Minimal Spanning Tree (MST) using Prim's Algorithm

The assignment requires designing and implementing a program based on a greedy algorithm to solve the Minimal Spanning Tree (MST) problem. The program should implement Prim's algorithm with different data structures, such as two-dimensional arrays representing weight matrices or adjacency lists and heaps. Additionally, the program should include a brute force search algorithm for comparison purposes. The assignment also requires analyzing the efficiency of the algorithms and generating graphs to test the program.

Data Structures and Algorithms
Objectives
Design and implement a program based on a greedy algorithm to solve the Minimal Spanning
Tree (MST) problem;
Choose and implement appropriate data structures for the algorithm;
Analyse the efficiency of different implementations of the algorithm in comparison with the
brute force algorithm.
Task
You should write a single program which implements Prim’s algorithm with different data structures,
as well as the brute force search algorithm, to find the MST of an undirected, connected, weighted
graph.
Program
Your program should read a symmetric matrix from a text file that describes weighted edges of an
undirected, connected graph and find the MST that is saved in an output file as a sequence of edges of
the MST. The program also displays the numbers of vertices and edges in the graph and the time spent
to find its MST for each data structure used in Prim’s and the brute force search algorithms, which can
be saved in another output file as well for your later analysis.
Your program should only measure the time spent by the algorithm with its data structure to find the
MST so that it is a proper design to use one method/function to implement an algorithm and its
associated data structure. For an algorithm that operates on a weight matrix, it takes the weight matrix
stored in a two-dimensional array as its parameter; for an algorithm that operates on adjacency lists, it
takes adjacency lists you created from the weight matrix. You may create your own list data structures
based on arrays. No STL or Java Collection or other collection framework can be used. In the part of
the algorithm implementation, you should not use any library functions including maximal or minimal
functions but create your own functions to operate on arrays.
Your program should be readable and well commented.
In addition, you needs to create a small program or script to generate the weight matrix for a graph of
various vertices and edges, saved to a text file. When you create graphs, you need consider the density
and connectivity of graphs. You may use a program/script by other people, with reference to the
source, to generate these matrices.

Data Structures and Algorithms
Brute force search algorithm
The algorithm operates on a two-dimensional array that represents the weight matrix.
Prim’s algorithm
The algorithm operates on one of the following data structures:
1. two-dimensional array that represents the weight matrix and unordered arrays;
2. adjacency lists and heaps.
Requirements
(10 marks)
1. Program
Implement the brute force search algorithm and Prim’s algorithm operating on two data
structures: matrix and heaps. (2 marks for each)
2. Report
a. Cover page
Student name
Subject code
Student number
Email ID
(0 mark; your assignment will not be marked if there is not this section)
b. Introduction (around 200 words)
Describe application scenarios where the MST is applied and identify one application
as the background and purpose of your experiments. You should interpret well the
meanings of the vertices and edge weights, and why it is an MST problem in your
identified application. Cite at least three references. (1 mark)
c. Methods (around 300 words)
Describe algorithms you used in your experiments and data you used to produce the
results. (1 mark)
d. Result analysis (no more than 600 words)
Analyse the time complexity of your algorithms and discuss your results. You need to
produce results with substantial differences in time spent for each algorithm and data
structure. You should use at least one plot to present the results in terms of time spent
and graph sizes. (2 marks)
e. Conclusion (around 50 words)
Summarise your findings and interpretations.
(0 mark; -1 mark if there is not this section)
f. References
(0 mark; -1 mark if there is not this section; -0.5 marks for each improper reference)
Other requirements
You must cite references from academic sources. Internet URLs including Wiki pages are not
generally acceptable except they are used for links to resources.
All your programs including scripts will have the following header:

Your programs can be compiled and executed with bash scripts called a3compile and
a3run, respectively, on Ubuntu setup in the lab.
o The script a3run should be configured to run for a small graph that can finish
within a fraction of a second.
o The script should be configurable to run for a graph of any size.
o The script can execute a program/script to generate the matrix before execute your
MST
program.
o Failure to compile and run your program to produce results from your scripts will
receive 0 mark.
Write a text file named readme to explain how your matrix is created, special
consideration of your program compilation and execution, or any information related to your
program that is necessary to configure and run your program to produce the results in your
report. All your results reported in the report must be possibly produced by your submitted
programs with easy configuration described in the readme file.
Report, named report.pdf, is created in the PDF format.
Failure to meet any requirements above may result in loss of marks.
Submission instructions
Your completed assignment should contain your source code including all programs and
scripts, readme and report.pdf in a zipped file named ass3.zip. You should not include
any graph matrices in the submission. In this assignment, all input files will be generated by your
program/scripts.
To submit your assignment, transfer your ass3.zip file to banshee and run the
command:
turnin -c csci203 -a 3 ass3.zip
from the directory containing your file.
1. Late submissions will be marked with a 25% deduction for each day.
2. Submissions more than three days late will not be marked, unless an extension has been
granted.
3. If you need an extension apply through SOLS, if possible before the assignment deadline.
4. Plagiarism is treated seriously. Use of code not created by you without citation is plagiarism.
If we suspect any work is copied, all students involved are likely to receive zero for the entire
assignment.