Objectives: This program will allow you to build and manipulate linked lists

Problem Specification: You will design and implement a class to represent a polynomial in x (e.g. x³+3x+3). Your class will allow a client to perform a wide range of operations on a given polynomial; these operations are detailed below, in the implementation section.

Implementation: You will design (using ADTs with UML) and implement two classes: Polynomial and Term.

The Term class will be used to represent each term in a polynomial. In the polynomial x³+3x+3, x³, 3x, and 3 are each terms. You may assume that term coefficients and exponents are integers.

The Polynomial class, as it's name suggests, will represent an entire polynomial. Your Polynomial class must store a polynomial as a linked list of terms. You must include the following operations in the Polynomial class interface:

• A default constructor.
• A non-default constructor that takes a polynomial stored in a string as input (e.g. "1*x^3+3*x^1+3*x^0") and constructs the corresponding linked list of terms. You may assume that the terms in the polynomial are only ever added, never subtracted. Furthermore, you may assume that each polynomial term is of the form c*x^e, where c and e are integers. The link list should store terms in order of descending exponents. Also, the link list should not store two terms with the same exponents; that is, the polynomial 1*x^4+2*x^4 should be stored as 3*x^4.
• A copy constructor.
• A destructor that recursively deallocates the Polynomial's linked list.
• Print, which should store the polynomial in a given ostream. The method prototype should appear as follows:
  
     void Print (ostream& OutOS) const;
  
  
• Evaluate, which should take in a value for x (where x is an integer) and output the polynomial value.
• Graph, which should take in a domain of integer values defined by the beginning and end of the domain and an ostream in which to store the corresponding range of polynomial values.
• Add, whose method prototype appears as follows:
  
     void AddPolynomial (const Polynomial& ToAdd);
  
  Add should take in a Polynomial (i.e. ToAdd) as input and add the input polynomial to the object polynomial. The result should be stored in the object polynomial.

Required Testing: Use the following as the Polynomial class client:

CPolynomial p1 ("3*x^2+40*x^1+203*x^0+35*x^1");
CPolynomial p2 ("1*x^3+1*x^4+2*x^2+1*x^0");

p1.Print(cout);
cout << endl;

p2.Print(cout);
cout << endl;

cout << p1.Evaluate(0)<< endl;

p1.Graph (cout, 0, 10);

p1.AddPolynomial(p2);

p1.Print(cout);
cout << endl;

p2.Print(cout);
cout << endl;


The following output should be produced:

3*x^2+75*x^1+203*x^0
1*x^4+1*x^3+2*x^2+1*x^0
203
p(0)=203
p(1)=281
p(2)=365
p(3)=455
p(4)=551
p(5)=653
p(6)=761
p(7)=875
p(8)=995
p(9)=1121
p(10)=1253
1*x^4+1*x^3+5*x^2+75*x^1+204*x^0
1*x^4+1*x^3+2*x^2+1*x^0

Extra Credit:

• (+2) Add a method to the Polynomial class that converts the polynomial to it's derivative.
• (+5) Add a method to the Polynomial class that converts the polynomial to it's integral. The method should take in one point (i.e. x- and y-coordinates) through which the intregal passes.