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day13.rs
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day13.rs
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//! # Claw Contraption
//!
//! Each claw machine is a system of two linear equations:
//!
//! ```none
//! (Button A X) * (A presses) + (Button B X) * (B presses) = Prize X
//! (Button A Y) * (A presses) + (Button B Y) * (B presses) = Prize Y
//! ```
//!
//! Shortening the names and representing as a matrix:
//!
//! ```none
//! [ ax bx ][ a ] = [ px ]
//! [ ay by ][ b ] = [ py ]
//! ```
//!
//! To solve we invert the 2 x 2 matrix then premultiply the right column.
use crate::util::iter::*;
use crate::util::parse::*;
type Claw = [i64; 6];
pub fn parse(input: &str) -> Vec<Claw> {
input.iter_signed().chunk::<6>().collect()
}
pub fn part1(input: &[Claw]) -> i64 {
input.iter().map(|row| play(row, false)).sum()
}
pub fn part2(input: &[Claw]) -> i64 {
input.iter().map(|row| play(row, true)).sum()
}
/// Invert the 2 x 2 matrix representing the system of linear equations.
fn play(&[ax, ay, bx, by, mut px, mut py]: &Claw, part_two: bool) -> i64 {
if part_two {
px += 10_000_000_000_000;
py += 10_000_000_000_000;
}
// If determinant is zero there's no solution.
let det = ax * by - ay * bx;
if det == 0 {
return 0;
}
let mut a = by * px - bx * py;
let mut b = ax * py - ay * px;
// Integer solutions only.
if a % det != 0 || b % det != 0 {
return 0;
}
a /= det;
b /= det;
if part_two || (a <= 100 && b <= 100) {
3 * a + b
} else {
0
}
}