N-Queens.h

/*
 Author:     Annie Kim, anniekim.pku@gmail.com
 Date:       Apr 24, 2013
 Update:     Jul 25, 2013
 Problem:    N-Queens
 Difficulty: Medium
 Source:     http://leetcode.com/onlinejudge#question_51
 Notes:
 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: Recursion (DFS). Use bit-manipulation solution (See N-QueensII for more details).
 */

class Solution {
public:
    vector<vector<string> > solveNQueens(int n) {
        vector<vector<string> > res;
        vector<string> sol;
        solveNQueensRe(n, 0, 0, 0, sol, res);
        return res;
    }
    
    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 avail = ~(row | ld | rd);
        for (int i = n-1; i >= 0; --i)
        {
            int pos = 1 << i;
            if (avail & 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();
            }
        }
    }
};