module Exercise_6 where

import           Data.Ratio
import           Data.List

{-WETT-}
traceFractran :: [Rational] -> Integer -> [Integer]
traceFractran fs n = n : case find (\f -> n `mod` denominator f == 0) fs of
    Just f  -> traceFractran fs $ floor $ fromIntegral n * f
    Nothing -> []
{-TTEW-}

{-traceFractran2 :: [Rational] -> Integer -> [Integer]
traceFractran2 fs n = scanl (\n -> concat [ traceFractran2 fs $ floor $ fromIntegral n * f | f <- fs, n `mod` denominator f == 0]) n

traceFractran :: [Rational] -> Integer -> [Integer]
traceFractran fs n = n : concat [ traceFractran fs $ floor $ fromIntegral n * f | f <- fs, n `mod` denominator f == 0]
-}

--traceFractranSimple :: [Rational] -> Integer -> [Integer]
--traceFractranSimple fs n = n : case find (\f -> n `mod` denominator f == 0) fs of
--    Just f  -> traceFractranSimple fs $ floor $ fromIntegral n * f
--    Nothing -> []

{-traceFractran :: [Rational] -> Integer -> [Integer]
traceFractran fs n = n : head (map (\a -> traceFractran fs (div (n * numerator a) (denominator a))) (filter (\a -> mod n (denominator a) == 0) fs))
-}