Question

Write a progam in java that determines the number of real zeros of a polynomial. input for the program should be a list of strings containing only "+" or "-", for the size of the polynomial.

Answer 1

A class which will calculate the real roots of a polynomial, when given the coefficients.

Polynomial.java

import java.util.*;


public class Polynomial

{

    private static final double ROOT_LEEWAY = 0.000000001;

    private double[] coefficients;

    private double remainder;

    public Polynomial(double[] coefficients, double remainder)

    {

        this.coefficients = coefficients;

        this.remainder = remainder;

    }

    

    public Polynomial(double[] coefficients)

    {

        this.coefficients = coefficients;

        this.remainder = 0;

    }

    

    public ArrayList<Double> possibleRoots()

    {

        ArrayList<Double> possibilities = new ArrayList<Double>();

        double p = coefficients[coefficients.length - 1];

        double q = coefficients[0];

        

        ArrayList<Double> pFactors = findFactors(p);

        ArrayList<Double> qFactors = findFactors(q);

        

        for (Double pFactor : pFactors)

            for (Double qFactor : qFactors)

            {

                double possibility = pFactor / qFactor;

                if (!possibilities.contains(possibility))

             possibilities.add(possibility);

            }

            

        return possibilities;

    }

    

    public ArrayList<Double> realRoots()

    {

        ArrayList<Double> roots = new ArrayList<Double>();

        ArrayList<Double> possibleRoots = possibleRoots();

        

        for (Double possibleRoot : possibleRoots)

        {

            double pluggedIn = plugin(possibleRoot);

         if (Math.abs(pluggedIn) <= ROOT_LEEWAY)

         roots.add(possibleRoot);

        }

        

        return roots;

    }

    

    public double plugin(double x)

    {

        double answer = 0;

        for (int i = 0; i < coefficients.length; i++)

            answer += coefficients[i] * Math.pow(x, coefficients.length - (i + 1));

        return answer;

    }

    

    public Polynomial divide(double divisor)

    {

        double[] newCoefficients = new double[coefficients.length - 1];

        newCoefficients[0] = coefficients[0];

        

        for (int i = 1; i < newCoefficients.length; i++)

            newCoefficients[i] = (newCoefficients[i - 1] * divisor) + coefficients[i];

        

        double remainder = (newCoefficients[newCoefficients.length - 1] * divisor) + coefficients[coefficients.length - 1];

        return new Polynomial(newCoefficients, remainder);

    }

    

    public double getRemainder()

    {

        return remainder;

    }

    

    public double[] getCoefficients()

    {

        return coefficients;

    }

    

    private ArrayList<Double> findFactors(double num)

    {

        ArrayList<Double> factors = new ArrayList<Double>();

        for (int i = (int)(-num); i <= num; i++)

         if (num / i == (int)(num / i))

         factors.add((double)i);

        

        return factors;

    }

}
hope you got the answer