module Exercise05 where

import Data.Bits
import Data.List

-- 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 lengthC <= 0 then [] else snd $mapAccumR (\consumed position -> let count = countAt position in (count * scaleFactor, count - consumed)) 0 [0 .. log2 lengthC]
  where
    lengthC = minimum ds
    scaleFactor = 2 ^ length ds
    dsGrouped = map (\x -> (head x, genericLength x)) $group $sortOn (* (-1)) ds -- Sort descending for more smaller multiplications and group to save unnecessary calculations
    countAt position = foldr (\(lengthDim, times) acc -> shiftR lengthDim position ^ times * acc) 1 dsGrouped -- shiftR by position = div by 2^position

{-TTEW-}