2024 day 13, part 2

I looked at this problem, said yep, we've got some simultaneous equations
with a bit of a cost factor built in, and then promptly *forgot* they can
be solved computationally.

This puzzle made me feel pretty silly.

README.md

@@ -5,8 +5,8 @@
 My Elixir solutions for [Advent of Code](https://adventofcode.com/) (all years).
 
 <!-- stars start -->
-<p><img src="https://img.shields.io/static/v1?label=Total&message=444%20stars&style=for-the-badge&color=green" alt="444 stars" /></p>
-<p><a href="./lib/y2024/"><img src="https://img.shields.io/static/v1?label=2024&message=25%20stars&style=for-the-badge&color=yellow" alt="25 stars" /></a><br />
+<p><img src="https://img.shields.io/static/v1?label=Total&message=445%20stars&style=for-the-badge&color=green" alt="445 stars" /></p>
+<p><a href="./lib/y2024/"><img src="https://img.shields.io/static/v1?label=2024&message=26%20stars&style=for-the-badge&color=yellow" alt="26 stars" /></a><br />
 <a href="./lib/y2023/"><img src="https://img.shields.io/static/v1?label=2023&message=44%20stars&style=for-the-badge&color=green" alt="44 stars" /></a><br />
 <a href="./lib/y2022/"><img src="https://img.shields.io/static/v1?label=2022&message=%E2%AD%90%EF%B8%8F%2050%20stars%20%E2%AD%90%EF%B8%8F&style=for-the-badge&color=brightgreen" alt="50 stars" /></a><br />
 <a href="./lib/y2021/"><img src="https://img.shields.io/static/v1?label=2021&message=46%20stars&style=for-the-badge&color=green" alt="46 stars" /></a><br />

lib/y2024/README.md

@@ -2,7 +2,7 @@
 
 My Elixir solutions for [Advent of Code 2024](https://adventofcode.com/2024).
 
-<!-- stars 2024 start --><img src="https://img.shields.io/static/v1?label=2024&message=25%20stars&style=for-the-badge&color=yellow" alt="25 stars" /><!-- stars 2024 end -->
+<!-- stars 2024 start --><img src="https://img.shields.io/static/v1?label=2024&message=26%20stars&style=for-the-badge&color=yellow" alt="26 stars" /><!-- stars 2024 end -->
 
