Generate all Parentheses II

• Time : $O(2^A)$
• Space : $O(A)$

void helper(string& s, int open, int fin, vector<string>& res) {
    if(open == 0 and fin == 0) res.push_back(s);
    else {
        if(open < fin) {
            s.push_back('(');
            helper(s,open + 1, fin, res);
            s.pop_back();
        }
        if(open) {
            s.push_back(')');
            helper(s,open - 1, fin - 1, res);
            s.pop_back();
        }
    }
}
vector<string> Solution::generateParenthesis(int A) {
    vector<string> res;
    helper(string() = "", 0, A, res);
    return res;
}