Algorithms, Fall 2021

This course provides an introduction to the design and analysis of computer algorithms, with a particular emphasis on the use of principles of mathematical induction in designing algorithms. Its goal is to acquaint the students with basic computer algorithms and their design principles and to cultivate the students' ability in designing and analyzing algorithms independently. }

• 01/23: grade report available; please send inquiries, if any, to the instructor by 2PM 01/25 (Tue.).
• 01/11: notes/slides for Dynamic Programming revised.
• 12/28: notes/slides for NP-Completeness available.
• 12/28: notes/slides for Reduction available.
• 12/21: notes/slides for Dynamic Programming available.
• 12/07: notes/slides for Advanced Graph Algorithms available.
• 11/29: Suggested Solutions to Midterm Problems available.
• 11/23: notes/slides for Basic Graph Algorithms available.
• 11/09: notes/slides for String Processing available.
• 11/02: old exams.
• 10/26: notes/slides for Searching and Sorting available.
• 10/26: notes/slides for A Supplement to Data Structures available.
• 10/19: notes/slides for Design by Induction available.
• 10/12: notes/slides for Analysis of Algorithms available.
• 09/28: notes/slides for Introduction and for Mathematical Induction available.
• 09/28: this website created to complement the NTU COOL site for this course.

Yih-Kuen Tsay (蔡益坤), NTU IM Dept., 3366-1189, Xtsay@ntu.edu.twX (between the enclosing pair of X's).

Tuesday 2:20~5:20PM, Room 103, Management Building 2.
TA sessions will be scheduled prior to some of the class meetings between 1:20 and 2:10PM; see the course schedule below.

Tuesday 1:30~2:00PM, Wednesday 1:30~2:00PM, or by appointment, Room 1108, Management Building 2.

Wei-Cheng Liu (劉韋成), Xr09725026@ntu.edu.twX (between the enclosing pair of X's).
Jack Su (蘇俊杰), Xr09725002@ntu.edu.twX (between the enclosing pair of X's).

• [M] Introduction to Algorithms - A Creative Approach, U. Manber, Addison-Wesley, 1989. (Four copies of this book have been put on reserve at NTU Library in the B1-教師指定參考書區 under 演算法(BM-4). Additionally, eleven copies are available for loan; please contact one of the TAs.)
• [C] Introduction to Algorithms, Third Edition, T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein, MIT Press, 2009. (開發圖書代理; one copy of this book has been put on reserve at NTU Library in the B1-教師指定參考書區 under (FF-9).)

We will try to cover most of Manber's book plus supplementary material, including a few chapters of the book by Cormen et al. (Note: a TA session will precede a class meeting whose date is marked with an *. There are six TA sessions on 10/12, 10/26, 11/09, 11/30, 12/21, and 01/04.)

• Introduction [M: Ch. 1; C: Ch. 1,2] (.5 week: 09/28a) [notes, slides]
• Mathematical Induction [M: Ch. 2; C: Ch. 4] (1.5 weeks: 09/28b, 10/05) [notes, slides]
• Analysis of Algorithms [M: Ch. 3; C: Ch. 2,3,4] (1 week: 10/12*) [notes, slides]
• Design by Induction [M: Ch. 5] (1 week: 10/19) [notes, slides]
• Data Structures: A Supplement [M: Ch. 4; C: Ch. 6,13,21] (.5 week: 10/26a*) [notes, slides, Building an AVL Tree (Illustration)]
• Searching and Sorting [M: Ch. 6; C: Ch. 6,7,8,9] (1.5 weeks: 10/26b, 11/02) [notes, slides, Heapsort (Illustration), Bottom-Up Heap Building (Illustration)]
• String Processing [M: Ch. 6; C: Ch. 32] (1 week: 11/09*) [notes, slides, Construction of a Huffman Tree (Illustration)]
• Midterm (2021/11/16)
• Graph Algorithms: Basic [M: Ch. 7; C: Ch. 22,23,24,25,26] (2 weeks: 11/23, 11/30*) [notes, slides, Dijkstra's Algorithm (Illustration), Prim's Algorithm (Illustration)]
• Graph Algorithms: Advanced [M: Ch. 7; C: Ch. 22,23,24,25,26] (2 weeks: 12/07, 12/14) [notes, slides]
• Dynamic Programming [C: Ch.15] (1 week: 12/21*) [notes, slides]
• Reduction [M: Ch. 10; C: Ch. 29] (.5 week: 12/28a) [notes, slides]
• NP-Completeness [M: Ch. 11; C: Ch. 34] (1.5 weeks: 12/28b, 2022/01/04*) [notes, slides]
• Final (2022/01/11)
• NP-Completeness Continued [M: Ch. 11; C: Ch. 34] (1 week: 01/18)
• Wrap-Up Discussions (1 week: 01/25)

• Mathematical Induction (a Wikipedia page)
• Structural Induction (a Wikipedia page)
• MIT OpenCourseWare: Introduction to Algorithms
• Stanford Coursera: Algorithms
• What is an Algorithm? (M.Y. Vardi, Communications of the ACM, Volume 55 Issue 3, March 2012)
• Sorting Algorithms Animations
• Graph Animations with Combinatorica
• The P versus NP Problem (Stephen Cook)
• The website of ICPC (International Collegiate Programming Contest)

Homework 20%, Participation 10%, Midterm 35%, Final 35%.