module AufgabeFFP8
where

import Data.Array
import Data.List hiding ((\\))
import Test.QuickCheck

type Nat = Int

-- Minfree basic version

minfree_bv :: [Int] -> Int
minfree_bv xs = head ([0..] \\ xs)

(\\) :: Eq a => [a] -> [a] -> [a]
xs \\ ys = filter (\x -> x `notElem` ys) xs

-- Minfree checklist

minfree_chl :: [Int] -> Int
minfree_chl = search . checklist

search :: Array Int Bool -> Int
search = length . takeWhile id . elems

checklist :: [Int] -> Array Int Bool
checklist xs = accumArray (||) False (0,n)
                (zip (filter (<=n) xs) (repeat True))
                where n = length xs
         
-- minfree countlist
       
minfree_col :: [Int] -> Int
minfree_col = search0 . assocs . countlist

countlist :: [Int] -> Array Int Int
countlist xs = accumArray (+) 0 (0,n) (zip xs (repeat 1))
  where n = length xs
  
sort :: [Int] -> [Int]
sort xs = concat [replicate k x | (x,k) <- assocs $ countlist xs]

search0 :: [(Int, Int)] -> Int
search0 [] = -1
search0((i,0):_) = i
search0 (x:xs) = search0 xs

-- minfree basic daq

minfree_b :: [Int] -> Int
minfree_b xs = if (null ([0..b-1] \\ us))
    then (head ([b..] \\ vs))
    else (head ([0..] \\ us))
    where
      b = 1 + (length xs) `div` 2
      (us, vs) = partition (<b) xs
      
-- minfree refined daq

minfree_r :: [Int] -> Int
minfree_r = minfrom_r 0

minfrom_r :: Nat -> [Nat] -> Nat
minfrom_r a xs
  | null xs   = a
  | length us == b-a =  minfrom_r b vs
  | otherwise = minfrom_r b us
  where 
    b = a + 1 + (length xs) `div` 2
    (us, vs) = partition (<b) xs

-- minfree optimized daq (p262)
    
minfree_o :: [Int] -> Int
minfree_o xs = minfrom_o 0 (length xs, xs)

minfrom_o :: Int -> (Int, [Int]) -> Int
minfrom_o a (n, xs)
  | n == 0    = a
  | m == b-a  = minfrom_o b (n-m, vs)
  | otherwise = minfrom_o a (m, us)
  where
    (us,vs) = partition (<b) xs
    b       = a + 1 + n `div` 2
    m       = length us
    
-- true daq implementations

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))
      
-- minfree basic daq higher order

b_indiv :: Int -> [Int] -> Bool
b_indiv l xs = length xs < l

b_solve :: [Int] -> [Int]
b_solve = id

b_divide :: Int -> [Int] -> [[Int]]
b_divide b xs = [us, vs]
  where (us,vs) = partition (<b) xs
  
b_combine :: Int -> [Int] -> [[Int]] -> [Int]
b_combine b _ (us:vs:[]) = if (null ([0..b-1] \\ us))
    then ([b..] \\ vs)
    else ([0..] \\ us)
  
minfree_bhof :: [Int] -> Int
minfree_bhof xs = head $ divideAndConquer (b_indiv (length xs)) b_solve (b_divide b) (b_combine b) xs
  where b = 1+(length xs) `div` 2
  
-- minfree refined daq higher order
									

-- refined divide-and-conquer mittels higher order function
--minfree_rhof :: [Int] -> Int
--minfree_rhof = divideAndConquer r_indiv r_solve r_divide r_combine 
--
--r_indiv :: (Int, [Int]) -> Bool
--r_indiv (a, xs) 

-- optimised divide-and-conquer mittels higher order function
--minfree_ohof :: [Int] -> Int



-- QuickCheck part

functions = [ minfree_bv, minfree_chl, minfree_col,
					minfree_b, minfree_r, minfree_o,
					minfree_bhof]

-- calc values of all function
calc_all :: [Int] -> [Int]
calc_all xs = [ f xs | f <- functions ]

-- check if all values of a list are the same
all_eq :: [Int] -> Bool
all_eq (x:[]) = True
all_eq (x:y:xs) 
	| x == y = all_eq (y:xs)
	| otherwise = False

-- check if a list contains no duplicates
--no_dups :: [Int] -> Bool
--no_dups [] = True
--no_dups (x:xs) 
--	| x `elem` xs = False
--	| otherwise = no_dups xs

prop_allImplsEq_a :: [Int] -> Bool
prop_allImplsEq_a xs = all_eq $ calc_all (nub xs)

-- keine negativen listenelemented durch vorbedingung entfernt
prop_allImplsEq_b :: [Int] -> Property
prop_allImplsEq_b xs = all (>=0) xs ==> all_eq $ calc_all (nub xs)