Problem Set 3

Due before the start of lecture on October 28, 2025.
See below for a summary of the policies regarding late submissions.

Preliminaries

Homework is due prior to the start of lecture. If it is submitted more than 10 minutes after the start of lecture, it will be considered a full day late. There will be a 10% deduction for late submissions that are made by 11:59 p.m. on the Sunday after the deadline, and a 20% deduction for submissions that are made after that Sunday and before the start of the next lecture. We will not accept any homework that is more than 7 days late. Plan your time carefully, and don’t wait until the last minute to begin an assignment. Starting early will give you ample time to ask questions and obtain assistance.

Revised: Because PS 3 overlapped the midterm, we are waiving the usual late penalties for submissions made by 11:59 p.m. on the Sunday after the deadline, and we are reducing the usual 20% late penalty to 10%. If you submit during the usual 10% late window, Gradescope will still mark your submission as late, but we will not apply a late penalty.

In your work on this assignment, make sure to abide by our policies on academic conduct.

If you have questions while working on this assignment, please come to office hours, post them on Ed Discussion, or email cscie22-staff@lists.fas.harvard.edu

Part I

40 points total

Creating the necessary folder

Create a subfolder called ps3 within your e22 folder, and put all of the files for this assignment in that folder.

Creating the necessary file

The problems from Part I will all be completed in a single PDF file. To create it, you should do the following:

1. Access the template that we have created by clicking on this link and signing into your Google account as needed.

2. When asked, click on the Make a copy button, which will save a copy of the template file to your Google Drive.

3. Select File->Rename, and change the name of the file to ps3_partI.

4. Add your work for the problems from Part I to this file.

5. Once you have completed all of these problems, choose File->Download->PDF document, and save the PDF file on your machine. The resulting PDF file (ps3_partI.pdf) is the one that you will submit. See the submission guidelines at the end of Part I.

Problem 1: Counting multiples in a list of integers

8 points total; 4 points each part

Suppose that you have a linked list of integers containing nodes that are instances of the following class:

public class IntNode {
    private int val;
    private IntNode next;
}

You may assume that the integers in these nodes are always positive.

1. Write a method named numMultRecur(first, n) that takes a reference first to the first node in a linked list of IntNode objects and an integer n, and that uses recursion to determine the number of multiples of n in the list. (Hint: An integer x is a multiple of n if the expression x % n evaluates to 0).

2. Write a method named numMultIter(first, n) that uses iteration to perform the same task.

You do not need to code up these methods (or any method from Part I) as part of a class. Simply put the methods in your ps3_partI file. You may assume that the methods you write are static methods of the IntNode class.

Problem 2: Choosing an appropriate list implementation

12 points total; 4 points each part

In lecture, we considered two different implementations of the list ADT: ArrayList and LLList. For each of the following applications, decide which list implementation would be better for that particular application. Your should consider both time efficiency and space efficiency, and you should assume that both implementations have an associated iterator like the LLListIterator that we discussed in lecture. Explain your answers.

1. You need to keep track of the orders placed to your online store. At the start of each month, you start with an empty list; as orders are made, you add them to the list. The number of orders varies greatly from month to month. You regularly display the list of orders, starting with the most recent order and working backwards chronologically towards the least recent one.

2. The human resources department in your company wants you to maintain its weekly list of workshops. The number of workshops is fairly consistent from week to week. The workshops will be added to the list in chronological order, and they will also be displayed in that order.

3. You are maintaining a list of information about all of the courses that are being offered in the coming semester. Each course has an id number between 1 and 5000, and you decide to use that id number as the position of the course’s record in the list. Once the list of courses is created, there are very few additions or removals. However, you need to frequently access the items in the list during the course registration period. Every time that a student registers for a course, you need to access that course’s record in the list so that you can increment the course’s count of enrolled students.

Problem 3: Reversing a linked list

12 points total

Consider the following method, which takes a list that is an instance of our LLList class from lecture and creates and returns a new list that is a reverse of the original list:

public static LLList reverse(LLList list) {
    LLList rev = new LLList();

    for (int i = list.length() - 1; i >= 0; i--) {
        Object item = list.getItem(i);
        rev.addItem(item, rev.length());
    }

    return rev;
}

Note that the original list is not altered.

1. What is the worst-case running time of this algorithm? Don’t forget to take into account the time efficiency of the underlying list operations, getItem() and addItem(). Use big-O notation, and explain your answer briefly.

