# Homework 1: Functions, Control

*Due by 11:59pm on Thursday, August 31*

## Instructions

Download hw01.zip.

**Submission:** When you are done, submit the assignment by uploading all code files you've edited to Gradescope. 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 Gradescope. 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:

**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 of`hw01.py`

, you can just call`add(2,3)`

instead of`operator.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`

Use Ok to run the local syntax checker (which checks that you didn't modify any of the provided code other than the two blanks):

`python3 ok -q a_plus_abs_b_syntax_check`

### 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`

or`min`

function:`>>> max(1, 2, 3) 3 >>> min(-1, -2, -3) -3`

Use Ok to test your code:

`python3 ok -q two_of_three`

Use Ok to run the local syntax checker (which checks that you used only a single line for the body of the function):

`python3 ok -q two_of_three_syntax_check`

### 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 divides`a`

, you can use the expression`a % b == 0`

, which can be read as, "the remainder of dividing`a`

by`b`

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!

## Check Your Score Locally

You can locally check your score on each question of this assignment by running

`python3 ok --score`

**This does NOT submit the assignment!** When you are satisfied with your score, submit the assignment to Gradescope to receive credit for it.

## Submit

Make sure to submit this assignment by uploading any files you've edited **to the appropriate Gradescope assignment.** For a refresher on how to do this, refer to Lab 00.

If you completed all problems correctly, you should see that your score is 6.0 in the autograder output by Gradescope. 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.