adventofcode2023/day24/src/main.rs

use num::ToPrimitive;
use std::fs::read_to_string;
use std::time::Instant;

fn get_numbers_in_line_split_iter<T: std::str::FromStr>(str: &str) -> impl Iterator<Item=T> + '_ {
    str.split([' ', ',']).filter_map(|substr| substr.parse::<T>().ok())
}

struct Hailstone {
    pos: (i64, i64, i64),
    vel: (i64, i64, i64),
}

enum LineIntersection<T: PartialOrd> {
    // Has position of intersection
    Intersects((T, T)),
    // Has coefficient of the line (a, b, c), with line being ax + bx + c = 0
    Colinear((T, T, T)),
    None,
}

// lXpY = line X point Y
fn xy_intersection<T>(l1p1: (T, T), l1p2: (T, T), l2p1: (T, T), l2p2: (T, T)) -> LineIntersection<T>
    where T: PartialOrd + std::ops::Neg<Output=T> + std::ops::Sub<Output=T> + num::Zero,
          for<'a> &'a T: std::ops::Sub<Output=T> + std::ops::Mul<Output=T> + std::ops::Div<Output=T>
{
    let l1xdiff = &l1p1.0 - &l1p2.0;
    let l1ydiff = &l1p1.1 - &l1p2.1;
    let l2xdiff = &l2p1.0 - &l2p2.0;
    let l2ydiff = &l2p1.1 - &l2p2.1;
    let denom = &l1xdiff * &l2ydiff - &l1ydiff * &l2xdiff;
    if denom == T::zero() {
        let proj1 = &l1p1.0 * &l1ydiff - &l1p1.1 * &l1xdiff;
        let proj2 = &l2p1.0 * &l1ydiff - &l2p1.1 * &l1xdiff;
        if &proj1 - &proj2 == T::zero() {
            return LineIntersection::Colinear((l1xdiff, -l1ydiff, -proj1));
        } else {
            return LineIntersection::None;
        }
    }
    let l1det = (&l1p1.0 * &l1p2.1) - (&l1p1.1 * &l1p2.0);
    let l2det = (&l2p1.0 * &l2p2.1) - (&l2p1.1 * &l2p2.0);
    let detx = &l1det * &l2xdiff - &l2det * &l1xdiff;
    let dety = &l1det * &l2ydiff - &l2det * &l1ydiff;
    LineIntersection::Intersects((&detx / &denom, &dety / &denom))
}

fn vec_add<T>(v1: (T, T, T), v2: (T, T, T)) -> (T, T, T)
    where T: std::ops::Add<Output=T> {
    (v1.0 + v2.0, v1.1 + v2.1, v1.2 + v2.2)
}

fn cross_prod<T>(v1: (T, T, T), v2: (T, T, T)) -> (T, T, T)
    where T: std::ops::Sub<T, Output=T>, for<'a> &'a T: std::ops::Mul<&'a T, Output=T> {
    (&v1.1 * &v2.2 - &v1.2 * &v2.1, &v1.2 * &v2.0 - &v1.0 * &v2.2, &v1.0 * &v2.1 - &v1.1 * &v2.0)
}