2. Rewrite this method to improve its time efficiency by improving the ways in which the method manipulates the LLList objects. Your new method should not modify the original list in any way. Make the new method as efficient as possible. You should assume that this method is not part of the LLList class, and therefore it doesn’t have direct access to the fields of the LLList objects. In addition, you may assume that the LLList objects include support for the list-iterator functionality discussed in lecture.

   Note: In the ps3_partII.zip file that you will download for Part II, we have included a file called Problem3.java that contains the original version of the reverse method and a main method with some preliminary test code. You are welcome to use that file to test the correctness of your new version of the method, although we encourage you to convince yourself of its correctness before you test it in VS Code.

3. What is the worst-case running time of the improved algorithm? Use big-O notation, and explain your answer briefly.

Problem 4: Working with stacks and queues

8 points; 4 points each part

1. Write a method remAllStack(Stack<Object> stack, Object item) that takes a stack and an item, and that removes all occurrences of that item from the stack. After the removals, the remaining items should still be in the same order with respect to each other. For example, if you have a stack that contains (from top to bottom) {5, 2, 7, 2, 10}, if you use the method to remove all occurrences of 2, the resulting stack should contain (from top to bottom) {5, 7, 10}.

   Important guidelines:

   • Your method may use either another stack or a queue to assist it. It may not use an array, linked list, or other data structure. When choosing between a stack or a queue, choose the one that leads to the more efficient implementation.

   • You should assume that the method does not have access to the internals of the collection objects, and thus you can only interact with them using the methods in the interfaces that we discussed in lecture.

   • Although you aren’t writing this method as part of a class, you should use appropriate Java syntax. The methods should be static and should not return a value.

2. Write a method remAllQueue(Queue<Object> queue, Object item) that takes a queue and an item, and that removes all occurrences of that item from the queue. After the removals, the remaining items should still be in the same order with respect to each other. For example, if you have a queue that contains (from front to rear) {5, 2, 7, 2, 10} and you use the method to remove all occurrences of 2, the resulting queue should contain (from front to rear) {5, 7, 10}. The same guidelines that we specified for remAllStack() also apply here.

Submitting your work for Part I

Submit your ps3_partI.pdf file by taking the following steps:

1. If you still need to create a PDF file, open your file on Google Drive, choose File->Download->PDF document, and save the PDF file on your machine.

2. Click on the name of the assignment in the list of assignments on Gradescope. You should see a pop-up window labeled Submit Assignment. (If you don’t see it, click the Submit or Resubmit button at the bottom of the page.)

3. Choose the Submit PDF option, and then click the Select PDF button and find the PDF file that you created. Then click the Upload PDF button.

4. You should see a question outline along with thumbnails of the pages from your uploaded PDF. For each question in the outline:

   • Click the title of the question.
   • Click the page(s) on which your work for that question can be found.

   As you do so, click on the magnifying glass icon for each page and doublecheck that the pages that you see contain the work that you want us to grade.

5. Once you have assigned pages to all of the problems in the question outline, click the Submit button in the lower-right corner of the window. You should see a box saying that your submission was successful.

Part II

60-70 points total

Preparing for Part II

Begin by downloading the following zip file: ps3_partII.zip

Unzip this archive, and you should find a folder named ps3_partII, and within it the files you will need for Part II.

Keep all of the files in the ps3_partII folder, and open that folder in VS Code using the File->Open Folder or File->Open menu option.

Note: VS Code will show an “Unchecked cast” warning for the lines in the ArrayStack and ArrayQueue constructors that create the array for the items field and cast it to be of type T[]. You can safely ignore these warnings.

Problem 5: Rewriting linked-list methods

30 points

If you haven’t already done so, complete the steps above to prepare for this and the remaining problems in Part II.

In lecture, we’ve been looking at linked lists of characters that are composed of objects from the StringNode class. The class includes a variety of methods for manipulating these linked lists, and many of these methods provide functionality that is comparable to the methods found in Java String objects.

Some of the existing StringNode methods use recursion, while others use iteration (i.e., a loop!). In this problem, you will rewrite several of the methods so that they use the alternative approach.

0. Before you get started, we recommend that you put a copy of the original StringNode class in a different folder, so that you can compare the behavior of the original methods to the behavior of your revised methods.

