algorithms-and-data-structures-report

Simple report that analyze insertion and quick sort, search tree, red-black tree, connected components and MST Prim.

The report is based on three exercises assigned by the Professor.

Exercise 1:

Write one or more Python programs to:

Generate a random array with suitable behaviour
Implement Insertion Sort algorithm
Implement Quick Sort or Merge Sort algorithm

Write a program that performs tests by measuring execution times of the previous algorithms on:

Sets of data of increasing size(array with 10,100,1000 ... data)
With randomly generated input data and sets of data that represent the best/worst cases for an algorithm

Exercise A:

We want to analyze the differences between Binary Search Trees and Red Black Trees To do this, we'll have to:

Write Python programs that implement RB tree from the BS tree's code that we saw during class.
- Probably the BS tree's implementation that we saw during class should be completed with missing methods or attributes
- For the RB trees is not mandatory to consider the deletion (insertion is mandatory)
Write the programs that execute some tests (experiments) that will help us to understand the advantages and disadvantages of BS trees

Exercise F:

Write the below programs to study the algorithm for finding the connected components:

Randomly generated graphs with an arbitrary nodes cardinality and a given probability of existance of edges(for example given a adj matrix with all zeros, change value to 1 with a given probability)
Randomly generated weighted graphs
Finding of connencted components
Prim's algorithm
Priority queue data structure (with min-hash)
A program that conducts experiment on random graphs with a growing dimension and edge presence

Heavily based on Introduction to Algorithms Third Edition, published by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.[CLRS] and Artificial Intelligence: A Modern Approach. For the Python code I was also inspired by the repository: aimacode.

Installation Guide

Navigate in the Anaconda Prompt and select your environment for example: conda activate pyenv

To download the repository:

git clone https://github.com/Filmon97/algorithms-and-data-structures-report.git

Then you need to install the basic dependencies to run the project on your system:

pip install -r requirements.txt

(This is only for me) To read the report you will need to fetch the LaTeX code from the overleaf repository (You don't have the creds):

cd algorithms-and-data-structures-report

git submodule init

git submodule update

Visual Studio Code

While you are in the Anaconda Prompt run:

code .

to open the project in Visual Studio Code

If you want to run the test suite:

pip install pytest

Then to run the tests:

pytest

Index of Algorithms

Here is a table of the implemented algorithms, the name of the implementation in the repository, and the file where they are implemented.

Name	File	Tests
`insertion_sort`	`sort.py`	Done
`quick_sort`	`sort.py`	Done
`insert`	`tree.py`	Done
`insert_fixup`	`tree.py`	Done
`find`	`tree.py`	Done
`inorder`	`tree.py`	Done
`tree_height`	`tree.py`	Done
`minimum`	`tree.py`	Done
`maximum`	`tree.py`	Done
`left_rotate`	`tree.py`	Done
`right_rotate`	`tree.py`	Done
`postorder`	`tree.py`	Done
`connected_components`	`graph.py`	Done
`mst_prim`	`graph.py`	Done

Index of Data Structures

Here is a table of the implemented data structures, the name of the implementation in the repository, and the file where they are implemented.

Name	File	Tests
`Node`	`tree.py`	Done
`BinarySearchTree`	`tree.py`	Done
`RedBlackTree`	`tree.py`	Done
`Graph`	`graph.py`	Done
`PriorityQueue`	`utils.py`	Done

filmon-arefayne / algorithms-and-data-structures-report