TreeLevel

TreeLevel[tree,levelspec]

gives a list of all subtrees of tree on levels specified by levelspec.

TreeLevel[tree,levelspecelem]

gives a list of the element elem of subtrees on levels specified by levelspec.

TreeLevel[levelspec]

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

Details and Options

  • TreeLevel lists the subtrees on any range of levels in a Tree object. The list of subtrees can be given in many different orders, including depth-first and breadth-first traversals.
  • TreeLevel[tree,levelspec] gives a list of the subtrees on the given levels. This can also be expressed as TreeLevel[tree,levelspec"Subtree"].
  • TreeLevel[tree,levelspec"Data"] gives a list of the data on the given levels.
  • TreeLevel uses standard level specifications:
  • nlevels 1 through n
    Alllevels 0 through Infinity
    Infinitylevels 1 through Infinity
    {n}level n only
    {n1,n2}levels n1 through n2
    "Leaves"level -1 only
    "NonLeaves"levels 0 through -2
  • A positive level n+1 consists of all subtrees of tree that are children of subtrees on level n.
  • Level 0 corresponds to the root of the tree.
  • Level -1 corresponds to the leaves.
  • A negative level -(n+1) consists of all subtrees whose children are on levels -1, -2, …, -n, with highest level -n.
  • TreeLevel traverses subtrees in a left-to-right, depth-first order, with children visited before their parents.
  • TreeLevel[…,TreeTraversalOrderorder] allows visiting subtrees in different orders, such as depth-first and breadth-first traversals.
  • TreeLevel[levelspec][tree] is equivalent to TreeLevel[tree,levelspec].

Examples

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Basic Examples  (3)

Extract the subtrees on the second level:

Extract the data on a range of levels:

Use the operator form of TreeLevel:

Scope  (8)

Level Specifications  (7)

Extract the subtrees on all levels:

Extract the subtrees on levels 1, 2 and 3:

Extract the subtrees only on level 3:

Extract levels 0 through 2:

Extract all levels, starting at level 1:

Extract also level 0:

Negative levels:

Positive and negative levels can be mixed:

Extract the leaves:

Extract the non-leaves:

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

Elements  (1)

Extract the subtrees (default):

Extract the data:

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:

Applications  (2)

Extract subtrees at successive levels from the root:

Extract subtrees at successive levels from the bottom:

Properties & Relations  (4)

TreeLevel[tree,levelspec] is equivalent to TreeChildren@TreeExtract[tree,TreeLevel[levelspec]]:

Level[expr,levelspec] is equivalent to TreeLevel[ExpressionTree[expr,"Subexpressions"],levelspec"Data"]:

Level[expr,levelspec,HeadsTrue] is equivalent to TreeLevel[ExpressionTree[expr,"Subexpressions",HeadsTrue],levelspec"Data"] for positive levels:

TreeLeaves gives the subtrees at level -1:

Possible Issues  (1)

TreeLevel by default starts at level 1, so does not extract the whole tree:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2023_treelevel, author="Wolfram Research", title="{TreeLevel}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/TreeLevel.html}", note=[Accessed: 19-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2023_treelevel, organization={Wolfram Research}, title={TreeLevel}, year={2022}, url={https://reference.wolfram.com/language/ref/TreeLevel.html}, note=[Accessed: 19-April-2024 ]}