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This was a very interesting problem in my opinion. It is a classic exercise in simulation, especially related to population growth. The constraints are small enough that you can brute-force and you'll be fine. Some techniques worth mentioning:
1/ Use a hash set for quick verification whether a point is in the generation
2/ Hash using the boundaries - using 7 as a ...
I think a HashTable (of a HashSet) is a very convenient way to represent a tree. It gives you instant access to any element of the tree if there is a unique id representing each node. The problem (and code) below exemplifies this point. Once the representation is there, performing a Depth-First Search becomes very trivial. Code is down below, cheers, ACC.
This is an interesting problem where you do need a priority queue in order to simulate the game (remember to use Max-Color as the priority since the dequeuing is based on smaller priorities first), but the tricky part here is that you cannot enqueue in the main loop while each round simulation is going on otherwise you'll starve lower priority colors. Hence in the middle of t...