Function Repository Resource:

TrueCountQ

Determine if the count of elements satisfying a given test at specified levels of an expression falls within a defined range

Contributed by: Phileas Dazeley-Gaist

ResourceFunction["TrueCountQ"][n][{e₁,e₂,…}]

yields True if exactly n elements of the list {e₁,e₂,…} are True.

ResourceFunction["TrueCountQ"][{min,max}][{e₁,e₂,…}]

yields True if between min and max elements of the list {e₁,e₂,…} are True.

ResourceFunction["TrueCountQ"][countspec,test][{e₁,e₂,…}]

yields True if test[e_i] is True for a number of elements of {e₁,e₂,…} that satisfies countspec.

ResourceFunction["TrueCountQ"][countspec,test,levelspec][expr]

yields True if test is True for a number of elements of expr that satisfies countspec, with test applied to all parts of expr at levels specified by levelspec.

ResourceFunction["TrueCountQ"][][{e₁,e₂,…}]

yields True if exactly one element of the list {e₁,e₂,…} is True.

Details

The countspec argument can take the following forms:

exactly n True

{min,max}

between min and max True

The countspec argument values can be 0, positive integers, and ∞.

ResourceFunction["TrueCountQ"] uses standard level specifications. See Sequence Specifications.

levels 1 through n

Infinity

levels 1 through Infinity

{n}

level n only

{n₁,n₂}

levels n₁ through n₂

ResourceFunction["TrueCountQ"][n,test,levelspec][expr] is equivalent to TrueQ[Length[Cases[Flatten[Map[test,expr,levelspec]],True]]===n].

ResourceFunction["TrueCountQ"][{min,max},test,levelspec][expr] is equivalent to TrueQ[Min[{min,max}]<=Length[Cases[Flatten[Map[test,expr,levelspec]],True]]<=Max[{min,max}]].