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TreeMap

Updated in 14[Experimental]

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TreeMap[f,tree]

applies f to the data of each subtree of tree.

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TreeMap[f,tree,levelspec]

applies f to the data of subtrees on levels of tree specified by levelspec.

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TreeMap[f,tree,levelspecelems]

applies f to the elements elems of subtrees on levels specified by levelspec.

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TreeMap[f]

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

Details and Options

  • TreeMap allows a function to be applied to elements of subtrees on any range of levels in a Tree object. The function can be applied to the subtrees in many orders, including depth-first and breadth-first traversals.
  • Structural elements elem for levelspecelem include:
  • Additional elements include:
  • "OriginalData"the original data of the subtree
    "OriginalChildren"the original children of the subtree
    "OriginalSubtree"the original subtree
    "OriginalChildrenData"the original data of the children
    "Position"the position of the subtree
    "Index"the index of the subtree in the list of siblings
    "LevelPair"the non-negative and negative levels of the subtree
    "Level"the non-negative level of the subtree from the root
    "NegativeLevel"the negative level of the subtree from the leaves
  • TreeMap uses standard level specifications as in TreeLevel:
  • nlevels 1 through n
    Infinitylevels 1 through Infinity
    {n}level n only
    {n1,n2}levels n1 through n2
    Alllevels 0 through Infinity
    "Leaves"level -1 only
    "NonLeaves"levels 0 through -2
  • The default value for levelspec in TreeMap is {0,Infinity}.
  • TreeMap traverses subtrees in a left-to-right, depth-first order, with children visited before their parents.
  • TreeMap has the same options as Tree, with the following addition:
  • TreeTraversalOrder Automaticvisit subtrees in different orders, such as depth-first and breadth-first traversals
  • TreeMap[f][tree] is equivalent to TreeMap[f,tree].

Examples

open allclose all

Basic Examples  (5)Summary of the most common use cases

Map f at the data of a tree:

In[2]:=2
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https://wolfram.com/xid/0enygxjns-uvu8cl
Out[2]=2

Map f on the specified levels:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-i86m1e
Out[1]=1

Map f at the subtrees of a tree:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-c3mwam
Out[2]=2

Supply the position as an additional argument:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-gpvc3r
Out[2]=2

Use the operator form of TreeMap:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-3p0osi
Out[1]=1

Scope  (12)Survey of the scope of standard use cases

Level Specifications  (5)

Map on all levels (default):

In[2]:=2
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https://wolfram.com/xid/0enygxjns-og41r1
In[3]:=3
✖
https://wolfram.com/xid/0enygxjns-ruefj2
Out[3]=3

Map on levels 1 through 2:

In[4]:=4
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https://wolfram.com/xid/0enygxjns-zzwnef
Out[4]=4

Map only on level 2:

In[5]:=5
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https://wolfram.com/xid/0enygxjns-liiocn
Out[5]=5

Map on levels 0 through 2:

In[6]:=6
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https://wolfram.com/xid/0enygxjns-x26jum
Out[6]=6

Map on all levels, starting at level 1:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-dw2a13
Out[1]=1

Map also on level 0:

In[2]:=2
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https://wolfram.com/xid/0enygxjns-zjk81
Out[2]=2

Negative levels:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-uxkye4
In[2]:=2
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https://wolfram.com/xid/0enygxjns-2vkget
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0enygxjns-g3zrna
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0enygxjns-zj65f7
Out[4]=4

Positive and negative levels can be mixed:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-ilts77
Out[1]=1

Map on the leaves:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-4n99bf
Out[1]=1

Map on the non-leaves:

In[2]:=2
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https://wolfram.com/xid/0enygxjns-ipt3km
Out[2]=2

Elements  (7)

Map at the data (default):

In[2]:=2
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https://wolfram.com/xid/0enygxjns-limfmi
Out[2]=2

Map at the original data:

In[4]:=4
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https://wolfram.com/xid/0enygxjns-4c8lnu
Out[4]=4

Map at the subtrees:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-7widce
Out[2]=2

Map at the original subtrees:

In[2]:=2
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https://wolfram.com/xid/0enygxjns-7lxnya
Out[4]=4

Map at the children:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-2toz6g
Out[2]=2

Map at the original children:

In[2]:=2
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https://wolfram.com/xid/0enygxjns-u54uun
Out[4]=4

Map at the data of the children:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-cphd62
Out[2]=2

Map at the original data of the children:

In[2]:=2
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https://wolfram.com/xid/0enygxjns-xpza0n
Out[4]=4

Supply the position as an additional argument:

In[1]:=1
✖
https://wolfram.com/xid/0enygxjns-os1lu9
Out[2]=2

Supply the index rather than the position:

In[2]:=2
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https://wolfram.com/xid/0enygxjns-o8up9f
Out[4]=4

Supply the level specifications as an additional argument:

In[1]:=1
✖
https://wolfram.com/xid/0enygxjns-3eo7d1
Out[2]=2

Supply the level rather than both level specifications:

