Project Euler – Problem 14 Solution

You can become a serverless blackbelt. Enrol to my 4-week online workshop Production-Ready Serverless and gain hands-on experience building something from scratch using serverless technologies. At the end of the workshop, you should have a broader view of the challenges you will face as your serverless architecture matures and expands. You should also have a firm grasp on when serverless is a good fit for your system as well as common pitfalls you need to avoid. Sign up now and get 15% discount with the code yanprs15!

Problem

The following iterative sequence is defined for the set of positive integers:

n –> n/2 (n is even)

n –> 3n + 1 (n is odd)

Using the rule above and starting with 13, we generate the following sequence:

13 –> 40 –> 20 –> 10 –> 5 –> 16 –> 8 –> 4 –> 2 –> 1

It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.

Which starting number, under one million, produces the longest chain?

NOTE: Once the chain starts the terms are allowed to go above one million.

Solution

let nextNumber n = if n%2L = 0L then n/2L else 3L*n+1L

let findSequenceLength n =
    let mutable count = 1L
    let mutable current = n

    while current > 1L do
        current <- nextNumber current
        count <- count + 1L
    count

let longestSeq = &#91;1L..999999L&#93; |> Seq.maxBy findSequenceLength

Having played around with several other approaches, I finally settled down on this solution though I had to use mutable variables in a while loop which is somewhat dissatisfying but it performs quite a bit better than the more functional approach.

As you probably know already, in F# everything is immutable by default and to make a mutable variable you have to mark the variable with the mutable keyword. To assign a value to a mutable variable you need to use the <- operator.

Anyways, the above code is fairly simple, with the findSequenceLength function doing the bulk of the work and returns the number of elements in a sequence using a while loop. It can be equally be written using a more functional (but slower) approach but building the sequence with Seq.unfold and counting the length of the sequence

// the sequence returned by Seq.unfold does not include 1, so for completeness sake, add 1 to the length
let findSequenceLength n = Seq.length(Seq.unfold (fun x -> if x = 1L then None else Some(x, nextNumber x)) n) + 1
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 I help companies go faster for less by adopting serverless technologies successfully.

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.


Skill up your serverless game with this hands-on workshop.

My 4-week Production-Ready Serverless online workshop is back!

This course takes you through building a production-ready serverless web application from testing, deployment, security, all the way through to observability. The motivation for this course is to give you hands-on experience building something with serverless technologies while giving you a broader view of the challenges you will face as the architecture matures and expands.

We will start at the basics and give you a firm introduction to Lambda and all the relevant concepts and service features (including the latest announcements in 2020). And then gradually ramping up and cover a wide array of topics such as API security, testing strategies, CI/CD, secret management, and operational best practices for monitoring and troubleshooting.

If you enrol now you can also get 15% OFF with the promo code “yanprs15”.

Enrol now and SAVE 15%.


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!