## Vowel Shifter

Hello all!

This week we have another practice problem for the Bloomsburg Competition coming up.  This problem is a vowel shifter and the description goes as follows:

Write a program that prompts the user for a sentence and modifies it by shifting each vowel like this:
• a→ e
• e→ i
• i→ o
• o→ u
• u→ a
In other words, each “a” in the original sentence becomes an “e”, each “e” in the original sentence becomes an “i”, and so on, and similarly for capital letters.

We’ll start this program off by creating two lists for each of our vowel sets. These will be called vowelsupper and vowelslower.

vowels = ["a", "e", "i", "o", "u", "a"]
vowelsupper = ["A", "E", "I", "O", "U", "A"]

Next we need to grab our input from the user using phrase = str(raw_input("Enter a sentence.\n")) (Sidenote: The \n at the end of the sentence is an escape operator that just starts a new line.).  Next we need to create a way to iterate through our users input to find and replace vowels with our new shifted vowels.  We do this using a for loop.  A for loop is just a loop that repeats a set number of times and often is used to create a changing variable for the program. Inside this loop we want to use a conditional statement to check if each letter in the phrase is a vowel, and if it is a vowel we want to check if it is upper or lower case. After doing this we will shift the vowel and add the new vowel to our shifted phrase. Then we just repeat this process until we have iterated through the entire original string.

for i in range(len(phrase)):
if phrase[i] in vowelslower or phrase[i] in vowelsupper:
if phrase[i].islower():
shift += vowelslower[vowelslower.index(phrase[i])+1]
else:
shift += vowelsupper[vowelsupper.index(phrase[i])+1]
else:
shift += phrase[i]

Now we have all the main components needed to create our program.  After combining them all together our final code will look like this:

vowelslower = ["a", "e", "i", "o", "u", "a"]
vowelsupper = ["A", "E", "I", "O", "U", "A"]
shift = ""
phrase = str(raw_input("Enter a sentence.\n"))
for i in range(len(phrase)):
if phrase[i] in vowelslower or phrase[i] in vowelsupper:
if phrase[i].islower():
shift += vowelslower[vowelslower.index(phrase[i])+1]
else:
shift += vowelsupper[vowelsupper.index(phrase[i])+1]
else:
shift += phrase[i]
print(shift)

And now we have a working solution for Problem #2!  This solution is posted on my GitHub as well.

Thanks for reading and have a wonderful day!
~ Corbin

## Okapi and Preparing for the Bloomsburg Competition

Hello all!

I’ve been on a bit of a ‘hiatus’ lately, I’ve been busy with life things and haven’t had a chance to work on any posts here.  But a quick update, I won first place at regionals for the Pennsylvania Junior Academy of Science so I’m going to states in May and I’ll be making a post on that project soon.  I’ve also been preparing the programming club at my school for an upcoming competition at Bloomsburg University where we will be competing.  Because of this we have been doing practice problems and so I will be posting and explaining my solutions to them here.

Our first practice problem is called Okapi.  The problem description goes as follows:

The game of Okapi is played by rolling three dice. A payout in dollars is determined by the rolled numbers according to the following rule:

• If the three numbers are the same, the player wins the sum of those three numbers.
• If only two of the numbers are the same, the player wins the sum of the two equal numbers.
• For three different numbers, the player wins nothing.

Write a program that prompts the user for three dice rolls and outputs the payout.

We need to begin this problem by taking user input using rolls = input("Enter dice rolls: ") which prompts the user for input and sets rolls equal to their input. Next we need to parse out their answer into three separate rolls, this is rather easy and just a matter of indexing the user input. In order to do this we just need to create variables for each roll and then set them to the correct index of rolls using the following code: roll_one, roll_two, roll_three = int(rolls[0]), int(rolls[1]), int(rolls[2]). Now that we have our rolls assigned we just need to use a bunch of conditional statements to determine the output.  Our final code will look like this:

