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Intersection Algorithms

Intersection Algorithms

Project Goals

This assignment invites you to implement a program that features multiple algorithms for computing the intersection between a data container. Specifically, you will implement and experimentally evaluate the following intersection algorithms: (i) a list-based approach with a single for loop, (ii) a list-based approach with a double for loop, (iii) a tuple-based approach with a single for loop, and (iv) a tuple-based approach with a double for loop. In addition to adding source code to the provided Python files, you will conduct an experiment to determine which algorithm is the fastest and estimate by how much it is faster. As you enhance your technical skills and explore the experimental evaluation of algorithms, you will continue to program with tools such as VS Code and a terminal window and the Python programming language and the Poetry package manager.

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 data container intersection problem called intersection. After you finish a correct implementation of all the program's features, running it with the command poetry run intersection --number 10000 --maximum 25 --profile --approach ListDouble will produce output like the following. This output shows that it took approximately 2.210 seconds to compute the intersection of two lists that each contain 10,000 randomly generated values with the maximum value in each list being 25. Importantly, this invocation of the intersection program configures it to run the ListDouble algorithm that uses a doubly-nested for loop to compute the intersection of the lists. Did you notice that this program produces profiling data about how long it took to run the intersection program with the ListDouble algorithm? This is because of the fact that it uses the Pyinstrument package to collect execution traces and efficiency information about the program.

🔬 Here's profiling data from computing an intersection with random data
containers of 10000!

  _     ._   __/__   _ _  _  _ _/_   Recorded: 14:01:19  Samples:  2207
 /_//_/// /_\ / //_// / //_'/ //     Duration: 2.211     CPU time: 2.203
/   _/                      v4.0.3

Program: intersection --number 10000 --maximum 25 --profile --approach ListDouble

2.210 intersection  intersection/
└─ 2.210 compute_intersection_list_double  intersection/
   ├─ 2.051 [self]
   └─ 0.159 list.append  <built-in>:0
         [2 frames hidden]  <built-in>

It is worth noting that you do not have to run intersection in the profile mode that uses Pyinstrument. For instance, running the program with poetry run intersection --number 10 --maximum 25 --display --approach ListDouble would run the program with the ListDouble algorithm and perform the same computation without collecting the performance data. When run with this command, intersection would produce output like the following. Note that when the program is run with the --display flag and without the --profile flag it shows the two input data containers and their computed intersection — without reporting any details about the efficiency of the algorithm. This mode is ideal when you want to confirm that your implementation of intersection is perform the correct computation and less useful when you are running experiments to study the program's performance.

✨ Here are the details about the intersection computation!

Performed intersection with:
---> the first data container: [22, 10, 21, 11, 2, 7, 4, 16, 22, 23]
---> the second data container: [16, 17, 23, 24, 12, 4, 21, 1, 18, 19]
Computed the intersection as the data container: [21, 4, 16, 23]

Don't forget that you can display intersection's help menu and learn more about its features by typing poetry run intersection --help to display the following:

Usage: intersection [OPTIONS]

  Compute the intersection of data containers.

  --number INTEGER                [default: 5]
  --maximum INTEGER               [default: 25]
  --profile / --no-profile        [default: False]
  --display / --no-display        [default: False]
  --approach [ListSingle|TupleSingle|ListDouble|TupleDouble]
                                  [default: TupleSingle]
  --install-completion            Install completion for the current

  --show-completion               Show completion for the current shell,
                                  to copy it or customize the

  --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 explained in the next section, you are invited to add the features needed to ensure that intersection produces the expected output!


Don't forget that if you want to run the intersection program you must use your terminal window to first go into the GitHub repository containing this project and then go into the intersection directory that contains the project's source code. Finally, remember that before running the program you must run poetry install to add its dependencies, such as Pyinstrument, Pytest, and Rich.

Adding Functionality

If you study the file intersection/intersection/ you will see that it has many TODO markers that designate the parts of the program that you need to implement before intersection will produce correct output. To ensure that the program works correctly, you must implement all of these functions before you start to run the experiments.

  • def generate_random_container(size: int, maximum: int, make_tuple: bool = False) -> Union[List[int], Tuple[int, ...]]
  • def compute_intersection_list_double(input_one: List[Any], input_two: List[Any]) -> List[Any]
  • def compute_intersection_list_single(input_one: List[Any], input_two: List[Any]) -> List[Any]

The function called generate_random_container should automatically create either a tuple or a list of the specified size and only containing values that are less than or equal to the maximum. The function called compute_intersection_list_single should follow the implementation strategy of its counterpart function called compute_intersection_tuple_single while still using the functions appropriate for the list structured type. Moreover, the compute_intersection_list_double should follow the implementation of compute_intersection_tuple_double except for the fact that it should populate an list through the use of a doubly-nested for loop. As a reference, here is the source code for the compute_intersection_tuple_single function:

def compute_intersection_tuple_single(
    input_one: Tuple[Any, ...], input_two: Tuple[Any, ...]
) -> Tuple[Any, ...]:
    """Compute the intersection of two provided tuples."""
    result: Tuple[Any, ...] = ()
    for element in input_one:
        if element in input_two:
            result += (element,)
    return result

According to the type signature of this function on lines 1 and 2, the compute_intersection_tuple_single function accepts as input two tuples that can contain Any type of data and be of an arbitrary size. Lines 6 through 8 of this function show that it uses the combination of a for loop and an if statement to compute the intersection of the tuples called input_one and input_two. After finding those elements that these tuples contain in common, compute_intersection_tuple_single returns the result on line 9. Since this function processes tuples it is possible that the intersection of the input parameters will be a result that contains a value more than once. It is also worth noting that, since the tuple structured type is immutable, this function uses the += operator on line 8 to create a new tuple each time that it adds data to the result variable. You will empirically study the efficiency of this approach!

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

  • Is the intersection of two data containers faster with a list or a tuple?
  • Is the intersection of two data containers faster with a double or single for loop?
  • Overall, what is the fastest approach for computing the intersection of two data containers?

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 black 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 task fixformat and it will automatically reformat the source code. Make sure to examine the pyproject.toml file for other convenient tasks that you can use to both check and improve your project!

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?

collected 4 items

tests/ .......

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!


Don't forget that when you commit source code or technical writing to your GitHub repository for this project, it will trigger the run of a GitHub Actions workflow. If you are a student at Allegheny College, then running this workflow consumes build minutes for the course's organization! As such, you should only commit to your repository once you have made substantive changes to your project and you are ready to confirm its correctness. Before you commit to your GitHub repository, you can still run checks on your own computer by using Poetry and GatorGrader.

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/ 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 intersection program. When you are writing your performance evaluation make sure that you both explain what performance trends are evident and why you think the algorithms yield these trends. Finally, you should reflect on how the experimental evaluation of a program's performance is more nuanced than you might have initially expected before starting to work on this project.

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.


Before you finish all of the required deliverables required by this project is worth pausing to remember that the instructor will give advance feedback to any learner who requests it through GitHub and Discord at least 24 hours before the project's due date! Seriously, did you catch that? This policy means that you can have a thorough understanding of ways to improve your project before its final assessment! To learn more about this opportunity, please read the assessment strategy for this site.

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.

Updated: 2023-02-10   Created: 2021-08-12
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