LeetCode_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.."]
]

　分析： The classic recursive problem.
1. Use a int vector to store the current state,  A[i]=j refers that the ith row and jth column is placed a queen.
2. Valid state:  not in the same column, which is A[i]!=A[current], not in the same diagonal direction: abs(A[i]-A[current]) != r-i

3. Recursion: 
       Start:   placeQueen(0,n)
        if current ==n then print result
        else
            for each place less than n,
                 place queen
                if current state is valid, then place next queen   place Queen(cur+1,n)
           end for
        end if

class Solution {
public:
 void record(vector<int> row)
    {
        vector<string> temp;
        for(int i = 0; i< n ; i++)
        {
            string str(n,'.');
            str[row[i]] = 'Q';
            temp.push_back(str);
        }
        res.push_back(temp) ;
    }
    bool isValid(vector<int> row, int curRow)
    {
        for(int i = 0; i< curRow; i++)
          if(row[i] == row[curRow] || abs(row[i] - row[curRow]) == curRow - i)
              return false;
              
        return true;
    }
    void nqueue(vector<int> row,int curRow)
    {
        if(curRow == n)
        {
            record(row);
            return ;
        }
        for(int i = 0; i< n ;i++)
        {
            row[curRow] = i;
            if(isValid(row,curRow))
                   nqueue(row,curRow+1);
        }
    }
    vector<vector<string> > solveNQueens(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        res.clear();
        if( n < 1 ) return res;
        this->n = n;
         vector<int> row(n,-1);
        nqueue(row, 0);
        return res;
    }
private:
    int n;
    vector<vector<string> > res;
};

http://yucoding.blogspot.com/2013/01/leetcode-question-59-n-queens.html