www.mikescher.com/www/statics/aoc/2018/13_solution-2.linq

<Query Kind="Program" />

class Rail
{
    public int X,Y;
    public Rail N,E,S,W;
}
class Cart
{
	public bool C=false;
	public Dir D;
	public Rail R;
	public int Mem = 0;
}
enum Dir { N = 0, E = 1, S = 2, W = 3 }

void Main()
{
	(List<Rail> rails, List<Cart> carts) = Parse(File.ReadAllLines(Path.Combine(Path.GetDirectoryName(Util.CurrentQueryPath), @"13_input.txt")));

	int cc = carts.Count;
	for (int gen = 0; ; gen++)
	{
		foreach (var c in carts.OrderBy(c => c.R.Y * 10000 + c.R.X))
		{
			if (c.C)continue;
			switch (c.D)
			{
				case Dir.S:
					Move(c, new[] { (Dir.E, c.R.E), (Dir.S, c.R.S), (Dir.W, c.R.W) });
					break;
				case Dir.W:
					Move(c, new[] { (Dir.S, c.R.S), (Dir.W, c.R.W), (Dir.N, c.R.N) });
					break;
				case Dir.N:
					Move(c, new[] { (Dir.W, c.R.W), (Dir.N, c.R.N), (Dir.E, c.R.E) });
					break;
				case Dir.E:
					Move(c, new[] { (Dir.N, c.R.N), (Dir.E, c.R.E), (Dir.S, c.R.S) });
					break;
			}

			var dc = carts.FirstOrDefault(oc => oc != c && oc.R == c.R && !oc.C);
			if (dc != null) { c.C = dc.C = true; cc-=2; }
			if (cc == 1) { $"{carts.Single(p => !p.C).R.X},{carts.Single(p => !p.C).R.Y} after {gen}".Dump(); return; }

		}
		//foreach (var c in carts) $"{c.R.X}|{c.R.Y}|{c.D}".Dump();"------".Dump();
	}

}

void Move(Cart c, IEnumerable<(Dir, Rail)> options)
{
	var outs = options.Where(p => p.Item2 != null).ToList();
	if (outs.Count == 1)
	{
		c.R = outs[0].Item2;
		c.D = outs[0].Item1;
	}
	else
	{
		c.R = outs[c.Mem % 3].Item2;
		c.D = outs[c.Mem % 3].Item1;
		c.Mem++;
	}

}

void Dump(List<Rail> rails, List<Cart> carts)
{
	int maxx = rails.Max(r => r.X) + 1;
	int maxy = rails.Max(r => r.Y) + 1;

	var b = new StringBuilder();
	for (int yy = 0; yy < maxy; yy++)
	{
		for (int xx = 0; xx < maxx; xx++)
		{
			var cc = carts.FirstOrDefault(c => c.R.X == xx && c.R.Y == yy);
			if (cc != null)
			{
				if (cc.D == Dir.N) b.Append('^');
				if (cc.D == Dir.E) b.Append('>');
				if (cc.D == Dir.S) b.Append('v');
				if (cc.D == Dir.W) b.Append('<');
			}
			else if (rails.Any(r => r.X == xx && r.Y == yy))
			{
				b.Append('.');
			}
			else
			{
				b.Append(' ');
			}
		}
		b.AppendLine();
	}
	b.ToString().Dump();
	"".Dump();
}

(List<Rail>, List<Cart>) Parse(string[] line)
{
	var rails = new Dictionary<(int, int), Rail>();
	var carts = new List<Cart>();

	Rail get(int x, int y) { if (rails.TryGetValue((x, y), out var v)) return v; Rail r = new Rail { X = x, Y = y }; rails.Add((x, y), r); return r; }

	char last = ' ';
	for (int y = 0; y < line.Length; y++)
	{
		last = ' ';
		for (int x = 0; x < line[y].Length; x++)
		{
			char c = line[y][x];
			if (c == ' ') continue;

			switch (c)
			{
				case '-':
					{
						var rr = get(x, y);
						var ra = get(x - 1, y);
						var rb = get(x + 1, y);
						rr.W = ra; ra.E = rr;
						rr.E = rb; rb.W = rr;
					}
					break;
				case '|':
					{
						var rr = get(x, y);
						var ra = get(x, y - 1);
						var rb = get(x, y + 1);
						rr.N = ra; ra.S = rr;
						rr.S = rb; rb.N = rr;
					}
					break;
				case '+':
					{
						var rr = get(x, y);
						var ra = get(x, y - 1);
						var rb = get(x + 1, y);
						var rc = get(x, y + 1);
						var rd = get(x - 1, y);
						rr.N = ra; ra.S = rr;
						rr.E = rb; rb.W = rr;
						rr.S = rc; rc.N = rr;
						rr.W = rd; rd.E = rr;
					}
					break;
				case '/':
					if (last == '-' || last == '+')
					{
						var rr = get(x, y);
						var ra = get(x - 1, y);
						var rb = get(x, y - 1);
						rr.W = ra; ra.E = rr;
						rr.N = rb; rb.S = rr;
					}
					else
					{
						var rr = get(x, y);
						var ra = get(x + 1, y);
						var rb = get(x, y + 1);
						rr.E = ra; ra.W = rr;
						rr.S = rb; rb.N = rr;
					}
					break;
				case '\\':
					if (last == '-' || last == '+')
					{
						var rr = get(x, y);
						var ra = get(x - 1, y);
						var rb = get(x, y + 1);
						rr.W = ra; ra.E = rr;
						rr.S = rb; rb.N = rr;
					}
					else
					{
						var rr = get(x, y);
						var ra = get(x + 1, y);
						var rb = get(x, y - 1);
						rr.E = ra; ra.W = rr;
						rr.N = rb; rb.S = rr;
					}
					break;
				case '^':
					{
						var rr = get(x, y);
						var ra = get(x, y - 1);
						var rb = get(x, y + 1);
						rr.N = ra; ra.S = rr;
						rr.S = rb; rb.N = rr;
						carts.Add(new Cart { D = Dir.N, R = rr, });
					}
					break;
				case 'v':
					{
						var rr = get(x, y);
						var ra = get(x, y - 1);
						var rb = get(x, y + 1);
						rr.N = ra; ra.S = rr;
						rr.S = rb; rb.N = rr;
						carts.Add(new Cart { D = Dir.S, R = rr, });
					}
					break;
				case '>':
					{
						var rr = get(x, y);
						var ra = get(x - 1, y);
						var rb = get(x + 1, y);
						rr.W = ra; ra.E = rr;
						rr.E = rb; rb.W = rr;
						carts.Add(new Cart { D = Dir.E, R = rr, });
					}
					break;
				case '<':
					{
						var rr = get(x, y);
						var ra = get(x - 1, y);
						var rb = get(x + 1, y);
						rr.W = ra; ra.E = rr;
						rr.E = rb; rb.W = rr;
						carts.Add(new Cart { D = Dir.W, R = rr, });
					}
					break;
			}
			last = c;
		}
	}

	return (rails.Select(p => p.Value).ToList(), carts);
}