# Makeup Exam 1: ADTs, Algorithms, and Object-Oriented Design

Assigned
Wednesday, 3 April 2019
Due
Thursday, 11 April 2019
Submitting
See the instructions below.

This examination is now released. You may not discuss it with anyone (other than Samuel A. Rebelsky).

## Preliminaries

Some students did not seem to understand the level of detail and correctness I expect on my exams. So, in spite of my general “no makeups” policy, I am giving a makeup exam for exam 1. Each problem replaces the corresponding problem number on exam 1. That is, problem 1 on the makeup will replace problem 1 on exam 1, problem 2 on the makeup will replace problem 2 on exam 1, and so on and so forth. You may choose to do as many or as few problems as you would like. In each case, I will take the higher of the original grade for that problem number and the replacement grade.

Any code that deviates significantly from the Google Java Style Guidelines (e.g., that uses a tab or four spaces as the indent or that uses a capital letter to name a method or variable) will receive a zero. Any utility code that includes a print statement will receive a zero.

My grading of the makeup problems will likely be more cursory than my grading of the original exam. In particular, I am likely to run unit tests and base my grade primarily on the results of those tests.

### Exam Format

This is a take-home examination. You may use any time or times you deem appropriate to complete the exam, provided you return it to me by the due date.

This is a makeup examination. There will not be a further makeup for missed problems on the examination.

I expect that someone who has mastered the material and works at a moderate rate should have little trouble completing the exam in a reasonable amount of time. In particular, this exam is likely to take you about six hours (plus time for the prologue and epilogue), depending on how well you’ve learned the topics and how fast you work. (When I do the problems, I will report how long each one took me.)

### Prologue

This examination has a required prologue that must be completed by 10:30 p.m. on Friday, 5 April 2019. The prologue is intended to help you get started thinking about the examination. Failure to turn in the prologue by the deadline will result in a zero on the makeup.

Send a message to rebelsky@grinnell.edu entitled CSC 207 Makeup 1 Prologue (Your Name), substituting your name for “Your Name”. In that message, include the following.

A. An approach that you expect to help you succeed on the exam. Some answers from the past: Review the outlines, Start early, Get enough sleep, Work on it a little each day, Identify questions and email them to Sam. You can use one of these or, better yet, you can come up with one on your own.

C. A time estimate for how long it will take you to solve each problem.

### Epilogue

This examination has an epilogue that must be completed by 5pm on Friday, 12 April 2019. The epilogue is intended to help you reflect carefully on the examination. The epilogue is required. Failure to turn in the epilogue will result in a zero on the makeup.

Send a message to rebelsky@grinnell.edu entitled CSC 207 Makeup 1 Epilogue (Your Name), substituting your name for “Your Name”. In that message, include the following.

A. For each problem, (a) indicate how long you spent on the problem, (b) describe the key ideas that the problem explored, (c) describe any challenges you faced on the problem, and (d) compare your estimate to your actual time spent and indicate what might account for the disparity.

B. Suggest an approach that will make you more successful on the next examination.

This examination is open book, open notes, open mind, open computer, and open Web. However, it is closed person. That means you should not talk to other people about the exam. Other than as restricted by that limitation, you should feel free to use all reasonable resources available to you.

As always, you are expected to turn in your own work. If you find ideas in a book or on the Web, be sure to cite them appropriately. If you use code that you wrote for a previous lab or homework, cite that lab or homework and the other members of your group. If you use code that you found on the course Web site, be sure to cite that code. You need not cite the code provided in the body of the examination.

Although you may use the Web for this exam, you may not post your answers to this examination on the Web. (You certainly should not post them to GitHub unless you create a private repository for your exam.) And, in case it’s not clear, you may not ask others (in person, via email, via IM, via IRC, by posting a “please help” message, or in any other way) to put answers on the Web.

