Description
In this assignment, you will implement a polynomial and operations on it using a linked list.
Background
Read Section 3.1 in the textbook for background on polynomials and polynomial arithmetic.
A polynomial may be represented using a linked list as follows: for every term in the polynomial there is one entry in the linked list
consisting of the term’s coefficient and degree. The entries are ordered according to ASCENDING values of degree, i.e. lowest degree term
first, then next lowest degree term and so on, all the way up to the highest degree term. IMPORTANT: Zero-coefficient terms are NOT
stored.
For example, the following polynomial (the symbol ‘^’ is used to mean ‘raised to the power’):
4x^5 – 2x^3 + 2x +3
can be represented as the linked list of terms:
(3,0) -> (2,1) -> (-2,3) -> (4,5)
where each term is a (coefficient,degree) pair.
Notes about representation:
Terms are stored in ASCENDING order of degrees from front to rear in a non-circular linked list.
Zero-coefficient terms are NOT stored.
An EMPTY (zero) polynomial is represented by a linked list with NO NODES in it, i.e. referenced by NULL.
Coefficients are real numbers
Degrees are POSITIVE integers, except if there is a constant term, in which case the degree is zero.
There will not be more than one term in the same degree.
If you do not represent all your polynomials (the initial inputs as well as those you get out of doing arithmetic on polynomials) as
above, you will lose credit even if your results are mathematically correct.
Implementation and Grading
At the bottom of the Autolab assignment page, under Handouts, you will see a polynomial_project.zip file, which is an Eclipse project
file. Download it to your computer. DO NOT unzip it.
Instead, follow the instructions on the Eclipse page under the section “Importing a Zipped Project into Eclipse” to get the entire project
into your Eclipse workspace.
You will see a project called Polynomial with the following classes in package poly:
Node
Term
Polynomial
Polytest
(Aside from these, there are also three sample input files, described in the Running the Program section below.)
You need to complete the implementation of the Polynomial class where indicated in the following methods:
Method Grading Points
evaluate 10
add 25
multiply 25
You may use Math class methods as needed.
There is no formal requirement of efficiency for any of the methods. However, every test case run will be timed out after 3 seconds, which
is plenty of time even for inefficient code. If your method is timed out on a test case you will get no credit for that test.
Note: You will get a zero if you use any other data structure (e.g. array/arraylist) anywhere in your implementation, for any reason, even
if it has nothing to do with the actual polynomial operations. You must work with linked lists ONLY all the way through.
Do not change Node and Term in any way. You will not be submitting them, and we will be using the original versions to test your
Polynomial implementation.
If you wish to change Polytest, feel free. You will not be submitting it, and we will not be using it to grade your Polynomial
submission.
Observe the following rules while working on Polynomial.java:
Only fill in the code in the methods add, multiply, and evaluate where indicated.
In methods that return a Polynomial (add and multiply), the polynomial that is returned must be represented as described in the
“Notes about representation” part of the Background section above.
Your method will not get credit if the returned polynomial does not adhere to this representation, even it is mathematically
correct.
Also see the “Notes about empty (zero) polynomials” at the end of the Running the program section below.
DO NOT remove the package line at the top of the file.
DO NOT remove any of the import statements.
DO NOT add any import statements.
DO NOT change the headers of ANY of the given methods
DO NOT change/remove any of the given class fields
DO NOT add any new class fields – this includes variables and classes.
YOU MAY add new helper methods, but you must declare them private.
Before you submit, make sure to check your code against the original Polynomial.java, Term.java, and Node.java files to make sure
you have adhered to the rules above.
Running the program
There are three sample input files for you to test (they should be under the project folder in Eclipse):
A file ptest1.txt that contains the polynomial
4x^5 – 2x^3 + 2x + 3
A file ptest2.txt that contains the polynomial
8x^4 + 4x^3 – 3x + 9
A file ptest1opp.txt that contains the polynomial
-4x^5 + 2x^3 – 2x – 3
(the negation of the polynomial in ptest1)
In each of these files, each line is a term, with the first value being the coefficient, and the second value being the degree. The terms are
listed in descending order of degrees and the respective non-zero coefficients. Remember that when you store a polynomial in a linked
list, you will store it in ascending order of degrees. (This is actually already implemented by the Polynomial constructor when it reads a
polynomial from an input file. All you have to do is make sure you stick with this rule when you add and multiply.)
You may assume that we will NOT test with an invalid polynomial file, i.e. every test input file will either have at least one term in the
correct format, or will be empty (see Notes about empty (zero) polynomials below). So you don’t need to check for validity of input.
Here’s a sample run of the driver, Polytest. Apart from ptest1.txt, ptest2.txt, and ptest1opp.txt, a fourth test polynomial file,
ptestnull.txt is also used. This is an empty file that stands for a null (zero) polynomial – you will need to create this yourself. See notes
after the test run for special instructions regarding zero polynomials.
