Red Black Tree vs AVL Tree: Data Structure

Difference Between Red Black Tree vs AVL Tree

Red Black Tree: A red-black tree is referred as self-balancing binary search tree. In red-black, each node stores an extra bit that determines the color of the node in red-black tree either red or black. These colors determine that the tree remains balanced or not, while performing insertions and deletions. The red-black tree is used to reduce the number of rotations while inserting and deleting the node and try to maintain the complexity around O(log n), where n is total number elements in the red-black tree.

Why Red-Black Trees?

If we talk about Binary Search Tree, then its operations (e.g. insert, delete, search etc.) generally take O(log n) time where n is the total number of nodes in binary search tree. if we are using skewed binary tree, then the cost of these operations may become O(n). To overcome this problem, we have another tree which is called AVL tree, then why we need of red - black trees. To answer this question, we need to consider the situation of AVL trees, the AVL trees don’t provide the guarantee that how many rotations are required to balance the height of AVL tree but in red-black trees, they provide guarantee that maximum two rotations are required to balance the height of red-black tree. So, we can say if your application involves more insertions and deletions, then Red-Black should be used and if searching is frequent operation and insertions and deletions are less frequent, then AVL trees should be used over the red-black trees

Properties of Red-Black Trees: -

• Referred as a self-balancing Binary Search Tree
• Every node is either Red or Black
• Root is always Black
• Every leaf which is NILL is Black
• If node is Red then its children are Black
• Every path from a node to any of its descendent NILL node has same number of Black nodes.
• The height of the red - black if it has n node, is h<=2 log(n+1)

Complexity of Red-Black Trees

The time complexity of red-black in all operations (e.g. insertion, deletion, searching) is O(log n).

AVL Tree

AVL Tree is referred to as self – balanced or height-balanced binary search tree where the difference between heights of its left sub-tree and right sub-tree (Balance Factor) can't be more than one for all nodes covered by a tree.

We can say a tree is balanced if the balance factor of each node of a tree is in between -1 to 1; otherwise, a tree is considered as unbalanced and need to balance.

                        Balance Factor (node) = height (left (node)) – height (right (node))

• If the balance factor is 1 of any node of the tree, then we can say the height of the left sub - tree is higher than the height of the right sub - tree of the node in the AVL tree.
• If the balance factor is 0 of any node of the tree, then we can say the height of the left sub - tree is equal to the height of the right sub - tree of the node in the AVL tree.
• If the balance factor is -1 of any node of the tree, then we can say the height of the left sub - tree is lower than the height of the right sub - tree of the node in the AVL tree.

Time Complexity of AVL Tree

The rotations of the AVL tree take constant time. It is a self-balanced tree, so the time complexity of all the operations (e.g., insertion, deletion and searching) is O (log n).

Comparison Table: -

Parameter	Red Black Tree	AVL Tree
Used for	When application involves more insertion and deletion	When searching is on the higher priority.
Insertion and Deletion	Insertion and deletion are easy because only few rotations are required to balance the tree in insertion or deletion.	Insertion and Deletion are complex in AVL tree as it requires multiple rotations to balance the tree.
Searching	Red black is not used for efficient searching because it is roughly balanced tree instead of strictly balanced.	Efficient searching can be done by AVL tree because it is strictly balanced.
Color of the node	We color the node of red black tree either red or black.	No color is required in case of AVL tree.
Balance factor	It does not contain any balance factor. It stores only one bit of information that denotes either Red or Black color of the node.	Each node has a balance factor in AVL tree whose value can be 1, 0, or -1. It requires extra space to store the balance factor per node.