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Day 24 implement linear algebraic solution for part2
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@zebalu
zebalu committed Dec 25, 2023
1 parent 23d31f9 commit 1ea30c2
Showing 1 changed file with 99 additions and 35 deletions.
134 changes: 99 additions & 35 deletions aoc2023/src/main/java/io/github/zebalu/aoc2023/days/Day24.java
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Original file line number Diff line number Diff line change
@@ -1,26 +1,36 @@
package io.github.zebalu.aoc2023.days;

import java.nio.file.*;
import java.util.List;
import java.util.*;

public class Day24 {
public static void main(String[] args) {
String input = readInput(); //example; readInput();
System.out.println(input);
System.out.println(input.lines().count());
List<Hail> hails = input.lines().map(Hail::read).toList();
System.out.println(hails);
hails.stream().forEach(h->System.out.println(h.slopeOnPlain()));
Hail a = new Hail(new Coord(0,0,0), new Coord(1,1,0));
Hail b = new Hail(new Coord(0,1,0), new Coord(-1,1,0));
Hail b2 = new Hail(b.positionAfter(-5), new Coord(-1,1,0));
System.out.println(b2);
System.out.println(a.intersectOnPlain(b));
System.out.println(a.intersectOnPlain(b2));
System.out.println(a.isIntersectionInFutureOnPlain(a.intersectOnPlain(b)));
System.out.println(b.isIntersectionInFutureOnPlain(b.intersectOnPlain(a)));
System.out.println(countCollisionsInTestArea(hails, 200000000000000L, 400000000000000L));
//System.out.println(countCollisionsInTestArea(hails, 7, 27));
List<Hail> hails = readInput().lines().map(Hail::read).toList();
System.out.println(part1(hails));
System.out.println(part2(hails));
}

private static long part1(List<Hail> hails) {
return countCollisionsInTestArea(hails, 200_000_000_000_000L, 400_000_000_000_000L);
}

private static long part2(List<Hail> hails) {
// for the details, please find: https://github.com/DeadlyRedCube/AdventOfCode/blob/1f9d0a3e3b7e7821592244ee51bce5c18cf899ff/2023/AOC2023/D24.h#L66-L294
// explains, how to get linear equation system correctly
var m = createLinearMatrix(find3UsableHails(hails));
solve(m);
long x = (long)m[0][6];
long y = (long)m[1][6];
long z = (long)m[2][6];
return x+y+z;
}

private static String readInput() {
try {
return Files.readString(Path.of("day24.txt").toAbsolutePath());
} catch(Exception e) {
throw new IllegalStateException(e);
}
}

private static int countCollisionsInTestArea(List<Hail> hails, long min, long max) {
Expand All @@ -40,11 +50,76 @@ private static int countCollisionsInTestArea(List<Hail> hails, long min, long ma
return count;
}

private static String readInput() {
try {
return Files.readString(Path.of("day24.txt").toAbsolutePath());
} catch(Exception e) {
throw new IllegalStateException(e);
private static List<Hail> find3UsableHails(List<Hail> hailsOrig) {
var hails = hailsOrig.stream().sorted(Comparator.comparingLong(h->h.velocity.x)).toList();
List<Hail> result = new ArrayList<>();
for(int aInd = 0; aInd < hails.size() - 2 && result.size() < 3; ++aInd) {
Hail a = hails.get(aInd);
for(int bInd = aInd+1; bInd<hails.size()-1 && result.size()<3; ++bInd) {
Hail b = hails.get(bInd);
if(!a.velocity.equals(b.velocity)) {
for(int cInd=bInd+1; cInd < hails.size()&&result.size()<3; ++cInd) {
Hail c = hails.get(cInd);
if(!a.velocity.equals(c.velocity) && !b.velocity.equals(c.velocity)) {
result.add(a);
result.add(b);
result.add(c);
}
}
}
}
}
if(result.size()<3) {
throw new NoSuchElementException("Can not find 3 usable hails");
}
return result;
}

