Converting whole program from Int to BigInteger [closed]

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So I already have this whole entire class done in Int and now I had to convert it to BigInteger. Main objective is so I can store the coefficients as the BigIntegers for large coefficients. I am getting a null pointer error with the code but I knew that BigInteger was immutable and needed that format. Just maybe another eye or maybe I'm just not doing this correctly.

public class Polynomial {

private BigInteger[] coef;  // coefficients

private int deg;     // degree of polynomial (0 for the zero polynomial)



    /** Creates the constant polynomial P(x) = 1.
      */
    public Polynomial(){
        coef = new BigInteger[1];
        coef[0] = BigInteger.valueOf(1);
        deg = 0;
    }



    /** Creates the linear polynomial of the form P(x) =  x + a.
      */
    public Polynomial(int a){
        coef = new BigInteger[2];
        coef[1] = BigInteger.valueOf(1);
        coef[0] = BigInteger.valueOf(a);
        deg = 1;
    }




    /** Creates the polynomial P(x) = a * x^b.
      */
    public Polynomial(int a, int b) { 
        coef = new BigInteger[b+1];
        coef[b] = BigInteger.valueOf(a);
        deg = degree();
    }
    public Polynomial(BigInteger a, int b) { 
        coef = new BigInteger[b+1];
        coef[b] = a;
        deg = degree();
    }






    /** Return the degree of this polynomial (0 for the constant polynomial).
      */
    public int degree() {
        int d = 0;
        for (int i = 0; i < coef.length; i++)
            if (coef[i] != BigInteger.valueOf(0)) d = i;
        return d;
    }





    /** Return the sum of this polynomial and b, i.e., return c = this + b.
      */
    public Polynomial plus(Polynomial b) {
        Polynomial a = this;
        Polynomial c = new Polynomial(0, Math.max(a.deg, b.deg));
        for (int i = 0; i <= a.deg; i++) c.coef[i] = c.coef[i].add(a.coef[i]);
        for (int i = 0; i <= b.deg; i++) c.coef[i] = c.coef[i].add(b.coef[i]);

        c.deg = c.degree();
        return c;
    }






    /** Return the difference of this polynomial and b, i.e., return (this - b).
      */
    public Polynomial minus(Polynomial b) {
        Polynomial a = this;
        Polynomial c = new Polynomial(0, Math.max(a.deg, b.deg));
        for (int i = 0; i <= a.deg; i++) c.coef[i] = c.coef[i].add(a.coef[i]);
        for (int i = 0; i <= b.deg; i++) c.coef[i] = c.coef[i].subtract(b.coef[i]);

        c.deg = c.degree();
        return c;
    }






    /** Return the product of this polynomial and b, i.e., return (this * b).
      */
    public Polynomial times(Polynomial b) {
        Polynomial a = this;
        Polynomial c = new Polynomial(0, a.deg + b.deg);
        for (int i = 0; i <= a.deg; i++)
            for (int j = 0; j <= b.deg; j++)
                c.coef[i+j] = c.coef[i+j].add(a.coef[i].multiply(b.coef[j]));
        c.deg = c.degree();
        return c;
    }






    /** Return the composite of this polynomial and b, i.e., return this(b(x))  - compute using Horner's method.
      */
    public Polynomial compose(Polynomial b) {
        Polynomial a = this;
        Polynomial c = new Polynomial(0, 0);
        for (int i = a.deg; i >= 0; i--) {
            Polynomial term = new Polynomial(a.coef[i], 0);
            c = term.plus(b.times(c));
        }
        return c;
    }




    /** Return true whenever this polynomial and b are identical to one another.
      */
    public boolean equals(Polynomial b) {
        Polynomial a = this;
        if (a.deg != b.deg) return false;
        for (int i = a.deg; i >= 0; i--)
            if (a.coef[i] != b.coef[i]) return false;
        return true;
    }





    /** Evaluate this polynomial at x, i.e., return this(x).
      */
    public int evaluate(int x) {
        int p = 0;
        for (int i = deg; i >= 0; i--){
            coef[i] = coef[i].add(BigInteger.valueOf(x * p));
        p = coef[i].intValue();
    }
        return p;
    }






