Google·Software Engineer·Onsite - System Design / Architecture·Senior

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Apr 2026

Summary

Google system design round for a software engineer role. The question was a follow-up to a grid-based BFS problem, pushing into dynamic updates and data structure trade-offs. Pretty intense once the constraints started piling on.

Questions Asked (1)

You have a grid where taxis can come online or go offline at any time. Design a system that keeps track of the shortest distance from every cell to the nearest currently active taxi, and handles updates efficiently as taxis appear and disappear.

System DesignAlgorithms & Data StructuresTechnical Trade-offs

Author's notes

Started with the naive answer: just re-run multi-source BFS every time something changes.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (grid size, number of taxis, update frequency, query patterns) and then propose a multi-source BFS approach for static scenarios. For dynamic updates, discuss incremental recomputation strategies such as maintaining a priority queue of affected cells or using a dynamic programming approach with lazy updates. Finally, analyze trade-offs between update time and query time, and suggest optimizations like spatial partitioning or caching.

Pro tip: Demonstrate awareness of real-world constraints by discussing how to handle frequent updates without recomputing the entire grid, and mention the possibility of using a distributed system if the grid is massive. Also, proactively discuss how to handle tie-breaking or multiple taxis at the same distance.

1. Clarify Requirements and Constraints

Ask about grid dimensions, number of taxis, frequency of online/offline events, and query patterns (e.g., point queries vs. full grid updates). This determines the appropriate data structures and algorithms.

2. Propose a Baseline Solution

For a static set of taxis, use multi-source BFS from all active taxis to compute distances to all cells in O(N) time, where N is the number of cells. This establishes a foundation.

3. Handle Dynamic Updates

When a taxi comes online, run BFS from it and update distances where the new distance is smaller. When a taxi goes offline, identify cells that were uniquely served by it and recompute their distances, possibly using a priority queue or by re-running BFS from other taxis.

4. Optimize for Efficiency

Discuss incremental algorithms, such as maintaining a distance map and only updating affected regions. Consider using a k-d tree or spatial indexing to quickly find nearby taxis for recomputation.

5. Analyze Trade-offs and Scalability

Compare time complexities of different approaches (e.g., O(N) per update vs. O(log N) with advanced structures). Discuss memory usage, concurrency, and potential distributed solutions for very large grids.

Key Points to Mention

Multi-source BFS for initial distance computation
Incremental update strategies for online/offline events
Use of priority queues or Dijkstra-like algorithms for dynamic updates
Spatial partitioning or indexing to limit recomputation scope
Trade-offs between update latency and query latency
Handling edge cases like multiple taxis at same distance or no active taxis

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