Copyright	(c) The University of Glasgow 2002
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	libraries@haskell.org
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Tree

Contents

Trees and Forests
Construction
Elimination
Ascii Drawings

Description

Multi-way Trees and Forests

The Tree a type represents a lazy, possibly infinite, multi-way tree (also known as a rose tree).

The Forest a type represents a forest of Tree as.

Synopsis

data Tree a = Node {
- rootLabel :: a
- subForest :: [Tree a]
}
type Forest a = [Tree a]
unfoldTree :: (b -> (a, [b])) -> b -> Tree a
unfoldForest :: (b -> (a, [b])) -> [b] -> [Tree a]
unfoldTreeM :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
unfoldForestM :: Monad m => (b -> m (a, [b])) -> [b] -> m [Tree a]
unfoldTreeM_BF :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
unfoldForestM_BF :: Monad m => (b -> m (a, [b])) -> [b] -> m [Tree a]
foldTree :: (a -> [b] -> b) -> Tree a -> b
flatten :: Tree a -> [a]
levels :: Tree a -> [[a]]
drawTree :: Tree String -> String
drawForest :: [Tree String] -> String

Trees and Forests

data Tree a Source #

Non-empty, possibly infinite, multi-way trees; also known as rose trees.

Constructors

Node
Fields rootLabel :: a label value subForest :: [Tree a] zero or more child trees

