Question

following code searches for one zero point of a polynomial function. It uses recursion technique:

    private static double funktion(int[] koef, double x){
        return koef[0] * Math.pow(x,4) + koef[1] * Math.pow(x,3) + 
               koef[2] * Math.pow(x,2) + koef[3]*x + koef[4]; 
    }

    private static double nullstelle(double a, double b, int[] koef){
        double middle = (a + b)/2;
        double result = middle; 
        if(Math.abs(a-b) > 0.00001){
            double sin = funktion(koef, middle);
            if(sin == 0){
                result = middle;
            }else if(Math.signum(funktion(koef, a)) == 
                             Math.signum(funktion(koef, middle))){
                result = nullstelle(middle, b, koef);
            }else{
                result = nullstelle(a, middle, koef);
            }
        }
        return result;
    }

I am wondering how to return all zero points. My ideas is to use an array but I am not sure how to do that. Any ideas?

I am not allowed to use anything else than arrays (e.g. hash tables or sets are not allowed)

Answer 1

First of all your solution as it stands suffers from one of the same problems as your previous question in that you can’t guarantee that you’ll get the zero calculation exactly correct. Unfortunately, this time you can’t use the simple solution of checking that a and b have opposite signs because, for an arbitrary polynomial, a zero need not imply the function crosses the y = 0 line e.g. y = x^4.

Anyway, to answer your question:

1. create an array of size 4 of type Double. Use null to denote that an array slot is empty. As your function is a quartic, there is a maximum of four zeroes.
2. pass the array as a parameter in your function.
3. when you have detected a zero, fill in the first free slot left in the array with the value of the zero.

No actual Java provided because this is homework.