Openai·Machine Learning Engineer·Technical Phone Screen·Senior

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Jul 2026

Summary

Interviewed for an ML Engineer role at OpenAI and got hit with a grid simulation problem that felt more like a competitive programming warmup than anything ML-related. Interesting problem but I kept second-guessing my BFS approach the whole time.

Questions Asked (1)

Given an n x m grid where cells are either infected or healthy, and infection spreads in discrete time steps (a healthy cell becomes infected if it has at least K infected neighbors), return the minimum number of time steps until the entire grid is infected, or -1 if it's impossible.

Algorithms & Data Structures

Author's notes

My first instinct was multi-source BFS and that direction was right, but K not being 1 threw me off.

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AI HintsAI Generated

Suggested Approach

Model the infection spread as a multi-source BFS where each cell's infection time is determined by when it accumulates at least K infected neighbors. Use a priority queue to process cells in order of infection time, updating neighbor counts and enqueueing cells when their count reaches K. If all cells become infected, return the maximum infection time; otherwise, return -1.

Pro tip: Clarify edge cases upfront: K=0 means all cells are infected at time 0, and if no initial infected cells exist and K>0, return -1 immediately. Also, mention that the BFS can be optimized by only tracking healthy cells' neighbor counts.

1. Understand the problem and constraints

Restate the problem to ensure clarity: grid size, infection rule, and goal. Discuss edge cases like K=0, no initial infected cells, and K greater than max possible neighbors.

2. Choose the right algorithm

Recognize this as a multi-source BFS with a threshold condition. Explain why a simple BFS won't work directly and why a priority queue (or bucket queue) is needed to process cells in order of infection time.

3. Design the data structures

Use a 2D array to store infection times (or -1 for uninfected). Maintain a count of infected neighbors for each healthy cell, and a priority queue (min-heap) of cells that will become infected, keyed by time.

4. Simulate the infection process

Initialize the queue with all initially infected cells at time 0. While the queue is not empty, pop the cell with the smallest time, and for each healthy neighbor, increment its infected neighbor count; if it reaches K, compute its infection time (current time + 1) and push it into the queue.

5. Determine the result and handle impossibility

After the simulation, check if all cells are infected. If yes, return the maximum infection time; otherwise, return -1. Discuss time and space complexity.

Key Points to Mention

Multi-source BFS with a priority queue to handle varying infection times.
Tracking infected neighbor counts for each healthy cell to avoid redundant checks.
Time complexity: O(n*m log(n*m)) with a heap, or O(n*m) with bucket queue if times are bounded.
Space complexity: O(n*m) for storing infection times and neighbor counts.
Edge cases: K=0, no initial infected cells, K larger than possible neighbors, and disconnected components.
Correctness argument: infection times are monotonic, and processing in order ensures each cell is infected at the earliest possible time.

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