def okapi():
rolls = input("Enter dice rolls: ")
roll_one, roll_two, roll_three = int(rolls[0]), int(rolls[1]), int(rolls[2])
if roll_one == roll_two and roll_two == roll_three:
print("The payout is $", roll_one*3, ".") elif roll_one == roll_two: print("The payout is$", roll_one+roll_two, ".")
elif roll_two == roll_three:
print("The payout is $", roll_two+roll_three, ".") elif roll_one == roll_three: print("The payout is$", roll_one+roll_three, ".")
else:
print("The payout is $0.") And now we have a working solution to problem #1! Another solution can be found on my GitHub, it’s the same premise but just less readable. I’ll most likely be posting around weekly again soon. Thanks for reading and have a wonderful day! ~ Corbin ## More 3D Printing and Fine Tuning Hello all! Lately, I’ve been working with my 3D Printer and I want to talk about some of the things I’ve been doing to get better prints from it. In my previous post, I forgot to say what 3D Printer I actually have and if I’ve made any modifications to it. I currently have the Monoprice Maker Select V2 printer. I only have a singular mod on my printer, and that is a custom filament holder, so there is little to no effect on print quality by this mod. My venture with trying to fine-tune my printer began when I purchased some new filament, specifically the Hatchbox Blue PLA. This filament was a great choice because it is a very high-quality filament despite being only around$20 USD.  Before purchasing this I had been printing with the Monoprice Transparent PLA, but that filament had several issues where layers would poorly adhere to each other and it wouldn’t attach to the bed properly.  I’m unsure of why but the new filament has completely fixed this, my layers are now flawless except for some wobble from the printer moving fast.  I also haven’t had to use blue tape or glue on my bed at all since using this new filament.

After getting the new filament I felt a surge of adventure to experiment more with my slicer settings and try to make my prints even better.  For those who may not know, a slicer is a software that takes a file containing a 3D Object and slices it into layers of certain thickness and outputs this as a G-Code file.  This G-Code file is then loaded on the printer and controls what all of the axes and motors on the printer do.

Onto what I changed and experimented with.  The slicer I use is Cura and it’s made by Ultimaker, it’s a free slicer and in my experience works very well.  This is by no means meant to be a post about how to tune your printer, or how to use a slicer, this is just my experience that I find interesting and hope you do too.  I began my experimentation with changing my printing speeds.  While attempting to do complex prints I would get lots of artifacts and ghosting.  I realized that, if the printer is doing a complex print with many small parts, it’s going to shake a lot because I don’t have it braced and its frame is made out of sheet metal.  So in order to fix this, I turned the print speeds down from 60 mm/s to 35 mm/s, a drastic decrease but it worked very well.

The next major change I made with my slicer settings was to find the best flow rate for my extruder.  The flow rate is the amount of filament that the printer pushes out while printing a layer.  I found through some testing that my printer tends to underextrude filament, meaning it needs to push more.  I found that a good setting for my flow rate is around 110%-115%, but this depends on the print.

The final 2 major changes I made were with my temperature and my wall count.  I changed my printing temperature down to C from my previous C after I notice that the extruder was melting the filament below it over again and ruining prints.  So the Hatchbox Filament is definitely more susceptible to heat than the Monoprice Filament.  The final change I made was my wall count.  The wall count is quite literally the number of walls the printer makes, and with my 0.4 mm nozzle size I was originally using a wall count of 2 for a thickness of 0.8 mm, but this turned out to be extremely fragile in some cases so I bumped it up to 3 walls (Often referred to as perimeters) meaning I have a thickness of 1.2 mm.  This made my prints very durable compared to before and even made complex prints turn out better.

Overall these changes really upped my print quality, and I’m very happy that I can print complex models now.  The testing took a lot of trial and effort but really paid off in the end.  Learning about all of the different G-Code specifics was also a great experience.  And lastly I’ll leave you with the final fruit of my efforts:

Thanks for reading and have a wonderful day!
~ Corbin

## An Introduction to Machine Learning Topics

Hello all!

So after my post last week, I received some feedback saying that I should better explain what the concepts that I was talking about are and why / how we use them. So in this post I’m going to attempt to explain most of the concepts I used in my last post.

