day 13 puzzle 2

progress.yaml

@@ -22,3 +22,5 @@
   stars: 2
 12:
   stars: 2
+13:
+  stars: 2

res/examples/day13.txt

@@ -0,0 +1,15 @@
+Button A: X+94, Y+34
+Button B: X+22, Y+67
+Prize: X=8400, Y=5400
+
+Button A: X+26, Y+66
+Button B: X+67, Y+21
+Prize: X=12748, Y=12176
+
+Button A: X+17, Y+86
+Button B: X+84, Y+37
+Prize: X=7870, Y=6450
+
+Button A: X+69, Y+23
+Button B: X+27, Y+71
+Prize: X=18641, Y=10279

src/day13/puzzle1.typ

@@ -0,0 +1,86 @@
+#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()),
+      y: int(match-p.captures.last()),
+    )
+  )
+}
+
+#let in-line(v1, v2) = {
+  let f1 = v2.x / v1.x
+  let f2 = v2.y / v1.y
+  return f1 == f2
+}
+
+#let solve(input) = {
+  let machines = input.split("\n\n")
+  machines = machines.map(parse-machine)
+
+  let total = 0
+  for m in machines {
+    let totals = ()
+    let are-inline = in-line(m.a, m.b)
+    for b in range(101) {
+      let bx = b * m.b.x
+      let by = b * m.b.y
+      let rx = m.prize.x - bx
+      let ry = m.prize.y - by
+      if rx < 0 or ry < 0 {
+        break
+      }
+      let rax = calc.rem(
+        rx,
+        m.a.x
+      )
+      let ray = calc.rem(
+        ry,
+        m.a.y
+      )
+      if rax != 0 or ray != 0 {
+        continue
+      }
+
+      let a1 = calc.div-euclid(
+        rx,
+        m.a.x
+      )
+      let a2 = calc.div-euclid(
+        ry,
+        m.a.y
+      )
+      if a1 != a2 or a1 > 100 {
+        continue
+      }
+      totals.push(b + a1 * 3)
+      if not are-inline {
+        break
+      }
+    }
+    if totals.len() != 0 {
+      total += calc.min(..totals)
+    }
+  }
+  return total
+}
+
+#show-puzzle(
+  13, 1,
+  solve,
+  example: 480
+)

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
+)