Quiz 1

Due by 11:59pm on Friday, 9/4

Instructions

Download quiz01.zip. Inside the archive, you will find a file called quiz01.py, along with a copy of the OK autograder.

Complete the quiz and submit it before 11:59pm on Friday, 9/4. You must work alone, but you may talk to the course staff (see Asking Questions below). You may use any course materials, including an interpreter, course videos, slides, and readings. Please do not discuss these specific questions with your classmates, and do not scour the web for answers or post your answers online.

Your submission will be graded automatically for correctness. Your implementations do not need to be efficient, as long as they are correct. We will apply additional correctness tests as well as the ones provided. Passing these tests does not guarantee a perfect score.

Asking Questions: If you believe you need clarification on a question, make a private post on Piazza. Please do not post publicly about the quiz contents. If the staff discovers a problem with the quiz or needs to clarify a question, we will email the class via Piazza. You can also come to office hours to ask questions about the quiz or any other course material, but no answers or hints will be provided in office hours.

Submission: When you are done, submit with python3 ok --submit. You may submit more than once before the deadline; only the final submission will be scored.

Using OK

The ok program helps you test your code and track your progress. The first time you run the autograder, you will be asked to log in with your @berkeley.edu account using your web browser. Please do so. Each time you run ok, it will back up your work and progress on our servers. You can run all the doctests with the following command:

python3 ok

To test a specific question, use the -q option with the name of the function:

python3 ok -q <function>

By default, only tests that fail will appear. If you want to see how you did on all tests, you can use the -v option:

python3 ok -v

If you do not want to send your progress to our server or you have any problems logging in, add the --local flag to block all communication:

python3 ok --local

When you are ready to submit, run ok with the --submit option:

python3 ok --submit

Readings: You might find the following references useful:

You can watch a video of the solution to Fall 2014 quiz 1 if you want to see an example of how to solve similar problems.

Question 1: Diff

Implement a function diff that takes three integers x, y, and z. It returns whether subtracting one of these numbers from another gives the third.

def diff(x, y, z):
    """Return whether one argument is the difference between the other two.

    x, y, and z are all integers.

    >>> diff(5, 3, 2) # 5 - 3 is 2
    True
    >>> diff(2, 3, 5) # 5 - 3 is 2
    True
    >>> diff(2, 5, 3) # 5 - 3 is 2
    True
    >>> diff(-2, 3, 5) # 3 - 5 is -2
    True
    >>> diff(-5, -3, -2) # -5 - -2 is -3
    True
    >>> diff(-2, 3, -5) # -2 - 3 is -5
    True
    >>> diff(2, 3, -5)
    False
    >>> diff(10, 6, 4)
    True
    >>> diff(10, 6, 3)
    False


    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q diff

Question 2: Abundant

Implement a function abundant that takes a positive integer n. It prints all ways of multiplying two positive integers to make n. It returns whether n is an abundant number, meaning that the sum of its proper divisors is greater than n. A proper divisor of n is an integer smaller than n that evenly divides n.

Hint: To print 1 * 2, use the expression print(1, '*', 2)

def abundant(n):
    """Print all ways of forming positive integer n by multiplying two positive
    integers together, ordered by the first term. Then, return whether the sum
    of the proper divisors of n is greater than n.

    A proper divisor of n evenly divides n but is less than n.

    >>> abundant(12) # 1 + 2 + 3 + 4 + 6 is 16, which is larger than 12
    1 * 12
    2 * 6
    3 * 4
    True
    >>> abundant(14) # 1 + 2 + 7 is 10, which is not larger than 14
    1 * 14
    2 * 7
    False
    >>> abundant(16)
    1 * 16
    2 * 8
    4 * 4
    False
    >>> abundant(20)
    1 * 20
    2 * 10
    4 * 5
    True
    >>> abundant(22)
    1 * 22
    2 * 11
    False
    >>> r = abundant(24)
    1 * 24
    2 * 12
    3 * 8
    4 * 6
    >>> r
    True


    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q abundant

Question 3: Amicable

Implement a function amicable that takes a positive integer n. It returns the smallest amicable number greater than n.

Two different numbers are both amicable if the sum of the proper divisors of each is equal to the other. Any number that's part of such a pair is an amicable number.

Hint: You may want to create a separate function to sum proper divisors.

def amicable(n):
    """Return the smallest amicable number greater than positive integer n.

    Every amicable number x has a buddy y different from x, such that
    the sum of the proper divisors of x equals y, and
    the sum of the proper divisors of y equals x.

    For example, 220 and 284 are both amicable because
    1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 is 284, and
    1 + 2 + 4 + 71 + 142 is 220

    >>> amicable(5)
    220
    >>> amicable(220)
    284
    >>> amicable(284)
    1184
    >>> r = amicable(5000)
    >>> r
    5020


    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q amicable