Question

Write a Python module that solves a problem.

Answer 1

Sure! Let’s create a Python module that solves a common problem: calculating the nth Fibonacci number. The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1.

The nth Fibonacci number can be calculated using a few different methods, but for simplicity, we will implement an iterative approach as well as a recursive approach.

### Fibonacci Module

Here's how the Python module could look:

```python
# fibonacci.py

def fibonacci_iterative(n):
"""
Calculate the nth Fibonacci number using an iterative approach.

Args:
n (int): The index of the Fibonacci sequence.

Returns:
int: The nth Fibonacci number.

Raises:
ValueError: If n is less than 0.
"""
if n < 0:
raise ValueError("n must be a non-negative integer.")
elif n == 0:
return 0
elif n == 1:
return 1

a, b = 0, 1
for _ in range(2, n + 1):
a, b = b, a + b
return b

def fibonacci_recursive(n):
"""
Calculate the nth Fibonacci number using a recursive approach.

Args:
n (int): The index of the Fibonacci sequence.

Returns:
int: The nth Fibonacci number.

Raises:
ValueError: If n is less than 0.
"""
if n < 0:
raise ValueError("n must be a non-negative integer.")
elif n == 0:
return 0
elif n == 1:
return 1

return fibonacci_recursive(n - 1) + fibonacci_recursive(n - 2)

if __name__ == "__main__":
import sys

if len(sys.argv) != 3:
print("Usage: python fibonacci.py <method: iterative|recursive> <n>")
sys.exit(1)

method = sys.argv[1].lower()
n = int(sys.argv[2])

if method == "iterative":
result = fibonacci_iterative(n)
elif method == "recursive":
result = fibonacci_recursive(n)
else:
print("Unknown method. Choose either 'iterative' or 'recursive'.")
sys.exit(1)

print(f"The {n}th Fibonacci number is: {result}")
```

### How to use the module

1. Save the code above into a file named `fibonacci.py`.
2. Open a terminal or command prompt.
3. Navigate to the directory where `fibonacci.py` is located.
4. Execute the script using one of the following commands:

For the iterative approach:
```bash
python fibonacci.py iterative 10
```

For the recursive approach:
```bash
python fibonacci.py recursive 10
```

Replace `10` with any non-negative integer `n` to calculate the nth Fibonacci number.

### Explanation

- The module defines two functions: `fibonacci_iterative` and `fibonacci_recursive` which calculate the nth Fibonacci number using iterative and recursive methods, respectively.
- It checks that the input is valid (non-negative integer) and raises a `ValueError` for invalid inputs.
- When the module is run directly, it accepts command-line arguments to specify the method and the desired Fibonacci number index.

Feel free to modify or expand upon this module as needed!