I went with DFS first because it felt more natural to write quickly.
Start by clarifying the problem and edge cases, then present a BFS or DFS solution that treats the grid as a graph and explores all 8 directions from each unvisited land cell. After coding, analyze time and space complexity, and discuss how to avoid recursion limits by using an iterative BFS or an explicit stack for DFS.
Pro tip: Mention that you can mutate the input grid to mark visited cells (e.g., set '1' to '0') to save space, but note the trade-off of altering input data. Also, for very large grids, an iterative BFS with a queue is often safer and more memory-efficient than recursive DFS.
Confirm the problem details: 8-directional connectivity, grid dimensions, and whether the input can be modified. Discuss edge cases like empty grid, all water, or all land.
Decide between BFS and DFS. Explain that BFS uses a queue and avoids recursion limits, while DFS is simpler but may cause stack overflow on large grids.
Iterate through each cell; when a '1' is found, increment island count and traverse all connected '1's using BFS/DFS, marking visited cells (e.g., set to '0').
State time complexity O(m*n) since each cell is visited once, and space complexity O(min(m,n)) for BFS queue or O(m*n) for DFS recursion stack in worst case.
For very large grids, use iterative BFS with a queue to avoid recursion limits. Alternatively, use an explicit stack for DFS. Discuss memory optimizations like in-place marking.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.