Data Structures Assignment 2 Solution

Purpose: To give you experience implementing and using linked data structures.

Goal 1: To design and implement a class LinkedDS<T> that will act as a linked data structure for accessing Java Objects. Your LinkedDS<T> class will primarily implement two interfaces – PrimQ<T> and Reorder. The details of these interfaces are explained in the files PrimQ.java and Reorder.java. Read these files over very carefully before implementing your LinkedDS<T> class.

Goal 2: To utilize your LinkedDS<T> class to store and manipulate arbitrary length integers. We can think of an integer as a sequence of decimal digits. For example, the number 1234 could be stored as the digit '1' followed by the digit '2' followed by the digit '3' followed by the digit '4'. We will store these digits in a linked chain. Clearly, to perform operations on a number that is stored in this fashion, we must access the digits one at a time in some systematic way. More specific details follow below.

DETAILS

Details 1: For the details on the functionality of your LinkedDS<T> class, carefully read over the files PrimQ.java, Reorder.java, and Assig2A.java provided on the CourseWeb folder where you find this assignment description. You must use these files as specified and cannot remove/alter any of the code that is already written in them. There are different ways of implementing the PrimQ<T> and Reorder interface methods, some of which are more efficient than others. Use only the best way of implementing these methods in this assignment. A lot of pencil and paper work is recommended before actually starting to write your code. Your LinkedDS<T> class header should be:

public class LinkedDS<T> implements PrimQ<T>, Reorder

The only instance variables allowed inside the LinkedDS<T> class are protected Node firstNode;

1 Assignment adapted from Dr. John Ramirez’s class.

protected int numberOfEntries;

Important Note: The primary data structure within LinkedDS<T> class must be a linked chain. You may not use any predefined Java collection class (e.g., ArrayList) for your LinkedDS<T> data.

Note that the following methods are added to the Reorder interface in this assignment as compared to Assignment 1.

public void leftShift(int num)

Shift the contents of the data structure num places to the left (assume the beginning is the leftmost node), removing the leftmost num nodes. For example, if a data structure has 8 nodes in it (numbered from 1 to 8), a leftShift of 3 would shift out nodes 1, 2 and 3 and the old node 4 would now be node 1. If num <= 0 leftShift should do nothing and if num >= the length of the data structure, the result should be an empty data structure.

public void rightShift(int num)

Same idea as leftShift above, but in the opposite direction. For example, if a data structure has 8 nodes in it (numbered from 1 to 8) a rightShift of 3 would shift out nodes 8, 7 and 6 and the old node 5 would now be the last node in the data structure. If num <= 0 rightShift should do nothing and if num >= the length of the data structure, the result should be an empty data structure.

Note that in the method implementation you may not create any new Node objects. The purpose of these methods is to rearrange the Nodes that already exist. To see how these should work, it is strongly recommended to draw one or more pictures.

You will also need to write the following constructors:

public LinkedDS()

public LinkedDS(LinkedDS<T> oldList)

The first constructor simply initializes the list to an empty state, and the second generates a new list that is a copy of the argument list (copying all of the nodes inside the old list).

Finally, you will need to override the following method:

public String toString();

This method will return a String that is the result of all of the data in the list being appended together, separated by spaces.

After you have finished your coding of LinkedDS<T>, the Assig2A.java file provided for you should compile and run correctly and should give output identical to the output shown in A2Out.txt.

Important Notes:

1) All of your LinkedDS methods must be implemented in an efficient way, utilizing the underlying linked chain. For example, a poor implementation of a left rotation could be done via repeated calls to X = removeItem() and addItem(X). However, doing this would require multiple

traversals of the list and has a very bad run-time (think arithmetic series). This and similar implementations are not allowed and if implemented in this way you will not receive credit.

2) The methods should NOT create any new Node objects. Rather, they should move the Node objects currently in the list into other locations. You may use temporary Node variables for these methods, but you may not create any new Nodes.

Details 2: The second part of this assignment is to write the ReallyLongInt class with the specifications as given below. You may assume all numbers will be non-negative.

Inheritance: ReallyLongInt must be a subclass of LinkedDS. However, since LinkedDS is generic while

ReallyLongInt is not generic, you should use the following header:

public class ReallyLongInt extends LinkedDS<Integer> implements Comparable<ReallyLongInt>

Note that rather than T, the underlying element data type is now Integer. This means that the individual digits of your ReallyLongInt will be Integer objects.

Data: The data for this class is inherited and you may not add any additional instance variables. You will certainly need method variables for the various operations but the only instance variables that you need are those inherited from LinkedDS. In order to have access inside ReallyLongInt to the data fields of LinkedDS, you will need to change their access modifiers to protected.

Operations: Your ReallyLongInt class must implement the methods shown below, which are similar to the methods described in Assignment 1. Note that the compareTo() method is necessary for the Comparable interface.

private ReallyLongInt()

The default constructor will create an "empty" ReallyLongHex. Note that this leaves the number in an inconsistent state (having no actual value), so it should only be used within the class itself as a utility method (for example, you will probably need it in your add() and subtract() methods). For this reason, it is a private method.

public ReallyLongInt(String s)

The string s consists of a valid sequence of digits with no leading zeros (except for the number 0 itself – a special case) . Insert the digits as Integer objects, such that the most significant digit is at the beginning. For example, the String "456202" would be stored in a ReallyLongInt as:

firstNode --> 4 --> 5 --> 6 --> 2 --> 0 --> 2 (note: actual Nodes are not shown but implicit). public ReallyLongInt(ReallyLongInt other)

This just requires a call to super. However, it is dependent upon a correct implementation of the copy constructor for the LinkedDS class.

public String toString()

Return a string that accurately shows the integer as we would expect to see it. Based on the way we have stored the integer, this should be accomplished by going forward through the array.

