Time Complexity

Now it is in week 6, half of the fall semester! Wow, time is so fast!

Course topic now is about Time Complexity. This is very similar to what I learnt in CSC165. But since I did not understand time complexity well in CSC165, I listened to the lecture carefully and will go to office hour to ask any questions that pops up in my mind.

We are learning complexity of recursive functions. Unwinding is a mostly used way to find the lower and upper bounds of a function. This is a different approach from how find the lower bound in CSC165. First, develop a special case and then apply for more general case, for example, first suppose n to be the power of 2 and then apply n to arbitrary numbers.

But there was one thing that I did not understand in class this week. Professor drew a picture to prove that a function was non-decreasing. I did not understand how this picture related to the decreasing of a function. So I went to the section on Thursday night. After the lecture, I asked professor Heap what did this graph mean. The professor explained patiently that since at first we supposed n to a power of 2 and this was not a general case, we wanted a more general case to apply to the unwinding. To apply the unwinding to a general case, we used the upper and lower bound of  log(n) to get an arbitrary number. First prove T was not decreasing and then used the relationship between n and n nod and the unwinding to develop an inequality that contained T(n) on one side of the unequal sign and n on the other side. In this way, we could find out both the upper bound and lower bound of a function.


After professor's Heap's explanation, I found I got a better understanding of  how to develop the upper and lower bound for a function.  Asking questions to professor helps a lot. He can always explain things well and he is very patient. ^_^

Feel much better for Structual and Well-ordering Induction

The midterm test made me feel I need more understanding in Structural and Well-ordering Induction.

I googled on line but could not find much useful explanation. But luckily I remembered we have a discussion board. I went to the discussion board and found with no surprise that I was not the only one who did not understand Structural and Well-ordering Induction well. In the specific tag, somebody provided a pdf that explain Structural and Well-ordering Induction. I opened the file and as I read through, I found this file very helpful. It solved my problems that when should I use Well-ordering Induction and also explain the difference between Structual induction and Simple Induction. To my undertstanding, Structural Induction could use Simple Induction as an approach to prove things. If we want to prove something that has a specific structure, we could use Structural Induction.

Well-ordering Induction is more likely to use during a provement. It does not like Simple Induction or Complete Induction that have a certain format, it is used as a part of the provement. I remembered professor Heap said it is more often used in the material we are going to learn in a few weeks.

First English Bolg

Let's talk about something else apart from study ^_^

First English blog! Wow~ very interesting!

I am very happy to share my CSC236 learning experience with everyone here. I wrote blogs before but it was not in English ( it was in my native language haha~), so actually this is my first English blog and it sounds like a challenge to me! I will keep wrting up things so that we can exchange our learning experience here~

I finally finished my first CSC236 term test this Wednesday. How does everybody feel? I think it was not very hard but I think I need to go over more about structual induction, since it is very like simple induction and I was a little bit mixed. I think I am ok with simple and complete induction but I need to work more on well-ordering. I can understand the principle but I don't know how to use it to solve problems. What I plan to do is to read the course textbook and google is always there to help~
Hope I can get a better understanding soon~

Hope everyone has a nice sleep.

 

 

Midterm 1 is coming!

Up to now, we have learnt Simple Induction, Complete Induction, Structural Induction and Well-ordering Induction.

Simple Induction and Complete Induction was not so hard for me, actually I found they were easy to understand. But Structual Induction and Well-ordering were not so clear to me. I could understand the class material but I was confused about the application. When and where should I use Structural or Well-ordering Induction?

The first midterm test is coming and I was a little bit nervous since it is the first test in this course. I didn't do well in CSC165 so I was alway careful and tried to understand all the course notes in CSC236 and hope to get a better grade. I think I am going to read through the textbook and try to make every point clearer.

Assigment 1 Office Hour

So as I said, I went to professor Heap's office hour for the assignment.

There were five or six people waiting in the line. I was hoping they were all coming for this assignment because this way I could hear more about the assignment. ^_^

So when it was my turn, I talked to professor Heap about my question. He thought for a few second and told me my problem was that if I did it in my way then I was not proving what supposed to be proved in the question. I was proving the other way around. I was confused at first, because I thought my logic was correct, but after professor Heap explained to me once and once again, I suddenly realized where did I go wrong. It was to prove "any binary string that begins and ends with the same bit has an even number of occurrences of substrings from {01; 10}" but what I did was to make a provement for "any binary string that  has an even number of occurrences of substrings from {01; 10} begins and ends with the same bit." My induction hypothesis made my conclusion go to the other way around and this was why I felt my induction step was wierd but could not tell how.

After I solved my question, I stayed in professor Heap's office and listened to other students' comments or questions. I liked this atmosphere. It made me feel like I had a wide range of knowledge, like our professor, ^_^ and I felt confident to talk in a group. I also liked to learn with people and listen to their questions becasue everyone may have different idea and thoughts and we can always make a supplement to each other. It helps everyone to progress on study.

Assignment 1

The first assignment is about Induction.

We learnt Simple Induction and Complete Induction in the first two weeks. I thought this assignment aimed to let us practise how to use induction to prove things.

I started to prepare for this assignment today, read relevant contents on the textbook and did a summary of the course notes. Then I thought I was ready enough for this assignment. I read the assignemnt sheet and found it was not so hard although there were lots of things needed to be considered, for example, Simple and Complete, which was better to use for each question?  What was the base case if I used Simple Induction and what was the case that cannot be included in the general case if I used Complete Induction?

As what I always did, my plan was to first write up the answers and then discuss with professor Heap. When I was writing the assignment, I found my approach to do question four was a little bit wierd. I didn't know where did I do wrong but I had the feeling that I missed something important in my induction. So I was going to bring my questing to the office hour and hope I could get some feedback.