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.

advent-of-code-2021.csproj

@@ -72,6 +72,9 @@
 	  <None Update="inputs\18.txt">
 	    <CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
 	  </None>
+	  <None Update="inputs\19.txt">
+	    <CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
+	  </None>
 	  <None Update="inputs\20.txt">
 	    <CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
 	  </None>

inputs/19.txt

@@ -0,0 +1,856 @@
+--- scanner 0 ---
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+
+--- scanner 1 ---
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+
+--- scanner 2 ---
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+
+--- scanner 3 ---
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+
+--- scanner 4 ---
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+
+--- scanner 5 ---
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+
+--- scanner 6 ---
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+
+--- scanner 7 ---
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+
+--- scanner 8 ---
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+
+--- scanner 9 ---
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+
+--- scanner 10 ---
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+
+--- scanner 11 ---
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+
+--- scanner 12 ---
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+
+--- scanner 13 ---
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+
+--- scanner 14 ---
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+
+--- scanner 15 ---
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+
+--- scanner 16 ---
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+
+--- scanner 17 ---
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+
+--- scanner 18 ---
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+
+--- scanner 19 ---
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+
+--- scanner 20 ---
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+
+--- scanner 21 ---
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+
+--- scanner 22 ---
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+
+--- scanner 23 ---
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+
+--- scanner 24 ---
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+
+--- scanner 25 ---
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+
+--- scanner 26 ---
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+
+--- scanner 27 ---
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+
+--- scanner 28 ---
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+
+--- scanner 29 ---
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+
+--- scanner 30 ---
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src/19.cs

