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TreeLevel
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TreeLevel

[Experimental]

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TreeLevel[tree,levelspec]

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

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TreeLevel[tree,levelspecelem]

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

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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

open allclose all

Basic Examples  (3)Summary of the most common use cases

Extract the subtrees on the second level:

In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-ynsdz6
Out[2]=2

Extract the data on a range of levels:

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-x1c5g2
Out[1]=1

Use the operator form of TreeLevel:

In[1]:=1
✖
https://wolfram.com/xid/0i1mnkxwu-x8v6xu
Out[1]=1

Scope  (8)Survey of the scope of standard use cases

Level Specifications  (7)

Extract the subtrees on all levels:

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-70t03t
Out[1]=1

Extract the subtrees on levels 1, 2 and 3:

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-u64yj5
In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-o94lnv
Out[2]=2

Extract the subtrees only on level 3:

In[3]:=3
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https://wolfram.com/xid/0i1mnkxwu-4csw25
Out[3]=3

Extract levels 0 through 2:

In[4]:=4
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https://wolfram.com/xid/0i1mnkxwu-s2gdvt
Out[4]=4

Extract all levels, starting at level 1:

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-eg4ctt
Out[1]=1

Extract also level 0:

In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-1vzax2
Out[2]=2

Negative levels:

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-effz78
In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-mnssvw
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0i1mnkxwu-ppusdz
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0i1mnkxwu-yuv5x2
Out[4]=4

Positive and negative levels can be mixed:

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-feddft
Out[1]=1

Extract the leaves:

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-ylvvnp
Out[1]=1

Extract the non-leaves:

In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-besmsn
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-ym9b5o
Out[1]=1

Elements  (1)

Extract the subtrees (default):

In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-rmgi1y
Out[2]=2

Extract the data:

In[3]:=3
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https://wolfram.com/xid/0i1mnkxwu-qj5son
Out[3]=3

Options  (3)Common values & functionality for each option

TreeTraversalOrder  (3)

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

In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-5tcyv1
Out[2]=2

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

In[4]:=4
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https://wolfram.com/xid/0i1mnkxwu-17bium
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-clwpbg
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-4765gg
Out[1]=1

Applications  (2)Sample problems that can be solved with this function

Extract subtrees at successive levels from the root:

In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-2gr6y3
Out[2]=2

Extract subtrees at successive levels from the bottom:

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-w2yqhk
Out[1]=1

Properties & Relations  (4)Properties of the function, and connections to other functions

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

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-rkjw55
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-10kek8
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0i1mnkxwu-9nlt0t
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-thglzm
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-hyca58
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0i1mnkxwu-3lofev
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-epadq4
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-x6ybmf
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0i1mnkxwu-hsc0zr
Out[3]=3

TreeLeaves gives the subtrees at level -1:

In[1]:=1
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https://wolfram.com/xid/0i1mnkxwu-4k9bjm
In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-4gdab5
Out[2]=2

Possible Issues  (1)Common pitfalls and unexpected behavior

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

In[2]:=2
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https://wolfram.com/xid/0i1mnkxwu-vi9w5r
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0i1mnkxwu-hgamyh
Out[3]=3
Wolfram Research (2021), TreeLevel, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeLevel.html (updated 2022).
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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).

✖
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.

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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

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

BibTeX

@misc{reference.wolfram_2025_treelevel, author="Wolfram Research", title="{TreeLevel}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/TreeLevel.html}", note=[Accessed: 28-May-2025 ]}

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@misc{reference.wolfram_2025_treelevel, author="Wolfram Research", title="{TreeLevel}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/TreeLevel.html}", note=[Accessed: 28-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_treelevel, organization={Wolfram Research}, title={TreeLevel}, year={2022}, url={https://reference.wolfram.com/language/ref/TreeLevel.html}, note=[Accessed: 28-May-2025 ]}

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@online{reference.wolfram_2025_treelevel, organization={Wolfram Research}, title={TreeLevel}, year={2022}, url={https://reference.wolfram.com/language/ref/TreeLevel.html}, note=[Accessed: 28-May-2025 ]}