If you're a competitive programmer, you've probably heard of a variety of data structures such as binary search trees, heaps, and segment trees. But have you ever heard of the Chtholly tree? This unique data structure was invented by Ghost_Dragon and has gained popularity for its efficiency and versatility in solving a range of problems.
At its core, the Chtholly tree is a dynamic version of the binary search tree. It supports three main operations: adding an element, deleting an element, and querying the number of elements within a given range. These operations are performed in O(log n) time, making the Chtholly tree an excellent choice for competitive programming challenges that involve frequently modifying and querying a set of data.
One of the unique features of the Chtholly tree is its ability to maintain both the set of elements and the number of times each element appears. This is achieved by using a technique called fractional cascading, which essentially allows the Chtholly tree to store more information than a regular binary search tree while maintaining the same efficiency.
The Chtholly tree has been applied to a variety of problems in competitive programming, including range queries, range updates, and maintaining a set of unique elements with counts. It has also been used in algorithms for finding the kth smallest element in a range and for solving dynamic connectivity problems.
So, how can you start using the Chtholly tree in your own programming challenges? Fortunately, there are a variety of resources available online to help you get started. Ghost_Dragon's original Codeforces blog post provides an excellent introduction to the Chtholly tree, including its basic structure and its implementation using C++. You can also find additional resources and code examples on GitHub, where other programmers have shared their own implementations and solutions to various problems.
In summary, the Chtholly tree is a powerful and versatile data structure that has gained popularity in the competitive programming community. Its efficient time complexity and ability to maintain both elements and counts make it an excellent choice for a variety of problems involving dynamic data sets. So why not give the Chtholly tree a try in your next programming challenge? Who knows, it might just help you solve the problem with a little more ease and speed!