dmo-test

A math problem, a solution in python

Setup

Clone the repository:

git clone [email protected]:pynchia/dmo-test.git

Descend into the main directory of the application:

cd dmo-test/

Create the python virtual environment:

python3 -m venv .venv

Activate the virtual environment:

. .venv/bin/activate

Upgrade pip:

pip install -U pip

Install the requirements:

the external packages first

pip install -r requirements.txt

and then the internal modules

pip install -e .

Execute the tests

pytest

Launch the application

The command

runme --help

shows the available options.

For example, the command

runme --size 100

calculates the steps it takes the cm sequence to converge to one for m in the range of 1 to 10

The application can also generate a diagram on file.

For example, the command

runme --size 100 --diagram

generates the file steps-100.png in the same directory

Notes

The application covers points b) and d) of the assignment, i.e.

b) Adapt the implementation to calculate the number of steps for each m ∈ [1, 10000].
d) Print the number of steps for each m ∈ [1, 10000] as diagram.`

Point a) is covered by specific tests and by the code that relies on it

a) Implement a program to calculate the number of steps to reach 1 the first time for any given m ∈ N .

Point c), i.e.

c) Try to improve the implementation to calculate the steps as fast as possbile.

is covered implicitly by the use of memoization

Of course the set of values for m could in principle be split into chunks and assigned to several processes.

For that purpose python's multiprocessing module would be a good candidate.

Nota Bene: threads are not useful when applied to computation intensive applications like this one, at least when using the standard CPython interpreter (due to the GIL).

Of course there may be a mathematical way to reduce the cm(n) sequence to a one-step calculation instead of having to iterate/recurse.

Unfortunately I am not Gauss and I hadn't much time to devote to that kind of solution, so I haven't even attempted to find a formula.

I hope my deliverables show the way I work as a software engineer.

I am available for any clarification.

Best regards,

Mauro Bertolotto Bianc