module AufgabeFFP5
where
	
import Data.Array
	
newtype Table a b = Tbl (Array b a)
  deriving Show

newTable :: (Ix b) => [(b, a)] -> Table a b
newTable l = Tbl (array (lo, hi) l)
  where
    indices = map fst l
    lo = minimum indices
    hi = maximum indices

findTable :: (Ix b) => Table a b -> b -> a
findTable (Tbl a) i = a ! i

updTable :: (Ix b) => (b, a) -> Table a b -> Table a b
updTable p@(i, x) (Tbl a) = Tbl (a // [p])

dynamic :: (Ix coord) => (Table entry coord -> coord -> entry) -> (coord, coord) -> (Table entry coord)
dynamic compute bnds = t
  where
    t = newTable (map (\coord -> (coord, compute t coord)) (range bnds))

-------------------------------------------------------------------------------

bndsAS :: Array Int Int -> ((Int, Int), (Int, Int))
bndsAS a = ((l,l), (h,h))
  where
    (l,h) = bounds a 

compAS :: Array Int Int -> Table Int (Int, Int) -> (Int, Int) -> Int
compAS a t (i,j)
  | i == j = a ! j
  | i<j = compAS a t (j,i)
  | otherwise = findTable t (i-1, j) + a!i
  
asDyn :: Array Int Int -> (Int, Int) -> Int
asDyn a (i,j) = findTable t (i,j)
  where
      t = dynamic (compAS a) (bndsAS a)

-- maximum function for tables
tblMax :: Table Int (Int,Int) -> Int
tblMax (Tbl a) = maximum $ elems a

mas :: Array Int Int -> Int
mas a = tblMax $ dynamic (compAS a) (bndsAS a)