 ## Benchmarks
 
@@ -38,5 +38,6 @@ day 11, part 1        838.21        1.19 ms     ±4.86%        1.21 ms        1.
 day 11, part 2         19.52       51.22 ms     ±1.86%       51.26 ms       53.37 ms
 day 12, part 1          7.16      139.70 ms     ±1.82%      139.22 ms      144.95 ms
 day 12, part 2          6.84      146.22 ms     ±1.32%      145.82 ms      151.25 ms
-day 13, part 1          4.91      203.63 ms     ±0.46%      203.49 ms      206.75 ms
+day 13, part 1        1.31 K      765.25 μs     ±3.72%         754 μs      837.77 μs
+day 13, part 2        1.33 K      753.73 μs     ±3.42%      744.42 μs      822.51 μs
 ```

lib/y2024/day13.ex

@@ -2,7 +2,10 @@ defmodule Y2024.Day13 do
   use Advent.Day, no: 13
 
   @doc """
-  iex> Day13.part1([%{buttons: %{a: %{x: 94, y: 34, cost: 3}, b: %{x: 22, y: 67, cost: 1}}, prize: %{x: 8400, y: 5400}}])
+  iex> Day13.part1([
+  ...>   %{buttons: %{a: %{x: 94, y: 34, cost: 3}, b: %{x: 22, y: 67, cost: 1}},
+  ...>     prize: %{x: 8400, y: 5400}}
+  ...> ])
   280
   """
   def part1(machines) do
@@ -14,51 +17,63 @@ defmodule Y2024.Day13 do
     end)
   end
 
-  # @doc """
-  # iex> Day13.part2("update or delete me")
-  # "update or delete me"
-  # """
-  # def part2(input) do
-  #   input
-  # end
+  @doc """
+  # iex> Day13.part2([
+  # ...>   %{buttons: %{a: %{x: 26, y: 66, cost: 3}, b: %{x: 67, y: 21, cost: 1}},
+  # ...>     prize: %{x: 10000000012748, y: 10000000012176}}
+  # ...> ])
+  # 459236326669
+  """
+  def part2(machines) do
+    machines
+    |> Enum.map(&find_solution/1)
+    |> Enum.reduce(0, fn
+      %{a: a, b: b}, acc -> acc + a.tokens + b.tokens
+      nil, acc -> acc
+    end)
+  end
 
   @doc """
   iex> Day13.find_solution(%{buttons: %{a: %{x: 94, y: 34, cost: 3}, b: %{x: 22, y: 67, cost: 1}}, prize: %{x: 8400, y: 5400}})
   %{a: %{presses: 80, tokens: 240}, b: %{presses: 40, tokens: 40}}
   """
-  def find_solution(%{buttons: %{a: a, b: b}, prize: prize}) do
-    a_presses = Enum.min([100, div(prize.x, a.x), div(prize.y, a.y)])
-    b_presses = Enum.min([100, div(prize.x, b.x), div(prize.y, b.y)])
+  def find_solution(%{buttons: %{a: button_a, b: button_b}, prize: prize}) do
+    # There are two simultaneous equations that need solving = flip the
+    # button formulas we have to solve for a and b.
+    a = %{one: button_a.x * button_b.cost, two: button_a.y * button_b.cost}
+    b = %{one: button_b.x * button_a.cost, two: button_b.y * button_a.cost}
+    c = %{one: prize.x, two: prize.y}
+
+    a_presses = (b.two * c.one - b.one * c.two) / (b.two * a.one - b.one * a.two)
 
-    result =
-      for(
-        a_press <- 0..a_presses,
-        b_press <- 0..b_presses,
-        do: {a_press, b_press, a.cost * a_press + b.cost * b_press}
-      )
-      |> Enum.sort_by(fn {_, _, cost} -> cost end)
-      |> Enum.find(fn {a_press, b_press, _cost} ->
-        a_press * a.x + b_press * b.x == prize.x && a_press * a.y + b_press * b.y == prize.y
-      end)
+    # The last part should really be b.one but doesn't need the cost factor applied
+    b_presses = (a.one * trunc(a_presses) - c.one) / (-1 * button_b.x)
 
-    if result do
+    # Fractional values aren't valid - you can't press a button 0.5 times
+    if a_presses == trunc(a_presses) && b_presses == trunc(b_presses) do
       %{
-        a: %{tokens: a.cost * elem(result, 0), presses: elem(result, 0)},
-        b: %{tokens: b.cost * elem(result, 1), presses: elem(result, 1)}
+        a: %{presses: trunc(a_presses), tokens: trunc(a_presses) * button_a.cost},
+        b: %{presses: trunc(b_presses), tokens: trunc(b_presses) * button_b.cost}
       }
+    else
+      nil
     end
   end
 
   @doc """
-  iex> Day13.parse_input("Button A: X+94, Y+34\\nButton B: X+22, Y+67\\nPrize: X=8400, Y=5400")
+  iex> Day13.parse_input("Button A: X+94, Y+34\\nButton B: X+22, Y+67\\nPrize: X=8400, Y=5400", 0)
   [%{buttons: %{a: %{x: 94, y: 34, cost: 3}, b: %{x: 22, y: 67, cost: 1}}, prize: %{x: 8400, y: 5400}}]
   """
-  def parse_input(input) do
+  def parse_input(input, offset) do
     input
     |> String.split("\n\n", trim: true)
     |> Enum.map(fn machine ->
       [a, b, prize] = String.split(machine, "\n", trim: true)
-      %{buttons: %{a: parse_button(a, 3), b: parse_button(b, 1)}, prize: parse_prize(prize)}
+
+      %{
+        buttons: %{a: parse_button(a, 3), b: parse_button(b, 1)},
+        prize: parse_prize(prize, offset)
+      }
     end)
   end
 
@@ -67,11 +82,11 @@ defmodule Y2024.Day13 do
     %{cost: cost, x: String.to_integer(x), y: String.to_integer(y)}
   end
 
-  defp parse_prize(string) do
+  defp parse_prize(string, offset) do
     [[x], [y]] = Regex.scan(~r/\d+/, string)
-    %{x: String.to_integer(x), y: String.to_integer(y)}
+    %{x: String.to_integer(x) + offset, y: String.to_integer(y) + offset}
   end
 
-  def part1_verify, do: input() |> parse_input() |> part1()
-  # def part2_verify, do: input() |> parse_input() |> part2()
+  def part1_verify, do: input() |> parse_input(0) |> part1()
+  def part2_verify, do: input() |> parse_input(10_000_000_000_000) |> part2()
 end

test/y2024/day13_test.exs

@@ -4,5 +4,5 @@ defmodule Y2024.Day13Test do
   doctest Day13
 
   test "verification, part 1", do: assert(Day13.part1_verify() == 27157)
-  # test "verification, part 2", do: assert(Day13.part2_verify() == "update or delete me")
+  test "verification, part 2", do: assert(Day13.part2_verify() == 104_015_411_578_548)
 end