The main differences between Red-Black (RB) trees and AVL trees can be summarized in terms of their balancing mechanisms, performance characteristics, and use cases. Here is a detailed comparison:
Balancing Mechanisms
Red-Black Trees
Coloring and Properties: Each node in a Red-Black tree is colored either red or black. The tree maintains the following properties to ensure balance:
The root is always black.
All leaves (NIL nodes) are black.
Red nodes cannot have red children (no two red nodes can be adjacent).
Every path from a node to its descendant leaves has the same number of black nodes (black-height).
Balancing Operations: Red-Black trees use rotations and recoloring to maintain balance. The balancing is less strict compared to AVL trees, allowing the tree to be approximately balanced.
Insertion and Deletion: These operations may require up to two rotations and some recoloring to maintain the tree properties[2][3][5].
AVL Trees
Height Balance: AVL trees maintain a strict balance by ensuring that the heights of the left and right subtrees of any node differ by at most one. This is quantified using a balance factor, which must be -1, 0, or +1 for all nodes.
Balancing Operations: AVL trees use rotations to maintain balance. There are four types of rotations: single left, single right, left-right, and right-left.
Insertion and Deletion: These operations may require multiple rotations to maintain the strict balance, making them more complex but ensuring the tree remains more balanced[9][12][14].
Performance Characteristics
Red-Black Trees
Time Complexity: Both insertion and deletion operations have a time complexity of $$O(\log n)$$. However, due to the less strict balancing, Red-Black trees may have a slightly higher height compared to AVL trees, leading to potentially slower lookups.
Rotations: Red-Black trees generally require fewer rotations during insertion and deletion, making these operations faster compared to AVL trees[1][4][7].
AVL Trees
Time Complexity: AVL trees also have $$O(\log n)$$ time complexity for insertion, deletion, and lookup operations. Due to their stricter balancing, AVL trees tend to have a lower height, resulting in faster lookups.
Rotations: AVL trees may require more rotations during insertion and deletion, which can make these operations slower compared to Red-Black trees[4][12][18].