Because different students may be taking the exam at different times, you are not permitted to discuss the exam with anyone until after I have returned it. If you must say something about the exam, you are allowed to say “This is among the hardest exams I have ever taken. If you don’t start it early, you will have no chance of finishing the exam.” You may also summarize these policies. You may not tell other students which problems you’ve finished. You may not tell other students how long you’ve spent on the exam.

You must include both of the following statements on the cover sheet of the examination.

• I have neither received nor given inappropriate assistance on this examination.
• I am not aware of any other students who have given or received inappropriate assistance on this examination.

Please sign and date each statement. Note that the statements must be true; if you are unable to sign either statement, please talk to me at your earliest convenience. You need not reveal the particulars of the dishonesty, simply that it happened. Note also that inappropriate assistance is assistance from (or to) anyone other than Professor Rebelsky (that’s me). Presenting Your Work

You must present your exam to me in two forms, physically and electronically. If you fail to turn in both versions, you are unlikely to receive credit for the examination.

Physical copy: You must write all of your answers using the computer, print them out (you need only print the files you’ve changed), put them in order by problem, number the pages; put your name on the top of every page, write, sign, and date each of the academic honesty statements (provided you are able to do so); and hand me the printed copy or put it under my office door. If you fail to name and number the printed pages, you may suffer a penalty. If you fail to turn in a legible version of the exam, you are also likely to suffer some sort of penalty.

Electronic copy: You must also submit an electronic copy of your exam. You should create the electronic version by making a tarball of any relevant code and emailing me the tarball. Here are the steps for making a tarball.

• Within Eclipse, rename the project by replacing the “Your Name” in “Makeup 1 (Your Name)” to your name.
• Switch to the parent directory of your exam directory.
• Rename the directory containing your makeup examination from username-makeup-01 by replacing username with your username. For example, mine would be called rebelsky-makeup-01.
• Issue the command “tar cvzf username-makeup-01.tgz username-makeup-01”, except you should replace username with your username.
• Make sure that the tar file contains the appropriate contents using the command “tar tf username-makeup-01.tgz” (once again, substitute your own username). For example, if I were to check my tarball, I might see something like the following. (Note: To make things easier, I have allowed you to include .class files.)
$tar tf rebelsky-makeup01.tgz rebelsky-makeup-01/ rebelsky-makeup-01/.classpath rebelsky-makeup-01/.project rebelsky-makeup-01/bin/ rebelsky-makeup-01/src/ rebelsky-makeup-01/src/problem1/ rebelsky-makeup-01/src/problem2/ rebelsky-makeup-01/src/problem3/ rebelsky-makeup-01/src/problem4/ rebelsky-makeup-01/src/utils/ rebelsky-makeup-01/src/utils/TestUtils.java rebelsky-makeup-01/src/problem4/Directory.java rebelsky-makeup-01/src/problem4/Entry.java rebelsky-makeup-01/src/problem3/LinkedStack.java rebelsky-makeup-01/src/problem3/Node.java rebelsky-makeup-01/src/problem2/Experiment.java rebelsky-makeup-01/src/problem2/QuicksortDNF.java rebelsky-makeup-01/src/problem1/Example1.java rebelsky-makeup-01/src/problem1/Example2.java rebelsky-makeup-01/src/problem1/FilteredIterator.java rebelsky-makeup-01/bin/problem1/ rebelsky-makeup-01/bin/problem2/ rebelsky-makeup-01/bin/problem3/ rebelsky-makeup-01/bin/problem4/ rebelsky-makeup-01/bin/utils/ rebelsky-makeup-01/bin/utils/TestUtils.class rebelsky-makeup-01/bin/problem4/Directory$1.class
rebelsky-makeup-01/bin/problem4/Directory\$2.class
rebelsky-makeup-01/bin/problem4/Directory.class
rebelsky-makeup-01/bin/problem4/Entry.class
rebelsky-makeup-01/bin/problem3/Node.class
rebelsky-makeup-01/bin/problem2/Experiment.class
rebelsky-makeup-01/bin/problem2/QuicksortDNF.class
rebelsky-makeup-01/bin/problem1/Example1.class
rebelsky-makeup-01/bin/problem1/Example2.class
rebelsky-makeup-01/bin/problem1/FilteredIterator.class


Code: In many problems, I ask you to write code. Unless I specify otherwise in a problem, you should write working code and include examples that show that you’ve tested, or at least experimented with, the code.

