CS 211: Computer Architecture, Spring 2024
Programming Assignment 1: Introduction to C (50 points)
Instructor: Prof. Santosh Nagarakatte
Due: February 9, 2024 at 5pm Eastern Time.
Introduction
The goal of this assignment is to get you started with programming in C, as well as compiling,
linking, running, and debugging. Your task is to write 5 small C programs. Your program must
follow the input-output guidelines listed in each section exactly, with no additional or missing
output. You can assume that we will provide well-defined test cases.
No cheating or copying will be tolerated in this class. If you use any large language models (LLMs)
such as ChatGPT/Bard/LLama or other models and as a result, your code is similar to another
student’s code in the class, it will be considered a violation of academic integrity. You should not
be using large language models to copy-paste your code. Your assignments will be automatically
checked with plagiarism detection tools that are pretty powerful. Hence, you should not look at your
friend’s code or copy-paste any code from LLMs or the Internet. See CS department’s academic
integrity policy at:
http://academicintegrity.rutgers.edu/
First: Is the Input a Product of 2 or 3 Given Numbers? (5 Points)
You have to write a program that given an array of integers determines if a particular integer input
being queried is a product of 2 or 3 numbers in the array. If it is such a product, then you have to
output yes. Otherwise, you will output no.
Input-Output format: Your program will take the file name as input. The first line in the input
file provides the total number of integers in the input array. The next line will provide the list of
these input integers. The third line in the input file provides the number of inputs queried. The
subsequent lines are the queries that will the provide the specific input and the number 2 or 3. For
example, if you have a query line of the form: 21 2, then you are checking if 21 is a product of 2
numbers from the input integer array. If so, output yes.
Here is a sample input file. Let us call file1.txt
5
3 7 8 11 17
4
21 2
12 2
1309 3
15 3
1
In the above file, the input array has 5 integers whose entries are 3, 7, 8, 11, and 17 respectively.
There are 4 queries being done. The first query asks if 21 is a product of 2 integers in the array.
The output is yes because 21 = 3 ∗ 7. In contrast, the answer is no for the query: 12 2. This is
because 12 is not a product of any two integers in the input array.
Your output will contain the same number of lines as the number of query lines in the input file.
Each line will either say yes if the corresponding input in the query is a product of the specified
numbers or no if the corresponding input is not a product of the specified numbers.
The sample execution is as shown.
$./first file1.txt
yes
no
yes
no
We will not give you improperly formatted files. You can assume that the files exist and all the
input files are in proper format as above. See the submission organization format at the end of the
assignment for more details.
Second: Ordered Linked List (10 points)
In this part, you have to implement a linked list that maintains a list of integers in sorted order.
For example, if a list already contains 2, 5 and 8, then 1 will be inserted at the start of the list, 3
will be inserted between 2 and 5 and 10 will be inserted at the end.
Input format: This program takes a file name as an argument from the command line. The file
contains successive lines of input. Each line contains a string, either INSERT or DELETE, followed
by a space and then an integer. For each of the lines that starts with INSERT, your program should
insert that number in the linked list in sorted order if it is not already there. Your program should
not insert any duplicate values. If the line starts with a DELETE, your program should delete the
value if it is present in the linked list. Your program should silently ignore the line if the requested
value is not present in the linked list. After every INSERT and DELETE, your program should print
the content of the linked list. The values should be printed in a single line separated by a single
space. There should be no leading or trailing white spaces in each line of the output. You should
print EMPTY if the linked list is empty.
Output format: At the end of the execution, your program should have printed the content of
the linked list after each INSERT or DELETE operation. Each time the content is printed, the values
should be on a single line separated by a single space. There should be no leading or trailing white
spaces in each line of the output.You should print EMPTY if the linked list is empty. You can assume
that there will be at least one INSERT or DELETE in each file.
2
Example Execution:
Lets assume we have 2 text files with the following contents:
file1.txt:
INSERT 1
INSERT 2
DELETE 1
INSERT 3
INSERT 4
DELETE 4
INSERT 5
DELETE 5
file2.txt:
INSERT 1
DELETE 1
INSERT 2
DELETE 2
INSERT 3
DELETE 3
INSERT 4
DELETE 4
INSERT 5
DELETE 5
Then the result will be:
$./second file1.txt
1
1 2
2
2 3
2 3 4
2 3
2 3 5
2 3
$./first file2.txt
1
EMPTY
2
EMPTY
3
EMPTY
4
EMPTY
5
EMPTY
3
Third: Matrix Exponentiation (10 points)
This program will test your ability to manage memory using malloc() and provide some experience
dealing with 2D arrays in C. Your task is to create a program that computes Mn where M is a
square matrix (the dimensions of the matrix will be k × k where k is the number of rows) and a
number n ≥ 0. In summary, you need to multiply the matrix with itself n times.
Input format: The program will take the file name as input. The first line in the file will provide
the number of rows in the matrix. The subsequent lines will provide the contents of the matrix.
The numbers are tab separated. The last line in the file after the contents of the matrix will contain
the exponent n. For example, a sample input file “file.txt”:
3
1 2 3
4 5 6
7 8 9
2
The first number (3) refers to the number of rows in the square matrix. The dimensions of the
matrix will be 3 × 3. The exponent is 2. Hence, the program is required to compute M2
. You can
assume that the input will be properly formatted. The output on executing the program with the
above input is shown below. The output numbers should be tab separated. There should not be
extra tabs or spaces at the end of the line or the end of the file.
30 36 42
66 81 96
102 126 150
Fourth: Binary Search Tree (10 Points)
You have to implement a binary search tree. The tree must satisfy the binary search tree property:
the key in each node must be greater than all keys stored in the left sub-tree, and smaller than all
keys in right sub-tree. You have to dynamically allocate space for each node and free the space for
the nodes at the end of the program.
Input format: This program takes a file name as an argument from the command line. The file
is either blank or contains successive lines of input. Each line starts with a character, either i’ or
’s’, followed by a tab and then an integer. For each line that starts with ’i’, your program should
insert that number in the binary search tree if it is not already there. If it is already present, you
will print ”duplicate” and not change the tree. If the line starts with a ’s’, your program should
search for the value.
Output format: For each line in the input file, your program should print the status/result of
the operation. For an insert operation, the program should print either “inserted” with a single
space followed by a number, the height of the inserted node in the tree, or ”duplicate” if the value
4
is already present in the tree. The height of the root node is 1. For a search, the program should
either print ‘’present”, followed by the height of the node, or “absent” based on the outcome of the
search.
Example Execution: Lets assume we have a file file1.txt with the following contents:
i 5
i 3
i 4
i 1
i 6
s 1
Executing the program in the following fashion should produce the output shown below:
$./eighth file1.txt
inserted 1
inserted 2
inserted 3
inserted 3
inserted 2
present 3
Fifth: Matrix Determinant(15 points)
In linear algebra, the determinant is a value that can be computed with a square matrix. The
determinant describes some properties about the square matrix. Determinants are used for solving
linear equations, computing inverses, etc, and is an important concept in linear algebra. In the
fifth part of the assignment, you will write a program that computes the determinant of any n × n
matrix. You will have to carefully manage malloc and free instructions to successfully compute
the determinants.
Determinant
Given a square n × n matrix M, we will symbolize the determinant of M as Det(M). You can
compute Det(M) as follows:
1×1 matrix The determinant of the 1 ×1 matrix is the value of the element itself. For example,
Det(

