leetcode——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:

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

用到卡特兰数的思想：“（”出现的次数不少于“）”出现的次数。

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

        vector<string > ret;

        dfs(ret, "", n, n);

        return ret;

        
    }
    void dfs(vector<string> &ret, string tmp, int left, int right)
    {
        if (0 == left && 0 == right)
        {
            ret.push_back(tmp);
            return;
        }
        else if (left > 0)
            dfs(ret, tmp + '(', left - 1, right);

        if (left < right)
            dfs(ret, tmp + ')', left, right - 1);
    }

};