Homework 1: Functions

Due: Thursday 09/03 @ 11:59pm
Points: 1
Download: hw01.zip

To receive credit, you must solve each problem and then complete a short checkoff interview about your solution. You may use Preceptor for the interview or come to office hours to be interviewed by a member of the course staff. If the interviews are not working, please still submit your working code on time or request an extension by the deadline. Staff will be doing in-person checkoffs for up to 3 business days after the assignment deadline (including any approved extension). If a checkoff happens more than 3 business days after the regular deadline, staff may ask to confirm your extended deadline via Flextensions. You will submit a Provenance bundle that includes a record of how you used VS Code, including interactions with Preceptor. Please do not use AI tools other than Preceptor for this assignment.

Readings:

Getting Started Videos:

If you feel stuck, these videos may provide some helpful direction for tackling the coding problems on this assignment.

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Required Questions

Q1: A Plus Abs B

Python's operator module contains two-argument functions such as add and sub for Python's built-in arithmetic operators. For example, add(2, 3) evalutes to 5, just like the expression 2 + 3.

Fill in the blanks in the following function to add a to the absolute value of b, without calling the abs function. 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)
    5
    >>> a_plus_abs_b(2, -3)
    5
    >>> a_plus_abs_b(-1, 4)
    3
    >>> a_plus_abs_b(-1, -4)
    3
    """
    if b < 0:
        f = _____
    else:
        f = _____
    return f(a, b)

python3 -m pytest -k 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)
    5
    >>> two_of_three(5, 3, 1)
    10
    >>> two_of_three(10, 2, 8)
    68
    >>> two_of_three(5, 5, 5)
    50
    """
    return _____

Hint: Consider using the max or min function:
>>> max(1, 2, 3)
3
>>> min(-1, -2, -3)
-3

python3 -m pytest -k 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
    5
    >>> largest_factor(80) # factors are 1, 2, 4, 5, 8, 10, 16, 20, 40
    40
    >>> largest_factor(13) # factors are 1, 13
    1
    """
    "*** YOUR CODE HERE ***"

Hint: To check if b evenly divides a, use the expression a % b == 0, which can be read as, "the remainder when dividing a by b is 0."

python3 -m pytest -k largest_factor

Q4: Hailstone

Douglas Hofstadter's Pulitzer-prize-winning book, Gödel, Escher, Bach, poses the following mathematical puzzle.

Pick a positive integer n as the start.
If n is even, divide it by 2.
If n is odd, multiply it by 3 and add 1.
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 length.

    >>> a = hailstone(10)
    10
    5
    16
    8
    4
    2
    1
    >>> a
    7
    >>> b = hailstone(1)
    1
    >>> b
    1
    """
    "*** 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: If you see 4.0 but want just 4, try using floor division // instead of regular division /.

python3 -m pytest -k hailstone

Fun fact: In 2019, there was a major development in understanding how the hailstone conjecture works for most numbers! This 2026 StarTalk interview with Terence Tao discusses the problem.

Submit

Run Provenance: Prepare Submission Bundle from the VS Code command palette to create your submission zip, and upload that zip to Gradescope. For a refresher on how to do this, refer to Lab 00.