euler008.hs

import Data.List
import Data.Char

-- Find the greatest product of five consecutive digits in the 1000-digit number.
--
--      73167176531330624919225119674426574742355349194934
--      96983520312774506326239578318016984801869478851843
--      85861560789112949495459501737958331952853208805511
--      12540698747158523863050715693290963295227443043557
--      66896648950445244523161731856403098711121722383113
--      62229893423380308135336276614282806444486645238749
--      30358907296290491560440772390713810515859307960866
--      70172427121883998797908792274921901699720888093776
--      65727333001053367881220235421809751254540594752243
--      52584907711670556013604839586446706324415722155397
--      53697817977846174064955149290862569321978468622482
--      83972241375657056057490261407972968652414535100474
--      82166370484403199890008895243450658541227588666881
--      16427171479924442928230863465674813919123162824586
--      17866458359124566529476545682848912883142607690042
--      24219022671055626321111109370544217506941658960408
--      07198403850962455444362981230987879927244284909188
--      84580156166097919133875499200524063689912560717606
--      05886116467109405077541002256983155200055935729725
--      71636269561882670428252483600823257530420752963450


-- The main breakthrough here was that "subsequences" in Data.List doesn't do what I thought; it seems to retrieve permutations too 
-- tails and take 5 seems to work as expected to go through the combinations 5 at a time and the product 
-- function avoids having to do a list comp or something

-- The number specified in the problem. 
number :: Integer
number      = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450

-- Turn our string into a list of digits to make it a bit easier to use
--candidates  = map digitToInt number

-- find the max of the products of each 5 element sublist of the tails of our list of candidates
--largest     = maximum $ map (product . take 5) $ tails candidates

euler008 = maximumBy (\a b -> compare (snd a) (snd b)) 
           $ map (\xs -> (xs, product xs)) 
           $ nLengthSubSeq 13 
           $ digits number

digits = map (`mod` 10) . reverse . takeWhile (> 0) . iterate (`div` 10)

fromDigits = foldl addDigit 0
   where addDigit num d = 10*num + d

nLengthSubSeq _ [] = []
nLengthSubSeq n xss@(_:xs) = if length xss < n
                             then []
                             else (take n xss) : (nLengthSubSeq n xs)