Meta·Software Engineer·Onsite - Coding / Algorithms·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Meta SWE coding round, one question the whole time, grid BFS. Felt pretty focused but also like they were waiting for me to say the magic words about multi-source traversal.

Questions Asked (1)

You're given a 2D grid where cells are either walls, gates, or empty rooms. Fill each empty room with the shortest distance to the nearest gate using four-directional movement. Walk through your approach, justify why you'd use multi-source BFS over other strategies, and analyze time and space complexity. Also handle edge cases like multiple gates, fully enclosed rooms, and large grids.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I started with the naive thing, single-source BFS from each gate separately, and the interviewer let me finish before asking what the complexity was.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and constraints, then propose a multi-source BFS from all gates simultaneously to compute shortest distances to empty rooms. Explain why BFS is optimal for unweighted grids, walk through the algorithm, and analyze time and space complexity. Finally, discuss edge cases and potential optimizations.

Pro tip: Emphasize that multi-source BFS avoids redundant work by processing all gates in parallel, and mention that in-place modification of the grid is acceptable if the problem allows it, saving space.

1. Clarify the problem and constraints

Ask about grid size, whether gates are guaranteed, and if modifying the grid in-place is allowed. Confirm that distance is measured in number of steps (Manhattan distance) and that walls block movement.

2. Propose multi-source BFS

Explain that you'll enqueue all gates initially, then perform BFS level by level, updating empty rooms with the current distance. This ensures each room gets the minimum distance from any gate.

3. Justify BFS over alternatives

Compare with running BFS from each empty room (O(rooms * gates) worst-case) or Dijkstra (overkill for unweighted). Highlight that multi-source BFS is O(m*n) time and handles multiple gates efficiently.

4. Analyze complexity and edge cases

State time complexity O(m*n) since each cell is visited once, and space O(m*n) for the queue. Discuss edge cases: no gates (return unchanged), fully enclosed rooms (remain INF), and large grids (BFS is optimal).

5. Discuss implementation details and optimizations

Mention using a queue, directions array, and in-place updates. Optionally, suggest using a 2D array for distances if in-place is not allowed, and note that BFS naturally handles multiple gates.

Key Points to Mention

Multi-source BFS treats all gates as sources at distance 0, ensuring shortest paths.
Time complexity O(m*n) because each cell is enqueued at most once.
Space complexity O(m*n) for the queue in worst case (e.g., all gates).
Edge case: no gates -> grid unchanged; fully enclosed rooms remain INF.
Alternative approaches like BFS from each empty room are less efficient (O(rooms * gates)).
In-place modification is possible if allowed, saving extra space.

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