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

Project Euler - Problem #25

Description

The Fibonacci sequence is defined by the recurrence relation:

    F_(n) = F_(n−1) + F_(n−2), where F_(1) = 1 and F_(2) = 1.

Hence the first 12 terms will be:

    F_(1) = 1
    F_(2) = 1
    F_(3) = 2
    F_(4) = 3
    F_(5) = 5
    F_(6) = 8
    F_(7) = 13
    F_(8) = 21
    F_(9) = 34
    F_(10) = 55
    F_(11) = 89
    F_(12) = 144

The 12th term, F_(12), is the first term to contain three digits.
What is the first term in the Fibonacci sequence to contain 1000 digits?
    Solution

    open System.Numerics

    //tail-recursion to return Fibonacci based on length of a number's string
    let rec fibsRecTailBigIntSingle (x:BigInteger) (y:BigInteger) acc max =
        let lenY = (y.ToString()).Length
        if lenY >= max then
            acc + 1
        else
            let next = x + y
            let item = acc + 1
            fibsRecTailBigIntSingle y next item max

    let Prob25_1 = fibsRecTailBigIntSingle 1I 1I 1 1000

    Comments

    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

    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

    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 )