Cheat to solve Day 13 Part 2

README.md

@@ -2,7 +2,7 @@
 
 My (attempted) solutions to [Advent of Code 2020](https://adventofcode.com/2020) in Elixir.
 
-<img width="978" alt="image" src="https://user-images.githubusercontent.com/498229/102176995-f132c000-3ee5-11eb-9dc5-7eb450c4d68f.png">
+<img width="978" alt="image" src="https://user-images.githubusercontent.com/498229/102243688-c9237b00-3f3e-11eb-9b64-5700113eee16.png">
 
 ## Strategy
 

day13/README

@@ -21,6 +21,9 @@ minutes to wait. Take the minimum.
 $ elixir day13part2.exs
 *runs forever*
 
+$ elixir day13part2-cheating.exs
+741745043105674
+
 Thoughts:
 
 Another one that's impossible to brute force. Currently stuck.
@@ -39,6 +42,15 @@ is important.
 Going to come back to this later with a clear mind. Not sure I'll get it without a hint.
 Seems like I have a knowledge gap.
 
+** Update 16 Dec - 3 days later **
+
+I did lots of reading into the Chinese Remainder Theorem, but wasn't able to work out
+how to apply that here. I'm giving in and asking for help. Voltone on Elixir Forum had
+the answer, so I adapted it to my program and it outputted the right answer - so I'm
+claiming the star :P, although I'm not going to claim I solved this, so I added that
+version to day13part2-cheating.exs with credit. Will definitely come back to this to
+understand it properly.
+
 
 +------------------+
 | Overall Thoughts |

day13/day13part2-cheating.exs

@@ -0,0 +1,36 @@
+defmodule Day13Part2 do
+  def run do
+    File.read!("input")
+    |> String.split(["\n", ","], trim: true)
+    |> Enum.drop(1)
+    |> Enum.map(&parse_schedule/1)
+    |> Enum.with_index()
+    |> Enum.reject(&match?({:any, _}, &1))
+    |> Enum.reduce({0, 1}, &find_sequential_departures/2)
+    |> elem(0)
+    |> IO.puts()
+  end
+
+  def parse_schedule(id) do
+    case Integer.parse(id) do
+      {id, ""} -> id
+      _ -> :any
+    end
+  end
+
+  # Adapted from voltone's solution ❤️
+  # https://elixirforum.com/t/advent-of-code-2020-day-13/36180/6
+  defp find_sequential_departures({bus, index}, {t, step}) do
+    if rem(t + index, bus) == 0 do
+      {t, lcm(step, bus)}
+    else
+      find_sequential_departures({bus, index}, {t + step, step})
+    end
+  end
+
+  defp lcm(a, b) do
+    div(a * b, Integer.gcd(a, b))
+  end
+end
+
+Day13Part2.run()

day13/input

@@ -0,0 +1,2 @@
+1002460
+29,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,41,x,x,x,x,x,x,x,x,x,601,x,x,x,x,x,x,x,23,x,x,x,x,13,x,x,x,17,x,19,x,x,x,x,x,x,x,x,x,x,x,463,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,37