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:

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

Analyse: As long as number of "(" is smaller than n, we can push "(", as long as number of ")" is smaller than "(", we can push ")". 

Runtime: 0ms.

class Solution {
public:
    vector<string> generateParenthesis(int n) {
        vector<string> result;
        if(!n) return result;
        
        helper(n, 0, 0, result, "");
        return result;
    }
    
    void helper(int n, int left, int right, vector<string>& result, string temp) {
        if(left == n && right == n) {
            result.push_back(temp);
            return;
        }
        if(left < n) helper(n, left + 1, right, result, temp + "(");
        if(right < left && right < n) helper(n, left, right + 1, result, temp + ")");
    }
};