Generate Parentheses

class Solution {

    public List<String> generateParenthesis(int n) {
        generateParenthesisHelper(n, 0, 0, "");
        return ans;
    }

    List<String> ans = new ArrayList<>();

    public void generateParenthesisHelper(int n, int openCount, int closeCount, String current){

        //if total number of open and close brackets is n*2 because n pairs are allowed
        if(openCount + closeCount == n*2){
            ans.add(new String(current));
            return;
        }

        //If we have more open brackets, we can add a closing one
        if(openCount > closeCount && openCount < n){

            //add open bracket
            generateParenthesisHelper(n, openCount+1, closeCount, current += "(");

            //bracktack
            current = current.substring(0, current.length()-1);

            //add closing bracket
            generateParenthesisHelper(n, openCount, closeCount+1, current += ")");

        //if open brackets are equal to n, we cannot add anymore open brackets
        }else if(openCount == n){
            generateParenthesisHelper(n, openCount, closeCount+1, current += ")");

        //otherwise, the only option is to start with open bracket
        }else{
            generateParenthesisHelper(n, openCount+1, closeCount, current += "(");
        }

    }

}

class Solution {

    public List<String> generateParenthesis(int n) {
        List<String> ans = new ArrayList();
        // Start the backtracking process with an empty StringBuilder, 0 open parentheses, 0 close parentheses, and the given n.
        backtrack(ans, new StringBuilder(), 0, 0, n);
        return ans;
    }

    public void backtrack(List<String> ans, StringBuilder cur, int open, int close, int max){

        // When the current combination's length reaches the desired length (2*n), add it to the result list.
        if (cur.length() == max * 2) {
            ans.add(cur.toString());
            return;
        }

        // If we can add more opening parentheses, add one and recursively backtrack.
        if (open < max) {
            cur.append("("); // Add an opening parenthesis.
            // Recursively call backtrack with an increased open count.
            backtrack(ans, cur, open+1, close, max);
            cur.deleteCharAt(cur.length() - 1); // Remove the last added character (backtrack).
        }

        // If we have more open parentheses than close parentheses, add a closing parenthesis and recursively backtrack.
        if (close < open) {
            cur.append(")"); // Add a closing parenthesis.
            // Recursively call backtrack with an increased close count.
            backtrack(ans, cur, open, close+1, max);
            cur.deleteCharAt(cur.length() - 1); // Remove the last added character (backtrack).
        }
    }
}