3

) = 3
2 × 2 matrix The determinant of a 2 × 2 matrix can be computed using the following formula:
Det(

a b
c d
) = ad − bc
5
For example,
Det(

1 2
3 4
) = 1 × 4 − 2 × 3 = 4 − 6 = −2
3 × 3 matrix The determinant of a 3 × 3 matrix can be computed modularly. First, let’s define
a 3 × 3 matrix:
M =


a b c
d e f
g h i
?**7;
?**9;
The formula for computing the determinant of M is as follows:
Det(M) = a × Det(Ma) − b × Det(Mb) + c × Det(Mc)
The matrix Ma is a 2 × 2 matrix that can be obtained by eliminating the row and column that a
belongs to in M. More specifically, since a is on the first row and first column, we eliminate the
first row and first column from M:


a b c
d e f
g h i
?**7;
?**9;
This gives us a 2 × 2 matrix for Ma:
Ma =

e f
h i
Mb can be computed similarly. Since b is on the first row and second column, we eliminate the first
row and second column from M:


a b c
d e f
g h i
?**7;
?**9;
This gives us a 2 × 2 matrix for Mb:
Mb =

d f
g i
Mc can be computed by removing the first row and the third column from M since c is on the first
row and third column. Thus,


a b c
d e f
g h i
?**7;
?**9;
Mc =

d e
g h
Finally, the formula for computing the determinant of M is:
Det(M) = a × Det(

e f
h i
) − b × Det(

d f
g i
) + c × Det(

d e
g h
)
6
For example, we can compute the determinant of the following matrix,
M =


