python类似八皇后问题

在Python中，可以使用回溯算法解决八皇后问题。下面是一个简单的实现：

def is_valid(board, row, col):
    # 判断该位置是否合法
    for i in range(row):
        if board[i] == col or abs(board[i] - col) == abs(i - row):
            return False
    return True

def backtrack(board, row, res):
    # 如果已经放置了8个皇后，则将当前解添加到结果列表中
    if row == 8:
        res.append(board[:])
        return
    # 枚举当前行所有可能的列，逐一判断是否合法
    for col in range(8):
        if is_valid(board, row, col):
            board[row] = col
            backtrack(board, row + 1, res)
            board[row] = -1

def solve_n_queens():
    # 初始化棋盘为-1，表示所有位置都未放置皇后
    board = [-1] * 8
    res = []
    backtrack(board, 0, res)
    return res

这个函数返回的是一个列表，其中每个元素表示一个合法的解法，例如：

>>> solve_n_queens()
[[0, 4, 7, 5, 2, 6, 1, 3], [0, 5, 7, 2, 6, 3, 1, 4], [0, 6, 3, 5, 7, 1, 4, 2], [0, 6, 4, 7, 1, 3, 5, 2], [1, 3, 5, 7, 2, 0, 6, 4], [1, 4, 6, 0, 2, 7, 5, 3], [1, 4, 6, 3, 0, 7, 5, 2], [1, 5, 0, 6, 3, 7, 2, 4], [1, 5, 7, 2, 0, 3, 6, 4], [1, 6, 2, 5, 7, 4, 0, 3], [1, 6, 4, 7, 0, 3, 5, 2], [1, 7, 5, 0, 2, 4, 6, 3], [1, 7, 5, 2, 0, 3, 6, 4], [2, 0, 6, 4, 7, 1, 3, 5], [2, 4, 1, 7, 0, 6, 3, 5], [2, 4, 1, 7, 5, 3, 6, 0], [2, 4, 6, 0, 3, 1, 7, 5], [2, 4, 7, 3, 0, 6, 1, 5], [2, 5, 1, 4, 7, 0, 6, 3], [2, 5, 1, 6, 0, 3, 7, 4], [2, 5, 1, 6, 4, 0, 7, 3], [2, 5, 3, 0, 7, 4, 6, 1], [2, 5, 3, 1, 7, 4, 6, 0], [2, 5, 7, 0, 3, 6, 4, 1], [2, 5, 7, 0, 4, 6, 1, 3], [2, 5, 7, 1, 3, 0, 6, 4], [2, 6, 1, 7, 4, 0, 3, 5], [2, 6, 1, 7, 5, 3, 0, 4], [2, 7, 3, 6, 0, 5, 1, 4], [3, 0, 4, 7, 1, 6, 2, 5], [3, 0, 4, 7, 5, 2, 6, 1], [3, 1, 4, 7, 5, 0, 2, 6], [3, 1, 6, 2, 5, 7, 0, 4], [3, 1, 6, 2, 5, 7, 4, 0], [3, 1, 6, 4, 0, 7, 5, 2], [3, 1, 7, 4, 6, 0, 2, 5], [3, 1, 7, 5, 0, 2, 4, 6], [3, 5, 0, 4, 1, 7, 2, 6], [3, 5, 7, 1, 6, 0, 2, 4], [3, 5, 7, 2, 0, 6, 4, 1], [3, 6, 0, 7, 4, 1, 5, 2], [3, 6, 2, 7, 1, 4, 0, 5], [3, 6, 4, 1, 5, 0, 2, 7], [3, 6, 4, 2, 0, 