Instances

Instances details

MonadFix Tree Source #	Since: containers-0.5.11
Instance details Defined in Data.Tree Methods mfix :: (a -> Tree a) -> Tree a Source #
MonadZip Tree Source #
Instance details Defined in Data.Tree Methods mzip :: Tree a -> Tree b -> Tree (a, b) Source # mzipWith :: (a -> b -> c) -> Tree a -> Tree b -> Tree c Source # munzip :: Tree (a, b) -> (Tree a, Tree b) Source #
Foldable Tree Source #	Folds in preorder
Instance details Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m Source # foldMap :: Monoid m => (a -> m) -> Tree a -> m Source # foldMap' :: Monoid m => (a -> m) -> Tree a -> m Source # foldr :: (a -> b -> b) -> b -> Tree a -> b Source # foldr' :: (a -> b -> b) -> b -> Tree a -> b Source # foldl :: (b -> a -> b) -> b -> Tree a -> b Source # foldl' :: (b -> a -> b) -> b -> Tree a -> b Source # foldr1 :: (a -> a -> a) -> Tree a -> a Source # foldl1 :: (a -> a -> a) -> Tree a -> a Source # toList :: Tree a -> [a] Source # null :: Tree a -> Bool Source # length :: Tree a -> Int Source # elem :: Eq a => a -> Tree a -> Bool Source # maximum :: Ord a => Tree a -> a Source # minimum :: Ord a => Tree a -> a Source # sum :: Num a => Tree a -> a Source # product :: Num a => Tree a -> a Source #
Foldable1 Tree Source #	Folds in preorder Since: containers-0.6.7
Instance details Defined in Data.Tree Methods fold1 :: Semigroup m => Tree m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Tree a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Tree a -> m Source # toNonEmpty :: Tree a -> NonEmpty a Source # maximum :: Ord a => Tree a -> a Source # minimum :: Ord a => Tree a -> a Source # head :: Tree a -> a Source # last :: Tree a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Tree a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Tree a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Tree a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Tree a -> b Source #
Eq1 Tree Source #	Since: containers-0.5.9
Instance details Defined in Data.Tree Methods liftEq :: (a -> b -> Bool) -> Tree a -> Tree b -> Bool Source #
Ord1 Tree Source #	Since: containers-0.5.9
Instance details Defined in Data.Tree Methods liftCompare :: (a -> b -> Ordering) -> Tree a -> Tree b -> Ordering Source #
Read1 Tree Source #	Since: containers-0.5.9
Instance details Defined in Data.Tree Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Tree a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Tree a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Tree a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Tree a] Source #
Show1 Tree Source #	Since: containers-0.5.9
Instance details Defined in Data.Tree Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Tree a -> ShowS Source # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Tree a] -> ShowS Source #
Traversable Tree Source #
Instance details Defined in Data.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree a -> f (Tree b) Source # sequenceA :: Applicative f => Tree (f a) -> f (Tree a) Source # mapM :: Monad m => (a -> m b) -> Tree a -> m (Tree b) Source # sequence :: Monad m => Tree (m a) -> m (Tree a) Source #
Applicative Tree Source #
Instance details Defined in Data.Tree Methods pure :: a -> Tree a Source # (<>) :: Tree (a -> b) -> Tree a -> Tree b Source # liftA2 :: (a -> b -> c) -> Tree a -> Tree b -> Tree c Source # (>) :: Tree a -> Tree b -> Tree b Source # (<*) :: Tree a -> Tree b -> Tree a Source #
Functor Tree Source #
Instance details Defined in Data.Tree Methods fmap :: (a -> b) -> Tree a -> Tree b Source # (<$) :: a -> Tree b -> Tree a Source #
Monad Tree Source #
Instance details Defined in Data.Tree Methods (>>=) :: Tree a -> (a -> Tree b) -> Tree b Source # (>>) :: Tree a -> Tree b -> Tree b Source # return :: a -> Tree a Source #
Generic1 Tree Source #
Instance details Defined in Data.Tree Associated Types type Rep1 Tree :: k -> Type Source # Methods from1 :: forall (a :: k). Tree a -> Rep1 Tree a Source # to1 :: forall (a :: k). Rep1 Tree a -> Tree a Source #
Lift a => Lift (Tree a :: Type) Source #	Since: containers-0.6.6
Instance details Defined in Data.Tree Methods lift :: Quote m => Tree a -> m Exp Source # liftTyped :: forall (m :: Type -> Type). Quote m => Tree a -> Code m (Tree a) Source #
Data a => Data (Tree a) Source #
Instance details Defined in Data.Tree Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Tree a -> c (Tree a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Tree a) Source # toConstr :: Tree a -> Constr Source # dataTypeOf :: Tree a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Tree a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Tree a)) Source # gmapT :: (forall b. Data b => b -> b) -> Tree a -> Tree a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Tree a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Tree a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Tree a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Tree a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Tree a -> m (Tree a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Tree a -> m (Tree a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Tree a -> m (Tree a) Source #
Generic (Tree a) Source #
Instance details Defined in Data.Tree Associated Types type Rep (Tree a) :: Type -> Type Source # Methods from :: Tree a -> Rep (Tree a) x Source # to :: Rep (Tree a) x -> Tree a Source #
Read a => Read (Tree a) Source #
Instance details Defined in Data.Tree Methods readsPrec :: Int -> ReadS (Tree a) Source # readList :: ReadS [Tree a] Source # readPrec :: ReadPrec (Tree a) Source # readListPrec :: ReadPrec [Tree a] Source #
Show a => Show (Tree a) Source #
Instance details Defined in Data.Tree Methods showsPrec :: Int -> Tree a -> ShowS Source # show :: Tree a -> String Source # showList :: [Tree a] -> ShowS Source #
NFData a => NFData (Tree a) Source #
Instance details Defined in Data.Tree Methods rnf :: Tree a -> () Source #
Eq a => Eq (Tree a) Source #
Instance details Defined in Data.Tree Methods (==) :: Tree a -> Tree a -> Bool # (/=) :: Tree a -> Tree a -> Bool #
Ord a => Ord (Tree a) Source #	Since: containers-0.6.5
Instance details Defined in Data.Tree Methods compare :: Tree a -> Tree a -> Ordering # (<) :: Tree a -> Tree a -> Bool # (<=) :: Tree a -> Tree a -> Bool # (>) :: Tree a -> Tree a -> Bool # (>=) :: Tree a -> Tree a -> Bool # max :: Tree a -> Tree a -> Tree a # min :: Tree a -> Tree a -> Tree a #
type Rep1 Tree Source #	Since: containers-0.5.8
Instance details Defined in Data.Tree type Rep1 Tree = D1 ('MetaData "Tree" "Data.Tree" "containers-0.6.7" 'False) (C1 ('MetaCons "Node" 'PrefixI 'True) (S1 ('MetaSel ('Just "rootLabel") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1 :*: S1 ('MetaSel ('Just "subForest") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (List :.: Rec1 Tree)))
type Rep (Tree a) Source #	Since: containers-0.5.8
Instance details Defined in Data.Tree type Rep (Tree a) = D1 ('MetaData "Tree" "Data.Tree" "containers-0.6.7" 'False) (C1 ('MetaCons "Node" 'PrefixI 'True) (S1 ('MetaSel ('Just "rootLabel") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Just "subForest") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [Tree a])))

type Forest a = [Tree a] Source #

This type synonym exists primarily for historical reasons.

