I went with representing the frequencies as a tuple and a simulation step was:

defp simulate({s0, s1, s2, s3, s4, s5, s6, s7, s8}, days) when days > 0 do
  simulate({s1, s2, s3, s4, s5, s6, s7 + s0, s8, s0}, days - 1)
end

Full solution

It’d be nice to see an Nx solution here, it fits this problem very nicely.

I enjoyed this one!

defmodule Aoc.Y2021.Day06 do
  @moduledoc """
  Solved https://adventofcode.com/2021/day/6
  """
  import Aoc.Helper.IO

  def run_part1(), do: get_input() |> solve_part1()
  def run_part2(), do: get_input() |> solve_part2()

  def solve_part1(data), do: solve(data, 80)
  def solve_part2(data), do: solve(data, 256)

  def solve(data, days), do: data |> fish_count() |> simulate(days) |> Enum.sum()
  def fish_count(data), do: Enum.map(0..8, fn n -> Map.get(Enum.frequencies(data), n, 0) end)

  def simulate(fish_count, 0), do: fish_count

  def simulate([zeroth, first, second, third, fourth, fifth, sixth, seventh, eighth], days) do
    simulate([first, second, third, fourth, fifth, sixth, seventh + zeroth, eighth, zeroth], days - 1)
  end

  defp get_input(), do: get_integer_input("2021", "06", ",")
end

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.