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DESIGN AND ANALYSIS OF ALGORITHM FULL NOTES
- 1. CS6402-DESIGN AND ANALYSIS OFALGORITHMS M.SNEHAPRIYA AP/CSE
- 2. OBJECTIVES The student shouldbe made to: • Understand the fundamental of algorithm. • Learn the algorithm analysis techniques. • Become familiar with the different algorithm design techniques. • Understand the limitations of Algorithm power. • Overcome the computing problems.
- 4. SYLLABUS • UNIT I INTRODUCTION9 Notion of an Algorithm – Fundamentals of Algorithmic Problem Solving – Important Problem Types – Fundamentals of the Analysis of Algorithm Efficiency – Analysis Framework – Asymptotic Notations and its properties – Mathematical analysis for Recursive and Non-recursive algorithms
- 5. SYLLABUS UNIT II BRUTEFORCE AND DIVIDE-AND- CONQUER 9 Brute Force - Closest-Pair and Convex-Hull Problems- Exhaustive Search - Traveling Salesman Problem - Knapsack Problem - Assignment problem. Divide and conquer methodology – Merge sort – Quick sort – Binary search – Multiplication of Large Integers – Strassen’s Matrix Multiplication-Closest-Pair and Convex-Hull Problems.
- 6. SYLLABUS UNIT III DYNAMICPROGRAMMING AND GREEDY TECHNIQUE 9 Computing a Binomial Coefficient – Warshall’s and Floyd’ algorithm – Optimal Binary Search Trees – Knapsack Problem and Memory functions. Greedy Technique– Prim’s algorithm- Kruskal's Algorithm- Dijkstra's Algorithm-Huffman Trees. .
- 7. SYLLABUS UNIT IV ITERATIVEIMPROVEMENT 9 The Simplex Method-The Maximum-Flow Problem – Maximum Matching in Bipartite Graphs- The Stable marriage Problem.
- 8. SYLLABUS UNIT V COPINGWITH THE LIMITATIONS OF ALGORITHM POWER 9 Limitations of Algorithm Power-Lower-Bound Arguments- Decision Trees-P, NP and NP-Complete Problems--Coping with the Limitations - Backtracking – n-Queens problem – Hamiltonian Circuit Problem – Subset Sum Problem-Branch and Bound – Assignment problem – Knapsack Problem – Traveling Salesman Problem- Approximation Algorithms for NP – Hard Problems – Traveling Salesman problem – Knapsack problem.
- 9. Highlights of unit1 •Fundamentals of Algorithmic Problem Solving • Analysis Framework • Recursive and Non-recursive algorithms.
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- 13. Highlights of unit2 •Traveling Salesman Problem • Knapsack Problem • Strassen’s Matrix Multiplication • Convex-Hull Problems
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- 17. Highlights of unit3 •Warshall’s and Floyd’ algorithm • Optimal Binary Search Trees • Prim’s algorithm • Dijkstra's Algorithm
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- 21. Highlights of unit4 •The Maximum-Flow Problem • Maximum Matching in Bipartite Graphs • The Stable marriage Problem.
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- 25. Highlights of unit5 •Backtracking • n-Queens problem • Approximation Algorithms for NP • Decision Trees-P
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- 28. Text books TEXT BOOK: AnanyLevitin, “Introduction to the Design and Analysis of Algorithms”, Third Edition, Pearson Education, 2012. REFERENCES: • Thomas H.Cormen, Charles E.Leiserson, Ronald L. Rivest and Clifford Stein, “Introduction to Algorithms”, Third Edition, PHI Learning Private Limited, 2012. • Alfred V. Aho, John E. Hopcroft and Jeffrey D. Ullman, “Data Structures and Algorithms”, Pearson Education, Reprint 2006. • Donald E. Knuth, “The Art of Computer Programming”, Volumes 1& 3 Pearson Education, 2009. Steven S. Skiena, “The Algorithm Design Manual”, Second Edition, Springer, 2008. • http://nptel.ac.in/
- 29. SEMINAR TOPICS UNIT 1: AnalysisFramework UNIT 2: Quick sort UNIT 3: Prim’s algorithm UNIT 4: The Maximum-Flow Problem UNIT 5: n-Queens problem
- 30. ASSIGNMENT TOPICS UNIT 1: AsymptoticNotations UNIT 2: Multiplication of Large Integers UNIT 3: Warshall’s and Floyd’ algorithm UNIT 4: Maximm Matching in Bipartite Graphs UNIT 5: Assignment problem