71 lines
1.9 KiB
Python
71 lines
1.9 KiB
Python
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from argparse import ArgumentParser
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import sys
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sys.setrecursionlimit(10**7)
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OFFSET = 10_000_000_000_000
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def parse_line(line: str) -> tuple[int, int]:
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line = line.strip()
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_, coords = line.split(":", 1)
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coords = coords.strip()
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x_part, y_part = coords.split(",")
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x_val = x_part.strip()[1:].replace("=", "")
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y_val = y_part.strip()[1:].replace("=", "")
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return int(x_val), int(y_val)
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def parse_input(in_path: str) -> list[list[str]]:
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with open(in_path, "r") as f:
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content = f.read().strip()
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blocks = content.split("\n\n")
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res = []
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for block in blocks:
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lines = block.strip().splitlines()
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if len(lines) == 3:
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res.append(lines)
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return res
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def extended_gcd(a: int, b: int) -> tuple[int, int, int]:
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if b == 0:
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return a, 1, 0
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g, x1, y1 = extended_gcd(b, a % b)
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return g, y1, x1 - (a // b)*y1
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def solve_diophantine_system(xa: int, ya: int, xb: int, yb: int, xp: int, yp: int) -> tuple[int, int] | None:
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# Solve: xa*a + xb*b = xp and ya*a + yb*b = yp
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D = xa*yb - xb*ya
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if D == 0:
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return None
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a_num = yb*xp - xb*yp
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b_num = xa*yp - ya*xp
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if a_num % D != 0 or b_num % D != 0:
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return None
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a0 = a_num // D
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b0 = b_num // D
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if a0 < 0 or b0 < 0:
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return None
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return a0, b0
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def main(in_path: str) -> int:
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machines = parse_input(in_path)
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costs = []
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for m in machines:
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xa, ya = parse_line(m[0])
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xb, yb = parse_line(m[1])
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xp, yp = parse_line(m[2])
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xp += OFFSET
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yp += OFFSET
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sol = solve_diophantine_system(xa, ya, xb, yb, xp, yp)
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if sol is not None:
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a, b = sol
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costs.append(3*a + b)
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if not costs:
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return 0
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return sum(costs)
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if __name__ == "__main__":
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parser = ArgumentParser()
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parser.add_argument("-f", "--file", required=True)
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args = parser.parse_args()
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print(main(args.file))
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