## Description

Modify the LinkedBag implementation in order to implement operations on polynomials

of one parameter. For example the polynomial

-3*x^7 + 4.1 * x^5 + 7 * x^3 + 9 * x^0

can be represented as:

head_ptr_→ [-3, 7] → [4.1, 5] → [7, 3] → [9, 0] → nullptr

The degree of the above polynomial is 7.

In order to achieve this you need to do the following:

a) Modify the Node class so that it now holds two items: coefficient_ and exponent_.

The first node in the above example has coefficient_ = -3 and exponent_ = 7.

That means that instead of GetItem() you will have GetCoefficient() and

GetExponent(), instead of SetItem() you will have SetCoefficient() and

SetExponent(), etc. Modify all other functions accordingly.

b) You will also need to modify the LinkedBag class in various ways. You can now

call it LinkedPolynomial. Also, there is no need to use the BagInterface.h class.

i. Remove the functions ToVector() and Remove() from the

LinkedPolynomial implementation.

ii. Modify the Add() function so that it now adds at the end of the list. Note,

that now the Add() will take two parameters, a coefficient and an

exponent. Also Add() should not add a node with an exponent that is

already there. So for example the following code:

LinkedPolynomial polynomial;

polynomial.Add(-3, 7);

polynomial.Add(4.1, 5);

polynomial.Add(7, 3);

polynomial.Add(8.1, 5);

Should result to

head_ptr_→ [-3, 7] → [4.1, 5] → [7, 3] → nullptr

The last Add() did not have any effect because a node with exponent 5

was already there.

iii. Add a member function called DisplayPolynomial() that will traverse the

list and will cout the coefficients and exponents. Note that this is a const

function. Display in the following form:

-3 * x^ 7 + 4.1 * x^ 5 + 7 * x^3 + 9 * x^0

iv. Add a member function called Degree() that returns the degree of the

polynomial (or -1 if the polynomial is empty). Note that this is a const

function.

In the previous example polynomial.Degree() should return 7.

v. Add a member function called ItemType Coefficient(const ItemType&

exponent) that will return the coefficient of a given exponent. For example

polynomial.Coefficient(5) should return 4.1. Note that this is a const

function.

vi. Add a member function called bool ChangeCoefficient(ItemType

new_coefficient, ItemType exponent) that changes a coefficient for a given

exponent. For example if you call polynomial.ChangeCoefficient(100, 3)

the resulting polynomial will change to

head_ptr_→ [-3, 7] → [4.1, 5] → [100, 3] → [9, 0] → nullptr

The function returns true if the exponent was in the original polynomial

and false otherwise.

In order to test the above do the following:

a) Write a client function (you can place it on top of main())

LinkedPolynomial CreatePolynomialFromInput() that prompts the

user to provide a sequence of coefficients/exponents and then uses the

Add() member function to add them to the Polynomial.

b) Then write a client function called TestPolynomial() that first calls

CreatePolymomialFromInput() to generate a new polynomial and then

does the following in sequence:

Calls the DisplayPolymomial() function.

couts the Degree() of the Polymomial.

Asks the user to provide an exponent.

couts the Coefficient(exponent).

Asks the user for a new coefficient (call it new_coefficient).

Calls the functions ChangeCoefficient(new_coefficient, exponent) and

couts its return value (either true of false).

Calls the DisplayPolynomial() function.

———————————————————————————————————————

Finally, write a member function to add a given polynomial to the current one:

void AddPolynomial(const LinkedPolynomial &b_polynomial). So if the

b_polynomial is

head_ptr_→ [1, 8] → [2, 5] → [-8, 0] → nullptr

Then the current polynomial will change to:

head_ptr_→ [1, 8] → [-3, 7] → [6.1, 5] → [7, 3] → [1, 0] → nullptr

In order to test the above write a function called TestAddition() that does the following:

Calls the function CreatePolynomialFromInput() twice to generate two polynomials

polynomial1 and polynomial2. Adds the second one the the first one (i.e. calls

polynomial1.AddPolynomials(polynomial2)). And finally displays the result by calling

polynomial1.DisplayPolynomial().