Wavelet Trees: An Elegant Approach to Rank Queries on Sequences

This blog post introduces the Wavelet Tree, an elegant data structure for answering rank queries on sequences over large alphabets. Achieving a time complexity of O(log₂A) (where A is the alphabet size), it organizes a string into a hierarchy of bit vectors. The post details Wavelet Tree construction and querying, highlighting optimization techniques using RRR structures or other binary rank indexes for compression and speed. An implementation in Francisco Claude's Compressed Data Structure Library (libcds) is recommended for practical application.