module Exercise_12 where

import           Control.Monad   (ap)
import           Data.List       (nub, sortOn, union)
import           Test.QuickCheck (quickCheck)

{-H12-}
isPrime :: Int -> Bool
isPrime n
  | n <= 1 = False
  | otherwise = primeAux (n-1)
  where
    primeAux 1 = True
    primeAux i = n `mod` i /= 0 && primeAux (i-1)

-- returns all primes up to the passed number
primes :: Int -> [Int]
primes n = [i | i<-[2..n], isPrime i]

{-WETT-}
inf = enumFrom 1 -- to avoid parentheses

-- I used the fact that Haskell sort is stable
encrypt :: String -> String
encrypt = map snd . sortOn (not . isPrime . fst) . zip inf

decrypt :: String -> String
decrypt = map fst . sortOn snd . ap zip (flip union inf . primes . length)
-- if I understand it right, ap is a kind of prefix notation for <*>, and in fact
-- it's just a Haskell function corresponding to S combinator. But I know (almost)
-- nothing about monads, so that could be absolutely wrong. Anyway, it works!

-- pointful solution, same number of tokens, but less fun:
-- decrypt xs = map fst $ sortOn snd $ zip xs $ primes (length xs) `union` inf
{-TTEW-}