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:

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

   void generateParenthesisRecurse(string &s, int x, int y, int n, vector<string> &v)  
   {  
     if(y>x)return;  
     if (x+y == n)  
     {  
       if(x==y)  
         v.push_back(s);  
       return;  
     }  
     s[x+y] = '(';  
     generateParenthesisRecurse(s, x+1, y, n, v);  
     s[x+y] = ')';  
     generateParenthesisRecurse(s, x, y+1, n, v);  
   }  
   
   vector<string> generateParenthesis(int n) {  
     vector<string> V;  
     string s;  
     for (int i = 0; i<n*2; i++)s+='(';  
     generateParenthesisRecurse(s, 0, 0, n*2, V);  
     return V;  
   }