In[2]:=2
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https://wolfram.com/xid/0enygxjns-8t8lih
Out[4]=4

Supply the negative level rather than both level specifications:

In[3]:=3
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https://wolfram.com/xid/0enygxjns-t7i43a
Out[6]=6

Supply a sequence of elements as arguments:

In[1]:=1
✖
https://wolfram.com/xid/0enygxjns-z3ggwx
Out[2]=2

Options  (3)Common values & functionality for each option

TreeTraversalOrder  (3)

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

In[2]:=2
✖
https://wolfram.com/xid/0enygxjns-5tcyv1
Out[3]=3

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

In[5]:=5
✖
https://wolfram.com/xid/0enygxjns-kk8x29
Out[6]=6

Visit 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
✖
https://wolfram.com/xid/0enygxjns-osp4wq
Out[1]=1

Visit 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
✖
https://wolfram.com/xid/0enygxjns-r7lxyi
Out[1]=1

Properties & Relations  (6)Properties of the function, and connections to other functions

Children are visited before their parents:

In[2]:=2
✖
https://wolfram.com/xid/0enygxjns-8402bf
Out[1]=1
Out[2]=2

TreeScan does the same as TreeMap but without returning a result:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-cjhvh1
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0enygxjns-rq2wqe
Out[3]=3
Out[2]=2

TreeMap[f,tree,levelspec] is equivalent to TreeMapAt[f,tree,TreeLevel[levelspec]]:

In[1]:=1
✖
https://wolfram.com/xid/0enygxjns-39l2x5
Out[1]=1

Construct a tree from the heads in an expression:

In[1]:=1
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https://wolfram.com/xid/0enygxjns-rdybzq
Out[1]=1

TreeMap maps on the data of subtrees in a tree:

In[2]:=2
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https://wolfram.com/xid/0enygxjns-ua6c1d
Out[2]=2

This corresponds to mapping on the heads and leaves in an expression:

In[3]:=3
✖
https://wolfram.com/xid/0enygxjns-xohbvz
Out[3]=3

Map can map on the heads and leaves directly:

In[4]:=4
✖
https://wolfram.com/xid/0enygxjns-2swenz
In[5]:=5
✖
https://wolfram.com/xid/0enygxjns-05t4xe
Out[5]=5

Construct a tree from the atoms in an expression:

In[1]:=1
✖
https://wolfram.com/xid/0enygxjns-7bxt43
Out[1]=1

TreeMap can map on the data of just the leaves in a tree:

In[2]:=2
✖
https://wolfram.com/xid/0enygxjns-r3ek67
Out[2]=2

This corresponds to mapping on the atoms in an expression:

In[3]:=3
✖
https://wolfram.com/xid/0enygxjns-ro9mlw
Out[3]=3

Map can map on the atoms in an expression directly:

In[4]:=4
✖
https://wolfram.com/xid/0enygxjns-s0zk5i
Out[4]=4

TreeFold applies a function to the data and results for the children:

In[1]:=1
✖
https://wolfram.com/xid/0enygxjns-i1962k
Out[1]=1

TreeMap can compute the same result:

In[2]:=2
✖
https://wolfram.com/xid/0enygxjns-mh0fxu
Out[4]=4

The new data of the root is the result of TreeFold:

In[3]:=3
✖
https://wolfram.com/xid/0enygxjns-krmvr5
Out[3]=3

Possible Issues  (1)Common pitfalls and unexpected behavior

TreeMap by default starts at level 1, so does not apply the function to the whole tree:

In[2]:=2
✖
https://wolfram.com/xid/0enygxjns-obmaad
Out[2]=2
In[4]:=4
✖
https://wolfram.com/xid/0enygxjns-hd3y18
Out[4]=4
Wolfram Research (2021), TreeMap, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeMap.html (updated 2024).
✖
Wolfram Research (2021), TreeMap, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeMap.html (updated 2024).

Text

Wolfram Research (2021), TreeMap, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeMap.html (updated 2024).

✖
Wolfram Research (2021), TreeMap, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeMap.html (updated 2024).

CMS

Wolfram Language. 2021. "TreeMap." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/TreeMap.html.

✖
Wolfram Language. 2021. "TreeMap." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/TreeMap.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_treemap, author="Wolfram Research", title="{TreeMap}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/TreeMap.html}", note=[Accessed: 10-July-2025 ]}

✖
@misc{reference.wolfram_2025_treemap, author="Wolfram Research", title="{TreeMap}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/TreeMap.html}", note=[Accessed: 10-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_treemap, organization={Wolfram Research}, title={TreeMap}, year={2024}, url={https://reference.wolfram.com/language/ref/TreeMap.html}, note=[Accessed: 10-July-2025 ]}

✖
@online{reference.wolfram_2025_treemap, organization={Wolfram Research}, title={TreeMap}, year={2024}, url={https://reference.wolfram.com/language/ref/TreeMap.html}, note=[Accessed: 10-July-2025 ]}