# L-12 MCS 275 Mon 8 Feb 2010 : find a path through a maze

from numpy import *
import random

def PrintMaze(M):
   """
   Writes the maze to screen, spaces if free, # is blocked.
   """
   s = '     '
   for j in range(0,M.shape[1]):
      s = s + '%3d' % j
   print s
   for i in range(0,M.shape[0]):
      s = '%3d :' % i
      for j in range(0,M.shape[1]):
         if M[i,j] == 0:
            s = s + '   '
         elif M[i,j] == -1:
            s = s + '###'
         else:
            s = s + '%3d' % M[i,j]
      print s

def RandomMaze(rows,cols):
   """
   Returns a random integer matrix with dimensions in rows and cols,
   indicating free positions with 0 and occupied positions with -1.
   Free positions are at [0,0] and [rows-1,cols-1].
   """
   M = zeros((rows,cols),int)
   for i in range(0,rows):
      for j in range(0,cols):
         M[i,j] = random.randint(-1,0)
   M[0,0] = 0
   M[rows-1,cols-1] = 0
   return M

def MakeMaze(rows,cols):
   """
   Returns a random integer matrix with dimensions in rows and cols,
   indicating free positions with 0 and occupied positions with -1.
   Free positions are at [0,0] and [rows-1,cols-1].
   """
   M = RandomMaze(rows,cols)
   while True:
      PrintMaze(M)
      i = input('to change, give i (-1 if not) : ')
      if i < 0: break
      j = input('to change, give j (-1 if not) : ')
      if j < 0: break
      if M[i,j] == -1:
         M[i,j] = 0
      else:
         M[i,j] = -1
   return M

def Search(M,i,j,k):
   """
   Search a path upwards, starting at (i,j)-th position.
   Markes visited tiles with increasing numbers.
   Returns M and a boolean indicating the arrival.
   """
   M[i,j] = k
   if i == M.shape[0] - 1 and j == M.shape[1] - 1:
      return (M,True)
   else:
      b = False
      if i < M.shape[0]-1:
         if M[i+1,j] == 0: (M,b) = Search(M,i+1,j,k+1)
      if not b and j < M.shape[1]-1:
         if M[i,j+1] == 0: (M,b) = Search(M,i,j+1,k+1)
      if not b and i > 0:
         if M[i-1,j] == 0: (M,b) = Search(M,i-1,j,k+1)
      if not b and j > 0:
         if M[i,j-1] == 0: (M,b) = Search(M,i,j-1,k+1)
      return (M,b)

def main():
   """
   prompts for dimension of a grid
   """
   r = input('give #rows : ')
   c = input('give #columns : ')
   M = MakeMaze(r,c)
   PrintMaze(M)
   (M,b) = Search(M,0,0,1)
   if b:
      print 'path found'
   else:
      print 'no path found'
   PrintMaze(M)

main()