Design and Analysis of Algorithms

I will begin the course by explaining the fundamentals of Design and Analysis of Algorithms, with special emphasis on understanding algorithm efficiency. A major focus of my teaching will be on asymptotic analysis, which helps students evaluate how an algorithm performs as the input size grows. I will explain asymptotic notations in depth, including Big O, Big Omega, and Big Theta, starting from very basic intuition and gradually moving to formal definitions. Students will learn how these notations represent worst case, best case, and average case behavior of algorithms, and why they are important for comparing different solutions to the same problem.

I will also cover little o and little omega notations to help students clearly understand strict upper and lower bounds. Through multiple examples, I will demonstrate how to analyze simple loops, nested loops, recursive algorithms, and common code patterns to derive time complexity expressions. Special attention will be given to solving recurrence relations using substitution method, recursion tree method, and Master’s theorem, as these are essential for analyzing divide and conquer algorithms.

In addition to theoretical explanations, I will provide practical problem solving sessions where students practice finding time and space complexity for real algorithms such as searching, sorting, and basic graph traversal techniques. I will explain common mistakes students make while calculating complexity and how to avoid them. The goal is to ensure that students develop strong confidence in asymptotic analysis, are able to justify their answers clearly in exams, and can apply these concepts effectively while designing efficient algorithms in real world and competitive programming scenarios.