Based on problems by Jerry Cain, Eric Roberts, Nick Bowman, Sonja Johnson-Yu, Kylie Jue, and the current CS106A staff.
This assignment consists of multiple short problems to give you practice with several different concepts in Python (e.g., variables, control structures, etc.) as well as two longer programs. You can download the starter code for this project under the “Assignments” tab on the CS106A website. The starter project will provide Python files for you to write your programs in.
The assignment is broken up into two parts. The first part of the assignment will give you practice writing short programs (we call them “sandcastles”). In the second part of the assignment you’ll get the chance to create two larger programs. In the spirit of learning how to code, in this assignment we’re going to use code to help others learn! The second part of this assignment includes a mini version of Khan(-sole) Academy as well as a program to show users how to compute interest in a bank account.
If you feel comfortable doing so, we’d appreciate it if you could let us know your preferred name and your preferred pronouns. Also, if you can provide an audio recording of the pronunciation of your name, that would be great. Of course, this information is optional to provide and you can provide any portion of it that you like. These questions have no impact on your grade. The information just helps us provide you with a more personalized experience in the class. You can provide this information at the website: https://cs198.stanford.edu/profile
“Sandcastle” problems are meant to be fairly straightforward and make sure you’re solid on particular concepts (like control flow, variables, and functions) before moving on to writing larger programs. They’re kind of like building sandcastles in a sandbox – they’re meant to be fun to do and no one gets hurt. Please make sure you do these six problems before moving on to other parts of the assignment.
"""
This program is just meant to test your understanding
of variables, control flow, and functions.
"""
def mystery():
x = 3
x = 5 - x / 2
print(x)
def main():
x = 1
while x < 20:
print("x = " + str(x))
mystery()
x *= 2
print("x = " + str(x))
if __name__ == "__main__":
main()
Write a program in the file subtract_numbers.py that reads two real numbers from the user and prints the first number minus the second number. You can assume the user will always enter valid real numbers as input (negative values are fine). Yes, we know this problem is really similar to a problem we did in class – that’s why this problem is a sandcastle! A sample run of the program is shown below (user input is in italics):
This program subtracts one number from another.
Enter first number: 5.5
Enter second number: 2.1
The result is 3.4.
Write a program in the file liftoff.py that prints out the calls for a spaceship that is about to launch. Countdown the numbers from 10 to 1 and then write “Liftoff!” Your program should include a for loop using range. A sample run of the program is below.
10
9
8
7
6
5
4
3
2
1
Liftoff!
Write a program in the file random_numbers.py that prints 10 random integers (each random integer should have a value between 0 and 100, inclusive). Your program should use a constant named NUM_RANDOM, which determines the number of random numbers to print (with a value of 10). It should also use constants named MIN_RANDOM and MAX_RANDOM to determine the minimal and maximal values of the random numbers generated (with respective values 0 and 100). To generate random numbers, you should use the function random.randint() from Python’s random library (which we discussed in class). A sample run of the program is shown below.
35
10
45
59
45
100
8
31
48
6
Humans first landed on the moon on July 20, 1969. People have often wondered how much they would weigh if they were on the moon. It turns out that on the moon, you would weigh 16.5% of your weight on Earth. Write a program moon_weight.py that asks the user for their weight (you can assume is a real-valued input is given by the user) and prints out their weight on the moon. If the user enters a negative value (yes, they’re being mean and trying to break your program), you should just print out that weights can’t be negative. Remember when writing your solution, that it’s good programming style to use constants where appropriate. Two sample runs of the program are shown below (user input is in italics).
Sample run 1 (note the imprecision of floating-point numbers in the answer)
Enter your weight: 165.3
Your weight on the moon is 27.274500000000003
Sample run 2
Enter your weight: -13
Sorry, you can't have a negative weight.
