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


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-')
    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)
    >>> a_plus_abs_b(2, -3)
    if b < 0:
        f = _____
        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)
    >>> two_of_three(5, 3, 1)
    >>> two_of_three(10, 2, 8)
    >>> two_of_three(5, 5, 5)
    "*** 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
    >>> largest_factor(9) # n*n-1 is 80; factors are 1, 2, 4, 5, 8, 10, ...
    "*** 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)
    >>> if_function(False, 2, 3)
    >>> if_function(3==2, 3+2, 3-2)
    >>> if_function(3>2, 3+2, 3-2)
    if condition:
        return true_result
        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()
    if c():
        return t()
        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, 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

    >>> a = hailstone(10)
    >>> a
    "*** 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)

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.