Homework 1: Functions, Control
Due by 11:59pm on Thursday, September 1
Instructions
Download hw01.zip.
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. Check that you have successfully submitted
your code on okpy.org. See Lab 0 for more instructions on
submitting assignments.
Using Ok: If you have any questions about using Ok, please refer to this guide.
Readings: You might find the following references useful:
Important: The lecture on Monday 8/29 will cover readings 1.3-1.5, which contain the material required for question 4. (Control)
Grading: Homework is graded based on
correctness. Each incorrect problem will decrease the total score by one point. There is a homework recovery policy as stated in the syllabus.
This homework is out of 2 points.
Getting Started Videos
These videos may provide some helpful direction for tackling the problems on this assignment.
To see these videos, you should be logged into your berkeley.edu email.
Required Questions
Q1: A Plus Abs B
Python's operator
module defines binary functions for Python's intrinsic arithmetic operators. For example, calling operator.add(2,3)
is equivalent to calling the expression 2 + 3
; both will return 5
.
Note that when the
operator
module is imported into the namespace, like at the top ofhw01.py
, you can just calladd(2,3)
instead ofoperator.add(2,3)
.
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.
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_plus_abs_b(-1, 4)
3
>>> a_plus_abs_b(-1, -4)
3
"""
if b < 0:
f = _____
else:
f = _____
return f(a, b)
Use Ok to test your code:
python3 ok -q a_plus_abs_b
Q2: 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(i, j, k):
"""Return m*m + n*n, where m and n are the two smallest members of the
positive numbers i, j, and k.
>>> 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
"""
return _____
Hint: Consider using the
max
ormin
function:>>> max(1, 2, 3) 3 >>> min(-1, -2, -3) -3
Use Ok to test your code:
python3 ok -q two_of_three
Q3: 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."
Use Ok to test your code:
python3 ok -q largest_factor
Q4: 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.
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
>>> b = hailstone(1)
1
>>> b
1
"""
"*** YOUR CODE HERE ***"
Hailstone sequences can get quite long! Try 27. What's the longest you can find?
Note that if
n == 1
initially, then the sequence is one step long.
Hint: Recall the different outputs from using regular division/
and floor division//
Use Ok to test your code:
python3 ok -q hailstone
Curious about hailstones or hailstone sequences? Take a look at these articles:
- Check out this article to learn more about how hailstones work!
- In 2019, there was a major development in understanding how the hailstone conjecture works for most numbers!
Submit
Make sure to submit this assignment by running:
python3 ok --submit
If you completed all problems correctly, you should see that your score is 6.0 in terminal. Each homework assignment counts for 2 points, so in this case you will receive the full 2 points for homework. Remember that every incorrect question costs you 1 point, so a 5.0/6.0 on this assignment will translate to a 1.0/2.0 homework grade for this assignment.