Python/数独求解器/方法工作不正确

问：

我正在尝试在 Python 中实现数独求解器，但我的一种方法无法正常工作，尽管它非常简单且简短。我的代码中有一个（零表示框为空）和一个列表，其中包含每个框的可能数字。因此，这种有问题的方法是，一旦找到一个框，它就会简单地更改它的值，并从同一框、列和网格中的其他可能数组中删除这个特定的数字。sudoku_gridpossibility_arrayschange_value(row, column, value)

这是代码（我只放了相关的部分 - 还有其他方法只是应用不同的消除技术 - 我做了一些跟踪，发现问题出在这种方法中出于某种原因 - ：

    sudoku_grid = [
        [4, 2, 9, 0, 0, 3, 0, 0, 0],
        [3, 7, 0, 1, 0, 0, 9, 0, 0],
        [0, 0, 0, 2, 9, 0, 3, 0, 0],
        [8, 3, 0, 0, 1, 0, 4, 0, 6],
        [0, 0, 0, 8, 0, 0, 7, 5, 0],
        [7, 4, 5, 9, 3, 0, 0, 1, 0],
        [9, 0, 0, 7, 0, 0, 0, 3, 1],
        [2, 5, 7, 0, 0, 0, 6, 0, 0],
        [6, 0, 3, 0, 0, 9, 8, 0, 7]
    ]
    possibility_arrays = []
    for _ in range(9):
        possibility_arrays.append([])
    for s in range(9):
        for x in range(9):
            possibility_arrays[x].append([])

    def is_valid(row, column, num):
        # Check if the number already exists in the row
        if num in sudoku_grid[row]:
            return False

        # Check if the number already exists in the column
        for i in range(9):
            if sudoku_grid[i][column] == num:
                return False

        # Check if the number already exists in the 3x3 grid
        start_row = (row // 3) * 3
        start_col = (column // 3) * 3
        for a in range(start_row, start_row + 3):
            for b in range(start_col, start_col + 3):
                if sudoku_grid[a][b] == num:
                    return False

        return True

    def change_value(row, column, value):

        if is_valid(row,column,value):
            sudoku_grid[row][column] = value
            possibility_arrays[row][column] = []

            for k in range(9):
                if value in possibility_arrays[k][column]:
                    possibility_arrays[k][column].remove(value)
                if value in possibility_arrays[row][k]:
                    possibility_arrays[row][k].remove(value)

            start_row = (row // 3) * 3
            start_col = (column // 3) * 3
            for a in range(start_row, start_row + 3):
                for b in range(start_col, start_col + 3):
                    if value in possibility_arrays[a][b]:
                        possibility_arrays[a][b].remove(value)
        else:
            print("THERE IS A MISTAKE")

以下是经过一些消除的过程：possibility_arrays

[[], [], [], [], [], [], [1], [8], [5]],
[[], [], [], [], [4, 5], [4, 5], [], [6], [2]],
[[], [], [], [], [], [4, 8], [], [7, 8], [4]],
[[], [], [], [], [], [], [], [], []],
[[], [], [], [], [2, 4], [2, 4], [], [], [3]],
[[], [], [], [], [], [6], [], [], []],
[[], [], [], [], [2, 6], [2, 6], [], [], []],
[[], [], [], [3], [8], [1], [], [], []],
[[], [], [], [], [5], [], [], [], []],

当我放置代码时，它只是按预期删除了 6，因为它在同一列中，但也从中删除了 6 并变成这样：change_value(5, 5, possibility_array[5][5][0])possibility_array[6][5]possibility_arrays[6][4]

[[], [], [], [], [], [], [1], [8], [5]]
[[], [], [], [], [4, 5], [4, 5], [], [6], [2]]
[[], [], [], [], [], [4, 8], [], [7, 8], [4]]
[[], [], [], [], [], [], [], [], []]
[[], [], [], [], [2, 4], [2, 4], [], [], [3]]
[[], [], [], [], [], [], [], [], []]
[[], [], [], [], [2], [2], [], [], []]
[[], [], [], [3], [8], [1], [], [], []]
[[], [], [], [], [5], [], [], [], []]

我不知道它有时是如何不正确地工作并且工作完全正常的。正如我所说，我只在这两种状态之间放了这条线（）。数组彼此之间没有关系，它们是单独的。为什么会发生这种情况？change_value(5, 5, possibility_array[5][5][0])