N-Queens

C++：

class Solution {
public:
    std::vector<std::vector<std::string> > solveNQueens(int n) {
        std::vector<std::vector<std::string> > res;
        std::vector<std::string> nQueens(n, std::string(n, '.'));
        std::vector<int> flag_col(n, 1), flag_45(2 * n - 1, 1), flag_135(2 * n - 1, 1);
        solveNQueens(res, nQueens, flag_col, flag_45, flag_135, 0, n);
        return res;
    }
private:
    void solveNQueens(std::vector<std::vector<std::string> > &res, std::vector<std::string> &nQueens, std::vector<int> &flag_col, std::vector<int> &flag_45, std::vector<int> &flag_135, int row, int &n) {
        if (row == n) {
            res.push_back(nQueens);
            return;
        }
        for (int col = 0; col != n; ++col)
            if (flag_col[col] && flag_45[row + col] && flag_135[n - 1 + col - row]) {
                flag_col[col] = flag_45[row + col] = flag_135[n - 1 + col - row] = 0;
                nQueens[row][col] = 'Q';
                solveNQueens(res, nQueens, flag_col, flag_45, flag_135, row + 1, n);
                nQueens[row][col] = '.';
                flag_col[col] = flag_45[row + col] = flag_135[n - 1 + col - row] = 1;
            }
    }
};

Java：

public class Solution {
    public List<List<String>> solveNQueens(int n) {
        char[][] board = new char[n][n];
        for(int i = 0; i < n; i++)
            for(int j = 0; j < n; j++)
                board[i][j] = '.';
        List<List<String>> res = new ArrayList<List<String>>();
        dfs(board, 0, res);
        return res;
    }
    
    private void dfs(char[][] board, int colIndex, List<List<String>> res) {
        if(colIndex == board.length) {
            res.add(construct(board));
            return;
        }
        
        for(int i = 0; i < board.length; i++) {
            if(validate(board, i, colIndex)) {
                board[i][colIndex] = 'Q';
                dfs(board, colIndex + 1, res);
                board[i][colIndex] = '.';
            }
        }
    }
    
    private boolean validate(char[][] board, int x, int y) {
        for(int i = 0; i < board.length; i++) {
            for(int j = 0; j < y; j++) {
                if(board[i][j] == 'Q' && (x + j == y + i || x + y == i + j || x == i))
                    return false;
            }
        }
        
        return true;
    }
    
    private List<String> construct(char[][] board) {
        List<String> res = new LinkedList<String>();
        for(int i = 0; i < board.length; i++) {
            String s = new String(board[i]);
            res.add(s);
        }
        return res;
    }
}