Day 19 solution
Cribbed heavily from https://www.reddit.com/r/adventofcode/comments/rjpf7f/comment/hp5k554/?utm_source=share&utm_medium=web2x&context=3 because this problem breaks my brain in so many ways. I understand the approach, but I got twisted up in my own head trying to write down the solution, so instead I started from a working copy and optimized it (a little bit) to make sure I understood what it was doing.
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176
src/19.cs
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176
src/19.cs
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namespace aoc2021;
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internal class Day19 : Day
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{
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internal override void Go()
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{
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var lines = Util.ReadAllLines("inputs/19.txt");
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var scanners = new List<HashSet<Vector3>>();
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foreach (var line in lines)
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{
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if (line.StartsWith("--"))
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{
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scanners.Add(new());
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}
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else if (string.IsNullOrEmpty(line))
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{
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continue;
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}
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else
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{
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var points = line.Split(',');
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scanners[^1].Add((Convert.ToInt32(points[0]), Convert.ToInt32(points[1]), Convert.ToInt32(points[2])));
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}
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}
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var result = Part1(scanners);
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Part2(result);
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}
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record struct Vector3(int X, int Y, int Z)
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{
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public static implicit operator Vector3((int x, int y, int z) value) => new(value.x, value.y, value.z);
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public static Vector3 operator+(Vector3 p, Vector3 v) => (p.X + v.X, p.Y + v.Y, p.Z + v.Z);
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public static Vector3 operator-(Vector3 p1, Vector3 p2) => (p1.X - p2.X, p1.Y - p2.Y, p1.Z - p2.Z);
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public int DistanceTo(Vector3 other) => (int)(Math.Pow(other.X - X, 2) + Math.Pow(other.Y - Y, 2) + Math.Pow(other.Z - Z, 2));
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public int ManhattanDistanceTo(Vector3 other)
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{
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var (dx, dy, dz) = this - other;
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return Math.Abs(dx) + Math.Abs(dy) + Math.Abs(dz);
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}
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public Vector3 Transform(Vector3 up, int rotation)
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{
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Vector3 reoriented = up switch
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{
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(0, +1, 0) => (X, Y, Z),
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(0, -1, 0) => (X, -Y, -Z),
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(+1, 0, 0) => (Y, X, -Z),
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(-1, 0, 0) => (Y, -X, Z),
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(0, 0, +1) => (Y, Z, X),
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(0, 0, -1) => (Y, -Z, -X),
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_ => throw new Exception("Invalid up vector")
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};
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return rotation switch
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{
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0 => reoriented,
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1 => (reoriented.Z, reoriented.Y, -reoriented.X),
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2 => (-reoriented.X, reoriented.Y, -reoriented.Z),
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3 => (-reoriented.Z, reoriented.Y, reoriented.X),
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_ => throw new Exception("Invalid rotation")
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};
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}
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}
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private static readonly (int, int, int)[] Axes = new[]
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{
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( 0, +1, 0),
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( 0, -1, 0),
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(+1, 0, 0),
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(-1, 0, 0),
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( 0, 0, +1),
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( 0, 0, -1)
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};
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private static (IEnumerable<Vector3> alignedBeacons, Vector3 translation, Vector3 up, int rotation)? Align(ICollection<Vector3> beacons1, ICollection<Vector3> beacons2)
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{
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// Fix beacons1, rotate beacons2
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for (int axis = 0; axis < Axes.Length; axis++)
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{
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for (int rotation = 0; rotation < 4; rotation++)
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{
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var rotatedBeacons2 = new HashSet<Vector3>(beacons2.Select(b => b.Transform(Axes[axis], rotation)));
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foreach (var b1 in beacons1)
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{
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// Assume b1 matches some b2
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foreach (var matchingB1InB2 in rotatedBeacons2)
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{
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// Move all b2 so matchingB1InB2 matches b1, in scanner 1 coordinates
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var delta = b1 - matchingB1InB2;
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var transformedBeacons2 = rotatedBeacons2.Select(b => b + delta);
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// How many overlaps did we get?
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var intersection = new HashSet<Vector3>(transformedBeacons2);
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intersection.IntersectWith(beacons1);
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if (intersection.Count >= 12)
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{
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// Found the right orientation
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return (transformedBeacons2, delta, Axes[axis], rotation);
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}
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}
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}
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}
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}
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return null;
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}
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private static (IEnumerable<HashSet<Vector3>> scans, IEnumerable<HashSet<Vector3>> scanners) Reduce(IEnumerable<HashSet<Vector3>> scans, IEnumerable<HashSet<Vector3>> scanners)
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{
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var toRemove = new HashSet<int>();
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for (int i = 0; i < scans.Count() - 1; i++)
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{
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for (int j = i + 1; j < scans.Count(); j++)
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{
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if (toRemove.Contains(j))
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{
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// Already merged
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continue;
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}
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var alignment = Align(scans.ElementAt(i), scans.ElementAt(j));
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if (alignment != null)
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{
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// Convert all scanners from j coordinates to i coordinates
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foreach (var s in scanners.ElementAt(j))
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{
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var scanner = alignment.Value.translation + s.Transform(alignment.Value.up, alignment.Value.rotation);
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scanners.ElementAt(i).Add(scanner);
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}
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// Merge the scan sets
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scans.ElementAt(i).UnionWith(alignment.Value.alignedBeacons);
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toRemove.Add(j);
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}
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}
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}
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// Skip all scans and scanners that were merged
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return (scans.Where((_, i) => !toRemove.Contains(i)), scanners.Where((_, i) => !toRemove.Contains(i)));
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}
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private static ICollection<Vector3> Part1(List<HashSet<Vector3>> input)
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{
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using var t = new Timer();
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IEnumerable<HashSet<Vector3>> scans = input;
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IEnumerable<HashSet<Vector3>> scanners = input.Select((_) => new HashSet<Vector3> { (0, 0, 0) }).ToList();
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while (scans.Count() > 1)
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{
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// Note that this will loop forever if there is no alignment
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(scans, scanners) = Reduce(scans, scanners);
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}
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var allBeacons = scans.ElementAt(0);
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t.Stop();
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Logger.Log($"<+black>> part1: <+white>{allBeacons.Count}<r>");
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return scanners.ElementAt(0);
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}
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private static void Part2(ICollection<Vector3> scanners)
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{
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using var t = new Timer();
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var scannerList = scanners.ToList();
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var farthest =
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Enumerable.Range(0, scannerList.Count - 1)
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.SelectMany(i => Enumerable.Range(i + 1, scannerList.Count - i - 1).Select(j => (i, j)))
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.Max(pair => scannerList[pair.i].ManhattanDistanceTo(scannerList[pair.j]));
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t.Stop();
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Logger.Log($"<+black>> part2: <+white>{farthest}<r>");
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}
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}
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@ -37,6 +37,7 @@ else
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"16" => new Day16(),
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"17"=> new Day17(),
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"18" => new Day18(),
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"19" => new Day19(),
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_ => new Day20(),
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};
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day.Go();
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