Documentation: You should document classes, interfaces, fields, and methods using Javadoc-style comments. You should specify preconditions and postconditions for each method.

Care: Just as you should be careful and precise when you write code and documentation, so should you be careful and precise when you write prose. Please check your spelling and grammar. Since I should be equally careful, the whole class will likely receive one point of extra credit for each error in spelling or grammar you identify on this exam. I will limit that form of extra credit to five points.

Partial credit: I may give partial credit for partially correct answers. I am best able to give such partial credit if you include a clear set of work that shows how you derived your answer. You ensure the best possible grade for yourself by clearly indicating what part of your answer is work and what part is your final answer.

### Getting Help

I may not be available at the time you take the exam. If you feel that a question is badly worded or impossible to answer, note the issue you have observed and attempt to reword the question in such a way that it is answerable. You should also feel free to send me electronic mail at any time of day.

I will also reserve time at the start of each class before the exam is due to discuss any general questions you have on the exam.

### Unit tests

I will distribute unit tests on Saturday, after I have received the prologues. You will have the option of installing them in your project.

### Obtaining the exam code

You can download a tarball of the starter code for the examination. You can unpack that file with “tar xvzf username-makeup-01.tgz”.

Once you have downloaded the code, you should import that top-level directory into Eclipse. You should see a project named “Makeup 1 (Your Name)”.

## Problems

### Problem 1: Filtered iterators

This problem is a makeup for the tests of the average method. However, the content has no conceptual relation to that previous problem.

Your classmates, Ida, Rae, Tor, Phil, and Ted, have enjoyed many aspects of object oriented design, but also like to think functionally. They’ve started to look at approaches to working with iterators. Recalling the introduction to lambdas, they start to think about iterators and predicates, and ways to print out all the values for which a predicate holds. For example,

package problem1;

import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;
import java.util.function.Predicate;

/**
* An example of iteration and filtering with predicates.
*/
public class Example1 {
public static void main(String[] args) throws Exception {
PrintWriter pen = new PrintWriter(System.out, true);
Integer[] values = new Integer[] {1, 2, 3, 4, 5, 6, 7, 8};
Iterator<Integer> it = Arrays.asList(values).iterator();
Predicate<Integer> even = (i) -> (i % 2) == 0;

while (it.hasNext()) {
Integer i = it.next();
if (even.test(i)) {
pen.println(i);
} // if
} // while

pen.close();
} // main(String[])
} // class Example1


As in the lambda tutorial, they’ve decided they want to think a bit more about the design, this time using a bit more of an object-oriented design approach. In particular, Ida, Rae, Tor, Phil, and Ted suggest that we create a class that they call FilteredIterator, which incorporates the predicate more directly in the iterator.

package problem1;

import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;

/**
* An example of iteration and filtering with predicates.
*/
public class Example2 {
public static void main(String[] args) throws Exception {
PrintWriter pen = new PrintWriter(System.out, true);
Integer[] values = new Integer[] {1, 2, 3, 4, 5, 6, 7, 8};
Iterator<Integer> fit =  new FilteredIterator<Integer>(
Arrays.asList(values).iterator(), (i) -> (i % 2) == 1);

while (fit.hasNext()) {
Integer i = fit.next();
pen.println(i);
} // while

pen.close();
} // main(String[])

} // class Example2


Unfortunately, they are struggling to figure out the details. They’ve created a template, but need someone else to fill in the details. Do so.

