Finding all combinations of well-formed brackets

Question

This came up while talking to a friend and I thought I\'d ask here since it\'s an interesting problem and would like to see other people\'s solutions.

The task is to

Answer 1

why cant this is as simple as this, this idea is quite simple

brackets(n) --> '()' + brackets(n-1) 0 '(' + brackets(n-1) + ')' 0 brackets(n-1) + '()'

where 0 is the concatenation operation above

public static Set brackets(int n) {
    if(n == 1){
        Set s = new HashSet();
        s.add("()");
        return s;
    }else{
        Set s1 = new HashSet();
        Set s2 = brackets(n - 1);
        for(Iterator it = s2.iterator(); it.hasNext();){
            String s = it.next();
            s1.add("()" + s);
            s1.add("(" + s + ")");
            s1.add(s + "()");
        }
        s2.clear();
        s2 = null;
        return s1;
    }
}