From f071afb02b8d19a2ef284c38c62dc5df2f51bc3a Mon Sep 17 00:00:00 2001
From: Bruno BELANYI <bruno@belanyi.fr>
Date: Sun, 13 Dec 2020 07:39:21 +0100
Subject: [PATCH] 2020: d13: ex2: add solution

---
 2020/d13/ex2/ex2.py | 45 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 45 insertions(+)
 create mode 100755 2020/d13/ex2/ex2.py

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()