Fix: Binary search first occurrence and add property-based tests

[tusharynayaka]

Description of Change
Updated the binary search algorithm to return the first occurrence of an item when duplicates exist in the collection, rather than returning any random occurrence.
Added a check to see if the element immediately to the left of the found midpoint is also the target item.
If it is, the search continues to the left side to find the true first index.
Updated doctests to verify this behavior.

Checklist:
[x] I have read CONTRIBUTING.md.
[x] This pull request is all my own work -- I have not plagiarized.
[x] I know that pull requests will not be merged if they fail the automated tests.
[x] This PR only changes one algorithm file.
[x] All filenames are in all lowercase characters with no spaces or dashes.
[x] All functions and variable names follow Python naming conventions.
[x] All function parameters and return values are annotated with Python type hints.
[x] All functions have doctests that pass the automated testing.
[x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: Fixes #13840

[tusharynayaka]

All CI checks are now passing. I have updated binary_search.py to return the first occurrence of an item as requested and resolved the unrelated Ruff/Mypy linting errors in jump_search.py, hash_table_with_linked_list.py, and linear_discriminant_analysis.py that were blocking the build. Ready for final review

[OliCheesman]

Hi @tusharynayaka. Do you know if this project is still active? Will your code be reviewed soon?

[tusharynayaka]

Hi @tusharynayaka. Do you know if this project is still active? Will your code be reviewed soon?

@OliCheesman
Ig this is still active...
I tried to fix the bugs in the same whether it will be reviewed or not I am unsure ..... but really hope it gets reviewed and it passes all test cases....

[tusharynayaka]

Applied the feedback from the previous thread. Tests are passing and I'm ready for a final sign-off to get this merged.