To start off I’m just gonna break things down and list out the terms I’ll be defining.  In order to do machine learning you should usually have at least two sets of data, a learning set and a testing set of data.  Machine learning is also usually broken down into two main forms, these are supervised and unsupervised learning.  These then break out into the three common types of machine learning problems.  Underneath supervised learning we have classification and regression problems.  And underneath unsupervised learning we have clustering problems.  There’s a handy infographic I found to represent this:As SciKit Learn puts it “Machine learning is about learning some properties of a data set and then testing those properties against another data set.”  In this way, we can define our two data sets.  Our training set is the dataset we are training the computer to recognize data properties off of, and our testing set is what we are trying to predict or classify based on the properties we found.

Now we can move on to the two main types of machine learning, supervised and unsupervised learning.  Supervised learning is defined as a problem in which we feed the program some data as our training set, and that data has additional characteristics that we keep from it.  We then feed it that hidden data as our testing set, and task it with predicting the characteristics.

Underneath supervised learning, we have classification and regression.  Classification is when we feed the program a set of already labelled data, and use that as our training set.  We then feed the program some unlabelled data, and have it predict what that data is based off of our labelled training set.  In my previous post this is what I was doing with handwriting recognition.  Regression is feeding a set of data that has one or more continuous variables to the program, and having it predict the relationship between the variables and the results observed.  This task is a bit weird to envision but I find I can understand it better if I think of an example.  The one that makes the most sense to me is inputting a set of data with three salmon variables, length, age, and weight.  A regression problem using this data would be having the computer predict the length of a salmon based on its age and weight.

Unsupervised learning is defined as a problem in which our training set consists of an infinite amount of input values, but no corresponding target values.  This means our program will be finding common factors in the data reacting based on the absence or presence of them.  A common approach to this is clustering, in which you feed the computer a set of data, and it will separate this data into the common groups of data that share similar characteristics.

I hope this clarifies some of the things from my last post on classification that might be a bit unclear, and feel free to leave a comment if you would like any clarification or I made an error somewhere.

Thanks for reading and have a wonderful day!
~ Corbin

## Diving into Machine Learning

Hello all!

So lately I’ve been messing with machine learning because I’ve always been interested in it and it’s just very cool and interesting to me.  I’d like to talk a bit about what I’ve been doing and struggling with and show some examples. I will be working with scikit learn for Python, and it comes with 3 datasets. Iris and Digits are for classification and Boston House Prices are for regression. Simply put classification is identifying something like a handwritten number as the correct number it is and regression is essentially finding a line of best fit for a dataset.  I still have a lot to learn about sklearn and machine learning in general, but I find it really interesting nonetheless and thought you guys would too.

So my code begins with the import of a bunch of libraries.  The only ones I use in my example here are sklearn and matplotlib, the others are simply either dependencies or libraries I plan to use in the future.

import sklearn
from sklearn import datasets
import numpy as np
import pandas as pd
import quandl
import matplotlib.pyplot as plt
from sklearn import svm

In this import, sklearn is the main library I’m using to fit my data and predict things, sklearn.datasets comes with the 3 base datasets Iris Digits and Boston Housing Prices.  I don’t know much about sklearn.svm, but I do know that it is the support vector machine which essentially separates our inputted data and runs our actual machine learning, so when we input testing data it can determine what number we have written. Numpy is a science / math library that adds support for larger multidimensional arrays and matrices. Pandas is a library for data analysis. Quandl is a financial library that lets me pull a lot of data that I can use for linear regression in the future. And matplotlib and it’s sub-library pyplot allow me to output the handwriting data.
So far my code for the recognition looks like this:

clf = svm.SVC(gamma=0.001, C=100)
clf.fit(digits.data[:-1], digits.target[:-1])
clf.predict(digits.data[-1:])
plt.figure(1, figsize=(3, 3))
plt.imshow(digits.images[-1], cmap=plt.cm.gray_r, interpolation='nearest')
plt.show()

