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 = recursive ds []

-- dimensions, interim result => new interim result
recursive :: [Integer] -> [Integer] -> [Integer]
recursive ds xs =  if c > 0 then recursive ds (old ++ rest ++ [c]) else xs
    where 
        l =  length xs
        d = fromIntegral (length ds)
        c = getCubiodCount ds l
        rest = [(xs !! (l - 1)) - (c * 2 ^ d) | l /= 0]
        old = if l == 0 then [] else take (l - 1) xs

-- dimensions, length => count
getCubiodCount :: [Integer] -> Int -> Integer
getCubiodCount ds l = product [d `div` (2 ^ l) | d <- ds]



{-TTEW-}