WBTrees

Provides a basic implementation of weight-balanced binary trees.

The WBTrees library contains classes as follows:

• A list by a weight-balanced binary tree, with all O(log n) basic operations
  • WBList<T>
• A set and a map by weight-balanced binary search trees, which can be accessed by index in O(log n) time
  • WBSet<T>
  • WBMultiSet<T>
  • WBMap<TKey, TValue>
  • WBMultiMap<TKey, TValue>

All these trees are constructed from Node<T> objects.

See Wiki for more information.
This library is written in C#. You are welcome to port this to other languages.

Features

A List by a Weight-Balanced Binary Tree

Provides the WBList<T> class as a list with all O(log n) basic operations.
You can also use a WBList<T> as a (high-grade) double-ended queue (deque).

The following table compares time complexities of System.Collections.Generic.List<T> and WBList<T>:

Operation	List<T>	WBList<T>
Get by Index	O(1)	O(log n)
Set by Index	O(1)	O(log n)
Remove by Index	O(n)	O(log n)
Insert by Index	O(n)	O(log n)
Prepend	O(n)	O(log n)
Add	O(1)	O(log n)
Get All	O(n)	O(n)

A Set and a Map by Weight-Balanced Binary Search Trees

Provides the WBSet<T>, WBMultiSet<T>, WBMap<TKey, TValue> and WBMultiMap<TKey, TValue> classes, which can be accessed by index in O(log n) time. All these classes are derived from the WBTreeBase<T> class.
You can also use a WBMultiSet<T> or a WBMultiMap<TKey, TValue> as a priority queue with stable sorting or a double-ended priority queue.

The following table compares time complexities of System.Collections.Generic.SortedSet<T> and WBSet<T>:

Operation	SortedSet<T>	WBSet<T>
Get by Item	O(log n)	O(log n)
Remove by Item	O(log n)	O(log n)
Add	O(log n)	O(log n)
Get by Index	O(n)	O(log n)
Remove by Index	O(n)	O(log n)
Get Index by Item	O(n)	O(log n)
Get All	O(n)	O(n)

Algorithm

Both WBList<T> and WBTreeBase<T> are weight-balanced binary trees (not necessarily searchable by items). The Node<T> class contains the Count property that contributes to both self-balancing and fast access by index (order).

Target Frameworks

• .NET 5
• .NET Standard 2.0
  • .NET Core 2.0, .NET Framework 4.6.1, etc.

Setup

The WBTrees library is published to NuGet Gallery. Install the NuGet package via Visual Studio, etc.

You can also download a single source file here for competitive programming, etc.

Usage

See Usage on Wiki for coding.

Release Notes

• v1.0.4 The first release.