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Commonest

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Commonest[list] gives a list of the elements that are the most common in list.
Commonest[list, n] gives a list of the n most common elements in list.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= Commonest[{b, a, c, 2, a, b, 1, 2}]
Out[1]= {b, a, 2}

In[2]:= Commonest[{b, a, c, 2, a, b, 1, 2}, 4]
Out[2]= {b, a, c, 2}

In[3]:= Commonest[{b, a, c, 2, a, b, 1, 2}, UpTo[6]]
Out[3]= {b, a, c, 2, 1}

In[4]:= Commonest[{1, 2, 2, 3, 3, 3, 4}]
Out[4]= {3}

In[5]:= Commonest[{a, E, Sin[y], E, a, 7}]
Out[5]= {a, E}

Implementation notes

Algorithm. builtin_commonest (in src/list.c) tallies element multiplicities with a HashTable (one pass, O(N)), recording each distinct element's count and first-appearance index. The tallies are packed into CommonestItem records and sorted by descending count (ties broken by first occurrence) to find the maximum multiplicity. Without a count argument it returns every element sharing the maximum count; Commonest[list, n] / Commonest[list, UpTo[n]] returns up to the n most frequent.

Data structures. Parallel Expr** / int64_t* arrays for unique elements and their multiplicities, a HashTable mapping element → index, and a CommonestItem array (element, count, first_index) used for the stable sort.

  • Protected.
  • When several elements occur with equal frequency, Commonest picks first the ones that occur first in list.
  • Commonest[list, n] returns the n commonest elements in the order they appear in list.
  • Commonest[list, UpTo[n]] returns the n commonest elements, or as many as are available.
  • A message Commonest::dstlms is generated if there are fewer distinct elements than requested by an integer n.

Attributes: Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= Commonest[{1, 2, 2, 3, 3, 3, 4}]
Out[1]= {3}

In[1]:= Commonest[{a, b, a, c, b, a, d, b}, 2]
Out[1]= {a, b}

In[1]:= Commonest[Table[Mod[k^2, 7], {k, 0, 20}]]
Out[1]= {1, 4, 2}

Notes

Commonest[list] returns every element tied for the highest frequency; Commonest[list, n] returns the n most common. The quadratic-residue example above shows the three nonzero residues mod 7 each occurring equally often.