TreeCases

TreeCases[tree,pattern]

gives a list of subtrees of tree with data matching pattern.

TreeCases[tree,pattern,levelspec]

gives a list of all subtrees of tree on levels specified by levelspec with data that matches the pattern.

TreeCases[tree,pattern,levelspec,n]

gives the first n subtrees in tree with data that matches the pattern.

TreeCases[pattern]

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

Details

  • TreeCases lists the subtrees with data matching any pattern on any range of levels in a Tree object. The list of matches can be given in many different orders, including depth-first and breadth-first traversals.
  • TreeCases[tree,pattern] tests all the subtrees of tree in turn to try to find ones with data that matches pattern.
  • TreeCases 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 TreeCases is {0,Infinity}.
  • TreeCases traverses subtrees in a left-to-right, depth-first order, with children visited before their parents.
  • TreeCases[,TreeTraversalOrderorder] allows visiting subtrees in different orders, such as depth-first and breadth-first traversals.
  • TreeCases[pattern][tree] is equivalent to TreeCases[tree,pattern].

Examples

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Basic Examples  (4)

Find the subtrees whose data is an even number:

Find the inner subtrees whose data is an even number:

Find the first three subtrees whose data is a prime number:

Use the operator form of TreeCases:

Scope  (6)

Find the subtrees whose data is an odd integer:

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

Find the leaf subtrees whose data is an odd integer:

Find the inner subtrees whose data is an odd integer:

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

Use TreeCases as an operator form in a tree position specification:

Options  (3)

TreeTraversalOrder  (3)

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

Specify a top-down, right-to-left variant:

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

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

Properties & Relations  (5)

TreeCases extracts the positions given by TreePosition:

TreeCount gives the number of matching subtrees given by TreeCases:

TreeCases[tree,pattern,Infinity] is equivalent to TreeChildren@TreeExtract[tree,TreeCases[pattern]]:

Cases[expr,pattern,levelspec] is equivalent to TreeData/@TreeCases[ExpressionTree[expr,"Subexpressions"],pattern,levelspec]:

Cases[expr,pattern,levelspec,HeadsTrue] is equivalent to TreeData/@TreeCases[ExpressionTree[expr,"Subexpressions",HeadsTrue],pattern,levelspec] for positive levels:

Possible Issues  (1)

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

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2022_treecases, author="Wolfram Research", title="{TreeCases}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/TreeCases.html}", note=[Accessed: 29-September-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_treecases, organization={Wolfram Research}, title={TreeCases}, year={2021}, url={https://reference.wolfram.com/language/ref/TreeCases.html}, note=[Accessed: 29-September-2022 ]}