Design and Analysis of Algorithms

The Design and Analysis of Algorithms course provides students with a comprehensive understanding of fundamental algorithmic techniques used to solve computational problems efficiently. The course emphasizes the principles of algorithm design, correctness, and performance analysis using mathematical and asymptotic techniques. Students will develop the ability to compare multiple algorithmic approaches and select appropriate solutions based on time and space complexity.

The course begins with Introduction to Algorithm Design, covering algorithmic fundamentals, asymptotic notations, complexity analysis, recurrence relations, and the evaluation of algorithm efficiency. It then explores the Divide and Conquer paradigm, including recursive problem solving, binary search, merge sort, quick sort, and related applications.

The third module focuses on Greedy and Dynamic Programming techniques, enabling students to solve optimization problems using greedy strategies and dynamic programming approaches. Topics include minimum spanning trees, shortest path algorithms, knapsack problems, matrix chain multiplication, and longest common subsequence.

The final module introduces Backtracking and Branch and Bound Algorithms, emphasizing systematic search techniques for solving combinatorial optimization problems. Students will study applications such as N-Queens, graph coloring, Hamiltonian cycle, traveling salesperson problem, and 0/1 knapsack using branch and bound.

By the end of the course, students will be able to design efficient algorithms, analyze their computational complexity, implement advanced algorithmic paradigms, and apply appropriate problem-solving strategies to real-world computational challenges.