1. Rewrite the length() method. Remove the existing recursive implementation of the method, and replace it with one that uses iteration instead.

2. Rewrite the toUpperCase() method. Remove the existing iterative implementation of the method, and replace it with one that uses recursion instead. No loops are allowed.

3. Rewrite the printReverse() method so that it uses iteration. This method is easy to implement using recursion–as we have done in StringNode.java–but it’s more difficult to implement using iteration. Here are two possible iterative approaches, either of which will receive full credit:

   • reverse the linked list before printing it: This approach is the trickier of the two, but we recommend it because it uses less memory, and it will give you more practice with manipulating linked lists. Remember that you may not use the toString() method for this or any other method. In addition, you should not use the print() method. Finally, don’t forget to restore the linked list to its original form!

   • use an array: Create an array of type char that is large enough to hold all of the characters in the string and use it to help you with the problem.

4. Rewrite the removeFirst() method. Remove the existing iterative implementation of the method, and replace it with one that uses recursion instead. No loops are allowed.

5. Rewrite the copy() method. Remove the existing recursive implementation of the method, and replace it with one that uses iteration instead.

Remember: Draw diagrams to help you in your work!

Problem 6: More fun with StringNodes

10 points; required of grad-credit students; “partial” extra credit for others

The guidelines for Problem 5 also apply here.

1. Add a new method with the following header:

   public static StringNode substring(StringNode str, int start, int end)
   

   This method may use either iteration or recursion to create a new linked list that represents the substring of str that begins with the character at index start and ends with the character at index end - 1 (the character at index end is not included, following the convention used by the substring method in the String class). For example, if you run this test code:

   StringNode s4 = StringNode.convert("hello");
   StringNode s5 = StringNode.substring(s4, 1, 3);
   System.out.println(s4);
   System.out.println(s5);
   

   you should see the following output:

   hello
   el
   

   The method should not change the original linked list, and it should not use any of the existing StringNode methods.

   Special cases:

   • The method should throw an IllegalArgumentException if the indices are out of bounds, or if end is less than start.
   • If the indices are valid and end is equal to start, the method should return null (representing an empty string).
   • If end is not equal to start and str is null, the method should throw an IllegalArgumentException.

   Note: Depending on how you implement the method, you may not need to explicitly check for all of these conditions. For example, in a recursive implementation, if the initial values for the indices are too large, the recursive calls should eventually get to a call in which str is null.

2. Add a new method with the following header:

   public static int nthIndexOf(StringNode str, int n, char ch)
   

   This method must use recursion to find and return the index of the nth occurrence of the character ch in the string str, or -1 if there are fewer than n occurrences of ch in str.

   For example, given the linked list s4 created in the example given above for the substring method:

   • nthIndexOf(s4, 1, 'l') should return 2, because the first occurrence of 'l' in "hello" has an index of 2.

   • nthIndexOf(s4, 2, 'l') should return 3, because the second occurrence of 'l' in "hello" has an index of 3.

   • nthIndexOf(s4, 3, 'l') should return -1, because there are not three occurrences of 'l' in "hello".

   The method should return -1 if str is null, or if n is less than or equal to 0.

Problem 7: Removing occurrences of an item from a list

18 points

Assume that we want list objects to support the following method:

boolean removeAll(Object item)

This method should take an arbitrary item, and it should removes all occurrences of that item from the list. If one or more occurrences of the item are removed, the method should return true. If there were no occurrences of the item to begin with, it should return false.

Create two implementations of this method: one as part of the ArrayList class, and one as part of the LLList class. Both classes can be found in the ps3_partII folder.

Important: For full credit, both methods should:

• run in O(n) time, where n is the number of items in the list
• use no more than a constant (O(1)) amount of additional memory.

In order to do so, your methods will need to manipulate the internals of the list (i.e., the underlying array or linked list) themselves, and they will need to do so as efficiently as possible.

In addition, you should make sure that your ArrayList version of the method doesn’t leave any extraneous references to objects in the items array. For example, let’s say that you have 9 items in the ArrayList. If a call to removeAll() removes 3 of them, you should end up with an array in which the first 6 elements hold references to actual items, and all of the remaining elements are null.

