2024 day 13.

src/holt59/aoc/2024/day13.py

@@ -1,7 +1,79 @@
+import math
+from dataclasses import dataclass
 from typing import Any, Iterator
 
+import parse  # pyright: ignore[reportMissingTypeStubs]
+
 from ..base import BaseSolver
 
 
+@dataclass(frozen=True)
+class Machine:
+    prize: tuple[int, int]
+    button_a: tuple[int, int]
+    button_b: tuple[int, int]
+
+
+def read_machine(block: str) -> Machine:
+    ba = parse.parse(  # type: ignore
+        """Button A: X{bax:d}, Y{bay:d}
+Button B: X{bbx:d}, Y{bby:d}
+Prize: X={px:d}, Y={py:d}""",
+        block,
+    )
+    return Machine(
+        prize=(ba["px"], ba["py"]),  # type: ignore
+        button_a=(ba["bax"], ba["bay"]),  # type: ignore
+        button_b=(ba["bbx"], ba["bby"]),  # type: ignore
+    )
+
+
+def diophantine(a: int, b: int, c: int) -> tuple[int, int]:
+    q, r = divmod(a, b)
+    if r == 0:
+        return (0, c // b)
+    else:
+        u, v = diophantine(b, r, c)
+        return (v, u - q * v)
+
+
+def solve(machine: Machine) -> int:
+    (ax, ay), (bx, by), (px, py) = machine.button_a, machine.button_b, machine.prize
+    dx, dy = math.gcd(ax, bx), math.gcd(ay, by)
+
+    if px % dx != 0 or py % dy != 0:
+        return 0
+
+    xa, xb = diophantine(ax, bx, px)
+    ya, yb = diophantine(ay, by, py)
+
+    # expr (x): xa - kx * bx / dx, xb + kx * ax / dx
+    # expr (y): ya - ky * by / dy, yb + ky * ay / dy
+
+    num = ay * (ya - xa) + by * (yb - xb)
+    den = (ax * by - ay * bx) // dx
+
+    if num % den != 0:
+        return 0
+
+    kx = num // den
+    pa, pb = xa - kx * bx // dx, xb + kx * ax // dx
+    return 3 * pa + pb
+
+
 class Solver(BaseSolver):
-    def solve(self, input: str) -> Iterator[Any]: ...
+    def solve(self, input: str) -> Iterator[Any]:
+        machines = [read_machine(block) for block in input.split("\n\n")]
+
+        yield sum(map(solve, machines))
+
+        shift = 10000000000000
+        machines = [
+            Machine(
+                prize=(shift + m.prize[0], shift + m.prize[1]),
+                button_a=m.button_a,
+                button_b=m.button_b,
+            )
+            for m in machines
+        ]
+        yield sum(map(solve, machines))

src/holt59/aoc/inputs/tests/2024/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