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Instant-use add-on functions for the Wolfram Language

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 DepthLeafCountSort

Source Notebook

Sort expressions by depth and leaf count

Contributed by: Jan Mangaldan (original work by Stephen Wolfram)

ResourceFunction["DepthLeafCountSort"][list]

sort a List of expressions list by depth and leaf count.

Details and Options

ResourceFunction["DepthLeafCountSort"] effectively sorts based on the global structure of expressions, while Sort sorts "lexicographically," looking only at the "early parts" of expressions.
This is the method of sorting used to order theorems in A New Kind of Science, page 817.

Examples

Basic Examples (2) 

Sort a List of expressions by depth and leaf count:

In[1]:=
ResourceFunction["DepthLeafCountSort"][{f[g[a]], f[a, b, c], f[a, b]}]
Out[1]=
Image

Generate a List of expressions:

In[2]:=
gr = Groupings[{a, b, c, d, e}, CenterDot -> 2]
Out[2]=
Image

Show the tree forms of the expressions:

In[3]:=
TreeForm /@ gr
Out[3]=
Image

Sort by depth and leaf count:

In[4]:=
TreeForm /@ ResourceFunction["DepthLeafCountSort"][gr]
Out[4]=
Image

Properties and Relations (2) 

Sort sorts first by length, then based on lexicographic ordering:

In[5]:=
Sort[{f[g[a]], f[a, b, c], f[c, d], f[a, b]}]
Out[5]=
Image

DepthLeafCountSort sorts first by Depth then LeafCount:

In[6]:=
ResourceFunction[ "DepthLeafCountSort"][{f[g[a]], f[a, b, c], f[c, d], f[a, b]}]
Out[6]=
Image

Generate a List of expressions:

In[7]:=
gr = Groupings[{a, b, c, d}, CirclePlus -> 2]
Out[7]=
Image

Sort uses a lexicographic ordering:

In[8]:=
TreeForm /@ Sort[gr]
Out[8]=
Image

DepthLeafCountSort orders expressions by their depth and then by their leaf count:

In[9]:=
TreeForm /@ ResourceFunction["DepthLeafCountSort"][gr]
Out[9]=
Image

An equivalent ordering using SortBy:

In[10]:=
TreeForm /@ SortBy[gr, {Depth, LeafCount}]
Out[10]=
Image

Version History

  • 1.0.0 – 01 October 2020

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