Homework 2: Function writing

HW
Week03
Published

January 29, 2026

Note: This assignment must be submitted in github classroom.

Writing functions: Advent of Code

For more than a decade, Eric Wastl has been masterminding the Advent of Code. Each year, on December 1st, a series of puzzles is released. You need to solve all, of course, to save Christmas.

The following is Advent of Code question 1 from 2025:

You arrive at the secret entrance to the North Pole base ready to start decorating. Unfortunately, the password seems to have been changed, so you can’t get in. A document taped to the wall helpfully explains:

“Due to new security protocols, the password is locked in the safe below. Please see the attached document for the new combination.”

The safe has a dial with only an arrow on it; around the dial are the numbers 0 through 99 in order. As you turn the dial, it makes a small click noise as it reaches each number.

The attached document (your puzzle input) contains a sequence of rotations, one per line, which tell you how to open the safe. A rotation starts with an L or R which indicates whether the rotation should be to the left (toward lower numbers) or to the right (toward higher numbers). Then, the rotation has a distance value which indicates how many clicks the dial should be rotated in that direction.

So, if the dial were pointing at 11, a rotation of R8 would cause the dial to point at 19. After that, a rotation of L19 would cause it to point at 0.

Because the dial is a circle, turning the dial left from 0 one click makes it point at 99. Similarly, turning the dial right from 99 one click makes it point at 0.

So, if the dial were pointing at 5, a rotation of L10 would cause it to point at 95. After that, a rotation of R5 could cause it to point at 0.

The dial starts by pointing at 50.

You could follow the instructions, but your recent required official North Pole secret entrance security training seminar taught you that the safe is actually a decoy. The actual password is the number of times the dial is left pointing at 0 after any rotation in the sequence.

For example, suppose the attached document contained the following rotations:

L68
L30
R48
L5
R60
L55
L1
L99
R14
L82

Following these rotations would cause the dial to move as follows:

  • The dial starts by pointing at 50.
  • The dial is rotated L68 to point at 82.
  • The dial is rotated L30 to point at 52.
  • The dial is rotated R48 to point at 0.
  • The dial is rotated L5 to point at 95.
  • The dial is rotated R60 to point at 55.
  • The dial is rotated L55 to point at 0.
  • The dial is rotated L1 to point at 99.
  • The dial is rotated L99 to point at 0.
  • The dial is rotated R14 to point at 14.
  • The dial is rotated L82 to point at 32.

Because the dial points at 0 a total of three times during this process, the password in this example is 3.

Questions

Write your answers directly into this document. Make sure that it is clear which question you answer.

  1. Write a function stops_at_zero with parameters start (the starting position) and sequence (the input as a vector), that recursively counts the number of times the dial stops at a zero.

Make sure that your function returns 3 for the following call:

stops_at_zero(50, c("L68", "L30", "R48", "L5", "R60", "L55", "L1", "L99", "R14", "L82"))
Error in `stops_at_zero()`:
! could not find function "stops_at_zero"

What result does your function give for the larger input? Most likely, your function will return an error for the larger input. Make sure to include error = TRUE in the corresponding code chunk so that the markdown document still runs to completion.

  1. What is the largest number that the recursive function runs? If that number is larger than 2000, report the result for the first 2000 lines of input. Otherwise report the number of zeros from the largest run.

  2. Rewrite the stops_at_zero function as a loop. Do the results match?

  3. Create a data frame from the input with variables direction (“L”, “R”) and numeric variable degree. The function cumsum creates a vector of cumulative sums. Use that to add a variable dial_at to the data frame that keeps track of where the dial points to after each rotation. Compare the overall number of times that the dial stops at zero to your previous results.

  4. Reflect on the three different approaches to solve the question. Which of these approaches do you like the best? How does the data frame fit into the programming approach? Is it more of an iterative or a functional approach?

  5. An engineering friend insists that the rotations should be expressed properly in degrees rather than integers. Create two variations of the degree variable called angle and radians that contain the rotation as an angle measured in degrees from 0 to 360 (or -180 to 180) and as the corresponding radians (360 = 2\(\pi\)).
    Now derive the corresponding variables dial_at_angle and dial_at_radians. How many times does the dial stop at zero now? Make sure to use the function near instead of a direct comparison to 0. Why are these numbers still different?

  6. Assume that dial_at has the correct result. Calculate the relative error for dial_at_angle and dial_at_radians (for non-zero values of dial_at). Plot the densities and discuss the results.

Before your final submission, make sure that your file renders without error.