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 #13

Description

  • Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.
  • Number is listed in solution, for brevity

Solution

//libraries for BitArray and BigInteger, respectively
open System.Collections
open System.Numerics

//array of Big integer
let hugeArray =
    [|
    37107287533902102798797998220837590246510135740250I;
    46376937677490009712648124896970078050417018260538I;
    74324986199524741059474233309513058123726617309629I;
    91942213363574161572522430563301811072406154908250I;
    23067588207539346171171980310421047513778063246676I;
    89261670696623633820136378418383684178734361726757I;
    28112879812849979408065481931592621691275889832738I;
    44274228917432520321923589422876796487670272189318I;
    47451445736001306439091167216856844588711603153276I;
    70386486105843025439939619828917593665686757934951I;
    62176457141856560629502157223196586755079324193331I;
    64906352462741904929101432445813822663347944758178I;
    92575867718337217661963751590579239728245598838407I;
    58203565325359399008402633568948830189458628227828I;
    80181199384826282014278194139940567587151170094390I;
    35398664372827112653829987240784473053190104293586I;
    86515506006295864861532075273371959191420517255829I;
    71693888707715466499115593487603532921714970056938I;
    54370070576826684624621495650076471787294438377604I;
    53282654108756828443191190634694037855217779295145I;
    36123272525000296071075082563815656710885258350721I;
    45876576172410976447339110607218265236877223636045I;
    17423706905851860660448207621209813287860733969412I;
    81142660418086830619328460811191061556940512689692I;
    51934325451728388641918047049293215058642563049483I;
    62467221648435076201727918039944693004732956340691I;
    15732444386908125794514089057706229429197107928209I;
    55037687525678773091862540744969844508330393682126I;
    18336384825330154686196124348767681297534375946515I;
    80386287592878490201521685554828717201219257766954I;
    78182833757993103614740356856449095527097864797581I;
    16726320100436897842553539920931837441497806860984I;
    48403098129077791799088218795327364475675590848030I;
    87086987551392711854517078544161852424320693150332I;
    59959406895756536782107074926966537676326235447210I;
    69793950679652694742597709739166693763042633987085I;
    41052684708299085211399427365734116182760315001271I;
    65378607361501080857009149939512557028198746004375I;
    35829035317434717326932123578154982629742552737307I;
    94953759765105305946966067683156574377167401875275I;
    88902802571733229619176668713819931811048770190271I;
    25267680276078003013678680992525463401061632866526I;
    36270218540497705585629946580636237993140746255962I;
    24074486908231174977792365466257246923322810917141I;
    91430288197103288597806669760892938638285025333403I;
    34413065578016127815921815005561868836468420090470I;
    23053081172816430487623791969842487255036638784583I;
    11487696932154902810424020138335124462181441773470I;
    63783299490636259666498587618221225225512486764533I;
    67720186971698544312419572409913959008952310058822I;
    95548255300263520781532296796249481641953868218774I;
    76085327132285723110424803456124867697064507995236I;
    37774242535411291684276865538926205024910326572967I;
    23701913275725675285653248258265463092207058596522I;
    29798860272258331913126375147341994889534765745501I;
    18495701454879288984856827726077713721403798879715I;
    38298203783031473527721580348144513491373226651381I;
    34829543829199918180278916522431027392251122869539I;
    40957953066405232632538044100059654939159879593635I;
    29746152185502371307642255121183693803580388584903I;
    41698116222072977186158236678424689157993532961922I;
    62467957194401269043877107275048102390895523597457I;
    23189706772547915061505504953922979530901129967519I;
    86188088225875314529584099251203829009407770775672I;
    11306739708304724483816533873502340845647058077308I;
    82959174767140363198008187129011875491310547126581I;
    97623331044818386269515456334926366572897563400500I;
    42846280183517070527831839425882145521227251250327I;
    55121603546981200581762165212827652751691296897789I;
    32238195734329339946437501907836945765883352399886I;
    75506164965184775180738168837861091527357929701337I;
    62177842752192623401942399639168044983993173312731I;
    32924185707147349566916674687634660915035914677504I;
    99518671430235219628894890102423325116913619626622I;
    73267460800591547471830798392868535206946944540724I;
    76841822524674417161514036427982273348055556214818I;
    97142617910342598647204516893989422179826088076852I;
    87783646182799346313767754307809363333018982642090I;
    10848802521674670883215120185883543223812876952786I;
    71329612474782464538636993009049310363619763878039I;
    62184073572399794223406235393808339651327408011116I;
    66627891981488087797941876876144230030984490851411I;
    60661826293682836764744779239180335110989069790714I;
    85786944089552990653640447425576083659976645795096I;
    66024396409905389607120198219976047599490197230297I;
    64913982680032973156037120041377903785566085089252I;
    16730939319872750275468906903707539413042652315011I;
    94809377245048795150954100921645863754710598436791I;
    78639167021187492431995700641917969777599028300699I;
    15368713711936614952811305876380278410754449733078I;
    40789923115535562561142322423255033685442488917353I;
    44889911501440648020369068063960672322193204149535I;
    41503128880339536053299340368006977710650566631954I;
    81234880673210146739058568557934581403627822703280I;
    82616570773948327592232845941706525094512325230608I;
    22918802058777319719839450180888072429661980811197I;
    77158542502016545090413245809786882778948721859617I;
    72107838435069186155435662884062257473692284509516I;
    20849603980134001723930671666823555245252804609722I;
    53503534226472524250874054075591789781264330331690I |]

//created my own function to sum an array of Big integer  
let rec SumHugeArray (counter:int) (acc:BigInteger) arr =
    if counter = (Array.length arr) then
        acc
    else
        let accumulator = arr.[counter] + acc
        SumHugeArray (counter+1) accumulator arr

//fairly straightforward solution
let tryIt =
    let num = SumHugeArray 0 0I hugeArray
    let result = num.ToString()
    result.Substring(0,10)

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