Leetcode 22. Generate Parentheses

class Solution {
public:
    vector<string> generateParenthesis(int n) {
        vector<string> result;
        push(0, 0, result, "", n, '(');
        return result;
    }
    
private:
    void push(int left, int right, vector<string>& result, string s, const int n, char ch) {
        s += ch;
        if(ch == '(') {
            left++;
        }
        else {
            right++;
        }
        if(left > n || right > n || right > left) {
            return;
        }
        if(s.length() == 2 * n) {
            result.push_back(s);
            return;
        }
        push(left, right, result, s, n, '(');
        push(left, right, result, s, n, ')');
    }
};