From ff27ee12511c11b56cf40f91e0587430cfe5661e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Stefan=20B=C3=BChler?= <stbuehler@web.de>
Date: Sun, 13 Dec 2020 11:45:07 +0100
Subject: [PATCH] day 13

---
 data/day13/input |  2 ++
 src/bin/day13.rs | 69 ++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 71 insertions(+)
 create mode 100644 data/day13/input
 create mode 100644 src/bin/day13.rs

diff --git a/data/day13/input b/data/day13/input
new file mode 100644
index 0000000..36f269f
--- /dev/null
+++ b/data/day13/input
@@ -0,0 +1,2 @@
+1000186
+17,x,x,x,x,x,x,x,x,x,x,37,x,x,x,x,x,907,x,x,x,x,x,x,x,x,x,x,x,19,x,x,x,x,x,x,x,x,x,x,23,x,x,x,x,x,29,x,653,x,x,x,x,x,x,x,x,x,41,x,x,13
diff --git a/src/bin/day13.rs b/src/bin/day13.rs
new file mode 100644
index 0000000..a250d0d
--- /dev/null
+++ b/src/bin/day13.rs
@@ -0,0 +1,69 @@
+const INPUT: &str = include_str!("../../data/day13/input");
+
+struct Input {
+	now: i128,
+	bus_intervals: Vec<Option<i128>>,
+}
+
+impl Input {
+	fn parse(data: &str) -> Self {
+		let mut lines = data.lines();
+		let now = lines.next().unwrap().parse::<i128>().unwrap();
+		let bus_intervals = lines.next().unwrap().split(',').map(|part| {
+			if part == "x" {
+				None
+			} else {
+				Some(part.parse::<i128>().unwrap())
+			}
+		}).collect();
+		Self { now, bus_intervals }
+	}
+}
+
+fn extended_gcd(a: i128, b: i128) -> (i128, i128, i128) {
+	// invariant: r == s*a + t*b
+	// old: .0, current: .1
+	let mut r = (a as i128, b as i128);
+	let mut s = (1, 0);
+	let mut t = (0, 1);
+
+	while r.1 != 0 {
+		let q = r.0 / r.1;
+		r = (r.1, r.0 - q * r.1);
+		s = (s.1, s.0 - q * s.1);
+		t = (t.1, t.0 - q * t.1);
+	}
+	(r.0 as i128, s.0 as i128, t.0 as i128)
+}
+
+
+fn main() {
+	let input = Input::parse(INPUT);
+	let (wait, interval) = input.bus_intervals.iter().filter_map(|&interval| {
+		let interval = interval?;
+		let wait = interval - ((input.now - 1) % interval) - 1;
+		Some((wait, interval))
+	}).min().unwrap();
+	println!("Waiting {} minutes for bus {}: {}", wait, interval, wait * interval);
+
+	// searching T: T == offset (mod interval)
+	let mut offs_interval: Vec<(i128, i128)> = input.bus_intervals.iter().enumerate().filter_map(|(ndx, &interval)| {
+		let interval = interval?;
+		// T + ndx == 0 (mod interval)
+		// => offset == -ndx (mod interval)
+		let offset = (interval - (ndx as i128) % interval) % interval;
+		Some((offset, interval))
+	}).collect();
+	// println!("{:?}", offs_interval);
+	let start = offs_interval.remove(0);
+	let result = offs_interval.into_iter().fold(start, |(a_off, a_int), (b_off, b_int)| {
+		let (g, s, t) = extended_gcd(a_int, b_int);
+		assert_eq!(a_off % g, b_off % g);
+		let ai = a_int / g;
+		let bi = b_int / g;
+		let next_int = ai * bi * g;
+		let next_off = a_off * t * bi + b_off * s * ai;
+		((next_off % next_int + next_int) % next_int, next_int)
+	});
+	println!("Requested pattern occurs at: {}", result.0);
+}