Overall I feel that this course has a great learning experience both in terms of the material in my future cs career but also in terms of how to learn material.
Friday 5 April 2013
Reflection
Today is the last day of classes for this semester and that means the last day of this course. I felt that this course was a challenge. The course material was difficult to understand when newly introduced and took alot of time to wrap my head around and fully grasp which was something that I was not really used to. This course made me reflect on how I learn and how to learn in the future as I had to adjust in grasp the concepts.
Last Week
This week was very hectic as it was the last week of classes this semester. Had been working on both the 148 project as well as assignment 3 for 165. I felt assignment 3 went fairly well as I felt confident in my answers. I had some questions about the material as I was completing the assignment but I feel that I got enough experience and help with the topics that I was able to complete them.
I approached the questions about big Oh and Omega by looking over the lecture notes as well as the tutorial handout on the subject. Furthermore I felt that using graphing software to illustrate the functions ,as Professor Heap advised, was extremely helpful.
Thursday 4 April 2013
Penny Piles
For my problem solving episode I decided to attempt to solve the Penny Piles problem.
Step 1: Understanding the problem
Given two drawers, left and right with the left drawer holding n pennies(n being a positive integer), what combinations of pennies in either drawer can be reached using the following operations?
Left:If there are an even number of penny in the left drawer, half may be transferred to the right drawer. Otherwise the pennies in that drawer must be left alone.
Right:If there are an even number of penny in the right drawer, half may be transferred to the left drawer. Otherwise the pennies in that drawer must be left alone.
In this problem solving episode the unknown is the number of integers than can be found by executing the above functions on the drawers with the left containing n pennies.
Step 2: Devising a Plan
My first approach to this problem was to utilize brute force so I could observe a pattern.
I decided to use tree diagrams as I felt that the problem fit the criteria of a tree data structure.
Step 3: Carrying Out a Plan:
After drawing these tree diagrams I compiled a table.
The rows highlighted in red are numbers of n where n values where found.
Values of n that are of base 2^x produce all integers in their range([0,...n])
Odd numbers only produced themselves as they are not divisible by 2.
Even numbers with prime factors other than 2 produced 2 numbers, themselves and their other prime factor.
I still could not find a pattern so I decided to automate by production of further results using Python.
def penny_piles(L):
numbers_found = [L[0],L[1]]
if L[0] % 2 == 0:
left= L[0] // 2
right = L[1] + left
numbers_found += penny_piles([left, right])
if L[1] % 2 == 0 and L[1] != 0:
right = L[1] // 2
left = L[0] + right
numbers_found += penny_piles([left, right])
elif L[0] % 2 == 1 or L[1] % 2 == 1:
return L
numbers_found = remove_duplicates(numbers_found)
return numbers_found
def remove_duplicates(L):
L.sort()
for x in L:
if L.count(x) > 1:
y = L.count(x)
while y > 1:
L.remove(x)
y -= 1
return L
Step 1: Understanding the problem
Given two drawers, left and right with the left drawer holding n pennies(n being a positive integer), what combinations of pennies in either drawer can be reached using the following operations?
Left:If there are an even number of penny in the left drawer, half may be transferred to the right drawer. Otherwise the pennies in that drawer must be left alone.
Right:If there are an even number of penny in the right drawer, half may be transferred to the left drawer. Otherwise the pennies in that drawer must be left alone.
In this problem solving episode the unknown is the number of integers than can be found by executing the above functions on the drawers with the left containing n pennies.
Step 2: Devising a Plan
My first approach to this problem was to utilize brute force so I could observe a pattern.
I decided to use tree diagrams as I felt that the problem fit the criteria of a tree data structure.
Step 3: Carrying Out a Plan:
N
|
Numbers found
|
Total number not including 0
|
1
|
0,1
|
1
|
2
|
0,1,2
|
2
|
3
|
0,3
|
1
|
4
|
0,1,2,3,4
|
4
|
5
|
0,5
|
1
|
6
|
0,3,6
|
2
|
7
|
0,7
|
1
|
8
|
0,1,2,3,4,5,6,7,8
|
8
|
9
|
0,9
|
1
|
10
|
0,5,10
|
2
|
11
|
0,11
|
1
|
12
|
0,3,6,9,12
|
4
|
Values of n that are of base 2^x produce all integers in their range([0,...n])
Odd numbers only produced themselves as they are not divisible by 2.
Even numbers with prime factors other than 2 produced 2 numbers, themselves and their other prime factor.
I still could not find a pattern so I decided to automate by production of further results using Python.
def penny_piles(L):
numbers_found = [L[0],L[1]]
if L[0] % 2 == 0:
left= L[0] // 2
right = L[1] + left
numbers_found += penny_piles([left, right])
if L[1] % 2 == 0 and L[1] != 0:
right = L[1] // 2
left = L[0] + right
numbers_found += penny_piles([left, right])
elif L[0] % 2 == 1 or L[1] % 2 == 1:
return L
numbers_found = remove_duplicates(numbers_found)
return numbers_found
def remove_duplicates(L):
L.sort()
for x in L:
if L.count(x) > 1:
y = L.count(x)
while y > 1:
L.remove(x)
y -= 1
return L
As confirmed by graph, numbers n that are of 2^x produce n numbers and odd numbers produced 1 number.
