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CS2040S: Data Structures and Algorithms
Problem Set 3

Collaboration Policy. You are encouraged to work with other students on solving these problems. However, you must write up your solution by yourself. We may, randomly, ask you
questions about your solution, and if you cannot answer them, we will assume you have cheated. In
addition, when you write up your solution, you must list the names of every collaborator, that is,
every other person that you talked to about the problem (even if you only discussed it briefly). You
can do so in Coursemology by adding a Comment. Any deviation from this policy will be considered
cheating, and will be punished severely, including referral to the NUS Board of Discipline.
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Problem 1. (The Sorting Detectives)
We have six impostors on our hands. Each claims to be Mr. QuickSort, the most popular
sorting algorithm around. However, only one of these six is telling the truth. Four of the other
five are just harmless imitators, Mr. BubbleSort, Ms. SelectionSort, Mr. InsertionSort, and
Ms. MergeSort. Beware, however, one of the impostors is not a sorting algorithm! Dr. Evil
maliciously returns unsorted arrays! And he won’t be easy to catch. He will try to trick you by
often returning correctly sorted arrays. Especially on easy instances, he’s not going to slip up.
Your job is to investigate, and identify who is who. Attached to this problem set, you will find
six sorter implementations: (i) SorterA.class, (ii) SorterB.class, (iii) SorterC.class, (iv)
SorterD.class, (v) SorterE.class, and (vi) SorterF.class.
These are provided in a single JAR file: Sorters.jar. Each of these class files contains a class
that implements the ISort interface which supports the following method:
public void sort(KeyValuePair[] array);
You can find the code for the KeyValuePair class attached as well. It is a simple container that
holds two integers: a key and a value. The sort routines will sort the array of objects by key.
You can test these sorting routines in the normal way: create an array, create a sorter object, and
sort. See the example file SortTestExample.java.
You can then use the StopWatch to measure how fast each of these sorting routines runs. Each
sorting algorithm has some inputs on which it is fast, and some inputs on which it is slow. Some
sorting algorithms are stable, while others are not. Using these properties, you can figure out the
real identities of the sorters, and also identify Dr. Evil.
Beware, however, that these characters can be deceptive. While they cannot hide their asymptotic
running time, they may well choose to run consistently slower than you expect. (For example, you
should not assume that QuickSort is always the fastest.) Evidence based on comparison of runtime
across different sorters will not be accepted. Only evidence based on asymptotic running time are
valid.
IntelliJ tips: Refer to setup.mp4 on Coursemology for instructions on setting up PS3 in IntelliJ.
Note: You are only allowed to modify SortingTester.java in your submission. Any modifications made to the other files provided (i.e., ISort.java, KeyValuePair.java, and StopWatch.java)
will not be accepted.
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Problem 1.a. Write a routine boolean checkSort(ISort sorter, int size) that runs a test
on an array of the specified size to determine if the specified sorting algorithm sorts correctly.
Problem 1.b. Write a routine boolean isStable(ISort sorter, int size) that runs a test
on an array of the specified size to determine if the specified sorting algorithm is stable.
Problem 1.c. Write whatever additional code you need in order to test the sorters to determine
which is which. All evidence you give below must rely on properties of the sorting algorithms, along
with data from your tests that supports your claim.
Problem 1.d. What is the true identity of SorterA? Give the evidence that proves your claim.
Problem 1.e. What is the true identity of SorterB? Give the evidence that proves your claim.
Problem 1.f. What is the true identity of SorterC? Give the evidence that proves your claim.
Problem 1.g. What is the true identity of SorterD? Give the evidence that proves your claim.
Problem 1.h. What is the true identity of SorterE? Give the evidence that proves your claim.
Problem 1.i. What is the true identity of SorterF? Give the evidence that proves your claim.
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