Define disjoint set and answer the following questions. i. Show that after all edges are processed by CONNECTED-COMPONENTS, two vertices are in the same connected component if and only if they are in the same set. ii. During the execution of CONNECTED-COMPONENTS on an undirected graph G(V,E) with k connected components, how many times is FIND-SET called? How many times is UNION called? Express your answers in terms of IVI, |E|, and k.

What do you mean by disjoint set data structure? Suppose that CONNECTED- COMPONENTS is run on the undirected graph G=(V,E), where V = { a, b, c, d, e, f, g, h, i, j, k} and the edges of E are processed in the order (d, i), (f, k), (g, i), (b, g), (a, h), (i, j), (d, k), (b, j), (d, f), (g, j), (a, e). List the vertices in each connected component after each iteration of lines 3-5.