Skip to content

Instantly share code, notes, and snippets.

What would you like to do?
Python3 Maze Generator with Disjoint Set
from random import randint, sample
from sys import argv
from time import sleep
height, width = [int(dim) for dim in argv[1:]]
except (IndexError, ValueError) as ve:
print("Usage:\n$ <height> <width>")
if not width or not height:
# Just for animation purposes
TOTAL_TIME = 10 # at most, and in seconds (roughly double than observed values)
parent = list(range(width*height))
rank = [0] * len(parent)
def find(n):
if parent[n] != n:
parent[n] = find(parent[n])
return parent[n]
def union(a, b):
u, v = find(a), find(b)
if u == v:
if rank[u] > rank[v]:
parent[v] = u
parent[u] = v
if rank[v] == rank[u]:
rank[v] += 1
def get_coords(num):
return num // width, num % width
def disp_maze(width=1, height=1, maze={}, timedelta=0.01):
# Perhaps can be made more concise
for i in range(height+1):
print('+', end='')
for j in range(width):
if ((i-1, j), (i, j)) in maze or i == 0 or i == height:
seq = '--'
seq = ' '
if ((i, j), (i, j+1)) in maze or ((i-1, j), (i-1, j+1)) in maze \
or j == width-1:
end = '+'
elif seq == '--' or i == 0 or i == height:
end = '-'
end = ' '
print(seq, end=end)
if i == height:
for j in range(width):
if ((i, j-1), (i, j)) in maze or j == 0 and i != 0:
seq = '| '
seq = ' '
print(seq, end='')
if i != height-1:
row_last_wall = '|'
row_last_wall = ''
# To get back to 0th row ceiling to rerender the new maze layout
print("\033[%dA" % 2*(height+1))
sleep(timedelta) # To slow down, for animation
if __name__ == '__main__':
edges_of_cells = {
edge for num in parent[:-1]
for edge in ((num, num+1), (num, num+width))
if not (edge[0] % width == width-1 and edge[1]-edge[0] < width) and \
edge[1] <= parent[-1]
timedelta = TOTAL_TIME / len(edges_of_cells)
maze = set()
# Display initial state of maze
disp_maze(width, height, maze, 0)
# while there is more than 1 set of connected cells
while len(set([find(n) for n in parent])) > 1:
rand_edge = sample(edges_of_cells, 1)[0]
u, v = find(rand_edge[0]), find(rand_edge[1])
if u != v:
union(u, v)
maze.add((get_coords(rand_edge[0]), get_coords(rand_edge[1])))
disp_maze(width, height, maze, timedelta)
# maze = maze.union(
# {
# (get_coords(edge[0]), get_coords(edge[1]))
# for edge in edges_of_cells
# }
# )
# The code commented above works, but we'll use the following for a nicer
# animation
while edges_of_cells:
maze.add(tuple(get_coords(num) for num in edges_of_cells.pop()))
disp_maze(width, height, maze, timedelta)
# To get back to 0th row ceiling to rerender the new maze layout
# To reach the end of display
# 2*(height+1) is probably a higher number but works
print("\033[%dB" % (2*height))

Generate Mazes with Disjoint Sets!

This script generates mazes that satisfy the following properties:

  • There are no cycles in the maze
  • Maze is always solvable
  • Every cell is reachable from every other cell

The script also animates the maze-building process on the command-line (this was actually trickier than the maze generating algorithm itself)!


$ python3 <height> <width>


(gif may take a while to load)


I learned this algorithm from the lecture slides by Brian Curless.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment