Fibonacci

This Python program calculates the Fibonacci number at a given position using matrix exponentiation, which makes it efficient for large inputs.

How it Works

The program consists of two main functions: fibonacci(n) and main().

fibonacci(n)

This function calculates the Fibonacci number at position n. It uses a 2x2 matrix [[1, 1], [1, 0]], which is raised to the power of (n-1) using numpy's linalg.matrix_power function. If n is 0, the function returns 0. Otherwise, it returns the element at position [0][0] of the resulting matrix, which is the Fibonacci number at position n.

main()

This function is the entry point of the program. It prompts the user to enter a positive integer, which is passed to the fibonacci(n) function. The function measures the execution time of the fibonacci(n) function and stores the result.

The result, along with the execution time, is then written to a file named "result.txt". If the file already exists, the program asks the user if they want to overwrite it. If the user answers anything other than "y", the program terminates.

How to Run

To run the code in this repository, follow these steps:

Open a terminal or command prompt and navigate to the project directory.
If the venv directory doesn't exist in the project's root directory, create a virtual environment by running the following command:
```
python -m venv venv
```
Activate the virtual environment by running the following command:
```
venv\Scripts\activate
```

You should see (venv) at the beginning of your command prompt, indicating that the virtual environment is active.

Once the virtual environment is activated, run the code using the following command:
```
python -m test
```

This command will execute the test module, which corresponds to the test.py file in the project directory.

After running the code, you can deactivate the virtual environment by running the following command:
```
venv\Scripts\deactivate
```

This will return you to your normal command prompt.

Note: Make sure you have the necessary dependencies installed in your virtual environment before running the code. If you encounter any missing dependencies, you can install them using pip install <package-name> while the virtual environment is active.

Dependencies