// Get integer intersecting line at the right timeframes: (x, y, z), (vx, vy, vz)
fn get_intersecting_line(hailstones: &[Hailstone]) -> ((i64, i64, i64), (i64, i64, i64)) {
    // Moving the frame of reference to hailstones[0] so we can compute the rest around origin
    // With one line being reduced to start (0, 0, 0) and velocity (0, 0, 0) it'll be simpler
    let map_pos = hailstones[0].pos;
    let map_vel = hailstones[0].vel;
    let hails = hailstones[1..=2].iter().map(
        |hail| {
            let pos = ((hail.pos.0 - map_pos.0) as i128, (hail.pos.1 - map_pos.1) as i128, (hail.pos.2 - map_pos.2) as i128);
            let vel = ((hail.vel.0 - map_vel.0) as i128, (hail.vel.1 - map_vel.1) as i128, (hail.vel.2 - map_vel.2) as i128);
            (pos, vel)
        }
    ).collect::<Vec<_>>();
    // cross product of vectors from origin to two points of the first other line
    let plane1 = cross_prod(hails[0].0, vec_add(hails[0].0, hails[0].1));
    // cross product of vectors from origin to two points of the second other line
    let plane2 = cross_prod(hails[1].0, vec_add(hails[1].0, hails[1].1));
    // cross product of thw two planes to reduce the space to a single line
    let line = cross_prod(plane1, plane2);
    // The line now represents a good direction with potentially wrong length (not a problem),
    // and potentially wrong sign (a problem)
    // find the smallest possible vel using gcd
    let gcd = [line.0, line.1, line.2].iter()
        .fold(0i128, |acc, &elem| num::integer::gcd(acc, elem));
    let mut vel = (line.0 / gcd, line.1 / gcd, line.2 / gcd);
    // We need to find the start point
    // We know of one line at (0, 0, 0) due to mapping, we'll use it with another line to figure
    // out the exact starting position (mapped)
    // start + t0 * vel = 0  - the line at 0
    // start + t1 * vel = p1 + t1*vel1  - the other line
    // becomes
    // start = p1 + t1 * (vel1 - vel)
    // start = -t0 * vel
    // get rid of start
    // t0 * vel + t1 * (vel1 - vel) = -p1  - the vectors are 3 dimensional and we have 2 variables
    // solve system of just taking the x and y from vectors
    let mut det = vel.0 * (hails[1].1.1 - vel.1) - vel.1 * (hails[1].1.0 - vel.0);
    let mut t0 = -hails[1].0.0 * (hails[1].1.1 - vel.1) / det + hails[1].0.1 * (hails[1].1.0 - vel.0) / det;
    let mut start = (-t0 * vel.0, -t0 * vel.1, -t0 * vel.2);
    // check on other 2 hailstones if the answer is consistent, otherwise flip sign
    let mut wrong = false;
    let rock_pos = [start.0, start.1, start.2];
    let rock_vel = [vel.0, vel.1, vel.2];
    'outer: for i in 0..2 {
        let mut last_solution: Option<i128> = None;
        let hail_pos = [hails[i].0.0, hails[i].0.1, hails[i].0.2];
        let hail_vel = [hails[i].1.0, hails[i].1.1, hails[i].1.2];
        for j in 0..3 {
            let denom = rock_vel[j] - hail_vel[j];
            if denom != 0 {
                let new_solution = (hail_pos[j] - rock_pos[j]) / denom;
                if new_solution < 0 {
                    wrong = true;
                    break 'outer;
                }
                match last_solution {
                    None => last_solution = Some(new_solution),
                    Some(s) => {
                        if s != new_solution {
                            wrong = true;
                            break 'outer;
                        }
                    }
                }
            }
        }
    }
    // flip the sign
    if wrong {
        vel = (-vel.0, -vel.1, -vel.2);
        det = vel.0 * (hails[1].1.1 - vel.1) - vel.1 * (hails[1].1.0 - vel.0);
        t0 = -hails[1].0.0 * (hails[1].1.1 - vel.1) / det + hails[1].0.1 * (hails[1].1.0 - vel.0) / det;
        start = (-t0 * vel.0, -t0 * vel.1, -t0 * vel.2);
    }
    let start_unmapped = (start.0 as i64 + map_pos.0, start.1 as i64 + map_pos.1, start.2 as i64 + map_pos.2);
    let vel_unmapped = (vel.0 as i64 + map_vel.0, vel.1 as i64 + map_vel.1, vel.2 as i64 + map_vel.2);
    (start_unmapped, vel_unmapped)
}

fn main() {
    let time_start = Instant::now();
    let input_str = read_to_string("input.txt").unwrap();
    let time_start_no_io = Instant::now();
    // Shift the interval to be centered around 0, avoids numerical errors
    const COORD_SHIFT: i64 = -3e14 as i64;
    const MIN_POS: f64 = -1e14;
    const MAX_POS: f64 = 1e14;
    let hailstones = input_str.lines().map(|line| {
        let mut it = get_numbers_in_line_split_iter::<i64>(line);
        Hailstone {
            pos: (it.next().unwrap() + COORD_SHIFT, it.next().unwrap() + COORD_SHIFT, it.next().unwrap() + COORD_SHIFT),
            vel: (it.next().unwrap(), it.next().unwrap(), it.next().unwrap()),
        }
    }).collect::<Vec<_>>();
    // Part 1
    let mut count1 = 0;
    for (i, h1) in hailstones.iter().enumerate() {
        for h2 in hailstones[i + 1..].iter() {
            let l1p1 = (h1.pos.0 as f64, h1.pos.1 as f64);
            let l1p2 = ((h1.pos.0 + h1.vel.0) as f64, (h1.pos.1 + h1.vel.1) as f64);
            let l2p1 = (h2.pos.0 as f64, h2.pos.1 as f64);
            let l2p2 = ((h2.pos.0 + h2.vel.0) as f64, (h2.pos.1 + h2.vel.1) as f64);
            match xy_intersection(l1p1, l1p2, l2p1, l2p2) {
                LineIntersection::Intersects((xr, yr)) => {
                    let (x, y) = (xr.to_f64().unwrap(), yr.to_f64().unwrap());
                    // Check if it's not in the past, thankfully velocity components are never 0
                    if (x - h1.pos.0 as f64) / h1.vel.0 as f64 >= 0.
                        && (x - h2.pos.0 as f64) / h2.vel.0 as f64 >= 0. {
                        if x >= MIN_POS && x <= MAX_POS && y >= MIN_POS && y <= MAX_POS {
                            count1 += 1;
                        }
                    }
                }
                LineIntersection::Colinear((_, _, _)) => {
                    // Seems this case isn't used
                    // otherwise I'd have to check if they go in the same direction
                }
                LineIntersection::None => {
                }
            }
        }
    }
    // Part 2
    let (start, vel) = get_intersecting_line(&hailstones);
    let corrected_start = (start.0 - COORD_SHIFT, start.1 - COORD_SHIFT, start.2 - COORD_SHIFT);
    let summed_coords = corrected_start.0 + corrected_start.1 + corrected_start.2;
    let elapsed = time_start.elapsed().as_micros();
    let elapsed_no_io = time_start_no_io.elapsed().as_micros();
    println!("Time: {}us", elapsed);
    println!("Time without file i/o: {}us", elapsed_no_io);
    println!("Count1: {}", count1);
    println!("Start: {:?}, vel: {:?}", corrected_start, vel);
    println!("Summed start coords: {:?}", summed_coords);
}