To facilitate testing, we have added a constructor to both classes that takes an array of type Object containing the initial contents of the list. Given these constructors, you can test your methods using examples that look like this:

String[] letters = {"a", "b", "c", "a", "c", "d", "e", "a"};
ArrayList list1 = new ArrayList(letters);
System.out.println(list1);
System.out.println(list1.removeAll("a"));
System.out.println(list1.removeAll("c"));
System.out.println(list1.removeAll("x"));
System.out.println(list1);

LLList list2 = new LLList(letters);
System.out.println(list2);
System.out.println(list2.removeAll("a"));
System.out.println(list2.removeAll("x"));
System.out.println(list2);

which should produce the following output:

{a, b, c, a, c, d, e, a}
true
true
false
{b, d, e}
{a, b, c, a, c, d, e, a}
true
false
{b, c, c, d, e}

Problem 8: Palindrome tester

12 points

A palindrome is a string like "radar", "racecar", and "abba" that reads the same in either direction. To enable longer palindromes, we can ignore spaces, punctuation, and the cases of the letters. For example:

"A man, a plan, a canal, Panama!"

is a palindrome, because if we ignore spaces and punctuation and convert everything to lowercase we get

"amanaplanacanalpanama"

which is a palindrome.

In the file Problem8.java that we’ve included in the ps3_partII folder, implement the static method called isPal() whose header we have provided. This method should take a String object as a parameter and determine if it is a palindrome, returning true if it is and false if it is not.

A string of length 1 and an empty string should both be considered palindromes. Throw an exception for null values.

Although this problem could be solved using recursion or an appropriately constructed loop that manipulates the String object directly, your method must use an instance of one or more of the following collection classes from the ps3_partII folder:

• ArrayStack
• LLStack
• ArrayQueue
• LLQueue

You must not use any other data structure, including arrays or linked lists other than the ones that are “inside” instances of the above collections. Rather, you should put individual characters from the original string into an instance of one or more of the above collections, and use those collection object(s) to determine if the string is a palindrome.

For full credit, you should:

• Write your method so that spaces, punctuation, and the cases of the letters don’t prevent a string from being a palindrome. To put it another way, make sure that your method only considers characters in the string that are letters of the alphabet and that it ignores the cases of the letters. See our example above.

• Make your method as efficient as possible. In particular:

  • You should perform only one iteration over the original String object. After that one iteration, any additional manipulations of the characters should be done using the collection object(s) that you have chosen to use.

  • You may not use the equals() method from the String class to compare two strings. Rather, you should only compare individual characters (i.e., individual values of type char) using the == operator.

  • More generally, because we want to avoid unnecessary scanning, you may not use any of the built-in String methods except charAt() and length().

Hints:

• When constructing the collection object(s) that you decide to use, you will need to specify the appropriate data type for the items in the collection. Because char values are primitives, you should use the corresponding “wrapper” class, which is called Character.

• You may also find it helpful to use the Character.toLowerCase() or Character.toUpperCase() method.

• char values are essentially integers, so you can compare them just as you would compare integers.

Submitting your work for Part II

You should submit only the following files:

• StringNode.java
• ArrayList.java
• LLList.java
• Problem8.java

You do not need to submit any of the other files.

Here are the steps:

1. Click on the name of the assignment in the list of assignments. You should see a pop-up window with a box labeled DRAG & DROP. (If you don’t see it, click the Submit or Resubmit button at the bottom of the page.)

2. Add all three files to the box labeled DRAG & DROP. You can either drag and drop the files from their folder into the box, or you can click on the box itself and browse for the files.

3. Click the Upload button.

4. You should see a box saying that your submission was successful. Click the (x) button to close that box.

5. The Autograder will perform some tests on your file. Once it is done, check the results to ensure that the tests were passed. If one or more of the tests did not pass, the name of that test will be in red, and there should be a message describing the failure. Based on those messages, make any necessary changes. Feel free to ask a staff member for help.

   Note: You will not see a complete Autograder score when you submit. That is because additional tests will be run later, after the final deadline for the submission has passed. For such problems, it is important to realize that passing all of the initial tests does not necessarily mean that you will ultimately get full credit on the problem. You should always run your own tests to convince yourself that the logic of your solutions is correct.

6. If needed, use the Resubmit button at the bottom of the page to resubmit your work. Important: Every time that you make a submission, you should submit all of the files for that Gradescope assignment, even if some of them have not changed since your last submission.

7. Near the top of the page, click on the box labeled Code. Then click on the name of each file to view its contents. Check to make sure that you see the code that you want us to grade.

Last updated on October 14, 2025.