Fibonacci Algorithms¶

Project Goals¶

This assignment invites you to implement a program that features multiple algorithms for computing the numbers in the Fibonacci sequence that is recursively defined by the following equations for the \(n\)-th Fibonacci number \(F(n)\).

This recursive definition of the Fibonacci sequences yields the values \(0, 1, 1, 2, 3, 5, \ldots\) where the value of any Fibonacci number, denoted \(F(n)\), is computed by adding together \(F(n-1)\) and \(F(n-2)\) and the other starting values are defined in the first two equations. Since there are different ways to compute the values in the Fibonacci sequence, this project invites you to implement and evaluate their performance.

Specifically, you will implement and experimentally evaluate the following Fibonacci algorithms: (i) a list-based approach that uses iteration, (ii) a list-based approach that uses recursion, (iii) a tuple-based approach that uses iteration, and (iv) a tuple-based approach using recursion. Along with adding source code to the provided Python files, you will conduct an experiment to determine which algorithm is the fastest and aim to understand why it is the best based on its choice of a data container (i.e., list or tuple) and its algorithmic approach (i.e., iterative or recursive).

Project Access¶

If you are a student enrolled in a Computer Science class at Allegheny College, you can access this assignment by clicking the link provided to you in Discord. Once you click this link it will create a GitHub repository that you can clone to your computer by following the general-purpose instructions in the description of the technical skills. Specifically, you will need to use the git clone command to download the project from GitHub to your computer. Now you are ready to add source code and documentation to the project!

Expected Output¶

This project invites you to implement a Python program, called fibonaccicreator, that features different ways to compute all of the numbers in the Fibonacci sequence up to a specified maximum number. After you finish a correct implementation of all the program's features, running it with the command poetry run fibonaccicreator --number 10 --approach recursivelist --display, it will produce output like the following.

🧳 Awesome, the chosen type of approach is the recursivelist!

🧮 The program will compute up to the 10th Fibonacci number!

✨ This is the output from the recursivelist function:

[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]

🤷 So, was this an efficient approach for storing the Fibonacci sequence?

Estimated overall memory according to the operating system:
   30.484375 megabytes

Estimated peak memory according to the operating system:
   38.78515625 megabytes

Estimated execution time according to the simple timer:
    0.01 seconds

This output shows that, for instance, the zeroth Fibonacci number is 0, the fifth Fibonacci number is 5, and the tenth Fibonacci number is 55. This program output also shows the amount of memory consumed by the recursive implementation of the Fibonacci calculation that stores the data in a list that contains 11 values in it. Importantly, this output also shows that, since the program had to compute so few of the numbers in the Fibonacci sequence, it did so in an amount of time that was not measurable by the program's execution timer. It is worth noting that if you run the fibonaccicreator to request a different data container and algorithm combination with a command like poetry run fibonaccicreator --number 10 --approach iterativetuple --display it should produce the same numbers in the Fibonacci sequence. With that said, remember that if you are running an experiment to evaluate the performance of fibonaccicreator when it computes a large Fibonacci number, you should not use the --display parameter since it will cause too much output to appear in your terminal window.

Don't forget that you can display fibonaccicreator's help menu and learn more about its features by typing poetry run fibonaccicreator --help to show the following output. This help menu shows that fibonaccicreator also has a --pyinstrument flag that enables it to produce a web-based output that shows the function calls made by the fibonaccicreator and the performance results created by the Pyinstrument package.

 Usage: fibonaccicreator [OPTIONS]

 Create the list of Fibonacci values in a specified approach.

╭─ Options ─────────────────────────────────────────────────────────────╮
│ *  --approach                TEXT                [default: None]      │
│                                                  [required]           │
│ *  --number                  INTEGER             [default: None]      │
│                                                  [required]           │
│    --display                                                          │
│    --pyinstrument                                                     │
│    --install-complet…        [bash|zsh|fish|pow  Install completion   │
│                              ershell|pwsh]       for the specified    │
│                                                  shell.               │
│                                                  [default: None]      │
│    --show-completion         [bash|zsh|fish|pow  Show completion for  │
│                              ershell|pwsh]       the specified shell, │
│                                                  to copy it or        │
│                                                  customize the        │
│                                                  installation.        │
│                                                  [default: None]      │
│    --help                                        Show this message    │
│                                                  and exit.            │
╰───────────────────────────────────────────────────────────────────────╯

Please note that the provided source code does not contain all of the functionality to produce the output displayed in this section. As the next section explains, you should add the features needed to ensure that fibonaccicreator produces the expected output!

