def aldous_broder(maze):
"""Complete the maze using the Aldous-Broder algorithm.
(If the starting maze has no passages, then this algorithm
will produce all possible mazes with equal probability.)
"""
while maze.has_empty_cells():
d = random_direction()
if maze.cell_is_empty(d):
maze.carve(d)
else:
maze.move(d)
return maze
def _lerw(maze, c, stopping_set):
"""Perform a loop-erased random walk from starting position c
until an element of stopping_set is hit.
"""
path = [c]
path_indices_by_cell = {c: [0]}
maze.move(*c)
while maze.cursor_cell() not in stopping_set:
if maze.move(random_direction()):
c = maze.cursor_cell()
if c in path_indices_by_cell and path_indices_by_cell[c]:
prev_index = path_indices_by_cell[c][-1]
for d in path[(prev_index + 1):]:
path_indices_by_cell[d].pop()
path = path[:(prev_index + 1)]
else:
path_indices_by_cell.setdefault(c, []).append(len(path))
path.append(c)
return path