Hashing, DSA Complete Syllabus

Course Curriculum: Mastering Hashing and Hash-Based Algorithms

This comprehensive course on hashing covers fundamental concepts, advanced techniques, and practical applications to ensure mastery in hashing as a data structure and algorithmic paradigm. It is designed to cater to learners from beginner to expert levels.

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Module 1: Introduction to Hashing

1. What is Hashing?
   • Definition and significance.
   • Importance of constant time operations.
2. Hash Functions
   • Concept and purpose of a hash function.
   • Properties of a good hash function.
3. Hashing Terminology
   • Keys, hash values, and hash codes.
   • Buckets and collision.
4. Applications of Hashing
   • Database indexing.
   • Cryptography.
   • Caching and memory management.

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Module 2: Hash Functions

1. Characteristics of a Good Hash Function
   • Uniform distribution.
   • Determinism and efficiency.
2. Types of Hash Functions
   • Division method.
   • Multiplication method.
   • Universal hashing.
3. Hash Functions in Practice
   • CRC (Cyclic Redundancy Check).
   • Jenkins hash.
   • MurmurHash.
4. Choosing a Hash Function
   • Trade-offs between speed, simplicity, and uniformity.

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Module 3: Hash Table Design and Implementation

1. Hash Table Basics
   • Structure and working of hash tables.
   • Hashing with chaining.
   • Open addressing.
2. Dynamic Hash Tables
   • Resizing and rehashing.
   • Load factor and its impact.
3. Efficiency Analysis
   • Time complexity of operations: O(1) for average case.
   • Factors affecting efficiency.

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Module 4: Collision Resolution Techniques

1. Chaining
   • Linked lists in hash buckets.
   • Variants like AVL or red-black trees in chaining.
2. Open Addressing
   • Linear probing.
   • Quadratic probing.
   • Double hashing.
3. Performance of Collision Resolution
   • Pros and cons of each technique.
   • Real-world use cases.

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Module 5: Advanced Hash Table Implementations

1. Dynamic Perfect Hashing
   • Concept of perfect hash functions.
   • Implementation details.
2. Cuckoo Hashing
   • Design principles.
   • Handling collisions effectively.
3. Hopscotch Hashing
   • Introduction and working.
   • Advantages over other techniques.
4. Robin Hood Hashing
   • Balancing probes.
   • Practical applications.

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Module 6: Hashing in Cryptography

1. Cryptographic Hash Functions
   • Properties: pre-image resistance, collision resistance.
   • Common algorithms: SHA-256, MD5.
2. Applications in Security
   • Password hashing and salting.
   • Digital signatures and certificates.
3. Cryptographic vs Non-Cryptographic Hash Functions
   • When to use cryptographic hashing.

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Module 7: Hashing in Data Structures

1. Hash-based Data Structures
   • Hash sets.
   • Hash maps/dictionaries.
   • Hash multi-maps.
2. Hashing with Augmented Data
   • Priority hashing.
   • Cache-aware hashing.
3. Bloom Filters
   • Probabilistic data structure for membership checks.
   • Implementation and applications.

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Module 8: Applications of Hashing

1. Databases and Indexing
   • Hash indexing in relational databases.
   • Use in NoSQL databases.
2. File Systems
   • Hashing in distributed file systems.
   • Deduplication using hashing.
3. Data Compression
   • Hashing for redundancy elimination.
4. Caching and Load Balancing
   • Hashing in web caches.
   • Consistent hashing for server distribution.

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Module 9: Hashing in Algorithms

1. String Matching
   • Rabin-Karp Algorithm.
   • Rolling hash techniques.
2. Subset and Frequency Problems
   • Count distinct elements.
   • Subarray sum queries with hashing.
3. Hashing in Graph Algorithms
   • Graph isomorphism.
   • Detecting cycles in a graph using hashing.
4. Hashing in Machine Learning
   • Feature hashing (hashing trick).
   • Hash tables in nearest neighbor searches.

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Module 10: Hashing in Competitive Programming

1. Common Hashing Problems
   • Two-sum problem using hash maps.
   • Anagrams grouping with hash values.
   • Longest consecutive sequence.
2. Optimization Techniques
   • Avoiding collisions in competitive scenarios.
   • Debugging hash-related issues.
3. Practice Problems
   • Platform-based challenges (Codeforces, LeetCode, HackerRank).

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Module 11: Distributed Hashing

1. Distributed Hash Tables (DHTs)
   • Concept and structure.
   • Examples: Chord, Kademlia.
2. Consistent Hashing
   • Ring-based model.
   • Applications in distributed systems.
3. Load Balancing with Hashing
   • Dynamic node addition and removal.
   • Hash partitioning strategies.

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Module 12: Hashing in Advanced Topics

1. Perfect Hashing
   • Static vs dynamic perfect hashing.
   • Applications in high-speed lookup systems.
2. Universal Hashing
   • Definition and mathematical properties.
   • Use in theoretical computer science.
3. Locality-Sensitive Hashing (LSH)
   • Approximate nearest neighbors.
   • Applications in image and text similarity.
4. Sparse Hashing
   • Efficient hashing for sparse datasets.

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Module 13: Real-world Hashing Challenges

1. Scaling Hash Tables
   • Handling extremely large datasets.
   • Partitioned hash tables.
2. Handling Collisions at Scale
   • Multi-level hashing strategies.
   • Probabilistic methods for large data.
3. Securing Hash-based Systems
   • Preventing hash collision attacks.
   • Salting and other security mechanisms.

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Module 14: Practical Projects and Case Studies

1. Building a Hash Table Library
   • From scratch implementation.
   • Performance tuning.
2. File Integrity System
   • Using cryptographic hashing for file verification.
3. Distributed Caching System
   • Consistent hashing-based implementation.
4. Real-time Log Monitoring
   • Efficient log deduplication with hashing.

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Module 15: Capstone Project and Final Assessment

1. Comprehensive Capstone Project
   • Design and implement a real-world application using advanced hashing techniques.
2. Final Examination
   • Theory and coding assessment.
3. Personalized Feedback
   • Review of strengths and areas for improvement.
4. Next Steps
   • Recommended topics for further study (e.g., graph hashing, database indexing).

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This syllabus ensures a robust understanding of hashing concepts, algorithms, and real-world applications, preparing learners for academic, competitive, and industrial excellence.