CountDistinct¶

Status: Stable

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

Description¶

CountDistinct[expr]

Gives the number of distinct elements of expr (of its values, for an association). One hash pass, O(n).

Examples (5)¶

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (2)¶

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

In[2]:= CountDistinct[<|"a" -> 1, "b" -> 1, "c" -> 2|>]
Out[2]= 2

Applications (3)¶

In[3]:= CountDistinct[{a, b, a, c, b, a}]
Out[3]= 3

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

Over an association, the distinct values

In[5]:= CountDistinct[<|x -> 1, y -> 1, z -> 2|>]
Out[5]= 2

Implementation notes¶

Algorithm. builtin_countdistinct returns the number of distinct elements of a non-atomic expression (the distinct values, for an association). It is the shared count_distinct core with a NULL function: every element is added to an ExprSet and the final set size is returned as an integer. One hash pass — no sorting, no DeleteDuplicates round-trip.

Data structures. ExprSet, a hash set over Expr* keyed by expr_hash and compared with expr_eq, sized once to the element count. A visible NDArray argument is de-listed up front (ops_delist_visible) so the count runs over ordinary elements.

Complexity / limits. O(n) amortised. A non-atomic first argument is required; otherwise CountDistinct::normal is emitted (through the message funnel) and the call is left unevaluated.

Attributes: Protected.

References¶

See also: SameQ

T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, Introduction to Algorithms, 3rd ed. (MIT Press, 2009), §11 (hash tables, open addressing).
Source: src/assoc_ops.c
Specification: docs/spec/builtins/data-structures.md
Tests: tests/test_assoc_ops.c

Notes & additional examples¶

Notes¶

CountDistinct[list] is the number of distinct elements — Length[Union[list]] computed in a single hash pass, without building the sorted set. Over an association it counts the distinct values. It answers the "how many different things are here?" question directly; use CountDistinctBy to count distinct values of a function of each element.