🔬 Finding the Longest Common Subsequence

✨ Table of Contents

• 🔬 Finding the Longest Common Subsequence
  • ✨ Table of Contents
  • ✨ Introduction
  • 👍 Seeking Assistance
  • ✈️ Project Overview
  • 🎉 Program Specification

✨ Introduction

If you are a student completing this project as part of a class at Allegheny College, you can check the schedule on the course website for the due date or ask the course instructor for more information about the due date or check the due date by clicking the appropriate box inside of this file. Please note that the content provided in the README.md file for this GitHub repository is an overview of the project and thus may not include the details for every step needed to successfully complete every project deliverable. This means that you may need to schedule a meeting during the course instructor's office hours to discuss aspects of this project.

👍 Seeking Assistance

Even though the course instructor will have covered all the concepts central to this project before you start to work on it, please note that not every detail needed to successfully complete the assignment will have been covered during prior classroom sessions. This is by design as an important skill that you must practice as an algorithm engineer is to search for and then understand and ultimately apply the technical content found in additional resources.

✈️ Project Overview

This project invites you to implement and use a program called lcsfinder that conducts an experiment to evaluate the performance of three different algorithms (i.e., recursive, dynamic, and calculate) that determine the longest common subsequence (LCS) of two strings that can contain either int or char data. The lcsfinder program should also include "timing instrumentation" that records the cost associated with the aforementioned algorithms for finding a longest common subsequence. For instance, the lcsfinder could use the timeit package to measure the performance of different LCS finding algorithms, following the pattern in the article measure execution time with timeit in Python. In summary, the specific algorithms and configurations that your lcsfinder program should evaluate include these and that you should experimentally evaluate with well-defined research questions are as follows:

• recursive LCS finder with both int and char data
• dynamic LCS finder with both int and char data
• calculate LCS finder with both int and char data

After cloning this repository to your computer, please take the following steps to get started on the project:

• To install the necessary software for running the lcsfinder program that you will create as a part of this project, you may consider installing and using the devenv tool, bearing in mind that it is not necessary for you to install the cachix program that may be referenced by these installation instructions. Please note that students who are using Windows 11 should first install Windows subsystem for Linux (wsl2) before attempting to install devenv. Once you have installed devenv and cloned this repository to your computer, you can cd into the directory that contains the pyproject.toml file and then type devenv shell. It is important to note that the first time you run this command it may complete numerous steps and take a considerable amount of time.
• Once this command completes correctly, you will have a Python development environment that contains a recent version of Python and Poetry! You can verify that you have the correct version of these two programs by typing:
  • python --version
  • poetry --version
• If you do not see a recent version of Python after typing the two aforementioned commands, then it is possible that some part of the installation process did not work correctly. If that occurs, then please read the following suggestions and talk with the course instructor and a student technical leader about what to do next.
• If some aspect of the installation with devenv did not work correctly, then please resolve what is wrong before proceeding further! Alternatively, you may install the aforementioned versions of Python and Poetry on your laptop using a tool like mise. With that said, please make sure that you use the most recent version of Python and Poetry to complete this project and, whenever possible, those versions match the ones chosen in GitHub Actions. This means that, to ensure that the results from running the experiments are consistent and, as best as is possible, comparable to the results from other computers, you should use exactly the same version of Python and Poetry on your laptop and in GitHub Actions. For instance, when you run lcsfinder in GitHub Actions, you should normally see that it is using at least Poetry version 2.0.0 and Python version 3.12.8.
• Before moving to the next step, you may need to again type poetry install in order to avoid the appearance of warnings when you next run the lcsfinder program. Now you can type the command poetry run lcsfinder --help and explore how to use the program.

🎉 Program Specification

Before implementing the program so that it adheres to the following requirements and produces the expected output, please note that the program will not work unless you add the required source code at the designated TODO markers. With that said, after you complete a correct implementation of all the lcsfinder's features you can run it with the command poetry run lcsfinder --algorithmtype dynamic --startsize 1 --runs 5 --datatype ints --strategy double and see that it produces output like the following. Please note that while the following example illustrates the type of output that the lcsfinder might produce it (a) may offer empirical results that are different than those that you see on your own laptop and (b) is only for a single example configuration for how you can run the lcsfinder program.

