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Project Euler Problem 8

October 11, 2011

In order to solve Project Euler Problem 8 we’ll build a sequence of all multiples and find one that is largest.

The sequence generation employs the combinator power of F# Core library:

  1. digits of 1000-digit number are put into char array
  2. char array converted into array of ints and then into a sequence of ints
  3. this sequence is sliced into sliding windows, each represented by array of 5 sequential digits
  4. this sequence of 5-element arrays is map-reduced into the sequence of array member products

 

let inline digit (x: char) = int(x) - int('0')  

let n = 
    "73167176531330624919225119674426574742355349194934" +
    "96983520312774506326239578318016984801869478851843" +
    "85861560789112949495459501737958331952853208805511" +
    "12540698747158523863050715693290963295227443043557" +
    "66896648950445244523161731856403098711121722383113" +
    "62229893423380308135336276614282806444486645238749" +
    "30358907296290491560440772390713810515859307960866" +
    "70172427121883998797908792274921901699720888093776" +
    "65727333001053367881220235421809751254540594752243" +
    "52584907711670556013604839586446706324415722155397" +
    "53697817977846174064955149290862569321978468622482" +
    "83972241375657056057490261407972968652414535100474" +
    "82166370484403199890008895243450658541227588666881" +
    "16427171479924442928230863465674813919123162824586" +
    "17866458359124566529476545682848912883142607690042" +
    "24219022671055626321111109370544217506941658960408" +
    "07198403850962455444362981230987879927244284909188" +
    "84580156166097919133875499200524063689912560717606" +
    "05886116467109405077541002256983155200055935729725" +
    "71636269561882670428252483600823257530420752963450"

let productsOf5Digits =
    n.ToCharArray()
    |> Array.map digit
    |> Array.toSeq
    |> Seq.windowed 5
    |> Seq.map (Array.reduce (*))

let problem008 () =
    productsOf5Digits |> Seq.max
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