Homework 1: Functions, Control

Due by 11:59pm on Thursday, September 1


Download hw01.zip.

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:

Important: The lecture on Monday 8/29 will cover readings 1.3-1.5, which contain the material required for question 4. (Control)

Grading: Homework is graded based on correctness. Each incorrect problem will decrease the total score by one point. There is a homework recovery policy as stated in the syllabus. This homework is out of 2 points.

Getting Started Videos

These videos may provide some helpful direction for tackling the problems on this assignment.

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Required Questions

Q1: A Plus Abs B

Python's operator module defines binary functions for Python's intrinsic arithmetic operators. For example, calling operator.add(2,3) is equivalent to calling the expression 2 + 3; both will return 5.

Note that when the operator module is imported into the namespace, like at the top of hw01.py, you can just call add(2,3) instead of operator.add(2,3).

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.

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)
    >>> a_plus_abs_b(-1, 4)
    >>> a_plus_abs_b(-1, -4)
    if b < 0:
        f = _____
        f = _____
    return f(a, b)

Use Ok to test your code:

python3 ok -q a_plus_abs_b

Q2: Two of Three

Write a function that takes three positive numbers as arguments and returns the sum of the squares of the two smallest numbers. Use only a single line for the body of the function.

def two_of_three(i, j, k):
    """Return m*m + n*n, where m and n are the two smallest members of the
    positive numbers i, j, and k.

    >>> 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 _____

Hint: Consider using the max or min function:

>>> max(1, 2, 3)
>>> min(-1, -2, -3)

Use Ok to test your code:

python3 ok -q two_of_three

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
    >>> 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

Q4: Hailstone

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
    >>> b = hailstone(1)
    >>> b
    "*** YOUR CODE HERE ***"

Hailstone sequences can get quite long! Try 27. What's the longest you can find?

Note that if n == 1 initially, then the sequence is one step long.
Hint: Recall the different outputs from using regular division / and floor division //

Use Ok to test your code:

python3 ok -q hailstone

Curious about hailstones or hailstone sequences? Take a look at these articles:

  • Check out this article to learn more about how hailstones work!
  • In 2019, there was a major development in understanding how the hailstone conjecture works for most numbers!


Make sure to submit this assignment by running:

python3 ok --submit

If you completed all problems correctly, you should see that your score is 6.0 in terminal. Each homework assignment counts for 2 points, so in this case you will receive the full 2 points for homework. Remember that every incorrect question costs you 1 point, so a 5.0/6.0 on this assignment will translate to a 1.0/2.0 homework grade for this assignment.