The base BFS part was fine, I've done enough flood-fill stuff to get through that quickly.
Model the infection as a multi-source BFS to compute infection times, then simulate day-by-day while tracking each infected cell's neighbor count and death condition. Use a queue to process newly infected cells and a priority queue or buckets to schedule deaths, ensuring O(NM) time.
Pro tip: Clarify the death condition early: 'if it ever had K or more simultaneously-infected neighbors during those D days' means we need to track the maximum neighbor count over the D-day window, not just at infection time. Also, confirm whether dead cells stop spreading infection.
Ask about edge cases: Do dead cells stop spreading? Does the D-day window include the infection day? Are initial infected cells subject to the same death rule? Confirm the definition of 'simultaneously-infected neighbors'.
Run multi-source BFS from all initially infected cells to determine the day each cell becomes infected. Store infection day in a 2D array.
Process days in order. For each day, update neighbor counts for all infected cells (including newly infected). Track the maximum neighbor count each cell has seen so far. If a cell reaches D days since infection and its max neighbor count >= K, mark it dead and count it.
Instead of scanning all cells each day, use a queue for new infections and a priority queue (or buckets by day) for scheduled deaths. Update neighbor counts only for cells adjacent to newly infected or dead cells.
Discuss time and space complexity: O(NM) for BFS and O(NM) for simulation. Mention trade-offs between simple day-by-day simulation and event-driven approach.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.