2023 - Day 24
This commit is contained in:
parent
72e4c18b31
commit
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GPG Key ID:
5A0CBFE3C3377FAA
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@ -8,6 +8,7 @@ edition = "2021"
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[dependencies]
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anyhow = "1.0.75"
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lazy_static = "1.4.0"
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nalgebra = "0.32.3"
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regex = "1.10.2"
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[features]
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300
2023/input/24/input
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300
2023/input/24/input
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||||
394189872421409, 331448531001974, 256407864771135 @ -31, -36, -20
|
||||
311925984995885, 332357949681136, 293917117060350 @ 30, -68, -59
|
||||
389447608973881, 380513707763144, 244720406589022 @ -126, -192, 51
|
||||
366016540138437, 277293281705376, 413687743953006 @ 130, 233, -794
|
||||
298178291530224, 268217681216719, 304180593974067 @ -38, 31, -38
|
||||
308018243676123, 296892693397840, 274894177156788 @ -130, -42, 32
|
||||
60232254901961, 170686288518732, 262671045190162 @ 89, 74, 51
|
||||
124745624448567, 151652758178730, 163358199121217 @ 31, 96, 150
|
||||
321860786503481, 302448169248892, 261445808573098 @ -12, -5, 20
|
||||
205692521446297, 89407037159596, 410049214010034 @ 36, 247, -158
|
||||
239982788772333, 137286217774368, 174295345603502 @ -56, 138, 147
|
||||
86731844681439, 259688488792764, 210340217835198 @ 70, -12, 103
|
||||
170808423768189, 228588666791260, 293948466808818 @ 19, 33, 12
|
||||
441057939686395, 343398690648711, 549228030221401 @ -265, -93, -736
|
||||
302443946246812, 240143840858176, 379420862083931 @ -22, 94, -186
|
||||
345088720716403, 315552253051151, 268545755397918 @ 159, 27, -65
|
||||
423724795313077, 308659354107536, 180782338151766 @ -63, 186, 493
|
||||
406798864217260, 293663253737166, 320278735045387 @ -88, 132, -304
|
||||
195154781190237, 364862205409626, 254799516896806 @ -47, -117, 59
|
||||
178932977335797, 251708835992206, 247843728908376 @ 45, 19, 62
|
||||
253349271834117, 283691186580304, 303498852558606 @ -9, -9, -21
|
||||
376761673051257, 285602705599686, 270257629743006 @ -41, 101, -41
|
||||
300882491178039, 290243550583162, 189772203039720 @ -68, -15, 146
|
||||
235369194657157, 421562658281976, 408227743490686 @ -55, -183, -115
|
||||
188646633711105, 318918710332479, 369157982422215 @ 73, -61, -110
|
||||
395512774201357, 315616825750976, 285497663723286 @ 96, 102, -266
|
||||
421677117457729, 302462002478370, 260176983480688 @ -57, 221, -114
|
||||
177175197731565, 341281080915196, 331441656855726 @ 43, -93, -41
|
||||
325478665927397, 441871023252256, 224988749860460 @ 21, -338, 102
|
||||
402136003642932, 333799366036756, 296817265196841 @ 8, -30, -290
|
||||
182104997730129, 336028786762480, 74550271859558 @ 52, -86, 285
|
||||
292043981673693, 259010054670568, 310880696340486 @ -98, 9, -16
|
||||
327463887597202, 275386444030262, 281725872502210 @ 96, 120, -69
|
||||
180350572694521, 204046517624548, 270869833505754 @ 15, 64, 37
|
||||
261796476524925, 143723242270984, 124690998413814 @ -90, 121, 198
|
||||
382022380467301, 363084132643328, 342504705272910 @ -51, -159, -293
|
||||
359686755049611, 309851948068594, 254216163279732 @ 18, 21, 12
|
||||
432383902550757, 325288945907500, 237103658765274 @ -139, 49, 58
