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Meta·Machine Learning Engineer·Technical Phone Screen·Senior

Senior
May 2026

Summary

Meta ML Engineer interview with a combinatorics-style coding problem. Pretty focused session, just the one question but they pushed on edge cases and efficiency.

Questions Asked (1)

Q1

You're given a table of cards with integer values. Each round, you can pick any three cards that sum to 15. Design a strategy to maximize the number of valid rounds you can complete.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

My first instinct was greedy and it was wrong, or at least incomplete.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints (e.g., can cards be reused? what if multiple triples sum to 15?) and then model it as a combinatorial optimization problem. Propose a greedy strategy with a proof of optimality or a counterexample, and discuss trade-offs between time complexity and optimality. If greedy fails, outline a dynamic programming or matching-based approach.

Pro tip: Start by asking clarifying questions to ensure you understand the problem correctly; interviewers often expect you to handle ambiguity. Then, before diving into code, explain your high-level approach and its complexity, showing you can think strategically.

1. Clarify the problem

Ask about constraints: Are cards removed after use? Can a card be used in multiple rounds? What if no valid triple exists? Is the goal to maximize rounds or something else?

2. Identify the problem type

Recognize this as a 3-dimensional matching or set packing problem, which is NP-hard in general. For specific sums like 15, there may be structure to exploit.

3. Propose a greedy strategy

Suggest a greedy approach: repeatedly find any triple summing to 15 and remove it. Discuss whether this is optimal (likely not in all cases) and provide a counterexample if possible.

4. Explore optimal algorithms

If greedy is suboptimal, consider dynamic programming (e.g., bitmask DP for small n) or integer linear programming. Analyze time and space complexity.

5. Discuss trade-offs and extensions

Compare approaches: greedy is fast but may not be optimal; DP is optimal but exponential. Mention potential ML angle: if this is a subproblem in a larger ML pipeline, could use heuristics or learned policies.

Key Points to Mention

  • Problem is equivalent to maximum 3-dimensional matching or set packing, which is NP-hard.
  • Greedy may fail; provide a counterexample (e.g., cards [5,5,5,10,5,0] where greedy picks 5+5+5=15 but optimal is 10+5+0=15 and then 5+5+5=15).
  • Dynamic programming with bitmask can solve for small n (n <= 20) in O(2^n * n^3) or similar.
  • For large n, use approximation algorithms or heuristics; discuss LP relaxation and rounding.
  • Consider if the problem has special structure (e.g., values bounded) that allows polynomial-time solution.
  • Connect to ML: if this is part of a feature engineering or data preprocessing step, discuss scalability and parallelization.

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