Chtholly Tree: A Brute-Force Data Structure for Efficient Range Queries

The Chtholly tree is a brute-force data structure designed by a Chinese student and first publicized on a Codeforces tutorial. It is a powerful and versatile data structure that can be used for many different types of problems, including range queries, range updates, and point updates.

One of the key features of the Chtholly tree is its ability to handle both range queries and range updates efficiently. This is achieved by using a combination of data structures, including balanced binary trees and bitmasks.

To implement the Chtholly tree in C++, we first need to define the basic structure of the tree. This can be done using a class or struct, and typically includes variables for the size of the tree, the number of elements, and an array or vector for storing the elements.

Next, we need to implement the key functions for the Chtholly tree, such as insert, erase, and query. These functions will typically involve manipulating the underlying data structures, such as the balanced binary trees and bitmasks, in order to efficiently perform the desired operations.

Here is a basic example of how to implement the Chtholly tree in C++:

class ChthollyTree {
private:
    int size;
    int elements;
    vector<int> data;

public:
    ChthollyTree(int size) {
        this->size = size;
        this->elements = 0;
        this->data.resize(size);
    }

    void insert(int element) {
        // Insert the element into the tree
    }

    void erase(int element) {
        // Remove the element from the tree
    }

    int query(int start, int end) {
        // Perform a range query and return the result
    }
};

The Chtholly tree can also be implemented in Rust. The basic structure of the tree is similar to the C++ implementation, but the syntax and function names may be slightly different. Here is an example of how to implement the Chtholly tree in Rust:

struct ChthollyTree {
    size: i32,
    elements: i32,
    data: Vec<i32>,
}

impl ChthollyTree {
    fn new(size: i32) -> ChthollyTree {
        ChthollyTree {
            size: size,
            elements: 0,
            data: vec![0; size as usize],
        }
    }

    fn insert(&mut self, element: i32) {
        // Insert the element into the tree
    }

    fn erase(&mut self, element: i32) {
        // Remove the element from the tree
    }

    fn query(&self, start: i32, end: i32) -> i32 {
        // Perform a range query and return the result
    }
}

Overall, the Chtholly tree is a powerful and efficient data structure that can be used for a wide range of problems. It is relatively easy to implement in both C++ and Rust, and can provide significant performance benefits compared to other data structures.

References:

  1. Codeforces tutorial by Ant_on
  2. Discussion of the Chtholly tree on Codeforces
  3. A detailed analysis of the Chtholly tree on a personal blog
  4. A video explanation of the Chtholly tree by a Chinese Youtuber
  5. A Github repository with an implementation