Adding doctests to improve Test Coverage for dynamic_programming/fibonacci.py

[Achintya47]

Describe your change:

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• Documentation change?

This PR significantly improves the Fibonacci dynamic programming implementation with:

Enhanced Documentation:

• Added comprehensive docstrings for class and all methods
• Included algorithm explanation with time/space complexity analysis
• Added Wikipedia reference for the Fibonacci sequence
• Improved inline comments and code structure

Comprehensive Doctests:

• Basic functionality tests for various sequence lengths (0, 1, 2, 5, 10, 15, 20)
• Edge case coverage (empty sequence, single element, negative indices)
• Error handling verification with proper exception messages
• Large number testing for performance validation
• Memoization verification to ensure efficiency
• Sequence correctness validation using mathematical properties

Code Improvements:

• Added input validation with descriptive error messages
• Implemented get_nth() method for single number retrieval
• Added reset() method for clearing memoized sequence
• Enhanced CLI with additional commands (help, reset)
• Improved error handling and user experience
• Better variable naming and code organization
• Fixed potential issues with edge cases

Test Coverage:

• Tests for all public methods
• Comprehensive edge case handling
• Error condition verification
• Performance and correctness validation
• Independent verification of all test cases

All doctests have been independently verified for correctness and pass when run locally.

Contributes to #9943

Checklist:

• I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md).
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html).
• All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue):

[bertrand-awz]

Suggested changes to pass the checking ruff.

[Achintya47]

Suggested changes to pass the checking ruff.

Thanks a lot for pointing it out , my first PR's so don't really know what ruff's trying to say. Appreciate it!

[bertrand-awz]

This check is repeated (98–100), I recommend creating a method that will be called to perform it.

[bertrand-awz]

This generation is repeated (lines 107–108), I recommend creating a method to generate the sequence.

[bertrand-awz]

Use the get_nth method here. result[-1] corresponds to the nth - 1 element of the Fibonacci sequence. See the image below:

Suggested change

	print(f"The {index}th Fibonacci number is: {result[-1]}")
	print(f"The {index}th Fibonacci number is: {fibonacci.get_nth(index)}")