Python如何实现回溯算法？问题求解策略

def backtrack(state, solution):
    """
    回溯算法框架
    :param state: 当前状态
    :param solution: 存储结果的列表
    :return: True if a solution is found, False otherwise
    """
    if is_solution(state):
        solution.append(state.copy())  # 存储结果的深拷贝
        return True

    for choice in get_choices(state):
        if is_valid(state, choice):
            apply_choice(state, choice)
            if backtrack(state, solution):
                pass # 可选：如果只需要一个解，可以提前返回
            remove_choice(state, choice)  # 回溯

    return False

def is_solution(state):
    """判断当前状态是否是解"""
    pass

def get_choices(state):
    """获取当前状态下所有可能的选择"""
    pass

def is_valid(state, choice):
    """判断当前选择是否有效"""
    pass

def apply_choice(state, choice):
    """应用当前选择，更新状态"""
    pass

def remove_choice(state, choice):
    """撤销当前选择，恢复状态"""
    pass

# 示例用法
initial_state = ...
solutions = []
backtrack(initial_state, solutions)
print(solutions)

def solve_sudoku(board):
    """
    解决数独问题
    :param board: 数独棋盘，用二维列表表示
    :return: True if the board is solvable, False otherwise
    """

    def find_empty_location(board):
        """找到一个空位置"""
        for row in range(9):
            for col in range(9):
                if board[row][col] == 0:
                    return row, col
        return None

    def is_valid(board, num, pos):
        """判断数字num是否可以放在pos位置"""
        row, col = pos

        # 检查行
        for i in range(9):
            if board[row][i] == num and i != col:
                return False

        # 检查列
        for i in range(9):
            if board[i][col] == num and i != row:
                return False

        # 检查3x3宫格
        box_row = row // 3
        box_col = col // 3
        for i in range(box_row * 3, box_row * 3 + 3):
            for j in range(box_col * 3, box_col * 3 + 3):
                if board[i][j] == num and (i, j) != pos:
                    return False

        return True

    def solve():
        """递归求解数独"""
        empty_location = find_empty_location(board)
        if not empty_location:
            return True  # 数独已解决

        row, col = empty_location

        for num in range(1, 10):
            if is_valid(board, num, (row, col)):
                board[row][col] = num

                if solve():
                    return True

                board[row][col] = 0  # 回溯

        return False

    if solve():
        return True
    else:
        return False

# 示例数独棋盘
board = [
    [5, 3, 0, 0, 7, 0, 0, 0, 0],
    [6, 0, 0, 1, 9, 5, 0, 0, 0],
    [0, 9, 8, 0, 0, 0, 0, 6, 0],
    [8, 0, 0, 0, 6, 0, 0, 0, 3],
    [4, 0, 0, 8, 0, 3, 0, 0, 1],
    [7, 0, 0, 0, 2, 0, 0, 0, 6],
    [0, 6, 0, 0, 0, 0, 2, 8, 0],
    [0, 0, 0, 4, 1, 9, 0, 0, 5],
    [0, 0, 0, 0, 8, 0, 0, 7, 9]
]

if solve_sudoku(board):
    for row in board:
        print(row)
else:
    print("No solution exists")