day(21): add solution

Signed-off-by: Matej Focko <me@mfocko.xyz>

samples/day21.txt

@@ -0,0 +1,11 @@
+...........
+.....###.#.
+.###.##..#.
+..#.#...#..
+....#.#....
+.##..S####.
+.##..#...#.
+.......##..
+.##.#.####.
+.##..##.##.
+...........

src/bin/day21.rs

@@ -0,0 +1,111 @@
+use std::collections::HashSet;
+
+use aoc_2023::*;
+use itertools::iproduct;
+
+type Position = Vector2D<isize>;
+
+lazy_static! {
+    static ref DIRECTIONS: Vec<Position> = vec![
+        Position::new(0, 1),
+        Position::new(0, -1),
+        Position::new(1, 0),
+        Position::new(-1, 0),
+    ];
+}
+const WIDTH: isize = 131;
+
+fn _mod(n: isize, m: isize) -> isize {
+    (m + (n % m)) % m
+}
+
+type Output1 = usize;
+type Output2 = f64;
+
+struct Steps<'a> {
+    plots: &'a HashSet<Position>,
+    positions: HashSet<Position>,
+}
+
+impl<'a> Steps<'a> {
+    fn new(plots: &'a HashSet<Position>) -> Self {
+        Self {
+            plots,
+            positions: HashSet::from([Position::new(65, 65)]),
+        }
+    }
+
+    fn move_gardener(&mut self) {
+        let mut next_positions = HashSet::new();
+
+        for (&pos, &dir) in iproduct!(self.positions.iter(), DIRECTIONS.iter()) {
+            let next_pos = pos + dir;
+            let cropped = Position::new(_mod(next_pos.x(), WIDTH), _mod(next_pos.y(), WIDTH));
+            if self.plots.contains(&cropped) {
+                next_positions.insert(next_pos);
+            }
+        }
+
+        self.positions = next_positions;
+    }
+}
+
+impl<'a> Iterator for Steps<'a> {
+    type Item = usize;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        let current = self.positions.len();
+        self.move_gardener();
+        Some(current)
+    }
+}
+
+struct Day21 {
+    plots: HashSet<Position>,
+}
+impl Solution<Output1, Output2> for Day21 {
+    fn new<P: AsRef<Path>>(pathname: P) -> Self {
+        let lines: Vec<String> = file_to_lines(pathname);
+
+        let plots = (0_isize..)
+            .zip(lines.iter())
+            .flat_map(move |(y, row)| {
+                (0_isize..).zip(row.chars()).filter_map(move |(x, c)| {
+                    if c != '#' {
+                        Some(Position::new(x, y))
+                    } else {
+                        None
+                    }
+                })
+            })
+            .collect();
+
+        Self { plots }
+    }
+
+    fn part_1(&mut self) -> Output1 {
+        Steps::new(&self.plots).nth(64).unwrap()
+    }
+
+    fn part_2(&mut self) -> Output2 {
+        let steps = Steps::new(&self.plots).take(328).collect_vec();
+
+        let (x0, y0) = (65_f64, steps[65] as f64);
+        let (x1, y1) = (196_f64, steps[196] as f64);
+        let (x2, y2) = (327_f64, steps[327] as f64);
+
+        let y01 = (y1 - y0) / (x1 - x0);
+        let y12 = (y2 - y1) / (x2 - x1);
+        let y012 = (y12 - y01) / (x2 - x0);
+
+        let n = 26501365_f64;
+
+        y0 + y01 * (n - x0) + y012 * (n - x0) * (n - x1)
+    }
+}
+
+fn main() -> Result<()> {
+    Day21::main()
+}
+
+test_sample!(day_21, Day21, 0, 0);