import java.util.Iterator;
import java.util.function.Predicate;

/**
* Iterators that filter elements that meet a predicate.
*
* @author Samuel A. Rebelsky
*/
public class FilteredIterator<T> implements Iterator<T> {
// +--------+------------------------------------------------------
// | Fields |
// +--------+

/**
* The underlying iterator.
*/
Iterator<T> iterator;

/**
* The predicate used to filter the iterator.
*/
Predicate<T> pred;

// +--------------+------------------------------------------------
// | Constructors |
// +--------------+

/**
* Create an iterator that filters the elements of iter using
* pred.
*/
public FilteredIterator(Iterator<T> iter, Predicate<T> pred) {
this.iterator = iter;
this.pred = pred;
} // FilteredIterator(Iterator<T>, Predicate<T>)

// +---------+-----------------------------------------------------
// | Methods |
// +---------+

/**
* Get the next value for which the predicate holds.
*
* @pre this.hasNext()
* @post pred.test(result) hold
*/
public T next() {
return this.iterator.next();
} // next()

/**
* Determine if there are any more values for which the predicate
* holds.
*/
public boolean hasNext() {
return this.iterator.hasNext();
} // hasNext()

/**
* Remove the most recent value returned by next.  If the preconditions
* are not met, throws an IllegalStateException.
*
* @pre There has been at least one call to this.next()
* @pre There have been no calls to this.remove() or this.hasNext()
*      since the last call to this.next()
*/
public void remove() {
throw new IllegalStateException("Not yet implemented.");
} // remove()
} // FilteredIterator


As you can tell, they’ve made a slight, but important, modification to the semantics of remove. They’ve decided that remove can throw an IllegalStateException if (a) the next method has not yet been called, (b) the remove method has already been called after the last call to the next method, or (c) the hasNext method has been called after the last call to the next method. (There’s a subtle reason to add the third case.)

Note that you do not need to explicitly indicate that remove might throw an IllegalStateException because those are a form of runtime exception. Not also that you do not need to worry about throwing a ConcurrentModificationException.

### Problem 2: Dutch national Quicksort

This problem is a makeup for the average method. The primary relationship of this problem to that problem are that both work with arrays.

Quinn and Sorrell are a bit frustrated by our current implementation of Quicksort. They say “Quicksort seems to do a lot of extra work when the pivot appears multiple times in the array. Why can’t we just group all of the elements equal to the pivot together, and only recurse on the values that are strictly smaller and strictly larger?”

Duff, Nat, and Fran say “That seems to be a task for the Dutch National Flag algorithm, which can partition an array into three sections: red, white, and blue, or, in this case, smaller, equal, and larger.”

Write a version of Quicksort that uses this approach. That is, it should partition the array into three parts and only recurse on the left and right subparts.

You may find it difficult to make the partition process a separate method, since, in addition to rearranging the items in the subarray, it now has to “return” two values: the lower bound and upper bound of the middle part of the subarray. That means that you should move the partitioning process into the middle of Quicksort.

Note: If you’ve forgotten, we sketched a version of the Dutch National Flag algorithm in class 20.

This problem is a makeup for the problem on sorted linked priority queues. Like that problem, it asks you to deal with linked structures, including iteration of those structures. It also asks you to do a bit more with iteration state.

Linus and Stacy have enjoyed our work with linked structures, and think we should continue that work. “We’ve done linked queues and linked priority queues, but it looks like we should implement stacks, too. That will give us a chance to play more with iterators.” Your instructor, Hugh DeWitt, suggests that Linus and Stacy have already one enough with linked structures, and perhaps it should be your turn. He asks that you implement linked stacks, which should have push, pop, top, isEmpty, isFull, and iterator methods. Stack iterators should iterate the stack from top to bottom. Your iterators must support the next, hasNext, and remove methods.

