Overview:
This course provides an in-depth study of fundamental algorithms and techniques for designing and analyzing efficient algorithms. It covers various algorithm design paradigms, algorithmic strategies, and methods for analyzing the correctness and efficiency of algorithms. Emphasis is placed on understanding the principles behind algorithm design rather than rote memorization of specific algorithms.
Course Objectives:
1. Understand fundamental concepts of algorithm design and analysis.
2. Learn various algorithm design paradigms and techniques.
3. Develop skills for analyzing the correctness and efficiency of algorithms.
4. Apply algorithmic principles to solve real-world problems.
5. Gain proficiency in expressing algorithms using pseudocode and analyzing their time and space complexity.
Topics Covered:
1. Introduction to Algorithms
- Basic terminology and concepts
- Analysis of algorithms: time and space complexity
2. Algorithm Design Techniques
- Divide and conquer
- Greedy algorithms
- Backtracking
3. Sorting and Searching Algorithms
- Comparison-based sorting algorithms (e.g., Merge Sort, Quick Sort)
- Non-comparison-based sorting algorithms (e.g., Counting Sort, Radix Sort)
- Binary search and its variants
- Hashing and hash functions
4. Graph Algorithms
- Graph representation and traversal (e.g., BFS, DFS)
- Shortest path algorithms (e.g., Dijkstra's algorithm, Bellman-Ford algorithm)
- Minimum spanning tree (e.g., Prim's algorithm, Kruskal's algorithm)
- Principles of dynamic programming
- Examples: Longest common subsequence, Matrix chain multiplication
- Advanced topics in dynamic programming
6. Advanced Topics
- String algorithms (e.g., pattern matching, string matching)
- Approximation algorithms
- NP-completeness and computational intractability
7. Algorithmic Analysis Techniques
- Asymptotic analysis (big O, omega, theta notation)
- Recurrence relations
- Amortized analysis
- Space complexity analysis
8. Applications and Case Studies
- Applications of algorithms in various domains (e.g., bioinformatics, cryptography, networking)
- Case studies of real-world algorithmic problems and solutions
Assessment:
Assessment methods may include assignments, programming projects, quizzes, midterm exams, and a final exam. Students are expected to demonstrate their understanding of algorithmic principles, ability to design and analyze algorithms, and proficiency in applying algorithms to solve problems.
Prerequisites:
A strong foundation in data structures, discrete mathematics, and programming (preferably in a language such as Python, Java, or C++) is recommended.
- Teacher: Akshay Rajput