ProjectEuler/haskell/src/0014.hs

{-
The following iterative sequence is defined for the set of positive integers:
n -> n/2 (n is even)
n -> 3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1.
It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
NOTE: Once the chain starts the terms are allowed to go above one million.
-}

import Data.List
import Data.Maybe
import Data.Function

(|>) = (&)

next_term :: Int -> Int
next_term 1 = 1
next_term x
  | even x    = div x 2
  | otherwise = (x * 3) + 1

gen_chain :: Int -> [Int]
gen_chain 1 = [1]
gen_chain s = [s] ++ gen_chain (next_term s)

solution :: Int
solution = chains !! (elemIndex biggest chains_size |> fromJust) |> head
  where
    chains = [1..1000000] |> map gen_chain
    -- For some reason if chains is used here it will fill all the memory
    chains_size = [1..1000000] |> map gen_chain |> map length
    biggest :: Int
    biggest = maximum chains_size

main :: IO ()
main = putStrLn ("Solution: " ++ show solution)