Ann, O, and Ying pipe up saying “We haven’t followed the full specifications for iterators. Aren’t iterator methods supposed to throw more than just IllegalStateExceptions in certain circumstances?” Hugh DeWitt agrees, and says that you should implement the more general expected behavior of iterators.

In particular, in addition to having your remove method throw an IllegalStateException if there has not been an appropriate prior call to next, you should also ensure that all of the iterator methods throw a ConcurrentModificationException if the stack has been modified by anything other than their iterator since the iterator was created. For example, if we create an iterator for a stack and then call push or pop on the underlying stack, requests to next or hasNext or remove in that iterator should throw a ConcurrentModificationException. Similarly, if we create two iterators for the same stack and call remove in one of them, that iterator should continue to work as expected, but the other iterator should throw a ConcurrentModificationException.

Fortunately, Hal and Phil have an idea for detecting modification. They suggest that a simple strategy is to have a counter associated with the stack and with each iterator. When you create an iterator, you copy the counter from the stack. Each time you modify the stack, you increment the stack’s counter. If you modify the stack with an iterator, you also increment the iterator’s counter. When any method in the iterator is called, you compare the counter in the iterator to the counter in the stack and throw an exception if they do not match.

### Problem 4: Array-based directories

This problem is a makeup for the problem on array-based queues. Like that problem, it asks you to deal with iteration in an array-based structure. The order of elements is a bit different in this problem, and you do not need to handle wraparound. However, you will have to worry about ordering and searching.

Dora, Ric, and Tori have decided that they want to to implement a data structure (or perhaps an ADT) that associates screen names and real names. They note that “although each person may have multiple screen names, there is only one real name per screen name”.

After consulting with the rest of the class, they decide that their structure, which they’ve decided to call a Directory, should have the following methods.

• set(String screen, String real) - Sets the real name associated with a screen name. If the screen name is already in the directory, updates it. If the screen name is not already in the directory, it adds it.
• get(String screen) - Gets the real name given a screen name. Throws an exception if their is no real name associated with the screen name.
• screenNames() - returns an iterator for the screen names that presents them in alphabetical order.
• realNames() - returns an iterator for the real names with an unspecified order.

Soren and Ted, think that we should store directory entries (basically, screen name/real name pairs) alphabetically by screen name. That way, it’s easy to iterate in alphabetical order. After their experience with sorted linked priority queues, they suggest that we might be better off using arrays, particularly because we can then use binary search for get.

Implement the Directory structure as a sorted array. Your get method should be O(log2n). Your set method should be O(log2n) if the screen name is already in the directory but can be O(n) if the screen name is not in the directory. If the array is not big enough, you will need to expand the array. When you expand, you should double the size.

Fortunately, Ann, O, and Ying are not in class during this discussion, so no one suggests that you need to worry about ConcurrentModificationExceptions. However, you do still need to worry about IllegalStateExceptions (and about the remove method).

Here you will find the questions students ask along the way and any answers I provide to those questions.

### Problem 1

It feels like I have to call the underlying iterator’s next within hasNext. Won’t I lose that value?

Not if you keep track of it.

### Problem 2

What should we use as the pivot?

I’m happy if you use the middle element of the subarray. You can also choose to use a randomly selected element, the median of three, or whatever else you think is reasonable.

### Problem 4

Do we have to implement remove?

Yes. For both iterators.

Where do we implement binary search?

In the find method.

Can we make the set method O(n log2 n)?

Nope. It should be no more than O(n), and it should be O(log2 n) it the screen name is already in the directory.

What is the hardest part of this problem?

In my case, it was getting binary search right so that I knew where to either look or shift from.

## Errata

Here you will find corrections to the examination, each of which earns everyone a modicum of extra credit (until a cap of five points is reached).

1. In the LinkedStack class, the isEmpty method appears as

public boolean isEmpty() {
return this.top != null;
} // isEmpty()


It should be

public boolean isEmpty() {
return this.top == null;
} // isEmpty()