aoc2025/src/bin/09.rs

use aoc::*;
use glam::I64Vec2;
use itertools::Itertools;
use rayon::prelude::*;
use std::collections::HashMap;

const INPUT: &str = include_str!("../../input/09");

fn main() {
    println!("Part 1: {}", part1(INPUT));
    println!("Part 2: {}", part2(INPUT));
}

#[test]
fn example() {
    assert_example!(part1, "09-test", 50);
    assert!(Line(I64Vec2::new(0, 10), I64Vec2::ZERO).contains(I64Vec2::new(0, 0)));
    assert!(Line(I64Vec2::new(0, 10), I64Vec2::ZERO).contains(I64Vec2::new(0, 10)));
    assert!(Line(I64Vec2::new(0, 10), I64Vec2::ZERO).contains(I64Vec2::new(0, 5)));
    assert!(!Line(I64Vec2::new(0, 10), I64Vec2::ZERO).contains(I64Vec2::new(0, 11)));
    assert!(!Line(I64Vec2::new(0, 10), I64Vec2::ZERO).contains(I64Vec2::new(1, 10)));
    assert!(!Line(I64Vec2::ONE, I64Vec2::ONE).contains(I64Vec2::new(1, 10)));
    assert!(Line(I64Vec2::ONE, I64Vec2::ONE).contains(I64Vec2::new(1, 1)));
    assert!(!Line(I64Vec2::ONE, I64Vec2::ONE).contains(I64Vec2::ZERO));
    assert_example!(part2, "09-test", 24);
}

fn part1(input: &str) -> u64 {
    Polygon::parse(input)
        .points
        .into_iter()
        .tuple_combinations()
        .map(Rect::from)
        .map(Rect::area)
        .max()
        .unwrap()
}

fn part2(input: &str) -> u64 {
    let polygon = Polygon::parse(input);
    let (polygon, uncompress) = polygon.compress();
    polygon
        .points
        .iter()
        .copied()
        .tuple_combinations()
        .par_bridge()
        .map(Rect::from)
        .filter(|&r| polygon.contains_rect(r))
        .map(|r| r.uncompress(&uncompress).area())
        .max()
        .unwrap()
}

struct Polygon {
    points: Vec<I64Vec2>,
    /// Contains vertical lines sorted by their x value in ascending order.
    /// This is important for contains_point, as that assumes the lines are in this order.
    /// This dramatically speeds up the raycast in contains_point, as the ray is cast in positive x direction.
    cached_vertical_lines: Vec<Line>,
}

/// Uncompress a polygon with this.
/// Maps from compressed coords to actual coords.
struct Uncompress {
    x: HashMap<i64, i64>,
    y: HashMap<i64, i64>,
}

impl Polygon {
    fn parse(input: &str) -> Self {
        let mut polygon = Self {
            points: input.lines().map(parse_line).collect(),
            cached_vertical_lines: Default::default(),
        };
        polygon.cache_vertical_lines();
        polygon
    }

    fn compress(mut self) -> (Self, Uncompress) {
        let compress_x: HashMap<i64, i64> = self
            .points
            .iter()
            .map(|p| p.x)
            .unique()
            .sorted()
            .enumerate()
            .map(|(i, x)| (x, i as i64))
            .collect();
        let compress_y: HashMap<i64, i64> = self
            .points
            .iter()
            .map(|p| p.y)
            .unique()
            .sorted()
            .enumerate()
            .map(|(i, y)| (y, i as i64))
            .collect();

        self.points = self
            .points
            .into_iter()
            .map(|p| I64Vec2::new(compress_x[&p.x], compress_y[&p.y]))
            .collect();
        self.cache_vertical_lines();

        let uncompress_x = compress_x.into_iter().map(|(x, i)| (i, x)).collect();
        let uncompress_y = compress_y.into_iter().map(|(y, i)| (i, y)).collect();

        (
            self,
            Uncompress {
                x: uncompress_x,
                y: uncompress_y,
            },
        )
    }

    fn contains_rect(&self, r: Rect) -> bool {
        r.outline().into_iter().all(|p| self.contains_point(p))
    }

