Due by 11:59pm on Sunday, 6/26

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:

Questions

Question 1

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.

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 2

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 _____

Use OK to test your code:

python3 ok -q two_of_three

Question 3

Write a function that takes an integer n greater than 1 and returns the largest integer smaller than n that evenly divides n.

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."

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
"""

Use OK to test your code:

python3 ok -q largest_factor

Question 4

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():

def t():

def f():

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 5

Douglas Hofstadter's Pulitzer-prize-winning book, Gödel, 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.

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
"""