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|
use nalgebra::{Matrix2, Matrix6, Point3, RowVector6, Vector2, Vector3, Vector6};
use nom::{
bytes::complete::tag,
character::complete::{i64, line_ending},
combinator::map,
multi::separated_list1,
sequence::{separated_pair, tuple},
IResult,
};
use std::fs;
fn main() -> Result<(), Box<dyn std::error::Error>> {
let input = fs::read_to_string("inputs/day_24.txt")?;
let parsed = Hailstones::parser(&input).unwrap().1;
dbg!(&parsed.count_intersections_2d(200000000000000., 400000000000000.));
let magic_rock = parsed.find_magic_throwing_rock();
dbg!(&magic_rock);
dbg!(
magic_rock.position.x as i64 + magic_rock.position.y as i64 + magic_rock.position.z as i64
);
Ok(())
}
#[derive(Debug)]
struct Hailstones(Vec<Hailstone>);
#[derive(Debug)]
struct Hailstone {
position: Point3<f64>,
velocity: Vector3<f64>,
}
impl Hailstones {
fn parser(input: &str) -> IResult<&str, Self> {
map(separated_list1(line_ending, Hailstone::parser), Hailstones)(input)
}
fn count_intersections_2d(&self, min: f64, max: f64) -> usize {
self.0
.iter()
.enumerate()
.map(|(i, hailstone)| {
self.0
.iter()
.skip(i + 1)
.filter(|other_hailstone| hailstone.intersects_2d(other_hailstone, min, max))
.count()
})
.sum()
}
fn find_magic_throwing_rock(&self) -> Hailstone {
(0..self.0.len())
.flat_map(move |h1| {
(h1 + 1..self.0.len()).flat_map(move |h2| {
(h2 + 1..self.0.len())
.flat_map(move |h3| (h3 + 1..self.0.len()).map(move |h4| [h1, h2, h3, h4]))
})
})
.take(1000000)
.map(|hailstones| {
let rock = self.find_magic_throwing_rock_for_hailstones(hailstones);
(
// the solution I'm after uses integers. This tries to find the minimum error.
rock.position.x.abs().fract()
+ rock.position.y.abs().fract()
+ rock.position.z.abs().fract()
+ rock.velocity.x.abs().fract()
+ rock.velocity.y.abs().fract()
+ rock.velocity.z.abs().fract()
+ self
.0
.iter()
.map(|h| rock.collition_time(&h).fract())
.sum::<f64>(),
rock,
)
})
.min_by(|(error_a, _), (error_b, _)| error_a.total_cmp(error_b))
.unwrap()
.1
}
fn find_magic_throwing_rock_for_hailstones(&self, hailstones: [usize; 4]) -> Hailstone {
// unknowns are (x, y, z, dx, dy, dz)
let h1 = &self.0[hailstones[0]];
let h2 = &self.0[hailstones[1]];
let h3 = &self.0[hailstones[2]];
let h4 = &self.0[hailstones[3]];
let coefficients: Matrix6<f64> = Matrix6::from_rows(&[
RowVector6::new(
h2.velocity.y - h1.velocity.y,
h1.velocity.x - h2.velocity.x,
0.,
h1.position.y - h2.position.y,
h2.position.x - h1.position.x,
0.,
),
RowVector6::new(
h2.velocity.z - h1.velocity.z,
0.,
h1.velocity.x - h2.velocity.x,
h1.position.z - h2.position.z,
0.,
h2.position.x - h1.position.x,
),
RowVector6::new(
0.,
h2.velocity.z - h1.velocity.z,
h1.velocity.y - h2.velocity.y,
0.,
h1.position.z - h2.position.z,
h2.position.y - h1.position.y,
),
RowVector6::new(
h4.velocity.y - h3.velocity.y,
h3.velocity.x - h4.velocity.x,
0.,
h3.position.y - h4.position.y,
h4.position.x - h3.position.x,
0.,
),
RowVector6::new(
h4.velocity.z - h3.velocity.z,
0.,
h3.velocity.x - h4.velocity.x,
h3.position.z - h4.position.z,
0.,
h4.position.x - h3.position.x,
),
RowVector6::new(
0.,
h4.velocity.z - h3.velocity.z,
h3.velocity.y - h4.velocity.y,
0.,
h3.position.z - h4.position.z,
h4.position.y - h3.position.y,
),
]);
let constants: Vector6<f64> = Vector6::new(
h1.position.y * h1.velocity.x
- h1.position.x * h1.velocity.y
- h2.position.y * h2.velocity.x
+ h2.position.x * h2.velocity.y,
h1.position.z * h1.velocity.x
- h1.position.x * h1.velocity.z
- h2.position.z * h2.velocity.x
+ h2.position.x * h2.velocity.z,
h1.position.z * h1.velocity.y
- h1.position.y * h1.velocity.z
- h2.position.z * h2.velocity.y
+ h2.position.y * h2.velocity.z,
h3.position.y * h3.velocity.x
- h3.position.x * h3.velocity.y
- h4.position.y * h4.velocity.x
+ h4.position.x * h4.velocity.y,
h3.position.z * h3.velocity.x
- h3.position.x * h3.velocity.z
- h4.position.z * h4.velocity.x
+ h4.position.x * h4.velocity.z,
h3.position.z * h3.velocity.y
- h3.position.y * h3.velocity.z
- h4.position.z * h4.velocity.y
+ h4.position.y * h4.velocity.z,
);
if let Some(coefficients_inverse) = coefficients.try_inverse() {
let unknowns = coefficients_inverse * constants;
Hailstone {
position: Point3::new(unknowns[0], unknowns[1], unknowns[2]),
velocity: Vector3::new(unknowns[3], unknowns[4], unknowns[5]),
}
} else {
panic!("No solution found, matrix didn't invert")
}
}
}
impl Hailstone {
fn parser(input: &str) -> IResult<&str, Self> {
map(
separated_pair(
map(
tuple((i64, tag(", "), i64, tag(", "), i64)),
|(x, _, y, _, z)| Point3::new(x as f64, y as f64, z as f64),
),
tag(" @ "),
map(
tuple((i64, tag(", "), i64, tag(", "), i64)),
|(x, _, y, _, z)| Vector3::new(x as f64, y as f64, z as f64),
),
),
|(initial_position, velocity)| Hailstone {
position: initial_position,
velocity,
},
)(input)
}
fn intersects_2d(&self, other: &Hailstone, min: f64, max: f64) -> bool {
let variables = Matrix2::new(
self.velocity.x,
-other.velocity.x,
self.velocity.y,
-other.velocity.y,
);
let constants = Vector2::new(
other.position.x - self.position.x,
other.position.y - self.position.y,
);
if let Some(variables_inverse) = variables.try_inverse() {
let intersection = variables_inverse * constants;
let self_t = intersection.x;
let other_t = intersection.y;
let intersection = self.position.xy() + self.velocity.xy() * self_t;
self_t >= 0.
&& other_t >= 0.
&& intersection.x >= min
&& intersection.x <= max
&& intersection.y >= min
&& intersection.y <= max
} else {
false
}
}
/// This is only intended for hail that definitely collides!
fn collition_time(&self, other: &Hailstone) -> f64 {
let tx = (self.position.x - other.position.x) / (other.velocity.x - self.velocity.x);
let ty = (self.position.y - other.position.y) / (other.velocity.y - self.velocity.y);
let tz = (self.position.z - other.position.z) / (other.velocity.z - self.velocity.z);
let t = tx.max(ty).max(tz); // sometimes one of these is zero!
assert!(t > 0.);
t
}
}
|
