Statements: This blog was written by me, but most of content  is quoted from book【Data Structure with Java Hubbard】 

【Description】

Apolynomialis a mathematical function of the form:

p(x) = a0xn+ a1xn–1+a2xn–2+ ???+an–1x + an The greatest exponent, n, is called the degreeof the polynomial. For example, p(x) = 7x4– 2 is abpolynomial of degree 4. The simplest polynomials are constant polynomialssuch as p(x) = 6 (degree 0) and linear polynomialssuch 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 Polynomialclass 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 termis a mathematical function of the form t(x) = cxe, where cis any real number and eis any nonnegative integer. The number ciscalled the coefficient, and the number eis called the exponent.To define a class whose objects represent polynomials, we use a linked list of Termobjects.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, andthe third element represents the (constant) term 5.

【Implement】

package com.albertshao.ds.polynomial;

//  Data Structures with Java, Second Edition
//  by John R. Hubbard
//  Copyright 2007 by McGraw-Hill

import java.util.*;

public class Polynomial {
  private List<Term> list = new LinkedList<Term>();
  public static final Polynomial ZERO = new Polynomial();

  private Polynomial() {
  }

  public Polynomial(double coef, int exp) {
    if (coef != 0.0) {
      list.add(new Term(coef, exp));
    }
  }

  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 Polynomial(Polynomial p) {  // copy constructor
    for (Term term : p.list) {
      this.list.add(new Term(term));
    }
  }

  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 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);
    }
  }
}

//  Data Structures with Java, Second Edition
//  by John R. Hubbard
//  Copyright 2007 by McGraw-Hill

package com.albertshao.ds.polynomial;

public class TestPolynomial {
	public static void main(String[] args) {
		Polynomial p = new Polynomial(3, -8, 0, 0, 2, 1);
		Polynomial q = new Polynomial(0, 5, 6, 9);
		System.out.println("p: " + p);
		System.out.println("p.degree(): " + p.degree());
		System.out.println("q: " + q);
		System.out.println("q.degree(): " + q.degree());
		System.out.println("p.plus(q): " + p.plus(q));
		System.out.println("q.plus(p): " + q.plus(p));
		System.out.println("p.plus(q).degree(): " + p.plus(q).degree());
		Polynomial z = new Polynomial(0);
		System.out.println("z: " + z);
		System.out.println("z.degree(): " + z.degree());
		System.out.println("p.plus(z): " + p.plus(z));
		System.out.println("z.plus(p): " + z.plus(p));
		System.out.println("p: " + p);
		Polynomial t = new Polynomial(8.88, 44);
		System.out.println("t: " + t);
		System.out.println("t.degree(): " + t.degree());
	}
}

【Result】

p: 3.00 - 8.00x + 2.00x^4 + 1.00x^5
p.degree(): 5
q: 5.00x + 6.00x^2 + 9.00x^3
q.degree(): 3
p.plus(q): 3.00 - 3.00x + 6.00x^2 + 9.00x^3 + 2.00x^4 + 1.00x^5
q.plus(p): 3.00 - 3.00x + 6.00x^2 + 9.00x^3 + 2.00x^4 + 1.00x^5
p.plus(q).degree(): 5
z: 0
z.degree(): -1
p.plus(z): 3.00 - 8.00x + 2.00x^4 + 1.00x^5
z.plus(p): 3.00 - 8.00x + 2.00x^4 + 1.00x^5
p: 3.00 - 8.00x + 2.00x^4 + 1.00x^5
t: 8.88x^44
t.degree(): 44