solve 2024 day 13

2024/README.md

@@ -3,7 +3,7 @@
 |  S  |  M  |  T  |  W  |  T  |  F  |  S  |
 | :-: | :-: | :-: | :-: | :-: | :-: | :-: |
 | [1] | [2] | [3] | [4] | [5] | [6] | [7] |
-| [8] | [9] | [10]| [11]| [12]|  13 |  14 |
+| [8] | [9] | [10]| [11]| [12]| [13]|  14 |
 |  15 |  16 |  17 |  18 |  19 |  20 |  21 |
 |  22 |  23 |  24 |  25 |     |     |     |
 
@@ -19,3 +19,4 @@
 [10]: ./lib/2024/10.ex
 [11]: ./lib/2024/11.ex
 [12]: ./lib/2024/12.ex
+[13]: ./lib/2024/13.ex

2024/lib/2024/13.ex

@@ -0,0 +1,76 @@
+import AOC
+
+aoc 2024, 13 do
+  def p1(input) do
+    input
+    |> read_machines()
+    |> Enum.map(&solve/1)
+    |> Enum.filter(&match?({:solution, a, b} when a <= 100 and b <= 100, &1))
+    |> Enum.map(&tokens_for_solution/1)
+    |> Enum.sum()
+  end
+
+  def p2(input) do
+    input
+    |> read_machines()
+    |> Enum.map(fn %{goal: {x, y}} = machine ->
+      %{machine | goal: {x + 10_000_000_000_000, y + 10_000_000_000_000}}
+    end)
+    |> Enum.map(&solve/1)
+    |> Enum.map(&tokens_for_solution/1)
+    |> Enum.sum()
+  end
+
+  defp solve(%{a: {ax, ay}, b: {bx, by}, goal: {x, y}}) do
+    # a * ax + b * bx = x
+    # a * ay + b * by = y
+
+    # a * ax + b * bx = x
+    #          a * ax = x - b * bx
+    #               a = (x - b * bx) / ax
+
+    #                        a * ay + b * by = y
+    #      ((x - b * bx) / ax) * ay + b * by = y
+    #    ((ay * (x - b * bx)) / ax) + b * by = y
+    # ((ay * x - ay * b * bx) / ax) + b * by = y
+    #     ay * x - ay * b * bx + b * by * ax = y * ax
+    #              b * by * ax - b * ay * bx = y * ax - x * ay
+    #                b * (by * ax - ay * bx) = y * ax - x * ay
+    #                                      b = (y * ax - x * ay) / (by * ax - ay * bx)
+
+    b = div(y * ax - x * ay, by * ax - ay * bx)
+    a = div(x - b * bx, ax)
+
+    if a * ax + b * bx == x and a * ay + b * by == y do
+      {:solution, a, b}
+    else
+      :impossible
+    end
+  end
+
+  defp tokens_for_solution({:solution, a, b}) do
+    3 * a + b
+  end
+
+  defp tokens_for_solution(_), do: 0
+
+  ## input
+
+  defp read_machines(str) do
+    ~r/Button A: X\+(\d+), Y\+(\d+)\nButton B: X\+(\d+), Y\+(\d+)\nPrize: X=(\d+), Y=(\d+)/m
+    |> Regex.scan(
+      str,
+      capture: :all_but_first
+    )
+    |> Enum.map(fn strings ->
+      [xa, ya, xb, yb, x, y] =
+        Enum.map(strings, &String.to_integer/1)
+
+      %{
+        a: {xa, ya},
+        b: {xb, yb},
+        goal: {x, y}
+      }
+    end)
+  end
+end

README.md

@@ -15,8 +15,8 @@
 | [2021] | **43/50** 🌟 | Elixir |
 | [2022] | **14/50** 🌟 | Elixir, Haskell |
 | [2023] | **19/50** 🌟 | Elixir, Haskell |
-| [2024] | **24/50** 🌟 | Elixir |
+| [2024] | **26/50** 🌟 | Elixir |
-| **Total** | **180** 🌟| |
+| **Total** | **182** 🌟| |
 
 [2015]: ./2015
 [2017]: ./2017