There are exactly ten ways of selecting three from five, 12345:
123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
In combinatorics, we use the notation, 5C3 = 10.
It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
How many, not necessarily distinct, values of nCr, for 1 <= n <= 100, are greater than one-million?
let factorial n = if (n = 0I) then 1I else [1I..n] |> List.reduce (*) let C n r = if r <= n then (factorial n) / ((factorial r) * (factorial (n - r))) else 0I let answer = [1I..100I] |> List.collect (fun n -> [1I..n] |> List.map (fun r -> C n r)) |> List.filter (fun x -> x > 1000000I) |> List.length
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.
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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.
- 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