[LeetCode]Generate Parentheses

题目描述：

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：

基本想法是用递归，当左括号数 < n, 可以继续放左括号，当右括号数<左括号数时，可以继续放右括号。 

class Solution {
public:
    vector<string> generateParenthesis(int n) {
        vector<string> result;
        if (n > 0) {
            generateParenthesis(n, "", 0, 0, result);
        }
        
        return result;
    }
private:
    void generateParenthesis(int n, string s, int l, int r, vector<string> &result) {
        if (l == n) {
            result.push_back(s.append(n - r, ')'));
            return;
        }
        generateParenthesis(n, s + '(', l + 1, r, result);
        
        if (r < l) {
           generateParenthesis(n, s + ')', l, r + 1, result); 
        }
    }
};