This question is related to linked-list representation of disjoint sets. Consider two sets Sx and Sy that have 3 and 5 elements, respectively. A union (UNION(x, y)) of the sets Sx and Sy represented by x and y, respectively will perform update(s) of the attribute .next.

A union (UNION(x,y)) of the sets Sx and Sy represented by x and y, respectively will perform 4 update(s) of the attribute.

Explanation:

The UNION (x, y) disjoint-set data structure unites the dynamic sets that contain x and y, say Sx and Sy, into a new set.  It is called the union of the two sets. Before the union operation, the two sets are disjoint.  After the union operation, the representative of the resulting set is some member of Sx and Sy or either Sx or Sy. The sets Sx and Sy are then destroyed to remove them from the union collection S.  So, four operations are required.

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