The BFS part clicked pretty fast but I almost started with a single-source approach and would've gotten the wrong answer.
Model the problem as a multi-source BFS where all initially rotten oranges are enqueued at time 0. Process level by level, incrementing time each level, and track the number of fresh oranges to detect impossibility. Return the final time if all fresh oranges rot, else -1.
Pro tip: Clarify edge cases upfront (e.g., no fresh oranges, no rotten oranges) and mention that BFS is optimal because each orange rots at the earliest possible minute. Also, discuss space-time trade-offs and potential optimizations like in-place marking.
Restate the problem to ensure clarity: grid with fresh (1), rotten (2), empty (0). Identify edge cases: no fresh oranges (return 0), no rotten oranges but fresh present (return -1), all empty (return 0).
Explain why BFS is ideal: it simulates the simultaneous rotting process level by level, ensuring minimum time. DFS or simulation would be inefficient.
Scan the grid to enqueue all rotten oranges and count fresh oranges. This sets up the multi-source BFS starting point.
Process the queue level by level, incrementing time after each level. For each rotten orange, check its 4 neighbors; if fresh, mark rotten, decrement fresh count, and enqueue.
After BFS, if fresh count is 0, return the elapsed time; otherwise, return -1. Discuss time and space complexity: O(m*n) time and space.
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