Random problem

tile.py

import string
import random

base_case = [
    [(0, 1), (1, 1), (1, 0)],   # 0, Top Left
    [(0, 0), (1, 0), (1, 1)],   # 1, Top Right
    [(0, 0), (0, 1), (1, 1)],   # 2, Bottom Left
    [(0, 1), (0, 0), (1, 0)]    # 3, Bottom Right
]

next_corner = [
    (0, 2, 1, 0),   # prev 0 Top Left 
    (3, 1, 1, 0),   # prev 1 Top Right
    (3, 2, 2, 0),   # prev 2 Bottom Left
    (3, 2, 1, 3),   # prev 3 Bottom Right
]

def tile(n: int, corner: int, r: int, c: int):
    """Place L tile, corner 0-3 TopLeft, TopRight, BottomLeft, BottomRight
        starting of row and col
    """
    if n == 1:
        return [tuple((r + dr, c + dc) for dr, dc in base_case[corner])]
    else:
        solution = []
        middle = 2**(n-1)
        solution.extend(tile(n-1, next_corner[corner][0], r, c))
        solution.extend(tile(n-1, next_corner[corner][1], r, c + middle))
        solution.extend(tile(n-1, next_corner[corner][2], r + middle, c))
        solution.extend(tile(n-1, next_corner[corner][3], r + middle, c + middle))
        solution.append(tuple((r + (middle-1) + dr, c + (middle-1) + dc) for dr, dc in base_case[corner]))
    return solution

def visualize(n, corner):
    w = 2**n
    board = [['.'] * w for _ in range(w)]
    for l in tile(n, corner, 0, 0):
        char = random.choice(string.ascii_letters)
        for r, c in l:
            board[r][c] = char
    for row in board:
        print('  '.join(row))