[ENHANCEMENT] Add Wavelet Tree Data Structure

[space0032]

Description

This Pull Request introduces the Wavelet Tree data structure to the datastructures/trees package in the repository. A Wavelet Tree is a highly efficient and versatile data structure used for compressed storage of sequences and answering complex range-based queries in O(log U) time.

The main operations implemented are:

1. rank(x, i): Determines how many times the value x appears from the beginning of the array up to the index i.
2. kthSmallest(l, r, k): Finds the k-th smallest element in the subarray [l, r].

The functionality is generalized to handle large input arrays with an arbitrary range of values (minValue and maxValue).

Files Added

1. WaveletTree.java: Contains the implementation of the Wavelet Tree data structure.
2. WaveletTreeTest.java: Contains JUnit test cases to validate the correctness of the methods and handle edge cases.

Complexity

• Time Complexity:
  • Tree Construction: $O(N \log U)$, where $N$ is the length of the array and $U$ is the range of the values.
  • Query Operations: $O(\log U)$ per query.
• Space Complexity:
  • $O(N \log U)$ for storing the bit vectors.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 94.28571% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 79.61%. Comparing base (54341c1) to head (a497bfe).

Files with missing lines	Patch %	Lines
...healgorithms/datastructures/trees/WaveletTree.java	94.28%	0 Missing and 6 partials ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #7414      +/-   ##
============================================
+ Coverage     79.53%   79.61%   +0.07%     
- Complexity     7175     7217      +42     
============================================
  Files           798      799       +1     
  Lines         23474    23579     +105     
  Branches       4617     4639      +22     
============================================
+ Hits          18670    18772     +102     
  Misses         4055     4055              
- Partials        749      752       +3     

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[Copilot]

Pull request overview

This PR adds a new WaveletTree data structure under com.thealgorithms.datastructures.trees, providing rank, select, and kthSmallest (quantile) queries over an integer sequence, along with JUnit tests validating core behavior.

Changes:

• Introduces WaveletTree implementation with rank(x, i), select(x, k), and kthSmallest(l, r, k).
• Adds JUnit test suite covering typical cases, invalid inputs, empty/singleton arrays, and negative values.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 6 comments.

File	Description
src/main/java/com/thealgorithms/datastructures/trees/WaveletTree.java	Adds the Wavelet Tree implementation and query methods.
src/test/java/com/thealgorithms/datastructures/trees/WaveletTreeTest.java	Adds JUnit tests for rank/select/kthSmallest, including some edge cases.

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[space0032]

The merged file is not showing up in the repo