Wolfram Language & System Documentation Center

TreeExtract

TreeExtract[tree,pos]

extracts the subtree of tree at the position specified by pos.

TreeExtract[tree,{pos₁,pos₂,…}]

extracts a list of subtrees of tree.

TreeExtract[tree,pos,h]

extracts subtrees of tree, applying h to each subtree.

TreeExtract[pos]

represents an operator form of TreeExtract that can be applied to a tree.

Details

TreeExtract allows extraction of properties of subtrees at any position in a Tree object.
For integers i, j, …, TreeExtract[tree,{i,j,…}] extracts the subtree at position {i,j,…}. »
TreeExtract can use the position specifications returned by TreePosition as well as extended forms as used in functions such as TreeInsert and TreeReplacePart. »
An individual position specification pos can be given as {part₁,part₂,…}, where part specifications part_i include:

	i	the i child
	-i	the i child from the end
	{i₁,i₂,…}	the list of children with part numbers i₁, i₂, …
	All	all children
	m;;n	children m through n
	"key"	the child whose key is "key"
	Key[k]	the child with an arbitrary key k
	TreeLevel[levelspec]	the subtrees on levels specified by levelspec
	TreeCases[pattern]	the subtrees with data matching pattern
	TreeSelect[crit]	the subtrees for which crit gives True

In TreeExtract[tree,{p₁,p₂,…}], {p₁,p₂,…} is interpreted as a list of individual position specifications if all the p_i are lists. Otherwise, {p₁,p₂,…} will be taken to be an individual position specification. »
Specifications that extract multiple parts at one level retain the data at that level. »
TreeExtract works on trees containing an Association of subtrees, using the same specification for keys as in Part. »
TreeExtract[pos][tree] is equivalent to TreeExtract[tree,pos].

Examples

open all close all

Basic Examples (4)

Extract the second child of a tree:

Wolfram Language code: TreeExtract[[image], {2}]

Extract a subtree at any position:

Wolfram Language code: TreeExtract[[image], {3, 3}]

Extract a list of subtrees at several positions:

Wolfram Language code: TreeExtract[[image], {{1}, {2, 1}, {3, 3, 1}}]

Perform independent extractions at consecutive levels:

Wolfram Language code: TreeExtract[[image], {All, 2}]

Use the operator form of TreeExtract:

Wolfram Language code: TreeExtract[2][[image]]

Scope (23)

Part Specifications (9)

Extract the first child:

Wolfram Language code: TreeExtract[[image], 1]

Extract the second child from the end:

Wolfram Language code: TreeExtract[[image], -2]

Extract all children:

Wolfram Language code: TreeExtract[[image], All]

Extract the children at odd positions:

Wolfram Language code: TreeExtract[[image], 1 ;; -1 ;; 2]

Use Key to specify position:

Wolfram Language code: TreeExtract[[image], Key["b"]]

For string keys, Key is not needed:

Wolfram Language code: TreeExtract[[image], "b"]

Extract subtrees on a range of levels:

Wolfram Language code: TreeExtract[[image], TreeLevel[3]]

Extract subtrees matching a data pattern:

Wolfram Language code: TreeExtract[[image], TreeCases[_ ? OddQ]]

Extract subtrees with exactly two children:

Wolfram Language code: TreeExtract[[image], TreeSelect[Length[TreeChildren[#]] == 2&]]

Extract using different specifications:

Wolfram Language code: TreeExtract[[image], {TreeLevel[{2}], TreeCases[_ ? OddQ]}]

Single versus Multiple Positions (3)

Extract a single subtree from a tree:

Wolfram Language code: TreeExtract[[image], {3}]

Extract several subtrees from a tree:

Wolfram Language code: TreeExtract[[image], {{1}, {4}, {3}}]

Extract the subtree at position {1,3}:

Wolfram Language code: tree = [image];

Wolfram Language code: TreeExtract[tree, {1, 3}]

Extract the first and third subtrees of a tree:

Wolfram Language code: TreeExtract[tree, {{1}, {3}}]

Extract a length-one list of positions from the tree:

Wolfram Language code: TreeExtract[tree, {{1, 3}}]

Extract several subtrees of the tree:

Wolfram Language code: TreeExtract[tree, {{1, 2}, {3, 3}, {2, 1}}]

