2D interlocking puzzle script not working

Question

I tried this script but didn't go well.

def generate_grid():
    grid = np.zeros((10, 8), dtype=int)
    
    # Fill the first row with black and the last row with white
    grid[0] = 1
    grid[-1] = 0
    
    # Generate random grid until all conditions are met
    while True:
        grid[1:-1, :] = np.random.choice([0, 1], size=(8, 8), p=[0.5, 0.5])
        if check_conditions(grid):
            break
    
    return grid

def check_conditions(grid):
    # Condition 2: Check connectivity of black cells
    visited_black = np.zeros(grid.shape, dtype=bool)
    visited_gray = np.zeros(grid.shape, dtype=bool)

    # Find black and gray cells
    black_cells = np.argwhere(grid == 1)
    gray_cells = np.argwhere(grid == 0)
    
    # Check connectivity for black cells
    if len(black_cells) > 0:
        start_black_cell = black_cells[0]
        dfs(visited_black, grid, start_black_cell)
        if not np.all(visited_black[grid == 1]):
            return False
    
    # Check connectivity for gray cells
    if len(gray_cells) > 0:
        start_gray_cell = gray_cells[0]
        dfs(visited_gray, grid, start_gray_cell)
        if not np.all(visited_gray[grid == 0]):
            return False

    # Condition 3: Check sum of black cells
    total_cells = grid.size
    black_sum = np.sum(grid == 1)
    if black_sum < 0.4 * total_cells or black_sum > 0.6 * total_cells:
        return False

    return True

def dfs(visited, grid, cell):
    i, j = cell
    if i < 0 or i >= grid.shape[0] or j < 0 or j >= grid.shape[1] or visited[i, j] or grid[i, j] == 0:
        return
    visited[i, j] = True
    dfs(visited, grid, (i+1, j))
    dfs(visited, grid, (i-1, j))
    dfs(visited, grid, (i, j+1))
    dfs(visited, grid, (i, j-1))

def plot_grid(grid):
    plt.imshow(grid, cmap='binary', interpolation='nearest')
    plt.xticks([])
    plt.yticks([])
    plt.show()

grid = generate_grid()
plot_grid(grid)

def check_conditions(grid):
    # Condition 1: Check connectivity of black cells
    visited = np.zeros(grid.shape, dtype=bool)
    black_cells = np.argwhere(grid == 1)
    if len(black_cells) == 0:
        return False
    start_cell = black_cells[0]
    dfs(visited, grid, start_cell)
    if not np.all(visited[grid == 1]):
        return False

    # Condition 2: Check sum of black cells
    total_cells = grid.size
    black_sum = np.sum(grid == 1)
    if black_sum < 0.4 * total_cells or black_sum > 0.6 * total_cells:
        return False
    
    return True

when I tried this instead of the upper part, the script worked quite well as I wanted (black blocks are all connected).

enter image description here

However, I wanted the white part also be connected so that there is no isolated part without the connection with other clusters.

So modified the script as the top, but doesn't work. Can somebody help me?