aoc2023/day6: Update solution

Signed-off-by: Andrej Orsula <orsula.andrej@gmail.com>

README.md

@@ -46,7 +46,7 @@ My solutions to [Advent of Code](https://adventofcode.com) puzzles.
 | 0.419 µs  | 308.1 µs |
 | 53.39 µs  | 28.44 µs |
 | 16.38 µs  | 19.364 s |
-| 0.513 µs  | 2.463 ms |
+| 0.513 µs  | 0.650 µs |
 
 </td></tr>
 </table>

aoc2023/Cargo.toml

@@ -16,6 +16,7 @@ aoc-runner-derive = { workspace = true }
 indoc = { workspace = true }
 
 itertools = { version = "0.12" }
+num-integer = { version = "0.1" }
 rayon = { version = "1.8" }
 regex = { version = "1.10" }
 smallvec = { version = "1.11" }

aoc2023/src/day6.rs

@@ -26,6 +26,7 @@ mod utils {
     }
 
     impl RaceData {
+        /// Solver using brute force (faster than the quadratic formula for small inputs).
         pub fn n_record_breaks(&self) -> u64 {
             let (time, distance) = (self.time.parse().unwrap(), self.distance.parse().unwrap());
             match (1..time).find(|j| j * (time - j) > distance) {
@@ -34,6 +35,15 @@ mod utils {
             }
         }
 
+        /// Solver based on quadratic formula (much faster than brute force for large inputs).
+        pub fn n_record_breaks1(&self) -> u64 {
+            let (time, distance) = (
+                self.time.parse::<u64>().unwrap(),
+                self.distance.parse::<u64>().unwrap(),
+            );
+            2 * num_integer::sqrt(time.pow(2) / 4 - distance - 1) + (time % 2) + 1
+        }
+
         pub fn merge(sequence: &[Self]) -> Self {
             let (time, distance) = sequence.iter().fold(
                 Default::default(),
@@ -53,7 +63,7 @@ fn part1(input: &[utils::RaceData]) -> u64 {
 
 #[aoc(day6, part2)]
 fn part2(input: &[utils::RaceData]) -> u64 {
-    utils::RaceData::merge(input).n_record_breaks()
+    utils::RaceData::merge(input).n_record_breaks1()
 }
 
 #[cfg(test)]