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().
