Question

The second lab continues with the Polynomial class from the first lab by adding new methods for polynomial arithmetic to its source code. (There is no inheritance or polymorphism taking place yet in this lab.) Since the class Polynomial is designed to be immutable, none of the following methods should modify the objects this or other in any way, but return the result of that arithmetic operation as a brand new Polynomial object created inside that method.

public Polynomial add(Polynomial other)

Creates and returns a new Polynomial object that represents the result of polynomial addition of the two polynomials this and other. This method should not modify this or other polynomial in any way. Make sure that just like with the constructor, the coefficient of the highest term of the result is nonzero, so that adding the two polynomials 5x10 - x2 + 3x and -5x10 + 7, each having a degree 10, produces the result -x2 + 3x + 7 that has a degree of only 2 instead of 10.

public Polynomial multiply(Polynomial other)

Creates and returns a new Polynomial object that represents the result of polynomial multiplication of the two polynomials this and other. Polynomial multiplication works by multiplying all possible pairs of terms between the two polynomials and adding them together, combining terms of equal degree together into a single term.

Here is my polynomial class:

public class Polynomial{
private int[] data;
private int degree;
  
public Polynomial(int[] coefficients){
int len = coefficients.length;
data = new int[coefficients.length];
for (int i = 0; i<coefficients.length; i++){
data[i] = coefficients[i];
}

for (int i = len-1; i>=0; i--){
if (data[i] != 0){
degree = i;
break;
}
}
}
  
public long evaluate(int x){
int coeffs[]={1,2,3,4}; //change it according to question
long sum = 0;
long input = 1;
for (int i = 0; i < coeffs.length; i++) {
sum += coeffs[i] * input;
input *= x;
}
return sum;
}
  
public int getCoefficient(int k){
if (k <= degree && k >=0){
return data[k];
}
else {
return -1;
}
}
  
public int getDegree(){
return degree;
}
}
  

Answer 1

//Polynomial.java

public class Polynomial {

      

       private int[] data;

       private int degree;

      

       public Polynomial(int[] coefficients){

             int len = coefficients.length;

             data = new int[coefficients.length];

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

                    data[i] = coefficients[i];

             }

             for (int i = len-1; i>=0; i--){

                           if (data[i] != 0){

                                 degree = i;

                                 break;

                           }

             }

       }

      

       public long evaluate(int x){

             int coeffs[]={1,2,3,4}; //change it according to question

             long sum = 0;

             long input = 1;

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

                    sum += coeffs[i] * input;

                    input *= x;

             }

             return sum;

       }

      

       public int getCoefficient(int k){

             if (k <= degree && k >=0){

                    return data[k];

             }

             else {

                    return -1;

             }

       }

      

       public int getDegree(){

             return degree;

       }

      

       // method to add 2 polynomial

       public Polynomial add(Polynomial other)

       {

             Polynomial result;

             // if degree of this polynomial is greater than other

             if(degree > other.getDegree())

             {

                    result = new Polynomial(data); // create the result polynomial same as this

                    // add the coefficients of other polynomial to result

                    for(int i=0;i<=other.getDegree();i++)

                    {

                           result.data[i] += other.data[i];

                    }

             }

             else

             {

                    result = new Polynomial(other.data); // create the result polynomial same as other

                    // add the coefficients of this polynomial to result

                    for(int i=0;i<=degree;i++)

                    {

                           result.data[i] += data[i];

                    }

             }

            

             return result; // return the resultant polynomial

       }

      

       // method to multiply two polynomials

       public Polynomial multiply(Polynomial other)

       {

             Polynomial result;

             // get the resultant degree

             int res_degree = degree + other.degree;

             int res_coeff[] = new int[res_degree+1]; // create a coefficents array of degree res_degree

             // set all elements to 0

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

                    res_coeff[i] = 0;

            

             result = new Polynomial(res_coeff); // create a resultant polynimial using res_coeff

            

             // loop to multiply two polynomials

             for(int i=0;i<=degree;i++)

             {

                    for(int j=0;j<=other.getDegree();j++)

                           result.data[i+j] += data[i]*other.data[j]; // in multiplication the degrees are added

             }

            

             return result; // return the resultant polynomial

       }

      

       // toString method to return the string representation of polynomial

       public String toString()

       {

             String polyStr = "";

             for(int i=data.length-1;i>0;i--)

             {

                    if(data[i] != 0)

                    {

                           if(polyStr.length() == 0)

                           {

                                 if(Math.abs(data[i]) != 1)

                                        polyStr += data[i];

                                 else

                                 {

                                        if(data[i] < 0)

                                               polyStr += "-";

                                 }

                                 polyStr += "x"+i;

                           }else

                           {

                                 if(data[i] > 0)

                                        polyStr += " + ";

                                 else

                                        polyStr += " - ";

                                 if(Math.abs(data[i]) != 1)

                                        polyStr += (int)Math.abs(data[i]);

                                 polyStr += "x"+i;

                           }

                    }

             }

            

             if(polyStr.length() == 0)

             {

                    polyStr += data[0];

             }else

             {

                    if(data[0] != 0)

                    {

                           if(data[0] > 0 )

                                 polyStr += " + ";

                           else

                                 polyStr += " - ";

                           polyStr += (int)Math.abs(data[0]);

                    }

             }

            

             return polyStr;

       }

       public static void main(String[] args) {

            

             // test the add and multiply methods

             int coeffs1[] = {0,3,-1,0,0,0,0,0,0,0,5};

             int coeffs2[] = {7,0,0,0,0,0,0,0,0,0,-5};

            

             Polynomial poly1 = new Polynomial(coeffs1);

             Polynomial poly2 = new Polynomial(coeffs2);

             System.out.println("Polynomial1 :"+poly1);

             System.out.println("Polynomial2 :"+poly2);

            

             Polynomial addPoly = poly1.add(poly2);

             System.out.println("Polynomial1 + Polynomial2 : "+addPoly);

            

             Polynomial mulPoly = poly1.multiply(poly2);

             System.out.println("Polynomial1 * Polynomial2 : "+mulPoly);

       }

}

//end of Polynomial.java

Output: