Feature/centroid decomposition

[saikirankanakala]

Description

Implements Centroid Decomposition for trees as requested in #7054.

Centroid Decomposition is a divide-and-conquer technique for tree data structures that recursively partitions trees by finding centroids - nodes whose removal creates balanced subtrees.

Changes

• Implement CentroidDecomposition with O(N log N) construction
• Add CentroidTree class with parent tracking and query methods
• Include buildFromEdges helper for easy tree construction
• Add comprehensive test suite with 20+ test cases
• Cover edge cases, validation, and various tree structures

Features

• Time Complexity: O(N log N) for construction
• Space Complexity: O(N)
• Applications: Distance queries, path counting, nearest neighbor searches
• Clean API with both edge list and adjacency list constructors
• Full Javadoc documentation with Wikipedia and tutorial references
• Robust input validation and error handling

Testing

• 20+ JUnit test cases covering:
  • Edge cases (single node, two nodes)
  • Common structures (linear, binary, star, complete trees)
  • Large trees (up to 10+ nodes)
  • Input validation (null checks, invalid edges, boundary conditions)
  • Centroid tree correctness verification

Closes #7054

---

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized it.
• All filenames are in PascalCase.
• All functions and variable names follow Java naming conventions.
• All new algorithms have a URL in their comments that points to Wikipedia or other similar explanations.
• All new code is formatted with standard Java formatting tools.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 93.65079% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 78.51%. Comparing base (fba6292) to head (bae00e4).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
...ms/datastructures/trees/CentroidDecomposition.java	93.65%	2 Missing and 2 partials ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #7086      +/-   ##
============================================
+ Coverage     78.46%   78.51%   +0.04%     
- Complexity     6745     6751       +6     
============================================
  Files           758      759       +1     
  Lines         22339    22402      +63     
  Branches       4384     4400      +16     
============================================
+ Hits          17529    17588      +59     
- Misses         4106     4108       +2     
- Partials        704      706       +2     

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[saikirankanakala]

Hi @DenizAltunkapan ,
All required checks have passed successfully, and the changes are ready from my end. The branch is also cleanly mergeable.

When you get a chance, please review and provide an approval so we can proceed with merging.
Thank you