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binary search tree haskell implementation
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| {- BINARY SEARCH TREE IMPLEMENTATION -} | |
| module Tree | |
| ( Tree(..) | |
| , pretty | |
| , size | |
| , depth | |
| , empty | |
| , contains | |
| , insert | |
| , delete | |
| , fromList | |
| , toList | |
| , balance | |
| ) where | |
| import qualified Data.Foldable as F | |
| data Tree a = Empty | Node a (Tree a) (Tree a) deriving (Read,Show) | |
| instance Functor Tree where | |
| fmap g Empty = Empty | |
| fmap g (Node a left right) = Node (g a) (fmap g left) (fmap g right) | |
| instance F.Foldable Tree where | |
| foldMap f Empty = mempty | |
| foldMap f (Node a left right) = F.foldMap f left `mappend` | |
| f a `mappend` | |
| F.foldMap f right | |
| {- DESCRIPT BST -} | |
| -- TODO: | |
| type Space = String | |
| incSpace :: Space -> Space | |
| incSpace space = space ++ " " | |
| -- Pretty print tree | |
| pretty :: (Show a) => Tree a -> Space -> IO () | |
| pretty Empty _ = putStr "" | |
| pretty (Node x left right) space = do | |
| putStrLn (space ++ show x) | |
| pretty left $ incSpace space | |
| pretty right $ incSpace space | |
| -- Size of tree | |
| size :: Tree a -> Int | |
| size = length . toList | |
| -- Depth of tree | |
| depth :: Tree a -> Int | |
| depth Empty = 0 | |
| depth (Node a left right) = max (1 + depth left) (1 + depth right) | |
| -- Check if tree is empty | |
| empty :: Tree a -> Bool | |
| empty Empty = True | |
| empty _ = False | |
| -- Check if x is in tree | |
| contains :: (Ord a) => a -> Tree a -> Bool | |
| contains _ Empty = False | |
| contains x (Node n left right) | |
| | x == n = True | |
| | x > n = contains x right | |
| | x < n = contains x left | |
| {- BST OPERATIONS -} | |
| -- Insert x into tree | |
| insert :: (Ord a) => a -> Tree a -> Tree a | |
| insert x Empty = Node x Empty Empty | |
| insert x (Node n left right) | |
| | x == n = Node n left right | |
| | x > n = Node n left (insert x right) | |
| | x < n = Node n (insert x left) right | |
| -- Delete x from tree | |
| delete :: (Ord a) => a -> Tree a -> Tree a | |
| delete _ Empty = Empty | |
| delete x (Node n left right) | |
| | x == n = fromList $ toList left ++ toList right | |
| | x > n = Node n left (delete x right) | |
| | x < n = Node n (delete x left) right | |
| -- Create list from tree | |
| toList :: Tree a -> [a] | |
| toList Empty = [] | |
| toList (Node x left right) = [x] ++ toList left ++ toList right | |
| -- Create tree from list | |
| fromList :: (Ord a) => [a] -> Tree a | |
| fromList [] = Empty | |
| fromList xs = foldl (\tree x -> insert x tree) Empty xs | |
| {- BALANCING BST -} | |
| -- Quicksort | |
| sort :: (Ord a) => [a] -> [a] | |
| sort [] = [] | |
| sort (e:xs) = sort [x | x <- xs, x <= e] ++ [e] ++ sort [x | x <- xs, x > e] | |
| -- Middle item of list | |
| middle :: [a] -> [a] | |
| middle [] = [] | |
| middle xs = xs !! midPos : [] | |
| where midPos = length xs `div` 2 | |
| -- Balanced list from unbalanced list | |
| balancedList :: (Ord a) => [a] -> [a] | |
| balancedList [] = [] | |
| balancedList xs = [m] ++ left ++ right | |
| where | |
| m = head . middle $ xs | |
| left = balancedList [x | x <- xs, x < m] | |
| right = balancedList [x | x <- xs, x > m] | |
| -- Balanced tree from unbalanced tree | |
| balance :: (Ord a) => Tree a -> Tree a | |
| balance Empty = Empty | |
| balance tree = fromList . balancedList . toList $ tree |
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