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.



from array import array
from collections import deque
import psyco
 
data = []
nrows = 0
px = py = 0
sdata = ""
ddata = ""
 
def init(board):
    global data, nrows, sdata, ddata, px, py
    data = filter(None, board.splitlines())
    nrows = max(len(r) for r in data)
 
    maps = {' ':' ', '.': '.', '@':' ', '#':'#', '$':' '}
    mapd = {' ':' ', '.': ' ', '@':'@', '#':' ', '$':'*'}
 
    for r, row in enumerate(data):
        for c, ch in enumerate(row):
            sdata += maps[ch]
            ddata += mapd[ch]
            if ch == '@':
                px = c
                py = r
 
def push(x, y, dx, dy, data):
    if sdata[(y+2*dy) * nrows + x+2*dx] == '#' or \
       data[(y+2*dy) * nrows + x+2*dx] != ' ':
        return None
 
    data2 = array("c", data)
    data2[y * nrows + x] = ' '
    data2[(y+dy) * nrows + x+dx] = '@'
    data2[(y+2*dy) * nrows + x+2*dx] = '*'
    return data2.tostring()
 
def is_solved(data):
    for i in xrange(len(data)):
        if (sdata[i] == '.') != (data[i] == '*'):
            return False
    return True
 
def solve():
    open = deque([(ddata, "", px, py)])
    visited = set([ddata])
    dirs = ((0, -1, 'u', 'U'), ( 1, 0, 'r', 'R'),
            (0,  1, 'd', 'D'), (-1, 0, 'l', 'L'))
 
    lnrows = nrows
    while open:
        cur, csol, x, y = open.popleft()
 
        for di in dirs:
            temp = cur
            dx, dy = di[0], di[1]
 
            if temp[(y+dy) * lnrows + x+dx] == '*':
                temp = push(x, y, dx, dy, temp)
                if temp and temp not in visited:
                    if is_solved(temp):
                        return csol + di[3]
                    open.append((temp, csol + di[3], x+dx, y+dy))
                    visited.add(temp)
            else:
                if sdata[(y+dy) * lnrows + x+dx] == '#' or \
                   temp[(y+dy) * lnrows + x+dx] != ' ':
                    continue
 
                data2 = array("c", temp)
                data2[y * lnrows + x] = ' '
                data2[(y+dy) * lnrows + x+dx] = '@'
                temp = data2.tostring()
 
                if temp not in visited:
                    if is_solved(temp):
                        return csol + di[2]
                    open.append((temp, csol + di[2], x+dx, y+dy))
                    visited.add(temp)
 
    return "No solution"
 
 
level = """\
#######
#     #
#     #
#. #  #
#. $$ #
#.$$  #
#.#  @#
#######"""
 
psyco.full()
init(level)
print level, "\n\n", solve()