Improve comments, docstrings in next_greatest_element.py

[JeevaRamanathan]

Describe your change:

The docstrings for all functions have been revised to provide more comprehensive explanations. These enhancements include detailed descriptions of the functions parameters, return values, and the time complexities associated with the algorithms they utilize.

• 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?

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. 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.
• All functions have doctests 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: "Fixes #ISSUE-NUMBER".

[tianyizheng02]

A few nitpicks, but otherwise looks good

[tianyizheng02]

LGTM, thanks for your fixes and for your contribution!