9.9 Write an algorithm to print all ways of arranging eight queens on an 8×8 chess board so that none of them share the same row, column or diagonal. In this case, “diagonal” means all diagonals, not just the two that bisect the board.

LeetCode上的原题，请参见我之前的博客N-Queens N皇后问题和N-Queens II N皇后问题之二。

class Solution {
public:
    vector<vector<int> > placeQueens(int n) {
        vector<vector<int> > res;
        vector<int> pos(n, -1);
        placeQueensDFS(pos, 0, res);
        return res;
    }
    void placeQueensDFS(vector<int> &pos, int row, vector<vector<int> > &res) {
        int n = pos.size();
        if (row == n) res.push_back(pos);
        else {
            for (int col = 0; col < n; ++col) {
                if (isValid(pos, row, col)) {
                    pos[row] = col;
                    placeQueensDFS(pos, row + 1, res);
                    pos[row] = -1;
                }
            }
        }
    }
    bool isValid(vector<int> &pos, int row, int col) {
        for (int i = 0; i < row; ++i) {
            if (col == pos[i] || abs(row - i) == abs(col - pos[i])) {
                return false;
            }
        }
        return true;
    }
};