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

Another inefficient but elegant answer =>

public static Set permuteParenthesis1(int num)
{   
    Set result=new HashSet();
    if(num==0)//base case
        {
            result.add("");
            return result;
        }
    else
        {
            Set temp=permuteParenthesis1(num-1); // storing result from previous result.
            for(String str : temp)
            {
                for(int i=0;i