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