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TreePosition[tree,pattern]

gives a list of the positions of subtrees of tree whose data matches pattern.

TreePosition[tree,pattern,levelspec]

finds only matches that appear on levels of tree specified by levelspec.

TreePosition[tree,pattern,levelspec,n]

gives the positions of the first n matches found.

TreePosition[pattern]

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

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
TreeTraversalOrder  
Applications  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page

TreePosition

TreePosition[tree,pattern]

gives a list of the positions of subtrees of tree whose data matches pattern.

TreePosition[tree,pattern,levelspec]

finds only matches that appear on levels of tree specified by levelspec.

TreePosition[tree,pattern,levelspec,n]

gives the positions of the first n matches found.

TreePosition[pattern]

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

Details and Options

  • TreePosition lists the positions of data matching any pattern on any range of levels in a Tree object. The list of matching positions can be given in many different orders, including depth-first and breadth-first traversals.
  • TreePosition[tree,pattern] tests all the subtrees of tree in turn to try to find ones with data that match pattern.
  • TreePosition returns a list of positions in a form suitable for use in TreeExtract, TreeReplacePart and TreeDelete.
  • A part specification {} returned by TreePosition represents the whole of tree.
  • TreePosition uses standard level specifications as in TreeLevel:
  • nlevels 1 through n
    Alllevels 0 through Infinity
    Infinitylevels 1 through Infinity
    {n}level n only
    {n1,n2}levels n1 through n2
  • The default value for levelspec in TreePosition is {0,Infinity}.
  • TreePosition traverses subtrees in a left-to-right, depth-first order, yielding lists of indices in lexicographic order.
  • TreePosition[…,TreeTraversalOrderorder] allows visiting subtrees in different orders, such as depth-first and breadth-first traversals.
  • TreePosition[pattern][tree] is equivalent to TreePosition[tree,pattern].

Examples

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Basic Examples  (4)

Find the positions of the subtrees whose data is an even number:

Wolfram Language code: TreePosition[[image], _ ? EvenQ]

Find the positions of the inner subtrees whose data is an even number:

Wolfram Language code: TreePosition[[image], _ ? EvenQ, {0, -2}]

Find the first three positions of prime numbers:

Wolfram Language code: TreePosition[[image], _ ? PrimeQ, All, 3]

Use the operator form of TreePosition:

Wolfram Language code: TreePosition[9][[image]]

Scope  (5)

Find the positions of the subtrees whose data is an odd integer:

Wolfram Language code: TreePosition[[image], _ ? OddQ]

Find the positions of the subtrees at levels 1 and 2 whose data is an odd integer:

Wolfram Language code: TreePosition[[image], _ ? OddQ, 2]

Find the positions of the leaf subtrees whose data is an odd integer:

Wolfram Language code: TreePosition[[image], _ ? OddQ, {-1}]

Find the positions of the inner subtrees whose data is an odd integer:

Wolfram Language code: TreePosition[[image], _ ? OddQ, {0, -2}]

Find the first four positions of the subtrees whose data is an odd integer:

Wolfram Language code: TreePosition[[image], _ ? OddQ, All, 4]

Options  (3)

TreeTraversalOrder  (3)

By default, subtrees are visited in a depth-first order, with parents visited after their children:

Wolfram Language code: TreePosition[[image], _, TreeTraversalOrder -> "DepthFirst"]

Specify a top-down variant:

Wolfram Language code: TreePosition[[image], _, TreeTraversalOrder -> {"DepthFirst", "TopDown"}]

This lists the positions in lexicographic order:

Wolfram Language code: LexicographicSort[%]

Visit subtrees in a breadth-first order, with nodes on the same level from the root visited before the nodes on the next level:

Wolfram Language code: TreePosition[[image], _, TreeTraversalOrder -> "BreadthFirst"]

This lists the positions in canonical order:

Wolfram Language code: Sort[%]

Visit subtrees in a leaves-first order, with nodes on the same level from the leaves visited before the nodes on the next level:

Wolfram Language code: TreePosition[[image], _, TreeTraversalOrder -> "LeavesFirst"]

Applications  (1)

Compute the level with the most nodes:

Wolfram Language code: Commonest[Length /@ TreePosition[[image], _]]

Properties & Relations  (4)

TreeCases extracts the positions given by TreePosition:

Wolfram Language code: tree = [image];
Wolfram Language code: TreeCases[tree, _ ? PrimeQ]
Wolfram Language code: TreePosition[tree, _ ? PrimeQ]
Wolfram Language code: TreeExtract[tree, %]

TreeCount gives the number of matching positions given by TreePosition:

Wolfram Language code: TreePosition[[image], x]
Wolfram Language code: TreeCount[[image], x]

Position[expr,pattern,levelspec,HeadsFalse] is equivalent to TreePosition[ExpressionTree[expr,"Subexpressions"],pattern,levelspec]:

Wolfram Language code: Position[{{1, 4, a, 0}, {b, 3, 2, 2}, {c, c, 5, 5}}, _, All, Heads -> False]
Wolfram Language code: ExpressionTree[{{1, 4, a, 0}, {b, 3, 2, 2}, {c, c, 5, 5}}, "Subexpressions"]
Wolfram Language code: TreePosition[%, _, All]

Position[expr,pattern,levelspec] is equivalent to TreePosition[ExpressionTree[expr,"Subexpressions",HeadsTrue],pattern,levelspec]-1 for positive levels:

Wolfram Language code: Position[{1, 2, f[a, b]}, _, {0, Infinity}]
Wolfram Language code: ExpressionTree[{1, 2, f[a, b]}, "Subexpressions", Heads -> True]
Wolfram Language code: TreePosition[%, _, {0, Infinity}]
Wolfram Language code: % - 1

Possible Issues  (1)

TreePosition by default starts at level 1, so does not visit the root:

Wolfram Language code: TreePosition[[image], _, 1]
Wolfram Language code: TreePosition[[image], _, {0, 1}]
Wolfram Research (2021), TreePosition, Wolfram Language function, https://reference.wolfram.com/language/ref/TreePosition.html (updated 2021).

Text

Wolfram Research (2021), TreePosition, Wolfram Language function, https://reference.wolfram.com/language/ref/TreePosition.html (updated 2021).

CMS

Wolfram Language. 2021. "TreePosition." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/TreePosition.html.

APA

Wolfram Language. (2021). TreePosition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TreePosition.html

BibTeX

@misc{reference.wolfram_2026_treeposition, author="Wolfram Research", title="{TreePosition}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/TreePosition.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_treeposition, organization={Wolfram Research}, title={TreePosition}, year={2021}, url={https://reference.wolfram.com/language/ref/TreePosition.html}, note=[Accessed: 13-June-2026]}