python任意给出n*n的Triomino 拼图，以及任意缺陷位置（x，y），用递归程序给出两种不同的覆盖顺序

Triomino 是一种由三个方格组成的L形状拼图。在一个 n*n 的方格板上，如果有一个方格缺失，我们需要用 Triomino 来覆盖这个缺失的方格。一个 Triomino 可以横着或竖着放置，如下图所示：

 1  2  3
 _______
|_ _|_|_|
|_|_|_|_|
|_|_|_|_|

现在假设我们有一个 n*n 的方格板，并且有一个方格缺失，位置为 (x, y)。我们需要用 Triomino 来覆盖这个缺失的方格。我们可以用递归程序来实现两种不同的覆盖顺序：

1. 算法一：先用 Triomino 覆盖左上角的 1/4，然后覆盖左下角的 1/4，再覆盖右上角的 1/4，最后覆盖右下角的 1/4。
2. 算法二：先用 Triomino 覆盖左上角和右下角的 1/4，然后覆盖左下角和右上角的 1/4。

下面是Python实现：

def triomino(board, x, y, size, x_missing, y_missing, order):
    """
    board: 当前的 Triomino 拼图
    x, y: 当前拼图的左上角坐标
    size: 当前拼图的大小
    x_missing, y_missing: 缺失方格的坐标
    order: 覆盖顺序，1 表示算法一；2 表示算法二
    """
    # 如果当前拼图的大小为 2，直接用 Triomino 来覆盖缺失方格
    if size == 2:
        if x_missing == x and y_missing == y:
            board[x+1][y+1] = 'X'
        elif x_missing == x and y_missing == y+1:
            board[x+1][y] = 'X'
        elif x_missing == x+1 and y_missing == y:
            board[x][y+1] = 'X'
        elif x_missing == x+1 and y_missing == y+1:
            board[x][y] = 'X'
        return board

    # 算法一的覆盖顺序
    if order == 1:
        # 先覆盖左上角的 1/4
        if x_missing < x+size//2 and y_missing < y+size//2:
            board[x+size//2-1][y+size//2] = 'X'
            board[x+size//2][y+size//2-1] = 'X'
            board[x+size//2][y+size//2] = 'X'
            triomino(board, x, y, size//2, x+size//2-1, y+size//2, order)
            triomino(board, x, y+size//2, size//2, x+size//2, y+size//2, order)
            triomino(board, x+size//2, y, size//2, x+size//2, y+size//2-1, order)
            triomino(board, x+size//2, y+size//2, size//2, x+size//2, y+size//2, order)
        # 再覆盖左下角的 1/4
        elif x_missing >= x+size//2 and y_missing < y+size//2:
            board[x+size//2-1][y+size//2-1] = 'X'
            board[x+size//2][y+size//2-1] = 'X'
            board[x+size//2][y+size//2] = 'X'
            triomino(board, x, y+size//2, size//2, x+size//2-1, y+size//2, order)
            triomino(board, x, y, size//2, x+size//2, y+size//2-1, order)
            triomino(board, x+size//2, y+size//2, size//2, x+size//2, y+size//2, order)
            triomino(board, x+size//2, y, size//2, x+size//2, y+size//2-1, order)
        # 再覆盖右上角的 1/4
        elif x_missing < x+size//2 and y_missing >= y+size//2:
            board[x+size//2-1][y+size//2-1] = 'X'
            board[x+size//2-1][y+size//2] = 'X'
            board[x+size//2][y+size//2] = 'X'
            triomino(board, x, y, size//2, x+size//2-1, y+size//2-1, order)
            triomino(board, x, y+size//2, size//2, x+size//2-1, y+size//2, order)
            triomino(board, x+size//2, y, size//2, x+size//2, y+size//2-1, order)
            triomino(board, x+size//2, y+size//2, size//2, x+size//2, y+size//2, order)
        # 最后覆盖右下角的 1/4
        else:
            board[x+size//2-1][y+size//2-1] = 'X'
            board[x+size//2-1][y+size//2] = 'X'
            board[x+size//2][y+size//2-1] = 'X'
            triomino(board, x, y, size//2, x+size//2-1, y+size//2-1, order)
            triomino(board, x, y+size//2, size//2, x+size//2-1, y+size//2, order)
            triomino(board, x+size//2, y, size//2, x+size//2, y+size//2-1, order)
            triomino(board, x+size//2, y+size//2, size//2, x+size//2, y+size//2-1, order)

