(22)Generate Parentheses

class Solution {
public:
    vector<string> ans;
    
    void solve(int n, int open, int close, string &t) //open for open bracket count and close for close bracket count
    {
        if(t.length() == 2*n) //i.e. if n==3 then 3*2=6 makes a parentheses
        {
            ans.push_back(t);
            return;
        }
        
        if(open < n) 
        {
            t += "(";
            solve(n, open+1, close, t);
            t.pop_back();//backtracking ,Because in recursive call we do same thing again and again
        }         
        
        if(close < open) 
        {
            t += ")";
            solve(n, open, close+1, t);
            t.pop_back();//backtracking , it removes the last character of the string 
        }
    }
    
    vector<string> generateParenthesis(int n) 
    {
        string t;
        solve(n, 0, 0, t);
        return ans;
    }
};

//Time Complexity:- O(n^2)