@@ -0,0 +1,176 @@
+namespace aoc2021;
+
+internal class Day19 : Day
+{
+    internal override void Go()
+    {
+        var lines = Util.ReadAllLines("inputs/19.txt");
+        var scanners = new List<HashSet<Vector3>>();
+        foreach (var line in lines)
+        {
+            if (line.StartsWith("--"))
+            {
+                scanners.Add(new());
+            }
+            else if (string.IsNullOrEmpty(line))
+            {
+                continue;
+            }
+            else
+            {
+                var points = line.Split(',');
+                scanners[^1].Add((Convert.ToInt32(points[0]), Convert.ToInt32(points[1]), Convert.ToInt32(points[2])));
+            }
+        }
+
+        var result = Part1(scanners);
+        Part2(result);
+    }
+
+    record struct Vector3(int X, int Y, int Z)
+    {
+        public static implicit operator Vector3((int x, int y, int z) value) => new(value.x, value.y, value.z);
+        public static Vector3 operator+(Vector3 p, Vector3 v) => (p.X + v.X, p.Y + v.Y, p.Z + v.Z);
+        public static Vector3 operator-(Vector3 p1, Vector3 p2) => (p1.X - p2.X, p1.Y - p2.Y, p1.Z - p2.Z);
+
+        public int DistanceTo(Vector3 other) => (int)(Math.Pow(other.X - X, 2) + Math.Pow(other.Y - Y, 2) + Math.Pow(other.Z - Z, 2));
+
+        public int ManhattanDistanceTo(Vector3 other)
+        {
+            var (dx, dy, dz) = this - other;
+            return Math.Abs(dx) + Math.Abs(dy) + Math.Abs(dz);
+        }
+
+        public Vector3 Transform(Vector3 up, int rotation)
+        {
+            Vector3 reoriented = up switch
+            {
+                (0, +1, 0) => (X, Y, Z),
+                (0, -1, 0) => (X, -Y, -Z),
+                (+1, 0, 0) => (Y, X, -Z),
+                (-1, 0, 0) => (Y, -X, Z),
+                (0, 0, +1) => (Y, Z, X),
+                (0, 0, -1) => (Y, -Z, -X),
+                _ => throw new Exception("Invalid up vector")
+            };
+
+            return rotation switch
+            {
+                0 => reoriented,
+                1 => (reoriented.Z, reoriented.Y, -reoriented.X),
+                2 => (-reoriented.X, reoriented.Y, -reoriented.Z),
+                3 => (-reoriented.Z, reoriented.Y, reoriented.X),
+                _ => throw new Exception("Invalid rotation")
+            };
+        }
+    }
+
+    private static readonly (int, int, int)[] Axes = new[]
+    {
+        ( 0, +1,  0),
+        ( 0, -1,  0),
+        (+1,  0,  0),
+        (-1,  0,  0),
+        ( 0,  0, +1),
+        ( 0,  0, -1)
+    };
+
+    private static (IEnumerable<Vector3> alignedBeacons, Vector3 translation, Vector3 up, int rotation)? Align(ICollection<Vector3> beacons1, ICollection<Vector3> beacons2)
+    {
+        // Fix beacons1, rotate beacons2
+        for (int axis = 0; axis < Axes.Length; axis++)
+        {
+            for (int rotation = 0; rotation < 4; rotation++)
+            {
+                var rotatedBeacons2 = new HashSet<Vector3>(beacons2.Select(b => b.Transform(Axes[axis], rotation)));
+
+                foreach (var b1 in beacons1)
+                {
+                    // Assume b1 matches some b2
+                    foreach (var matchingB1InB2 in rotatedBeacons2)
+                    {
+                        // Move all b2 so matchingB1InB2 matches b1, in scanner 1 coordinates
+                        var delta = b1 - matchingB1InB2;
+                        var transformedBeacons2 = rotatedBeacons2.Select(b => b + delta);
+
+                        // How many overlaps did we get?
+                        var intersection = new HashSet<Vector3>(transformedBeacons2);
+                        intersection.IntersectWith(beacons1);
+                        if (intersection.Count >= 12)
+                        {
+                            // Found the right orientation
+                            return (transformedBeacons2, delta, Axes[axis], rotation);
+                        }
+                    }
+                }
+            }
+        }
+        return null;
+    }
+
+    private static (IEnumerable<HashSet<Vector3>> scans, IEnumerable<HashSet<Vector3>> scanners) Reduce(IEnumerable<HashSet<Vector3>> scans, IEnumerable<HashSet<Vector3>> scanners)
+    {
+        var toRemove = new HashSet<int>();
+        for (int i = 0; i < scans.Count() - 1; i++)
+        {
+            for (int j = i + 1; j < scans.Count(); j++)
+            {
+                if (toRemove.Contains(j))
+                {
+                    // Already merged
+                    continue;
+                }
+
+                var alignment = Align(scans.ElementAt(i), scans.ElementAt(j));
+                if (alignment != null)
+                {
+                    // Convert all scanners from j coordinates to i coordinates
+                    foreach (var s in scanners.ElementAt(j))
+                    {
+                        var scanner = alignment.Value.translation + s.Transform(alignment.Value.up, alignment.Value.rotation);
+                        scanners.ElementAt(i).Add(scanner);
+                    }
+                    // Merge the scan sets
+                    scans.ElementAt(i).UnionWith(alignment.Value.alignedBeacons);
+                    toRemove.Add(j);
+                }
+            }
+        }
+        // Skip all scans and scanners that were merged
+        return (scans.Where((_, i) => !toRemove.Contains(i)), scanners.Where((_, i) => !toRemove.Contains(i)));
+    }
+
+    private static ICollection<Vector3> Part1(List<HashSet<Vector3>> input)
+    {
+        using var t = new Timer();
+
+        IEnumerable<HashSet<Vector3>> scans = input;
+        IEnumerable<HashSet<Vector3>> scanners = input.Select((_) => new HashSet<Vector3> { (0, 0, 0) }).ToList();
+        while (scans.Count() > 1)
+        {
+            // Note that this will loop forever if there is no alignment
+            (scans, scanners) = Reduce(scans, scanners);
+        }
+
+        var allBeacons = scans.ElementAt(0);
+
+        t.Stop();
+        Logger.Log($"<+black>> part1: <+white>{allBeacons.Count}<r>");
+
+        return scanners.ElementAt(0);
+    }
+
+    private static void Part2(ICollection<Vector3> scanners)
+    {
+        using var t = new Timer();
+
+        var scannerList = scanners.ToList();
+        var farthest =
+            Enumerable.Range(0, scannerList.Count - 1)
+                .SelectMany(i => Enumerable.Range(i + 1, scannerList.Count - i - 1).Select(j => (i, j)))
+                .Max(pair => scannerList[pair.i].ManhattanDistanceTo(scannerList[pair.j]));
+
+        t.Stop();
+        Logger.Log($"<+black>> part2: <+white>{farthest}<r>");
+    }
+}

src/main.cs

@@ -37,6 +37,7 @@ else
         "16" => new Day16(),
         "17"=> new Day17(),
         "18" => new Day18(),
+        "19" => new Day19(),
         _ => new Day20(),
     };
     day.Go();