|
||||
199141995287962, 12205123960005, 135322914113123 @ 276, 653, 302
|
||||
388209037680334, 326840502219633, 280212599819923 @ 90, 11, -192
|
||||
398309490013959, 467459019065502, 435027019897864 @ -245, -216, -115
|
||||
438077885264229, 338437435266016, 251421696960654 @ -147, -33, -83
|
||||
142623030672997, 313922309635776, 172051026248046 @ 197, -48, 178
|
||||
211793103082053, 258637524078497, 413519499042315 @ -11, 5, -134
|
||||
316227539793914, 330807868031342, 320059762270916 @ -90, -76, -51
|
||||
363745515105897, 308033947226491, 241876133298636 @ 9, 29, 53
|
||||
229073101043463, 182441744874760, 375616182031518 @ -6, 114, -105
|
||||
311663766702322, 293169473612442, 266993157354132 @ -64, -12, 25
|
||||
165743821901955, 245775966807730, 293803407552466 @ 40, 19, 9
|
||||
349142785799508, 280261145006550, 287389255673128 @ 124, 164, -135
|
||||
299220074031339, 172470550513459, 207086145840829 @ -65, 163, 120
|
||||
51599932704531, 110067755093612, 120750763264579 @ 187, 186, 216
|
||||
362339688007455, 128526862135900, 213561367782111 @ 123, 898, 174
|
||||
318235966547318, 236743583502987, 172190463362498 @ -150, 21, 147
|
||||
243218064862137, 146112647037076, 312898709705706 @ -12, 173, -28
|
||||
248532762868587, 127913038997386, 306713186523936 @ -89, 124, 5
|
||||
356833591049452, 288318963368346, 175747488009196 @ -36, 56, 237
|
||||
429258217460035, 281264286545936, 199918966637106 @ -81, 462, 379
|
||||
288595615758281, 286112367984743, 301320148789454 @ 17, 15, -49
|
||||
434137829300957, 385164566787576, 251517643175406 @ -90, -513, -101
|
||||
226684015769909, 393228920796224, 237234101626834 @ 5, -162, 75
|
||||
277608974085399, 484613028229744, 346163443971816 @ -86, -266, -56
|
||||
439564663355742, 339477585210058, 360927913554417 @ -264, -84, -224
|
||||
243540738730971, 359735080690960, 250444934709888 @ -65, -114, 61
|
||||
414936626664123, 309300663907822, 216629185840824 @ -56, 125, 188
|
||||
397872703252389, 212898395772056, 240610671804790 @ -131, 297, 60
|
||||
123154693229737, 203455201989076, 290045021180228 @ 51, 52, 20
|
||||
268437039198703, 312957758717668, 372983507517126 @ -58, -56, -101
|
||||
290041101495914, 452525408726809, 261168521158394 @ 18, -305, 27
|
||||
94022340218020, 214444823962799, 233285115180485 @ 78, 39, 80
|
||||
187758784146701, 308231925236552, 42842321977264 @ 17, -54, 306
|
||||
298993330355122, 276052686620461, 298685552862006 @ -10, 31, -41
|
||||
332169842700025, 298970888104540, 302981537331018 @ -70, -11, -50
|
||||
194328822595255, 76283873425353, 136668594275728 @ 239, 459, 281
|
||||
120250832193905, 241032280181964, 229456138785466 @ 50, 11, 84
|
||||
151422919814977, 301022504515816, 378981998111542 @ 111, -38, -117
|
||||
96990387183037, 372867516983776, 14714289836806 @ 168, -134, 366
|
||||
274942199061477, 481640626788556, 14527007819946 @ -11, -317, 432
|
||||
224838145952262, 313821556817251, 263551720120806 @ 14, -55, 39
|
||||
403167845873627, 244787413886076, 196299464895806 @ -30, 432, 279
|
||||
423651938100112, 435225368641841, 336353363207841 @ -264, -201, -38
|
||||
289166585859768, 74894176976193, 138452721266517 @ 130, 605, 328
|
||||
431669875459573, 325370084156409, 252462190860946 @ -27, 143, -141
|
||||
390448274978984, 338265610742420, 231189470189675 @ 98, -54, 98
|
||||
237855310336712, 79275006966921, 512264534723696 @ -64, 191, -223
|
||||
430777549022346, 301130642558299, 294289756858713 @ -166, 153, -262
|
||||
222272412127973, 253877615323776, 267895382908238 @ 18, 27, 33
|
||||
165432519670262, 95007658128776, 226194378092481 @ 24, 182, 88
