def path_finder(maze):
maze = maze.split('\n')
maze = Maze(maze)
G = maze.get_graph_from_maze()
color = {i: "white" for i in G.keys()}
pred = {i: None for i in G.keys()}
cc = {i: None for i in G.keys()}
cc_num = [0]
dfs(G, color, pred, cc, cc_num)
start_idx = 0
exit_idx = maze.n * maze.m - 1
if start_idx not in G.keys() or exit_idx not in G.keys():
return False
elif cc[start_idx] != cc[exit_idx]:
return False
else:
return True
