Question

           Homework: Polynomial Using Array

Description: Implement a polynomial class

(1) Name your class Polynomial

(2) Use array of doubles to store the coefficients so that the coefficient for x^k is stored in the location [k] of the array.

(3) define the following methods:

a. public Polynomial()

   POSTCONDITION: Creates a polynomial represents 0

b. public Polynomial(double a0)

   POSTCONDITION: Creates a polynomial has a single x^0 term with coefficient a0

c. public Polynomial(Polynomial p)

   POSTCONDITION: Creates a polynomial that is the copy of p

d. public void add_to_coef(double amount, int exponent)

POSTCONDITION: Adds the given amount to the coefficient of the specified exponent.
Note: the exponent is allowed to be greater than the degree of the polynomial   
example: if p = x + 1, after p.add_to_coef(1, 2), p = x^2 + x + 1
  

e. public void assign_coef(double coefficient, int exponent)
POSTCONDITION: Sets the coefficient for the specified exponent.
Note: the exponent is allowed to be greater than the degree of the polynomial   

f. public double coefficient(int exponent)
POSTCONDITION: Returns coefficient at specified exponent of this polynomial.
Note: the exponent is allowed to be greater than the degree of the polynomial   
e.g. if p = x + 1; p.coeffcient(3) should return 0

g. public double eval(double x)
POSTCONDITION: The return value is the value of this polynomial with the given value for the variable x.
Do not use power method from Math, which is very low efficient

h. public string toString()

   POSTCONDITION: return the polynomial as a string like “2x^2 + 3x + 4”
   
Important only non-zero terms unless the polynomial is 0

i. public Polynomial add(Polynomial p)
POSTCONDITION:
this object and p are not changed   
return a polynomial that is the sum of p and this polynomial

j. public Polynomial multiply(Polynomial p)
POSTCONDITION:
this object and p should not be changed
returns a new polynomial obtained by multiplying this term and p. For example, if this polynomial is
2x^2 + 3x + 4 and p is 5x^2 - 1x + 7, then at the end of this function, it will return the polynomial 10x^4 + 13x^3 + 31x^2 + 17x + 28.

k. Write a single main method to test ALL the methods and classes.
You can hard code the polynomials, just like we did for the first homework.

Answer 1

Here is the code with the implementation as mentioned in the problem,

Polynomial.java

public class Polynomial {
    private double[] coef;  // coefficients
    private int deg;     // degree of polynomial (0 for the zero polynomial)

    public Polynomial(){
        coef = new double[1];
        deg = 0;
    }

    public Polynomial(double a0){
        coef = new double[]{a0};
        deg = degree();
    }

    public Polynomial(Polynomial p){
        coef = p.coef;
        deg = p.deg;
    }

    private void updateCoefficient(int power){
        coef = new double[power+1];
        deg = degree();
    }

    public void add_to_coef(double amount, int exponent){
        if(exponent < coef.length){
            coef[exponent] += amount;
        }
        else{
            double[] updatedCoef = new double[exponent+1];
            for(int i=0; i<coef.length; i++) updatedCoef[i] = coef[i];
            updatedCoef[exponent] = amount;
            coef = updatedCoef;
        }
        deg = degree();
    }

    public int degree() {
        int d = 0;
        for (int i = 0; i < coef.length; i++)
            if (coef[i] != 0) d = i;
        return d;
    }

    public void assign_coef(double coefficient, int exponent){
        if(exponent < coef.length){
            coef[exponent] = coefficient;
        }
        else{
            double[] updatedCoef = new double[exponent+1];
            for(int i=0; i<coef.length; i++) updatedCoef[i] = coef[i];
            updatedCoef[exponent] = coefficient;
            coef = updatedCoef;
        }
        deg = degree();
    }

    public double coefficient(int exponent){
        if(exponent < coef.length) return coef[exponent];
        return 0.0;
    }

    public double evaluate(double x) {
        double p = 0;
        for (int i = deg; i >= 0; i--)
            p = coef[i] + (x * p);
        return p;
    }

    public Polynomial add(Polynomial p){
        Polynomial a = this;
        Polynomial c;
        if(a.deg <= p.deg){
            c = new Polynomial(p);
            for (int i = 0; i <= a.deg; i++) c.coef[i] += a.coef[i];
        }
        else{
            c = new Polynomial(a);
            for (int i = 0; i <= p.deg; i++) c.coef[i] += p.coef[i];
        }
        c.deg = c.degree();
        return c;
    }

    public Polynomial multiply(Polynomial p){
        Polynomial a = this;
        Polynomial c = new Polynomial();
        c.updateCoefficient(this.deg + p.deg);
        for (int i = 0; i <= a.deg; i++)
            for (int j = 0; j <= p.deg; j++)
                c.coef[i+j] += (a.coef[i] * p.coef[j]);
        c.deg = c.degree();
        return c;
    }

    public String toString() {
        if (deg ==  0) return "" + coef[0];
        if (deg ==  1) return coef[1] + "x + " + coef[0];
        StringBuilder s = new StringBuilder(coef[deg] + "x^" + deg);
        for (int i = deg-1; i >= 0; i--) {
            if      (coef[i] == 0) continue;
            else if (coef[i]  > 0) s.append(" + ").append(coef[i]);
            else if (coef[i]  < 0) s.append(" - ").append(-coef[i]);
            if      (i == 1) s.append("x");
            else if (i >  1) s.append("x^").append(i);
        }
        return s.toString();
    }


    public static void main(String[] args) {
        Polynomial zero = new Polynomial();

        Polynomial p1   = new Polynomial(4);
        p1.assign_coef(2, 1);
        p1.assign_coef(5, 2);
        p1.add_to_coef(1,1);
        Polynomial p2   = new Polynomial(3);
        p2.assign_coef(2, 1);
        p2.assign_coef(5, 2);
        p2.add_to_coef(1,1);
        Polynomial mulPoly    = p1.multiply(p2);
        Polynomial addPoly    = p1.add(p2);

        System.out.println("Zero(x) =     " + zero);
        System.out.println("p1(x) =     " + p1);
        System.out.println("p2(x) =     " + p2);
        System.out.println("mulPoly(x) =        " + mulPoly);
        System.out.println("addPoly(x) =        " + addPoly);

        System.out.println("Polynomial 1 degree : "+ p1.degree());
        System.out.println("Polynomial 2 evaluated with x = 2 equals to : "+ p2.evaluate(2.0));
        System.out.println("Polynomial 1 coefficient with exponent 1 : " + p1.coefficient(1));

    }
}

OUTPUT :

If you have any doubts feel free to ask in the comments. Also please don't forget to upvote the solution.