C language please

In this exercise we will realize a structure representing a polynomial and the operations defined on it$.$

Define the constant in the file

#define

SIZE $20$

and define the following structures

typedef struct $\{$

int coefficient;

int power;

$\}$ Monom;

typedef struct $\{$

Monom$*$ monoms$[$SIZE$]$;

int numOfElements;

$\}$ Polynomial;

The structure Monom represents one term in a polynomial, for example: $5$x$^2.$ Each monomial will have the fields:

The coefficient of x $($whole number$)$ and the power of x $($whole number$).$

The structure Polynom will store the terms of the polynomial using an array of size SIZE of pointers to the monomial as well as its size $-$ the numbers of the terms of the polynomial.

The length of the polynomial will be at most SIZE, but this is not necessarily the degree of the polynomial. That is$,$ the polynomial $6$ x$^30+2$x is a valid polynomial because its length is less than$/$equal to $20,$ even though its degree is greater than $20.$ Apply the following functions:

$1.$ Monom$*$ createMonom$($int coefficient, int power$)$

This function will create a new monomial with the given coefficient and power. If a coefficient equal to $0$ is received, the function will return NULL.

$2.$void printMonom$($Monom monom$)$

This function will print a monomial in the appropriate format $($will be detailed later$).$ If an empty pointer is received, the function will return and do nothing.

$3.$void addMonom$($Polynom$*$ polynom, int coefficient, int power$)$

This function will add a monomial to a polynomial, in a free space as you wish, while handling the case where a monomial with the same power already exists

If an empty pointer is received, a coefficient equals $0$ or the polynomial is already SIZESIZE in length, the function will return and do nothing..

$4.$ void void printPolynom$($Polynom polynom$)$printPolynom$($Polynom polynom$)$

This function will print the entire polynomial in the appropriate format $($it will be detailed later$)$

$5.$ void void deletePolynom$($Polynom polynom$)$deletePolynom$($Polynom polynom$)$

This function will release all the memory allocated to the polynomial..

Monogram print format ::

For power $0$ only the coefficient will be printed

For power $1$ only the coefficient and x will be printed, for example: $5$x

For coefficient $1$ or $11--$ the coefficient will not be printed, for example :: $,$ x$^4,$ x$^4$x$^2$x$^2--$

For a power greater than $1$ or less than $1-$ the coefficient, x$,$ the sign $^$ and the power will be printed. For example: $5$x$^2$

Polynomial print format ::

The function printPolynomprintPolynom will print to the screen the terms of the polynomial sorted by power, from the largest to the smallest, with the plus sign before a positive coefficient and without spaces. For example: $22--7$x$+5+2$x$^7$x$+5+2$x$^--$x$^2$x$^255$

Printing in a different format than required will lead to points being deducted.

Write a file named PolynomPolynom.h$.$h in which you define the structures and methods.

Write a file called Polynom.cPolynom.c and implement the methods in it$.$

Write a file called main.c main.c in which you can create a polynomial and check the correctness of the implementation.

Sample main plan:

int

int main$()\{$ main$()\{$

Polynom Polynom polynom; polynom;

polynomial.numOfElements $=0$; polynomial.numOfElements $=0$; $//$ Initialize the number of elements$//$ Initialize the number of elements

addMonom$($&polynom, $3,2)$; addMonom$($&polynom, $3,2)$; $//3$x$^2//3$x$^2$

addMonom$($&polynom, $4,3)$; addMonom$($&polynom, $4,3)$; $//4$x$^3//4$x$^3$

addMonom$($&polynom, $5,2)$; addMonom$($&polynom, $5,2)$; $//$ Add $5$x$^2,$ update existing monom to $8$x$^2//$ Add $5$x$^2,$ update existing monom to $8$x$^2$

printPolynom$($polynom$)$; printPolynom$($polynom$)$; $//$ Print the polynomial$//$ Print the polynomial

deletePolynom$($polynom$)$; deletePolynom$($polynom$)$; $//$ Clean up$//$ Clean up

return return $0$;$0$;

$\}$

$\}$

Program output ::

$4$x$^3+8$x$^2$

$4$x$^3+8$x$^2$