Day 13

Author: tuukkasarvi

data/input_13.txt

@@ -0,0 +1,2 @@
+1014511
+17,x,x,x,x,x,x,41,x,x,x,x,x,x,x,x,x,643,x,x,x,x,x,x,x,23,x,x,x,x,13,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,29,x,433,x,x,x,x,x,37,x,x,x,x,x,x,x,x,x,x,x,x,19

day_13.py

@@ -0,0 +1,70 @@
+"""
+1.
+What is the ID of the earliest bus you can take to the airport multiplied by the number of
+minutes you'll need to wait for that bus?
+
+2.
+What is the earliest timestamp such that all of the listed bus IDs depart at offsets matching
+their positions in the list?
+"""
+import numpy as np
+
+filename = 'data/input_13.txt'
+
+
+def part1():
+    with open(filename) as fp:
+        lines = [line.strip("\n") for line in fp]
+    departure_after = int(lines[0])
+    buses = [int(item) for item in lines[1].split(",") if item != "x"]
+    departures = [departure_after - (departure_after % bus) + bus for bus in buses]
+    departure_earliest = min(departures)
+    bus = buses[departures.index(departure_earliest)]
+    print("Answer %d" % (bus * (departure_earliest - departure_after)))
+
+
+def is_solution(t, ids, offsets, l):
+    """ conditions are of form (t + offset) % ID = 0"""
+    return all([((t + offsets[i]) % ids[i]) == 0 for i in range(l)])
+
+
+def eda(ids, offsets):
+    """ It so happens that third offset (17 time units) from t must be divisible by
+    643, 17, 13, 29 and 37.
+    """
+    print([643] + list(np.array(ids)[np.array(ids) == np.abs(np.array(offsets) - 17)]))
+
+
+def search(ids, offsets, l):
+    """ Search over all multiples of 643 * 17 * 13 * 29 * 37 = 152476519.
+    Third offset from t must be divisible by 643, 17, 13, 29 and 37.
+    (t + 17) % 152476519 = 0.
+    """
+    a = 152476519
+    t = a - 17
+    print("Max solution: %d" % np.prod(ids))
+    print("Max iterations: %d" % (np.prod(ids) / a))
+    print("Average iterations: %d" % (np.prod(ids)/(2*a)))
+    while not is_solution(t, ids, offsets, l):
+        t += a
+        # print(t)
+    print("Iterations required: %d" % ((t + 17) / a))
+    return t
+
+
+def part2():
+    with open(filename) as fp:
+        lines = [line.strip("\n") for line in fp]
+    data = ["x" if item == "x" else int(item) for item in lines[1].split(",")]
+    ids = [int(item) for item in lines[1].split(",") if item != "x"]
+    offsets = [data.index(id) for id in ids]
+    l = len(ids)
+    # eda(ids, offsets)
+    t = search(ids, offsets, l)
+    print("Answer: %d" % t)
+
+
+if __name__ == '__main__':
+    part1()
+    print("****")
+    part2()