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
  | min > 0 = reverse $ decomposeDimension (toInteger (length ds) -1) (map (toReducedBinary $ log2 min) ds)
  | otherwise = []
  where
    min = minimum ds

decomposeDimension :: Integer -> [[Integer]] -> [Integer]
decomposeDimension 0 (ds : _) = ds
decomposeDimension dim (ds : dss) = zipWith (+) (zipWith (*) (scanl1 (\x y -> 2 * x + y) ds) cs) (zipWith (*) (scanl (\x y -> (2 ^ dim) * (x + y)) 0 cs) ds)
  where
    cs = decomposeDimension (dim -1) dss
decomposeDimension _ _ = []

toReducedBinary :: Integer -> Integer -> [Integer]
toReducedBinary _ 0 = []
toReducedBinary 0 x = [x]
toReducedBinary max x = toReducedBinary (max - 1) (x `div` 2) ++ [x `mod` 2]

{-TTEW-}