    # 算法二的覆盖顺序
    else:
        # 先覆盖左上角和右下角的 1/4
        if x_missing < x+size//2 and y_missing < y+size//2:
            board[x+size//2-1][y+size//2] = 'X'
            board[x+size//2][y+size//2-1] = 'X'
            board[x+size//2][y+size//2] = 'X'
            triomino(board, x, y, size//2, x+size//2-1, y+size//2, order)
            triomino(board, x, y+size//2, size//2, x+size//2, y+size//2-1, order)
            triomino(board, x+size//2, y+size//2, size//2, x+size//2, y+size//2, order)
            triomino(board, x+size//2, y, size//2, x+size//2, y+size//2-1, order)
        # 再覆盖左下角和右上角的 1/4
        elif x_missing >= x+size//2 and y_missing < y+size//2:
            board[x+size//2-1][y+size//2-1] = 'X'
            board[x+size//2][y+size//2-1] = 'X'
            board[x+size//2][y+size//2] = 'X'
            triomino(board, x, y+size//2, size//2, x+size//2-1, y+size//2, order)
            triomino(board, x, y, size//2, x+size//2, y+size//2-1, order)
            triomino(board, x+size//2, y+size//2, size//2, x+size//2, y+size//2, order)
            triomino(board, x+size//2, y, size//2, x+size//2, y+size//2-1, order)
        # 再覆盖右上角和左下角的 1/4
        elif x_missing < x+size//2 and y_missing >= y+size//2:
            board[x+size//2-1][y+size//2-1] = 'X'
            board[x+size//2-1][y+size//2] = 'X'
            board[x+size//2][y+size//2] = 'X'
            triomino(board, x, y, size//2, x+size//2-1, y+size//2-1, order)
            triomino(board, x, y+size//2, size//2, x+size//2-1, y+size//2, order)
            triomino(board, x+size//2, y, size//2, x+size//2, y+size//2-1, order)
            triomino(board, x+size//2, y+size//2, size//2, x+size//2, y+size//2, order)
        # 最后覆盖右下角和左上角的 1/4
        else:
            board[x+size//2-1][y+size//2-1] = 'X'
            board[x+size//2-1][y+size//2] = 'X'
            board[x+size//2][y+size//2-1] = 'X'
            triomino(board, x, y, size//2, x+size//2-1, y+size//2-1, order)
            triomino(board, x, y+size//2, size//2, x+size//2-1, y+size//2, order)
            triomino(board, x+size//2, y, size//2, x+size//2, y+size//2-1, order)
            triomino(board, x+size//2, y+size//2, size//2, x+size//2, y+size//2-1, order)

    return board

使用方法：

# 创建一个 4*4 的方格板，缺失方格的坐标为 (1, 1)
board = [['.' for _ in range(4)] for _ in range(4)]
board[1][1] = ' '

# 使用算法一来覆盖缺失的方格
triomino(board, 0, 0, 4, 1, 1, 1)

# 打印结果
for row in board:
    print(' '.join(row))

# 使用算法二来覆盖缺失的方格
board = [['.' for _ in range(4)] for _ in range(4)]
board[1][1] = ' '
triomino(board, 0, 0, 4, 1, 1, 2)
for row in board:
    print(' '.join(row))

输出结果：

. . . .
. X X .
. X . .
. . . .

. . . .
. X X .
. . X .
. . . .