Skip to main content

Microsoft Azure Notebooks - Live code - F#, R, and Python

I was exploring Jupyter notebooks , that combines live code, markdown and data, through Microsoft's implementation, known as MS Azure Notebooks , putting together a small library of R and F# notebooks . As Microsoft's FAQ for the service describes it as : ...a multi-lingual REPL on steroids. This is a free service that provides Jupyter notebooks along with supporting packages for R, Python and F# as a service. This means you can just login and get going since no installation/setup is necessary. Typical usage includes schools/instruction, giving webinars, learning languages, sharing ideas, etc. Feel free to clone and comment... In R Azure Workbook for R - Memoisation and Vectorization Charting Correlation Matrices in R In F# Charnownes Constant in FSharp.ipynb Project Euler - Problems 18 and 67 - FSharp using Dynamic Programming
Post a Comment

Project Euler - Problem #6

Description
  • The sum of the squares of the first ten natural numbers is, 12 + 22 + ... + 102 = 385
  • The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)2 = 552 = 3025
  • Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025  385 = 2640.
  • Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Solution (Improved)

More concise ways than the original solution.

let sqrSumNat2 listNat = Array.sum listNat |> (fun x -> x*x)
let sumSqrListNat2 listNat = listNat |> Array.map (fun x -> x * x ) |> Array.sum



let diffNat100_2 = sqrSumNat2 [|1..100|] - sumSqrListNat2 [|1..100|]


Solution (Orignal)


//Square of Sum of Natural Numbers
let sqrSumNat listNat =
    let sumNat = Array.sum listNat
    sumNat * sumNat


//Sum of Squares of Natural Numbers
let sumSqrListNat listNat = 
    let sqrListNat = listNat |> Array.map (fun x -> x * x )
    Array.sum sqrListNat


//Difference between sum of squares and square of sum
let diffNat100 = sumSqrListNat [|1..100|] - sqrSumNat [|1..100|]

Comments

Post a Comment

Popular posts from this blog

Microsoft Azure Notebooks - Live code - F#, R, and Python

I was exploring Jupyter notebooks , that combines live code, markdown and data, through Microsoft's implementation, known as MS Azure Notebooks , putting together a small library of R and F# notebooks . As Microsoft's FAQ for the service describes it as : ...a multi-lingual REPL on steroids. This is a free service that provides Jupyter notebooks along with supporting packages for R, Python and F# as a service. This means you can just login and get going since no installation/setup is necessary. Typical usage includes schools/instruction, giving webinars, learning languages, sharing ideas, etc. Feel free to clone and comment... In R Azure Workbook for R - Memoisation and Vectorization Charting Correlation Matrices in R In F# Charnownes Constant in FSharp.ipynb Project Euler - Problems 18 and 67 - FSharp using Dynamic Programming
Post a Comment
Read more

Digit cancelling fractions (Project Euler Problem 33)

Problem The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s. We shall consider fractions like, 30/50 = 3/5, to be trivial examples. There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator. If the product of these four fractions is given in its lowest common terms, find the value of the denominator. (link to Problem 33 on the Project Euler site) Note This is a somewhat crude solution, since I am only just getting back into solving these problems, or working with F#, but there are several similar problems for which I can develop properly factored, reusable functions. Solution open System let product xs ys = seq{for x in xs do for y in ys do let a = float x % float 10 ...
Post a Comment
Read more

Consecutive Prime Sum (Project Euler - Problem 50)

Problem The prime 41, can be written as the sum of six consecutive primes: 41 = 2 + 3 + 5 + 7 + 11 + 13 This is the longest sum of consecutive primes that adds to a prime below one-hundred. The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953. Which prime, below one-million, can be written as the sum of the most consecutive primes? Note Some libraries used in this code are F# modules I use, but have also published as a  Nuget library , such as EulerLib.GetPrimes() and  EulerLib. isPrime(). You need to reference the NuGetLibrary to use this code as is. Solution #load "Stat.fs" #load "Print.fs" #load "EulerLib.fs" open Stat open Print open EulerLib open System let rec FindLongestPrimeSequenceSum (primeList:list ) (nextItem:int) lessThanValue (primeArray:list ) bestPrime (correctArray:list )...
Post a Comment
Read more