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Harsh Mishra
Harsh Mishra

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Binary Search Tree, DSA Complete Syllabus

Course Curriculum: Mastering Binary Search Trees (BST) and Algorithms

This comprehensive course covers all aspects of Binary Search Trees (BSTs), from foundational concepts to advanced algorithms and real-world applications. By the end of the course, learners will have complete mastery over BSTs and their variants, enabling them to tackle theoretical and practical challenges.


Module 1: Introduction to Binary Search Trees

  1. Understanding Data Structures
    • Overview of hierarchical data structures.
    • Trees vs Graphs.
  2. What is a Binary Search Tree?
    • Definition and properties of BST.
    • Binary Tree vs Binary Search Tree.
    • Key features: ordered structure and dynamic nature.
  3. Real-world Applications of BSTs
    • Searching and indexing.
    • Range queries and dynamic datasets.
  4. Comparison with Other Data Structures
    • BST vs Arrays.
    • BST vs Linked Lists.
    • BST vs Heaps.
  5. Environment Setup
    • Tools and IDEs for BST implementation and practice.

Module 2: Fundamental BST Operations

  1. Node Structure
    • Defining a node.
    • Representation in memory.
  2. Insertion in BST
    • Iterative and recursive methods.
    • Time complexity analysis.
  3. Searching in BST
    • Finding a key in the BST.
    • Recursive vs iterative search.
  4. Deletion in BST
    • Removing leaf nodes, nodes with one child, and nodes with two children.
    • Handling successor and predecessor nodes.
  5. Traversal Techniques
    • Inorder traversal (sorted output).
    • Preorder and Postorder traversals.
    • Level-order traversal using queues.

Module 3: Properties and Characteristics

  1. Height of a BST
    • Calculating the height of a tree.
    • Balanced vs unbalanced trees.
  2. Depth and Levels
    • Understanding the depth of nodes.
    • Applications in algorithm design.
  3. Density and Size
    • Counting the number of nodes and their distribution.
    • Applications in memory management.
  4. Key Properties
    • Minimum and maximum keys.
    • Successor and predecessor of a node.

Module 4: Advanced BST Operations

  1. Balancing a BST
    • Issues with unbalanced BSTs.
    • Rotations to balance a BST.
  2. Lowest Common Ancestor (LCA)
    • Finding LCA using BST properties.
    • Applications in hierarchical data queries.
  3. Range Queries
    • Finding all keys in a given range.
    • Count of nodes in a range.
  4. Path Queries
    • Finding root-to-node paths.
    • Sum of nodes along a path.

Module 5: Variants of BST

  1. Self-Balancing BSTs
    • AVL Trees:
      • Rotations: single and double.
      • Balance factor and height updates.
    • Red-Black Trees:
      • Properties and color balancing.
      • Insertion and deletion.
    • Splay Trees:
      • Concept of self-adjusting trees.
      • Zig, Zag, and Zig-Zag rotations.
  2. Augmented BSTs
    • Size-based augmentation.
    • Order statistics (kth smallest/largest element).
    • Applications in interval trees.
  3. Treap
    • Combination of BST and heap properties.
    • Priority-based balancing.
  4. B-Trees and B+ Trees
    • Generalized BST for disk-based storage.
    • Structure and operations.

Module 6: Applications of BST

  1. Searching and Indexing
    • Efficient search operations.
    • Use in database indexing.
  2. Set and Map Implementation
    • BST as a base for set and map operations.
    • Key-value pair management.
  3. Interval Problems
    • Solving interval overlap problems.
    • Applications in event scheduling.
  4. Rank Queries
    • Dynamic rank calculation using augmented BSTs.
    • Finding the kth largest/smallest element.
  5. Graph Algorithms
    • Using BST in Kruskal's MST algorithm.
    • Storing graph edges dynamically.

Module 7: Optimizations and Complex Problems

  1. Optimizing Search Time
    • Balancing techniques for faster search.
    • Alternatives to plain BST for skewed datasets.
  2. Handling Duplicate Keys
    • Modified BST structures for duplicate handling.
    • Applications in multi-key datasets.
  3. Persistent BST
    • Creating versions of BSTs.
    • Applications in time-travel data systems.
  4. Memory Optimizations
    • Minimizing memory usage for large trees.
    • Representation techniques for compact storage.

Module 8: Practical Projects and Case Studies

  1. Dynamic Contact Manager
    • Implementing a BST-based contact search system.
  2. Range Query System
    • Designing a system for dynamic range queries.
  3. Event Scheduler
    • Using BST for scheduling and overlapping detection.
  4. Database Query Optimization
    • Designing a database indexer with BST.
  5. Real-time Leaderboard
    • Using augmented BST for rank updates.

Module 9: Competitive Programming with BST

  1. Common BST Problems
    • Problems from platforms like Codeforces, LeetCode, and HackerRank.
  2. Problem-Solving Techniques
    • Identifying BST-based solutions.
    • Debugging common issues.
  3. Time and Space Optimization
    • Avoiding skewed tree inefficiencies.
    • Reducing memory footprint.

Module 10: Real-world Applications of BST

  1. Operating Systems
    • Using BST in scheduling and memory allocation.
  2. Networking
    • BST in IP routing tables.
  3. Machine Learning
    • Decision trees as a BST application.
    • Feature splitting and pruning.
  4. Web Development
    • BST in autocomplete and search ranking.
  5. Big Data
    • Dynamic datasets and BST applications.

Module 11: Final Assessment and Mastery

  1. Comprehensive Coding Projects
    • Build a fully functional BST-based library.
    • Implement a dynamic priority queue with self-balancing BST.
  2. Capstone Project
    • Design and implementation of a real-world application leveraging BST.
  3. Final Examination
    • Theory and practical coding exam to assess mastery.
  4. Feedback and Next Steps
    • Personalized feedback for improvement.
    • Recommendations for further study (e.g., advanced trees like segment trees and Fenwick trees).

This curriculum provides a deep and exhaustive understanding of BSTs, covering foundational knowledge, advanced algorithms, and practical applications, ensuring complete mastery of the topic.

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