Advent of Code F# – Day 19

Check out my new course Learn you some Lambda best practice for great good! and learn the best practices for performance, cost, security, resilience, observability and scalability.

ps. look out for all my other solutions for Advent of Code challenges here.

 

Day 19

See details of the challenge here.

I initially approached today’s challenge as a dynamic programming exercise, but it quickly transpired that there’s a much better way to do it once I realised that part 1 is in fact the Josephus Problem and there’s a simple solution to it.

To understand the above, watch the YouTube video in the links section below.

 

Part 2

Realizing the folly of their present-exchange rules, the Elves agree to instead
steal presents from the Elf directly across the circle. If two Elves are across
the circle, the one on the left (from the perspective of the stealer) is stolen
from. The other rules remain unchanged: Elves with no presents are removed from
the circle entirely, and the other elves move in slightly to keep the circle
evenly spaced.

For example, with five Elves (again numbered 1 to 5):

  • The Elves sit in a circle; Elf 1 goes first:
  1
5   2
 4 3
  • Elves 3 and 4 are across the circle; Elf 3’s present is stolen, being the one to
    the left. Elf 3 leaves the circle, and the rest of the Elves move in:
  1           1
5   2  -->  5   2
 4 -          4
  • Elf 2 steals from the Elf directly across the circle, Elf 5:
  1         1 
-   2  -->     2
  4         4 
  • Next is Elf 4 who, choosing between Elves 1 and 2, steals from Elf 1:
 -          2  
    2  -->
 4          4
  • Finally, Elf 2 steals from Elf 4:
 2
    -->  2  
 -

So, with five Elves, the Elf that sits starting in position 2 gets all the
presents.

With the number of Elves given in your puzzle input, which Elf now gets all the
presents?

I’m not aware of this variation to the Josephus Problem, but I’d wager that there would be some pattern to the results similar to part 1, so I put together a dynamic programming solution to get some outputs. (ps. the solution is not good enough for the input as it’ll take too long to return)

With the help of this I can see a pattern emerging:

n : answer

1 : 1
2 : 2
3 : 3
4 : 1
5 : 2
6 : 3
7 : 5
8 : 7
9 : 9
10 : 1
11 : 2
12 : 3
13 : 4
14 : 5
15 : 6
16 : 7
17 : 8
18 : 9
19 : 11
20 : 13
21 : 15
22 : 17
23 : 19
24 : 21
25 : 23
26 : 25
27 : 27
28 : 1
29 : 2
30 : 3

  • where n is a power of 3 then the answer is itself
  • else n can be expressed as m + l where m is a power of 3
  • where l <= m (eg. n = 5 = 3 + 2 where m = 3 and l = 2) then the answer is just l
  • else the answer is m + (l – m) * 2 (eg. n = 7 = 3 + 4 where m = 3 and l = 4 and m + (l – m) * 2 = 5)

 

Links

Liked this article? Support me on Patreon and get direct help from me via a private Slack channel or 1-2-1 mentoring.
Subscribe to my newsletter


Hi, I’m Yan. I’m an AWS Serverless Hero and the author of Production-Ready Serverless.

I specialise in rapidly transitioning teams to serverless and building production-ready services on AWS.

Are you struggling with serverless or need guidance on best practices? Do you want someone to review your architecture and help you avoid costly mistakes down the line? Whatever the case, I’m here to help.

Hire me.


Check out my new podcast Real-World Serverless where I talk with engineers who are building amazing things with serverless technologies and discuss the real-world use cases and challenges they face. If you’re interested in what people are actually doing with serverless and what it’s really like to be working with serverless day-to-day, then this is the podcast for you.


Check out my new course, Learn you some Lambda best practice for great good! In this course, you will learn best practices for working with AWS Lambda in terms of performance, cost, security, scalability, resilience and observability. We will also cover latest features from re:Invent 2019 such as Provisioned Concurrency and Lambda Destinations. Enrol now and start learning!


Check out my video course, Complete Guide to AWS Step Functions. In this course, we’ll cover everything you need to know to use AWS Step Functions service effectively. There is something for everyone from beginners to more advanced users looking for design patterns and best practices. Enrol now and start learning!


Are you working with Serverless and looking for expert training to level-up your skills? Or are you looking for a solid foundation to start from? Look no further, register for my Production-Ready Serverless workshop to learn how to build production-grade Serverless applications!

Find a workshop near you