Newman Conway Sequence Iterative

This repository is part of the problem set and class activity for Algorithmic Approaches in Unit 4.

Learning Goals

• Practice converting recursive to iterative functions in Python
• Practice using memoization with Dynamic Programming

One-Time Activity Setup

Follow these directions once, at the beginning of the activity:

1. Navigate to the folder where you wish to save activities. This could be your projects folder, or you may want to create a new folder for all of your activities.

   If you followed Ada's recommended file system structure, you can navigate to your projects folder with the following command:

   $ cd ~/Developer/projects

   Or, if you want to create a new folder for all of your activities:

   $ cd ~/Developer
   $ mkdir activities
   $ cd activities

   If you've already created an activities directory, you can navigate to it with the following command:

   $ cd ~/Developer/activities

2. In Github click on the "Fork" button to fork the repository to your Github account. This will make a copy of the activity in your Github account.

3. "Clone" the activity into your working folder. This command makes a new folder named for the activity repository, and then puts the activity into this new folder.

   $ git clone <clone_url_for_the_activity>

   The <> syntax indicates a placeholder. You should replace <clone_url_for_the_activity> with the actual URL you'd use to clone this repository. If you click the green "Code" button on the GitHub page for this repository, you'll see a URL that you can copy to your clipboard.

   Use ls to confirm there's a new activity folder

4. Move your location into this activity folder

   $ cd <repository_directory>

   The <repository_directory> placeholder should be replaced with the name of the activity folder. If you're not sure what the folder is named, remember that you can use ls to list the contents of your current location.

5. Create a virtual environment named venv for this activity:

   $ python3 -m venv venv

6. Activate this environment:

   $ source venv/bin/activate

   Verify that you're in a python3 virtual environment by running:

   • $ python --version should output a Python 3 version
   • $ pip --version should output that it is working with Python 3

7. Install dependencies once at the beginning of this activity with

   # Must be in activated virtual environment
   $ pip install -r requirements.txt

   Not all activities will have dependencies, but there will still be an included requirements.txt file.

Summary of one-time activity setup:

• Fork the activity repository
• cd into your working folder, such as your projects or activities folder
• Clone the activity onto your machine
• cd into the folder for the activity
• Create the virtual environment venv
• Activate the virtual environment venv
• Install the dependencies with pip

Activity Development Workflow

1. When working on this activity, always ensure that your virtual environment is activated:

   $ source venv/bin/activate

2. If you want to work on another project from the same terminal window, you should deactivate the virtual environment when you are done working on the activity:

   $ deactivate

Classroom Activity

About the Newman-Conway Sequence

In this exercise we will write a method to model the Newman-Conway Sequence using iterative and dynamic programming.

The Newman-Conway Sequence is the one which generates the following values:

1 1 2 2 3 4 4 4 5 6 7 7 ….. by following the following formula:

P(1) = 1 P(2) = 1

for all n > 2:

P(n) = P(P(n - 1)) + P(n - P(n - 1))

In the live code, you were tasked with writing a recursive function. In this class Activity, you are tasked with writing a function which iteratively generates a list of the first N numbers of Newman-Conway's Sequence using Dynamic Programming (memoization).

Example 1:

Input: 5

Output: [1,1,2,2,3]

Example 2:

Input: 1

Output: [1]

Example 3:

Input: n = 3

Output: [1,1,2]

Running Tests

Use the tests provided in the test_newman_conway.py file to verify that your code is working correctly. You can verify the tests are working in one of two ways:

1. Run pytest in the terminal (make sure you are in the venv!)
2. Set up the testing environment in the VSCode Testing Pane
   1. Click on the beaker icon and click Configure Python Tests
   2. Select pytest from the list that appears
   3. Select tests from the new list that appears.
3. Verify the tests show up in the Testing Pane.
4. Run the tests to make sure they are all passing!