LeafCount

LeafCount[expr]

gives the total number of indivisible subexpressions in expr.

Details

  • LeafCount gives a measure of the total "size" of an expression.
  • LeafCount counts the number of subexpressions in expr that correspond to "leaves" on the expression tree.
  • LeafCount is based on FullForm representation of expressions.
  • Numbers with heads Rational and Complex are treated as composite objects, just as in FullForm.

Examples

open allclose all

Basic Examples  (1)

Find the number of "leaves" in an expression tree:

Applications  (3)

Find leaf count measures of the sizes of successive integrals:

Make Simplify pick expressions with minimum LeafCount:

Find leaf counts in combinator expressions [more info]:

Properties & Relations  (2)

LeafCount includes the head and all elements inside it:

For most expressions, LeafCount equals the count matching Blank[] at level {-1}:

LeafCount counts Rational and Complex numbers using their FullForm:

Count treats Rational and Complex as atoms:

Possible Issues  (5)

LeafCount is based on the FullForm of expressions:

LeafCount counts elements in rational and complex numbers just as in FullForm:

Integers of any size are still treated as single expression leaves:

LeafCount treats SparseArray objects as single expression leaves:

Unlike TreeForm, LeafCount takes into consideration the structure of expression heads:

This shows the expression tree whose leaves are counted by LeafCount:

Wolfram Research (1988), LeafCount, Wolfram Language function, https://reference.wolfram.com/language/ref/LeafCount.html.

Text

Wolfram Research (1988), LeafCount, Wolfram Language function, https://reference.wolfram.com/language/ref/LeafCount.html.

BibTeX

@misc{reference.wolfram_2021_leafcount, author="Wolfram Research", title="{LeafCount}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/LeafCount.html}", note=[Accessed: 17-May-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_leafcount, organization={Wolfram Research}, title={LeafCount}, year={1988}, url={https://reference.wolfram.com/language/ref/LeafCount.html}, note=[Accessed: 17-May-2021 ]}

CMS

Wolfram Language. 1988. "LeafCount." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LeafCount.html.

APA

Wolfram Language. (1988). LeafCount. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LeafCount.html