// Mart Lubbers, s4109503
// Camil Staps, s4498062

implementation module BinSearchTree

import StdEnv
import BinTree

insertTree :: a (BTree a) -> BTree a | Ord a
insertTree e BLeaf = BNode e BLeaf BLeaf
insertTree e (BNode x le ri)
| e <= x = BNode x (insertTree e le) ri
| e >  x = BNode x le (insertTree e ri)

deleteTree :: a (BTree a) -> (BTree a) | Eq, Ord a
deleteTree e BLeaf = BLeaf
deleteTree e (BNode x le ri)
| e <  x = BNode x (deleteTree e le) ri
| e == x = join le ri
| e >  x = BNode x le (deleteTree e ri)
where
    join :: (BTree a) (BTree a) -> (BTree a)
    join BLeaf b2 = b2
    join b1 b2 = BNode x b1` b2
    where
        (x,b1`) = largest b1
        
        largest :: (BTree a) -> (a,(BTree a))
        largest (BNode x b1 BLeaf) = (x,b1)
        largest (BNode x b1 b2)   = (y,BNode x b1 b2`)
        where
            (y,b2`) = largest b2


is_geordend :: (BTree a) -> Bool | Ord a // meest algemene type
is_geordend BLeaf = True
is_geordend (BNode x le ri) = (foldr (&&) True (map ((>) x) (members le))) && (foldr (&&) True (map ((<=) x) (members ri))) && is_geordend le && is_geordend ri
where
    members :: (BTree a) -> [a]
    members BLeaf = []
    members (BNode x le ri) = [x:(members le) ++ (members ri)]

is_gebalanceerd :: (BTree a) -> Bool | Ord a // meest algemene type
is_gebalanceerd BLeaf = True
is_gebalanceerd (BNode x le ri) = abs ((depth le) - (depth ri)) <= 1 && is_gebalanceerd le && is_gebalanceerd ri
where
    depth :: (BTree a) -> Int
    depth BLeaf = 0
    depth (BNode x le ri) = max (depth le) (depth ri) + 1