Classic connected components problem, BFS or DFS both work fine.
This is a classic connected components problem on a grid. Use DFS or BFS to traverse each unvisited building cell and mark all reachable building cells as visited, incrementing the community count for each traversal. Alternatively, use Union-Find to group adjacent buildings and count distinct sets.
Pro tip: Clarify edge cases upfront (empty grid, no buildings, all buildings) and mention that you can optimize space by modifying the grid in-place if allowed, or use a visited matrix otherwise. Also, discuss trade-offs between DFS (recursion depth risk) and BFS (queue memory) for large grids.
Restate the problem: count connected components of 1s in a binary grid using 4-directional adjacency. Ask about grid size limits, whether the grid can be modified, and if diagonal connections count (they don't).
Select between DFS, BFS, or Union-Find. DFS/BFS are simpler for grid traversal; Union-Find is efficient for dynamic connectivity but overkill here. Explain your choice.
Iterate through each cell; when encountering an unvisited '1', increment the count and launch a traversal (DFS/BFS) to mark all connected '1's as visited. Use a visited matrix or modify the grid in-place.
State time complexity O(m*n) and space complexity O(m*n) for visited matrix or O(min(m,n)) for BFS queue in worst case. Discuss edge cases: empty grid, no buildings, all buildings, single row/column.
Walk through a small example to verify correctness, e.g., grid = [[1,1,0],[0,1,0],[0,0,1]] should return 2. Mention potential pitfalls like stack overflow with DFS on large grids.
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Acknowledge that the problem shifts from in-memory to external-memory processing, requiring a streaming or chunked approach. Discuss trade-offs between time, space, and I/O, and propose a concrete algorithm like external sorting or distributed processing. Emphasize the need to handle data that cannot fit in memory by processing in chunks and using disk or multiple machines.
Pro tip: Mention that you would first clarify the exact constraints (e.g., grid size, memory limit, whether it's a one-time or repeated operation) because the optimal solution depends heavily on these factors. This shows you think like a senior engineer who avoids premature optimization.
Ask about the grid size, available memory, whether the grid is static or dynamic, and the expected output. This determines whether a streaming, chunked, or distributed approach is best.
Decide between external memory algorithms (e.g., external sorting, chunked processing) or distributed frameworks (e.g., MapReduce, Spark) based on scale and infrastructure.
Outline how to read the grid in blocks, process each block, and combine results. For example, use a sliding window for local computations or a two-pass approach for global aggregations.
Discuss how to minimize disk I/O and network transfer, and how to parallelize work. Mention techniques like buffering, compression, and partitioning.
Propose testing with smaller datasets and profiling to ensure the solution scales. Be ready to adjust based on actual performance metrics.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.