Instructions/Lectures

1. Introduction: Problem and problem solving, Algorithms, complexity analysis etc.
2. How to write algorithms: psedocodes (using elementary addition algorithm)
3. Sorting algorithms
4. Complexity Analysis of Insertion Sort.
5. Asymptotic Behavior of Algorithms
6. Asymptotic Efficiency of Algorithms: Formal and mathematical definitions and properties.
7. Methods for Asymptotic Analysis: Tight bound, upper bound, lower bound etc.
8. Comments on growth functions, bounding summations, recurrences, graphs, trees, etc.
9. Dynamic Programming Technique.
10. Basic Elements of Dynamic Programming.
11. Applicability of Dynamic Programming.
12. Chain Matrix Multiplication Problem
13. Naive Algorithm the Problem
14. Dynamic Programming Approach for the Problem
15. Dynamic Programming Formulation for the Problem.
16. Implementation of Dynamic Programming Rules
17. Example: Chain Matrix Multiplication
18. Recursive Implementation of the Problem
19. Memoization
20. Introduction: Polygons and Triangulations
21. Minimum-Weight Convex Polygon Triangulation
22. Correspondence to Binary Trees
23. Dynamic Programming Solution for Triangulation
24. Convex Hull Algorithms
25. Convex Hull Problem and Approaches
26. Determination of Extreme Edges
27. Graham Scan Algorithm
28. Running Time Computations
29. Amortized Analysis: Aggregate Method and Stack Operations (multipop)
30. Correctness of Graham Scan
31. Comments on Problem Reduction
32. Reduction Example: Use of Hull Algorithm to Sort.
33. Conclusion: Some more comments on problem and problem solving, Comments on inductive reasoning, problem or statement formulation, two working examples.

1. Thomas Cormen,  Charles Leiserson,  Ronald Rivest, and  Cliff Stein,  Introduction to Algorithms, McGraw Hill Publishing Company and MIT Press, 2001 (2nd Edition).