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:

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

Solution:

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

return res;
}

void dfs(int n, int left, int right, string str, vector<string> &res)
{
if(left > n || left + right > 2 * n) return ;
if(left == n && right == n)
{
res.push_back(str);
return ;
}
if(left <= n) dfs(n, left + 1, right, str + "(", res);
if(right <= n && left > right) dfs(n, left, right + 1, str + ")", res);
}
};