[LeetCode] Generate Parentheses

Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

For example, given n = 3, a solution set is:

"((()))", "(()())", "(())()", "()(())", "()()()"

想到的就是DFS，backtrace

class Solution {
        vector<string> m_strs;
    public:
        void backtrace(string  str, int leftPaNum, int paNum)
        {   
            if(leftPaNum == paNum && str.size() == 2*paNum)
            {   
                m_strs.push_back(str);
                return;
            }   
            if(leftPaNum == paNum)
            {   
                str += ")";
                backtrace(str, leftPaNum, paNum);
            }   
            else
            {   
                // left num == right num
                if(leftPaNum  == (str.size()-leftPaNum) )
                {   
                    str += "(";
                    backtrace(str, leftPaNum + 1, paNum);
                }   
                else// left num > right num
                {   
                    str += "(";
                    backtrace(str, leftPaNum + 1, paNum);
                    str.erase(str.end() - 1); 
                    str += ")";
                    backtrace(str, leftPaNum, paNum);
                }   
            }   
        }   

        vector<string> generateParenthesis(int n)
        {
            m_strs.clear();
            string str;
            backtrace(str, 0, n);
            return m_strs;
        }
};