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Waymo·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
May 2026

Summary

Waymo SWE interview with a grid partitioning problem that exposed a real gap in my ability to handle randomness constraints under pressure. I had the right instinct but the wrong execution, and only figured out the proper approach after the fact.

Questions Asked (1)

Q1

Given an m×n grid and 4 tokens (numbered 1 to 4), write an algorithm to randomly populate the grid so that each token occupies exactly the same number of cells, each token's region is contiguous (4-directional connectivity), and the entire grid is covered.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

I went straight to BFS and got partway there but completely fell apart on the randomness part.

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AI HintsAI Generated

Suggested Approach

Start by clarifying constraints (m, n, divisibility by 4) and defining the problem as partitioning the grid into four equal-area connected regions. Then propose a randomized algorithm that grows regions from seeds while maintaining connectivity and coverage, and discuss trade-offs between simplicity and guarantees.

Pro tip: Mention that perfect randomness with hard constraints is NP-hard in general, so practical solutions use randomized growth with backtracking or local swaps, and always validate the result.

1. Clarify constraints and feasibility

Confirm that m*n is divisible by 4 and discuss edge cases (e.g., small grids, non-rectangular shapes). If not divisible, explain impossibility.

2. Choose a randomized region-growing strategy

Select four distinct seed cells (one per token) and iteratively expand each region into unassigned neighboring cells, using a randomized order to ensure fairness.

3. Ensure contiguity and equal size

Track region sizes and only allow expansion that keeps each region connected. Stop when each region reaches exactly m*n/4 cells.

4. Handle dead-ends and guarantee coverage

If a region cannot expand without disconnecting, use backtracking or local swaps between regions to resolve conflicts and achieve full coverage.

5. Validate and discuss trade-offs

After generation, verify contiguity, equal sizes, and coverage. Discuss time/space complexity and trade-offs between randomness, efficiency, and guarantee of success.

Key Points to Mention

  • Feasibility condition: m*n must be divisible by 4; otherwise, no solution exists.
  • Randomized region growing with seeds ensures contiguity and equal sizes if carefully managed.
  • Use of a queue or priority queue to manage expansion order and maintain connectivity.
  • Backtracking or local search (e.g., swapping cells between regions) to resolve dead-ends and ensure full coverage.
  • Validation step: check that each token's cells are 4-connected, each has exactly m*n/4 cells, and all cells are assigned.
  • Trade-offs: pure random assignment may violate constraints; region growing with backtracking is more reliable but may be slower.

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