Fix: incorrect output for Binary Search with duplicate elements #13840

[sreejabavandla]

Fix incorrect output for Binary Search when list contains duplicates (Fixes #13840)

Describe your change:

Fixed a bug in the binary search algorithm that caused incorrect output when the list contained duplicate elements.

• Updated the condition to correctly return the index of the first matching element.
• Ensured the loop continues searching the left half when a duplicate is found.
• Verified behavior with lists containing multiple identical values.

• [ ] Add an algorithm?
• [x] Fix a bug or typo in an existing algorithm?
• [ ] Add or change doctests?
• [ ] Documentation change?

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 function 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.
• [ ] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. (Not applicable here)
• [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".

[prsai0110]

Hi! Thanks for reviewing. Please let me know if any changes are needed. I’ve followed the contributing guidelines and added doctests. Looking forward to feedback!