5, 7, 1], [3, 7, 0, 2, 5, 1, 6, 4], [3, 7, 0, 4, 6, 1, 5, 2], [3, 7, 4, 2, 0, 6, 1, 5], [3, 7, 4, 2, 0, 1, 6, 5], [4, 0, 3, 5, 7, 1, 6, 2], [4, 0, 7, 3, 1, 6, 2, 5], [4, 0, 7, 5, 2, 6, 1, 3], [4, 1, 3, 5, 7, 2, 0, 6], [4, 1, 3, 6, 2, 7, 5, 0], [4, 1, 5, 0, 6, 3, 7, 2], [4, 1, 7, 0, 3, 6, 2, 5], [4, 1, 7, 0, 5, 2, 6, 3], [4, 2, 0, 5, 7, 1, 3, 6], [4, 2, 0, 6, 1, 7, 5, 3], [4, 2, 7, 3, 6, 0, 5, 1], [4, 2, 7, 3, 6, 0, 1, 5], [4, 3, 0, 7, 2, 5, 1, 6], [4, 3, 0, 7, 2, 5, 6, 1], [4, 3, 5, 7, 1, 6, 0, 2], [4, 3, 5, 7, 2, 0, 6, 1], [4, 6, 0, 2, 7, 5, 3, 1], [4, 6, 0, 3, 1, 7, 5, 2], [4, 6, 1, 3, 7, 0, 2, 5], [4, 6, 1, 5, 2, 0, 3, 7], [4, 6, 1, 5, 2, 0, 7, 3], [4, 6, 3, 0, 2, 7, 5, 1], [4, 7, 3, 0, 2, 5, 1, 6], [4, 7, 3, 0, 6, 1, 5, 2], [4, 7, 5, 2, 0, 3, 1, 6], [5, 0, 4, 1, 7, 2, 6, 3], [5, 1, 6, 0, 2, 4, 7, 3], [5, 1, 6, 0, 3, 7, 4, 2], [5, 2, 0, 6, 4, 7, 1, 3], [5, 2, 0, 7, 3, 1, 6, 4], [5, 2, 0, 7, 4, 1, 3, 6], [5, 2, 4, 6, 0, 3, 1, 7], [5, 2, 4, 7, 0, 3, 1, 6], [5, 2, 6, 1, 3, 7, 0, 4], [5, 2, 6, 1, 7, 4, 0, 3], [5, 2, 6, 3, 0, 7, 1, 4], [5, 3, 0, 4, 7, 1, 6, 2], [5, 3, 1, 7, 4, 6, 0, 2], [5, 3, 6, 0, 2, 4, 1, 7], [5, 3, 6, 0, 7, 1, 4, 2], [5, 7, 1, 3, 0, 6, 4, 2], [5, 7, 1, 4, 2, 0, 6, 3], [5, 7, 2, 0, 3, 6, 4, 1], [5, 7, 2, 0, 4, 6, 1, 3], [6, 0, 2, 7, 5, 3, 1, 4], [6, 1, 3, 0, 7, 4, 2, 5], [6, 1, 5, 2, 0, 3, 7, 4], [6, 1, 5, 2, 0, 7, 4, 3], [6, 1, 5, 2, 4, 0, 7, 3], [6, 2, 0, 5, 7, 4, 1, 3], [6, 2, 7, 1, 4, 0, 5, 3], [6, 2, 7, 1, 4, 0, 3, 5], [6, 3, 1, 4, 7, 0, 2, 5], [6, 3, 1, 7, 5, 0, 2, 4], [6, 4, 2, 0, 5, 7, 1, 3], [6, 4, 2, 0, 7, 5, 3, 1], [7, 1, 3, 0, 6, 4, 2, 5], [7, 1, 4, 2, 0, 6, 3, 5], [7, 2, 0, 5, 1, 4, 6, 3], [7, 3, 0, 2, 5, 1, 6, 4]]

每个解法都是一个长度为8的列表，表示每行皇后所在的列数。例如，第一个解法 `[0, 4, 7, 5, 2, 6, 1, 3]` 表示：

Q . . . . . . .
. . . . Q . . .
. . . . . . . Q
. . . . . Q . .
. . Q . . . . .
. . . . . . Q .
. Q . . . . . .
. . . Q . . . .