|
||||
281007118242885, 330242484331812, 296563154696266 @ -35, -75, -16
|
||||
359290360054469, 394969290711776, 300557072988910 @ -60, -223, -88
|
||||
5
2023/input/24/test-1
Normal file
5
2023/input/24/test-1
Normal file
|
|
@ -0,0 +1,5 @@
|
|||
19, 13, 30 @ -2, 1, -2
|
||||
18, 19, 22 @ -1, -1, -2
|
||||
20, 25, 34 @ -2, -2, -4
|
||||
12, 31, 28 @ -1, -2, -1
|
||||
20, 19, 15 @ 1, -5, -3
|
||||
221
2023/src/bin/day24.rs
Normal file
221
2023/src/bin/day24.rs
Normal file
|
|
@ -0,0 +1,221 @@
|
|||
#![feature(test)]
|
||||
extern crate nalgebra as na;
|
||||
use std::{str::FromStr, convert::Infallible, collections::HashMap};
|
||||
|
||||
use anyhow::Result;
|
||||
use aoc::Solver;
|
||||
use na::{SMatrix, SVector};
|
||||
|
||||
// -- Runners --
|
||||
fn main() -> Result<()> {
|
||||
Day::solve()
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
|
||||
#[test]
|
||||
fn part1_test1() -> Result<()> {
|
||||
Day::test(Day::part1, "test-1", 2)
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn part1_solution() -> Result<()> {
|
||||
Day::test(Day::part1, "input", 13149)
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn part2_test1() -> Result<()> {
|
||||
Day::test(Day::part2, "test-1", 47)
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn part2_solution() -> Result<()> {
|
||||
Day::test(Day::part2, "input", 1033770143421619)
|
||||
}
|
||||
|
||||
// Benchmarks
|
||||
extern crate test;
|
||||
#[bench]
|
||||
#[ignore]
|
||||
fn part1_bench(b: &mut test::Bencher) {
|
||||
Day::benchmark(Day::part1, b)
|
||||
}
|
||||
#[bench]
|
||||
#[ignore]
|
||||
fn part2_bench(b: &mut test::Bencher) {
|
||||
Day::benchmark(Day::part2, b)
|
||||
}
|
||||
}
|
||||
|
||||
#[derive(Debug, Clone, Copy)]
|
||||
struct Hailstone {
|
||||
px: f64,
|
||||
py: f64,
|
||||
pz: f64,
|
||||
vx: f64,
|
||||
vy: f64,
|
||||
vz: f64
|
||||
}
|
||||
|
||||
impl Hailstone {
|
||||
fn intersect_2d(&self, other: &Hailstone) -> Option<(f64, f64)> {
|
||||
let dx = self.px - other.px;
|
||||
let dy = self.py - other.py;
|
||||
|
||||
let d = self.vy * other.vx - self.vx * other.vy;
|
||||
|
||||
let t1 = (other.vy*dx - other.vx * dy) / d;
|
||||
let t2 = (self.vy * dx - self.vx*dy) / d;
|
||||
|
||||
if t1.is_sign_negative() || t2.is_sign_negative() {
|
||||
// Intersection is in the past
|
||||
return None;
|
||||
}
|
||||
|
||||
let x = self.px + self.vx * t1;
|
||||
let y = self.py + self.vy * t1;
|
||||
|
||||
if x.is_infinite() || y.is_infinite() {
|
||||
// Paths are parallel
|
||||
return None;
|
||||
}
|
||||
|
||||
Some((x, y))
|
||||
}
|
||||
}
|
||||
|
||||
impl FromStr for Hailstone {
|
||||
type Err = Infallible;
|
||||
|
||||
fn from_str(s: &str) -> Result<Self, Self::Err> {
|
||||
let parts: Vec<f64> = s.split([',', '@']).map(|part| part.trim().parse().unwrap()).collect();
|
||||
|
||||
Ok(Hailstone {
|
||||
px: parts[0],
|
||||
py: parts[1],
|
||||
pz: parts[2],
|
||||
vx: parts[3],
|
||||
vy: parts[4],
|
||||
vz: parts[5],
|
||||
})
|
||||
}
|
||||
}
|
||||
|
||||
fn mode(numbers: &[usize]) -> usize {
|
||||
let mut occurrences = HashMap::<_, usize>::new();
|
||||
|
||||
for &value in numbers {
|
||||
*occurrences.entry(value).or_insert(0) += 1;
|
||||
}
|
||||
|
||||
println!("{occurrences:?}");
|
||||
|
||||
occurrences.into_iter().max_by_key(|&(_, count)| count).map(|(value, _)| value).unwrap()
|
||||
}
|
||||
|
||||
// -- Solution --
|
||||
pub struct Day;
|
||||
impl aoc::Solver for Day {
|
||||
type Output1 = usize;
|
||||
type Output2 = usize;
|
||||
|
||||
fn day() -> u8 {
|
||||
24
|
||||
}
|
||||
|
||||
