N-Queens II

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.."]
]

Solution: 1. Recursion.
2. Recursion + bit version. (fast)
The idea is from http://www.matrix67.com/blog/archives/266 (in chinese).
3. Iteration.

class Solution {
public:
    int totalNQueens(int n) {
        int res = 0;
        totalNQueensRe(n, 0, 0, 0, res);
        return res;
    }
    
    void totalNQueensRe(int n, int row, int ld, int rd, int &total)
    {
        if(row == (1 << n) - 1) {
            total++;
            return;
        }
        
        int valid = ~(row | ld | rd);
        for(int i = n - 1; i >= 0; --i) {
            int pos = 1 << i;
            if (valid & pos)
                totalNQueensRe(n, row | pos, (ld | pos) << 1, (rd | pos) >> 1, total);
        }
    }
};