# Homework 1: Control hw01.zip

Due by 11:59pm on Thursday, 8/30

## Instructions

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:

Grading: Homework is graded based on effort, not correctness. However, there is no partial credit; you must show substantial effort on every problem to receive any points.

## Homework Questions

### Q1: A Plus Abs B

Fill in the blanks in the following function 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``

### Q2: Two of Three

Write a function that takes three positive numbers and returns the sum of the squares of the two largest numbers. Use only a single line 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
"""
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``

### 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
"""
``````

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: 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 `c`, `t`, and `f` such that `with_if_statement` prints the number `2`, but `with_if_function` prints both `1` and `2`.

``````def with_if_statement():
"""
>>> result = with_if_statement()
2
>>> print(result)
None
"""
if c():
return t()
else:
return f()

def with_if_function():
"""
>>> result = with_if_function()
1
2
>>> print(result)
None
"""
return if_function(c(), t(), f())

def c():

def t():

def f():
``````

Hint: If you are having a hard time identifying how an `if` statement and `if_function` differ, consider the rules of evaluation for `if` statements and call expressions.

Use Ok to test your code:

``````python3 ok -q with_if_statement
python3 ok -q with_if_function``````

### Q5: Hailstone

Douglas Hofstadter's Pulitzer-prize-winning book, GĂ¶del, Escher, Bach, poses the following mathematical puzzle.

1. Pick a positive integer `n` as the start.
2. If `n` is even, divide it by 2.
3. If `n` is odd, multiply it by 3 and add 1.
4. 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
"""
``````

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! They do not resemble any exam questions or relate directly to any required content in the course. Feel free to skip them.

### Q6: Quine

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.

A program that prints itself is called a Quine. Place your solution in the multi-line string named `quine`.

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