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APPLICATION: A Polynomial CLASS A polynomial is a mathematical function of the form: The greatest exponent, n, is called the degree of the polynomial. For example, p(x) = 7x 4 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) = cx e, 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) = 3x 2 2x + 5 could be represented as a list of three elements, where the first element represents the term 3x 2, the second element represents the term 2x, and the third element represents the (constant) term 5. EXAMPLE 7.7 A Polynomial Class
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p(x) = a0 x n + a1 x n 1 + a2 x n 2 +
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public class Polynomial { private List<Term> list = new LinkedList<Term>(); public static final Polynomial ZERO = new Polynomial(); private Polynomial() { } // default constructor
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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; } }
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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)); }
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} 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;