Due by 11:59pm on Monday, 1/30


Download hw01.zip. The homework problems can be found in the problems directory and the quiz problems can be found in the quiz directory. You must run python3 ok --submit twice: once inside the problems directory, and once inside the quiz directory.

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:

Homework Questions

For this set of problems, you must run ok from within the problems directory. Remember that you may choose to work with a partner on homework questions.

Question 1

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 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)
    >>> two_of_three(5, 3, 1)
    >>> two_of_three(10, 2, 8)
    >>> two_of_three(5, 5, 5)
    return _____

Use OK to test your code:

python3 ok -q two_of_three

Question 3

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
    >>> largest_factor(80) # factors are 1, 2, 4, 5, 8, 10, 16, 20, 40
    >>> largest_factor(13) # factor is 1 since 13 is prime
    "*** 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."

Use OK to test your code:

python3 ok -q largest_factor

Question 4

Let's 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.

Hint: If you are having a hard time identifying how the if statement and if function differ, first try to get them to print out different values.

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.

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

    >>> 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

Quiz Questions

For this set of problems, you must run ok from within the quiz directory. While homework questions may be completed with a partner, please remember that quiz questions must be completed alone.

Question 6: Multiple

Write a function that takes in two numbers and returns the smallest number that is a multiple of both.
def multiple(a, b):
    """Return the smallest number n that is a multiple of both a and b.

    >>> multiple(3, 4)
    >>> multiple(14, 21)
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q multiple

Question 7: Unique Digits

Write a function that returns the number of unique digits in a positive integer.
def unique_digits(n):
    """Return the number of unique digits in positive integer n

    >>> unique_digits(8675309) # All are unique
    >>> unique_digits(1313131) # 1 and 3
    >>> unique_digits(13173131) # 1, 3, and 7
    >>> unique_digits(10000) # 0 and 1
    >>> unique_digits(101) # 0 and 1
    >>> unique_digits(10) # 0 and 1
    "*** YOUR CODE HERE ***"

Hint: You may find it helpful to first define a function has_digit(n, k), which determines whether a number n has digit k.

Use OK to test your code:

python3 ok -q unique_digits