CS 1723 Section 1T, Summer 1998 Assignment 4

Polynomial Differentiation

Your assignment is to complete a program that accepts a polynomial in one variable (x) on standard input and prints its first derivative on standard output. Input will be plain text, using ^ for the exponentiation operator (e.g., x^2 is x²). For example, if the input is:

2x^7 - 4x^4 + 3x^2 - 4

then the output should be:

14x^6 - 16x^3 + 6x

On the runner system, in directory ~djimenez/cs1723/diff (the full path is /home/staff3/djimenez/cs1723/diff) you will find a Makefile and several .h and .c files that combine to read, construct, and print polynomials as linked lists of terms called monomials. Each monomial is something like 2x⁷ and is represented as a struct like this:

typedef struct _mono {
	double	coeff, power;
} mono;

where coeff is the coefficient x is multiplied by and power is the exponent x is raised to. Note that a zero power implies a constant (i.e., coeff time x⁰), and a zero coefficient implies the entire term is zero and should be left out of the polynomial.

The file calc.c contains a driver program that reads in a polynomial as a linked list (so you don't have to worry about how to do that), prints the polynomial on the screen (again, you don't have to do that), calls a function you will write to differentiate the polynomial, then prints the derivative.

The file mono.h contains declarations for the mono struct above and declarations used by a file called mono.c that reads in terms; this C file is only used internally and you don't need to look at it.

The file poly.h declares an abstract data type poly for polynomials. poly is a pointer type to a linked list of mono terms. Some functions declared in this file and defined in poly.c are:

void insert_poly (poly *, mono); This function inserts a mono term at the end of a polynomial.
void create_poly (poly *); This function initializes a poly to be empty (i.e., empty linked list, NULL pointer).
void destroy_poly (poly *); This function frees storage from a poly; you probably won't need to use it.
poly get_poly (void); This function gets a polynomial from standard input, returning it as a list. It's called in the main function; you won't need to use it.
void print_poly (poly); This function prints a polynomial to standard output in a nice format. It's used in the main function. You can use it for debugging purposes, but you won't need to use it for what you turn in.

The file diff.h declares a single function, poly differentiate (poly);. Your assignment is to write this function. It accepts poly linked list and returns a new poly linked list (without modifying the old one) that contains the derivative. You should write this function (and any support functions you will need) in a file called diff.c. An empty diff.c is provided that just returns NULL so that you can get everything compiled before you get everything working.

To Do This Assignment

Make a subdirectory in your account (or on your home computer) called diff.
Copy everything from my diff directory on runner to your diff directory, including the Makefile.
Type make to make the program.
Run it and try it on some sample inputs; it won't differentiate, but it will read in and echo polynomials.
Write the code for diff.c so that it works with the given calc.c. Do not modify any of the files except for diff.c since I will be checking your assignment with my own versions.

Test your program. You may use the following polynomials to test your program:

18
x
-2x^7 - 3x^6 + 5x^2 - 18
x^2 + 2x^2 - 8x^-14 + 4
3x^10 - 2x^10 + 8x^2 + 10x^2 - x^100

To turn in the assignment, e-mail your C file from your runner account to the instructor with
```
Mail -s "Assignment 4" djimenez@ringer.cs.utsa.edu < diff.c
```
Make sure your name is in your well-commented C file.

Extra Credit

This assignment is worth 10 points. The following options are available for up to 5 points extra credit:

For 2 points extra credit, write your differentiate function so that any term that is equal to zero (such as the derivative of a constant) is left out, unless it is the only term in the polynomial. For example, the derivative of 18 would be printed as 0, but the derivative of x^2 + 18 would be printed as 2x (as opposed to 2x + 0.
For 3 points extra credit, write differentiate to combine terms of the same degree. For example, the derivative of x^2 + 2x^2 is 2x + 4x, but should be combined as simply 6x. Note that e.g. x - x is 0, so you should do this part before the other part to receive the full 5 points of extra credit.

This program is due by midnight, Tuesday, June 23, 1998.