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Harsh Mishra
Harsh Mishra

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Hashing, DSA Complete Syllabus

#dsa #datastructures #algorithms

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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).

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

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