Description
Question 1
Consider the following algorithm:
Algorithm 1: Mystery(A, n)
Input : Array A of n numbers a0, · · · an−1 with n ≥ 1
Output: See question (a) below
1 if n = 1 then
2 Print the message ”Mystery solved”
3 else
4 j ← 1
5 while j ≤ n − 1 do
6 if aj−1 > aj then
7 swap aj−1 and aj
8 Print n, j, and the array elements
9 j ← j + 1
10 Mystery(A, n-1)
(a) Using A = (9,5,11,3,2) as the input array, hand-trace Mystery, showing the output.
(b) Determine the running time T(n) as a function of the number of comparisons made on line
6, and then indicate its time and space efficiency (i.e., O and Ω bounds).
(c) Determine the running time T(n) as a function of the number of swaps made on line 7,
and indicate its time and space efficiency.
(d) Suggest an improvement, or a better algorithm altogether, and indicate its time and space
efficiency. If you cannot do it, explain why it cannot be done?
(e) Can Mystery be converted into an iterative algorithm? If it cannot be done, explain why;
otherwise, do it and determine its running time complexity in terms of the number of
comparisons of the array elements.
Question 2
For each of the following pairs of functions, either f(n) is O(g(n)), f(n) is Ω(g(n)), or f(n) is
Θ(g(n)). For each pair, determine which relationship is correct. Justify your answer.
# f(n) g(n)
(a) 4n log n + n
2
log n
(b) 8 log n
2
(log n)
2
(c) log n
2 + n
3
log n + 3
(d) n
√
n + log n log n
2
(e) 2
n + 10n 10n
2
(g) log2 n log n
(h) n log2 n
(i) √
n log n
(j) 4
n 5
n
(k) 3
n n
n
2 COMP 352
2 Programming Problem (50 marks)
The researchers at a medical center wish they had taken a computer programming course way
back when they were at medical school. These days, in addition to attending their research, they
find themselves entangled with having to learn the R and Python languages in order to wrangle,
visualize and model data collected from patients.1,2 They simply have no time and no patience
for R or Python! So they have decided to hire you as a programmer to assist, providing you with
a bit of background information and a clear description of your task.
The researchers have discovered that, when certain cells are introduced into a new environment,
the cells quickly form colonies. To study the effectiveness of a drug they are developing, they
need to figure out the size and number of the colonies in the environment. Fortunately, they can
map the environment onto a grid of 0s and 1s that might, for example, look something like this:
0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1
1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1
0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1
1 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0
0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1
The locations on the grid each have a row and a column coordinates. A 1 or 0 at a location
indicates, respectively, the presence or absence of a cell at that location. Colonies are formed
by neighboring cells. Two cells are considered neighbors, if their locations are adjacent either
horizontally, vertically, or diagonally. Thus, the maximum number of neighbors a cell can have
is 3 for a corner cell, 5 for a cell on a single border, and 8 for a cell not on the borders. Given
this background information, you are tasked with developing a ColonyExplorer program that
explores and labels the colonies (if any). For example, using the grid above, your ColonyExplorer
should produce the following information:
– – – A A – A A – – – B B B – C C C – C
D – – – – A – – – A – – – – – C C C C C
– D – – A – – – A – A – – – – – – C C C
D D D – – A – A – – – – E – C C – C C –
– D D D – A A A – F – – E – C – C C – C
A: 14
B: 3
C: 20
D: 8
E: 2
F: 1
The information shows that there are six colonies
labeled A, B, C, D, E, and F on the grid with size
14, 3, 20, 8, 2, and 1, respectively.
1Why being a programmer will make me a better doctor
25 Reasons Some Doctors are Learning to Code
3 COMP 352
2.1 Requirements
(a) In this programming assignment, you will be developing your ColonyExplorer program
(i.e., class) in two versions.
Both versions must implement an algorithm named ExploreAndLabelColony.
In version 1 of ColonyExplorer, the ExploreAndLabelColony algorithm is recursive.
In version 2 of ColonyExplorer, the ExploreAndLabelColony algorithm is non-recursive.
