Year 2024 Day 13

Author: maneatingape

README.md

@@ -84,6 +84,7 @@ Performance is reasonable even on older hardware, for example a 2011 MacBook Pro
 | 10 | [Hoof It](https://adventofcode.com/2024/day/10) | [Source](src/year2024/day10.rs) | 38 |
 | 11 | [Plutonian Pebbles](https://adventofcode.com/2024/day/11) | [Source](src/year2024/day11.rs) | 248 |
 | 12 | [Garden Groups](https://adventofcode.com/2024/day/12) | [Source](src/year2024/day12.rs) | 289 |
+| 13 | [Claw Contraption](https://adventofcode.com/2024/day/13) | [Source](src/year2024/day13.rs) | 14 |
 
 ## 2023
 

benches/benchmark.rs

@@ -87,5 +87,5 @@ benchmark!(year2023
 );
 
 benchmark!(year2024
-    day01, day02, day03, day04, day05, day06, day07, day08, day09, day10, day11, day12
+    day01, day02, day03, day04, day05, day06, day07, day08, day09, day10, day11, day12, day13
 );

src/lib.rs

@@ -67,5 +67,5 @@ library!(year2023 "Restore global snow production."
 );
 
 library!(year2024 "Locate the Chief Historian in time for the big Christmas sleigh launch."
-    day01, day02, day03, day04, day05, day06, day07, day08, day09, day10, day11, day12
+    day01, day02, day03, day04, day05, day06, day07, day08, day09, day10, day11, day12, day13
 );

src/main.rs

@@ -139,5 +139,5 @@ run!(year2023
 );
 
 run!(year2024
-    day01, day02, day03, day04, day05, day06, day07, day08, day09, day10, day11, day12
+    day01, day02, day03, day04, day05, day06, day07, day08, day09, day10, day11, day12, day13
 );

src/year2024/day13.rs

@@ -0,0 +1,64 @@
+//! # 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::parse::*;
+use crate::util::iter::*;
+
+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
+    }
+}

tests/test.rs

@@ -80,5 +80,5 @@ test!(year2023
 );
 
 test!(year2024
-    day01, day02, day03, day04, day05, day06, day07, day08, day09, day10, day11, day12
+    day01, day02, day03, day04, day05, day06, day07, day08, day09, day10, day11, day12, day13
 );

tests/year2024/day13.rs

@@ -0,0 +1,30 @@
+use aoc::year2024::day13::*;
+
+const EXAMPLE: &str = "\
+Button A: X+94, Y+34
+Button B: X+22, Y+67
+Prize: X=8400, Y=5400
+
+Button A: X+26, Y+66
+Button B: X+67, Y+21
+Prize: X=12748, Y=12176
+
+Button A: X+17, Y+86
+Button B: X+84, Y+37
+Prize: X=7870, Y=6450
+
+Button A: X+69, Y+23
+Button B: X+27, Y+71
+Prize: X=18641, Y=10279";
+
+#[test]
+fn part1_test() {
+    let input = parse(EXAMPLE);
+    assert_eq!(part1(&input), 480);
+}
+
+#[test]
+fn part2_test() {
+    let input = parse(EXAMPLE);
+    assert_eq!(part2(&input), 875318608908);
+}