# Homework 1: Control

*Due by 11:59pm on Tuesday, 10/8*

## Instructions

Download hw01.zip.

**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`

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

### 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."

### 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():
"*** YOUR CODE HERE ***"
def t():
"*** YOUR CODE HERE ***"
def f():
"*** YOUR CODE HERE ***"
```

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.

### Q5: Hailstone

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.

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?