Insertion
Inserting a new node in a Red-Black Tree involves a two-step process: performing a standard binary search tree (BST) insertion, followed by fixing any violations of Red-Black properties.
Insertion Steps
- BST Insert: Insert the new node like in a standard BST.
- Fix Violations:
- If the parent of the new node is black, no properties are violated.
- If the parent is red, the tree might violate the Red Property, requiring fixes.
Fixing Violations During Insertion
After inserting the new node as a red node, we might encounter several cases depending on the colors of the node’s parent and uncle (the sibling of the parent):
- Case 1: Uncle is Red: Recolor the parent and uncle to black, and the grandparent to red. Then move up the tree to check for further violations.
- Case 2: Uncle is Black:
- Sub-case 2.1: Node is a right child: Perform a left rotation on the parent.
- Sub-case 2.2: Node is a left child: Perform a right rotation on the grandparent and recolor appropriately.
Introduction to Red-Black Tree
Binary search trees are a fundamental data structure, but their performance can suffer if the tree becomes unbalanced. Red Black Trees are a type of balanced binary search tree that use a set of rules to maintain balance, ensuring logarithmic time complexity for operations like insertion, deletion, and searching, regardless of the initial shape of the tree. Red Black Trees are self-balancing, using a simple color-coding scheme to adjust the tree after each modification.
Table of Content
- What is a Red-Black Tree?
- Properties of Red-Black Trees
- Example of Red-Black Tree
- Why Red-Black Trees?
- Comparison with AVL Tree:
- Interesting points about Red-Black Tree:
- Basic Operations on Red-Black Tree:
- 1. Insertion
- 2. Searching
- 3. Deletion
- 4. Rotation
- Left Rotation
- Right Rotation
- When to Perform Rotations?
- Implementation of Red-Black Tree:
- Advantages of Red-Black Trees:
- Disadvantages of Red-Black Trees:
- Applications of Red-Black Trees: