代码实现

以下是一个基于递归和回溯思想的 Python 代码实现，用于解决数独问题：

def solve_sudoku(board):
    """
    Solve the Sudoku puzzle using recursive backtracking.
    """
    # Find the first empty cell
    row, col = find_empty_cell(board)

    # If all cells are filled, the puzzle is solved
    if row is None:
        return True

    # Try all possible values in the empty cell
    for num in range(1, 10):
        if is_valid_move(board, row, col, num):
            board[row][col] = num

            # Recursively solve the rest of the puzzle
            if solve_sudoku(board):
                return True

            # If the recursive call fails, undo the move and try the next value
            board[row][col] = 0

    # If none of the values work, the puzzle is unsolvable
    return False


def find_empty_cell(board):
    """
    Find the first empty cell in the Sudoku puzzle.
    """
    for row in range(9):
        for col in range(9):
            if board[row][col] == 0:
                return row, col
    return None, None


def is_valid_move(board, row, col, num):
    """
    Check if a move is valid in the Sudoku puzzle.
    """
    # Check if the value already exists in the row
    if num in board[row]:
        return False

    # Check if the value already exists in the column
    if num in [board[i][col] for i in range(9)]:
        return False

    # Check if the value already exists in the 3x3 box
    box_row, box_col = row // 3 * 3, col // 3 * 3
    if num in [board[i][j] for i in range(box_row, box_row + 3) for j in range(box_col, box_col + 3)]:
        return False

    # If the move is valid, return True
    return True

这段代码使用了递归和回溯思想，用于逐个尝试填充数字，并检查是否满足数独的规则。如果在某个格子中无法填入任何数字，就回溯到上一个格子重新尝试。如果最终填充完成，就说明数独问题已经解决。