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Design and Analysis of Algorithms

Design and Analysis of Algorithms. 4 th Semester Computer Engineering Spring 2015 Conf.dr.ing. Ioana Sora ioana.sora@cs.upt.ro. Our goal:. design algorithms that are correct and efficient. The Need for Correctness.

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Design and Analysis of Algorithms

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  1. Design and Analysis of Algorithms 4th Semester Computer Engineering Spring 2015 Conf.dr.ing. Ioana Sora ioana.sora@cs.upt.ro

  2. Our goal: designalgorithms that are correct andefficient

  3. The Need for Correctness • Much too often, algorithms are designed in an ad-hoc manner and “validated” through testing on a few particular data sets …

  4. The algorithm: A:array[1..n] of integer for i=1 to n-1 do if A[i]>A[i+1] swap(A[i], A[i+1]) The “tests”: Example of a “sorting algorithm” 5, 1, 2, 7, 6 15, 2, 4, 17,16 But it does not work for 3, 2, 1, 5, 4 !

  5. The Need for Correctness • Much too often, algorithms are designed in an ad-hoc manner and “validated” through testing on a few particular data sets … • The fact that an algorithm passed a number of tests on certain data sets DOES NOT guarantee that the algorithm is correct • The fact that an algorithm fails a test on ONE data set proves that it is NOT correct

  6. A:array[1..n] of integer for l:=n downto 1 for i=1 to l-1 do if A[i]>A[i+1] swap(A[i], A[i+1]) How can we know for surethat the algorithm is correct ? (Other than simply believing the programming textbooks ;-)) The Bubblesort Algorithm

  7. Analyzing Algorithms • We need methods and metrics to analyze algorithms for: • Correctness • Methods for proving correctness • Efficiency • Time complexity, Asymptotic analysis

  8. Designing Algorithms • Ok, so you will know (will learn) how to analyze a given algorithm. • But where do these algorithms come from ? • Clever people already designed a plethora of solutions (algorithms) for different problems and we find them in textbooks, internet, etc. • But how will you design solutions for new problems ?

  9. How to learn algorithms ? http://www.neatorama.com/twaggies/2010/11/07/no-112-robcorddry/

  10. Kruskal’s algorithm Prim’s algorithm • Design methods: • Greedy • Design by Induction • Divide and Conquer • Dynamic Programming Floyd’s algorithm Dijkstra’s algorithm Tarjan’s algorithm

  11. What about data structures ? • Fundamental data structures: • Model fundamental data • lists, queues, graphs • Special data structures: • Created to optimize a specific (set of) operation(s) for a specific context • Search trees, balanced trees • Optimal trees • Disjoint sets

  12. Course Goals • Learn to design algorithms that are correct and efficient • How do we know that: • an algorithm is correct ? -> correctness proofs • an algorithm is efficient ? -> analysis of algorithms (time complexity) • How to design solutions for new problems ? • Learning general techniques for design • Studying a set of well-known algorithms, to serve as examples of success stories for applying general design techniques • Become aware that good algorithms are key parts of software engineering practice !

  13. Course Schedule • Review: Analysis • Proving Correctness of Algorithms. Induction • Design of Algorithms by Induction • Dynamic Programming • Graphs • Data structures: Search Trees, Balanced trees, Augmented data structures • Great algorithms in real life problems: • Data compression • Search engines

  14. Textbooks

  15. Course Webpage All official information related to the Algorithm Design and Analysis classes: http://bigfoot.cs.upt.ro/~ioana/algo/

  16. Lab Assignments • Comprise different types of exercises: • Questions - to be solved with pen on paper • Simple implementation problems - implement something that was described in the course • Algorithm design problems • This kind of assignments require to: • Describe the proposed algorithm • Analyze your algorithm (prove correctness and efficiency) • Implement the algorithm • Tool projects • Complex projects containing also a part of algorithm design and implementation • They are optional, but: in order to get a 10 for the lab activity, you have to do at least one tool project

  17. Examination and Grading • Final grade = 2/3 final written exam + 1/3 work during the semester • Written exam: • Questions and Algorithm design problems (such as these the lab description above) • Work during the semester: • Lab assignments • Lab quizzes • Tool project (for 10) • Optional bonus points: for exceptional activity = doing more than one optional tool project during the semester, you can gain extra-points to the grade of your final written exam

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