leetcode51. 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.."]
]

class Solution {
public:
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> res;
        vector<string> nQueens(n, string(n, '.'));
        solveNQueens(res, nQueens, 0, n);
        return res;
    }
private:
    void solveNQueens(vector<vector<string>>& res, vector<string>& nQueens,
            int row, int n) {
        if (row == n) {
            res.push_back(nQueens);
            return;
        }

        for (int col = 0; col < n; col++) {
            if (isValid(nQueens, row, col, n)) {
                nQueens[row][col] = 'Q';
                solveNQueens(res,nQueens,row+1,n);
                nQueens[row][col] = '.';
            }
        }
    }

    bool isValid(vector<string>& nQueens, int row, int col, int n) {
        for (int i = 0; i < row; i++) {
            if (nQueens[i][col] == 'Q')
                return false;
        }

        for(int i=row-1,j=col-1;i>=0 && j>=0;--i,--j){
            if(nQueens[i][j] == 'Q')
                return false;
        }

        for(int i= row-1,j=col+1;i>=0 && j<n;--i,++j){
            if(nQueens[i][j] == 'Q')
                return false;
        }
        return true;
    }
};