Due by 11:59pm on Monday, 10/12


Download quiz02.zip. Inside the archive, you will find a file called quiz02.py, along with a copy of the OK autograder.

Complete the quiz and submit it before 11:59pm on Monday, 10/12. 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:

Reminder. Every node in a tree t is the root value of some subtree of t.

Definition. A subset S of nodes is tree-consistent if, for every node n included in S, S also includes all nodes in the subtree for which n is the root value. In other words, a tree-consistent subset of nodes contains all the nodes in a collection of subtrees.

For any tree, the set of all nodes and the empty set are both tree-consistent.


x = tree(-1, [tree(1),
              tree(3, [tree(-4),
y = tree(1, [tree(-1, [tree(2)]),
             tree( 8, [tree(-7)]),
             tree(-3, [tree(-3)]),
             tree(-4, [tree(3),
                       tree(7, [tree(-4),

In x, if 3 is included then -4 and -5 must be included because 3 is the root value of a subtree containing -4 and -5. Therefore, the set of nodes {3, -4, -5} is tree-consistent, but {3} and {3, -4} are not. The tree-consistent subset with the highest sum is {1}.

In y, the tree-consistent subset with the highest sum is {2, 8, -7, 3, 7, -4, -2}:

Question 1: Subtree Sum

Implement subtreesum, which takes a tree t as an argument. It returns the maximum sum of a tree-consistent subset of the nodes in t.

def subtreesum(t):
    """Return the maximum sum of any tree-consistent subset of nodes in t.

    >>> subtreesum(tree(5))
    >>> subtreesum(tree(-5, [tree(6)]))
    >>> subtreesum(tree(-5, [tree(6, [tree(-2)])]))
    >>> subtreesum(tree(-2))

    >>> subtreesum(x)
    >>> subtreesum(y)
    >>> subtreesum(tree(20, branches(y))) # Max sum includes all nodes
    "*** YOUR CODE HERE ***"

def treesum(t):
    """Return the sum of all node values in t."""
    return root(t) + sum([treesum(b) for b in branches(t)])

Use OK to test your code:

python3 ok -q subtreesum

Question 2: Mint

Complete the Mint and Coin classes so that the coins created by a mint have the correct year and worth.

  • Each Mint instance has a year stamp. The update method sets the year stamp to the current_year class attribute of the Mint class.
  • The create method takes a subclass of Coin and returns an instance of that class stamped with the mint's year (which may be different from Mint.current_year if it has not been updated.)
  • A Coin's worth method returns the cents value of the coin plus one extra cent for each year of age beyond 50. A coin's age can be determined by subtracting the coin's year from the current_year class attribute of the Mint class.

Use OK to test your code:

python3 ok -q Mint
class Mint:
    """A mint creates coins by stamping on years.

    The update method sets the mint's stamp to Mint.current_year.

    >>> mint = Mint()
    >>> mint.year
    >>> dime = mint.create(Dime)
    >>> dime.year
    >>> Mint.current_year = 2100  # Time passes
    >>> nickel = mint.create(Nickel)
    >>> nickel.year     # The mint has not updated its stamp yet
    >>> nickel.worth()  # 5 cents + (85 - 50 years)
    >>> mint.update()   # The mint's year is updated to 2100
    >>> Mint.current_year = 2175     # More time passes
    >>> mint.create(Dime).worth()    # 10 cents + (75 - 50 years)
    >>> Mint().create(Dime).worth()  # A new mint has the current year
    >>> dime.worth()     # 10 cents + (160 - 50 years)
    >>> Dime.cents = 20  # Upgrade all dimes!
    >>> dime.worth()     # 20 cents + (160 - 50 years)
    current_year = 2015

    def __init__(self):

    def create(self, kind):
        "*** YOUR CODE HERE ***"

    def update(self):
        "*** YOUR CODE HERE ***"

class Coin:
    def __init__(self, year):
        self.year = year

    def worth(self):
        "The worth is a coin's face value + 1 cent for each year over age 50."
        "*** YOUR CODE HERE ***"

class Nickel(Coin):
    cents = 5

class Dime(Coin):
    cents = 10