You could just go on merging sets with each other.

For i from 0 to n-1 , find all sets from i+1 to n-1 which have a non empty intersection with set i. Union set i with all those sets and replace i with the union set.

If you use a disjoint set data structure this will be quadratic or O(n^2)

EDIT: On further thought you need to merge from the end and backwards.