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))

-------------------------------------------------------------------------------
-- 1.
-------------------------------------------------------------------------------

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

-- fill the table. Lower half below diagonal not necessary
-- but filled with the symmetric value
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

-- computes distance-sum-table for array
asTbl :: Array Int Int -> Table Int (Int, Int)
asTbl a = dynamic (compAS a) (bndsAS a)

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

-- maximum of the array's distance-sums
mas :: Array Int Int -> Int
mas a = tblMax $ asTbl a

-------------------------------------------------------------------------------
-- 2.
-------------------------------------------------------------------------------

-- all indices where the value equals to the maximum distance-sum
amas :: Array Int Int -> [(Int, Int)]
amas a = [(i,j) | ((i,j),v) <- (assocs array), i<=j, v>=maxAS]
  where
    t@(Tbl array) = asTbl a
    maxAS = tblMax t

-------------------------------------------------------------------------------
-- 3.
-------------------------------------------------------------------------------

-- computes index with maximum index-difference
maxL :: [(Int, Int)] -> (Int, Int)
maxL [] = error "maximum of empty list"
maxL [x] = x
maxL (x:xs)
  | l x >= l maxTail = x
  | otherwise = maxTail
  where
    l (x,y) = y-x
    maxTail = maxL xs

-- index with maximum distance-sum and maximum index-difference
lmas :: Array Int Int -> (Int, Int)
lmas a = maxL $ amas a

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

divideAndConquer :: (p->Bool) -> (p->s) -> (p->[p]) -> (p->[s]->s) -> p -> s
divideAndConquer indiv solve divide combine initPb = dAC initPb
  where
    dAC pb
      | indiv pb = solve pb
      | otherwise = combine pb (map dAC (divide pb))


-------------------------------------------------------------------------------
-- 4.
-------------------------------------------------------------------------------

mi_indiv :: [a] -> Bool
mi_indiv a = length a <= 1

mi_solve :: (Ix a, Show a) => (b -> Bool) -> [(a,b)] -> [(a,b)]
mi_solve wf [(a,b)]
  | wf b = [(a,b)]
  | otherwise = []

mi_divide :: [a] -> [[a]]
mi_divide (x:xs) = [[x], xs]

mi_combine :: [a] -> [[a]] -> [a]
mi_combine _ [] = error "No matching index"
mi_combine a (x:xs)
  | null x = mi_combine a xs
  | otherwise = [head x]

minIndex :: (Ix a, Show a) => Array a b -> (b -> Bool) -> a
minIndex a wf = fst $ head $ divideAndConquer mi_indiv (mi_solve wf) mi_divide mi_combine $ assocs a