Data.Tree.Util

Tree-related utilities.

Documentation

>>> :{
let myTree = Node 0 [ Node 1 []
                    , Node 2 []
                    , Node 3 [ Node 4 [] ]
                    ]
:}

data TreeNode v a

Nodes in a tree are typically either an internal node or a leaf node

Constructors

InternalNode v

LeafNode a

Instances

Bifunctor TreeNode

Defined in Data.Tree.Util

Methods

bimap :: (a -> b) -> (c -> d) -> TreeNode a c -> TreeNode b d

first :: (a -> b) -> TreeNode a c -> TreeNode b c

second :: (b -> c) -> TreeNode a b -> TreeNode a c

Bitraversable TreeNode

Defined in Data.Tree.Util

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> TreeNode a b -> f (TreeNode c d)

Bifoldable TreeNode

Defined in Data.Tree.Util

Methods

bifold :: Monoid m => TreeNode m m -> m

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> TreeNode a b -> m

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> TreeNode a b -> c

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> TreeNode a b -> c

(Eq v, Eq a) => Eq (TreeNode v a)

Defined in Data.Tree.Util

Methods

(==) :: TreeNode v a -> TreeNode v a -> Bool

(/=) :: TreeNode v a -> TreeNode v a -> Bool

(Show v, Show a) => Show (TreeNode v a)

Defined in Data.Tree.Util

Methods

showsPrec :: Int -> TreeNode v a -> ShowS

show :: TreeNode v a -> String

showList :: [TreeNode v a] -> ShowS

_TreeNodeEither :: Iso' (TreeNode v p) (Either v p)

A TreeNode is isomorphic to Either

Zipper on rose trees

data Zipper a

Zipper for rose trees

Constructors

Zipper

Fields

• focus :: Tree a
• ancestors :: [([Tree a], a, [Tree a])]

Instances

Eq a => Eq (Zipper a)

Defined in Data.Tree.Util

Methods

(==) :: Zipper a -> Zipper a -> Bool

(/=) :: Zipper a -> Zipper a -> Bool

Show a => Show (Zipper a)

Defined in Data.Tree.Util

Methods

showsPrec :: Int -> Zipper a -> ShowS

show :: Zipper a -> String

showList :: [Zipper a] -> ShowS

root :: Tree a -> Zipper a

Create a new zipper focussiong on the root.

up :: Zipper a -> Maybe (Zipper a)

Move the focus to the parent of this node.

firstChild :: Zipper a -> Maybe (Zipper a)

Move the focus to the first child of this node.

>>> firstChild $ root myTree
Just (Zipper {focus = Node {rootLabel = 1, subForest = []}, ancestors = [([],0,[Node {rootLabel = 2, subForest = []},Node {rootLabel = 3, subForest = [Node {rootLabel = 4, subForest = []}]}])]})

nextSibling :: Zipper a -> Maybe (Zipper a)

Move the focus to the next sibling of this node

>>> (firstChild $ root myTree) >>= nextSibling
Just (Zipper {focus = Node {rootLabel = 2, subForest = []}, ancestors = [([Node {rootLabel = 1, subForest = []}],0,[Node {rootLabel = 3, subForest = [Node {rootLabel = 4, subForest = []}]}])]})

prevSibling :: Zipper a -> Maybe (Zipper a)

Move the focus to the next sibling of this node

allChildren :: Zipper a -> [Zipper a]

Given a zipper that focussses on some subtree t, construct a list with zippers that focus on each child.

allTrees :: Zipper a -> [Zipper a]

Given a zipper that focussses on some subtree t, construct a list with zippers that focus on each of the nodes in the subtree of t.

unZipperLocal :: Zipper a -> Tree a

Creates a new tree from the zipper that thas the current node as root. The ancestorTree (if there is any) forms the first child in this new root.

constructTree :: [([Tree a], a, [Tree a])] -> Maybe (Tree a)

Constructs a tree from the list of ancestors (if there are any)

findEvert :: (a -> Bool) -> Tree a -> Maybe (Tree a)

Given a predicate on an element, find a node that matches the predicate, and turn that node into the root of the tree.

running time: \(O(nT)\) where \(n\) is the size of the tree, and \(T\) is the time to evaluate a predicate.

>>> findEvert (== 4) myTree
Just (Node {rootLabel = 4, subForest = [Node {rootLabel = 3, subForest = [Node {rootLabel = 0, subForest = [Node {rootLabel = 1, subForest = []},Node {rootLabel = 2, subForest = []}]}]}]})
>>> findEvert (== 5) myTree
Nothing

findEvert' :: (Tree a -> Bool) -> Tree a -> Maybe (Tree a)

Given a predicate matching on a subtree, find a node that matches the predicate, and turn that node into the root of the tree.

running time: \(O(nT(n))\) where \(n\) is the size of the tree, and \(T(m)\) is the time to evaluate a predicate on a subtree of size \(m\).

findPath

Arguments

:: (a -> Bool)

is this node a starting node

-> (a -> Bool)

is this node an ending node

-> Tree a

-> Maybe [a]

Function to extract a path between a start node and an end node (if such a path exists). If there are multiple paths, no guarantees are given about which one is returned.

running time: \(O(n(T_p+T_s)\), where \(n\) is the size of the tree, and \(T_p\) and \(T_s\) are the times it takes to evaluate the isStartingNode and isEndingNode predicates.

>>> findPath (== 1) (==4) myTree
Just [1,0,3,4]
>>> findPath (== 1) (==2) myTree
Just [1,0,2]
>>> findPath (== 1) (==1) myTree
Just [1]
>>> findPath (== 1) (==2) myTree
Just [1,0,2]
>>> findPath (== 4) (==2) myTree
Just [4,3,0,2]

findNode :: (a -> Bool) -> Tree a -> Maybe [a]

Given a predicate on a, find (the path to) a node that satisfies the predicate.

>>> findNode (== 4) myTree
Just [0,3,4]

findNodes :: (Tree a -> Bool) -> Tree a -> [[a]]

Find all paths to nodes that satisfy the predicate

running time: \(O(nT(n))\) where \(n\) is the size of the tree, and \(T(m)\) is the time to evaluate a predicate on a subtree of size \(m\).

>>> findNodes ((< 4) . rootLabel) myTree
[[0],[0,1],[0,2],[0,3]]
>>> findNodes (even . rootLabel) myTree
[[0],[0,2],[0,3,4]]
>>> let size = length in findNodes ((> 1) . size) myTree
[[0],[0,3]]

levels :: Tree a -> NonEmpty (NonEmpty a)

BFS Traversal of the rose tree that decomposes it into levels.

running time: \(O(n)\)