一、課程說明 (Course Description)



There are many problems around us, and they need some fast and

good methods to be solved.  For instance, 



  (i)  Suppose that we have been very lazy the last few weeks, 

       and suddenly, we find that 10 homeworks A,B,C,D,E,..., J

       will be due next week.   The homeworks have different deadlines,

       and some will be on Monday, some will be on Friday.  

       We have an estimation of how fast we can finish each homework.



       Questions:  Can we finish all of them?  

                   If so, which one should we do first, which one next?

 

  (ii) Suppose that our school has 100 landmarks (such as the library, 

       the EECS building, the main gate, etc), and you want to design 

       a system so that if a user enters any two landmarks (say, A and B), 

       your system can immediately suggest a shortest route from A to B.



       Of course, you can find all the 100x100 routes by yourself, but 

       it would be better if you can write a computer program to do it

       for you.  Is there any efficient computer program for this problem?



To solve a particular problem, there are usually many different methods.  

For instance, in Problem (i), we can try all possible arrangements of the 

homeworks A,B,C,D,E, ... and see if they can all be finished in time.  

However, we need to try 10! arrangements, and this would take a long time.

On the other hand, if we want to finish all the homeworks, it seems that

we should do the one whose deadline is nearest first, and then do the one

whose deadline is second nearest, and so on.  There may be other methods 

we can try.  One question arises:  Among all methods, is there one which

is always faster and better than the others?   



In this course, we will look at a lot of fundamental problems that are solved 

daily around us, and we will study their solutions (that is, the methods or 

the algorithms, and show how to analyze the performance of the 

solutions.  We will also introduce general techniques to help us design a good 

algorithm when we face a new problem.





二、指定用書 (Text Book)  

    Introduction to algorithms, 2nd edition, the MIT press, 2001

    by T. Cormen, C. E. Leiserson, and R. L. Rivest 



三、參考書籍 (References)   

    1. Introduction to the Design and Analysis of Algorithms,

       by R. C. T. Lee, R. C. Chang, S. S. Tseng, and Y. T. Tsai



    更多參考書籍 (More References)   

    2. Algorithms in C++, (or Algorithms in Java), by R. Sedgewick

    3. The Art of Computer Programming, by D. E. Knuth



四、教學方式 (Teaching Method)  

    Lectures and Tutorials (Lectures in English)



五、教學進度 (Syllabus)



　I.   Mathematical Foundations

        1. Introduction

　      2. Growth of Functions

        3. Summations

        4. Recurrences



  II.  Sorting and Order Statistics

        6. Heapsort

        7. Quicksort

        8. Sorting In Linear Time

        9. Medians and Order Statistics



  III. Data Structures:  Self Study



  IV.  Advanced Design and Analysis Techniques

       15. Dynamic Programming

       16. Greedy Algorithms

       17. Amortized Analysis

       

  V.   Advanced Data Structures

       19. Binomial Heaps

       20. Fibonacii Heaps

       21. Data Structures for Disjoint Sets

       

  VI.  Graph Algorithms

       22. Elementary Graph Algorithms

       23. Minimum Spanning Trees

       24. Single-Source Shortest Paths

       25. All-Pairs Shortest Paths

       26. Maximum Flow

       

  VII. Selected Topics

       28. Matrix Operations

       32. String Matching

       34. NP-Completeness

       35. Approximation Algorithms

       **. Branch-and-Bound



六、成績考核 (Evaluation)   

    To be announced



七、可連結之網頁位址 (Web links) 

    Please visit the link of past year's course for a reference