As for even numbers; numbers that are even and only have the prime factors 2 and another prime produce only 2 numbers.
However I was not able to produce a pattern for even numbers.
Step 4: Looking back
I was not able to create an algorithm for predicting the
As for even numbers; numbers that are even and only have the prime factors 2 and another prime produce only 2 numbers.
However I was not able to produce a pattern for even numbers.
Step 4: Looking back
I was not able to create an algorithm for predicting the
Saturday 30 March 2013
Revelations
During this week I was going over the concepts I needed to know to complete assignment 3 and was unsure of my understanding of the finding the constant for big Oh, omega and theta. I decided that since the computer science help center was open from 4-6 on Thursday before I had my 6-8 anthropology lecture I would drop by and ask a couple of questions. However when I got there there was no T.A on duty.I was a little upset but I decided that I would take the time to focus on the material and use the examples from lecture and tutorial. After the first half an hour I was still a bit confused yet I continued on. After a couple more looks through the material I started to get a hang of the material.
I decided to break the problem into two separate inequalities instead of doing them together which simplified
the question. Then I read over the notes so gain a better understanding of what must be done with each side of the inequality. After all this I had a better understanding of material and had a sort of revelation.
I decided to break the problem into two separate inequalities instead of doing them together which simplified
the question. Then I read over the notes so gain a better understanding of what must be done with each side of the inequality. After all this I had a better understanding of material and had a sort of revelation.
Problem Solving
I have completely forgot about the problem solving aspect requires for the slogs. I have been browsing other sloggers problem solving entries and here are some that I found interesting:
The problem solving solution entitled: "Diagonals, Where the Formulas Actually Show " was the best problem solving example I have seen. The author Omar Hamdan did a fantastic job of explaining the problem and logic in solving the problem. He then created informative tables to present his data. I found his overall presentation and reasoning in his problem solving to be very impressive. I hope to make a problem solving case similar to his in terms of presentation, organization and reasoning.
Another problem solving entry by a fellow Slogger was Piles of Pennies by Mohammad Abubakr. I really liked what he did in his entry due to his use of Python coding. When I encountered this problem in lecture I also thought about using code in my solution to this problem.
The problem solving solution entitled: "Diagonals, Where the Formulas Actually Show " was the best problem solving example I have seen. The author Omar Hamdan did a fantastic job of explaining the problem and logic in solving the problem. He then created informative tables to present his data. I found his overall presentation and reasoning in his problem solving to be very impressive. I hope to make a problem solving case similar to his in terms of presentation, organization and reasoning.
Another problem solving entry by a fellow Slogger was Piles of Pennies by Mohammad Abubakr. I really liked what he did in his entry due to his use of Python coding. When I encountered this problem in lecture I also thought about using code in my solution to this problem.
Tuesday 26 March 2013
Studying
Today I spent a good portion of my day going over Big O notion specifically in preparation for assignment 3. With there having been some time since I had written down my notes I felt lost in my understanding of Big O so I decided that I would search up explanations on Google and came across this explanation http://stackoverflow.com/questions/487258/plain-english-explanation-of-big-o.After this I decided to watch some videos on YouTube that helped illustrate these concepts further.
These explanations helped clear up the beginning portions of the concept of Big O that I had forgotten and allowed me to better understand the slides that Professor Heap had posted. It is really remarkable how the internet can provide such an amazing source of reference and help that is suitable for all different types of learners at different paces.
Sunday 24 March 2013
Lessons
I has been a while since I last posted to my SLOG. Assignment 2 and the test have pasted and they were eye openers. I had initially intended to work on the assignment by myself, which I felt would force me to grasp the material thoroughly, however I felt a bit overwhelmed and eventually partnered up. My partner and I were confident in our answers however we ended up doing badly on that assignment. The test was better than the assignment but could have been better.
This experience has taught me the importance of seeking help when I am confronted with material that I do not understand. I suffered this problem in high school were I would ignore concepts that I did not have a solid understanding of, and continue with trying to remedy the problem. I plan on tackling this problem by using the various resources available at the university. I started this initiative this week when I visited Prof. Heap's office hours because I did not understand the concept of the break point in regards to the Big oh notation. Prof Heap provided an amazing explanation that really helped me with my understanding of the subject and I left that office smarter than I walked in.
This experience has taught me the importance of seeking help when I am confronted with material that I do not understand. I suffered this problem in high school were I would ignore concepts that I did not have a solid understanding of, and continue with trying to remedy the problem. I plan on tackling this problem by using the various resources available at the university. I started this initiative this week when I visited Prof. Heap's office hours because I did not understand the concept of the break point in regards to the Big oh notation. Prof Heap provided an amazing explanation that really helped me with my understanding of the subject and I left that office smarter than I walked in.
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