22. 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:

[
  "((()))",
  "(()())",
  "(())()",
  "()(())",
  "()()()"
]
解题思路：本题就是个递归。
当左括号大于右括号的时候，可以选择左或者右
当左括号等于右括号的时候选择右=左

class Solution {
public:
    void helper(vector<string>&res, int sum, int left, int right,string str){
        if(left+right==sum){
            if(left==right){
                res.push_back(str);
            }
            return ;
        }
        if(left<right)return;
        helper(res,sum,left+1,right,str+"(");
        if(left>right){
            helper(res,sum,left,right+1,str+")");
        }
        
    }
    vector<string> generateParenthesis(int n) {
        vector<string>res;
        helper(res,2*n,0,0,"");
        return res;
    }
};