fn part1(input: &str) -> Self::Output1 {
|
||||
let hailstones: Vec<_> = input.lines().flat_map(Hailstone::from_str).collect();
|
||||
|
||||
let range = if hailstones.len() == 5 {
|
||||
7.0..=27.0
|
||||
} else {
|
||||
200000000000000.0..=400000000000000.0
|
||||
};
|
||||
|
||||
hailstones.iter().enumerate().flat_map(|(index_a, a)| {
|
||||
hailstones.iter().enumerate().filter(|(index_b, _)| index_b < &index_a).filter_map(|(_, b)| {
|
||||
a.intersect_2d(b)
|
||||
}).collect::<Vec<_>>()
|
||||
}).filter(|&(x, y)| range.contains(&x) && range.contains(&y)).count()
|
||||
}
|
||||
|
||||
fn part2(input: &str) -> Self::Output2 {
|
||||
let h: Vec<_> = input.lines().flat_map(Hailstone::from_str).collect();
|
||||
|
||||
// Key insight for part 2 is
|
||||
// p_rock + v_rock * t_i = p_i + v_i * t_i
|
||||
// for every hailstone i
|
||||
//
|
||||
// This can be rewritten as
|
||||
// p_rock - p_i = t_i * (v_i - v_rock)
|
||||
// and since t_i is a scalar this means that
|
||||
// (p_rock - p_i) is parallel to (v_i - v_rock)
|
||||
// and therefore
|
||||
// c_i = (p_rock - p_i) x (v_i - v_rock) = 0
|
||||
// This holds true for every hailstone i, so
|
||||
// c_i = c_j
|
||||
// c_i = c_k
|
||||
// with i != j != k
|
||||
// Writing out these equations leads to a set of six linear equations
|
||||
// And can therefore be written in matrix form
|
||||
// A * solution = constant
|
||||
// And the solution can now be found using
|
||||
// solution = A^-1 * constant
|
||||
|
||||
let i = 0;
|
||||
let j = 1;
|
||||
// Due to numerical instability we run this with several different options for the third
|
||||
// hailstone
|
||||
let solutions: Vec<_> = (2..h.len()).map(|k| {
|
||||
// Constant in the matrix
|
||||
let c1 = h[i].vz - h[j].vz;
|
||||
let c2 = h[i].py - h[j].py;
|
||||
let c3 = h[j].vy - h[i].vy;
|
||||
let c4 = h[j].pz - h[i].pz;
|
||||
let c5 = h[i].vx - h[j].vx;
|
||||
let c6 = h[j].px - h[i].px;
|
||||
|
||||
let c7 = h[i].vz - h[k].vz;
|
||||
let c8 = h[i].py - h[k].py;
|
||||
let c9 = h[k].vy - h[i].vy;
|
||||
let c10 = h[k].pz - h[i].pz;
|
||||
let c11 = h[i].vx - h[k].vx;
|
||||
let c12 = h[k].px - h[i].px;
|
||||
|
||||
// Setup the matrix
|
||||
let matrix = SMatrix::<f64, 6, 6>::new(
|
||||
0.0, c1, c3, 0.0, c4, c2,
|
||||
-c1, 0.0, c5, -c4, 0.0, c6,
|
||||
-c3, -c5, 0.0, -c2, -c6, 0.0,
|
||||
0.0, c7, c9, 0.0, c10, c8,
|
||||
-c7, 0.0, c11, -c10, 0.0, c12,
|
||||
-c9, -c11, 0.0, -c8, -c12, 0.0
|
||||
);
|
||||
|
||||
// Get the inverse of the matrix
|
||||
let inverse = matrix.try_inverse().unwrap();
|
||||
|
||||
// Constant on the rhs
|
||||
let k1 = h[i].py*h[i].vz - h[j].py*h[j].vz + h[j].pz*h[j].vy - h[i].pz*h[i].vy;
|
||||
let k2 = h[i].pz*h[i].vx - h[j].pz*h[j].vx + h[j].px*h[j].vz - h[i].px*h[i].vz;
|
||||
let k3 = h[i].px*h[i].vy - h[j].px*h[j].vy + h[j].py*h[j].vx - h[i].py*h[i].vx;
|
||||
let k4 = h[i].py*h[i].vz - h[k].py*h[k].vz + h[k].pz*h[k].vy - h[i].pz*h[i].vy;
|
||||
let k5 = h[i].pz*h[i].vx - h[k].pz*h[k].vx + h[k].px*h[k].vz - h[i].px*h[i].vz;
|
||||
let k6 = h[i].px*h[i].vy - h[k].px*h[k].vy + h[k].py*h[k].vx - h[i].py*h[i].vx;
|
||||
|
||||
// Put them into a vector
|
||||
let k = SVector::<f64, 6>::new(k1, k2, k3, k4, k5, k6);
|
||||
|
||||
// Calclate the solution
|
||||
let solution = inverse * k;
|
||||
|
||||
// The sum of all elements of the starting position is the answer
|
||||
(solution[0] + solution[1] + solution[2]).round() as usize
|
||||
}).collect();
|
||||
|
||||
// The most common solution is the actual solution
|
||||
mode(&solutions)
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user