给出 n 代表生成括号的对数，请你写出一个函数，使其能够生成所有可能的并且有效的括号组合。

例如

给出 n = 3，生成结果为：
[
  "((()))",
  "(()())",
  "(())()",
  "()(())",
  "()()()"
]

代码

class Solution {
public:
    vector<string> generateParenthesis(int n) {
        vector<string> res;
        generateParenthesisDFS(n, n, "", res);
        return res;
    }
    void generateParenthesisDFS(int left, int right, string out, vector<string> &res) {
        if (left > right) return;
        if (left == 0 && right == 0) res.push_back(out);
        else {
            if (left > 0) generateParenthesisDFS(left - 1, right, out + '(', res);
            if (right > 0) generateParenthesisDFS(left, right - 1, out + ')', res);
        }
    }
};