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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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).

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