Although my understanding is rudimentary, I can explain a little bit of what this does. Clf is our estimator which is the actual machine that is learning, and that is what we pass out training data through with clf.fit().  Clf.fit() lets us pass data into the svm that we made clf off of, and it trains our machine to know what the numbers should look like.  I am passing all digits except for the last one through this function, because we will be testing with the last one.  We then pass a digit through clf using clf.predict(),  which passes data for a know handwritten digit, 8, through clf.  Our object clf then outputs the text <code>array([8])</code> which means that it has predicted our inputted number as 8.  If we print out digits.target[-1:] we can see it and determine if it was correct. We do this using out 3 lines from matplotlib that create the figure, print it, and then show it. The figure we get is this:

It’s a very low resolution, but it’s an 8! I think that this is brilliant, and I definitely need to learn more about what is happening here with my code. Machine learning is very cool and I definitely need to mess with it more and learn more.  So far I’m learning some of the basic elements like how to fit and predict things, how training and testing sets work, and a lot of the vocabulary that is used when talking about machine learning.  I can now actually talk about things like supervised and unsupervised learning, or classification and regression methods.  Along with this, I’m also learning more about other libraries like matplotlib, and how to write more pythonic (readable) code.  For anyone who wants to try this themselves, there’s a lot of really cool stuff online, but I’m using some of the resources from hangtwenty‘s GitHub repo dive-into-machine-learning.  It can be found here: https://github.com/hangtwenty/dive-into-machine-learning Hopefully by my next post I will have created a basic understanding of linear regression and I can create some cool examples using it, and in my next post I will attempt to give my explanation on how fitting, predicting, and training actually works.

Thanks for reading and have a wonderful day!
~ Corbin

Hello all!

So in May this year, I received a Monoprice MP Select 3D Printer. So far it has been an interesting experience, and I’d like to take this post to reflect upon what I’ve learned and struggled with. I’d also like to note that my experiences and solutions are my own and that if you want to try them, follow them at your own risk.

So over the past few months, I’ve run into only a few issues, but they have been very repetitive and hard to fix. The worst of these so far include print bed adhesion, nozzle jamming, and severe retraction problems.

### Retraction

By far retraction has been the most challenging problem I’ve faced with my printer. Retraction is when your printer will pull back filament inside the extruder slightly to retrieve pressure from the print head. This help reduce stringing in prints wh en the printer is making non-print moves. My issue arises from the stepper motor that drives the filament; I don’t quite know what is wrong with the motor yet (I’m waiting to get a new one before I disassemble the old one to diagnose it) but I know that it makes an uncomfortable whining noise and doesn’t push or pull the filament enough. This results in prints that have missing sections, very pool infill, separated layers, and many other issues. The only way I’ve found to fix this that actually works is to just turn off retraction when slicing my prints, and use a razor blade to cut off the strings and sand it down later. Hopefully, in the future, I can update and diagnose this feature

### Nozzle Jamming

Another issue I have encountered is nozzle jamming, and this was far easier to fix than my last issue. So, my method to fix this issue was to turn up the temperature of my extruder by 10 degrees Celsius. Another option is to drill out the nozzle, my printer came with a small drill bit to clear the opening, but I didn’t want to use this for fear of damaging the printer. And another method is to attach a cleaning piece to your filament as it runs to the extruder, but this only works if your problem is debris jamming the nozzle.

And finally, the easiest to fix issue I’ve had is bed adhesion. Now albeit my solution doesn’t replace the actual BuildTak, but it does fix the issue, and maybe a little too well. The solution to this that I chose was to put rough blue painters tape over my BuildTak to provide a better surface, and then use a glue stick to coat the tape and provide very good adhesion to the print surface. Overall I think that doing this has been the best solution for me rather than modding the printer and adding a removable build surface.

These have just been the issues that I have faced so far. I definitely think that 3D Printing is something more people should get involved in, as this technology is amazing and it has been an absolute blast printing out everything from D&D Miniatures to trumpet mouthpieces or part.

Thanks for reading and have a wonderful day!
~ Corbin

## Where I’ve been…

Hello all!