Benchmarking Tool for Finding the LCS

Type of list: dynamic
Data stored in list: ints
Benchmarking strategy: double
Number of runs: 5

Run 1 of 5 for dynamic algorithm using size  1 took  0.0000010220 seconds
Run 2 of 5 for dynamic algorithm using size  2 took  0.0000043790 seconds
Run 3 of 5 for dynamic algorithm using size  4 took  0.0000224020 seconds
Run 4 of 5 for dynamic algorithm using size  8 took  0.0007647710 seconds
Run 5 of 5 for dynamic algorithm using size 16 took  1.3258309710 seconds

Minimum execution time:  0.0000010220 seconds for run 1 with size 1
Maximum execution time:  1.3258309710 seconds for run 5 with size 16

Average execution time:  0.2653247090 seconds across runs 1 through 5

Some key aspects of the output that your implementation of the lcsfinder should preserve are as follows:

• The output should include diagnostic information that explains the type of algorithm (i.e., recursive or dynamic or calculate) and all the other command-line arguments that the user specified.
• The lcsfinder program should be able to automatically generate either char or int data. When it generates this data it must always ensure that the letters or the numbers that are generated according the constraints of a doubling experiment. This means that, for instance, it must always generate inputs that are of the size dictated by the current run of the doubling experiment.
• Although the lcsfinder program should be able to use a default strategy of a doubling experiment, you are also invited to implement and use additional strategies such as one that would increase the input size by an order of magnitude. With that said, please bear in mind the worst-case time complexity of the algorithms you are studying as you implement and run your benchmarks with the chosen strategy --- be careful, in particular, about the fact that some configurations of some algorithms may take a prohibitively long time to run!
• The output should have labels for each specific run that also shows the total number of runs requested by the user.
• Each line that shows a performance result should include the size of the input and then the amount of time in seconds that it took to perform the operation.
• The output should be formatted and justified so that it is easy to read, with numbers aligned to the right and with a consistent number of decimal places.
• After the display of the execution times that arise from each run of the benchmark, the output should show the minimum, maximum, and average execution time values across the runs of the benchmark.

Please note that your implementation of the lcsfinder program should work for all the specified experimental configurations in the introduction to the project and in the writing/reflection.md file. If you study the files in the lcsfinder/ directory you will see that they have many TODO markers that designate the functions you must implement so as to ensure that lcsfinder runs the desired experiment and produces the correct output. Once you complete a task associated with a TODO marker, make sure that you delete it and revise the prompt associated with the marker into a meaningful comment.

It is important to note that, at minimum, your experimentation with the lcsfinder must always operate according to the principles of a doubling experiment. This means that the lcsfinder must systematically increase the size of the instance of the str variables that are passed into the function that can find the longest common subsequence. Ultimately, you should design your own experiment and state and run experiments to answer your own research questions, focusing on these key issues to ensure that you meet the baseline requirements:

• If you have already installed the GatorGrade program that runs the automated grading checks provided by GatorGrader you can, from the repository's base directory, run the automated grading checks by typing gatorgrade --config config/gatorgrade.yml.
• You may also review the output from running GatorGrader in GitHub Actions.
• Don't forget to provide all the required responses to the technical writing prompts in the writing/reflection.md file.
• Please make sure that you completely delete the TODO markers and their labels from all the provided source code. This means that instead of only deleting the TODO marker from the code you should delete the TODO marker and the entire prompt and then add your own comments to demonstrate that you understand all the source code in this project.
• Please make sure that you also completely delete the TODO markers and their labels from every line of the writing/reflection.md file. This means that you should not simply delete the TODO marker but instead delete the entire prompt so that your reflection is a document that contains polished technical writing that is suitable for publication on your professional website.