print out maze path

maze_path.py

# -----------
# User Instructions:
#
# Modify the the search function so that it returns
# a shortest path as follows:
# 
# [['>', 'v', ' ', ' ', ' ', ' '],
#  [' ', '>', '>', '>', '>', 'v'],
#  [' ', ' ', ' ', ' ', ' ', 'v'],
#  [' ', ' ', ' ', ' ', ' ', 'v'],
#  [' ', ' ', ' ', ' ', ' ', '*']]
#
# Where '>', '<', '^', and 'v' refer to right, left, 
# up, and down motions. Note that the 'v' should be 
# lowercase. '*' should mark the goal cell.
#
# You may assume that all test cases for this function
# will have a path from init to goal.
# ----------

grid = [[0, 0, 1, 0, 0, 0],
        [0, 0, 0, 0, 0, 0],
        [0, 0, 1, 0, 1, 0],
        [0, 0, 1, 0, 1, 0],
        [0, 0, 1, 0, 1, 0]]
init = [0, 0]
goal = [len(grid)-1, len(grid[0])-1]
cost = 1

delta = [[-1, 0 ], # go up
         [ 0, -1], # go left
         [ 1, 0 ], # go down
         [ 0, 1 ]] # go right

delta_name = ['^', '<', 'v', '>']

def search(grid,init,goal,cost):
    # ----------------------------------------
    # modify code below
    # ----------------------------------------
    closed = [[0 for row in range(len(grid[0]))] for col in range(len(grid))]
    closed[init[0]][init[1]] = 1
    expand = [[' ' for row in range(len(grid[0]))] for col in range(len(grid))]

    x = init[0]
    y = init[1]
    g = 0

    open = [[g, x, y]]
    paths = []  #keeps list of actions and current block

    found = False  # flag that is set when search is complete
    resign = False # flag set if we can't find expand

    while not found and not resign:
        if len(open) == 0:
            resign = True
            return 'fail'
        else:
            open.sort()
            open.reverse()
            next = open.pop()
            
            x = next[1]
            y = next[2]
            g = next[0]
            
            if x == goal[0] and y == goal[1]:
                expand[x][y] = '*'
                found = True
            else:
                for i in range(len(delta)):
                    x2 = x + delta[i][0]
                    y2 = y + delta[i][1]
                    if x2 >= 0 and x2 < len(grid) and y2 >=0 and y2 < len(grid[0]):
                        #print 'next',x2,y2
                        if closed[x2][y2] == 0 and grid[x2][y2] == 0:
                            g2 = g + cost
                            open.append([g2, x2, y2])
                            closed[x2][y2] = 1
                            
                            if x==0 and y==0:
                                #print 'initial status'
                                paths.append([(x2,y2), [delta_name[i]]])
                            else:   
                                for j,p in enumerate(paths):
                                    (px,py),pl = p
                                    pl_copy = pl[:]
                                    if (x==px) & (y==py):
                                        pl_copy.append(delta_name[i])
                                        paths.append([(x2,y2), pl_copy])
                                    
                            
                           
    for p in paths:
        (px,py), pl = p
        if (px == goal[0]) & (py == goal[1]):
            optimal_path = pl
            #print 'optimal,length',optimal_path, len(optimal_path)
            break
    
    x0,y0=init
    for action in optimal_path:
        expand[x0][y0] = action
        idx = delta_name.index(action)
        dx,dy = delta[idx]
        x0 += dx
        y0 += dy
    
    
    return expand # make sure you return the shortest path

print search(grid,init,goal,cost)