data Tree a = Node (Tree a) a (Tree a) | Nil deriving Show

-- binarni strom ze zoznamu
treeToList :: Tree a -> [a]
treeToList Nil = []
treeToList (Node l v r) = (treeToList l) ++ [v] ++ (treeToList r)

listToTree :: [a] -> Tree a
listToTree [] = Nil
listToTree s = let
  l = length s `div` 2
  lp = take l s
  (c:pp) = drop l s
  in  (Node (listToTree lp) c (listToTree pp))

-- vyhledani prvku ve strome + reakce na selhani

hladaj :: Ord a => Tree a -> a -> Bool
hladaj Nil a = False
hladaj (Node l c r) x | x == c = True
                      | x < c = hladaj l x
                      | otherwise = hladaj r x

-- vybrat n-ty nejmensi prvek ze stromu
treeSize :: Tree a -> Int
treeSize Nil = 0
treeSize (Node l c r) = treeSize l + treeSize r + 1

nth :: Tree a -> Int -> Maybe a
nth Nil n = Nothing 
nth (Node l c r) n | treeSize l > n = nth l n
                   | treeSize l < n = nth r (n - treeSize l -1) 
                   | otherwise = Just c

-- nekonecny strom s pascalovym trojuhelnikem, treeTake
data Pastree = Pastree Int Pastree Pastree deriving Show

vyrobPastree :: Pastree
vyrobPastree = Pastree 1 (vPt [1,1] 0) (vPt [1,1] 1)
--vPt :: [Int] -> Int -> Pastree
vPt l o = let 
      novyseznam = zipWith (+) (l ++ [0]) (0:l)  
      in Pastree (l!!o) (vPt novyseznam o) (vPt novyseznam (o + 1))


pasDemo = let
  Pastree _ l _ = vyrobPastree
  Pastree _ _ r = l
  Pastree _ _ r' = r
  Pastree n _ _ = r'
  in n

takeTree :: Int -> Pastree -> Tree Int
takeTree 0 _ = Nil
takeTree n (Pastree a l r) = Node (nxt l) a (nxt r)
  where nxt = takeTree (n-1)