day 13 puzzle 2

progress.yaml

@@ -23,4 +23,4 @@
 12:
   stars: 2
 13:
-  stars: 1
+  stars: 2

src/day13/puzzle2.typ

@@ -0,0 +1,74 @@
+#import "/src/utils.typ": *
+
+#let parse-machine(lines) = {
+  let lines = lines.split("\n")
+  let match-a = lines.at(0).match(regex("Button A: X\\+(\d+), Y\\+(\d+)"))
+  let match-b = lines.at(1).match(regex("Button B: X\\+(\d+), Y\\+(\d+)"))
+  let match-p = lines.at(2).match(regex("Prize: X=(\d+), Y=(\d+)"))
+
+  return (
+    a: (
+      x: int(match-a.captures.first()),
+      y: int(match-a.captures.last()),
+    ),
+    b: (
+      x: int(match-b.captures.first()),
+      y: int(match-b.captures.last()),
+    ),
+    prize: (
+      x: int(match-p.captures.first()) + 10000000000000,
+      y: int(match-p.captures.last()) + 10000000000000,
+    )
+  )
+}
+
+#let mat-mul-v(mat, v) = {
+  return (
+    mat.at(0).at(0) * v.at(0) + mat.at(0).at(1) * v.at(1),
+    mat.at(1).at(0) * v.at(0) + mat.at(1).at(1) * v.at(1)
+  )
+}
+
+#let det(mat) = {
+  return mat.at(0).at(0) * mat.at(1).at(1) - mat.at(1).at(0) * mat.at(0).at(1)
+}
+
+#let solve(input) = {
+  let machines = input.split("\n\n")
+  machines = machines.map(parse-machine)
+
+  let total = 0
+  for m in machines {
+    let mat = (
+      (m.a.x, m.b.x),
+      (m.a.y, m.b.y)
+    )
+    let v = (m.prize.x, m.prize.y)
+    let mat2 = (
+      (mat.at(1).at(1), -mat.at(0).at(1)),
+      (-mat.at(1).at(0), mat.at(0).at(0)),
+    )
+
+    let (a, b) = mat-mul-v(mat2, v)
+
+    let d = det(mat)
+
+    // Check integer solution
+    if calc.rem(a, d) != 0 or calc.rem(b, d) != 0 {
+      continue
+    }
+    a = int(a / d)
+    b = int(b / d)
+
+    if a > 0 and b > 0 {
+      total += a * 3 + b
+    }
+  }
+  return total
+}
+
+#show-puzzle(
+  13, 2,
+  solve,
+  example: 875318608908
+)