Add RandomizedClosestPair Algorithm and Unit Tests

[aditya-7562]

Summary

Added Randomized Closest Pair of Points algorithm under the randomized category as per issue #6219.
This algorithm efficiently finds the minimum Euclidean distance between any two points in a 2D plane using a randomized divide-and-conquer approach.

Randomized Algorithm Approach

• Randomly shuffle the input points to avoid worst-case input ordering.
• Use a divide-and-conquer strategy by recursively splitting the point set.
• Maintain sorted orders in both x and y dimensions to allow efficient scanning.
• Construct a strip of points near the midline and examine only candidates within distance d.
• Return the minimum distance found among all point pairs.

Time Complexity

• Expected Time: O(n log n)
• Worst-Case Time: O(n log n)

Use Cases

• Geospatial clustering and mapping
• Nearest-neighbour search in 2D space
• Computational geometry in:
  • Robotics
  • Simulations
  • Computer graphics and game engines

Checklist

• I have read CONTRIBUTING.md
• This pull request is entirely my work (no plagiarism)
• All filenames follow PascalCase convention
• All function and variable names follow Java naming conventions
• A reference to Wikipedia is included in the class-level Javadoc
• Code has been formatted using:
  clang-format -i --style=file path/to/your/file.java

[codecov-commenter]

Codecov Report

❌ Patch coverage is 93.47826% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 74.41%. Comparing base (58ac54c) to head (88608f6).
⚠️ Report is 393 commits behind head on master.

Files with missing lines	Patch %	Lines
...healgorithms/randomized/RandomizedClosestPair.java	93.47%	2 Missing and 1 partial ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #6339      +/-   ##
============================================
+ Coverage     74.36%   74.41%   +0.04%     
- Complexity     5403     5419      +16     
============================================
  Files           680      681       +1     
  Lines         18842    18888      +46     
  Branches       3656     3665       +9     
============================================
+ Hits          14012    14055      +43     
- Misses         4274     4276       +2     
- Partials        556      557       +1     

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[aditya-7562]

👋 Hi maintainers,

I wanted to clarify that this PR has multiple commits because I’m a first-time contributor to this repository and was learning the contribution and CI process along the way.

I’ve since cleaned up the implementation, removed the private constructor test due to CodeQL/Infer warnings, and ensured the code follows all formatting, naming, and coverage guidelines. The Infer job is currently failing due to an OCaml dependency conflict (camlzip = 1.12), which appears unrelated to the actual code changes.

All required tests pass, and the patch coverage is above 93%. Please let me know if you'd prefer that I squash the commits or make any other changes.

Thank you for your time and for maintaining this amazing repository! 🙏

[siriak]

Looks good, thanks for contributing!