I’ve been a bit absent lately, well more for like a few months, but I’ve learned a lot and I’m ready to get back on my blogroll! Over the past few months, I’ve done a bunch of cool things that I’m gonna be putting posts up about, and I want to talk about what my new plan is here.

So the first thing you’ll notice is I have a new blog. My blog was transferred over to a docker container with WordPress and it’s all fresh and shiny now. (It’s also making me get involved with Docker a bit, but that’s a whole other topic.)

Over the past few months, I have…
– Attended MIT Splash and took a TON of really cool courses (And explored the gorgeous campus with my friends!)
– Contacted a professor and secured a research opportunity
– Taught myself some new cool stuff, such as Java and OOP basics
– Started a CS Independent Study where I’ve been learning new material for the AP CSA exam
– Gave a talk at HOPE 2018 and met a bunch of really cool humans
– Got a 3D Printer and have been having tons of fun making things

There have been other smaller events that have been cool, but that’s what I can quickly remember at the moment. Overall it’s been an amazing few months and I’m very happy to get back. I also would like to make a change to my blog, I want to be more personal and show my struggles on problems, show how I’m getting stuck and how I’m trying to solve new problems. And I’d love some input from you wonderful humans too! I’m going to attempt weekly posts again, I’m also gonna be showcasing more basic things I do and my projects rather than just Project Euler problems.

It’s great to be back!

Thanks for reading and have a wonderful day!
~ Corbin

## Mindsets and Prime Factorization

Hello all!

It’s been a while since I last posted, apologies. I’ll be doing another Project Euler problem today.

Problem 3:

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

I’d like to begin by saying that I spent way too long on this problem improving my code after I had already solved it. But this is a very good mindset to have when you are trying to become better at something. Due to the increased complexity of this problem, it is a good idea to write an algorithm for it, and I will likely do this for all future problems.

def largest_prime(n)
Iterate through each number up until the square root of n
If the iterable is prime and the modulo of the base and iterable is 0:
Append the iterable to some empty list
print the [-1] element of the list, and this is the largest prime

I decided on an algorithm where I will check every number’s divisibility and ‘prime-ness’ up until the square root of the original number. This works because you can have no prime factor larger than the square root of the number. Next, I add every valid number to some list, and then I go back and pick out the largest one from the list and this is the answer’s problem. Now I need to turn this into working code, and then from there, I can improve it.

def largest_prime(base):
primes = []
root = math.sqrt(base)
for i in range(int(root+1)):
if is_prime(i) == True and base%i == 0:
primes.append(i)
prime = primes[-1]
print(prime)
print(primes)

In theory, this code should work but now I need to make a function is_prime(n) that allows me to check if a number is prime for some boolean value. I’ll do this by checking every number up until the square root for divisibility, and if I find no divisibility other than 1 and the number itself then I will declare the number as prime.

def is_prime(n):
if n <= 1:
return False
for i in range(2, (int(math.sqrt(n))+1)):
if n%i == 0:
return False
return True

Although all of this code works, it is very inefficient. If I insert a timer using from time import * my code takes an average of roughly 7 seconds to run. I would like to cut this down to 1 second or less in any way I can. One way I can optimize the code is by removing my use of lists, but this only saves me ~1 second. This is where I’ll introduce recursion into my programming repertoire. Recursion is when you have a function that calls on itself repeatedly until the task is done. When the task is done the look breaks and returns your answer.

In order to do this problem using recursion, I have to redefine my algorithm. Instead of using another function is_prime(n) I’ll be taking each number, finding the lowest common divisor. I will then take this new number, (n/lcd), and perform the same method on it until I can no longer be divided and this final number is our largest prime factor.

def largest_prime(base):
start = clock()
for i in range(2, int(math.sqrt(base)+1)):
if base % i == 0:
return largest_prime(base/i)
print(base)
end = clock()
print(end-start)

