BFS gave TLE 7. DFS must be much more successful. Reasons: 1) Easy to construct the son. 2) Easy and without memory reconstruct the father. DFS-TLE10 Therefore exists some strong mathematics in the problem to speed up algos.
Yes, DFS is the way for this problem. My AC 0.015 solution can solve a 20x20 in about 700 recursions. Here's a hint for the problem: Pay close attention to the following sentence: "If the number of bacteria in a certain cell becomes 5, then 4 of them die because of overcrowding.". What would happen if this rule didn't exist?