# Homework 1

*Due by 11:59pm on Wednesday, 1/27*

## Instructions

Download hw01.zip. Inside the archive, you will find a file called hw01.py, along with a copy of the OK autograder.

**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. See Lab 0 for 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:

## Required questions

### Question 1

Register for a class account info through this link. After logging in through CalNet, request an account by clicking on the link under Your Inidividual Account. After accepting the conditions, fill out your information (name, student ID, email) under Account Registration. Then go to See Account under Your Individual Account. You will be presented with a course account and your username will be of the form cs61a-xxx. These accounts allow you to use instructional machines in the CS department and are useful if you do not have regular access a computer.

Fill out your username in the `your_course_username`

function. Make sure to include the quotes. For example, if your login was `cs61a-taa`

, your return statement should look like this:

`return 'cs61a-taa'`

If you do not have a CalNet account, see your TA to get a course account.

```
def your_course_username():
"""Return your course username.
>>> username = your_course_username()
>>> username.startswith('cs61a-')
True
"""
return '___'
```

Use OK to test your code:

`python3 ok -q your_course_username`

### Question 2

We've seen that we can give new names to existing functions. Fill in
the blanks in the following function definition for adding `a`

to the
absolute value of `b`

, without calling `abs`

.

```
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
"""
if b < 0:
f = _____
else:
f = _____
return f(a, b)
```

Use OK to test your code:

`python3 ok -q a_plus_abs_b`

### Question 3

Write a function that takes three *positive* numbers and returns the
sum of the squares of the two largest numbers. Use only a single
expression for the body of the function.

```
def two_of_three(a, b, c):
"""Return x*x + y*y, where x and y are the two largest members of the
positive numbers a, b, and c.
>>> two_of_three(1, 2, 3)
13
>>> two_of_three(5, 3, 1)
34
>>> two_of_three(10, 2, 8)
164
>>> two_of_three(5, 5, 5)
50
"""
"*** YOUR CODE HERE ***"
```

Use OK to test your code:

`python3 ok -q two_of_three`

### Question 4

Write a function that takes an integer `n`

**greater than 1** and returns the
largest integer smaller than `n`

that evenly divides `n*n-1`

.

*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."
However, it is possible to solve this problem without any `if`

or `while`

statements.

```
def largest_factor(n):
"""Return the largest factor of n*n-1 that is smaller than n.
>>> largest_factor(4) # n*n-1 is 15; factors are 1, 3, 5, 15
3
>>> largest_factor(9) # n*n-1 is 80; factors are 1, 2, 4, 5, 8, 10, ...
8
"""
"*** YOUR CODE HERE ***"
```

Use OK to test your code:

`python3 ok -q largest_factor`

### Question 5

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 `c`

, `t`

, and `f`

such that `with_if_statement`

returns the number `1`

, but `with_if_function`

does not (it can do
*anything* else):

```
def with_if_statement():
"""
>>> with_if_statement()
1
"""
if c():
return t()
else:
return f()
def with_if_function():
return if_function(c(), t(), f())
def c():
"*** YOUR CODE HERE ***"
def t():
"*** YOUR CODE HERE ***"
def f():
"*** YOUR CODE HERE ***"
```

To test your solution, open an interactive interpreter

` python3 -i hw01.py`

and try calling `with_if_function`

and `with_if_statement`

to check that one
returns 1 and the other doesn't.

### Question 6

Douglas Hofstadter's Pulitzer-prize-winning book, *GĂ¶del, 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.

The sequence of values of `n`

is often called a Hailstone sequence,
because hailstones also travel up and down in the atmosphere before
falling to earth. 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?

Use OK to test your code:

`python3 ok -q hailstone`

## Extra questions

Extra questions are not worth extra credit and are entirely optional. They are designed to challenge you to think creatively!

### Question 7

Write a one-line program that prints itself, using only the following features of the Python language:

- Number literals
- Assignment statements
- String literals that can be expressed using single or double quotes
- The arithmetic operators
`+`

,`-`

,`*`

, and`/`

- The built-in
`print`

function - The built-in
`eval`

function, which evaluates a string as a Python expression - The built-in
`repr`

function, which returns an expression that evaluates to its argument

You can concatenate two strings by adding them together with `+`

and repeat a
string by multipying it by an integer. Semicolons can be used to separate
multiple statements on the same line. E.g.,

```
>>> c='c';print('a');print('b' + c * 2)
a
bcc
```

Hint: Explore the relationship between single quotes, double quotes, and the
`repr`

function applied to strings.

Place your solution in the multi-line string named `challenge_question_program`

.

*Note*: No tests will be run on your solution to this problem.