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.
A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before.
Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.
How many starting numbers below ten million will arrive at 89?
let max = 10000000 // build up a cache for all the numbers from 1 to 10 million let cache = Array.init (max+1) (fun n -> match n with | 0 | 1 -> Some(false) | 89 -> Some(true) | _ -> None) // define function to add the square of the digits in a number let addSquaredDigits n = n.ToString().ToCharArray() |> Array.sumBy (fun c -> pown (int(c.ToString())) 2) // define function to take an initial number n and generate its number chain until // it gets to a number whose subsequent chain ends with 1 or 89, which means that // all previous numbers will also end in the same number let processChain n = let rec processChainRec n (list: int list) = if cache.[n] = None then processChainRec (addSquaredDigits n) (list@[n]) else list |> List.iter (fun n' -> cache.[n'] <- cache.[n]) processChainRec n  // go through all the numbers from 2 to 10 million using the above function [2..10000000] |> List.iter processChain // how many numbers whose number chain ends with 89? let answer = cache |> Array.filter (fun n -> n = Some(true)) |> Array.length
This is actually a fairly simple problem, with the main challenge being how to make it run fast enough to obey with the one minute rule which is where the cache comes in.
Using the property that if a chain starting with the number n, i.e. n, n1, n2, …, ends in 89 then the chain starting with any of the numbers n1, n2, … will also end in 89 we can minimise the amount of computation required by caching previous results. Note I didn’t have to mark the cache as mutable in this case because the Array construct in F# is a fixed-sized, zero-index, mutable collections of elements.
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.
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!
Here is a complete list of all my posts on serverless and AWS Lambda. In the meantime, here are a few of my most popular blog posts.
- Lambda optimization tip – enable HTTP keep-alive
- You are wrong about serverless and vendor lock-in
- You are thinking about serverless costs all wrong
- Just how expensive is the full AWS SDK?
- Many faced threats to Serverless security
- We can do better than percentile latencies
- Yubl’s road to Serverless
- AWS Lambda – should you have few monolithic functions or many single-purposed functions?
- AWS Lambda – compare coldstart time with different languages, memory and code sizes
- Guys, we’re doing pagination wrong
- Top 10 Serverless framework best practices