module DatabaseDesign.Ampersand.Input.ADL1.UU_BinaryTrees 
   ( BinSearchTree(..)
   , tab2tree
   , btFind
   , btLocateIn
   )
   where

   data BinSearchTree av
    = Node (BinSearchTree av) av (BinSearchTree av)
    | Nil


   tab2tree :: [av] -> BinSearchTree av
   tab2tree tab = tree
    where
     (tree,[]) = sl2bst (length tab) tab
     sl2bst 0 list     = (Nil   , list)
     sl2bst n list     
      = let 
         ll = (n - 1) `div` 2 ; rl = n - 1 - ll
         (lt,a:list1) = sl2bst ll list 
         (rt,  list2) = sl2bst rl list1
        in (Node lt a rt, list2)



   btFind :: (a -> b -> Ordering) -> BinSearchTree (a, c) -> b -> Maybe c
   btLocateIn :: (a -> b -> Ordering) -> BinSearchTree a      -> b -> Maybe a
   btFind     = btLookup fst snd
   btLocateIn = btLookup id id
   btLookup  key val cmp (Node Nil  kv Nil)
     =  let comp = cmp (key kv)
            r    = val kv
        in \i -> case comp i of
                 LT -> Nothing    
                 EQ -> Just r
                 GT -> Nothing 

   btLookup key val cmp (Node left kv Nil) 
     =  let comp = cmp (key kv)
            findleft = btLookup key val cmp left
            r    = val kv
        in \i -> case comp i of
                 LT -> Nothing    
                 EQ -> Just r
                 GT -> findleft i 

   btLookup key val cmp (Node Nil kv right )
     =  let comp      = cmp (key kv)
            findright = btLookup key val cmp right
            r         = val kv
            in \i -> case comp i of
                     LT -> findright i   
                     EQ -> Just r
                     GT -> Nothing 

   btLookup key val cmp (Node left kv right)
     =  let comp = cmp (key kv)
            findleft  = btLookup key val cmp left
            findright = btLookup key val cmp right
            r    = val kv
        in \i -> case comp i of
                 LT -> findright i    
                 EQ -> Just r
                 GT -> findleft i

   btLookup _ _ _ Nil   =  const Nothing