module Exercise05 where

-- May or may not be useful: computes the logarithm base 2 (rounded down) of the given number.
-- You don't have to move this into the WETT tags if you want to use it.
log2 :: (Integral a, Num b) => a -> b
log2 = let go acc n = if n <= 1 then acc else go (acc + 1) (n `div` 2) in go 0

{-WETT-}

decompose :: [Integer] -> [Integer]
decompose ds = if containsZero ds then [] else decomposeHelper ds 0 maxDim (toInteger (length ds))
    where maxDim = toInteger (length (bin (minimum ds)) - 1)

containsZero :: [Integer] -> Bool
containsZero [] = False
containsZero (x:xs) 
    | x == 0 = True
    | otherwise = containsZero xs

--Übersetzt input int in binär darstellung
bin :: Integer -> [Integer]
bin 0 = []
bin int = (int `mod` 2) : bin (int `div` 2)

decomposeHelper :: [Integer] -> Integer -> Integer -> Integer -> [Integer] -- input - preVol - current Dimension - Dimension 
decomposeHelper xs vol 0 _ = [x]
    where   x = product (ggV xs 1) - vol 

decomposeHelper xs vol currDim maxDim = decomposeHelper xs (vol + x * (2^(currDim * maxDim))) (currDim - 1) maxDim ++ [x]
    where   x = (product (ggV xs (2^currDim)) - vol) `div` (2^(currDim * maxDim))
            
ggV :: [Integer] -> Integer -> [Integer] -- berechnet den größte zweier potenz welches x element von xs teilt
ggV [] _ = []
ggV (x:xs) num = (x `div` num) * num : ggV xs num

{-TTEW-}