Generic Red-Black Tree and its C# Implementation

The focus of this installment of the Educator's Corner is on tree construction – red-black trees. Some of the material for this column is taken from Chapter 13 of the forthcoming book " Modern Software Development Using C#/.NET " by Richard Wiener. This book will be published by Thomson, Course Technology in the Fall, 2005. A fascinating and important balanced binary search tree is the red-black tree. Rudolf Bayer invented this important tree structure in 1972, about 10 years after the introduction of AVL trees. He is also credited with the invention of the B-tree, a structure used extensively in database systems. Bayer referred to his red-black trees as " symmetric binary B-trees. " Red-black trees, as they are now known, like AVL trees, are " self-balancing ". Whenever a new object is inserted or deleted, the resulting tree continues to satisfy the conditions required to be a red-black tree. The computational complexity for insertion or deletion can be shown to be O(log 2 n), similar to an AVL tree. Red black trees are important in practice. They are used as the basis for Java's implementation of its standard SortedSet collection class. There is no comparable collection in the C# standard collections so a C# implementation of red-black trees might be useful. The rules that define a red-black tree are interesting because they are less constrained than the rather strict rules associated with an AVL tree. Each node is assigned a color of red or black. This can be accomplished using a field of type bool in class Node (true if the node is red and false if it is black). The formal rules that define a red-black binary search tree are the following: 1. Every node is colored either red or black. 2. The root node is always black. 3. Every external node (null child of a leaf node) is black. 4. If a node is red, both of its children are black. 5. Every path from the root to an external node contains the same number of black nodes.