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| module AVLTree where | |
| data BT = L | N Int BT BT deriving (Show, Eq) | |
| -- Nice, small and useful functions | |
| empty = L | |
| -- You could say, depth L == Nothing depth (N v L L) == Just 0, but works for | |
| -- me better this way: | |
| depth L = 0 | |
| depth (N _ t u) = (max (depth t) (depth u)) + 1 | |
| inorder :: BT -> [Int] | |
| inorder L = [] | |
| inorder (N v t u) = inorder t ++ [v] ++ inorder u | |
| left (N _ t _) = t | |
| right (N _ _ u) = u | |
| value (N v _ _) = v | |
| btmin = head . inorder | |
| -- FIXME: Could be cleaner BT -> Int using left and right of BT | |
| balFactor :: BT -> BT -> Int | |
| balFactor t u = (depth t) - (depth u) | |
| -- Tricky but easy: we return a binary list with the route to the node | |
| search :: BT -> Int -> Maybe [Int] | |
| search L s = Nothing | |
| search (N v t u) s | |
| | v == s = Just [] | |
| | (search t s) /= Nothing = fmap ((:) 0) (search t s) | |
| | (search u s) /= Nothing = fmap ((:) 1) (search u s) | |
| | otherwise = Nothing | |
| -- Complementary to search: get the node with the path | |
| getelem :: BT -> [Int] -> Maybe Int | |
| getelem L _ = Nothing | |
| getelem (N v _ _) [] = Just v | |
| getelem (N v t u) (x:xs) | |
| | x == 0 = getelem t xs | |
| | otherwise = getelem u xs | |
| -- If you get confused (I do), check this nice picture: | |
| -- http://en.wikipedia.org/wiki/Image:Tree_Rebalancing.gif | |
| balanceLL (N v (N vl tl ul) u) = (N vl tl (N v ul u)) | |
| balanceLR (N v (N vl tl (N vlr tlr ulr)) u) = (N vlr (N vl tl tlr) (N v ulr u)) | |
| balanceRL (N v t (N vr (N vrl trl url) ur)) = (N vrl (N v t trl) (N vr url ur)) | |
| balanceRR (N v t (N vr tr ur)) = (N vr (N v t tr) ur) | |
| -- Balanced insert | |
| insert :: BT -> Int -> BT | |
| insert L i = (N i L L) | |
| insert (N v t u) i | |
| | i == v = (N v t u) | |
| | i < v && (balFactor ti u) == 2 && i < value t = balanceLL (N v ti u) | |
| | i < v && (balFactor ti u) == 2 && i > value t = balanceLR (N v ti u) | |
| | i > v && (balFactor t ui) == -2 && i < value u = balanceRL (N v t ui) | |
| | i > v && (balFactor t ui) == -2 && i > value u = balanceRR (N v t ui) | |
| | i < v = (N v ti u) | |
| | i > v = (N v t ui) | |
| where ti = insert t i | |
| ui = insert u i | |
| -- Balanced delete | |
| delete :: BT -> Int -> BT | |
| delete L d = L | |
| delete (N v L L) d = if v == d then L else (N v L L) | |
| delete (N v t L) d = if v == d then t else (N v t L) | |
| delete (N v L u) d = if v == d then u else (N v L u) | |
| delete (N v t u) d | |
| | v == d = (N mu t dmin) | |
| | v > d && abs (balFactor dt u) < 2 = (N v dt u) | |
| | v < d && abs (balFactor t du) < 2 = (N v t du) | |
| | v > d && (balFactor (left u) (right u)) < 0 = balanceRR (N v dt u) | |
| | v < d && (balFactor (left t) (right t)) > 0 = balanceLL (N v t du) | |
| | v > d = balanceRL (N v dt u) | |
| | v < d = balanceLR (N v t du) | |
| where dmin = delete u mu | |
| dt = delete t d | |
| du = delete u d | |
| mu = btmin u | |
| -- Test Functions | |
| load :: BT -> [Int] -> BT | |
| load t [] = t | |
| load t (x:xs) = insert (load t xs) x | |
| unload :: BT -> [Int] -> BT | |
| unload t [] = t | |
| unload t (x:xs) = delete (unload t xs) x | |
| sort :: [Int] -> [Int] | |
| sort = inorder . (load empty) | |
| isBalanced L = True | |
| isBalanced (N _ t u) = isBalanced t && isBalanced u && abs (balFactor t u) < 2 | |
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