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.