Construction

unfoldTree :: (b -> (a, [b])) -> b -> Tree a Source #

Build a (possibly infinite) tree from a seed value in breadth-first order.

unfoldTree f b constructs a tree by starting with the tree Node { rootLabel=b, subForest=[] } and repeatedly applying f to each rootLabel value in the tree's leaves to generate its subForest.

For a monadic version see unfoldTreeM_BF.

Examples

Expand

Construct the tree of Integers where each node has two children: left = 2*x and right = 2*x + 1, where x is the rootLabel of the node. Stop when the values exceed 7.

let buildNode x = if 2*x + 1 > 7 then (x, []) else (x, [2*x, 2*x+1])
putStr $ drawTree $ fmap show $ unfoldTree buildNode 1

1
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+- 2
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`- 3
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   +- 6
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   `- 7

unfoldForest :: (b -> (a, [b])) -> [b] -> [Tree a] Source #

Build a (possibly infinite) forest from a list of seed values in breadth-first order.

unfoldForest f seeds invokes unfoldTree on each seed value.

For a monadic version see unfoldForestM_BF.

unfoldTreeM :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a) Source #

Monadic tree builder, in depth-first order.

unfoldForestM :: Monad m => (b -> m (a, [b])) -> [b] -> m [Tree a] Source #

Monadic forest builder, in depth-first order

unfoldTreeM_BF :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a) Source #

Monadic tree builder, in breadth-first order.

See unfoldTree for more info.

Implemented using an algorithm adapted from /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design, by Chris Okasaki, ICFP'00/.

unfoldForestM_BF :: Monad m => (b -> m (a, [b])) -> [b] -> m [Tree a] Source #

Monadic forest builder, in breadth-first order

See unfoldForest for more info.

Implemented using an algorithm adapted from /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design, by Chris Okasaki, ICFP'00/.

Elimination

foldTree :: (a -> [b] -> b) -> Tree a -> b Source #

Fold a tree into a "summary" value in depth-first order.

For each node in the tree, apply f to the rootLabel and the result of applying f to each subForest.

This is also known as the catamorphism on trees.

Examples

Expand

Sum the values in a tree:

foldTree (\x xs -> sum (x:xs)) (Node 1 [Node 2 [], Node 3 []]) == 6

Find the maximum value in the tree:

foldTree (\x xs -> maximum (x:xs)) (Node 1 [Node 2 [], Node 3 []]) == 3

Count the number of leaves in the tree:

foldTree (\_ xs -> if null xs then 1 else sum xs) (Node 1 [Node 2 [], Node 3 []]) == 2

Find depth of the tree; i.e. the number of branches from the root of the tree to the furthest leaf:

foldTree (\_ xs -> if null xs then 0 else 1 + maximum xs) (Node 1 [Node 2 [], Node 3 []]) == 1

You can even implement traverse using foldTree:

traverse' f = foldTree (\x xs -> liftA2 Node (f x) (sequenceA xs))

Since: containers-0.5.8

flatten :: Tree a -> [a] Source #

Returns the elements of a tree in pre-order.

  a
 / \    => [a,b,c]
b   c

Examples

Expand

flatten (Node 1 [Node 2 [], Node 3 []]) == [1,2,3]

levels :: Tree a -> [[a]] Source #

Returns the list of nodes at each level of the tree.

  a
 / \    => [[a], [b,c]]
b   c

Examples

Expand

levels (Node 1 [Node 2 [], Node 3 []]) == [[1],[2,3]]

Ascii Drawings

drawTree :: Tree String -> String Source #

2-dimensional ASCII drawing of a tree.

Examples

Expand

putStr $ drawTree $ fmap show (Node 1 [Node 2 [], Node 3 []])

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+- 2
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`- 3

drawForest :: [Tree String] -> String Source #

2-dimensional ASCII drawing of a forest.

Examples

Expand

putStr $ drawForest $ map (fmap show) [(Node 1 [Node 2 [], Node 3 []]), (Node 10 [Node 20 []])]

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+- 2
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`- 3

10
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`- 20