Homework 1

Due Tuesday 3-Sep, at 9:00pm

To start

1. Download and install Thonny
2. Create a folder named ‘hw1’
3. Download hw1.py to that folder
4. Edit hw1.py using Thonny and modify the functions as required
5. When you have completed and fully tested hw1, submit hw1.py to Gradescope. For this hw, you may submit up to 20 times (which is way more than you should require), but only your last submission counts.

Some important notes

1. This homework is solo. You may not collaborate or discuss it with anyone outside of the course, and your options for discussing with other students currently taking the course are limited. See the academic honesty policy for more details.
2. After you submit to Gradescope, make sure you check your score. If you aren’t sure how to do this, then ask a CA or Professor.
3. There is no partial credit on Gradescope testcases. Your Gradescope score is your Gradescope score.
4. Read the last bullet point again. Seriously, we won’t go back later and increase your Gradescope score for any reason. Even if you worked really hard and it was only a minor error…
5. Do not hardcode the test cases in your solutions.
6. The starter hw1.py file includes test functions to help you test on your own before you submit to Gradescope. When you run your file, problems will be tested in order. If you wish to temporarily bypass specific tests (say, because you have not yet completed some functions), you can comment out individual test function calls at the bottom of your file in main(). However, be sure to uncomment and test everything together before you submit! Ask a CA if you need help with this.
7. Remember the course’s academic integrity policy. Solving the homework yourself is your best preparation for exams and quizzes; cheating or short-cutting your learning process in order to improve your homework score will actually hurt your course grade long-term.
8. Do not use string indexing, loops, lists, list indexing, or recursion this week. The autograder will reject your submission entirely if you do.

Problems

1. Breaking the ice on Discord [5 pts]
   We will be using Discord this semester as the course discussion board and question and answer forum. You should have received an invite to the course Discord server during the first week of classes.
   If you have never used Discord before, consider the following tips:
   1. A Beginner's Guide to Discord can be a helpful resource in understanding the basics of a Discord server.
   2. If you are creating a Discord account, it is probably a good idea not to use your real name as your username or overall display name.
   3. Once you join the class Discord server, there are rules that you will need to agree to. You will also need to change your Server Nickname to be your real name. (Don't worry, this server nickname is only visible to other members of the class. Your username and display name on other parts of Discord are unaffected.)
   4. You should download and install the Discord app on your computer (or phone or tablet). This will ensure you get notifications whenever there are announcements and notifications about the course.

   If you have used Discord before, feel free to use your existing account. However, please note that your Discord username will be visible with your profile, even after you change your server nickname. (So if having other people see your Discord username would be embarrassing, then keep that in mind...)

   For this task, do the following:
   1. Join the Discord server using the link sent to you via email.
   2. Follow the instructions on the server in order to agree to the rules and check the box.
   3. Using the channel for private questions, ask a private question that just says, "Does it seem like I've setup Discord properly?" One of the staff will respond.
   4. Post a reply to the existing public question that was posted by the course staff.


2. isValidYearOfBirth(year) [5 pts]
   Imagine that you are writing a software that validates personal information entered by the users. Write the function isValidYearOfBirth(year) which, given a value year, returns True if it is an integer value that represents a valid year of birth, False otherwise. Keep in mind that, according to Wikipedia, the oldest person was born in 1907.


3. numberOfPoolBalls(rows) [5 pts]
   Pool balls are arranged in rows where the first row contains 1 pool ball and each row contains 1 more pool ball than the previous row. Thus, for example, 3 rows contain 6 total pool balls (1+2+3). With this in mind, write the function numberOfPoolBalls(rows) that takes a non-negative int value, the number of rows, and returns another int value, the number of pool balls in that number of full rows. For example, numberOfPoolBalls(3) returns 6. We will not limit our analysis to a "rack" of 15 balls. Rather, our pool table can contain an unlimited number of rows. Hint: you may want to briefly read about Triangular Numbers. Also, remember not to use loops!


4. getTheCents(n) [10 pts]
   Write the function getTheCents(n) which takes a value n (which represents a payment in US dollars) as input and returns the number of cents in the payment. If n is an int, the function should return 0, as it has 0 cents; otherwise, if it isn't a float, it should also return 0, because a non-number payment make no cents (ha!). You can assume that n will have up to 2 decimal places. For instance,
   getTheCents(3) == 0 getTheCents(3.00) == 0 getTheCents(3.96) == 96 getTheCents(3.95) == 95 getTheCents(3.1) == 10 getTheCents(3.11) == 11


5. isPerfectCube(n) [10 pts]
   Write the function isPerfectCube(n) that takes a possibly-non-int value, and returns True if it is an int or float that is a perfect cube (that is, if there exists an integer m such that m**3 == n), and False otherwise. Do not crash on non-numbers nor on negative numbers.


6. isSymmetricNumber(n) [20 pts]
   We define a number as symmetric if it is an integer, non-negative, and its left and right halves are identical. For example, 99 and 2020 are symmetric numbers, but 4554 and 789987 are not. With this in mind, write the function isSymmetricNumber(n), which takes a value n and returns True if n is a symmetric number and False otherwise. Notes: The numbers can be arbitrarily large. For example, 444555666444555666 is a symmetric number.


7. Area Within Three Lines [20 pts]
   Solve the CS Academy problem "Area Within Three Lines". You must solve the problem directly on the website, doing all of your testing there. Do not write the solution in Thonny (or a different IDE) and copy/paste it into the website.
   
   
8. colorBlender(rgb1, rgb2, midpoints, n) [25 pts]
   This problem implements a color blender, inspired by this tool. In particular, we will use it with integer RGB values (it also does hex values and RGB% values, but we will not use those modes). Note that RGB values contain 3 integers, each between 0 and 255, representing the amount of red, green, and blue respectively in the given color, where 255 is "entirely on" and 0 is "entirely off".
   
   For example, consider this case. Here, we are combining crimson (rgb(220, 20, 60)) and mint (rgb(189, 252, 201)), using 3 midpoints, to produce this palette (using our own numbering convention for the colors, starting from 0, as the tool does not number them):
   
   
   color0: rgb(220, 20, 60) color1: rgb(212, 78, 95) color2: rgb(205, 136, 131) color3: rgb(197, 194, 166) color4: rgb(189, 252, 201)
   
   There are 5 colors in the palette because the first color is crimson, the last color is mint, and the middle 3 colors are equally spaced between them.
   
   So we could ask: if we start with crimson and go to mint, with 3 midpoints, what is color #1? The answer then would be rgb(212, 78, 95).
   
   One last step: we need to represent these RGB values as a single integer. To do that, we'll use the first 3 digits for red, the next 3 for green, the last 3 for blue, all in base 10 (decimal, as you are accustomed to). Hence, we'll represent crimson as the integer 220020060, and mint as the integer 189252201.
   
   With all that in mind, write the function colorBlender(rgb1, rgb2, midpoints, n), which takes two integers representing colors encoded as just described, a non-negative integer number of midpoints, and a non-negative integer n, and returns the nth color in the palette that the tool creates between those two colors with that many midpoints. If n is out of range (too small or too large), return None.
   
   For example, following the case above: colorBlender(220020060, 189252201, 3, 1) returns 212078095
   
   Hint: RGB values must be ints, not floats. When calculating midpoint colors, you can mostly use the built-in round function. However, the built-in round function has one major flaw: it varies in whether it chooses to round .5 up or down (ugh!). You can fix this by doing an extra check for whether a number is <number>.5 and choosing to always round up in that case.