I tried to solve the problem in a mathematical way, like a Fibonacci sequence. I believe there’s a better way than mine in math.
qhwa
egze
mudasobwa
Creator of Cure
egze
Cool. We tried to build a DynamicSupervisor solution today at work. Our solution was similar to yours. We quickly stumbled into the process limit of the VM. We could increase it enough for part 1 to work, but the maximum amount was still not enough for part 2 without going multi-node. Maybe we can explore it next time 
Also we tried casting but then the count of fishes would be wrong.
0
mudasobwa
Creator of Cure
jarimatti
I think there is an elegant mathematical way, using linear algebra: the amount of fish that have specific day can be modeled as a vector, where element 0 is the amount of fish that have 0 days left. Total number of fish at any given day is the sum of elements of that vector.
We can multiply that vector with a matrix K, that produces the next day’s fish counts. Here’s what K could look like (apologies for Octave/Matlab syntax, I used that to verify the approach):
K0 = [
0 0 0 0 0 0 1 0 1;
1 0 0 0 0 0 0 0 0;
0 1 0 0 0 0 0 0 0;
0 0 1 0 0 0 0 0 0;
0 0 0 1 0 0 0 0 0;
0 0 0 0 1 0 0 0 0;
0 0 0 0 0 1 0 0 0;
0 0 0 0 0 0 1 0 0;
0 0 0 0 0 0 0 1 0
];
# Fun fact: matrix for computing any initial condition to day 80 is:
K80 = K0 ^ 80;
# Get day 1 from day 0 counts per day:
v1 = v0 * K;
# Get day 80 from day 0 counts per day:
v80 = v0 * K80;
Full code here for my input: aoc2021_day6.m
I’ve yet to figure out how to do this in Elixir fluently and it seems it’s time to learn some Nx. 
4
jarimatti
OK, that was more fun than expected. (pun not intended)
Nx solution module over here: Aoc2021.Day6.LinAlg
Nx multiply and especially Nx.power are done by element, so I had to resort to reduce when multiplying the tensors. Otherwise it pretty much follows the Octave style. I like Nx so far, this was easy to install and play around with.
4
qhwa
Thank you for sharing this! This matrix is awesome!
I watched @josevalim 's video on day 6, and oh man, it was so amazing and blew my mind. In the end, he tried the same matrix idea with Nx. It was so delightful to watch him thinking, solving, and explaining.
3