    /// Raycast from left to right and check intersections with lines.
    fn contains_point(&self, p: I64Vec2) -> bool {
        // Interesting values for x
        let xs = self
            .cached_vertical_lines
            .iter()
            .take_while(|line| line.0.x < p.x)
            .filter(|l| {
                let ymin = l.0.y.min(l.1.y);
                let ymax = l.0.y.max(l.1.y);
                ymin <= p.y && p.y <= ymax
            })
            .map(|l| l.0.x)
            .chain([p.x])
            .sorted();

        let line_with = |p: I64Vec2| {
            self.cached_vertical_lines
                .iter()
                .take_while(|line| line.0.x <= p.x)
                .find(|line| line.contains(p))
                .copied()
        };

        let mut winding = 0;
        let mut on_line = false;

        for x in xs {
            let check = I64Vec2::new(x, p.y);
            if let Some(line) = line_with(check) {
                winding = line.winding();
                on_line = true;
            } else {
                on_line = false;
            }
        }

        winding < 0 || on_line
    }

    fn cache_vertical_lines(&mut self) {
        self.cached_vertical_lines = self
            .points
            .iter()
            .chain(self.points.first()) // close the loop
            .copied()
            .tuple_windows()
            .map(|(a, b)| Line(a, b))
            .filter(|l| l.is_vertical())
            .sorted_by_key(|line| line.0.x)
            .collect();
    }
}

#[derive(Clone, Copy, Debug)]
struct Line(I64Vec2, I64Vec2);

impl Line {
    /// true if p on line
    fn contains(self, p: I64Vec2) -> bool {
        if self.is_vertical() {
            let in_plane = p.x == self.0.x;
            let ymin = self.0.y.min(self.1.y);
            let ymax = self.0.y.max(self.1.y);
            let in_bounds = ymin <= p.y && p.y <= ymax;
            in_bounds && in_plane
        } else {
            let in_plane = p.y == self.0.y;
            let xmin = self.0.x.min(self.1.x);
            let xmax = self.0.x.max(self.1.x);
            let in_bounds = xmin <= p.x && p.x <= xmax;
            in_bounds && in_plane
        }
    }

    fn is_vertical(self) -> bool {
        self.0.x == self.1.x
    }

    fn winding(self) -> i64 {
        (self.1.y - self.0.y).signum()
    }

    fn all_points(self) -> Vec<I64Vec2> {
        if self.is_vertical() {
            let ymin = self.0.y.min(self.1.y);
            let ymax = self.0.y.max(self.1.y);
            let x = self.0.x;
            (ymin..=ymax).map(|y| I64Vec2::new(x, y)).collect()
        } else {
            let xmin = self.0.x.min(self.1.x);
            let xmax = self.0.x.max(self.1.x);
            let y = self.0.y;
            (xmin..=xmax).map(|x| I64Vec2::new(x, y)).collect()
        }
    }
}

#[derive(Copy, Clone)]
struct Rect(I64Vec2, I64Vec2);

impl Rect {
    fn area(self) -> u64 {
        (self.0.x.abs_diff(self.1.x) + 1) * (self.0.y.abs_diff(self.1.y) + 1)
    }

    fn uncompress(self, uncompress: &Uncompress) -> Self {
        Self(
            uncompress_i64vec2(self.0, uncompress),
            uncompress_i64vec2(self.1, uncompress),
        )
    }

    fn from((a, b): (I64Vec2, I64Vec2)) -> Self {
        Self(a, b)
    }

    fn lines(self) -> [Line; 4] {
        let x1 = self.0.x.min(self.1.x);
        let x2 = self.0.x.max(self.1.x);
        let y1 = self.0.y.min(self.1.y);
        let y2 = self.0.y.max(self.1.y);
        [
            Line(I64Vec2::new(x1, y1), I64Vec2::new(x2, y1)),
            Line(I64Vec2::new(x2, y1), I64Vec2::new(x2, y2)),
            Line(I64Vec2::new(x2, y2), I64Vec2::new(x1, y2)),
            Line(I64Vec2::new(x1, y2), I64Vec2::new(x1, y1)),
        ]
    }

    fn outline(self) -> Vec<I64Vec2> {
        self.lines()
            .into_iter()
            .flat_map(|l| l.all_points())
            .collect()
    }
}

fn uncompress_i64vec2(v: I64Vec2, uncompress: &Uncompress) -> I64Vec2 {
    I64Vec2::new(uncompress.x[&v.x], uncompress.y[&v.y])
}

fn parse_line(line: &str) -> I64Vec2 {
    let (x, y) = line.split_once(',').unwrap();
    I64Vec2::new(x.parse().unwrap(), y.parse().unwrap())
}