module Exercise_12 where

import Data.List 

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-}
isPrimeTuple = isPrime . fst --only checks whether first Element of Tuple is Prime

encrypt :: String -> String
encrypt xs = snd $ unzip $ fst a ++ snd a
  where a = partition isPrimeTuple $ enumFrom 1 `zip` xs

decrypt :: String -> String
decrypt xs = snd $ unzip $ sort $ zip primesxs xs ++ filter (`notElem` primesxs) (enumFrom 1) `zip` drop (length primesxs) xs
    where primesxs = primes $ length xs


{-TTEW-}
--recursive Implementation
decrypt2 :: String -> String
decrypt2 xs = decrypt' [1..length xs] xs (drop ( length $ primes $ length xs) xs)
decrypt' (y:ys) (x:xs) (a:as)
  | isPrime y = x : decrypt' ys xs (a:as)
  | otherwise = a : decrypt' ys (x:xs) as
decrypt' ys xs _ = take (length ys) xs