    /** Return the derivative of this polynomial.
      */
    public Polynomial differentiate() {
        if (deg == 0) return new Polynomial(0, 0);
        Polynomial deriv = new Polynomial(0, deg - 1);
        deriv.deg = deg - 1;
        for (int i = 0; i < deg; i++)
            deriv.coef[i] = coef[i + 1].multiply(BigInteger.valueOf(i+1));        
    return deriv;
    }





    /** Return a textual representationof this polynomial.
      */
    public String toString() {
        if (deg ==  0) return "" + coef[0];
        if (deg ==  1) return String.valueOf(coef[1]) + "x + " + String.valueOf(coef[0]);
        String s = String.valueOf(coef[deg]) + "x^" + deg;
        for (int i = deg-1; i > 0; i--) {
            if      (coef[i].intValue() == 0) continue;
            else if (coef[i].intValue()  > 0) s = s + " + " + ( coef[i].intValue());
            else if (coef[i].intValue()  < 0) s = s + " - " + (-coef[i].intValue());
            if      (i == 1) s = s + "x";
            else if (i >  1) s = s + "x^" + i;
        }
        return s;
    }






    public static void main(String[] args) {
        Polynomial zero = new Polynomial(1, 0);

        Polynomial p1   = new Polynomial(4, 3);
        Polynomial p2   = new Polynomial(3, 2);
        Polynomial p3   = new Polynomial(-1, 0);
        Polynomial p4   = new Polynomial(-2, 1);
        Polynomial p    = p1.plus(p2).plus(p3).plus(p4);   // 4x^3 + 3x^2  - 2x - 1

        Polynomial q1   = new Polynomial(3, 2);
        Polynomial q2   = new Polynomial(5, 0);
        Polynomial q    = q1.minus(q2);                     // 3x^2 - 5


        Polynomial r    = p.plus(q);
        Polynomial s    = p.times(q);
        Polynomial t    = p.compose(q);

        System.out.println("zero(x) =     " + zero);
        System.out.println("p(x) =        " + p);
        System.out.println("q(x) =        " + q);
        System.out.println("p(x) + q(x) = " + r);
        System.out.println("p(x) * q(x) = " + s);
        System.out.println("p(q(x))     = " + t);
        System.out.println("0 - p(x)    = " + zero.minus(p));
        System.out.println("p(3)        = " + p.evaluate(3));
        System.out.println("p'(x)       = " + p.differentiate());
        System.out.println("p''(x)      = " + p.differentiate().differentiate());


        Polynomial poly = new Polynomial();

        for(int k=0; k<=4; k++){
            poly = poly.times(new Polynomial(-k));
        }

        System.out.println(poly);
   }

}

Answer 1

So when you initialize your array of BigInteger, the values are null because you have specified an array of objects (if it was int[] then initial values are 0).

As you can see from your constructor:

public Polynomial(int a, int b) { 
     coef = new BigInteger[b+1];
     coef[b] = BigInteger.valueOf(a);
     deg = degree();
}

You have only assigned coef[b], the other values remain null.

Hence in first iteration of loop in method plus(Polynomial b), c.coef[0] is null hence NullPointerException when your loop tries to call c.coef[0].add(a.coef[0]).

Suggestion: define a method to initialize all the BigInteger values in an array to 0 to be consistent with declaration of int[] and call in your constructors. Example:

private static void initializeBigIntegerArray(BigInteger[] bigIntegers) {
   for (int i=0; i<bigIntegers.length; i++) {
      // So you don't overwrite anything you assign explicitly
      if (bigInteger[i] == null) {
         bigIntegers[i] = BigInteger.ZERO;
      }
   }
}

Answer 2

Recall that in Java an array of objects is actually an array of references to objects. So you need to create a BigInteger object for every array element. The entries you don't assign are not 0, they are null.

Answer 3

So in the plus method, you create this polynomial c whose backing array contains one zero, and several nulls. Then you go ahead and try to operate on all the coefficients in that polynomial, including all those nulls. So you're calling methods on variables for which an object hasn't been created yet, and that's what makes your null pointer problem.

When you create each polynomial, make sure you have a BigInteger created for every entry in the backing array.