1. Introduction to Algorithms, Specification of Algorithm, Complexity.pdf
- 1. Course Name: Design and Analysis of Algorithm Topic: Introduction to Algorithms, Specification of Algorithm Course code : CS 3102 Credits : 4 Mode of delivery : Hybrid (Power point presentation) Faculty : Mr. Sunil Kumar Patel Email-id : [email protected] B.TECH V SEM CSE ACADEMIC YEAR: 2023-2024 1 CS3102 (DAA), Dept. of CSE
- 2. Assessment criteria’s Assignment quiz Mid term examination End term Examination CS3102 (DAA), Dept. of CSE 2
- 3. Introduction to Algorithms, Asymptotic Notations, Complexity CS3102 (DAA), Dept. of CSE 3
- 4. Course Information • Course Handout • Communicate through eMail • Office hours • To be communicated • Grading policy • Will be communicated as per university guidelines CS3102 (DAA), Dept. of CSE 4
- 5. Syllabus • Introduction: Fundamentals of Algorithms, Important Problem Types, Analysis of algorithm efficiency. Analysis Framework: Asymptotic Notations and Basic Efficiency Classes. Mathematical Analysis of Nonrecursive and Recursive Algorithms: Brute force Techniques, Divide and Conquer. Decrease and Conquer: Insertion Sort, Depth First Search, Breadth First Search, Topological Sorting. Transform and Conquer: Presorting, BST, Heapsort. Space and Time tradeoffs: Input Enhancement in String Matching. Dynamic Programming: Warshall's and Floyd's Algorithms, The Knapsack Problem. Greedy Techniques: Prim's, Kruskal's and Dijkstra's Algorithm, Huffman Trees. Coping with limitations of algorithmic power. Backtracking: nQueens problem, Hamiltonian Circuit Problem, Subset Sum Problem. Branch and Bound: Assignment Problem, Knapsack Problem, TSP. P, NP, and NP-complete Problems. CS3102 (DAA), Dept. of CSE 5
- 6. More Information • Textbook •Introduction to Algorithms 3rd ,Cormen, Leiserson, Rivest and Stein, The MIT Press, • Fundamentals of Computer Algorithms, 2nd, Sartaj Sahni, Ellis Horowitz, Sanguthevar Rajasekaran • Others • Introduction to Design & Analysis Computer Algorithm 3rd, Sara Baase, Allen Van Gelder, Adison-Wesley, 2000. • Algorithms, Richard Johnsonbaugh, Marcus Schaefer, Prentice Hall, 2004. • Introduction to The Design and Analysis of Algorithms 2nd Edition, Anany Levitin, Adison-Wesley, 2007. CS3102 (DAA), Dept. of CSE 6
- 7. Course Objectives • CS1501.1 Analyse the running times of algorithms using asymptotic analysis. • CS1501.2 Demonstrate and Design algorithms using divide-and-conquer paradigm to solve business problems hence enhance skills. • CS1501.3 Illustrate the concept of greedy and dynamic-programming approach to solve real life problems to enhance entrepreneurship capabilities. • CS1501.4 Demonstrate the concept of backtracking and branch & bound algorithms. • CS1501.5 Synthesize and analyse various advanced algorithms concept such as graphs, string matching, approximation algorithms and complexity classes to enhance employability. CS3102 (DAA), Dept. of CSE 7
- 8. Why study algorithms and performance? • Algorithms help us to understand scalability. • Performance often draws the line between what is feasible and what is impossible. • Algorithmic mathematics provides a language for talking about program behavior. • Performance is the currency of computing. • The lessons of program performance generalize to other computing resources. CS3102 (DAA), Dept. of CSE 8
- 9. Two Distinct Choices CS3102 (DAA), Dept. of CSE 9
- 10. Applications CS3102 (DAA), Dept. of CSE 10
- 11. Asymptotic Performance • In this course, we care most about asymptotic performance • How does the algorithm behave as the problem size gets very large? • Running time • Memory/storage requirements • Bandwidth/power requirements/logic gates/etc. CS3102 (DAA), Dept. of CSE 11
- 12. Goal of the Course • Learning to solve real problems that arise frequently in computer application • Learning the basic principles and techniques used for answering the question: “How good, or, how bad is the algorithm” • Getting to know a group of “very difficult problems” categorized as “NP-Complete” CS3102 (DAA), Dept. of CSE 12
- 13. Design and Analysis, in general Design •Understanding the goal •Select the tools •What components are needed •How the components should be put together •Composing functions to form a process Analysis •How does it work? •Breaking a system down to known components •How the components relate to each other •Breaking a process down to known functions CS3102 (DAA), Dept. of CSE 13
- 14. Problem Solving In general: Understanding the problem Selecting the strategy Giving the steps Proving the correctness Trying to improve Using computer: Describing the problem: Selecting the strategy: Algorithm: Input / Output/Step: Analysis: Correct or wrong “good”or “bad” Implementation: Verification: CS3102 (DAA), Dept. of CSE 14
- 15. Probably the Oldest Algorithm CS3102 (DAA), Dept. of CSE 15
- 16. Euclid Algorithm: RecursiveVersion CS3102 (DAA), Dept. of CSE 16
- 17. Algorithmically Solvable Problem • Informally speaking • A problem for which a computer program can be written that will produce the correct answer for any valid input if we let it run long enough and allow it as much storage space as it needs. • Unsolvable(or un-decidable) problem • Problems for which no algorithms exist • the Halting Problem for Turing Machine CS3102 (DAA), Dept. of CSE 17
- 18. Criteria for Algorithm Analysis • Correctness • Amount of work done • Amount of space used • Simplicity, clarity • Optimality CS3102 (DAA), Dept. of CSE 18