Lecture-2(a): Complexity Analysis (Basics)

This undergraduate course on Analysis of Algorithms provides a comprehensive introduction to the principles of algorithm design and performance evaluation. Students will explore the core concepts of algorithm analysis, focusing on time and space complexity, and will gain hands-on experience with common algorithmic techniques used in problem-solving. The course begins with an understanding of basic algorithms and their classification, followed by complexity analysis using Big-O notation, where students learn to analyze and compare the efficiency of algorithms. Recursion is introduced as a fundamental concept, enabling students to solve problems that break down into simpler subproblems. Key topics include divide-and-conquer algorithms, such as merge sort and quicksort, and graph algorithms, like BFS, DFS, and shortest path algorithms. Students will also learn greedy algorithms and how to apply them to optimization problems. In-depth coverage of dynamic programming introduces techniques to solve problems by breaking them into overlapping subproblems. The course also covers essential algorithms for sorting and searching, and string matching algorithms. The final part of the course explores NP-completeness, introducing students to computational complexity theory. Advanced algorithms, including randomized, approximate, and genetic algorithms, are also discussed, offering insight into emerging techniques in the field.