USACO 2020 Gold December Contest, Replication

Problems and Contests
#1

In the problem Replication, in the problem statement, it says that every hour all the robots will move either north, south, east, or west. I got stuck on this part for a bit thinking that even once the center of the mass of robots got a place, they couldn’t just stop and keep replicating, they had to keep moving. However, in the solution, it says to observe that once we have reached a possible center-spot, we can stay and keep replicating from that spot until a robot hits the border. This contradicts the problem statement, which said the bots move every hour. Am I mistaken in this? I just want to make sure I interpret problems correctly in the future, because to me, when it says the swarm of robots move every hour in some direction means they cannot stay in place.

Thanks!

#2

You can move in one direction and then revert that move during the next timestep, which has the same effect.

#3

Oh snap, I just realized that would actually work. I was assuming that there would be a case where you move, replicate, and there wouldn’t be space to move back or something like that, but that would only be true if you cannot replicate more anyway.

Thanks!