The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, …
By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a triangle number then we shall call the word a triangle word.
Using words.txt (right click and ‘Save Link/Target As…’), a 16K text file containing nearly two-thousand common English words, how many are triangle words?
open System.IO // read the content of the file into an array of words let words = File.ReadAllLines (@"C:\TEMP\words.txt") |> Array.map (fun s -> s.Replace("\"", "")) |> Array.collect (fun s -> s.ToUpper().Trim().Split(',')) // function to calculate the word value of a word let wordValue word = word.ToString().ToCharArray() |> Array.map (fun c -> int(c) - int('A') + 1) |> Array.sum // convert all words to their corresponding word values let wordValues = words |> Array.map wordValue let maxWordValue = wordValues |> Array.max // the sequence of triangle numbers let naturalNumbers = Seq.unfold (fun state -> Some(state, state + 1)) 1 let T n = n * (n + 1) / 2 let TSeq = naturalNumbers |> Seq.map T let answer = TSeq |> Seq.takeWhile (fun t -> t <= maxWordValue) |> Seq.map (fun t -> wordValues |> Array.filter (fun n -> n = t) |> Array.length) |> Seq.sum
To get started on this problem, I first read all the words in the downloaded text file into an array of strings, each being one of the two thousand words. Then I build a function to calculate the word value of a word and converted the word array into an array of word values. The max word value is useful here because it allows me to cap how many elements in the T sequence I should check.
Enjoy what you’re reading? Subscribe to my newsletter and get more content on AWS and serverless technologies delivered straight to your inbox.
I’m an AWS Serverless Hero and the author of Production-Ready Serverless. I have run production workload at scale in AWS for nearly 10 years and I have been an architect or principal engineer with a variety of industries ranging from banking, e-commerce, sports streaming to mobile gaming. I currently work as an independent consultant focused on AWS and serverless.
In this course, we’ll cover everything you need to know to use AWS Step Functions service effectively. Including basic concepts, HTTP and event triggers, activities, design patterns and best practices.
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 thinking about serverless costs all wrong
- Many faced threats to Serverless security
- We can do better than percentile latencies
- I’m afraid you’re thinking about AWS Lambda cold starts all wrong
- 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