The Merging Problem

Say you want to count distinct colors in each subtree. For a node $v$, you need all colors from all children, plus $v$'s own color. You could maintain a set for each node. After processing children, merge all child sets into one set for $v$. The result contains all colors in $v$'s subtree. The question: how do you merge sets efficiently when there are many children and large sets?

If you pick the wrong merge order, you will copy the same elements over and over.