From 4c8beac3155278667fa7f99c27238a92157c05e6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?S=C3=B8ren=20Rasmussen?= <sr@jondahl.net>
Date: Mon, 14 Dec 2020 20:40:31 +0100
Subject: [PATCH] Day 13, part 2

---
 2020/13/main.py | 42 +++++++++++++++++++++++++++++++++++++++---
 1 file changed, 39 insertions(+), 3 deletions(-)

diff --git a/2020/13/main.py b/2020/13/main.py
index f9cf7d3..b321d56 100644
--- a/2020/13/main.py
+++ b/2020/13/main.py
@@ -1,3 +1,6 @@
+from functools import reduce
+
+
 test = (
 	939,
 	"7,13,x,x,59,x,31,19",
@@ -9,15 +12,48 @@ data = (
 )
 
 
-def part_1(departure, bus_ids):
+def part1(departure, bus_ids):
 	buses = [int(x) for x in bus_ids.split(",") if x != "x"]
 	distances = [(departure // x + 1) * x - departure for x in buses]
 	idx = distances.index(min(distances))
 	return buses[idx], distances[idx]
 
 
-id, wait = part_1(*test)
+def part2(bus_ids):
+	# t = bus_id % bus_id - idx
+	buses = [int(0 if x == "x" else x) for x in bus_ids.split(",")]
+	p = [x - buses.index(x) for x in buses if x != 0]
+	n = [x for x in buses if x != 0]
+	cr = chinese_remainder(n, p)
+	return cr
+
+
+def chinese_remainder(n, p):
+	prod = reduce(lambda a,b: a*b, n)
+
+	sum = 0
+	for div, rem in zip(n, p):
+		pp = prod // div
+		i = pow(pp, -1, div)
+		sum += rem * pp * i
+
+	return sum % prod
+
+
+id, wait = part1(*test)
 assert id*wait == 295
 
-id, wait = part_1(*data)
+id, wait = part1(*data)
 print(f"1: Answer is {id*wait}")
+
+assert chinese_remainder([3, 5, 7], [2, 3, 2]) == 23
+
+assert part2(test[1]) == 1068781
+assert part2("17,x,13,19") == 3417
+assert part2("67,7,59,61") == 754018
+assert part2("67,x,7,59,61") == 779210
+assert part2("67,7,x,59,61") == 1261476
+assert part2("1789,37,47,1889") == 1202161486
+
+ts = part2(data[1])
+print(f"2: Answer is {ts}")