Homework 1: Variables, Functions and Control
Due by 11:59pm on Wednesday, June 12
Instructions
Download hw1.zip.
Submission: When you are done, submit the hw1.py
file and a scanned image answer to question 1 on Gradescope. You may submit more than once before the deadline; only the
final submission will be scored.
Readings: You might find the following references useful:
Grading: Homework is graded based on correctness. Each incorrect problem will decrease the total score by one point. This homework constitutes 5% of the final grade.
Required Questions
Q1: Let's Practice Uploading on Gradescope
Draw a picture of the Emzini weCode logo and submit along with yourhw1.py
file on gradescope. Write your name and email in the picture. Draw on an actual piece of physical paper using either a pen or a pencil.
Q2: A Plus Abs B
Fill in the blanks in the following function for adding a
to the
absolute value of b
, without calling abs
. You may not modify any
of the provided code other than the two blanks.
from operator import add, sub
def a_plus_abs_b(a, b):
"""Return a+abs(b), but without calling abs.
>>> a_plus_abs_b(2, 3)
5
>>> a_plus_abs_b(2, -3)
5
>>> # a check that you didn't change the return statement!
>>> import inspect, re
>>> re.findall(r'^\s*(return .*)', inspect.getsource(a_plus_abs_b), re.M)
['return f(a, b)']
"""
if b < 0:
f = _____
else:
f = _____
return f(a, b)
Q3: Two of Three
Write a function that takes three positive numbers as arguments and returns the sum of the squares of the two smallest numbers. Use only a single line for the body of the function.
def two_of_three(x, y, z):
"""Return a*a + b*b, where a and b are the two smallest members of the
positive numbers x, y, and z.
>>> two_of_three(1, 2, 3)
5
>>> two_of_three(5, 3, 1)
10
>>> two_of_three(10, 2, 8)
68
>>> two_of_three(5, 5, 5)
50
>>> # check that your code consists of nothing but an expression (this docstring)
>>> # a return statement
>>> import inspect, ast
>>> [type(x).__name__ for x in ast.parse(inspect.getsource(two_of_three)).body[0].body]
['Expr', 'Return']
"""
return _____
Hint: Consider using the
max
ormin
function:>>> max(1, 2, 3) 3 >>> min(-1, -2, -3) -3
Q4: Largest Factor
Write a function that takes an integer n
that is greater than 1 and
returns the largest integer that is smaller than n
and evenly divides n
.
def largest_factor(n):
"""Return the largest factor of n that is smaller than n.
>>> largest_factor(15) # factors are 1, 3, 5
5
>>> largest_factor(80) # factors are 1, 2, 4, 5, 8, 10, 16, 20, 40
40
>>> largest_factor(13) # factor is 1 since 13 is prime
1
"""
"*** YOUR CODE HERE ***"
Hint: To check if
b
evenly dividesa
, you can use the expressiona % b == 0
, which can be read as, "the remainder of dividinga
byb
is 0."
Q5: If Function vs Statement
Let's try to write a function that does the same thing as an if
statement.
def if_function(condition, true_result, false_result):
"""Return true_result if condition is a true value, and
false_result otherwise.
>>> if_function(True, 2, 3)
2
>>> if_function(False, 2, 3)
3
>>> if_function(3==2, 3+2, 3-2)
1
>>> if_function(3>2, 3+2, 3-2)
5
"""
if condition:
return true_result
else:
return false_result
Despite the doctests above, this function actually does not do the
same thing as an if
statement in all cases. To prove this fact,
write functions cond
, true_func
, and false_func
such that with_if_statement
prints the number 47
, but with_if_function
prints both 42
and 47
.
def with_if_statement():
"""
>>> result = with_if_statement()
47
>>> print(result)
None
"""
if cond():
return true_func()
else:
return false_func()
def with_if_function():
"""
>>> result = with_if_function()
42
47
>>> print(result)
None
"""
return if_function(cond(), true_func(), false_func())
def cond():
"*** YOUR CODE HERE ***"
def true_func():
"*** YOUR CODE HERE ***"
def false_func():
"*** YOUR CODE HERE ***"
Hint: If you are having a hard time identifying how an
if
statement andif_function
differ, consider the rules of evaluation forif
statements and call expressions.
Q6: Hailstone
Douglas Hofstadter's Pulitzer-prize-winning book, Gödel, Escher, Bach, poses the following mathematical puzzle.
- Pick a positive integer
n
as the start. - If
n
is even, divide it by 2. - If
n
is odd, multiply it by 3 and add 1. - Continue this process until
n
is 1.
The number n
will travel up and down but eventually end at 1 (at least for
all numbers that have ever been tried -- nobody has ever proved that the
sequence will terminate). Analogously, a hailstone travels up and down in the
atmosphere before eventually landing on earth.
Breaking News (or at least the closest thing to that in math). There was a recent development in the hailstone conjecture in 2019 that shows that almost all numbers will eventually get to 1 if you repeat this process. This isn't a complete proof but a major breakthrough.
This sequence of values of n
is often called a Hailstone sequence. Write a
function that takes a single argument with formal parameter name n
, prints
out the hailstone sequence starting at n
, and returns the number of steps in
the sequence:
def hailstone(n):
"""Print the hailstone sequence starting at n and return its
length.
>>> a = hailstone(10)
10
5
16
8
4
2
1
>>> a
7
"""
"*** YOUR CODE HERE ***"
Hailstone sequences can get quite long! Try 27. What's the longest you can find?
Submit
Make sure to submit this assignment on Gradescope