2024-13

crates/core/src/year2024/day13.rs

@@ -1,18 +1,68 @@
-use crate::input::Input;
+use crate::input::{on_error, Input};
 
-pub const fn solve(_input: &Input) -> Result<u32, String> {
-    Ok(0)
+pub fn solve(input: &Input) -> Result<i64, String> {
+    let offset = input.part_values(0, 10_000_000_000_000);
+
+    input
+        .text
+        .split("\n\n")
+        .map(|s| {
+            let mut parts = s.split(&['+', '=', ',', '\n']);
+            let (a_x, a_y) = (parse_it(&mut parts)?, parse_it(&mut parts)?);
+            let (b_x, b_y) = (parse_it(&mut parts)?, parse_it(&mut parts)?);
+            let (prize_x, prize_y) = (
+                parse_it(&mut parts)? + offset,
+                parse_it(&mut parts)? + offset,
+            );
+            // a * a_x + b * b_x = prize_x
+            // a * a_y + b * b_y = prize_y
+            //    =>
+            // a = (prize_x - b * b_x) / a_x
+            // b = (prize_y - a * a_y) / b_y
+            //    => substitute b in equation for a and vice versa =>
+            // a = prize_x / a_x - (prize_y - a * a_y) * b_x / (a_x * b_y)
+            //    => multiply both sides with (a_x * b_y) =>
+            // (a_x * b_y) * a = prize_x * b_y - prize_y * b_x + a * a_y * b_x
+            //    => subtract (a * a_y * b_x) from both sides =>
+            // (a_x * b_y - a_y * b_x) * a = prize_x * b_y - prize_y * b_x
+            //    => (similarly for b) =>
+            let a = (prize_x * b_y - prize_y * b_x) / (a_x * b_y - a_y * b_x);
+            let b = (a_x * prize_y - a_y * prize_x) / (a_x * b_y - a_y * b_x);
+            Ok((3 * a + b)
+                * i64::from(a * a_x + b * b_x == prize_x && a * a_y + b * b_y == prize_y))
+        })
+        .sum()
+}
+
+fn parse_it<'a, I: Iterator<Item = &'a str>>(it: &mut I) -> Result<i64, String> {
+    it.nth(1)
+        .ok_or_else(on_error)?
+        .parse::<i64>()
+        .map_err(|_| on_error())
 }
 
 #[test]
 pub fn tests() {
     use crate::input::{test_part_one_no_allocations, test_part_two_no_allocations};
 
-    let test_input = "";
-    test_part_one_no_allocations!(test_input => 0);
-    test_part_two_no_allocations!(test_input => 0);
+    let test_input = "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_part_one_no_allocations!(test_input => 480);
 
     let real_input = include_str!("day13_input.txt");
-    test_part_one_no_allocations!(real_input => 0);
-    test_part_two_no_allocations!(real_input => 0);
+    test_part_one_no_allocations!(real_input => 37_297);
+    test_part_two_no_allocations!(real_input => 83_197_086_729_371);
 }