LeetCode 51. N-Queens

class Solution {
private:
    vector<bool> col,dia1,dia2;
    vector<vector<string>> res;  
    vector<string> generateBoard( int n, vector<int>&  row ){
        assert( row.size() == n);
        vector<string> board( n, string(n, '.'));
        for( int i = 0; i < n; i++)
            board[i][row[i]] = 'Q';
        return board;
    }
    
    void putQueen(int n, int index, vector<int>& row ){
        
        if( index == n ){
            res.push_back( generateBoard(n,row) );
            return;
        }
        
        for(int i = 0; i < n; i++){
            // 尝试将Index 行的皇后摆放在 i 列
            if( !col[i] && !dia1[index+i] && !dia2[index-i+n-1]){
                row.push_back(i);
                col[i] = true;
                dia1[index+i] = true;
                dia2[index-i+n-1] = true;
                putQueen( n, index+1, row);
                // roll back
                col[i] = false;
                dia1[index+i] = false;
                dia2[index-i+n-1] = false;
                row.pop_back();                
            }
        }
        return;     
    }
    
   
public: 
    vector<vector<string>> solveNQueens(int n) {
        res.clear(); 
        
        col = vector<bool>(n,false);
        dia1 = vector<bool>(2*n-1,false);
        dia2 = vector<bool>(2*n-1,false);
        
        vector<int> row;
        putQueen( n, 0, row);
        return res;
    }
};