Assignment Set - 4

Please write your Roll Number, Name and Assignment Number at the header of each program.

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Assignment 4.a:        Filename: a4a.c

The polynomial of degree n:

     a₀ + a₁x + a₂x² + ... + a_nxⁿ

can be represented by an array a[ ] of floating point numbers, where a[k] stores the coefficient a_k

(a)    Write a function: int readpoly(float arr[]) that does the following:

• It reads the degree of a polynomial
• It reads the coefficients of the polynomial and stores them in the array. Coefficients may be positive, negative, or zero.
• It returns the degree of the polynomial

Assume that none of the polynomials that are read have degree greater than 9. Choose the dimensions of your arrays accordingly.

(b)    Write a function that receives a polynomial as an input parameter, and returns its maximum and minimum coefficients as output parameters

• The polynomial is represented by an array, arr[ ], which is passed as input parameter.
• The degree of the polynomial is also passed as an input parameter.
• The output parameters are two separate variables maxcoeff and mincoeff respectively. 

(c)    Write a function: float evalpoly(float arr[], float x) that returns the value of the polynomial arr[ ] for a given value of x

        The Horner's method for evaluating polynomials works as follows. Rewrite the polynomial as:

             a₀ + x(a₁ + x(a₂ + x(... + x(a_n-1 + x(a_n)) ...)))

Now write a for-loop that starts from the inside of this expression and works outwards in each iteration.
In the first iteration we compute val = x(a_n)
In the second iteration we compute val = x(a_n-1 + val)
In the third iteration we compute val = x(a_n-2 + val)  ... and so on.

(d)    Write a function: void productpoly(float a[], float b[], float c[])
    that computes the product of two polynomials a[ ] and b[ ] and stores the product polynomial in c[ ].

The product of 3 + 2x - 5x² and 2 + 7x is the polynomial 6 + 25x + 4x² - 35x³
Choose the dimension of array c[ ] keeping in mind that the degree of the product is greater than that of a[ ] and b[ ]

Write a main( ) program that does the following steps:

1. It reads two polynomials A and B using the function readpoly( )
2. It uses the function productpoly( ) to compute the product of A and B and store it in C
3. It prints the coefficients of C
4. It uses the function of part (b) to print the minimum and maximum coefficients of A, B and C.
5. It reads a value of x, and uses the function evalpoly( ) to compute and print the value of A, B and C for that value of x. The user is prompted to repeat this step.

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