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CountDistinctBy

Status: Stable

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

Description

CountDistinctBy[expr, f]

Gives the number of distinct values of f[e] over the elements e of expr (the values, for an association).

Examples (5)

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

Basic examples (2)

In[1]:= CountDistinctBy[{1, 2, 3, 4, 5}, EvenQ]
Out[1]= 2

In[2]:= CountDistinctBy[{"apple", "avocado", "banana"}, StringTake[#, 1] &]
Out[2]= 2

Applications (3)

Two classes: even and odd

In[3]:= CountDistinctBy[{1, 2, 3, 4, 5, 6}, EvenQ]
Out[3]= 2

|x| takes three distinct values

In[4]:= CountDistinctBy[{-1, 1, -2, 3}, Abs]
Out[4]= 3

In[5]:= CountDistinctBy[Range[10], Mod[#, 3] &]
Out[5]= 3

Implementation notes

Algorithm. builtin_countdistinctby returns the number of distinct values of f[element]. It shares the count_distinct core with CountDistinct, passing the second argument as the key function: f is evaluated once per element (eval_call1) and the result added to an ExprSet; the final set size is the answer.

Data structures. An ExprSet hash set over the owned f-values (expr_hash/expr_eq), plus an array that owns each f[element] result for the duration of the pass. A visible NDArray argument is de-listed first (ops_delist_visible).

Complexity / limits. O(n) evaluations of f plus O(n) hashing. Requires a non-atomic first argument (CountDistinctBy::normal otherwise, via the message funnel); f is arbitrary, so no packed fast path applies.

Attributes: Protected.

References

Notes & additional examples

Notes

CountDistinctBy[list, f] counts the distinct values of f[element] — the number of groups GatherBy[list, f] would produce, without materialising the groups. It is a one-pass hash count: f is applied once per element and the distinct results are tallied. Use it to ask how many categories a key function induces.