private static double[][] createLinearMatrix(List<Hail> hails) {
if(hails.size() != 3) {
throw new IllegalArgumentException("It can only work with 3 hails; got: "+hails.size());
}
Coord ap = hails.get(0).position;
Coord av = hails.get(0).velocity;
Coord bp = hails.get(1).position;
Coord bv = hails.get(1).velocity;
Coord cp = hails.get(2).position;
Coord cv = hails.get(2).velocity;
// @formatter: off
double[][] result = {
{av.y-bv.y, -(av.x-bv.x), 0.0, -(ap.y-bp.y), ap.x-bp.x, 0.0, (bp.y*bv.x - bp.x*bv.y)-(ap.y*av.x-ap.x*av.y)},
{av.y-cv.y, -(av.x-cv.x), 0.0, -(ap.y-cp.y), ap.x-cp.x, 0.0, (cp.y*cv.x - cp.x*cv.y)-(ap.y*av.x-ap.x*av.y)},
{-(av.z-bv.z), 0.0, av.x-bv.x, ap.z-bp.z, 0.0, -(ap.x-bp.x), (bp.x*bv.z - bp.z*bv.x)-(ap.x*av.z-ap.z*av.x)},
{-(av.z-cv.z), 0.0, av.x-cv.x, ap.z-cp.z, 0.0, -(ap.x-cp.x), (cp.x*cv.z - cp.z*cv.x)-(ap.x*av.z-ap.z*av.x)},
{0.0, av.z-bv.z, -(av.y-bv.y), 0.0, -(ap.z-bp.z), ap.y-bp.y, (bp.z*bv.y - bp.y*bv.z)-(ap.z*av.y-ap.y*av.z)},
{0.0, av.z-cv.z, -(av.y-cv.y), 0.0, -(ap.z-cp.z), ap.y-cp.y, (cp.z*cv.y - cp.y*cv.z)-(ap.z*av.y-ap.y*av.z)}
};
// @formatter: on
return result;
}

/**
* Gauss elimination
*
* @param c the matrix of the linear equation
*/
private static void solve(double[][] c) {
for (int row = 0; row < c.length; row++) {
// 1. set c[row][row] equal to 1
double factor = c[row][row];
for (int col = 0; col < c[row].length; col++) {
c[row][col] /= factor;
}

// 2. set c[row][row2] equal to 0
for (int row2 = 0; row2 < c.length; row2++) {
if (row2 != row) {
double factor2 = -c[row2][row];
for (int col = 0; col < c[row2].length; col++) {
c[row2][col] += factor2 * c[row][col];
}
}
}
}
}

Expand All @@ -57,22 +132,17 @@ static Coord read(String desc) {
Long.parseLong(parts[2].strip())
);
}

}

private record IntersectCoords(double x, double y, double z) {
double distanceFromOnPlain(Coord coord) {
return Math.sqrt(Math.pow(x-coord.x,2.0)+Math.pow(y-coord.y, 2.0));
}
}

private record Hail(Coord position, Coord velocity) {
static Hail read(String desc) {
var parts = desc.split(" @ ");
return new Hail(Coord.read(parts[0]), Coord.read(parts[1]));
}
Coord positionAfter(long nanos) {
return new Coord(position.x+nanos*velocity.x, position.y+nanos*velocity.y, position.z+nanos*velocity.z);
}
double slopeOnPlain() {
double top = -velocity.y;
double bottom = -velocity.x;
Expand All @@ -94,12 +164,6 @@ IntersectCoords intersectOnPlain(Hail hail) {
boolean isIntersectionInFutureOnPlain(IntersectCoords intersection) {
return Math.signum(intersection.x-position.x) == Math.signum(velocity.x) && Math.signum(intersection.y-position.y) == Math.signum(velocity.y);
}

}

private static String example = """
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""";
}

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