day 6 part 2

This commit is contained in:
Dominic 2023-12-06 09:08:39 +01:00
parent 1d285ee38c
commit 146735881a
Signed by: msrd0
GPG key ID: DCC8C247452E98F9

View file

@ -30,35 +30,48 @@ fn parser() -> impl Parser<char, Vec<Game>, Error = Simple<char>> {
.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())?;
let mut result = 1;
println!(
"{}",
games
.iter()
.map(|game| ways2win(game.time, game.distance))
.product::<i64>()
);
let mut t = 0;
let mut d = 0;
for game in &games {
let t = game.time;
let d = game.distance + 1;
// 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 {
continue;
}
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);
result *= max - min + 1;
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!("{result}");
println!("{}", ways2win(t, d));
Ok(())
}