Homework 1

Due Tuesday 14-Jan, at 9:00pm

To start

1. Download and install Thonny (or use your preferred editor)
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. 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!


3. 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


4. 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.


5. 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.


6. 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.


7. colorHarmony(rgb1, rgb2) [30 pts]
   In this problem you will find a color that is in "harmony" with two other colors.

   Background

   Color theory can be used to determine what colors look nice together. This is useful in many areas, including CS, where it can be applied to the design of graphical user interfaces. The color wheel was invented in the 17th century by Sir Isaac Newton, who mapped the color spectrum onto a circle. The color wheel is the basis of color theory, because it shows the relationship between colors.
   

   

   
   On computers, there are multiple ways that colors are represented. One of the earliest, and simplest, ways is called RGB. An RGB representation of a color 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".
   
   A different way to represent colors is called HSV (Hue, Saturation, Value). In the HSV model, the color is mapped to the color wheel shown above, and the hue is the angle of where the color is, and saturation and value represent how "intense" the color looks. (Saturation and value aren't important for this assignment.) Given that the color wheel is a circle, the hue ranges from 0 to 360: 0 is red, 45 is a shade of orange, 55 is a shade of yellow, etc.
   
   

   Color Harmonies

   Colors that look good together are called a color harmony. Artists and designers use these to create a particular look or feel. You can use the color wheel above to find color harmonies by using a variety of rules. Color harmonies determine the relative positions of different colors in order to find colors that create a pleasing effect.
   
   In this task we will use the color wheel to find a color harmony based on the isosceles triad: a set of three colors that form an isosceles or -- even better -- an equilateral triangle.
   
   Given two colors c1, c2, your task is to determine a third color c3 that forms an isosceles triad, with the segment c1c2 being the base of the triangle. For example, consider the case where we pick two random colors on a color wheel:

   

   In this case, we've picked a shade of red (RGB: 255, 38, 0) and a shade of green (RGB: 0, 255, 34). The color that is in triadic harmony with this two is the one that completes an isosceles triangle with them on the color wheel, like so:

   

   That third color ends up being a shade of blue (RGB: 36, 0, 255)
   
   You can imagine how that same process (finding the color that completes the triangle) could be followed for any two colors on the color wheel.
   
   

   Calculating That Third Point

   So, given the RGB values for two colors, how do you find the third color in the triangle? The process is fairly straightforward:
   1. Determine the hue value (angle) of each of the two colors. In our example above, the red color has a hue value of 9 degrees and the green color has a hue value of 128 degrees. (Go look at the first color wheel in this problem, find those angles, and convince yourself this is true.)
   2. Base on those two angles, we can find the angle of the color (the hue) that is directly across from the midpoint between the two colors. (The formula for this is left as an exercise for the reader.) Note that it could be argued there are two different points that solve the problem (one triangle going each direction from the midpoint), but we are only concerned with the one that produces the larger triangle.
   3. We can convert the hue value of the third color into RGB values.
   
   
   

   A Few More Things

   • For the arguments and return value to/from this function, we need to represent 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. You will need to "extract" the individual red, green, and blue values from this integer.
   • You can convert colors between RGB and HSV using the formulas found here and here.
   • In order to simplify your task, we are going to consider only the colors that lie at the perimeter of the wheel. Note that, in the RGB representation of these colors, at least one of the R, G, or B components is entirely on (you can notice the "ff" in the hex representation), and at least one component is entirely off. This also means that the third color must also lie at the perimeter of the wheel.
   • Colors that lie at the perimeter have maximal saturation and value (S=100% and V=100%), so you can fix the values of S and V in any formulas.
   
   
   

   Your Task

   With all that in mind, write the function colorHarmony(rgb1, rgb2), which takes two integers representing colors at the perimeter of the wheel encoded as just described and returns the color in the wheel that forms a triadic harmony with those two colors.
   
   For example, following the case above: colorHarmony(255038000, 255034) returns 36000255 (note that 36000255 is the same integer value as 036000255, and the leading zeros is just an output formatting choice that we make when printing the value)
   
   To solve the task, first find the angles at which the given RGB color lie, then compute a third angle that corresponds to the RGB color that completes the isosceles triad. Lastly, convert the computed angle to the RGB color and that's your answer. If no such color exists, return None. If there are multiple solutions, return the solution with the smallest integer value. For example, colorHarmony(255255, 255000000) returns 128000255, although the color 128255000 is also a valid solution.
   
   To do this, you must write two helper functions:
   • rgbToAngle(rgb) to find the angle at which the RGB color lies.
     • This function takes an integer that encodes the RGB color as explained above and returns the angle a, in degrees, 0 <= a < 360, at which the color lies. For simplicity, the returned angle should be integer. If the color does not lie at the perimeter, or the rgb value is invalid, the function should return None.
   
   
   • angleToRGB(a) to convert the angle to the RGB color.
     • This function takes one float value representing an angle in degrees and returns an integer that represents the RGB color.
   
   
   You may write other helper functions if you think they would be useful, but you must at least write these two exactly as described, and then you must use them appropriately in your solution. Once you have written and tested your helper functions, then move on to writing your colorHarmony function, which of course should use your helper functions. That's the whole point of helper functions. They help!
   
   Note that helper functions help in several ways. First, they are logically simpler; they break down your logic into smaller chunks that are easier to reason over. Second, they are independently testable, so you can more easily isolate and fix bugs. And third, they are reusable, so you can use them as helper functions for other functions in the future. All good things!