CS502 Design and Analysis of Algorithms

CS502: Design and Analysis of Algorithms

CS502 Design and Analysis of Algorithms is a cornerstone course in computer science that teaches you how to design efficient solutions to computational problems and how to analyze their performance. This course moves beyond simply writing code that works; it focuses on writing code that works efficiently, scaling to handle large inputs and complex challenges. Understanding algorithms is fundamental to every area of computing.

The course is built on two primary pillars: design and analysis. You will learn a toolbox of algorithm design techniques—strategies for attacking new problems, such as divide-and-conquer, dynamic programming, and greedy algorithms. Simultaneously, you will learn the mathematical tools to analyze these algorithms, primarily through asymptotic notation (Big O). This analysis allows you to predict an algorithm's performance in terms of time and space, enabling you to make informed decisions about which algorithm to use for a given task.

Key Topics Covered:

• Asymptotic Analysis: Mastering Big O, Omega, and Theta notation to describe the worst-case, best-case, and average-case performance of algorithms.
• Algorithm Design Techniques:
  • Divide and Conquer: Solving problems by recursively breaking them down into smaller sub-problems (e.g., Merge Sort, Quick Sort).
  • Dynamic Programming: Solving complex problems by breaking them into a collection of simpler, overlapping sub-problems and storing their solutions (e.g., Fibonacci, Knapsack).
  • Greedy Algorithms: Making the locally optimal choice at each step with the hope of finding a global optimum (e.g., Dijkstra's algorithm, Kruskal's algorithm).
• Graph Algorithms: In-depth study of graph representations and algorithms for traversal (BFS, DFS), finding shortest paths (Dijkstra, Bellman-Ford), and minimum spanning trees (Prim, Kruskal).
• Data Structures: Advanced data structures that support efficient algorithms, such as heaps (priority queues), hash tables, and binary search trees.
• Complexity Theory: An introduction to the classes P and NP, and the concept of NP-completeness, which helps identify problems that are believed to be computationally 'hard' to solve.

Course Objectives:

1. Analyze the time and space complexity of algorithms using asymptotic notation.
2. Master key algorithm design paradigms: divide-and-conquer, dynamic programming, and greedy approaches.
3. Design and implement efficient algorithms for a variety of computational problems, especially those involving graphs.
4. Understand the fundamental concepts of computational complexity, including P, NP, and NP-completeness.
5. Develop strong problem-solving and critical-thinking skills.

This course provides the critical theoretical foundation for all other advanced courses in computer science, from artificial intelligence and machine learning to database systems and computer networks. It is essential for software engineering interviews and for writing high-performance, scalable code.