CS 61A Structure and Interpretation of Computer Programs
Spring 2017
INSTRUCTIONS
Mock Midterm 2
• You have 1 hour to complete the exam.
• The exam is closed book, closed notes, closed computer, closed calculator, except one 8.5” × 11” cheat sheet
of your own creation.
• Mark your answers on the exam itself. We will not grade answers written on scratch paper.
Last name
First name
Student ID number
Instructional account (cs61a-_)
BearFacts email
TA
Name of the person to your left
Name of the person to your right
All the work on this exam is my own.
(please sign)
2
1. (10 points) The Ugly Duckling
For each of the expressions in the table below, write the output displayed by the interactive Python interpreter when the expression is evaluated. If an error occurs, write “Error”. If a function is displayed write Function, if a generator is displayed write Generator.
The first box has been filled in for you. Assume that you have started python3 and executed the following statements:
all_ducks = [] class Duck:
ducks = 0
def __init__(self, name):
self.name = name all_ducks.append(self) Duck.ducks += 1
def __iter__(self): while True:
yield all_ducks[0]
first = all_ducks.pop(0) all_ducks.append(first)
def __str__(self): return “String Duck”
def __repr__(self):
return “Duck(” + self.name + “)”
def clean(self): all_ducks = []
return self
drake = Duckling(“drake”)
helen = drake.mother duck(“helen”) iter1 = iter(Duck(“temp”))
class Duckling:
mother_duck = Duck
def __init__(self, name):
Duck.__init__(self, name)
ducks = 0
def __repr__(self):
return “Duckling(” + \ self.name + “)”
class Swan(Duckling):
def
def
__init__(self, name=”autumn”): Duckling.__init__(self, name) self.mother_duck = \
self.mother_duck(“Swan”) __iter__(self):
Duckling.next=Duck.__iter__(self) while True:
yield next(Duckling.next)
print(“hi”) hi
Duckling.next
next(iter1)
Duck.all_ducks[0]
next(iter1)
all_ducks
Duck.ducks
next(iter1)
different = Swan() different.mother_duck.ducks
all_ducks [0]
new_iter = iter(different) next(new_iter)
clean(different.mother_duck)
next(iter1)
all_ducks
Name: 3 2. (10 points) Lost in Links
Assume linked lists are defined as follows:
class Link: empty = ()
def __init__(self, first, rest=empty):
assert rest is Link.empty or isinstance(rest, Link) self.first = first
self.rest = rest
Given a linked list and an interval [i, j], reverse all elements contained between the i and j indices, inclusive. Assume the linked list is 1-indexed (first element is denoted as 1), i < j, and the linked list has stricly more than j elements. Mutate the linked list.
def indexReverse(lnk, i, j): """
>>> ll = Link(1, Link(2, Link(3)))
>>> indexReverse(ll, 1, 2)
>>> ll
Link(2, Link(1, Link(3)))
>>> ll2 = Link(1, Link(2, Link(3, Link(4, Link(5))))) >>> indexReverse(ll2, 2, 4)
>>> ll2
Link(1, Link(4, Link(3, Link(2, Link(5)))))
“””
dummy = ______________________________ for _ in ______________________________:
dummy = ______________________________ reverse = Link.empty
cur = ___________________________________
for _ in ________________________________________:
next = _____________________________________________ cur.rest = _____________________________________________ reverse = _____________________________________________ cur = ______________________________
____________________________________________________________ ____________________________________________________________ ____________________________________________________________
4
3. (10 points) The Forbidden Forest (of Binary Trees)
Recall the implementation of a Tree:
class Tree:
def __init__(self, label, branches=[]):
for c in branches:
assert isinstance(c, Tree)
self.label = label self.branches = branches
def is_leaf(self):
return not self.branches
A Binary Search Tree is a tree where the left subtree contains only nodes with keys less than the node’s keys, and the right subtree contains only nodes with keys greater than the node’s keys. Both left and right subtree must also be Binary Search Trees.
class BST: empty = ()
def __init__(self, entry, left=empty, right=empty): self.entry = entry
self.left, self.right = left, right
Write a function is binary that takes in a Tree, tree, and returns True if tree is a Binary Search Tree and False otherwise.
def is_binary(tree): if is_leaf(tree):
return _________________________________ left = tree.left
right = tree.right
if __________________________________________________________________:
return _____________________________________________________________ return __________________________________________________________________
Now write a function insert that takes in a Binary Search Tree tree and value n and inserts n into the tree. It mutates tree and the return value is also a Binary Search Tree.
def insert(tree, n):
if tree is BST.empty:
_________________________________
to_change = tree.left if n < tree.label else tree.right
__________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________
__________________________________________________________________ What is the runtime of is binary if there are n nodes in tree? What is the runtime of insert?
Name: 5
4. (10 points) Perfect Engine!
You are in an apocalyptic society and have been charged with making an n-gen, or a generator that computes all of the n-perfect numbers. However, in this apocalyptic society, built-in AND user-defined Python multiplication is forbidden in any form!
You have a blueprint for building a few n-gins from a natural number generator:
A 2-gen:
1 2 3 4 5 6 7 8 9 ... 1 4 9 16 25 ...
A 3-gen:
1 2 3 4 5 6 7 8 9 ... 1 3 7 12 19 27 ... 1 8 27 ...
Hint: Here is how yield from works. When used inside an iterable yield from will issue each element from another iterable as though it was issued from the first iterable. The following code is equivalent:
def generator1 ():
for item in generator2 ():
yield item
# do more things in this generator
def generator1 ():
yield from generator2 ()
# more things on this generator
Now its your job to build the perfect n-gen and power society out of the apocalypse! Good luck!
def nats(): """
A generator that yields all natural numbers. Might be helpful!
"""
def perfect_ngen(n): """
>>> two_gen = perfect_ngen (2)
>>> next(two_gen) 1
>>> next(two_gen)
4
>>> next(two_gen) 9
>>> three_gen = perfect_ngen (3)
>>> next(three_gen) 1
>>> next(three_gen) 8
>>> next(three_gen) 27
“””
gen = create_skip(____, _______)
while _________________:
n = _________________
gen = create_skip(____, _______)
return gen
curr = 0 while True:
curr += 1 yield curr
def create_skip(n, if n == 1:
yield from
curr , skip = ________ , ________ for elem in ____________:
if skip == n:
___________________ else:
curr = __________________ skip = _________________ yield _________________
gen ):
____________