module Exercise_12 where

import Data.List (nub, (\\))
import Data.Bifunctor (first, second, bimap)
import Data.Tuple
import Control.Monad ((>=>), ap)
import Control.Applicative
import Control.Arrow ((&&&))
import System.IO

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-}
-- build substring from index list
ŧ :: String -> [Int] -> String
ŧ s=foldr((:)`fmap`s!!)[]

þ :: String -> [Int]
þ=map pred.primes.length

encrypt :: String -> String
encrypt=þ>>= \p s->s`ŧ`p++s`ŧ`(enumFromTo 0 (length s - 1)\\p)

-- insert character into string by (Index, Char) list
ø :: [(Int, Char)] -> String -> String
ø=flip(foldl(flip(splitAt.fst)>=>(uncurry(++).).flip(second.(:).snd)))
-- foldl receives String and (Int, Char), which have to flipped for pointfree variant
-- (splitAt . fst) :: (Int, Char) -> String -> (String, String)
-- (second . (:) . snd) :: (Int, Char) -> (String, String) -> (String, String)

decrypt :: String -> String
decrypt=þ>>=(uncurry ø.).(splitAt.length<**>fmap.first.zip)
-- 1. get prime index list by þ
-- 2. (splitAt.length<**>fmap.first.zip) receives this list and a string and returns ([(i, c)], s2)
--    where i = index of c to be inserted into s2
{-TTEW-}