This is my final piece of code and it takes ~0.0008 seconds to run. I am very happy with the results as the code is simple and condensed. I’d like to end this post by talking about mindsets and why they matter. When you’re trying to get better at something you should realize that your abilities are not as fixed as you think they are. I see this problem a lot in my high school, kids in my Pre-Calculus class often complain that they are bad at math but then when they like a topic we are learning in the class they do extremely well at it because they enjoy it and put effort into it. A good analogy of this is someone learning to play an instrument. When you’re practicing hitting higher notes on a trumpet you don’t squeak a note and say “I’m bad at this and I should just give up trumpet” you instead say “Okay, I need to put faster air through the trumpet” and you try again, so why not do this with other things you are trying to get good at? If you would like to know some more about mindsets I highly recommend Mindset: The New Psychology of Success by Carol Dweck. It details lots of information and research about growth mindsets and how they can improve your life.

Thanks for reading and have a wonderful day!
~ Corbin

## Functions in Programming, List Comprehension, and Even Fibonacci Numbers

Hello all!

Today I’ll be doing another Project Euler problem.

Problem 2:

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

There are many ways to do this problem, but I’ve chosen to create a series of functions that I can run to get Fibonacci numbers until some upper bound, and then the sum of even numbers in a list. I find that abstracting calculations like these into functions is a very easy way to make programs feel and look more organized as well as increasing reusability and convenience. A good example would be that I may need a Fibonacci sequence in a future problem, and using a function like this allows me to just paste this code into a future program and I can recall on it using fib(max) when needed. I’m going to begin by creating a function to find the Fibonacci numbers up to some upper bound. I’ll create the function fib(max) where max is the upper bound of the number we’ll be getting from the Fibonacci sequence. The best way I can come up with to create a Fibonacci sequence is to create a list and use fib[-1] and fib[-2] to grab the latest two numbers in the sequence. Next, I’ll add in a while loop that iterates through the Fibonacci sequence and places the numbers into the list fib[ ], to create the next Fibonacci number. This loop then breaks when we hit the upper bound we placed earlier. After this the function will return the newly filled list fib[ ].

def fib(max):
fib = [1, 2]
while(int(fib[-1] + fib[-2]) <= max):
fib.append(int(fib[-1]+fib[-2]))
return fib

Next, I need to create a function that will add the even numbers of a list together. I’ll call this function even_sum(list) and to create it I’m going to use something new I learned called List Comprehension. You can learn more about List Comprehension here but I’ll provide a quick overview. List Comprehension allows a smaller and more efficient way to create a list by placing a for loop inside of square brackets. We can also place operators such as if statements inside the brackets. Using this new tool my next function will look like this:

def even_sum(list):
return sum([i for i in list if i%2==0])

Now that we have both of our functions we can just combine the two and run them through each other like so:

even_sum(fib(4000000))

This now returns us with the sum of all even Fibonacci numbers up until 4 million!

Thanks for reading and have a wonderful day!
~ Corbin

I would like to give special thanks to Christian Ferko for teaching me about List Comprehension.

## Intro and Multiples of 3 and 5

Hello all!

I’ll insert a small introduction here. Welcome to my blog, my name is Corbin Frisvold and I’m a student interested in furthering my passions for Computer Science, Mathematics, and several other fields. Here my posts will primarily consist of my exploration into becoming a better programmer, but I will likely post other things around on the blog. Anyways, onto my first post!

Today I’m going to be doing a problem from Project Euler.
Problem 1:

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

I find it useful to just dive into the code for a small problem like this. We know we want a for loop iterating through 1000 and checking each number’s divisibility by 3 or 5. What I come out with is this:


sum = 0
for i in range(1000):
if i % 3 == 0:
sum += i
elif i % 5 == 0:
sum += i
print(sum)


What this code does is it creates a variable sum that will be used to store the sum of all our valid multiples. Then we use a for loop increment through all numbers between 1 and 1000. After running the program will print the output. Running this we get sum = 233168. And now we have solved Problem 1! My intention with post frequency is to post as much as I can, but I will attempt to keep a minimum frequency of 1 or 2 posts a week.

Thanks for reading and have a wonderful day!
~ Corbin