[Datastructure] Another usage of list: Polynomial

Statements: This blog was written by me, but most of content is quoted from book [Data Structure with Java hubbard]

[Description]

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