Enter the name of the polynomial file => ptest1.txt
4.0x^5 + -2.0x^3 + 2.0x + 3.0
1. ADD polynomial
2. MULTIPLY polynomial
3. EVALUATE polynomial
4. QUIT
Enter choice # => 1
Enter the file containing the polynomial to add => ptest2.txt
8.0x^4 + 4.0x^3 + -3.0x + 9.0
Sum: 4.0x^5 + 8.0x^4 + 2.0x^3 + -1.0x + 12.0
1. ADD polynomial
2. MULTIPLY polynomial
3. EVALUATE polynomial
4. QUIT
Enter choice # => 1
Enter the file containing the polynomial to add => ptest1opp.txt
-4.0x^5 + 2.0x^3 + -2.0x + -3.0
Sum: 0
1. ADD polynomial
2. MULTIPLY polynomial
3. EVALUATE polynomial
4. QUIT
Enter choice # => 1
Enter the file containing the polynomial to add => ptestnull.txt
0
Sum: 4.0x^5 + -2.0x^3 + 2.0x + 3.0
1. ADD polynomial
2. MULTIPLY polynomial
3. EVALUATE polynomial
4. QUIT
Enter choice # => 2
Enter the file containing the polynomial to multiply => ptest2
8.0x^4 + 4.0x^3 + -3.0x + 9.0
Product: 32.0x^9 + 16.0x^8 + -16.0x^7 + -20.0x^6 + 52.0x^5 + 38.0x^4 + -6.0x^3 + -6.0x^2 + 9.0x + 27.0
1. ADD polynomial
2. MULTIPLY polynomial
3. EVALUATE polynomial
4. QUIT
Enter choice # => 3
Enter the evaluation point x => 2
Value at 2.0: 119.0
1. ADD polynomial
2. MULTIPLY polynomial
3. EVALUATE polynomial
4. QUIT
Enter choice # => 4
The sample tests we have given you are just for starters. You will need to create other tests of your own on which you can run your code.
For every test you run, be careful to keep your test input in the same format as the test files provided, otherwise Polytest will not work
correctly. And make sure your test file is in the same folder as the other files, i.e. under Polynomial.
Note on translation from internal to output representation:
The toString method in the Polynomial class returns a string with the terms in descending order, fit for printing. (It processes the
ascending ordered terms of the input linked list in reverse order.) For illustration, see how the add method in Polytest prints the resulting
polynomial:
System.out.println(“Sum: ” + Polynomial.toString(Polynomial.add(poly1,poly2)) + “\n”);
Notes about empty (zero) polynomials:
If you want to test with an empty polynomial input, you should create a file with nothing in it. In Eclipse, you can do this by right
clicking on the project name in the package explorer view, then selecting New, then selecting File. Give a name, and click Finish.
You new file will show up under the project name folder in the package explorer view, and the file will be opened in the text editor
view. But don’t type anything in the file.
Remember that when you add two terms of the same degree, if you get a zero coefficient result term, it should not be added to the
result polynomial. As listed in the “Notes about representation” in the Background section, zero-coefficient terms are not stored.
The string representation of a zero polynomial is “0” – see the toString method of the Polynomial class. So, the Polytest driver
will print a zero for a zero polyomial input, or a zero polynomial that results from an operation performed on two polynomials.
Submission
Submit your Polynomial.java source file in Autolab.
If you are using Eclipse, refer to the instructions in the Eclipse page, under the section The Eclipse Workspace to know how to locate
Polynomial.java on your computer for uploading.
Grading Process
Your code will be auto-graded by a grading program (grader), that will run several test cases on each of evaluate, add, and
multiply.
The grader will NOT be run every time you submit – it will only be run twice, see the following.
The grader will be run once 48 hours before the regular deadline, so Feb 17 at 11PM, on your latest submission as of that time. The
grader will report whether your submission compiled, and if so, what score you got on the test cases that were run on your
submission. The test cases themselves will not be revealed at this time.
The grader will be run for the second (and last) time after all late submission deadlines have passed, i.e. after Feb 21, 11 PM, on
your latest submission as of that time. So if you submitted something before the regular deadline, but submitted again afterward,
during the late submission period, your last submission in the late period will be graded, and you will be assessed a penalty for
lateness (10 points per day).
We will not accept requests to grade any other submission other than the latest submission found by Autolab.
For each test case, the result computed by your code will be compared with that computed by our correct code. Each test case is a
unit of partial credit, so credits for a method are accumulated one test case at a time. There is no partial credit within a test case:
either your program works on a test case (full credit for that test case), or it doesn’t (no credit for that test case.)
Note that for the add and multiply multiply methods, the auto-grader will examine the resulting linked list, NOT printed output.
(The auto-grader does NOT use Polytest at all – that is just for your use.) In other words, the grading script will compare the linked
list structure of the correct result with the linked list structure in your implementation. For evaluate, the returned float value will
be checked.
If you call the add method in your multiply implementation, be aware that if your add implementation does not work correctly,
your multiply method’s correctness will be adversely impacted as well, and you will lose credit for it as well for the failed test
cases.
All printed output will be ignored. This also means if you threw in print statements for debugging and left them in your code, they
will have no bearing on the grading.
After the second and final grading run, the test cases used by the grader will be posted so you can run your program against them to
verify the grade report. Remember, verification means checking the in-memory contents of the linked list for add and multiply,
and the return value of evaluate — NOT what your program might print to output.