Due by 11:59pm on Friday, 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 1 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:

• Section 1.2
• Section 1.3
• Section 1.4
• Section 1.5

Required 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.

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 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 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 3

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 4

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
    """
    "*** 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 5

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.