How to express the data structure in the pesudocode of your algorithm
There are no set rules, but these type of details are sometimes omitted from the pseudocode listing. You might see something like

ALGORITHM(S, n):
For i = 1 to n do
   S = ADD(S, i)
EndFor


Then followed by something like "... the algorithm performs $\Theta(n)$ units of work assuming that the set $S$ is implemented as blah so that the addition of an element ADD(S,i) runs in blah time ..."