Added Heavy-Light Decomposition (HLD) for Efficient Tree Queries

[NithinU2802]

Description:
This PR introduces an implementation of Heavy-Light Decomposition (HLD) in Java, enabling efficient path queries (such as maximum, sum, or updates) on a tree using segment trees. HLD reduces query time complexity from O(N) to O(log N) by decomposing the tree into heavy and light chains. Instead of traversing the whole tree (O(N)), we use HLD to jump chains and use segment trees for fast path queries in O(logN).

✅ Features:

1. Supports path queries (e.g., max in path, sum in path).
2. Uses segment trees for efficient range queries.
3. Optimized tree decomposition and traversal.

Example:
Consider the below Tree

       1 (10)
      /   \
   2 (20)  3 (30)
   /   \
4 (40)  5 (50)

Path Queries and Expected Results

1. Maximum in Path (4 → 5)
   Path: 4 → 2 → 5
   Values along the path: {40, 20, 50}
   Max Value: 50

2. Maximum in Path (3 → 4)
   Path: 3 → 1 → 2 → 4
   Values along the path: {30, 10, 20, 40}
   Max Value: 40

Note: Edges are added with indices to define the tree's structure, while node values are initialized separately. This separation allows for flexible updates and queries without altering the tree's topology, ensuring greater efficiency in handling updates and queries.

I have a strong passion for algorithms, particularly their efficiency, and am eager to contribute to this project. Let me know if any changes are needed! 🚀😊

• 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 clang-format -i --style=file path/to/your/file.java

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 74.12%. Comparing base (63ce6b8) to head (da15d6d).

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #6169      +/-   ##
============================================
+ Coverage     73.97%   74.12%   +0.14%     
- Complexity     5157     5191      +34     
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  Files           662      663       +1     
  Lines         17681    17771      +90     
  Branches       3407     3422      +15     
============================================
+ Hits          13079    13172      +93     
+ Misses         4097     4096       -1     
+ Partials        505      503       -2     

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[siriak]

The code looks good, please fix PR checks so that I could merge it

[siriak]

Looks good, thanks a lot for adding this!