2024 day 13

puzzles/Y2024/D13/p1.py

@@ -0,0 +1,6 @@
+from typing import Any
+from .solve import solve
+
+
+def puzzle(input: str) -> Any:
+    return solve(input)

puzzles/Y2024/D13/p2.py

@@ -0,0 +1,6 @@
+from typing import Any
+from .solve import solve
+
+
+def puzzle(input: str) -> Any:
+    return solve(input, 10000000000000)

puzzles/Y2024/D13/solve.py

@@ -0,0 +1,63 @@
+import re
+from typing import Optional
+from dataclasses import dataclass
+
+
+@dataclass
+class Game:
+    da: tuple[int, int]
+    db: tuple[int, int]
+    target: tuple[int, int]
+
+
+def parse_games(input: str, addend: int = 0) -> list[Game]:
+    games = []
+    matches = re.findall(
+        r"""Button A: X\+(\d+), Y\+(\d+)
+Button B: X\+(\d+), Y\+(\d+)
+Prize: X=(\d+), Y=(\d+)""",
+        input,
+    )
+    for match in matches:
+        games.append(
+            Game(
+                (int(match[0]), int(match[1])),
+                (int(match[2]), int(match[3])),
+                (int(match[4]) + addend, int(match[5]) + addend),
+            )
+        )
+    print(len(games))
+    return games
+
+
+def get_tokens_for_win(game: Game) -> Optional[int]:
+    ax, ay = game.da
+    bx, by = game.db
+    target_x, target_y = game.target
+    # solve linear equation:
+    # (ax)a + (bx)b = target_x
+    # (ay)a + (by)b = target_y
+    # using matrices
+    # | ax, bx | | a | = | target_x |
+    # | ay, by | | b | = | target_y |
+    # find inverse
+    determinant = ax * by - bx * ay
+    inverse_matrix = [
+        [by / determinant, -bx / determinant],
+        [-ay / determinant, ax / determinant],
+    ]
+
+    # multiply the inverse matrix by target matrix to get result
+    a = inverse_matrix[0][0] * target_x + inverse_matrix[0][1] * target_y
+    b = inverse_matrix[1][0] * target_x + inverse_matrix[1][1] * target_y
+
+    int_a = int(round(a))
+    int_b = int(round(b))
+    if int_a * ax + int_b * bx == target_x and int_a * ay + int_b * by == target_y:
+        return int_a * 3 + int_b
+    else:
+        return None
+
+
+def solve(input: str, addend: int = 0) -> int:
+    return sum(get_tokens_for_win(game) or 0 for game in parse_games(input, addend))