“Re-writing” the function `MemberQ`

I am trying to program the function MemberQ using less then possible functions pre defined by Mathematica.
Until this now my code is:

MemberQ

meuMemberQ[f_,n_?NumericQ] /; (Length[Select[f, # == n &]] != 0):=True
meuMemberQ[f_,n_Symbol] /; (Length[Select[f, # == n &]] != 0) := True
meuMemberQ[f_,n_String] /; (Length[Select[f, # == n &]] != 0) := True
meuMemberQ[f_, n_] := False


There is a way to writing the same function but without using Select and Length?

Select

Length

Ps: It is just for exercise.

meuMemberQ2[f_, n_] := Intersection[f, n] === n

meuMemberQ3[f_,n_]:= SubsetQ[f, n]

Intersection

MatchQ

AnyTrue

Table

2 Answers
2

A recursive implementation:

meuMemberQ[n_, y___, n_] := True;
meuMemberQ[x_, y___, n_] := meuMemberQ[y, n];
meuMemberQ[, n_] := False;


This just cuts through the list step by step looking for an exact match of n_, and if it gets to an empty list it returns False.

n_

False

It will run into the iteration limit eventually, but if you need to use it with such long lists, there are things that can be done (such as using MemberQ).

MemberQ

A few alternatives:

ClearAll[meuMemberQ2, meuMemberQ3, meuMemberQ4]

meuMemberQ2[f_, n_] := Switch[n, Alternatives @@ f, True, _, False]
meuMemberQ3[f_, n_] := n /. Alternatives@@f ->True, _:> False

meuMemberQ4[OrderlessPatternSequence[n_,___], n_] := True
meuMemberQ4[_,_]:=False


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