Quiz 2
Due by 11:59pm on Monday, 10/12
Instructions
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.
Examples:
x = tree(-1, [tree(1),
tree(-2),
tree(3, [tree(-4),
tree(-5)])])
y = tree(1, [tree(-1, [tree(2)]),
tree( 8, [tree(-7)]),
tree(-3, [tree(-3)]),
tree(-4, [tree(3),
tree(-5),
tree(7, [tree(-4),
tree(-2)])])])
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))
5
>>> subtreesum(tree(-5, [tree(6)]))
6
>>> subtreesum(tree(-5, [tree(6, [tree(-2)])]))
4
>>> subtreesum(tree(-2))
0
>>> subtreesum(x)
1
>>> subtreesum(y)
7
>>> subtreesum(tree(20, branches(y))) # Max sum includes all nodes
11
"""
"*** 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 ayear
stamp. Theupdate
method sets theyear
stamp to thecurrent_year
class attribute of theMint
class. - The
create
method takes a subclass ofCoin
and returns an instance of that class stamped with themint
's year (which may be different fromMint.current_year
if it has not been updated.) - A
Coin
'sworth
method returns thecents
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 thecurrent_year
class attribute of theMint
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
2015
>>> dime = mint.create(Dime)
>>> dime.year
2015
>>> Mint.current_year = 2100 # Time passes
>>> nickel = mint.create(Nickel)
>>> nickel.year # The mint has not updated its stamp yet
2015
>>> nickel.worth() # 5 cents + (85 - 50 years)
40
>>> 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)
35
>>> Mint().create(Dime).worth() # A new mint has the current year
10
>>> dime.worth() # 10 cents + (160 - 50 years)
120
>>> Dime.cents = 20 # Upgrade all dimes!
>>> dime.worth() # 20 cents + (160 - 50 years)
130
"""
current_year = 2015
def __init__(self):
self.update()
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