class Solution {
    public List<String> generateParenthesis(int n) {
        /* you can find how many total no. of brackets will be generated 
        through catalan number 

        TC for interview purposes - O(n * 2^2n)
        */

         backtrack("" , 0 , 0 , n);
         return res;
    }
    public List<String> res = new ArrayList<>();

    //open -> open brackets , clost brackets
    public void backtrack(String sb , int open , int close , int n){
        //base condition
        if(sb.length() == 2*n){
            res.add(sb);
            return;
        }

        //always start with open bracket
        if(open < n)
        backtrack(sb + "(", open + 1 , close , n);

        //close brackets should always be lesser than open,make recursion 
        //tree to understand this better
        if(close < open)
        backtrack(sb + ")",open ,close+1 , n);
    }
}