Adding Functionality¶

If you study the file fibonaccicreator/fibonaccicreator/main.py you will see that it has many TODO markers that designate the parts of the program that you need to implement before fibonaccicreator will produce 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. To ensure that the program works correctly, you must implement all of these functions in the fibonacci module:

• def fibonacci_recursivelist(number: int) -> List[int]
• def fibonacci_recursivetuple(number: int) -> Tuple[int, ...]
• def fibonacci_iterativetuple(number: int) -> Tuple[int, ...]
• def fibonacci_iterativelist(number: int) -> List[int]

After finishing your implementation of fibonaccicreator you should conduct an experiment to evaluate the efficiency of the different algorithms that it provides. You should refer to the writing/reflection.md file for more details about the experiment that you should conduct and how you must configure the fibonaccicreator program to collect data. Ultimately, you need to answer the following three research questions:

• Is the fibonaccicreator faster when it uses the recursive or the iterative method?
• Is the fibonaccicreator faster when it stores data in a list or a tuple data container?
• Which configuration of the fibonaccicreator is the most memory efficient?
• Overall, what is the fastest approach for computing and storing the Fibonacci sequence?
• Overall, are there modes of the fibonaccicreator that are less suitable for Python?

Please note that there may be certain configurations of the fibonaccicreator program that prove to be very slow or prone to crashing if they receive certain types of inputs. This type of behavior is expected and something that you must investigate and work around whenever possible as you design and conduct your experiments. As you are collecting and analyzing the experimental results for this project, please do not report on performance data values that arise from a run of the program that crashed during the experiment.

Running Checks¶

If you study the source code in the pyproject.toml file you will see that it includes the following section that specifies different executable tasks like lint. If you are in the intersection directory that contains the pyproject.toml file and the poetry.lock file, the tasks in this section make it easy to run commands like poetry run task lint to automatically run all of the linters designed to check the Python source code in your program and its test suite. You can also use the command poetry run task fixformat to confirm that your source code adheres to the industry-standard format defined by the black tool. If it does not adhere to the standard then you can run the command poetry run black primality tests and it will automatically reformat the source code.

Along with running tasks like poetry run task lint, you can leverage the relevant instructions in the technical skills to run the command gatorgrade --config config/gatorgrade.yml to check your work. If your work meets the baseline requirements and adheres to the best practices that proactive programmers adopt you will see that all the checks pass when you run gatorgrade. You can study the config/gatorgrade.yml file in your repository to learn how the GatorGrade program runs GatorGrader to automatically check your program and technical writing. If your program has all of the anticipated functionality, you can run the command poetry run task test and see that the test suite produces output like the following. Can you add comments to the test suite to explain how the test cases work? It is worth noting that the name of the test suite is test_fibonacci because the functions mentioned in the previous section exist in the fibonacci module. Can you add comments to explain how these tests work? What are the key components of every test case created with Pytest?

collected 5 items

tests/test_fibonacci.py .....

This project comes with other tasks that you can run once you have used Poetry to install all of the dependencies. For instance, if you find that your Python source code is not in adherence with the required formatting rules, you can run poetry run task black to automatically return it to the correct format! You can also run commands like poetry run task mypy to check the program's use of data types and poetry run task pylint to ensure that your source code adheres to other established programming conventions. You can use these built-in tasks to understand and improve your code's quality!

Project Reflection¶

Once you have finished both of the previous technical tasks, you can use a text editor to answer all of the questions in the writing/reflection.md file. For instance, you should provide the output of the Python program in a fenced code block, explain the meaning of the Python source code segments that you implemented, and answer all of the other questions about your experiences in completing this project. A specific goal of the reflection for this project is to evaluate the efficiency of the different algorithms and data containers implemented as part of the fibonaccicreator program.

In addition to explicitly answering the aforementioned research questions, please make sure that you explain why the performance trends are evident in your data by referencing and explaining the source code that implements each of the algorithms implemented in the fibonaccicreator. Once you have finished addressing the prompts in the writing/reflection.md file that have TODO makers given as reminders, make sure that you either delete the prompt or carefully integrate a revised version of it into your writing.

Project Assessment¶

Since this project is an engineering effort, it is aligned with the evaluating and creating levels of Bloom's taxonomy. You can learn more about how a proactive programming expert will assess your work by examining the assessment strategy. From the start to the end of this project you may make an unlimited number of reattempts at submitting source code and technical writing that meet all aspects of the project's specification.

Seeking Assistance¶

Emerging proactive programmers who have questions about this project are invited to ask them in either the GitHub discussions forum or the Proactive Programmers Discord server. Before you ask your question, please read the advice concerning how to best participate in the Proactive Programmers community. If you find a mistake in this project, please describe it and propose a solution by creating an issue in the GitHub Issue Tracker.