AVL TREES vs RB TREE

  AVL Trees vs RB Trees

     Okay, what exactly is the situation with RedBlackTrees? They're all over the place! Instead of AvlTrees, universities are teaching them. They're manifesting themselves in the kernel. They appear to be the most popular BalancedTree. Why? Red Black Trees are faster to insert and remove than AVL trees since they require less rotations due to their more flexible balance.

   The self-balancing binary search tree may automatically alter the node's position to keep the tree's depth at a minimum. The distance between the root node and the deepest leaf node is the tree's depth. Increasing the efficiency of various tree operations can be done by ensuring that the depth is short enough. However, maintaining the binary search tree's self-balance will take a long time. Red-black trees and AVL trees are two well-known self-balancing data structures.

RB Tree: 

A binary search tree with the following red-black features is known as a red-black tree. Every node has a red or black colour. Every (NULL) leaf is black. Both of a node's children are black if it is red.

 

AVL Tree: 

The AVL Tree is a height balanced binary search tree in which each node has a balance factor that is computed by subtracting the height of the right sub-tree from the height of the left sub-tree.

We'll compare the Red Black Tree and the AVL Tree in this post.

 Red Black tree:

Properties:

1. Painting each node with one or two colours provides self-balancing (Red or Black).

2. When Tree is changed, a new tree is created, which is then reorganised and repainted.

3. Each node in the tree requires one bit of colour information.

Red Black Tree's constraints are as follows:

1. Root is always a dark colour.

2. All null leaves are black, as are both offspring of the red node.

3. There are the same number of black nodes on every simple path from a given node to any of its descendant leaves.

4. The path from the root to the farthest leaf is about twice as lengthy as the journey from the root to the nearest leaf.

AVL(Adelson-Velskii and Landis) Tree

Properties:

1. The height difference between the node's left and right subtrees should be smaller than 2.

2. When the heights of two child subtrees of a node diverge by more than one, re-balancing is performed.

3. As far as retrievals are concerned, faster retrievals are carefully balanced.

Differences:

1. Because they are more precisely balanced, AVL trees give faster lookups than Red Black Trees.

2. Red Black Trees are easier to install and remove than AVL trees because their relaxed balance necessitates fewer rotations.

3. AVL trees maintain balance factors or heights with each node, necessitating the storage of an integer per node, but the Red Black Tree just requires 1 bit of data per node. 

4. Most language libraries, such as map, multimap, and multiset in C++, use Red Black Trees, but AVL trees are used in databases where faster retrievals are necessary.

Diiference between AVL Tree and RB Tree w.r.t Time Complexity:

Conclusion:

The excellent condition of tight height balancing is sacrificed by the red-black tree. The red-black tree can be searched and inserted at a time complexity of O (log2 n), Delete operation, at the cost of the red-black tree. Furthermore, any imbalance will be corrected within three rotations due to its design. Of course, there are better ones, but the more sophisticated data structure can achieve balance in just one spin, but the red-black tree can provide a "cheap" answer. Although the red-black tree has the same method time complexity as the AVL tree, it outperforms it statistically.