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Algorithm Design

Algorithm Design. Nattee Niparnan Dept. of Computer Engineering, Chulalongkorn University. The Course. Midterm 40% Final 40% Something else 20% Quiz 10% Lab 10%. Yes, we have labs. This year, we introduce lab You will be required to participate in “online” activities

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Algorithm Design

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  1. Algorithm Design NatteeNiparnan Dept. of Computer Engineering, Chulalongkorn University

  2. The Course • Midterm 40% • Final 40% • Something else 20% • Quiz 10% • Lab 10%

  3. Yes, we have labs • This year, we introduce lab • You will be required to participate in “online” activities • Writing code (in C language) • Teacher and TA will help you

  4. Topics • Analysis • Asymptotic notation • Big O analysis • NP-Complete • Design • Divide and Conquer • Dynamic Programming • Graph Algorithm • Greedy Algorithm • Search There will be labs for each of these topics

  5. Books : Required • Algorithms, S. Dasgupta, C. Papadimitriou and U. Vazirani, McGraw-Hill, 2008

  6. Books : Supplemental • การวิเคราะห์และออกแบบอัลกอริทึม, สมชาย ประสิทธิ์จูตระกูล, NECTEC, 2544 • Data Structure & Algorithm Analysis, Mark Allen Weiss. • Introduction to Algorithms 2nd edition, T. Cormen, C. Leiserson, R. Rivest, C. Stein, MIT Press & McGraw-Hill, 2001. • Introduction to Algorithms: A Creative Approach, UdiManber.

  7. Web • Webboard • http://www.cp.eng.chula.ac.th/webboard/viewforum.php?f=18 • Lab • http://www.nattee.net/teaching/ • You can also find my slides there

  8. Introduction Chapter 0

  9. What is an algorithm? • A precise instruction based on elementary operation • Which takes something as an input and process it to some output • Usually to solve some problems

  10. What is Problem? • A task with precise description of admissible input • and the “property” of the desired output • E.g., GCD • Given two positive integers (input) • Determine GCD of the given integers • (express the property of the desired output) • GCD is well defined

  11. Problem Instance • Determining GCD is a problem • How many actual problems? • GCD of 1,2 ? • GCD of 234,42? • ??? • Problem instance • A problem with a specific input • E.g., find a GCD of 42 and 14

  12. Purpose of this class • “how to design an algorithm for given problems” • Analysis • Synthesis  emphasized…. • Correctness • For any instances, it must produce appropriate output • Efficient!!

  13. Calculating Fibonacci Sequence • Fibonacci sequence • 1,1,2,3,5,7,8,13,21,34,55,89,144,233,377,610,987,1597,2584

  14. The Problem • Input: • a positive number N • Output: • Fn (the nth Fibonacci Number) • Example instances • Ex. 1: N = 10 • Ex. 2: N = 15 • Ex. 3: N = 0 N = -4 is not an instances of this problem!!!

  15. Approach 1 • Array based • DP (linear)

  16. Approach 2 F(9) • Recursive (exponential) F(8) F(7) F(7) F(6) F(6) F(5) … … … …

  17. Approach 3 • Divide and Conquer (logarithmic)

  18. Approach 3 • Find exponential • Divide and Conquer (logarithmic)

  19. Approach 4 • Closed form solution (constant) Golden Ratio

  20. Conclusion • Difference Design  Difference Performance • This class emphasizes on designing “efficient algorithm”

  21. Algorithm Again • It is the essence of the computation

  22. Side Note on Algorithm • Named after a Persian mathematician “Muhammad ibn Musa Khwarizmi” • Wrote book on linear equation • Introduce number 0

  23. Topics Overview Analysis part

  24. Asymptotic Notation • Measurement of “efficiency” of algorithms • How to compare two algorithms • How to predict behavior of the algorithm

  25. Big O analysis • How to determine Big O of some code • Recurrent Relation

  26. NP-Complete • What computer could solve • Efficiently • Inefficiently • The difference between “Efficiency” and “Inefficiency”

  27. Topics Overview Synthesis part

  28. Divide and Conquer • Solve a problem instance by dividing into smaller instance • Based on induction

  29. Dynamic Programming • Reduce redundancy computation • For the case when there are several overlapping subproblem

  30. Greedy Algorithm • Solve the problem by doing the best for the current step • Proof of correctness

  31. Graph Algorithm • Algorithm related to graph structure • Shortest Path • Minimal Spanning Tree

  32. Search • Solve the problem by enumeration • Systematical enumeration • Performance improvement

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