2 7 6
9 5 1
4 3 8
?**7;
?**9;
as follows:
Det(M) = 2 × Det(

5 1
3 8
) − 7 × Det(

9 1
4 8
) + 6 × Det(

9 5
4 3
) = 2(37) − 7(68) + 6(7) = −360
n×n matrix Computing the determinant of an n×n matrix can be considered as a scaled version
of computing the determinant of a 3 × 3 matrix. First, let’s say we’re given an n × n matrix,
M =







x1,1 x1,2 x1,3 . . . x1,n
x2,1 x2,2 x2,3 . . . x2,n
x3,1 x3,2 x3,3 . . . x3,n
.
.
.
.
.
.
.
.
.
.
.
.
xn,1 xn,2 xn,3 . . . xn,n
?**7;
?**8;
?**8;
?**8;
?**8;
?**8;
?**9;
In essence, we have to pivot each element in the first row and create (n − 1) × (n − 1) matrix for
each pivot element (in the case of computing the determinant of 3 × 3 matrix, we had Ma that
corresponds to a, etc).
For example, when we pivot x1,1, we create the corresponding (n − 1) × (n − 1) matrix for x1,1 by
deleting the 1st row and 1st column:
M1,1 =







x1,1 x1,2 x1,3 . . . x1,n
x2,1 x2,2 x2,3 . . . x2,n
x3,1 x3,2 x3,3 . . . x3,n
.
.
.
.
.
.
.
.
.
.
.
.
xn,1 xn,2 xn,3 . . . xn,n
?**7;
?**8;
?**8;
?**8;
?**8;
?**8;
?**9;
=





x2,2 x2,3 . . . x2,n
x3,2 x3,3 . . . x3,n
.
.
.
.
.
.
.
.
.
xn,2 xn,3 . . . xn,n
?**7;
?**8;
?**8;
?**8;
?**9;
Similarly, we can create M1,2, M1,3, . . . by pivoting x1,2, x1,3, and so on:
M1,2 =







x1,1 x1,2 x1,3 . . . x1,n
x2,1 x2,2 x2,3 . . . x2,n
x3,1 x3,2 x3,3 . . . x3,n
.
.
.
.
.
.
.
.
.
.
.
.
xn,1 xn,2 xn,3 . . . xn,n
?**7;
?**8;
?**8;
?**8;
?**8;
?**8;
?**9;
=





x2,1 x2,3 . . . x2,n
x3,1 x3,3 . . . x3,n
.
.
.
.
.
.
.
.
.
xn,1 xn,3 . . . xn,n
?**7;
?**8;
?**8;
?**8;
?**9;
M1,3 =







x1,1 x1,2 x1,3 . . . x1,n
x2,1 x2,2 x2,3 . . . x2,n
x3,1 x3,2 x3,3 . . . x3,n
.
.
.
.
.
.
.
.
.
.
.
.
xn,1 xn,2 xn,3 . . . xn,n
?**7;
?**8;
?**8;
?**8;
?**8;
?**8;
?**9;
=





