074-digit-factorial-chains.hs

#!/usr/bin/env runhaskell 
{- https://projecteuler.net/problem=74
Problem 74
Digit factorial chains

The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:

1! + 4! + 5! = 1 + 24 + 120 = 145

Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:

169 → 363601 → 1454 → 169
871 → 45361 → 871
872 → 45362 → 872

It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,

69 → 363600 → 1454 → 169 → 363601 (→ 1454)
78 → 45360 → 871 → 45361 (→ 871)
540 → 145 (→ 145)

Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.

How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?
-}

import Data.Char as DC (digitToInt)

fac :: Int -> Int
fac n = product [1..n]

next :: Int -> Int
next = sum . map (fac . DC.digitToInt) . show

chainLength :: Int -> Int
chainLength x = chainLength' [x] x
chainLength' xs x =
  case elem x' xs of
    True -> 1
    False -> 1 + chainLength' (x':xs) x'
    where x' = next x

main :: IO ()
main = print . length . filter (== 60) $ map chainLength [1..999999]