Day 13

2020/day13.py

@@ -0,0 +1,42 @@
+import math
+import sys
+from functools import reduce
+from itertools import combinations
+
+
+def main():
+    lines = [line.rstrip() for line in sys.stdin]
+    earliest = int(lines[0])
+    ids = map(int, filter(lambda s: s != "x", lines[1].split(",")))
+
+    # Part 1
+    wait_times = {i: i - (earliest % i) for i in ids}
+    best_id, wait = min(wait_times.items(), key=lambda item: item[1])
+    print("Part 1:", best_id * wait)
+
+    # Part 2
+    # math shit
+    # https://en.wikipedia.org/wiki/Chinese_remainder_theorem wtf is going on
+    ids = []
+    rems = []
+    for i, v in enumerate(lines[1].split(",")):
+        if v != "x":
+            # import hint: you want to use negative indices for remainders to
+            # use it with CRT here.
+            rems.append(-i)
+            ids.append(int(v))
+    # are all bus IDs co-prime?
+    assert all(math.gcd(a, b) == 1 for a, b in combinations(ids, 2))
+    # CRT
+    # https://www.youtube.com/watch?v=zIFehsBHB8o
+    N = reduce(lambda a, b: a * b, ids, 1)
+    x = 0
+    for ni, ai in zip(ids, rems):
+        Ni = N // ni
+        x += ai * Ni * pow(Ni, -1, ni)
+    x %= N
+    print("Part 2:", x)
+
+
+if __name__ == "__main__":
+    main()