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Function Repository Resource:

MultisetIntersection

Source Notebook

Perform the intersection operation on multisets

Contributed by: Robert B. Nachbar (Wolfram Solutions)

ResourceFunction["MultisetIntersection"][list1,list2,]

gives a sorted list of the elements common to all the listi. The number of occurrences of each distinct element is the minimum of the counts in each of the listi.

ResourceFunction["MultisetIntersection"][assoc1,assoc2,]

gives an Association where the keys are the union of the keys in the associations associ and the values are the minimum of the merged values.

Details and Options

If the listi are considered as multisets, ResourceFunction["MultisetIntersection"] gives their intersection.
The listi must have the same head, but it need not be List.
The values of associ must be counts, that is, non-negative Integer values.

Examples

Basic Examples

Find largest subsets of elements common to all the lists given:

In[1]:=
ResourceFunction[
 "MultisetIntersection"][{1, 1, 2, 3}, {3, 1, 1, 1, 4}, {4, 1, 1, 3, 3}]
Out[1]=

Multisets as an Association of counts :

In[2]:=
ResourceFunction[
 "MultisetIntersection"][<|"a" -> 3, "b" -> 1, "c" -> 2, "d" -> 1|>,
 <|"a" -> 2, "b" -> 2, "c" -> 2, "e" -> 1|>,
 <|"a" -> 1, "b" -> 2, "c" -> 2, "e" -> 2|>]
Out[2]=

Scope

MultisetIntersection works with any head, not just List:

In[3]:=
ResourceFunction["MultisetIntersection"][f[a, b], f[c, a], f[b, b, a]]
Out[3]=

Properties and Relations

If there is no intersection, the result is {}:

In[4]:=
ResourceFunction["MultisetIntersection"][{a, b, b, c}, {d, e, f, f}]
Out[4]=

If there is no intersection of the Association multisets, the result is <||>:

In[5]:=
ResourceFunction[
 "MultisetIntersection"][<|a -> 1, b -> 2, c -> 1|>, <|d -> 1, e -> 1,
   f -> 2|>]
Out[5]=

Compare to Intersection:

In[6]:=
ResourceFunction[
 "MultisetIntersection"][{a, b, a, d, d}, {d, a, d, e, d}, {c, d, a, d}]
Out[6]=
In[7]:=
Intersection[{a, b, a, d, d}, {d, a, d, e, d}, {c, d, a, d}]
Out[7]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

See Also

License Information