I was doing reading on weighted quick-union using path compression. I have a clear understanding of why this is $O(1)$ with amortized analysis for union and find operations but do not understand how to address this special case.
Suppose we have $x$ items to start with, (all disjoint) and we perform a sequence of $m$ operations such that all calls to find come after all calls to union. I am trying to determine what kind of data structure could be used, because in my previous understanding of disjoint sets, the union operation is always dependent on the find operation.
Despite having this information about the order of operations, I do not quite see how it is useful- or, how it can be used to achieve an amortized analysis of $O(1)$. Also, not sure of how to approach the union operation without relying on calls to find.