Problem:
A polynomial function is a very famous mathematical function.
The greatest exponent, n, is called the degree of the polynomial. For example, p(x) = 7x4 2 is a
polynomial of degree 4. The simplest polynomials are constant polynomials such as p(x) = 6
(degree 0) and linear polynomials such as p(x) = 9x + 6 (degree 1). The unique zero polynomial
p(x) = 0 is defined to have degree 1. In this section we present a Polynomial class whose
instances represent mathematical polynomials and which supports the usual algebraic operations
on polynomials.
A polynomial can be regarded as a sum of distinct terms. A term is a mathematical function of
the form t (x) = cxe, where c is any real number and e is any nonnegative integer. The number c is
called the coefficient, and the number e is called the exponent.
To define a class whose objects represent polynomials, we use a linked list of Term objects.
For example, the polynomial p(x) = 3x2 2x + 5 could be represented as a list of three elements,
where the first element represents the term 3x2, the second element represents the term 2x, and
the third element represents the (constant) term 5.
Write a java program that computes the polynomial function.
The greatest exponent, n, is called the degree of the polynomial. For example, p(x) = 7x4 2 is a
polynomial of degree 4. The simplest polynomials are constant polynomials such as p(x) = 6
(degree 0) and linear polynomials such as p(x) = 9x + 6 (degree 1). The unique zero polynomial
p(x) = 0 is defined to have degree 1. In this section we present a Polynomial class whose
instances represent mathematical polynomials and which supports the usual algebraic operations
on polynomials.
A polynomial can be regarded as a sum of distinct terms. A term is a mathematical function of
the form t (x) = cxe, where c is any real number and e is any nonnegative integer. The number c is
called the coefficient, and the number e is called the exponent.
To define a class whose objects represent polynomials, we use a linked list of Term objects.
For example, the polynomial p(x) = 3x2 2x + 5 could be represented as a list of three elements,
where the first element represents the term 3x2, the second element represents the term 2x, and
the third element represents the (constant) term 5.
Write a java program that computes the polynomial function.
Output:
Not applicable
Solution:
public class Polynomial {
private List<Term> list = new LinkedList<Term>();
public static final Polynomial ZERO = new Polynomial();
private Polynomial() { // default constructor
}
public Polynomial(double coef, int exp) {
if (coef != 0.0) {
list.add(new Term(coef, exp));
}
}
public Polynomial(Polynomial p) { // copy constructor
for (Term term : p.list) {
this.list.add(new Term(term));
}
}
public Polynomial(double... a) {
for (int i=0; i<a.length; i++) {
if (a[i] != 0.0) {
list.add(new Term(a[i], i));
}
}
}
public int degree() {
if (list.isEmpty()) {
return -1;
} else {
return list.get(list.size()-1).exp;
}
public boolean isZero() {
return list.isEmpty();
}
public Polynomial plus(Polynomial p) {
if (this.isZero()) {
return new Polynomial(p);
}
if (p.isZero()) {
return new Polynomial(this);
}
Polynomial q = new Polynomial();
ListIterator<Term> it = list.listIterator();
ListIterator<Term> itp = p.list.listIterator();
while (it.hasNext() && itp.hasNext()) {
Term term = it.next();
Term pTerm = itp.next();
if (term.exp < pTerm.exp) {
q.list.add(new Term(term));
itp.previous();
} else if (term.exp == pTerm.exp) {
q.list.add(new Term(term.coef + pTerm.coef, term.exp));
} else { // (term.exp > pTerm.exp)
q.list.add(new Term(pTerm));
it.previous();
}
}
while (it.hasNext()) {
q.list.add(new Term(it.next()));
}
while (itp.hasNext()) {
q.list.add(new Term(itp.next()));
}
return q;
}
public String toString() {
if (this.isZero()) {
return "0";
}
Iterator<Term> it = list.iterator();
StringBuilder buf = new StringBuilder();
boolean isFirstTerm = true;
while (it.hasNext()) {
Term term = it.next();
double c = term.coef;
int e = term.exp;
if (isFirstTerm) {
buf.append(String.format("%.2f", c));
isFirstTerm = false;
} else {
if (term.coef < 0) {
buf.append(String.format(" - %.2f", -c));
} else {
buf.append(String.format(" + %.2f", c));
}
}
if (e == 1) {
buf.append("x");
} else if (e > 1) {
buf.append("x^" + e);
}
}
return buf.toString();
}
private static class Term {
private double coef;
private int exp;
public Term(double coef, int exp) {
if (coef == 0.0 || exp < 0) {
throw new IllegalArgumentException();
}
this.coef = coef;
this.exp = exp;
}
public Term(Term that) { // copy constructor
this(that.coef, that.exp);
}
}
}
