22.括号生成

题目
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：

[
"((()))",
"(()())",
"(())()",
"()(())",
"()()()"
]

思路
采用递归法

class Solution {
public:
    vector<string> generateParenthesis(int n) {
        vector<string> resultStr;
        string curStr;
        int open = 0, close = 0;
        backtrack(resultStr, curStr, open, close, n);
        return resultStr;

    }
    void backtrack(vector<string>&resultStr, string &curStr, 
        int open, int close, int max)
    {
        if (curStr.size() == max * 2)
        {
            resultStr.push_back(curStr);
            return;
        }
        if (open < max)
            backtrack(resultStr, curStr + "(", (open + 1), close, max);
        if (close < open)
            backtrack(resultStr, curStr + ")", (open), close + 1, max);
    }
};

int main(int argc, char* argv[])
{
    vector<string> result;
    int n = 3;
    result = Solution().generateParenthesis(3);
    system("pause");
    return 0;
}