Solve day 13 part 2

2020/day13_bus.py

@@ -36,6 +36,53 @@ def solve_part_1(notes) -> int:
 
 
 def solve_part_2(notes) -> int:
+    split = notes[1].split(",")
+    modulos = []
+    remainders = []
+    for position, bus_index in enumerate(split):
+        if bus_index == "x":
+            continue
+        bus_index = int(bus_index)
+        modulos.append(bus_index)
+        remainders.append(bus_index - position)
+    return chinese_remainder(modulos, remainders)
+
+
+def chinese_remainder(modulos, remainders):
+    """List of modulos, then list of remainders"""
+    # https://rosettacode.org/wiki/Chinese_remainder_theorem#Python
+    # License: https://www.gnu.org/licenses/old-licenses/fdl-1.2.html
+    total = 0
+    prod = functools.reduce(lambda a, b: a * b, modulos)
+    for modulo, remainder in zip(modulos, remainders):
+        p = prod // modulo
+        total += remainder * mul_inv(p, modulo) * p
+    return total % prod
+
+
+def mul_inv(a, b):
+    # https://rosettacode.org/wiki/Chinese_remainder_theorem#Python
+    # License: https://www.gnu.org/licenses/old-licenses/fdl-1.2.html
+    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
+
+
+if __name__ == "__main__":
+    n = [3, 5, 7]
+    a = [2, 3, 2]
+    print(chinese_remainder(n, a))
+
+
+def solve_part_2_iterative(notes) -> int:
     """Works but far too slow for the real deal."""
     split = notes[1].split(",")
     buses = list(map(int, filter(lambda bus: bus != "x", split)))
@@ -66,4 +113,4 @@ if __name__ == "__main__":
     main("inputs/day13-test4", None, 779210)
     main("inputs/day13-test5", None, 1261476)
     main("inputs/day13-test6", None, 1202161486)
-    main("inputs/day13", 4315)
+    main("inputs/day13", 4315, 556100168221141)