Openai·Software Engineer·Technical Phone Screen·Senior

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May 2026Remote

Summary

Got a coding question at OpenAI that was basically a twist on the classic rotting oranges problem, except with a threshold mechanic that changes everything about how you approach the BFS. Took me a bit to realize why my standard solution wasn't going to cut it.

Questions Asked (1)

Given an m x n grid where cells are either empty, healthy, or infected, simulate infection spreading each minute. The twist: a healthy cell only becomes infected if the number of currently infected neighbors is at or above a given threshold k. Return the number of minutes until no more healthy cells can be infected, or -1 if some healthy cell will never be infected.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was to just run BFS like the standard version of this problem and I started coding that up before I caught myself.

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AI HintsAI Generated

Suggested Approach

Model the grid as a graph and simulate the infection spread minute by minute using BFS, but with a twist: for each healthy cell, track the count of infected neighbors and only infect when the count reaches k. After the simulation, check if any healthy cells remain; if so, return -1, else return the total minutes elapsed.

Pro tip: Clarify whether k is fixed or can vary per cell, and discuss the trade-offs between simulating minute-by-minute versus using a priority queue to process cells by infection time. Also, mention that early termination is possible if no new infections occur in a minute.

1. Understand the problem and clarify constraints

Restate the problem in your own words and ask clarifying questions about k (fixed or per-cell), grid size limits, and whether diagonal neighbors count. Confirm the expected output for edge cases.

2. Choose the right algorithm and data structures

Decide between BFS simulation and a priority queue approach. Use a queue to process infected cells level by level, and maintain a separate grid to count infected neighbors for each healthy cell.

3. Simulate the infection spread

Initialize the queue with all initially infected cells. For each minute, process all cells in the current queue, update neighbor counts, and enqueue newly infected cells. Keep track of the number of minutes elapsed.

4. Handle termination and edge cases

After the simulation, check if any healthy cells remain. If yes, return -1; otherwise, return the total minutes. Also handle cases where no initial infected cells exist or k is zero.

5. Analyze complexity and discuss optimizations

Explain the time and space complexity (O(m*n) per minute in worst case, but can be optimized). Discuss potential optimizations like using a priority queue to process cells by infection time or early termination when no new infections occur.

Key Points to Mention

BFS simulation with a queue to process cells level by level (each level represents a minute).
Maintaining a separate count of infected neighbors for each healthy cell to avoid recomputing.
Handling the threshold k: if k is 0, all healthy cells become infected immediately; if k is greater than the maximum possible neighbors, some cells may never be infected.
Edge cases: no initially infected cells, all cells already infected, or healthy cells that are isolated and cannot reach k infected neighbors.
Time and space complexity: O(m*n) per minute in the worst case, but can be optimized to O(m*n) total using a priority queue or by processing only cells whose neighbor count changes.
Trade-offs between different approaches: BFS is simpler but may process cells multiple times; priority queue can be more efficient but requires careful implementation.

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