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Use a graph traversal algorithm like DFS or BFS to explore each unvisited land cell and mark all connected land cells as visited, incrementing the island count for each traversal. Alternatively, use Union-Find to group connected land cells and count distinct sets. Clearly state the time and space complexity.
Pro tip: Mention that you can optimize space by modifying the grid in-place (e.g., changing '1' to '0') to mark visited cells, but discuss the trade-off of mutating input. Also, be prepared to discuss handling edge cases like empty grid or all water.
Restate the problem to ensure understanding, ask about edge cases (empty grid, all water, all land) and constraints (grid size, recursion depth).
Decide between DFS, BFS, or Union-Find based on constraints and preferences. Explain why you chose it.
Describe the steps: iterate through each cell; when a '1' is found, increment count and traverse all connected '1's, marking them visited.
State time complexity O(rows*cols) and space complexity O(rows*cols) for visited set or recursion stack, or O(1) if modifying in-place.
Mention potential optimizations like early termination, using iterative BFS to avoid recursion limits, or Union-Find for dynamic scenarios.
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