Code Enhancements in merge_sort.py (#10911)

* Code Enhancements in merge_sort.py 

This enhanced code includes improved variable naming, error handling for user input, and more detailed docstrings. It's now more robust and readable.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>