N-Queens

The n-queens puzzle is the problem of placing n queens on an n*n chessboard such that no two queens attack each other.
Given an integer n, return all distinct solutions to the n-queens puzzle.
Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space respectively.
For example,
There exist two distinct solutions to the 4-queens puzzle:
[
[".Q..", // Solution 1
"...Q",
"Q...",
"..Q."],

["..Q.", // Solution 2
"Q...",
"...Q",
".Q.."]
]

class Solution {
public:
    vector<vector<string> > solveNQueens(int n) {
        vector<string> sol;
        vector<vector<string> > res;
        solveNQueensRe(n, 0, 0, 0, sol, res);
        return res;
    }
    // row bit: 指明前k行放在哪几列
    // ld bit:  当前左边对角线限制（从前一行）
    // rd bit:  当前右边对角线限制（从前一行）
    void solveNQueensRe(int n, int row, int ld, int rd, vector<string> &sol, vector<vector<string> > &res)
    {
        if(row == (1 << n) - 1) {
            res.push_back(sol);
            return;
        }
        int valid = ~(row | ld | rd); //位非运算
        for(int i = n - 1; i >= 0; i--) {
            int pos = 1 << i;
            if(valid & pos) {
                string s(n, '.');
                s[i] = 'Q';
                sol.push_back(s);
                solveNQueensRe(n, row | pos, (ld | pos) << 1, (rd | pos) >> 1, sol, res);
                sol.pop_back();
            }
        }
        
    }
};