我必须修改用整数实现的多项式，这样它也可以容纳BigIntegers [重复]

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How can I fix this “plus” method in Polynomial class using BigInteger 1 answer

如何使用BigInteger 1答案在Polynomial类中修复此“plus”方法

I have to modify a Polynomial implemented with integers, so that it can hold BigIntegers as well. I'm getting null pointer exception error. Please help!

我必须修改用整数实现的多项式,这样它也可以容纳BigIntegers。我得到空指针异常错误。请帮忙!

Exception at Graph.Polynomial.plus(Polynomial.java:59) and at Graph.Polynomial.main(Polynomial.java:189)

Graph.Polynomial.plus(Polynomial.java:59)和Graph.Polynomial.main(Polynomial.java:189)的异常

package Graph;
import java.math.BigInteger;
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] = new BigInteger("1");
    deg = 0;
}



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




/** Creates the polynomial P(x) = a * x^b.
  */
public Polynomial(BigInteger a, BigInteger b) {
     coef =  new BigInteger[b.intValue()+1];
     coef[b.intValue()] = 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]!= new BigInteger("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(new BigInteger(("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(new BigInteger("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(new BigInteger("0"), new BigInteger("a.deg").add(new BigInteger("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(new BigInteger("0"), new BigInteger("0"));
    for (int i = a.deg; i >= 0; i--) {
        Polynomial term = new Polynomial(a.coef[i], new BigInteger("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 BigInteger evaluate(BigInteger x) {
    BigInteger p = new BigInteger("0");
    for (int i = deg; i >= 0; i--)
        p = coef[i].add((new BigInteger("x").multiply(new BigInteger("p"))));
    return p;
}






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





/** Return a textual representation of this polynomial.
  */
public String toString() {
    if (deg ==  0) return "" + coef[0];
    if (deg ==  1) return coef[1] + "x + " + coef[0];
    String s = coef[deg] + "x^" + deg;
    for (int i = deg-1; i >= 0; i--) {
        if      (coef[i] == new BigInteger("0")) continue;
        else if (coef[i].signum()==1) s = s + " + " + ( coef[i]);
        else if (coef[i].signum()== -1) s = s + " - " + (coef[i].multiply(new BigInteger("-1")));
        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(new BigInteger("0"), new BigInteger("0"));

    Polynomial p1   = new Polynomial(new BigInteger("476867"), new BigInteger("8"));
    Polynomial p2   = new Polynomial(new BigInteger("3"), new BigInteger("2"));
    Polynomial p3   = new Polynomial(new BigInteger("-1"), new BigInteger("0"));
    Polynomial p4   = new Polynomial(new BigInteger("-2"), new BigInteger("1"));
    Polynomial p    = p1.plus(p2).plus(p3).plus(p4);

    Polynomial q1   = new Polynomial(new BigInteger("3"), new BigInteger("2"));
    Polynomial q2   = new Polynomial(new BigInteger("5"), new BigInteger("0"));
    Polynomial q    = q1.minus(q2);


    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(new BigInteger("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<=3; k++){
        poly = poly.times(new Polynomial(new BigInteger("-k")));
    }

    System.out.println(poly);
   }

   }

2 个解决方案

#1

When you create a polynomial with this constructor:

使用此构造函数创建多项式时:

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

most of the entries in the coef array will be null. This leads to a NPE when you later add two such polynomials with plus

coef数组中的大多数条目都将为null。当你稍后添加两个带加号的多项式时,这会导致NPE

#2

On line 58 you have

在第58行你有

Polynomial c = new Polynomial(new BigInteger(("0"), Math.max(a.deg, b.deg)));

多项式c = new多项式(new BigInteger((“0”),Math.max(a.deg,b.deg)));

I think you have a bug here.
This seems to create polynomial c of degree 0.

我觉得你这里有个bug。这似乎创建了0度的多项式c。

Basically you're calling this constructor.

基本上你是在调用这个构造函数。

BigInteger(String val, int radix)

BigInteger(String val,int radix)

I don't think this was your intention here,
maybe you put some brackets at some wrong places.

我不认为这是你的意图,也许你把一些括号放在错误的地方。

#1