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The rules for writing Roman numerals allow for many ways of writing each number (see FAQ:Roman Numerals). However, there is always a “best” way of writing a particular number.
For example, the following represent all of the legitimate ways of writing the number sixteen:
The last example being considered the most efficient, as it uses the least number of numerals.
The 11K text file, roman.txt (right click and ‘Save Link/Target As…’), contains one thousand numbers written in valid, but not necessarily minimal, Roman numerals; that is, they are arranged in descending units and obey the subtractive pair rule (see FAQ for the definitive rules for this problem).
Find the number of characters saved by writing each of these in their minimal form.
Note: You can assume that all the Roman numerals in the file contain no more than four consecutive identical units.
open System.IO // define the set of available roman numerals let romanNumerals = [(['I'],1I);(['I';'V'],4I);(['V'],5I);(['I';'X'],9I); (['X'],10I);(['X';'L'],40I);(['L'],50I);(['X';'C'],90I); (['C'],100I);(['C';'D'],400I);(['D'],500I);(['C';'M'],900I); (['M'],1000I)] // define function to get the numeric value of a roman numeral let getNumericValue (numeral:char) = snd (romanNumerals |> Seq.filter (fun (l, v) -> l.Length = 1 && l. = numeral) |> Seq.head) // define function to convert a roman numerals to its corresponding numeric value let toNumeric (numerals:string) = let rec toNumericRec ((head::tail):char list) (num:bigint) = match head, tail with | _,  -> num + getNumericValue head | _, hd::tl when getNumericValue head >= getNumericValue hd -> toNumericRec tail (num + getNumericValue head) | _, hd:: -> // subtractive pair as last number i.e. XIX - 19 num + getNumericValue hd - getNumericValue head | _, hd::tl -> // subtractive pair not as last number XCV - 95 toNumericRec tl (num + getNumericValue hd - getNumericValue head) toNumericRec (numerals.ToCharArray() |> Array.toList) 0I // converts an integer value to corresponding minimal roman numerals form let toMinimalRomanNumerals (value:bigint) = let rec toMinimalRomanNumeralsRec (value:bigint) (list:char list) = if value = 0I then list else let (list', value') = romanNumerals |> List.sortBy (fun (l, v) -> -v) |> Seq.filter (fun (l, v) -> v <= value) |> Seq.head toMinimalRomanNumeralsRec (value-value') (list@list') toMinimalRomanNumeralsRec value  let original = File.ReadAllLines(@"C:\TEMP\roman.txt") let minimal = original |> Array.map toNumeric |> Array.map toMinimalRomanNumerals let answer = let originalLen = original |> Array.sumBy (fun str -> str.Length) let minimalLen = minimal |> Array.sumBy (fun str -> str.Length) originalLen - minimalLen
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!
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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