[leetcode]Generate Parentheses

题目：

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:

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

思路：卡塔兰数。

c++实现：

class Solution {
public:
    vector<string> generateParenthesis(int n) {
		vector<string> res;
		string s = "";
		if(n <= 0)
		{
			return res;

		}
		generate(n, n, s, res);
		return res;
    }
	void generate(int l, int r, string s, vector < string > &res)
	{
		if(r < l)return;
		if(l == 0 && r == 0){
			res.push_back(s);
		}
		if(l>0)generate(l-1, r, s+"(", res);
		if(r>0)generate(l, r-1, s+")", res);
	}
};