Adapted code for Math Circle

random_NESW_maze.py

import random
from PIL import Image
imgx = 500; imgy = 500
image = Image.new("RGB", (imgx, imgy))
pixels = image.load()
mx = 10; my = 10 # width and height of the maze
maze = [[0 for x in range(mx)] for y in range(my)]
dx = [0, 1, 0, -1]; dy = [-1, 0, 1, 0] # 4 directions to move in the maze
color = [(0,0, 0), (255, 255, 255)] # RGB colors of the maze
# start the maze from a random cell
stack = [(random.randint(0, mx - 1), random.randint(0, my - 1))]

while len(stack) > 0:
    (cx, cy) = stack[-1]
    maze[cy][cx] = 1
    # find a new cell to add
    nlst = [] # list of available neighbors
    for i in range(4):
        nx = cx + dx[i]; ny = cy + dy[i]
        if nx >= 0 and nx < mx and ny >= 0 and ny < my:
            if maze[ny][nx] == 0:
                # of occupied neighbors must be 1
                ctr = 0
                for j in range(4):
                    ex = nx + dx[j]; ey = ny + dy[j]
                    if ex >= 0 and ex < mx and ey >= 0 and ey < my:
                        if maze[ey][ex] == 1: ctr += 1
                if ctr == 1: nlst.append(i)
    # if 1 or more neighbors available then randomly select one and move
    if len(nlst) > 0:
        ir = nlst[random.randint(0, len(nlst) - 1)]
        cx += dx[ir]; cy += dy[ir]
        stack.append((cx, cy))
    else: stack.pop()

# Print maze
for row in maze:
  print(row)

def moves(row,col,maze):
  """replace Maze entry with possible moves."""
  pos_moves = ["N","E","S","W"]
  print(row,col, maze[row][col])
  if maze[row][col] == 0:
    return []
  if row == 0:
    pos_moves.remove("N")
  elif maze[row-1][col] == 0:
    pos_moves.remove("N")
  if row == len(maze)-1:
    pos_moves.remove("S")
  elif maze[row+1][col] == 0:
    pos_moves.remove("S")
  if col == 0:
    pos_moves.remove("W")
  elif maze[row][col-1] == 0:
    pos_moves.remove("W")
  if col == len(maze[row])-1:
    pos_moves.remove("E")
  elif maze[row][col+1] == 0:
    pos_moves.remove("E")
  return pos_moves

new_maze = [[moves(i,j,maze) for j in range(len(maze[i]))] for i in range(len(maze))]

for row in new_maze:
  print(row)

# paint the maze
for ky in range(imgy):
    for kx in range(imgx):
        pixels[kx, ky] = color[maze[my * ky // imgy][mx * kx // imgx]]
image.save("Maze_" + str(mx) + "x" + str(my) + ".png", "PNG")