Openai·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

OpenAI SWE interview with a grid infection simulation problem. The problem had multiple sub-tasks ramping up in difficulty, which I wasn't fully expecting. Not a bad experience but the K-of-N neighbor counting tripped me up early.

Questions Asked (1)

Given an m x n grid where some cells start infected, and a healthy cell becomes infected each minute only if at least K of its 4-directional neighbors are currently infected, find the minute when all reachable cells are infected, or determine if some cells will never become infected.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was BFS and I went down that road for a few minutes before realizing the K-neighbor condition makes it way messier than standard BFS.

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AI HintsAI Generated

Suggested Approach

Model the problem as a multi-source BFS where each cell's infection time depends on when at least K neighbors are infected. Use a priority queue (min-heap) to process cells in order of infection time, updating neighbor counts and enqueueing cells when their infected neighbor count reaches K. After the process, check if any healthy cells remain; if so, they are unreachable.

Pro tip: Clarify that K is a global constant and that infection times are non-decreasing; using a priority queue ensures we process cells in the correct order, avoiding multiple passes. Also, mention that if K > 4, no cell can ever be infected unless initially infected.

1. Understand the problem and constraints

Restate the problem: given an m x n grid with initially infected cells, each minute a healthy cell becomes infected if at least K of its 4-directional neighbors are already infected. Determine the minute when all reachable cells are infected, or identify cells that never become infected.

2. Choose the right algorithm

Use a multi-source BFS with a priority queue (min-heap) to simulate the infection spread. Each cell's infection time is the earliest minute when its infected neighbor count reaches K.

3. Implement the simulation

Initialize a queue with all initially infected cells at time 0. For each cell, maintain a count of infected neighbors. When a cell is infected, increment the neighbor count for its healthy neighbors; if a neighbor's count reaches K, compute its infection time (current time + 1) and push it into the priority queue.

4. Track the maximum time and check for uninfected cells

Keep track of the maximum infection time encountered. After the queue is empty, scan the grid to see if any healthy cells remain. If so, they will never be infected; otherwise, return the maximum time.

5. Analyze complexity and edge cases

Discuss time complexity O(mn log(mn)) due to heap operations, and space complexity O(mn). Handle edge cases: K > 4, no initially infected cells, all cells initially infected, and disconnected regions.

Key Points to Mention

Multi-source BFS with priority queue (Dijkstra-like) to handle varying infection times.
Maintaining a count of infected neighbors for each cell to trigger infection when count >= K.
Time complexity O(mn log(mn)) and space complexity O(mn).
Edge cases: K > 4, no initially infected cells, all cells initially infected, and unreachable cells.
Correctness: infection times are non-decreasing, so processing in order of time ensures correctness.
Trade-offs: using a simple BFS with multiple passes vs. priority queue; priority queue is more efficient for large grids.

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