module Exercise_6 where

import Data.Ratio
import Data.Foldable
import Data.Maybe

{-WETT-}
traceFractran :: [Rational] -> Integer -> [Integer]
traceFractran fs 0 = []
traceFractran fs n = n:(traceFractran fs $ toInteger $ ceiling $ fromMaybe 0 $ find (\q -> denominator q == 1) $ map (fromInteger n*) fs)
{-TTEW-}

{-traceFractran fs n = traceFractranAux fs n [] --5
  where
--    traceFractranAux fs n acc 0 = acc
    traceFractranAux fs n acc = --c =
        let t = map ((fromInteger n)*) fs
            d = [q | q <- t, denominator q == 1]
        in
          if null d then reverse (n:acc) else reverse (traceFractranAux fs (toInteger (ceiling (head d))) (n:acc)) --(c-1))
-}
{-traceFractran fs n =
  let t = map ((fromInteger n)*) fs
      d = [q | q <- t, denominator q == 1]
  in
    if null d then [n] else n:(traceFractran fs $ toInteger $ ceiling $ head d)
-}


--traceFractran fs n =
--  let t:ts = filter (\q -> denominator q == 1) $ map ((fromInteger n)*) fs
--  in n:(traceFractran fs $ toInteger $ ceiling $ t)



isPowerOfTwo :: Integral a => a -> Bool
isPowerOfTwo n 
  | n == 1 = True
  | mod n 2 == 1 = False
  | otherwise = True && isPowerOfTwo (div n 2)