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.

Example:

Output: [
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.

Solution:

    void solveNQueens(vector<vector<std::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> &board, int row, int col, int n) {
        //check if the column had a queen before.
        for (int i = 0; i != row; ++i)
            if (board[i][col] == 'Q')
                return false;

        //check if the 45° diagonal had a queen before.
        for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; --i, --j)
            if (board[i][j] == 'Q')
                return false;

        //check if the 135° diagonal had a queen before.
        for (int i = row - 1, j = col + 1; i >= 0 && j < n; --i, ++j)
            if (board[i][j] == 'Q')
                return false;
        return true;
    }

    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string> > res;
        vector<string> nQueens(n, string(n, '.'));
        solveNQueens(res, nQueens, 0, n);
        return res;
    }