My first instinct was standard BFS and I almost forgot the diagonals.
Model the spread as a multi-source BFS on a graph where each cell is a node and edges connect to all 8 neighbors. Compute the maximum shortest-path distance from any initially infected cell to any uninfected cell; that distance is the number of days until no new infections occur. If there are no uninfected cells, return 0.
Pro tip: Clarify edge cases upfront: if the grid has no infected cells, the answer is 0 (no spread); if all cells are infected initially, also 0. Also mention that using a queue with level-order traversal naturally tracks days.
Confirm that infection spreads to all 8 neighbors (including diagonals) and that a cell once infected remains infected. Discuss edge cases: no infected cells, all cells infected, and grids with uninfected cells unreachable from any infected cell.
Treat each cell as a node with edges to its 8 neighbors. Use multi-source BFS starting from all initially infected cells simultaneously to compute the minimum time each cell becomes infected.
Initialize a queue with all infected cells and a day counter. Process the queue level by level (each level = one day), infecting uninfected neighbors and adding them to the queue. Stop when the queue is empty.
The number of days is the number of BFS levels processed minus 1 (or the maximum distance from any infected cell to any uninfected cell). If there are no uninfected cells, return 0.
State time complexity O(m*n) since each cell is visited once, and space complexity O(m*n) for the queue and visited set. 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.