CSC165 has been a great experience for me. at first, everything seems to be very hard and complicated. all the symbols and proof and stuff. I am so scared that I could not pass this course because of the logic stuff, However, if you understand the material, even the basic of it, everything seems to be a lot easier. I do not know about anyone else, but for me, I enjoy taking this course very much. I love this course, although, I do not know what my mark would be. It's great to be Dr. Heap student. I think he is very nice, he explain very clear and he made it sounds very interesting.
For me the most useful thing in 165 is the tutorial and the assignment, I did not mean that the class is not useful. It is very useful too, but after class, sometimes, I still feel quite confuse. After tutoril and assignment, I actually understand the material a lot better. I don't really like tutorial for other courses, but for 165 the tutorial is extremely useful because I get the notes, a very useful notes from TA and I can ask question when I get confuse with the material from the lecture.
At first, honestly, I thought Slog was the least useful task in csc165, but after I did it for the whole semester, I feel that it is actually very useful to keep me on track of the material, sometimes, i can even ask question and answer by TAs.
The most interesting part and I find it very enjoyable is the proof part, it comes very difficult and complicated at the beginning, but once I understand, it becomes very fun when you can actually solve the proof, it fells very satisfying if I can solve it, but sometimes, it can get very complicated too.
The challenge that I find the most in this course is from the halting material, the last chapter from the course notes, the reduction of halting problem. I don't understand at all how to do it, at least not yet I hope. i know the step how to do it, but the most difficult is to write the program. usually after tutorial and assignment, I will be able to understand the material better, but even after tutorial and assignment, I still don't understand how to write the program using the reduction. I do not know how to come up with the program.
Well, aside from the challenge, I like this course and I hope the test will not be so difficult.
Thank you especially for Prof. Heap for the really fun, useful, interesting, and enjoyable lecture. I am looking forward to attend your other class next year. Also, special thanks to my TA, Maria Tsimpoukelli for the very useful notes you gave us in tutorial, it helps a lot, and also for answering many of my questions...:)
Thursday, 4 April 2013
Tiling Problem
1. understand my problem.
in my understanding, I am suppose to come up with general procedure of this tiling problem. I am supposed to match the 1 x 2 tiles to 2 x n units.
2. Plan
My plan is i am going to draw the units with the actual size (my plan is to draw 2x1, 2x2, 2x3, 2x4, 2x5, 2x6, 2x7, and 2x8) and also draw several 1 x 2 tiles with different color to differentiate, also, some of them is horizontal, and some of them is vertical. Then i will try to match up the tiles to the unit in different ways to determine how many ways are there to tile each unit. then, I am going to record every different way and compare different size. After I have my data, I am going to try to determine the general formula to be able to know how many different way possible to tile 2 x n unit.
3. first, I am going to draw the unit and the tiles, here is the example on how i do it.
After I tried different way to tile the unit, I record it and here is the data I have got, I am using the 'v and h' code, v is vertical tile and h as horizontal tiles.
now, I compare the date in order to come up with the general formula.
It took me quite sometimes to figure out the formula, there is no much similarity between each other, I can see the pattern, it is quite obvious, for example, for 2 x n unit, there will be at least n number of way. But after that there is no obvious similarity. Until I see the total number of each different unit.
unit 2 x 3 where the total is 3 is the sum of the previous 2 units which are 2 + 1. Another example, unit 2 x 5, with the total of 8 is the sum of the total for unit 2 x 3 and 2 x 4 which -> 5 = 3 + 5. And this pattern works for all the units I have drawn. Therefore, I conclude, the general pattern for 2 x n unit is
Un = U(n-1) + U(n-2).
4. The challenge I find doing this problem are, first, it is not quite easy to record the data as n grows larger, I had to repeat for more that 4 times in order to get right result because as the unit grows bigger, more and more tiles can fit into the unit, and this means more possibilities of patterns.
second, coming up with the formula is not easy, because as I mentioned before, there is no obvious pattern that I can see from the data, I even make the color difference in order to see the difference.
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