- I have contracted some kind of sinus infection, so rn I have a -20 IQ debuff.
a,b
part a: nothing to say here.
part b: Before diving into the discussion, I timed how long 1000 cycles takes to compute, and apparently, it would take 1643175 seconds or just over 19 days to compute 1 billion cycles naively. How fun!
So, how do you cut down that number? First, that number includes a sparse map representation, so you can tick that box off.
Second is intuiting that the result of performing a cycle is cyclical after a certain point. You can confirm this after you've debugged whatever implementation you have for performing cycles- run it a few times on the sample input and you'll find that the result has a cycle length of 7 after the second interaction.
Once you've got that figured out, it's a matter of implementing some kind of cycle detection and modular arithmetic to get the right answer without having to run 1000000000 cycles. For the record, mine took about 400 cycles to find the loop.