day 6 part 2

inputs/day6.txt

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+Time:        42     68     69     85
+Distance:   284   1005   1122   1341

src/bin/day6.rs

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+#![forbid(elided_lifetimes_in_paths, unsafe_code)]
+
+use aoc23::read;
+use chumsky::{prelude::*, text::int};
+
+struct Game {
+	time: i64,
+	distance: i64
+}
+
+fn parser() -> impl Parser<char, Vec<Game>, Error = Simple<char>> {
+	let int_list = just(" ")
+		.repeated()
+		.ignore_then(int(10).separated_by(just(" ").repeated().at_least(1)));
+	just("Time:")
+		.ignore_then(int_list)
+		.then_ignore(just("\nDistance:"))
+		.then(int_list)
+		.map(|(times, dists): (Vec<String>, Vec<String>)| {
+			times
+				.into_iter()
+				.zip(dists)
+				.map(|(time, distance)| Game {
+					time: time.parse().unwrap(),
+					distance: distance.parse().unwrap()
+				})
+				.collect()
+		})
+		.then_ignore(just("\n"))
+		.then_ignore(end())
+}
+
+fn ways2win(t: i64, d: i64) -> i64 {
+	// we want the minimum a s.t. (t-a)*a > d,
+	// and the maximum a s.t.     (t-a)*a < d
+	// that means we have a quadratic function -a² + ta - d and we want to find
+	// its intersections with the axis
+
+	let discriminant = t * t - 4 * d;
+	if discriminant < 0 {
+		return 0;
+	}
+	let sqrt = (discriminant as f64).sqrt();
+	let min = ((t as f64 - sqrt) / 2.0).ceil() as i64;
+	let max = ((t as f64 + sqrt) / 2.0).floor() as i64;
+	eprintln!(
+		"t={t}, d={d}, min={min} ({}), max={max} ({})",
+		(t - min) * min,
+		(t - max) * max
+	);
+	assert!(max >= min);
+
+	max - min + 1
+}
+
+fn main() -> anyhow::Result<()> {
+	let games = read("inputs/day6.txt", parser())?;
+
+	println!(
+		"{}",
+		games
+			.iter()
+			.map(|game| ways2win(game.time, game.distance))
+			.product::<i64>()
+	);
+
+	let mut t = 0;
+	let mut d = 0;
+	for game in &games {
+		t = t * 10i64.pow((game.time as f64).log10().floor() as u32 + 1) + game.time;
+		d = d * 10i64.pow((game.distance as f64).log10().floor() as u32 + 1)
+			+ game.distance;
+	}
+	println!("{}", ways2win(t, d));
+
+	Ok(())
+}