Add edge cases for equilibrium index

[NeuroByte79]

Describe your change

• Add an algorithm
• Fix a bug or typo in an existing algorithm
• Add or change doctests
• Documentation change

Added additional doctests for the equilibrium index function to improve edge-case coverage.

Changes

• Added single-element array test.
• Added all-zero array test.
• Added negative-elements array test.
• Added mixed positive and negative elements test.
• Documented time and space complexity.

Testing

• Ran the doctest suite successfully.
• All tests passed.

Checklist

• I have read 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.
• All new Python files are placed inside an existing directory.
• All filenames are in 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.
• All doctests pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.