day13: TIL: Chinese Remainder Theorem

day13.py

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+import aoclib
+import math
+import sys
+
+DAY = 13
+TEST_SOLUTION_PART1 = 295
+TEST_SOLUTION_PART2 = 1068781
+
+
+def part1(test_mode=False):
+    my_input = aoclib.getInputAsArraySplit(day=DAY, split_char=",", test=test_mode)
+
+    my_arrival = int(my_input[0][0])
+    bus_ids = [int(i) for i in my_input[1] if i != 'x']
+    waiting_times = [i - my_arrival % i for i in bus_ids]
+    min_waiting_time = min(waiting_times)
+
+    return min_waiting_time * bus_ids[waiting_times.index(min_waiting_time)]
+
+
+def part2(test_mode=False):
+    my_input = aoclib.getInputAsArraySplit(day=DAY, split_char=",", test=test_mode)
+
+    bus_ids = {-i: int(v) for i, v in enumerate(my_input[1]) if v != 'x'}
+    lowest_common_multiple = math.lcm(*bus_ids.values())
+    base_multipliers = [lowest_common_multiple // interval for interval in bus_ids.values()]
+    modular_multiplicative_inverses = [
+        pow(base_multiplier, -1, interval)
+        for base_multiplier, interval
+        in zip(base_multipliers, bus_ids.values())
+    ]
+
+    return sum(
+        offset * multiplier * mmi
+        for offset, multiplier, mmi
+        in zip(bus_ids.keys(), base_multipliers, modular_multiplicative_inverses)
+    ) % lowest_common_multiple

inputs/13

@@ -0,0 +1,2 @@
+1008832
+23,x,x,x,x,x,x,x,x,x,x,x,x,41,x,x,x,x,x,x,x,x,x,449,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,13,19,x,x,x,x,x,x,x,x,x,29,x,991,x,x,x,x,x,37,x,x,x,x,x,x,x,x,x,x,17

inputs/13_test

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+939
+7,13,x,x,59,x,31,19
+17,x,13,19