Lecture Notes: Binary Tree Data Structure

Overview

• Binary Tree: A hierarchical data structure where each node has at most two children referred to as the left child and right child.
• Applications: Used for efficient storage and retrieval of data. Supports operations like insertion, deletion, and traversal.

Introduction

• Introduction to Binary Tree: Basics of binary tree structure and importance.
• Properties of Binary Tree: Includes characteristics and relationships in the tree.
• Types of Binary Tree: Different forms and structures of binary trees.
• Applications, Advantages, and Disadvantages: Pros and cons of using binary trees.
• Binary Tree (Array implementation): Implementation details using arrays.
• Complete Binary Tree: Description and properties.
• Perfect Binary Tree: Characteristics and definition.

Basic Operations

• Tree Traversal:
  • Inorder Traversal
  • Preorder Traversal
  • Postorder Traversal
  • Level Order Tree Traversal
• Max Depth or Height: Calculating maximum depth or height.
• Insertion: Methods for adding nodes.
• Deletion: Approaches for removing nodes.
• Enumeration of Binary Trees: Counting distinct structures.

Easy Problems

• Size of a Tree: Calculating total nodes.
• Max in Tree: Finding maximum value.
• Sum Tree: Verifying if it's a sum tree.
• Identical Trees: Checking if two trees are identical.
• Mirror Tree: Checking mirror symmetry.
• Cousins in Tree: Identifying cousin nodes.
• Perfect Binary Tree: Verification of tree completeness.
• Foldable Binary Trees: Checking foldability.
• Symmetric Tree: Determining symmetry.
• Subtree with Given Sum: Locating specific subtree sum.
• Succinct Encoding: Compact representation.
• Get Level of a Node: Determining node levels.
• Check for Complete Binary Tree: Verification of completeness.
• Depth Calculation: From preorder.

More Traversals

• BFS vs DFS for Binary Tree: Comparison of traversal methods.
• Iterative Traversals: Non-recursive methods.
• Morris Traversal: Traversal without stack or recursion.

Medium Problems

• Diameter of a Binary Tree: Calculating tree's diameter.
• Duplicate Subtrees: Identifying repeated structures.
• Edge Removal: Checking tree division potential.
• Spiral Order Traversal: Special traversal form.
• Reverse Level Order Traversal: Reverse order processing.
• Tree Construction: From various traversals.
• Cloning and Conversion: Creating copies and conversions.

Hard Problems

• Min Time to Burn from Leaf: Calculating burning time.
• Preorder Modification: Adjusting tree structure.
• Specific Tree Constructions: Using various representations and sequences.

Additional Resources

• Practice Problems: Explore more problems on Trees
• Quizzes: Take quizzes on Binary Trees
• Videos: Watch tutorial videos on Trees

Recommended Reading

• Properties of Binary Tree
• Applications, Advantages, and Disadvantages of Binary Tree