Model the grid as a graph where each building cell is a node and edges connect adjacent buildings. Then count the number of connected components using either BFS/DFS or Union-Find, iterating over all cells and incrementing the count when an unvisited building is found.
Pro tip: Clarify edge cases upfront (empty grid, no buildings, all buildings) and mention that you can optimize space by marking visited cells in-place (e.g., setting to 0) if mutation is allowed, but always confirm with the interviewer.
Confirm grid dimensions, connectivity (4-directional), and what constitutes a community. Ask about edge cases like empty grid or no buildings.
Decide between BFS/DFS (simpler, O(mn) time, O(mn) space for recursion/queue) and Union-Find (good for dynamic connectivity, O(mn α) time). Explain trade-offs.
Iterate through each cell; when a building is found, increment community count and traverse all connected buildings, marking them visited (e.g., set to 0 or use a visited set).
State time complexity O(mn) and space complexity O(mn) for visited set or O(min(m,n)) for BFS queue in worst case. Discuss potential optimizations.
Walk through small examples (e.g., single building, diagonal buildings, multiple communities) to verify correctness and handle edge cases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Acknowledge that the in-memory solution won't scale and propose an external memory approach that processes the grid in chunks. Discuss trade-offs between I/O, memory, and computation, and outline a concrete algorithm like external BFS or divide-and-conquer with disk-based storage.
Pro tip: Mention that you would first clarify the grid's characteristics (e.g., sparse vs. dense, access patterns) and the available resources (disk, memory, distributed system) before committing to a solution—this shows you think like a Google engineer who values problem framing.
Ask about grid size, memory limits, disk space, and whether the grid is static or dynamic. Confirm if the problem is BFS/DFS, shortest path, or something else.
Decide between chunked processing (e.g., block-based BFS) or distributed processing (e.g., MapReduce, Pregel). Consider if the grid can be compressed or represented sparsely.
Outline how to process the grid in blocks, using disk as intermediate storage. For BFS, maintain frontier on disk and process level by level, reading only necessary blocks.
Discuss time vs. I/O vs. memory trade-offs. Mention techniques like buffering, prefetching, and compression. Compare with distributed approaches if applicable.
Recap the approach, highlight its scalability, and note any assumptions. Offer to dive deeper into a specific aspect if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.