Red Black Tree Algorithm | Red Black Tree | Data Structures And Algorithms | Intellipaat
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A red-black tree is a binary search tree with one extra bit of storage per node: its color, which can be either RED or BLACK. By constraining the way nodes can be colored on any path from the root to a leaf, red-black trees ensure that no such path is more than twice as long as any other so that the tree is approximately balanced.
Each node of the tree now contains the fields color, key, left, right, and p. If a child or the parent of a node does not exist, the corresponding pointer field of the node contains the value NIL. We shall regard these NIL'S as being pointers to external nodes (leaves) of the binary search tree and the normal, key-bearing nodes as being internal nodes of the tree.
A red-black tree is a binary search tree with one extra bit of storage per node: its color, which can be either RED or BLACK. By constraining the way nodes can be colored on any path from the root to a leaf, red-black trees ensure that no such path is more than twice as long as any other so that the tree is approximately balanced.
Each node of the tree now contains the fields color, key, left, right, and p. If a child or the parent of a node does not exist, the corresponding pointer field of the node contains the value NIL. We shall regard these NIL'S as being pointers to external nodes (leaves) of the binary search tree and the normal, key-bearing nodes as being internal nodes of the tree.
A binary search tree is a red-black tree if it satisfies the following red-black properties:
1. Every node is either red or black.
2. Every leaf (NIL) is black.
3. If a node is red, then both its children are black.
4. Every simple path from a node to a descendant leaf contains the same number of black nodes.
Why Red-Black Trees?
Most of the BST operations (e.g., search, max, min, insert, delete.. etc.) take O(h) time where h is the height of the BST. The cost of these operations may become O(n) for a skewed Binary tree. If we make sure that the height of the tree remains O(log n) after every insertion and deletion, then we can guarantee an upper bound of O(log n) for all these operations. The height of a Red-Black tree is always O(log n) where n is the number of nodes in the tree.
Comparison with AVL Tree:
The AVL trees are more balanced compared to Red-Black Trees, but they may cause more rotations during insertion and deletion. So if your application involves frequent insertions and deletions, then Red-Black trees should be preferred. And if the insertions and deletions are less frequent and search is a more frequent operation, then the AVL tree should be preferred over the Red-Black Tree.
🔵 In this Red Black Tree Algorithm, we will cover the following topics:
0:00 - Introduction
2:46 - What is a Binary Search Tree?
4:09 - What is an AVL Tree?
8:54 - Properties of Red Black Tree
10:20 - Insertion Operation in Red Black Tree
17:56 - Coding Implementation of Red Black Tree
25:25 - Search Operation in Red Black Tree
26:40 - Delete Operation in Red Black Tree
29:03 - Applications of Red Black Tree
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