In geometry, you learned the Pythagorean theorem for the relationship among the lengths of the three sides of a right triangle:
a^2+b^2=c^2
which can alternatively be written as:
c =√(a^2+b^2 )
Write a program in the file pythagorean.py that gets two values for a and b as floats (you can assume that a and b will be positive real values) from the user and then calculates the solution of c and prints it. Recall that to compute square roots, you can use the function math.sqrt() from Python’s math library (which we discussed in class). A sample run of the program is shown below (user input is in italics):
Enter values to compute the Pythagorean theorem.
a: 9.7
b: 3.2
c = 10.21420579389313
Khan-sole Academy
Now that you’ve seen how programming can help us in a number of different areas, it’s time for you to implement Khan-sole Academy—a program that helps other people learn! In this problem, you’ll write a program in the file khansole_academy.pythat randomly generates simple addition problems for the user, reads in the answer from the user, and then checks to see if they got it right or wrong, until the user appears to have mastered the material.
More specifically, your program should be able to generate simple addition problems that involve adding two 2-digit integers (i.e., the numbers 10 through 99). The user should be asked for an answer to each problem. Your program should determine if the answer was correct or not, and give the user an appropriate message to let them know. Your program should keep giving the user problems until the user has gotten 3 problems correct in a row. (Note: the number of problems the user needs to get correctly in a row to complete the program is just one example of a good place to specify a constant in your program).
A sample run of the program is shown below (user input is in italics).
What is 51 + 79?
Your answer: 120
Incorrect. The expected answer is 130
What is 33 + 19?
Your answer: 42
Incorrect. The expected answer is 52
What is 55 + 11?
Your answer: 66
Correct! You've gotten 1 correct in a row.
What is 84 + 25?
Your answer: 109
Correct! You've gotten 2 correct in a row.
What is 26 + 58?
Your answer: 74
Incorrect. The expected answer is 84
What is 98 + 85?
Your answer: 183
Correct! You've gotten 1 correct in a row.
What is 79 + 66?
Your answer: 145
Correct! You've gotten 2 correct in a row.
What is 97 + 20?
Your answer: 117
Correct! You've gotten 3 correct in a row.
Congratulations! You mastered addition.
As a side note, one of the earliest programs Mehran wrote (with his friend Matthew) when he was first learning how to program was very similar to Khansole Academy. It was called “M&M’s Math Puzzles.” It was written in a language named BASIC on a computer that had 4K of memory (that’s 4 Kilobytes) and used cassette tapes (the same kind used for music in the 1970’s) to store information. Yeah, Mehran is old.
Computing Interest
We want to write a program compute_interest.py that helps a user compute how much interest their bank account will accrue over time. The program starts by asking the user for an initial account balance, which is entered as a float (you can assume a positive real-value is entered). The program then asks the user for a starting year and month as well as an ending year and month, all entered as integers. The program then asks the user for a monthly interest rate. For example, a 2% interest rate would be entered by the user as the value 0.02.
The program should print out the monthly balance in the account from the starting year/month up to and including the ending year/month with interest accruing monthly. The amount of interest earned each month is simply the amount in the account in that month multiplied by the interest rate entered by the user. So (using a 2% interest rate) an account with 1000.00 at the start of the month would earn 20.00 that month and have a total of 1020.00 at the start of the next month.
After printing the monthly balance projection, your program should then repeat the process of asking the user for a new interest rate and printing the monthly balance in the account using the same starting account balance, starting year/month, and ending year/month as the user initially entered in the program. The program should end if the user specifies a monthly interest rate of 0%.
You can assume that the user will always enter a valid (i.e., positive) value for the start/end year and an integer from 1 to 12 for the start/end month. If the starting year/month is the same as or after the ending year/month, your program should not ask for an interest rate, but rather simply print “Starting date needs to be before the ending date.” and then end without an error.
The values for the initial balance, the starting year/month, and the ending year/month are entered by the user. The monthly balance is simply printed as a float, so you don’t have to worry about rounding to the nearest cent.
Remember that it’s a good idea to decompose your program and use parameters with functions as needed to pass information around your program. That’s really part of good programming style.
Two sample runs of the program are shown below (user input is in italics).
Sample run 1 (showing what happens if the user enters a starts year/month that is after the ending year/month. Note the program simply ends without asking for an interest rate.)
Initial balance: 500.00
Start year: 2020
Start month: 9
End year: 2019
End month: 10
Starting date needs to be before the ending date.
