AdventOfCode/Days/Day16.cs

using System.Numerics;
using Spectre.Console;

namespace AdventOfCode.Days;

public class Day16 : Day
{
    public override int Number => 16;
    public override string Name => "Reindeer Maze";

    private const int Size = 141;

    private const char Wall = '#';
    private const char Empty = '.';
    private const char Start = 'S';
    private const char End = 'E';

    private static readonly Point DirectionUp = new(0, -1);
    private static readonly Point DirectionDown = new(0, 1);
    private static readonly Point DirectionLeft = new(-1, 0);
    private static readonly Point DirectionRight = new(1, 0);

    public override void RunPart1(bool display = true)
    {
        var (maze, start, end) = ParseMaze();

        var visited = new Dictionary<(Point Position, Point Direction), int>();

        var minimumScore = int.MaxValue;

        var toVisit = new Queue<(Point Position, Point Direction, int Score)>();

        toVisit.Enqueue((start, DirectionRight, 0));

        while (toVisit.Count > 0)
        {
            var (position, direction, score) = toVisit.Dequeue();

            if (visited.TryGetValue((position, direction), out var savedScore) && savedScore <= score)
            {
                continue;
            }

            visited[(position, direction)] = score;

            // Reached end
            if (position == end)
            {
                if (score < minimumScore)
                {
                    minimumScore = score;
                }

                continue;
            }

            // Try forward if there is no wall
            var destination = position + direction;

            if (maze[destination.X, destination.Y] is not Wall)
            {
                toVisit.Enqueue((destination, direction, score + 1));
            }

            // Also try changing direction
            toVisit.Enqueue((position, NextDirection(direction), score + 1000));
            toVisit.Enqueue((position, PreviousDirection(direction), score + 1000));
        }

        if (display)
        {
            AnsiConsole.MarkupLine($"[green]Lowest score: [yellow]{minimumScore}[/][/]");
        }
    }

    public override void RunPart2(bool display = true)
    {
        var (maze, start, end) = ParseMaze();

        var visited = new Dictionary<(Point Position, Point Direction), int>();

        var minimumScore = int.MaxValue;

        var toVisit = new Queue<(Point Position, Point Direction, int Score)>();

        toVisit.Enqueue((start, DirectionRight, 0));

        // First we need to find minimum score
        while (toVisit.Count > 0)
        {
            var (position, direction, score) = toVisit.Dequeue();

            if (visited.TryGetValue((position, direction), out var savedScore) && savedScore <= score)
            {
                continue;
            }

            visited[(position, direction)] = score;

            // Reached end
            if (position == end)
            {
                if (score < minimumScore)
                {
                    minimumScore = score;
                }

                continue;
            }

            // Try forward if there is no wall
            var destination = position + direction;

            if (maze[destination.X, destination.Y] is not Wall)
            {
                toVisit.Enqueue((destination, direction, score + 1));
            }

            // Also try changing direction
            toVisit.Enqueue((position, NextDirection(direction), score + 1000));
            toVisit.Enqueue((position, PreviousDirection(direction), score + 1000));
        }

        // Now that we have minimum score, we need to find all the paths that lead to this score
        var toVisitPath = new Stack<(Point Position, Point Direction, int Score, List<Point> Path)>();
        toVisitPath.Push((start, DirectionRight, 0, []));

        var minimumScorePaths = new List<List<Point>>();

        while (toVisitPath.Count > 0)
        {
            var (position, direction, score, path) = toVisitPath.Pop();

            if (score > minimumScore)
            {
                continue;
            }

            if (visited.TryGetValue((position, direction), out var savedScore) && savedScore < score)
            {
                continue;
            }

            path.Add(position);

            // Reached end
            if (position == end)
            {
                minimumScorePaths.Add(path);

                continue;
            }

            // Try forward if there is no wall
            var destination = position + direction;

            if (maze[destination.X, destination.Y] is not Wall)
            {
                toVisitPath.Push((destination, direction, score + 1, path));
            }

            // Also try changing direction
            toVisitPath.Push((position, NextDirection(direction), score + 1000, path.ToList()));
            toVisitPath.Push((position, PreviousDirection(direction), score + 1000, path.ToList()));
        }

        if (display)
        {
            AnsiConsole.MarkupLine($"[green]Unique positions in optimal paths: [yellow]{minimumScorePaths.SelectMany(l => l).ToHashSet().Count}[/][/]");
        }
    }

    private (char[,] Maze, Point Start, Point end) ParseMaze()
    {
        var maze = new char[Size, Size];
        Point start = default;
        Point end = default;

        var y = 0;
        foreach (var line in Input.AsSpan().EnumerateLines())
        {
            var x = 0;
            foreach (var symbol in line)
            {
                if (symbol is Start)
                {
                    start = new Point(x, y);

                    maze[x, y] = Empty;
                }
                else if (symbol is End)
                {
                    end = new Point(x, y);

                    maze[x, y] = Empty;
                }
                else
                {
                    maze[x, y] = symbol;
                }

                x++;
            }

            y++;
        }

        return (maze, start, end);
    }

    private static Point NextDirection(Point direction)
    {
        if (direction == DirectionUp)
        {
            return DirectionRight;
        }

        if (direction == DirectionRight)
        {
            return DirectionDown;
        }

        if (direction == DirectionDown)
        {
            return DirectionLeft;
        }

        if (direction == DirectionLeft)
        {
            return DirectionUp;
        }

        throw new ArgumentException("Invalid direction", nameof(direction));
    }

    private static Point PreviousDirection(Point direction)
    {
        if (direction == DirectionUp)
        {
            return DirectionLeft;
        }

        if (direction == DirectionLeft)
        {
            return DirectionDown;
        }

        if (direction == DirectionDown)
        {
            return DirectionRight;
        }

        if (direction == DirectionRight)
        {
            return DirectionUp;
        }

        throw new ArgumentException("Invalid direction", nameof(direction));
    }

    private readonly record struct Point(int X, int Y)
        : IAdditionOperators<Point, Point, Point>,
            ISubtractionOperators<Point, Point, Point>,
            IMultiplyOperators<Point, int, Point>
    {
        public static Point operator +(Point left, Point right)
        {
            return new Point(left.X + right.X, left.Y + right.Y);
        }

        public static Point operator -(Point left, Point right)
        {
            return new Point(left.X - right.X, left.Y - right.Y);
        }

        public static Point operator *(Point left, int right)
        {
            return new Point(left.X * right, left.Y * right);
        }

        public static Point operator *(int left, Point right)
        {
            return new Point(right.X * left, right.Y * left);
        }

        public static implicit operator Point((int X, int Y) point)
            => new(point.X, point.Y);
    }
}