module Exercise05 where

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 = let mult = 2 ^ length ds in if null ds || minimum ds < 1 then [] else snd $ mapAccumR (\prev this -> let prod = product this in (prod, prod - mult * prev)) 0 $ take (log2 (minimum ds) + 1) $ iterate (map (`div` 2)) ds

{- (pretty much) the same just less cramped, I don't think the preformance is affected by calculating minimum ds twice, so I went with the one line version 
decompose ds =
    let mult = 2 ^ length ds 
        lowest = minimum ds
    in  if null ds || lowest < 1 then [] else
        snd $ mapAccumR (\prev this -> let prod = product this in (prod, prod - mult * prev)) 0 $ 
        take (log2 lowest + 1) $ iterate (map (`div` 2)) ds
-}

{-TTEW-}

test :: Bool
test =  decompose [123] == [1 ,1 ,0 ,1 ,1 ,1 ,1] && decompose [6, 5] == [6, 2, 1] &&
        decompose [9, 6] == [6, 4, 2] && decompose [8, 4, 4] == [0, 0, 2] && 
        decompose [10 , 10, 10] == [0, 61, 0, 1] && decompose [10 , 5, 5] == [90 , 4, 2] && 
        decompose [6, 5, 4] == [24 , 4, 1] && decompose [9, 18, 27, 36] == [22680 , 1512 , 48, 24] &&
        null (decompose []) && null (decompose [0]) && null (decompose [0,9,12])

time :: Int -> Int
time a = length . show . sum . decompose $ replicate (10^4) (10^a)

time10 :: Int -> Int -> Int -> Int -> Int -> Int -> Int -> Int -> Int -> Int -> Int -- time10 12 12 12 12 12 12 12 12 12 12 -- time10 15 15 15 15 15 15 15 15 15 15
time10 a b c d e f g h i j = 
    (length . show . sum . decompose $ replicate (10^4) (10^a)) +
    (length . show . sum . decompose $ replicate (10^4) (10^b)) +
    (length . show . sum . decompose $ replicate (10^4) (10^c)) +
    (length . show . sum . decompose $ replicate (10^4) (10^d)) +
    (length . show . sum . decompose $ replicate (10^4) (10^e)) +
    (length . show . sum . decompose $ replicate (10^4) (10^f)) +
    (length . show . sum . decompose $ replicate (10^4) (10^g)) +
    (length . show . sum . decompose $ replicate (10^4) (10^h)) +
    (length . show . sum . decompose $ replicate (10^4) (10^i)) +
    (length . show . sum . decompose $ replicate (10^4) (10^j))