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:

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

思路：这是一道DFS题。规则是：在任意0-i的地方，"("的个数必须>=")"的个数才符合规则。因此，当left<n时，可使用"("，当left>right可使用")"。

class Solution {private:    vector<string> res;    string perRes;public:    void generateParenthesisHelper(int pos, int left, int right, int n) {        if (pos == 2*n) {            res.push_back(perRes);        }        else {            if (left < n) {                perRes[pos] = '(';                generateParenthesisHelper(pos+1, left+1, right, n);            }            if (left > right) {                perRes[pos] = ')';                generateParenthesisHelper(pos+1, left, right+1, n);            }        }    }    vector<string> generateParenthesis(int n) {         res.clear();         if(n <= 0) {             return res;         }         perRes.clear();         perRes.resize(2*n);         generateParenthesisHelper(0,0,0,n);         return res;    }};