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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[dependencies]
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anyhow = "1.0.75"
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anyhow = "1.0.75"
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lazy_static = "1.4.0"
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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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regex = "1.10.2"
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[features]
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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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||||||
|
145398660803727, 195609983658656, 242158434889096 @ 130, 110, 68
|
||||||
|
297475449394982, 131750381092515, 165719703479968 @ -84, 195, 173
|
||||||
|
382981082215082, 318082716962228, 217519872859947 @ -184, -54, 106
|
||||||
|
274508569926281, 337480597564942, 249069272308048 @ 113, -80, 45
|
||||||
|
409006873082037, 404306234256766, 306773089718196 @ 101, -620, -563
|
||||||
|
304326995325327, 252632813540085, 317502450159756 @ -29, 69, -71
|
||||||
|
335336102392062, 349032727458751, 147869871751056 @ -10, -107, 289
|
||||||
|
224490789327707, 138112263823786, 214964316118086 @ -13, 160, 103
|
||||||
|
257483144012212, 310616650691101, 220817557849225 @ 126, -23, 108
|
||||||
|
378616249658565, 487631090875856, 211845741661518 @ -137, -403, 127
|
||||||
|
256962996060820, 363038059754788, 382290100571323 @ 102, -134, -222
|
||||||
|
376113767407764, 419697564588036, 503311772819474 @ -68, -318, -717
|
||||||
|
411690063697784, 334901544443134, 250358939380980 @ -30, -32, -23
|
||||||
|
378730592174173, 292937924939892, 216595109883586 @ -21, 95, 144
|
||||||
|
386233907852537, 102017803023726, 148605073075956 @ -49, 797, 394
|
||||||
|
401023678402335, 326392143373252, 250508593182692 @ -80, -20, 12
|
||||||
|
187386788876757, 222440010076216, 5544716539566 @ 107, 89, 427
|
||||||
|
211506671096437, 295843684641176, 394227297865006 @ 59, -25, -157
|
||||||
|
170237159382989, 228511580730636, 335783635953320 @ 17, 32, -34
|
||||||
|
293589456751485, 294178241627518, 249641359155174 @ -7, -5, 51
|
||||||
|
439854842455119, 383935112515580, 293031876578902 @ -218, -316, -253
|
||||||
|
295518506383932, 200374788948199, 229951840543641 @ -114, 71, 84
|
||||||
|
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