x2,1 x2,2 x2,4 . . . x2,n
x3,1 x3,2 x3,4 . . . x3,n
.
.
.
.
.
.
.
.
.
.
.
.
xn,1 xn,2 xn,4 . . . xn,n
?**7;
?**8;
?**8;
?**8;
?**9;
Finally, you can compute the determinant of M using the following formula:
Det(M) = x1,1×Det(M1,1)−x1,2×Det(M1,2)+x1,3×Det(M1,3)−x1,4×Det(M1,4)+x1,5×Det(M1,5). . .
7
The above formula can be shortened to the following formula:
Det(M) = Σn
i=1(−1)i−1x1,i × Det(M1,i)
This general formula for computing the determinant of n × n matrix applies to all n. The formula
for computing the determinant of 2 × 2 and 3 × 3 matrix is exactly the same as this formula.
Input-Output format:
Your program should accept a file as command line input. The format of a sample file test3.txt
is shown below:
3
2 7 6
9 5 1
4 3 8
The first number (3) corresponds to the size of the square matrix (n). The dimensions of the matrix
will be n x n. You can assume that n will not be greater than 20. The rest of the file contains the
content of the matrix. Each line contains a row of the matrix, where each element is separated by
a tab. You can assume that there will be no malformed input and the matrices will always contain
valid integers.
Your program should output the determinant of the n × n matrix provided by the file.
Example Execution
A sample execution with above input file test3.txt is shown below:
$./fifth test3.txt
-360
Structure of your submission folder
All files must be included in the pa1 folder. The pa1 directory in your tar file must contain 5
subdirectories, one each for each of the parts. The name of the directories should be named first
through fifth (in lower case). Each directory should contain a c source file, a header file (if you
use it) and a Makefile. For example, the subdirectory first will contain, first.c, first.h (if you create
one) and Makefile (the names are case sensitive).
pa1
|- first
|-- first.c
|-- first.h (if used)
|-- Makefile
|- second
|-- second.c
|-- second.h (if used)
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|-- Makefile
|- third
|-- third.c
|-- third.h (if used)
|-- Makefile
|- fourth
|-- fourth.c
|-- fourth.h (if used)
|-- Makefile
|- fifth
|-- fifth.c
|-- fifth.h (if used)
|-- Makefile
Submission
You have to e-submit the assignment using Canvas. Your submission should be a tar file named
pa1.tar. To create this file, put everything that you are submitting into a directory (folder)
named pa1. Then, cd into the directory containing pa1 (that is, pa1’s parent directory) and run
the following command:
tar cvf pa1.tar pa1
To check that you have correctly created the tar file, you should copy it (pa1.tar) into an empty
directory and run the following command:
tar xvf pa1.tar
This should create a directory named pa1 in the (previously) empty directory.
The pa1 directory in your tar file must contain 5 subdirectories, one each for each of the parts.
The name of the directories should be named first through fifth (in lower case). Each directory
should contain a c source file, a header file and a make file. For example, the subdirectory first will
contain, first.c, first.h and Makefile (the names are case sensitive).
AutoGrader
We provide a custom autograder to test your assignment. The custom autograder is provided as
pa1 autograder.tar. Executing the following command will create the autograder folder.
$tar xvf pa1_autograder.tar
There are two modes available for testing your assignment with the custom autograder
9
First mode
Testing when you are writing code with a pa1 folder
(1) Lets say you have a pa1 folder with the directory structure as described in the assignment.
(2) Copy the folder to the directory of the autograder (i.e., pa1 autograder)
(3) Run the custom autograder with the following command
$python3 pa1 autograder.py
It will run your programs and print your scores.
Second mode
This mode is to test your final submission (i.e, pa1.tar)
(1) Copy pa1.tar to the pa1 autograder directory
(2) Run the autograder with pa1.tar as the argument.
The command line is
$python3 pa1 autograder.py pa1.tar
Scoring
The autograder will print out information about the compilation and the testing process. At the
end, if your assignment is completely correct, the score will something similar to what is given
below.
You scored
5.0 in second
5.0 in fourth
5.0 in third
7.5 in fifth
2.5 in first
Your TOTAL SCORE = 25.0 /25
Your assignment will be graded for another 25 points with test cases not given to you
Grading Guidelines
This is a large class so that necessarily the most significant part of your grade will be based on
programmatic checking of your program. That is, we will build the binary using the Makefile and
source code that you submitted, and then test the binary for correct functionality against a set of
inputs. Thus:
• You should not see or use your friend’s code either partially or fully. We will run
state of the art plagiarism detectors. We will report everything caught by the
tool to Office of Student Conduct.
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• You should make sure that we can build your program by just running make.
• Your compilation command with gcc should include the following flags: -Wall -Werror
-fsanitize=address,undefined -g
• You should test your code as thoroughly as you can. For example, programs should not crash
with memory errors.
• Your program should produce the output following the example format shown in previous
sections. Any variation in the output format can result in up to 100% penalty. Be
especially careful to not add extra whitespace or newlines. That means you will probably not
get any credit if you forgot to comment out some debugging message.
• Your folder names in the path should have not have any spaces. Autograder will
not work if any of the folder names have spaces.
Be careful to follow all instructions. If something doesn’t seem right, ask on discussion forum.
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