Solution to problem 13 part 2

src/P13.py

@@ -69,10 +69,12 @@
 # the number of minutes you'll need to wait for that bus?
 
 from copy import copy
+from math import gcd
 
 with open("files/P13.txt", "r") as f:
     start = int(f.readline())
-    buses = [int(bus) for bus in f.readline().strip().split(",") if bus != "x"]
+    buses_x = [bus for bus in f.readline().strip().split(",")]
+    buses = [int(bus) for bus in buses_x if bus != "x"]
 
 
 def part_1() -> None:
@@ -87,5 +89,121 @@ def part_1() -> None:
             wait += 1
 
 
+# --- Part Two ---
+
+# The shuttle company is running a contest: one gold coin for anyone that can
+# find the earliest timestamp such that the first bus ID departs at that time
+# and each subsequent listed bus ID departs at that subsequent minute. (The
+# first line in your input is no longer relevant.)
+
+# For example, suppose you have the same list of bus IDs as above:
+
+# 7,13,x,x,59,x,31,19
+
+# An x in the schedule means there are no constraints on what bus IDs must
+# depart at that time.
+
+# This means you are looking for the earliest timestamp (called t) such that:
+
+#     Bus ID 7 departs at timestamp t.
+#     Bus ID 13 departs one minute after timestamp t.
+#     There are no requirements or restrictions on departures at two or three
+# minutes after timestamp t.
+#     Bus ID 59 departs four minutes after timestamp t.
+#     There are no requirements or restrictions on departures at five minutes
+# after timestamp t.
+#     Bus ID 31 departs six minutes after timestamp t.
+#     Bus ID 19 departs seven minutes after timestamp t.
+
+# The only bus departures that matter are the listed bus IDs at their specific
+# offsets from t. Those bus IDs can depart at other times, and other bus IDs
+# can depart at those times. For example, in the list above, because bus ID 19
+# must depart seven minutes after the timestamp at which bus ID 7 departs, bus
+# ID 7 will always also be departing with bus ID 19 at seven minutes after
+# timestamp t.
+
+# In this example, the earliest timestamp at which this occurs is 1068781:
+
+# time     bus 7   bus 13  bus 59  bus 31  bus 19
+# 1068773    .       .       .       .       .
+# 1068774    D       .       .       .       .
+# 1068775    .       .       .       .       .
+# 1068776    .       .       .       .       .
+# 1068777    .       .       .       .       .
+# 1068778    .       .       .       .       .
+# 1068779    .       .       .       .       .
+# 1068780    .       .       .       .       .
+# 1068781    D       .       .       .       .
+# 1068782    .       D       .       .       .
+# 1068783    .       .       .       .       .
+# 1068784    .       .       .       .       .
+# 1068785    .       .       D       .       .
+# 1068786    .       .       .       .       .
+# 1068787    .       .       .       D       .
+# 1068788    D       .       .       .       D
+# 1068789    .       .       .       .       .
+# 1068790    .       .       .       .       .
+# 1068791    .       .       .       .       .
+# 1068792    .       .       .       .       .
+# 1068793    .       .       .       .       .
+# 1068794    .       .       .       .       .
+# 1068795    D       D       .       .       .
+# 1068796    .       .       .       .       .
+# 1068797    .       .       .       .       .
+
+# In the above example, bus ID 7 departs at timestamp 1068788 (seven minutes
+# after t). This is fine; the only requirement on that minute is that bus ID 19
+# departs then, and it does.
+
+# Here are some other examples:
+
+#     The earliest timestamp that matches the list 17,x,13,19 is 3417.
+#     67,7,59,61 first occurs at timestamp 754018.
+#     67,x,7,59,61 first occurs at timestamp 779210.
+#     67,7,x,59,61 first occurs at timestamp 1261476.
+#     1789,37,47,1889 first occurs at timestamp 1202161486.
+
+# However, with so many bus IDs in your list, surely the actual earliest
+# timestamp will be larger than 100000000000000!
+
+# What is the earliest timestamp such that all of the listed bus IDs depart at
+# offsets matching their positions in the list?
+
+
+# adapted from https://stackoverflow.com/questions/32728526/lcm-using-recursive
+def lcm(my_list: list[list[int]]) -> int:
+    lcm = my_list[0][0]
+    for pair in my_list[1:]:
+        lcm = lcm * pair[0] // gcd(lcm, pair[0])
+    return lcm
+
+
+def part_2() -> None:
+    my_buses = []
+    for idx, bus in enumerate(buses_x):
+        if bus != "x":
+            my_buses.append([int(bus), idx])
+
+    value = 0
+    add_to = 1
+    for i in range(1, len(my_buses)):
+        good = False
+        while not good:
+            good = True
+            for j in range(i + 1):
+                if (value + my_buses[j][1]) % my_buses[j][0] != 0:
+                    good = False
+                    break
+            if good is True:
+                # find the offset between buses
+                add_to = lcm(my_buses[:j])
+                break
+            else:
+                value += add_to
+
+    print(f"Solution to part 2 is {value}")
+
+
 if __name__ == "__main__":
     part_1()
+    part_2()