Sample run 2
Initial balance: 1000.00
Start year: 2020
Start month: 5
End year: 2022
End month: 3
Interest rate (0 to quit): 0.02
Year 2020, month 5 balance: 1000.0
Year 2020, month 6 balance: 1020.0
Year 2020, month 7 balance: 1040.4
Year 2020, month 8 balance: 1061.208
Year 2020, month 9 balance: 1082.43216
Year 2020, month 10 balance: 1104.0808032
Year 2020, month 11 balance: 1126.162419264
Year 2020, month 12 balance: 1148.6856676492798
Year 2021, month 1 balance: 1171.6593810022655
Year 2021, month 2 balance: 1195.0925686223109
Year 2021, month 3 balance: 1218.994419994757
Year 2021, month 4 balance: 1243.3743083946522
Year 2021, month 5 balance: 1268.2417945625452
Year 2021, month 6 balance: 1293.6066304537962
Year 2021, month 7 balance: 1319.478763062872
Year 2021, month 8 balance: 1345.8683383241296
Year 2021, month 9 balance: 1372.7857050906123
Year 2021, month 10 balance: 1400.2414191924245
Year 2021, month 11 balance: 1428.246247576273
Year 2021, month 12 balance: 1456.8111725277984
Year 2022, month 1 balance: 1485.9473959783543
Year 2022, month 2 balance: 1515.6663438979213
Year 2022, month 3 balance: 1545.9796707758796
Interest rate (0 to quit): 0.05
Year 2020, month 5 balance: 1000.0
Year 2020, month 6 balance: 1050.0
Year 2020, month 7 balance: 1102.5
Year 2020, month 8 balance: 1157.625
Year 2020, month 9 balance: 1215.50625
Year 2020, month 10 balance: 1276.2815624999998
Year 2020, month 11 balance: 1340.0956406249998
Year 2020, month 12 balance: 1407.1004226562497
Year 2021, month 1 balance: 1477.4554437890622
Year 2021, month 2 balance: 1551.3282159785153
Year 2021, month 3 balance: 1628.894626777441
Year 2021, month 4 balance: 1710.3393581163132
Year 2021, month 5 balance: 1795.8563260221288
Year 2021, month 6 balance: 1885.6491423232353
Year 2021, month 7 balance: 1979.9315994393971
Year 2021, month 8 balance: 2078.928179411367
Year 2021, month 9 balance: 2182.8745883819356
Year 2021, month 10 balance: 2292.0183178010325
Year 2021, month 11 balance: 2406.619233691084
Year 2021, month 12 balance: 2526.950195375638
Year 2022, month 1 balance: 2653.29770514442
Year 2022, month 2 balance: 2785.962590401641
Year 2022, month 3 balance: 2925.260719921723
Interest rate (0 to quit):0
Once you’ve completed all the required parts of the assignment, you might want to consider adding some extensions.
Extend Khansole Academy
You could consider extending your Khansole Academy program to, for example, add more problem types (subtraction, multiplication, division, and more). You could also consider problems beyond arithmetic. If you could build your own version of Khansole Academy, what would you use it to help people learn? Be creative and enjoy.
Hailstones
A separate (optional) problem you could consider writing is based on a problem in Douglas Hofstadter’s Pulitzer-prize-winning book Gödel, Escher, Bach. That book contains many interesting mathematical puzzles, many of which can be expressed in the form of computer programs. In Chapter XII, Hofstadter mentions a wonderful problem that is well within the scope of what you know. The problem can be expressed as follows:
Pick some positive integer and call it n.
If n is even, divide it by two.
If n is odd, multiply it by three and add one.
Continue this process until n is equal to one.
On page 401 of the Vintage edition of his book, Hofstadter illustrates this process with thfollowing example, starting with the number 15:
15 is odd, so I make 3n+1: 46
46 is even, so I take half: 23
23 is odd, so I make 3n+1: 70
70 is even, so I take half: 35
35 is odd, so I make 3n+1: 106
106 is even, so I take half: 53
53 is odd, so I make 3n+1: 160
160 is even, so I take half: 80
80 is even, so I take half: 40
40 is even, so I take half: 20
20 is even, so I take half: 10
10 is even, so I take half: 5
5 is odd, so I make 3n+1: 16
16 is even, so I take half: 8
8 is even, so I take half: 4
4 is even, so I take half: 2
2 is even, so I take half: 1
As you can see from this example, the numbers go up and down, but eventually—at least for all numbers that have ever been tried—comes down to end in 1. In some respects, this process is reminiscent of the formation of hailstones, which get carried upward by the winds over and over again before they finally descend to the ground. Because of this analogy, this sequence of numbers is usually called the Hailstone sequence, although it goes by many other names as well.