This version is allowed to use a linear data structure such as a stack, queue, list, or vector.
Both versions are required to be designed in pseudo code and implemented in Java.
(b) Starting from a given location on the grid, ExploreAndLabelColony explores the grid,
expanding and labeling all of the cells in a single colony originating from the starting
location. Taking as input a grid, the coordinates of a starting location, and a label,
ExploreAndLabelColony will either label that location and all its neighbors or do nothing,
depending on the presence or absence of a cell at the given location, respectively; either
way, ExploreAndLabelColony is required to return the size of the labeled colony.
(c) ColonyExplorer is responsible for ensuring that ExploreAndLabelColony is called starting at every location on the grid storing a 1. The reason is that ExploreAndLabelColony
locates only a single colony.
For example, using the first grid above and calling ExploreAndLabelColony for the first
time on the location at the top row and forth column will modify the grid only at the
locations labeled A, leaving all the other locations intact.
Once every grid location storing a 1 has been colonized, ColonyExplorer freezes the grid
by replacing the 0s on the grid with s (dashes) .
(d) ColonyExplorer is responsible for creating an initial grid of random number of rows and
columns in the range [5-20], and for filling the grid randomly with 0s and 1s.
(e) ColonyExplorer is responsible for generating the labels for ExploreAndLabelColony to
use during exploration. Use the alphabet letters A · · · Z and a · · · z as labels (in that order).
For simplicity, cycle through and reuse the same labels if necessary.
(f) Briefly explain the time and memory complexity for both versions of ExploreAndLabelColony.
Write your answers in a separate file and submit it together with the other programming
submissions.
For version 1, describe the type of recursion used in your implementation and its time and
memory complexity? Justify your answer. Also explain whether a tail-recursive version is
possible. If yes, you can earn bonus marks by submitting such a version.
For version 2, justify your choice of the particular data structure and why you chose it over
the other available structures (e.g., why you chose a stack and not a queue, etc.). Explain
whether your choice has an impact on the time and memory complexity.
(g) For each version provide test logs for at least 20 different initial grid configurations.
3 Deliverables
In this assignment, the programming question can be done in a team of two, if you wish. However,
the theory questions must be completed and submitted individually.
3.1 Answers to Theory Questions
For all questions, including the programming questions, the parts that require written answers,
pseudo-code, graphs, etc., you can express your answers into any number of files of any format,
including image files, plain text, hand-writing, Word, Excel, PowerPoint, etc.
However, no matter what program you are using, you must convert each and every file into a
PDF before submitting. This is to ensure the markers and you have exact same view of your
work regardless of the original file formats.
Whether or not you are in a team, you must each submit a copy of your written answers.
3.2 Solutions to Programming Question
Developing your programming work using a Java IDE such as NetBeans, Eclipse, etc., you are
required to submit the project folder(s) created by your Java IDE, together with any input files
used and output files produced by your program(s).
If you are in a team, you must to submit only ONE copy of your program project folders(s) and
input/output files.
3.3 What and How to Submit
1. Letting the # character denote the assignment number, create a folder as follows:
(a) If you are working individually, name your folder A# studentID, where studentID
denotes your student ID. Then, copy the PDF files you prepared for the theory questions together with your project folder(s) and input/output files to the A# studentID
folder.
(b) If you are working in a team, name your folder A# studentID1 studentID2, where
studentID1 denotes the ID number of the student who is responsible for submitting
the programming solutions for both of you, and studentID2 denotes the ID number
of the other team member. Then, the student whose ID number is studentID1 must
follow item (a), as if she/he completed the programming question individually. The
other team member must also follow item (a) above, but she/he must NOT include
the team’s programming solutions.
2. Compress the folder you created in (1) into a zip file with the same name as that of the
folder being compressed.
3. Upload the compressed file you created in item (2) to Moodle.
3.4 Last but not Least
To receive credit for your programming solutions, you must demo your program to your
marker, who will schedule the date and time for the demo for you (please refer to the course
outline for full details). If working in a team, both members of the team must be present
during the demo. Please notice that failing to demo your programming solution will result
in zero mark regardless of your submission.