To help you out with the assignment, I have implemented the methods above for you, with comments. See the code in ReallyLongInt.java.

public ReallyLongInt add(ReallyLongInt rightOp)

Return a NEW ReallyLongInt that is the sum of the current ReallyLongInt and the parameter

ReallyLongInt, without altering the original values. For example:

ReallyLongInt X = new ReallyLongInt("123456789");

ReallyLongInt Y = new ReallyLongInt("987654321");

ReallyLongInt Z;

Z = X.add(Y);

System.out.println(X + " + " + Y + " = " + Z);

should produce the output:

123456789 + 987654321 = 1111111110

Be careful to handle carries correctly and to process the digits in the correct order. Since the numbers are stored with the most significant digit at the beginning, the add() method can be implemented by first reversing then traversing both numbers in a systematic way. You should start at the beginning of each ReallyLongInt and traverse one time while doing the addition. Also, be careful to handle numbers with differing numbers of digits.

public ReallyLongInt subtract(ReallyLongInt rightOp)

Return a NEW ReallyLongInt that is the difference of the current ReallyLongInt and the parameter ReallyLongInt. Since ReallyLongInt is specified to be non-negative, if rightOp is greater than the current ReallyLongInt, you should throw an ArithmeticException. Otherwise, subtract digit by digit (borrowing if necessary) as expected. This method is tricky because it can result in leading zeros, which we don't want. Be careful to handle this case (and consider the tools provided by LinkedDS that will allow you to handle it). For example:

ReallyLongInt X = new ReallyLongInt("123456");

ReallyLongInt Y = new ReallyLongInt("123455");

ReallyLongInt Z;

Z = X.subtract(Y);

System.out.println(X + " - " + Y + " = " + Z);

should produce the output:

123456 - 123455 = 1

As with the add() method, be careful to handle numbers with differing numbers of digits. Also note that borrowing may extend over several digits. See RLITest.java for some example cases.

public int compareTo (ReallyLongInt rightOp)

Defined the way we expect compareTo to be defined for numbers. If one number has more digits than the other then clearly it is bigger (since there are no leading 0s). Otherwise, the numbers must be compared digit by digit. Since this requires the most significant digit to be processed first (which is at the front), we can just iterate through the digits as given.

public boolean equals(Object rightOp)

Defined the way we expect equals to be defined for objects – comparing the data and not the reference. Don't forget to cast rightOp to ReallyLongInt so that its array can be accessed (note: the argument here is Object rather than ReallyLongInt because we are overriding equals() from the version defined in class Object) . Note: This method can easily be implemented once compareTo() has been completed.

public ReallyLongInt multTenToThe(int num)

Return the result of Multiplying the current ReallyLongInt by 10num . Note that this can be done very simply through adding of 0's.

public ReallyLongInt divTenToThe(int num)

Return the result of Dividing the current ReallyLongInt by 10num . Note that this can be done very simply through shifting.

To verify that your ReallyLongInt class works correctly, you will use it with the program RLITest.java, which is provided for you on the Assignments CourseWeb page. Your output should match that shown in RLITest.txt.

Important Note:

Both the add() and subtract() methods are tricky and have different cases to consider. For these methods especially I recommend working out some examples on paper to see what needs to be considered before actually coding them.

EXTRA CREDIT

Here are a couple non-trivial extra credit ideas. Either one done well could get you the full 15 extra credit points. However, don't attempt either until you are confident that your required classes are working correctly.

• Allow the numbers to be signed, so that we can have both positive and negative numbers. This may require an extra instance variable (for the "sign") and will clearly affect many of your methods. If you choose this extra credit, you must submit it as a separate class (ReallyLongInt2) in addition to your original ReallyLongInt class. You must also submit a separate driver program to test / demonstrate your signed ReallyLongInt2 class.

• Add a multiply() method to your ReallyLongInt class. If you implement this you should also submit a separate driver program to test / demonstrate the multiply() method.

SUBMISSION REQUIREMENTS

You must submit, the following two complete, working source files for full credit:

1. LinkedDS.java

2. ReallyLongInt.java

The above two files must be created so that they work as described.

The idea from your submission is that the autograder can compile and run both of the unmodified main programs (Assig1A.java and RLITest.java) from the command line WITHOUT ANY additional files or changes, so be sure to test it thoroughly before submitting it.

If you cannot get the programs working as given, clearly indicate any changes you made and clearly indicate why (e.g., "I could not get the reverse() method to work, so I eliminated code that used it") on your Assignment Information Sheet. You will lose some credit for not getting it to work properly, but getting the main programs to work with modifications is better than not getting them to work at all. A template for the Assignment Information Sheet can be found in the assignment’s CourseWeb folder. You do not have to use this template but your sheet should contain the same information.

Note: If you use an IDE such as NetBeans, Eclipse, or IntelliJ, to develop your programs, make sure they will compile and run on the command line before submitting – this may require some modifications to your program (such as removing some package information).

RUBRICS

Please check the grading rubric on CourseWeb.

HINTS / NOTES

1. See file A2Out.txt to see how your output for Assig2A.java should look. As noted, your output when running Assig2A.java should be identical to this.

2. For Javadoc comments and code style, please refer to Appendix A of the textbook.