Demonstrate how to find a solution to a given Sokoban level. For the purpose of this task (formally, a PSPACE-complete problem) any method may be used. However a move-optimal or push-optimal (or any other -optimal) solutions is preferred.

Sokoban levels are usually stored as a character array where

 space is an empty square
 # is a wall
 @ is the player
 $ is a box
 . is a goal
 + is the player on a goal
 * is a box on a goal
#######
#     #
#     #
#. #  #
#. $$ #
#.$$  #
#.#  @#
#######
Sokoban solutions are usually stored in the LURD format, where lowercase l, u, r and d represent a move in that (left, up, right, down) direction and capital LURD represents a push.

Please state if you use some other format for either the input or output, and why.

For more information, see the Sokoban wiki.



using System.Collections.Generic;
using System.Linq;
using System.Text;
 
namespace SokobanSolver
{
    public class SokobanSolver
    {
        private class Board
        {
            public string Cur { get; internal set; }
            public string Sol { get; internal set; }
            public int X { get; internal set; }
            public int Y { get; internal set; }
 
            public Board(string cur, string sol, int x, int y)
            {
                Cur = cur;
                Sol = sol;
                X = x;
                Y = y;
            }
        }
 
        private string destBoard, currBoard;
        private int playerX, playerY, nCols;
 
        SokobanSolver(string[] board)
        {
            nCols = board[0].Length;
            StringBuilder destBuf = new StringBuilder();
            StringBuilder currBuf = new StringBuilder();
 
            for (int r = 0; r < board.Length; r++)
            {
                for (int c = 0; c < nCols; c++)
                {
 
                    char ch = board[r][c];
 
                    destBuf.Append(ch != '$' && ch != '@' ? ch : ' ');
                    currBuf.Append(ch != '.' ? ch : ' ');
 
                    if (ch == '@')
                    {
                        this.playerX = c;
                        this.playerY = r;
                    }
                }
            }
            destBoard = destBuf.ToString();
            currBoard = currBuf.ToString();
        }
 
        private string Move(int x, int y, int dx, int dy, string trialBoard)
        {
 
            int newPlayerPos = (y + dy) * nCols + x + dx;
 
            if (trialBoard[newPlayerPos] != ' ')
                return null;
 
            char[] trial = trialBoard.ToCharArray();
            trial[y * nCols + x] = ' ';
            trial[newPlayerPos] = '@';
 
            return new string(trial);
        }
 
        private string Push(int x, int y, int dx, int dy, string trialBoard)
        {
 
            int newBoxPos = (y + 2 * dy) * nCols + x + 2 * dx;
 
            if (trialBoard[newBoxPos] != ' ')
                return null;
 
            char[] trial = trialBoard.ToCharArray();
            trial[y * nCols + x] = ' ';
            trial[(y + dy) * nCols + x + dx] = '@';
            trial[newBoxPos] = '$';
 
            return new string(trial);
        }
 
        private bool IsSolved(string trialBoard)
        {
            for (int i = 0; i < trialBoard.Length; i++)
                if ((destBoard[i] == '.')
                        != (trialBoard[i] == '$'))
                    return false;
            return true;
        }
 
        private string Solve()
        {
            char[,] dirLabels = { { 'u', 'U' }, { 'r', 'R' }, { 'd', 'D' }, { 'l', 'L' } };
            int[,] dirs = { { 0, -1 }, { 1, 0 }, { 0, 1 }, { -1, 0 } };
            ISet<string> history = new HashSet<string>();
            LinkedList<Board> open = new LinkedList<Board>();
 
            history.Add(currBoard);
            open.AddLast(new Board(currBoard, string.Empty, playerX, playerY));
 
            while (!open.Count.Equals(0))
            {
                Board item = open.First();
                open.RemoveFirst();
                string cur = item.Cur;
                string sol = item.Sol;
                int x = item.X;
                int y = item.Y;
 
                for (int i = 0; i < dirs.GetLength(0); i++)
                {
                    string trial = cur;
                    int dx = dirs[i, 0];
                    int dy = dirs[i, 1];
 
                    // are we standing next to a box ?
                    if (trial[(y + dy) * nCols + x + dx] == '$')
                    {
                        // can we push it ?
                        if ((trial = Push(x, y, dx, dy, trial)) != null)
                        {
                            // or did we already try this one ?
                            if (!history.Contains(trial))
                            {
 
                                string newSol = sol + dirLabels[i, 1];
 
                                if (IsSolved(trial))
                                    return newSol;
 
                                open.AddLast(new Board(trial, newSol, x + dx, y + dy));
                                history.Add(trial);
                            }
                        }
                        // otherwise try changing position
                    }
                    else if ((trial = Move(x, y, dx, dy, trial)) != null)
                    {
                        if (!history.Contains(trial))
                        {
                            string newSol = sol + dirLabels[i, 0];
                            open.AddLast(new Board(trial, newSol, x + dx, y + dy));
                            history.Add(trial);
                        }
                    }
                }
            }
            return "No solution";
        }
 
        public static void Main(string[] a)
        {
            string level = "#######," +
                           "#     #," +
                           "#     #," +
                           "#. #  #," +
                           "#. $$ #," +
                           "#.$$  #," +
                           "#.#  @#," +
                           "#######";
            System.Console.WriteLine("Level:\n");
            foreach (string line in level.Split(','))
            {
                System.Console.WriteLine(line);
            }
            System.Console.WriteLine("\nSolution:\n");
            System.Console.WriteLine(new SokobanSolver(level.Split(',')).Solve());
        }
    }
}