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Tree23.hs
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Tree23.hs
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module Tree23
(Tree23 (..)
, insert
, lookup
-- , delete
, fromList
, toList)
where
import Prelude hiding (lookup)
import Test.QuickCheck
import Control.Monad
import qualified Data.Set as S
data Tree23 a = Empty
| N2 a ((Tree23 a), (Tree23 a))
| N3 (a,a) ((Tree23 a), (Tree23 a), (Tree23 a))
deriving (Eq)
instance (Show a) => Show (Tree23 a) where
show = showPrefix "" ""
where
showPrefix _ _ Empty = ""
showPrefix _ _ (N2 a (Empty,Empty)) =
show a
showPrefix pref1 pref2 (N2 a (l,r)) =
show a ++ "\n" ++
pref1 ++ pref2 ++ "|--" ++
(showPrefix (pref1 ++ pref2) "| " l) ++ "\n" ++
pref1 ++ pref2 ++ "`--" ++ (showPrefix (pref1 ++ pref2) " " r)
showPrefix pref1 pref2 (N3 (a,b) (Empty,Empty,Empty)) =
show a ++ "\n" ++
pref1 ++ pref2 ++ show b
showPrefix pref1 pref2 (N3 (a,b) (la,bab,gb)) =
show a ++ "\n" ++
pref1 ++ pref2 ++ show b ++ "\n" ++
pref1 ++ pref2 ++ "|--" ++
(showPrefix (pref1 ++ pref2) "| " la) ++ "\n" ++
pref1 ++ pref2 ++ "|--" ++
(showPrefix (pref1 ++ pref2) "| " bab) ++ "\n" ++
pref1 ++ pref2 ++ "`--" ++
(showPrefix (pref1 ++ pref2) " " gb)
data Builder a = Tr (Tree23 a)
| Rec a (Tree23 a) (Tree23 a)
deriving (Show)
empty = Empty
empty2 = (Empty, Empty)
empty3 = (Empty, Empty, Empty)
balanceL,balanceR,balanceM :: (Ord a) => Tree23 a -> Builder a -> Builder a
balanceL Empty _ = Tr Empty
balanceL _ (Tr Empty) = Tr Empty
balanceL (N2 y (ly, gy)) (Tr tree) =
Tr (N2 y (tree, gy))
balanceL (N2 y (ly, gy)) (Rec a l r) =
Tr (N3 (a,y) (l,r,gy))
balanceL (N3 (y,z) (ly, byz, gz)) (Tr tree) =
Tr (N3 (y,z) (tree, byz, gz))
balanceL (N3 (y,z) (ly, byz, gz)) (Rec a l r) =
Rec y (N2 a (l,r)) (N2 z (byz, gz))
balanceR _ t@(Tr Empty) = t
balanceR (N2 y (ly, gy)) (Tr tree) = Tr (N2 y (ly, tree))
balanceR (N2 y (ly, gy)) (Rec a l r) = Tr (N3 (y,a) (ly, l, r))
balanceR (N3 (y,z) (ly, byz, gz)) (Tr tree) =
Tr (N3 (y,z) (ly, byz, tree))
balanceR (N3 (y,z) (ly, byz, gz)) (Rec a l r) =
Rec z (N2 y (ly, byz)) (N2 a (l,r))
balanceM Empty (Tr Empty) = Tr Empty
balanceM (N2 {}) _ = undefined
balanceM (N3 (y,z) (ly, byz, gz)) (Tr tree) =
Tr (N3 (y,z) (ly, tree, gz))
balanceM (N3 (y,z) (ly, byz, gz)) (Rec a l r) =
Rec a (N2 y (ly, l)) (N2 z (r,gz))
insert' :: (Ord a) => a -> Builder a -> Builder a
insert' x (Tr Empty) = Tr (N2 x empty2)
insert' x (Tr (N2 y (Empty,Empty)))
| x == y = Tr (N2 x empty2)
| x < y = Tr (N3 (x,y) empty3)
| otherwise = Tr (N3 (y,x) empty3)
insert' x (Tr t@(N2 y (ly, gy)))
| x == y = Tr (N2 x (ly, gy))
| x < y = balanceL t (insert' x (Tr ly))
| otherwise = balanceR t (insert' x (Tr gy))
insert' x (Tr (N3 (y,z) (Empty, Empty, Empty)))
| x == y = Tr (N3 (x,z) empty3)
| x == z = Tr (N3 (y,x) empty3)