Forms Involving All (2)

Extract the children of the second child:

Wolfram Language code: tree = [image];

Wolfram Language code: TreeExtract[tree, {2}]

Equivalently:

Wolfram Language code: TreeExtract[tree, {2, All}]

Extract the second child of each child:

Wolfram Language code: TreeExtract[tree, {All, 2}]

Extract the first and third child of each child:

Wolfram Language code: TreeExtract[tree, {All, {1, 3}}]

Extract the first and third child of each child separately:

Wolfram Language code: TreeExtract[tree, {{All, 1}, {All, 3}}]

Extracting using All preserves the data at that level:

Wolfram Language code: TreeExtract[[image], {All, 1}]

Associations (5)

Extract a subtree from a tree containing an association by key:

Wolfram Language code: TreeExtract[[image], {Key[expr]}]

If the key is a string, the Key wrapper is optional:

Wolfram Language code: TreeExtract[[image], {"str"}]

Extract a subtree from a tree containing an association by key:

Wolfram Language code: TreeExtract[[image], {Key[1]}]

Extract a subtree from a tree containing an association by position:

Wolfram Language code: TreeExtract[[image], {1}]

Extract several subtrees from a tree containing an association:

Wolfram Language code: TreeExtract[[image], {{1}, {Key[1]}}]

Extract a nested subtree from a tree containing an association:

Wolfram Language code: TreeExtract[[image], {Key[3], 1}]

Extract several nested subtrees from a tree containing an association:

Wolfram Language code: TreeExtract[[image], {{Key[3], 1}, {3, 1}}]

Spans and Sublists (4)

Extract the third through fifth children of a list:

Wolfram Language code: TreeExtract[[image], {3 ;; 5}]

Extract the children at odd positions:

Wolfram Language code: TreeExtract[[image], {1 ;; -1 ;; 2}]

Extract the first three children from each child:

Wolfram Language code: TreeExtract[[image], {All, 1 ;; 3}]

Extract the first and last child from each child:

Wolfram Language code: TreeExtract[[image], {All, {1, -1}}]

Extract the first child of the second through fourth children:

Wolfram Language code: tree = [image];

Wolfram Language code: TreeExtract[tree, {2 ;; 4, 1}]

Extract the second child of the first, third and fourth children:

Wolfram Language code: TreeExtract[tree, {{1, 3, 4}, 2}]

Extract the first, second and fifth children of the last three children:

Wolfram Language code: TreeExtract[tree, {-3 ;; -1, {1, 2, 5}}]

Extract the first and fifth children of each child:

Wolfram Language code: TreeExtract[tree, {All, {1, 5}}]

Properties & Relations (10)

Construct a tree from the heads in an expression:

Wolfram Language code: ExpressionTree[1[2[3, 4], 5[6, 7]], "Heads"]

TreeExtract extracts a subtree of a tree:

Wolfram Language code: TreeExtract[%, {1}]

This corresponds to extracting a subexpression of an expression:

Wolfram Language code: TreeExpression[%, "Heads"]

Extract can extract subexpressions directly:

Wolfram Language code: Extract[1[2[3, 4], 5[6, 7]], {1}]

If pos is not a list, pos and {pos} are equivalent specifications:

Wolfram Language code: tree = [image];

Wolfram Language code: TreeExtract[tree, 3] === TreeExtract[tree, {3}]

Wolfram Language code: TreeExtract[tree, 3 ;; 5] === TreeExtract[tree, {3 ;; 5}]

For a list of integers {i,j,…}, TreeExtract[tree,{i,j,…}] is equivalent to …@TreeExtract[j]@TreeExtract[i]@tree:

Wolfram Language code: TreeExtract[[image], {2, 3}] === TreeExtract[3]@TreeExtract[2]@[image]

TreeExtract[tree,{{i₁,j₁,…},{i₂,j₂,…},…}] is equivalent to {TreeExtract[tree,{i₁,j₁,…}],TreeExtract[tree,{i₂,j₂,…}],…}:

Wolfram Language code: tree = [image];

Wolfram Language code: TreeExtract[tree, {{1 ;; 2, 1}, {2 ;; 3, 2}}] === {TreeExtract[tree, {1 ;; 2, 1}], TreeExtract[tree, {2 ;; 3, 2}]}

