module Exercise05 where


main = decompose [123]

-- 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 
    |not (null [n| n <- ds, n == 0 ]) = []
    |length ds == 1 && head ds < 2 = ds
    |length ds == 1 = let anzahlStell = log2 (minimum ds) in
         addElements [div n anzahlStell |n <- [0..anzahlStell] ] (decompose [head ds - 2 ^ anzahlStell])
    |otherwise = helpFunk [decompose [n]| n <- ds] 1

helpFunk:: [[Integer]] -> Integer -> [Integer]
helpFunk [] _ = []
helpFunk (xs:xss) iter 
    |null xss = xs
    |otherwise = let (first, second) = ifDifferent (xs, head xss) iter in
       helpFunk ([n | x <- [0..(length first-1)], n <- [sum ([first!!x * (second!!parts) * (2 ^ (parts - x))| parts <- [x..length second-1]] ++ [second!!x * (first!!parts) * (2 ^ ((parts - x ) * fromInteger iter)) | parts <-[x+1..length first - 1]]) ] ] : tail xss) (iter+1)
        

ifDifferent::([Integer], [Integer]) -> Integer -> ([Integer], [Integer])
ifDifferent paar iter
    | length (fst paar) == length (snd paar) = paar
    | length (fst paar) > length (snd paar) = ifDifferent (init(init (fst paar)) ++ [last (fst paar) * (2 ^ iter) + last(init (fst paar))], snd paar) iter
    | otherwise = ifDifferent (fst paar, init(init (snd paar)) ++ [last (snd paar) * 2 + last(init (snd paar))]) iter



addElements:: [Integer] -> [Integer] -> [Integer]
addElements f s = addElementsHelp f s []


addElementsHelp:: [Integer] -> [Integer] -> [Integer]-> [Integer]
addElementsHelp [] secondList result = result ++ secondList;
addElementsHelp firstList [] result = result ++ firstList 
addElementsHelp firstList secondList result = addElementsHelp (tail firstList) (tail secondList) (result ++ [head firstList + head secondList])
{-TTEW-}