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