This extends to the empty list:

Wolfram Language code: TreeExtract[tree, {}] === {}

Extracting position {} extracts the whole tree:

Wolfram Language code: TreeExtract[[image], {{}}]

TreeExtract extracts subtrees repeatedly if a position is mentioned repeatedly:

Wolfram Language code: TreeExtract[[image], {{1}, {3}, {1}}]

TreeExtract can use the lists of positions returned by TreePosition:

Wolfram Language code: tree = NestTree[Range[3# - 1, 3# + 1]&, 1, 2]

Wolfram Language code: TreePosition[tree, _ ? PrimeQ]

Wolfram Language code: TreeExtract[tree, %]

In TreeExtract[tree,{pos₁,pos₂,…},h], h wraps the result of extracting the subtrees at each of the pos_i:

Wolfram Language code: tree = [image];

Wolfram Language code: TreeExtract[tree, {{1, 2}, {3, 3}, {2, 1}}, h]

In TreeExtract[tree,pos,h], h wraps the result of extracting the subtree at position pos:

Wolfram Language code: TreeExtract[tree, {1, 2}, h]

Specifications that extract multiple parts at one level retain the data at that level:

Wolfram Language code: tree = [image];

Wolfram Language code: TreeExtract[tree, {All, 1}]

Wolfram Language code: TreeExtract[tree, {1 ;; 3, 1}]

Wolfram Language code: TreeExtract[tree, {{2, 4}, 1}]

TreeExtract[tree,{p₁,p₂,…}] treats {p₁,p₂,…} as a list of individual position specifications if all the p_i are lists:

Wolfram Language code: tree = [image];

For {{1,2},{3,4}}, the subtrees at positions {1,2} and {3,4} are extracted:

Wolfram Language code: TreeExtract[tree, {{1, 2}, {3, 4}}]

If any p_i is not a list, {p₁,p₂,…} is treated as a list of part specifications:

Wolfram Language code: TreeExtract[tree, {{1, 2}, 3}]

Wolfram Language code: TreeExtract[tree, {1, {3, 4}}]

For {{{1,2},{3,4}}}, parts 3 and 4 of parts 1 and 2 are extracted:

Wolfram Language code: TreeExtract[tree, {{{1, 2}, {3, 4}}}]

Possible Issues (2)

TreeExtract[tree,{}] returns an empty list of subtrees because the list of positions is empty:

Wolfram Language code: TreeExtract[[image], {}]

TreeExtract[tree,{{}}] extracts the subtree at position {}, which is the whole tree:

Wolfram Language code: TreeExtract[[image], {{}}]

A list of lists in the second argument is always interpreted as a list of position specifications:

Wolfram Language code: tree = [image];

Wolfram Language code: TreeExtract[tree, {{1, 2}}]

As a result, specifications that are equivalent in Part may be treated differently by TreeExtract:

Wolfram Language code: Part[TreeChildren[tree], {1, 2}] === Part[TreeChildren[tree], 1 ;; 2]

Wolfram Language code: TreeExtract[tree, {{1, 2}}] === TreeExtract[tree, {1 ;; 2}]

Use a list of lists and remove the extra list at the end if consistency between Part and TreeExtract is needed:

Wolfram Language code: First@TreeExtract[tree, {{{1, 2}}}] === First@TreeExtract[tree, {{1 ;; 2}}]

Top

More Learning

Tech Support

Wolfram Solutions

Wolfram Solutions For Education

Get Started

Grow Your Skills

Work with Us

Educational Programs for Adults

Educational Programs for Youth

Read

TreeExtract

Details

Examples

Basic Examples (4)

Scope (23)

Part Specifications (9)

Single versus Multiple Positions (3)

Forms Involving All (2)

Associations (5)

Spans and Sublists (4)

Properties & Relations (10)

Possible Issues (2)

Text

CMS

APA

BibTeX

BibLaTeX

TreeExtract

Details

Examples

Basic Examples (4)

Scope (23)

Part Specifications (9)

Single versus Multiple Positions (3)

Forms Involving All (2)

Associations (5)

Spans and Sublists (4)

Properties & Relations (10)

Possible Issues (2)

See Also

Related Guides

History

Text

CMS

APA

BibTeX

BibLaTeX