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[FEATURE REQUEST] Implement Heavy-Light Decomposition (HLD) for Efficient Tree Queries #6170

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@NithinU2802

Description

@NithinU2802

What would you like to Propose?

Description:
Implementation of Heavy-Light Decomposition (HLD), which is a powerful technique for efficiently processing path queries on trees. HLD allows operations like finding the maximum, sum, or updating values on a tree path in O(log N) time using segment trees.

Why is this needed?

  • Efficiently handles path queries (e.g., max/sum in path, LCA-based queries).
  • Optimizes tree traversal by decomposing it into heavy and light chains.
  • Reduces query complexity from O(N) to O(log N).

Proposed Solution:

  • Implement Heavy-Light Decomposition (HLD) in Java.
  • Use segment trees for efficient range queries.
  • Provide test cases to validate correctness.

Expected Outcome:
A fully functional HLD implementation in Java that can be used for tree-based queries in competitive programming and real-world applications.

Would love to contribute this feature! 🚀
Please refer to PR #6169 for the implementation. 😊

Issue details

Heavy-Light Decomposition (HLD) is a tree decomposition technique that enables efficient path queries (such as maximum, sum, and updates) and Lowest Common Ancestor (LCA) queries in O(log N) time.

Approach:

  1. DFS (Depth First Search) for Subtree Sizes - Calculate subtree sizes to determine the heavy child of each node.
  2. HLD Decomposition - Assign chain numbers to nodes. Keep heavy children in the same chain, and start a new chain for light children.
  3. Segment Tree - Store node values and support efficient path queries (max, sum, etc.).
  4. Query Execution - Move up chains and use the segment tree to get answers in O(log N).

Additional Information

Please let me know if any improvements are needed. 😊

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