Diagonals!
When we were initially given the Diagonal Count problem, I thought
'Okay, let's do this." But admittedly, it was probably on a higher level
of difficulty than expected compared to the previous ones. Fortunately we have
Polya's Problem Solving Techniques in mind to aid this journey of logical
justification and revelation. First of all to solve anything, we need to
understand what the problem is. I had to carefully read the issue twice - Once
when I scanned through to get the gist of it and the next to fully comprehend
it. So we're given a rectangle that's length and width is known by the make-up
of n columns and n rows. Of course m and n are positive whole numbers. We are
also given a line drawn from the upper-left corner to the bottom-right (the
diagonal!). Now what we need to do is devise a plan to concoct a formula with
the given information to figure out how many grid squares the line will pass
through. Just like mostly everyone in this class, I tried to find a pattern by
assigning different values to m and n. I also noticed that the shape forms two
equal right triangles, giving me an idea to perhaps somehow use the slope
(diagonal) in my formula. One more thing discovered in class was that the
interior squares crossed when n = m + 1 was the same as when m + n
-1. After a lot of thought and becoming more familiar with the problem by
reading through the solutions link provided, as well as other students' slogs,
it was clear this had several solutions, unfortunately, none that I came up
with on my own. I'm hoping Prof Heap goes over this problem and clears our
thinking soon...
Assignment 3
When this was posted, I had no
lack of work to already get done for my other courses leaving this task at the
bottom of my to-do list. When I did get to it however, I tried not to panic as
I went through. Most of it looked familiar so I wasn't too worried...until I
got to the last two questions.
Anyway, question 1 wasn't bad at
all. All it took was to sit down and clearly understand, plan, and implement.
As I was going through my solution, another shorter and more efficient approach
came to mind so I used that as well. Question 2 was similar to the ones we'd
done enough times in class, although it did take me more time to solve than
expected. Questions 3 and 4 were where I got stuck for a while, confused as to
how L'Hopital's Rule on limits was to be used. Thankfully, attending the next
lecture helped a lot where some hints were given. As for question 5 and 6, I
had to thoroughly go through the course notes, lecture slides, as well as
running a Google search on what the halting problem even is to attempt solving
them. Up until Question 5, I understood what’s being asked, but Question 6 had
me lost for hours. Fault on my side for not paying attention during the lecture
where this was covered. After a while, it didn't seem as challenging anymore
and my fear of getting that 20% on the question was gone. Again all these
problems required me to try out some approaches, some worked, and others
didn't. Some of them seemed to have worked, but once re-reading, mistakes were
found, but hopefully, I've created solid enough ones for the standards of this
course.
No comments:
Post a Comment