Trees in Data Structures

1. Introduction to Trees

Definition and Terminology
Types of Trees

2. Binary Trees

Definition
Properties
Types of Binary Trees
- Full Binary Tree
- Complete Binary Tree
- Perfect Binary Tree
- Balanced Binary Tree
- Degenerate (or pathological) Tree

3. Binary Search Trees (BST)

Definition
Properties
Operations
- Insertion
- Deletion
- Search
- Traversal (Inorder, Preorder, Postorder)

4. AVL Trees

Definition
Rotations
- Single Rotation
- Double Rotation
Insertion
Deletion
Balancing

5. Red-Black Trees

Definition
Properties
Rotations
- Left Rotation
- Right Rotation
Insertion
Deletion
Balancing

6. B-Trees

Definition
Properties
Operations
- Insertion
- Deletion
- Search

7. Trie (Prefix Tree)

Definition
Operations
- Insertion
- Search
- Deletion

8. Segment Trees

Definition
Operations
- Query
- Update

9. Fenwick Trees (Binary Indexed Trees)

Definition
Operations
- Update
- Query

10. N-ary Trees

Definition
Properties
Traversal Methods

11. Tree Traversal Algorithms

Depth-First Search (DFS)
- Inorder
- Preorder
- Postorder
Breadth-First Search (BFS)

12. Applications of Trees

Expression Trees
Syntax Trees
Decision Trees

13. Advanced Topics

Suffix Trees
Generalized Trees
Tree Isomorphism

14. Complexity Analysis

Time Complexity
Space Complexity