Generator

import java.util.ArrayList;

class sigmaStar {

    int length = 0;

    ArrayList<ArrayList<Integer>> setForLength;

    int iteration = 0;

    void powerSet() {

        setForLength = new ArrayList<ArrayList<Integer>>();

        ArrayList<Integer> originalArray = new ArrayList<>();

        setForLength.add(new ArrayList<Integer>());

        for(int i = 0; i < length; i++) {
            originalArray.add(i);
        }
        powerSetHelper(new ArrayList<Integer>(), originalArray, 0);
    }

    void powerSetHelper(ArrayList<Integer> array, ArrayList<Integer> originalArray, int index) {
        int i = index;

        while(i < originalArray.size()) {

            ArrayList<Integer> temp = copy(array);

            temp.add(originalArray.get(i));

            setForLength.add(temp);

            i++;

            powerSetHelper(temp, originalArray, i);
        }
    }


    //to make a deep copy
    ArrayList<Integer> copy(ArrayList<Integer> arrayToBeCopied) {

        ArrayList<Integer> copiedArray = new ArrayList<>();

        for(int value : arrayToBeCopied) {
            copiedArray.add(value);
        }
        return copiedArray;
    }


    String next () {

        String x1 = "";
        //when we move onto the strings of a length one greater than the previous string
        if (iteration == 0) {
            powerSet();
        }

        for(int i = 0; i < length; i++) {
            if(setForLength.get(iteration).contains(i)) {
                x1 += "b";
            }
            else {
                x1 += "a";
            }
        }

        iteration++;

        if (iteration == Math.pow(2, length) || length == 0) {
            length++;
            iteration = 0;
        }

        return x1;
    }


}


public class Main {

    public static void main(String[] args) {
        sigmaStar s = new sigmaStar();
        for(int i = 0; i < 220; i++) {
            System.out.println("STRING " + (i + 1) + " : " + s.next());
            
        }

    }
}