Start by clarifying the problem and identifying the multi-source BFS pattern, such as rotting oranges or walls and gates. Explain that you'll initialize a queue with all source nodes, then perform BFS level by level to compute distances or propagate states simultaneously. Discuss time and space complexity, and mention how this avoids redundant work compared to running BFS from each source separately.
Pro tip: Emphasize that multi-source BFS is essentially a BFS on a virtual super-source connected to all starting nodes, which unifies the search and guarantees the shortest distance from the nearest source. This shows deep understanding and can impress interviewers.
Ask questions to confirm the grid dimensions, movement directions, and what constitutes a source. Identify all starting nodes that should be enqueued initially.
Enqueue all source nodes with distance 0 (or appropriate initial value) and mark them as visited. Use a queue for BFS and a distance matrix or modify the grid in-place to track distances.
While the queue is not empty, process nodes level by level. For each node, explore its neighbors; if a neighbor is unvisited and valid, update its distance, mark visited, and enqueue it.
Check for empty grid, no sources, or unreachable cells. Ensure the BFS terminates when the queue is empty, and return the required result (e.g., max distance, modified grid).
State time complexity O(M*N) since each cell is processed once, and space complexity O(M*N) for the queue and distance storage. Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.