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TreeDepth[tree]

gives the maximum level of tree.

TreeDepth[tree,pattern]

gives the maximum level of the subtree with data matching pattern.

Details
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Basic Examples  
Scope  
Properties & Relations  
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TreeDepth

TreeDepth[tree]

gives the maximum level of tree.

TreeDepth[tree,pattern]

gives the maximum level of the subtree with data matching pattern.

Details

  • TreeDepth can give the maximum level of the subtree with data matching any pattern in a Tree object.
  • The depth of a tree is the maximum number of prior levels needed to reach the root from the leaves.
  • When counting the maximum level of a tree, empty lists of children contribute one level. »

Examples

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Basic Examples  (2)

Find the depth of a tree:

Wolfram Language code: TreeDepth[[image]]

Find the depth of an expression matching a pattern:

Wolfram Language code: TreeDepth[[image], 5]

Scope  (3)

Find the depth of a tree:

Wolfram Language code: TreeDepth[[image]]

Find the depth of a literal expression in a tree:

Wolfram Language code: tree = [image];
Wolfram Language code: TreeDepth[tree, Times]

If the expression appears in multiple nodes, TreeDepth gives the maximum depth:

Wolfram Language code: TreeDepth[tree, Power]

Find the depth of an expression matching an arbitrary pattern:

Wolfram Language code: TreeDepth[[image], n_ ? Negative]

Properties & Relations  (6)

TreeDepth[tree] is generally equivalent to TreeDepth[tree,_]:

Wolfram Language code: TreeDepth[[image]]
Wolfram Language code: TreeDepth[[image], _]

In TreeDepth[tree], empty lists of children contribute one level:

Wolfram Language code: TreeDepth[Tree[data, {}]]
Wolfram Language code: TreeDepth[Tree[data, {}], _]

TreeDepth[Tree[{tree1,tree2,…}]] gives 1+Max[TreeDepth[tree1],TreeDepth[tree2],…]:

Wolfram Language code: TreeDepth[[image]]
Wolfram Language code: % === 1 + Max[TreeDepth[[image]], TreeDepth[[image]]]

TreeDepth[Tree[data,None]] gives 0:

Wolfram Language code: TreeDepth[[image]]

TreeDepth[Tree[data,{}]] gives 1:

Wolfram Language code: TreeDepth[[image]]

TreeDepth can be computed using TreeFold:

Wolfram Language code: TreeDepth[[image]]
Wolfram Language code: % === TreeFold[{1 + Max@@#2&, 0&}, [image]]

Depth[expr] is equivalent to 1+TreeDepth[ExpressionTree[expr,"Subexpressions"]]:

Wolfram Language code: Depth[f[g, h[1]][x[2, 3], y[z]]]
Wolfram Language code: ExpressionTree[f[g, h[1]][x[2, 3], y[z]], "Subexpressions"]
Wolfram Language code: 1 + TreeDepth[%]

Depth[expr,HeadsTrue] is equivalent to 1+TreeDepth[ExpressionTree[expr,"Subexpressions",HeadsTrue]]:

Wolfram Language code: Depth[f[g, h[1]][x[2, 3], y[z]], Heads -> True]
Wolfram Language code: ExpressionTree[f[g, h[1]][x[2, 3], y[z]], "Subexpressions", Heads -> True]
Wolfram Language code: 1 + TreeDepth[%]
Wolfram Research (2021), TreeDepth, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeDepth.html (updated 2022).

Text

Wolfram Research (2021), TreeDepth, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeDepth.html (updated 2022).

CMS

Wolfram Language. 2021. "TreeDepth." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/TreeDepth.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_treedepth, author="Wolfram Research", title="{TreeDepth}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/TreeDepth.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_treedepth, organization={Wolfram Research}, title={TreeDepth}, year={2022}, url={https://reference.wolfram.com/language/ref/TreeDepth.html}, note=[Accessed: 13-June-2026]}