CountDistinctBy

CountDistinctBy[{e1, e2, ...}, f] gives the number of distinct values of f[ei] that occur.

CountDistinctBy[f] represents an operator form of CountDistinctBy that can be applied to an expression.

Examples

Count distinct values after applying a function:

CountDistinctBy[{-3, -2, -1, 1, 2, 3}, Abs]
(* 3 *)

Count words by length:

CountDistinctBy[{"cat", "dog", "bird", "fish"}, StringLength]
(* 2 *)

Please visit the official Wolfram Language Reference for more details.