Rough week gone by, so many assignments due in this one week. Finishing problem set #5 was straight forward, but going into the weekend A2 would give me and my partner quite a bit of trouble. Questions 2, 3 and 4 were fairly straight forward and didn't take too much time to tackle them.

Question 1 was another story, we spent most of our time on the ternary tree question as we couldn't find a suitable pattern or closed form to describe the relationship between the number of nodes and the number of non equivalent ternary trees. We had gone through many ways of counting the number of ternary trees including the grueling task of drawing out all of the possible ternary trees for nodes 1 to 4 and still to no avail, we couldn't pin down a closed form. Many of our findings hinted to a possible closed form where some numbers were repeated from the previous number of nodes, but there always seemed to be some constant that would hang around and we couldn't find a pattern that would derive these.

To solve this seemingly impossible question we took advantage of Danny's office hours and we asked him how we should go about finding the closed form. After showing him our pages of rough work he worked with us and helped us find a way to count the trees by grouping all the ternary trees the right side of the tree could make with the left side having 0 nodes, then having 1 node, and so on. This was really helpful and we returned home to take another crack at the question. We had it pretty much figured out but the deadline drew near and we were not able to piece together a full solution before handing it in. We managed to summarize how we would go about proving the formula but hopefully next time we won't get such a tough question.

Test #2 is next, lets hope for the best, good luck.

The midterm was returned to us last week and I was surprised to see I did a lot better than I thought. This was a relief but there are still two more term tests and assignments that can potentially bring my mark down. Hopefully the material doesn't get too hard as the course goes on.

I've began working on Assignment 2, the first two questions look pretty straight forward and I should be able to finish them before the weekend. Problem Set 4 came out a little late but the due date was extended. I am still going to try to finish it by Thursday night because I can't get to school in time for the early class and I would have to ask someone to hand it in for me. I still think people in the Thursday class get a disadvantage because they do not get a lecture that usually explains the concepts that are used to solve the week's problem set until after it is due. I think that we should be able to at least hand in the problem set after the first hour of class because in some cases that hour of lecture really helps with the problem set and some people just can't make it to the earlier class the next day. Maybe even let us electronically send the problem sets like the assignments to you as long as it is before the 10am deadline on Friday. I guess i could also search for the early class lecture slides and look them over to get a better of idea of how to tackle the problem sets, but it would be nice to have the same benefits of the earlier class.


This next week is going to be very busy for many of us with a bunch of assignments due next week and ongoing midterms. Hopefully after this next week things will die down a bit and we can have a relaxing weekend after A2 is done.

Edit: Just checked the boards and Prof. Heap will be taking problem sets on Monday from 11-3pm. Thanks!

I managed to finish A1 and Problem set #2 over the weekend. Feels good to have them off my back. Problem set #2 was pretty straight forward, Prof Heap gave an example in one of the lectures that helped a lot. I had more trouble with A1 especially Q2 with the lunch menus. I couldn't find a pattern between the lunch menus, or i didn't try hard enough. Either way I spent most of my time staring at this question and trying to make a menu for n>3 items. I looked to a friend for help and he pointed me in the right direction, giving me insight on how he found the pattern. After that it took a few minutes to devise and prove a technique and then I was done. Now to study for the midterm and hope for the best, good luck everyone.