Java: Generator of true's & false's combinations by giving the number N;

Question

I tied to simplify the task as much as possible, so I could apply it to my algorithm.

And here is the challenge for mathematicians and programmers:

I need to

Answer 1

Here's a simple version implemented using recursion

public void optionality_generator(int n){
    ArrayList strings = generatorHelper(n); 
    for(String s : strings){
        System.out.println(s);
    }
}

private ArrayList generatorHelper(int n){
    if(n == 1){
        ArrayList returnVal = new ArrayList();
        returnVal.add("0");
        returnVal.add("X");
        return returnVal;
    }
    ArrayList trueStrings = generatorHelper(n-1);
    for(String s : trueStrings){
        s += "0";
    }
    ArrayList falseStrings = generatorHelper(n-1);
    for(String s : falseStrings){
        s += "X";
    }
    trueStrings.addAll(falseStrings);
    return trueStrings;
}