Polynomial Addition and Subtraction

This is Java

Write a program that adds and subtracts two polynomials. Implement the algorithm four different ways. The first two implementations will use arrays and the third will use pointers. The forth is a set of linked lists in an array. Use the following interface for the 4 classes:

public interface PolynomialInterface

{

PolynomialInterface add(PolynomialInterface other);

// Effect: Adds value to owner of addPolynomial method.

// Postcondition: Return value = this + value.

PolynomialInterface subtract(PolynomialInterface other);

// Effect: Subtracts value from owner of addPolynomial method.

// Postcondition: Return value = this - value. void readPolynomial();

// Postcondition: polynomial read.

String toString();

// Postcondition: polynomial converted to string. }

The class must be able to read and print polynomials. Example: 4X4 + X3 - 3 + 4X4 - 2X3 + 4X 8X4 - X3 + 4X 3

The four ways to implement the requirements:

2- Create an array or ArrayList holding coefficients with the array indexes as exponents

3- Create and array or ArrayList of nodes, each node holding a term of the polynomial

4- Use a linked list of terms using pointers.

Polynomials are linked lists in one static array. Implementations 2, 3, and 4 require a class that will encapsulate a polynomial term unique to that particular implementation. The string from the constructor is a polynomial that each implementation must take apart and store each term in sorted order. All three implementations will follow the same basic algorithm to add two sorted polynomials. One array is used to store multiple polynomial instances and the free store. This array must be declared static so that it is available to all polynomial instances. There are two challenges in the first implementation. The first is converting the polynomial string given in the constructor into the terms of the polynomial. The second is taking the internal representation of the polynomial and converting it back to a string in the toString() method. The other three implementations will modify slightly the code from the first implementation for their constructor and toString() methods. Your code must use the Demo provided below.

public class PlynomialDemo { public static void main(String[] args) { // example strings constructor must handle // String s = "44"; // String s = "44x"; // String s = "4x^4+3x^3-3"; // String s = "4x^3-3x^11"; // String s = "44x^6-3x^10+4x^4"; // String s = "25x^5-3x^13+4x^12-78"; // String s ="34x^15-44x^14-3x^12+4x^31-78"; // String s1 = "44"; // String s2 = "44x-78"; // String s1 = "4x^4+3x^3-3"; // String s2 = "4x^6-3x^12"; String s1 = "4x^14-3x^12+4x^4+78"; String s2 = "-4x^4-3x^12+4x^17-78"; // String s1 = "4x^4+3x^11+4x^10"; // String s2 = "5x^14-3x^12+4x^19-78"; // String s1 = "4x^5+4x^4-3x^12-4x^41-78"; // String s2 = "-4x^4+3x^12+4x^41+78"; // Four implementations of the interface PolynomialInterface exAsIndex1 = new ArrayWithExponentAsIndexPolynomial(s1); PolynomialInterface exAsIndex2 = new ArrayWithExponentAsIndexPolynomial(s2); PolynomialInterface exAsIndex3; exAsIndex3 = exAsIndex1.add(exAsIndex2); System.out.println("First test is with array index as exponent. " ); // System.out.println("exAsIndex1 string is " + s1); System.out.println("exAsIndex1 = " + exAsIndex1); // System.out.println("exAsIndex2 string is " + s2); System.out.println("exAsIndex2 = " + exAsIndex2); System.out.println("exAsIndex3 = exAsIndex1.add(exAsIndex2) " + exAsIndex3); exAsIndex3 = exAsIndex1.subtract(exAsIndex2); // System.out.println("exAsIndex1 string is " + s1); // System.out.println("exAsIndex1 = " + exAsIndex1); // System.out.println("exAsIndex2 string is " + s2); //System.out.println("exAsIndex2 = " + exAsIndex2); System.out.println("exAsIndex3 = exAsIndex1.subtract(exAsIndex2) " + exAsIndex3); System.out.println(); PolynomialInterface sortA1 = new ArraySortedPolynomial(s1); PolynomialInterface sortA2 = new ArraySortedPolynomial(s2); PolynomialInterface sortA3; sortA3 = sortA1.add(sortA2); System.out.println("Second test is sorted array of terms."); // System.out.println("sortA1 string is " + s1); System.out.println("sortA1 = " + sortA1); // System.out.println("sortA2 string is " + s2); System.out.println("sortA2 = " + sortA2); System.out.println("sortA3 = sortA1.add(sortA2) " + sortA3); sortA3 = sortA1.subtract(sortA2); // System.out.println("sortA1 string is " + s1); //System.out.println("sortA1 = " + sortA1); // System.out.println("sortA2 string is " + s2); //System.out.println("sortA2 = " + sortA2); System.out.println("sortA3 = sortA1.subtract(sortA2) " + sortA3); System.out.println(); PolynomialInterface link1 = new LinkListPolynomial(s1); PolynomialInterface link2 = new LinkListPolynomial(s2); PolynomialInterface link3; System.out.println("Third test is linked list of terms."); // System.out.println("link1 string is " + s1); System.out.println("link1 = " + link1); // System.out.println("link2 string is " + s2); System.out.println("link2 = " + link2); link3 = link1.add(link2); System.out.println("sum of link1 and link2 = " + link3); // System.out.println("link1 string is " + s1); // System.out.println("link1 = " + link1); // System.out.println("link2 string is " + s2); //System.out.println("link2 = " + link2); link3 = link1.subtract(link2); System.out.println("link1 minus link2 = " + link3); System.out.println(); PolynomialInterface linkInArray1 = new LinkedListInArrayPolynomial(s1); PolynomialInterface linkInArray2 = new LinkedListInArrayPolynomial(s2); PolynomialInterface linkInArray3 = new LinkedListInArrayPolynomial(); System.out.println("Forth test is linked list of terms in an array."); //System.out.println("linkInArray1 string is " + s1); System.out.println("linkInArray1 = " + linkInArray1); // System.out.println("linkInArray2 string is " + s2); System.out.println("linkInArray2 = " + linkInArray2); linkInArray3 = linkInArray1.add(linkInArray2); System.out.println("sum of linkInArray1 and linkInArray2 = " + linkInArray3); linkInArray3 = linkInArray1.subtract(linkInArray2); System.out.println("linkInArray1 minus linkInArray2 = " + linkInArray3); } }