Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

GenerateAllValidParenthesis.java

public List<String> generateParenthesis(int n) {
    List<String> list = new ArrayList<>();
    backtrack(list, new StringBuilder(), 0, 0, n);
    return list;
}

private static void backtrack(List<String> list, StringBuilder sb, int open, int close, int n) {
    if(sb.length() == 2*n){
        list.add(sb.toString());
        return;
    }

    if(open < n){
        sb.append("(");
        backtrack(list, sb, open+1, close, n);
        sb.setLength(sb.length() - 1);
    }
    if(close < open){
        sb.append(")");
        backtrack(list, sb, open, close+1, n);
        sb.setLength(sb.length() - 1);
    }

    return;
}