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. Maximin 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)
5 Assignments: Best four * 37%
Remaining one * 3%
Midterm Quiz: 10%
Final Exam: 50%
-----------------------------------
Total 100%
Remark: You can discuss with your classmates and exchange
high level ideas in completing your homework.
However, you must complete your homework
by yourself, using your own wordings.
If someone is caught copying the others or letting
the others to copy, we will adopt the following policy:
1. If caught for the first time, 50% is multiplied
to the overall assignment scores.
E.g., If your scores in the assignments, quiz, and final
exam are originally 30/40, 6/10, and 35/50,
respectively. Then, the adjusted score will be:
15/40, 6/10, 35/50, so that in total, it becomes
56/100.
2. If caught for the second time, 0% is multiplied
to the overall assignment scores.
E.g., If your scores in the assignments, quiz, and final
exam are originally 30/40, 6/10, and 35/50,
respectively. Then, the adjusted score will be:
0/40, 6/10, 35/50, so that in total, it becomes
41/100.
Our tutors are very nice and they will give you (reasonable) hints and
supports if you encounter difficulties in completing the assignment.
They are also very responsible in ensuring fairness, so that they will
try their best to catch students who are copying the others.
七、可連結之網頁位址 (Web links)
To be announced