import Data.Char

lowers :: String -> Int
lowers xs = length [x | x <- xs, x >= 'a' && x <= 'z']

count :: Char -> String ->Int
count x xs = length [x' | x' <- xs, x==x']

positions :: Eq a => a -> [a] -> [Int]
positions x xs = [i | (x',i) <- zip xs [0..n], x == x']
  where n = length xs - 1

let2int :: Char -> Int
let2int c = ord c - ord 'a' --caracteres a unicode

int2let :: Int -> Char
int2let n = chr (ord 'a' + n)

shift :: Int -> Char -> Char
shift n c | isLower c = int2let ((let2int c + n) `mod` 26)
          | otherwise = c

cifrar :: Int -> String -> String
cifrar n xs = [shift n x | x <- xs]

table :: [Float]
table = [11.72,1.49, 3.87, 4.67,13.72,0.69,1.00,1.18,5.28,0.52,0.11,5.24,3.08,6.83,8.44,2.89,1.11,6.41,7.20,4.60,4.55,1.05,0.04,0.14,1.09,0.47]

porciento :: Int -> Int -> Float --fromIntegral :: Int a Float
porciento n m = (fromIntegral n / fromIntegral m) * 100

frec :: String -> [Float]
frec xs = [porciento (count x xs) n | x <- ['a'..'z']]
  where n = lowers xs 

chisqr :: [Float] -> [Float] -> Float
chisqr os es = sum [((o-e)^2)/e | (o,e) <- zip os es]

rotate :: Int -> [a] -> [a]
rotate n xs = drop n xs ++ take n xs

crack :: String -> String
crack xs = cifrar (-factor) xs
  where
    factor = head (positions (minimum chitab) chitab)
    chitab = [chisqr (rotate n table') table | n <- [0..25]]
    table' = frec xs