Python3：如何在矩阵中打印所有固定长度的对角线

Question

我目前正在从事井字游戏项目。我希望电路板具有自定义尺寸。但我不知道如何检查所有固定长度为 k 的行、列和对角线（k 是可定制的）。这里有一个例子来说明我的意思。

"""
For example if the board is a 4x4 matrix and I want to check the rows, cols, and diagonals of consecutive cells with fixed length of 3
"""
board = [[1, 2, 3, 4]
         [5, 6, 7, 8]
         [9, 10,11,12]
         [13,14,15,16]]
# Print all rows:
# Output: [1,2,3], [2,3,4], [5,6,7], [6,7,8], [9,10,11], [10,11,12], [13,14,15], [14,15,16]

# Print all cols:
# Output: [1,5,9], [5,9,13], [2,6,10], [6,10,14], [3,7,11], [7,11,15], [4,8,12], [8,12,16]

# Print all diagonals (beside 2 main diagonals there're more smaller diagonals):
# Output: [1,6,11], [6,11,16], [4,7,10], [7,10,13], [3,6,9], [2,7,12], [5,10,15], [8,11,14]

Answer 1

这是一个带有解释的工作代码。有多种方法可以解决这个问题，您选择的方式将取决于您将如何使用此代码。我选择创建在电路板上迭代的生成器。

import numpy as np
board = np.array( [
    [1, 2 ,3 ,4 ],
    [5, 6 ,7 ,8 ],
    [9, 10,11,12],
    [13,14,15,16]
    ])

为了更容易迭代电路板本身，我将其制成了一个numpy 数组，这样对列的迭代就和对行的迭代一样简单，检查尺寸等也是如此。

您需要的核心代码非常简单：将行、列或对角线传递给此函数和所需的大小，它将产生大小的子列表，直到它不再可以为止。

def get_sublist(line, size):
    i = 0
    length = len(line)
    while i<=length-size:
        yield line[i:i+size]
        i+=1     

然后，您需要做的就是像这样遍历板或转置板：

#for rows
for line in board:
    yield from get_sublist(line, size)

#for columns
for line in board.T
    yield from get_sublist(line, size)

最后，要遍历对角线，您可以使用方便的 numpy.diag 函数并执行完全相同的操作。对于对角线，只需翻转数组：

    #get the diagonals
    for d in range(-size, size+1):
        yield from get_sublist(np.diag(board, d), size)
    
    #get antidiagonals
    board = np.fliplr(board)
    for d in range(-size, size+1):
        yield from get_sublist(np.diag(board, d), size)

总而言之，完整的工作代码如下。我添加了一些检查，以免出现意外错误。我希望你能从中学到一些东西！

import numpy as np
board = np.array( [
    [1, 2 ,3 ,4 ],
    [5, 6 ,7 ,8 ],
    [9, 10,11,12],
    [13,14,15,16]
    ])


def get_sublist(line, size):
    i = 0
    length = len(line)
    while i<=length-size:
        yield line[i:i+size]
        i+=1            
    

def get_line(board, size, column=True):
    """Get sub-sections of rows or columns of board up to given size. column 
    decides if it iterates over rows or columns"""
    
    if not isinstance(column, bool):
        raise TypeError(f'row should be type bool, not {type(column)}')
    
    if size > board.shape[column]:
        raise ValueError(f'Cant get size {size} rows, board is {board.shape}')
    
    if column: 
        board = board.T
        
    for line in board:
        yield from get_sublist(line, size)
    
        
def get_diags(board, size):
    """Get sub-sections of the diagonals of the board for the given size"""
     
    if size > board.shape[0]:
        raise ValueError(f'Cant get size {size} rows, board is {board.shape}')
  
    #get the diagonals
    for d in range(-size, size+1):
        yield from get_sublist(np.diag(board, d), size)
    
    #get antidiagonals
    board = np.fliplr(board)
    for d in range(-size, size+1):
        yield from get_sublist(np.diag(board, d), size)
    

print(list(get_line(board, 3, column=True)))
print(list(get_line(board, 3, column=False)))
print(lies(get_diags(board, 3)))