Data.Tree

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

Returns the elements of a tree in pre-order.

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

Examples

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

2-dimensional ASCII drawing of a forest.

Examples

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

1
|
+- 2
|
`- 3

10
|
`- 20

2-dimensional ASCII drawing of a tree.

Examples

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

1
|
+- 2
|
`- 3

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

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))

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

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

Examples

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

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.

Monadic forest builder, in depth-first order

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.

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

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
|
+- 2
|  |
|  +- 4
|  |
|  `- 5
|
`- 3
   |
   +- 6
   |
   `- 7

Monadic tree builder, in depth-first order.

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.

This type synonym exists primarily for historical reasons.