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2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
let isEvenlyDivided(n, m) = n % m = 0 let isEvenlyDividedByAll(n, numbers) = numbers |> Seq.forall (fun x -> isEvenlyDivided(n, x)) let findSmallestCommonMultiple(numbers) = let max = Array.max(numbers) Seq.unfold (fun x -> Some(x, x + 1)) max |> Seq.filter (fun x -> isEvenlyDividedByAll(x, numbers)) |> Seq.head let commonMultiplier = findSmallestCommonMultiple [|1..20|]
Again, I build two functions to handle the logic of checking whether a number can be evenly divided by all the numbers in a supplied list. I have used another new function Seq.forall (I can’t find the MSDN doc for this function, but see List.forall instead) which tests each element in the list with the supplied predicate.
In order to find the smallest common multiple for all the numbers from 1 to 20, I first generated a sequence of all the natural numbers equal or greater than 20:
Seq.unfold (fun x –> Some(x, x + 1)) max // max is resolved to 20 by Array.max(numbers)
Then for each number I applied the predicate isEvenlyDividedByAll to see if it can be evenly divided by each of the numbers from 1 to 20, and finally, Seq.head returns the first element that matches the predicate and that’s our answer!
One last thing though, when you run this code you’ll see that it takes a rather long time to return. So to improve on the performance of this logic, you can add a small and yet effective step to only test numbers which are multiples of the largest number (20 in our case) in the list:
let findSmallestCommonMultiple(numbers) = let max = Array.max(numbers) Seq.unfold (fun x -> Some(x, x + 1)) 1 |> Seq.map (fun x -> x * max) |> Seq.filter (fun x -> isEvenlyDividedByAll(x, numbers)) |> Seq.head
Run the new findSmallestCommonMultiple function again and it now returns much much quicker :-)
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.
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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.
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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!
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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.
- All you need to know about caching for serverless applications
- 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?
- Check-list for going live with API Gateway and Lambda
- How to choose the right API Gateway auth method
- CloudFormation protip: use !Sub instead of !Join
- AWS Lambda – should you have few monolithic functions or many single-purposed functions?
- Guys, we’re doing pagination wrong
- Top 10 Serverless framework best practices
- How to break the “senior engineer” career ceiling
- My advice to junior developers