module Exercise05 where

import Data.List (sort)

-- 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-}
-- Try fit Block in the space size by size
fitBlocks :: [Integer] -> Integer -> Integer -> [Integer]
fitBlocks ds _ 0 = [product ds]
fitBlocks ds factor cubeIndex = result : smaller - (result * factor) : above -- remove space for bigger squares
  where
    bigCube = 2 ^ cubeIndex
    cubeNumbers = [x `quot` bigCube | x <- ds]
    result = product cubeNumbers
    (smaller : above) = fitBlocks ds factor (cubeIndex -1)

-- helper for fitBlocks
decomposeE :: [Integer] -> [Integer]
decomposeE (0 : _) = [] -- flat?
decomposeE ds@(minLength : _) = reverse result
  where
    dimentions = length ds
    minIndex = log2 minLength
    result = fitBlocks ds (2 ^ dimentions) minIndex

decompose :: [Integer] -> [Integer]
decompose ds = decomposeE (sort ds)

{-TTEW-}