Fix: Binary Search Incorrect Output for Duplicates

Previously, the binary_search function returned any matching index when duplicates were present.

This change modifies the implementation to return the first occurrence of the target element.

Changes made:

• Introduced a result variable to track the first occurrence
• Continued searching in the left half after finding a match
• Updated final return to return result instead of immediate index

Example:

Input: [1, 2, 2, 2, 3], target = 2
Output (before): could be 1, 2, or 3
Output (after): 1 (first occurrence)

This resolves issue: #13840

Describe your change:

• 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".