time/space complexity (e.g., O(2^n * k) for bitmask DP) and handle cases like k=0, no available days, or investors with empty availability.

Key Points to Mention

  • Bipartite matching interpretation: investors vs. days with capacity constraints.
  • Dynamic programming state design: mask of investors and number of days used.
  • Bitmask DP for small n (n ≤ 20) and its complexity O(2^n * k).
  • Max-flow reduction for large n: source→investors→days→sink with capacities and a super sink for k.
  • Handling the 'at most k days' constraint via an extra node or DP dimension.
  • Edge cases: k=0, no investors, investors with no available days, and duplicate days.

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