# Given a partition and an element, find the subset that includes this element

I am interested in the following simple problem: Let $$X$$ be a set and $$X_1\cup X_2\cup\cdots\cup X_k$$ be a finite partition of $$X$$. Given $$x\in X$$, find the subset $$X_i$$ for which $$x\in X_i$$. I am mostly interested in some general background on this problem. I'm stuck because I do not know of a canonical "name" for this problem.

Does this problem have a name, or is there a closely related problem that might generate some useful hits?

It is unlikely to have a "name" because it is trivial: it can be solved with a hashtable, array, self-balanced binary search tree, or any other data structure that maps $$x$$ to $$X_i$$.