You might want to write a Python program that reads in a number from the user and then displays the Hailstone sequence for that number, just as in Hofstadter’s book, followed by a line showing the number of steps taken to reach 1. For example, here’s a sample run of what such a program might look like (user input is in italics):
Enter a number: 17
17 is odd, so I make 3n + 1: 52
52 is even, so I take half: 26
26 is even, so I take half: 13
13 is odd, so I make 3n + 1: 40
40 is even, so I take half: 20
20 is even, so I take half: 10
10 is even, so I take half: 5
5 is odd, so I make 3n + 1: 16
16 is even, so I take half: 8
8 is even, so I take half: 4
4 is even, so I take half: 2
2 is even, so I take half: 1
The process took 12 steps to reach 1
Ancient Game of Nim
Nimm is an ancient game of strategy that is named after the old German word for "take." It is also called Tiouk Tiouk in West Africa and Tsynshidzi in China. Players alternate taking stones until there are zero left. The game of Nimm goes as follows:
The last player to take a stone loses. Here is an example execution:
There are 20 stones left
Player 1 would you like to remvoe 1 or 2 stones? 2
There are 18 stones left
Player 2 would you like to remove 1 or 2 stones? 2
There are 16 stones left
Player 1 would you like to remvoe 1 or 2 stones? 1
There are 15 stones left
Player 2 would you like to remove 1 or 2 stones? 2
There are 13 stones left
Player 1 would you like to remvoe 1 or 2 stones? 2
There are 11 stones left
Player 2 would you like to remove 1 or 2 stones? 1
There are 10 stones left
Player 1 would you like to remvoe 1 or 2 stones? 2
There are 8 stones left
Player 2 would you like to remove 1 or 2 stones? -1
Please enter 1 or 2:
There are 6 stones left
Player 1 would you like to remvoe 1 or 2 stones? 2
There are 4 stones left
Player 2 would you like to remove 1 or 2 stones? 2
There are 2 stones left
Player 1 would you like to remvoe 1 or 2 stones? 1
There are 1 stones left
Player 2 would you like to remove 1 or 2 stones? 1
Player 1 wins!
Write a program to play Nimm. To make your life easier we have broken the problem down into smaller milestones. You have a lot of time for this program. Take it slowly, piece by piece.
Milestone 1
Start with 20 stones. Repeat the process of removing stones and printing out how many stones are left until there are zero. Don't worry about whose turn it is. Don't worry about making sure only one or two stones are removed. Use the method input(msg) which prints msg and waits for the user to enter an input. Make sure to convert the input into an int.
Example of Milestone 1:
There are 20 stones left
Player 1 would you like to remvoe 1 or 2 stones? 2
There are 18 stones left
Player 2 would you like to remove 1 or 2 stones? 17
There are 1 stones left
Player 1 would you like to remvoe 1 or 2 stones? 3
Game Over
Milestone 2
Create a variable of type int to keep track of whose turn it is (remember there are two players). Tell the user whose turn it is. Each time someone picks up stones, change the player number.
Example of Milestone 2:
There are 20 stones left
Player 1 would you like to remvoe 1 or 2 stones? 1
There are 19 stones left
Player 2 would you like to remove 1 or 2 stones? 1
There are 18 stones left
Player 1 would you like to remvoe 1 or 2 stones? 17
There are 1 stones left
Player 1 would you like to remvoe 1 or 2 stones? 1
Game Over
Milestone 3
Make sure that each turn only one or two stones are removed. After you read a number of stones to remove from a user (their input), you can use the following pattern to check if it was valid and keep asking until it is valid.
while input_is_valid:
input = int(input("Please enter 1 or 2: "))
As a final touch, announce the winner after the game is over.