Rat position prediction is working

It's still painfully slow for cases with lots of rats, but I can definitely fix that with ~1 hour more of work.  For now I think it's best for Samara and Polina to start working on other algorithms that take advantage of rat position prediction and not worry about optimizing.  I'll try to do it by Wednesday, and I'll definitely be able to do it by next week.

Also, this still goes for rats that are under another piper's control.  We need to fix that.