diff --git a/2020/d13/ex2/ex2.py b/2020/d13/ex2/ex2.py new file mode 100755 index 0000000..bd76c7d --- /dev/null +++ b/2020/d13/ex2/ex2.py @@ -0,0 +1,45 @@ +#!/usr/bin/env python + +import math +import sys +from typing import Dict, List + + +def run_contest(timings: List[int]) -> int: + # https://rosettacode.org/wiki/Chinese_remainder_theorem#Python_3.6 + def mul_inv(a: int, b: int) -> int: + b0 = b + x0, x1 = 0, 1 + if b == 1: + return 1 + while a > 1: + q = a // b + a, b = b, a % b + x0, x1 = x1 - q * x0, x0 + if x1 < 0: + x1 += b0 + return x1 + + def chinese_remainder(residue_mapping: Dict[int, int]) -> int: + res = 0 + prod = math.prod(residue_mapping) + for n_i, a_i in residue_mapping.items(): + p = prod // n_i + res += a_i * mul_inv(p, n_i) * p + return res % prod + + residues = {t: -i for (i, t) in enumerate(timings) if t > 0} + return chinese_remainder(residues) + + +def solve(raw: List[str]) -> int: + return run_contest([int(i) if i != "x" else -1 for i in raw[1].split(",")]) + + +def main() -> None: + input = [line.strip() for line in sys.stdin.readlines()] + print(solve(input)) + + +if __name__ == "__main__": + main()