| x<y = Rec y (N2 x empty2) (N2 z empty2)
| x>z = Rec z (N2 y empty2) (N2 x empty2)
| otherwise = Rec x (N2 y empty2) (N2 z empty2)
insert' x (Tr t@(N3 (y,z) (ly, byz, gz)))
| x == y = Tr (N3 (x,z) (ly, byz, gz))
| x == z = Tr (N3 (y,x) (ly, byz, gz))
| x < y = balanceL t (insert' x (Tr ly))
| x > z = balanceR t (insert' x (Tr gz))
| otherwise = balanceM t (insert' x (Tr byz))
insert :: (Ord a) => a -> Tree23 a -> Tree23 a
insert x tree = balance $ insert' x (Tr tree)
balance (Tr tree) = tree
balance (Rec a l r) = N2 a (l,r)
--delete' :: (Ord a) => a -> Builder a -> Builder a
--delete' x (Tr Empty) = Tr Empty
--delete' x (Tr (N2 y (ly, gy))) | y == x = Tr (N3
-- |
--delete' x (Tr (T
lookup :: (Ord a) => a -> Tree23 a -> Maybe a
lookup _ Empty = Nothing
lookup a (N2 x (l,g))
| a == x = Just x
| a < x = lookup a l
| a > x = lookup a g
lookup a (N3 (x,y) (lx, bxy, gy))
| a == x = Just x
| a == y = Just y
| a < x = lookup a lx
| a > y = lookup a gy
| otherwise = lookup a bxy
isElem x tree =
case lookup x tree of
Nothing -> False
_ -> True
fromList :: (Ord a) => [a] -> Tree23 a
fromList = foldr insert Empty
--TODO: not efficient, fixme
toList :: (Ord a) => Tree23 a -> [a]
toList Empty = []
toList (N2 x (l,g)) = toList l ++ [x] ++ toList g
toList (N3 (x,y) (lx,bxy,gy)) = toList lx ++ [x] ++
toList bxy ++ [y] ++
toList gy
------------------------------------------------------------------
-- tests
------------------------------------------------------------------
instance (Ord a, Arbitrary a) => Arbitrary (Tree23 a) where
arbitrary = sized $ \n ->
do x <- choose (0,n)
lst <- sequence [ arbitrary | _ <- [1..x]]
return$ fromList lst
prop_duplicates :: [Int] -> Bool
prop_duplicates x = (c == b)
where
a = foldr insert Empty x
b = toList a
c = uniq x
uniq = S.toList . S.fromList
prop_duplicates2 :: Int -> Bool
prop_duplicates2 x = toList (fromList (replicate 1000 x)) == [x]
-- returns Just depth if tree is balanced
depth :: (Tree23 a) -> Maybe Int
depth Empty = Just 0
depth (N2 _ (l,g)) =
case (depth l, depth g) of
(Just x, Just y) ->
if x == y then Just (1+x) else Nothing
_ -> Nothing
depth (N3 _ (l,m,g)) =
case (depth l, depth m, depth g) of
(Just x, Just y, Just z) ->
if x == y && y == z then Just (1+x) else Nothing
_ -> Nothing
prop_balance :: Tree23 Int -> Bool
prop_balance x =
case depth x of
Nothing -> False
Just _ -> True
prop_find :: Tree23 Int -> Int -> Bool
prop_find x y = case lookup y (insert y x) of
Nothing -> False
Just a -> a == y
--prop_delete x y = prop_balance new_tree &&
-- find y x /= Nothing
-- where new_tree = delete y x
main = do
putStrLn "prop_find" >> quickCheck prop_find
putStrLn "prop_balance" >> quickCheck prop_balance
putStrLn "prop_duplicates2" >> quickCheck prop_duplicates2
putStrLn "prop_duplicates" >> quickCheck prop_duplicates