CS-251A Data Structures and Algorithms
"To iterate is human; to recurse divine" - L. Peter Deutch
Hints on How to Pass this Course Smiling
Welcome to Computer Science 308-251A: Data Structures and Algorithms. This course is an introduction to the design and analysis of algorithms. Below you will find a description of the main ingredients involved in taking this course with hints for passing, enjoying and making the best out of it. Please study it carefully.
This course is NOT a programming course and there will not be any programming assignments. The course is instead concerned with the principles behind the design of efficient algorithms for solving a variety of different classes of problems in different contexts. It is NOT concerned with the details of implementing algorithms on real computers with "real" programming languages such as FORTRAN II, APL, C or JAVA. Instead we will use idealized computers (mathematical models of computers if you like) such as the Straight-Edge-and-Compass, the Turing Machine and the Real RAM (Random Access Machine with real numbers as inputs) to measure the computational complexities of our algorithms. We will also use idealized data structures to study the algorithms and their storage requirements.
Although in this course we are concerned with designing algorithms that are ultimately intended for machines to process, we are NOT interested in communicating with the machines but rather with each other. We are interested in communicating with humans about algorithms. Therefore we will NOT use code in this course. Code was designed to be understood by machines not humans. We will describe algorithms in a natural language such as English and in the language of mathematics as has been done for thousands of years. Furthermore mathematics should not be confused with mathematical notation. The essence of mathematics lies in the precision of concepts and not in symbolic notation. Mathematical notation will be minimized. Algorithms described in code will get a mark of ZERO. Students using mathematical notation gratuitously will be penalized. Mathematical notation should be used only when absolutely necessary if it helps the reader. Remember that storage space is no longer a problem and we need not save precious space at the cost of making things difficult to read. In this course we will learn how to use English in a precise way.
One of the most important properties of an algorithm is its correctness. In fact this is so important that many people refuse to call a procedure an algorithm if it is not guaranteed to give the correct solution. Many "algorithms" inhabiting the computers in society at large are incorrect. This can cause great cost and tragic suffering. For example, patients have been killed by overdoses of radiation because of incorrect algorithms. The American astronauts aboard the space shuttle Challenger were killed because of an incorrect geometric algorithm used in rebuilding the booster rockets. In fact a nuclear world war could be caused by an incorrect algorithm. Therefore it is very important to design correct algorithms. In later computer science courses students often have trouble proving the correctness of algorithms. Therefore this course will concentrate on various techniques for proving the correctness of algorithms.
In later computer science courses students have the most trouble with induction proofs. In a very important sense this is the most relevant method of algorithm design and correctness proof for computer scientists since it lies at the heart of recursion and divide-and-conquer, two fundamental techniques for obtaining efficient algorithms. Therefore this course has as one goal for the students to master proofs by induction. Induction proofs will be a recurring theme in the course.
Students should consult the course web page regularly. It can be found at: http://www-cgrl.cs.mcgill.ca/~godfried/teaching.html. This page contains several sections we will now describe.
This section of the course web page details the performance evaluation of the students, the coordinates of the lecturer and teaching assistants, the text book used in the course and similar matters.
This web page contains the calendar of events for the course such as the in-class exam and quizzes, the dates the assignments are handed out and due, and a very short title of each lecture. The bulletin board at the beginning contains messages from me to you of important day to day events, matters related to the assignments, etc and must be checked every week-day.
This web page contains a detailed list of topics covered in every lecture. It contains the reading assignments made every week from the text book, handouts and web material. It also contains suggested play. While this section is not required, students are strongly encouraged to play with the applets suggested in this section. Students who do will be at an advantage as it greatly facilitates learning the material in this course.
This page contains an skeletal outline of the course contents.
This page contains much of the material that we will cover in the course that is not contained in the course text book (Udi Manber: Introduction to Algorithms). Many of the course reading assignments will concern pages in this section. Here you will also find alternate descriptions of material that is in the text book. It sometimes helps students to learn when they read different explanations of the same thing by different people. This web page also contains the applets for the suggested play section of the assignments. Finally, this page also serves as a library to satisfy your general curiosity concerning material that is interesting and directly relevant to the course. Hence it contains much more material than what we will cover and I do not expect you to read it all. However, I do suggest you browse through all of it and read what is most interesting to you.
There are two in-class tests and one final exam . All these are closed book. However, I am not interested in measuring your memory. Computers are much better than we humans at that. The tests will measure your ability to think creatively. Students often ask: what material will be covered in the test? My answer is always the same. I don't want to insult your intelligence by asking you to regurgitate material we have covered. A machine can do that much better than we can and I don't want to treat you like machines. I want to test you on what machines cannot do (yet), and that is to generalize or apply your knowledge to solve new problems in new contexts. Therefore my tests will always cover everything we have NOT covered in the course. The material I learned as a student in university concerning radios, cathode ray tubes and transistors is useless to me now. Many of the things I teach now did not exist ten years ago. The models of computation and algorithms we use now may be obsolete ten years from now. On the other hand, the creative problem solving techniques and critical thinking skills I learned as a student can be applied to things other than transistors, such as the latest trends in computational geometry. How can you do well on my tests? University is (still, thank heaven, although fast eroding) a place for discussing knowledge in a free and open atmosphere, and I encourage you to discuss all matters of the course with your class mates. On the other hand the modern harsh reality dictates that obtaining a university degree is also a certification method for certain skills - hence the tests. The best way to study for the tests in my course is to do the assignments and exercises on your own. Only personal discovery leads to true understanding. The text book by Udi Manber also contains many exercises at the end of each chapter with answers at the back of the book. Doing these exercises on your own is an excellent way to learn how to design algorithms in particular and how to think creatively and critically in general. Think of your brain as another muscle in your body. To get it in shape requires practice, practice and more practice.
Please write legibly. If the TA cannot read your assignment you will get ZERO. Whenever you are describing an algorithm you MUST always include a proof of correctness. NEVER say that something is obvious or use words such as "clearly....". Obviousness is always the enemy of correctness and sometimes insults the reader as well. Always give clear simple short arguments. Long convoluted sentences increase the probability that they are wrong. Pretend you are explaining things to your ten-year old sibling. Don't guess. If you are not sure of something say so. Clear thinking with a partial answer will be rewarded. Cloudy thinking with a full answer will be penalized.
I am unforgivingly strict with late assignments. Assignments MUST be handed in on the day due and BEFORE the lecture begins. Every day that the assignment is late, starting with the day due and including weekend days, will result in a penalty of 10% of the original worth of the assignment.
The TA's are responsible for marking the assignments and the quizzes and exam. If you have any questions about how you were marked please go see them. If you have general questions about the course material please see them too. They are there to help you.
If for some reason the TA's cannot help you please come and see me. In any case please come by sometime to say hello and tell me how you are doing in the course. My door is wide open during my office hours and I would love to meet you.