Red Black Tree

Red Black Trees also known as RB-tree is an attempt to make tree balance. We prefer to keep tree balance for the sake of reducing efforts for performing various operations like insertion, deletion, search etc. RB-tree are binary search trees where all nodes in the tree have an extra property: color. The nodes can be either red, black, or (occasionally) double black.

• The trees have the following properties:
  1. Root is black
  2. All the external nodes are dummy nodes with no elements, and they are colored black.
  3. The children of red nodes are always black (also the parent of red node must be black)
  4. All external nodes have the same black height (BH), where BH is defined as the number of black nodes from root to the external node.

Comaprison AVL Tree Vs RB Tree Red-Black Trees (RB trees) and AVL Trees are both types of self-balancing binary search trees, designed to maintain a balanced structure as elements are inserted and deleted. They serve similar purposes, but they have differences in their performance characteristics and use cases.

Parameter	AVL Tree	R-B tree
Balance Factor	AVL trees are more strictly balanced compared to RB trees.In AVL trees, the balance factor (the height difference between the left and right subtrees) of every node is restricted to be at most 1, ensuring a height-balanced tree. This results in faster look-up times but requires more rotations during insertion and deletion operations to maintain balance.	RB trees have less strict balance requirements.They ensure that the tree remains approximately balanced by coloring the nodes (red or black) and enforcing several properties. While they might not be as perfectly balanced as AVL trees, RB trees require fewer rotations to maintain balance, making insertion and deletion operations generally faster.
Insertion and Deletion	Insertions and deletions in AVL trees typically require more rotations, which can make them slower for these operations. Balancing an AVL tree can take multiple rotations in some cases.	RB trees require fewer rotations during insertion and deletion, making them more efficient for dynamic datasets where elements are frequently added or removed. RB trees are considered more practical for use in databases and file systems where there are many insertions and deletions.
Performance Considerations	AVL trees are well-suited for scenarios where read operations significantly outnumber write operations, as their read performance is generally better due to their stricter balance criteria.	RB trees are preferred when the dataset is more dynamic, and there are frequent insertions and deletions. Their performance is often better in situations with a mix of read and write operations, and they are commonly used in real-time systems.
Complexity	AVL trees tend to have more complex code for maintaining balance, which can lead to larger codebases and potentially more room for bugs.	RB trees are usually easier to implement, maintain, and debug due to their simpler balance maintenance.

In summary, the choice between RB trees and AVL trees depends on your specific use case and the balance between read and write operations in your application. AVL trees are better when you need faster read operations and can tolerate slower insertions and deletions. RB trees are better when you have a dynamic dataset with frequent insertions and deletions and need to maintain reasonable balance without sacrificing too much on read performance. Lets develop good understanding of RB-tree and its properties. [Click the following links to watch the video]

• Red Black Tree and Node Insertion Algorithm      [ read text]
• Steps to delete node from RB Tree
• Understanding RB Tree Deletion cases with an Example
• RB Tree Deletion Example-2

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