$3($a$)$ Provide in pseudocode or Java a modification of Depth First Graph Traversal so that it

counts the number of disconnected components in a graph and labels each vertex with

the subgraph component it belongs to$.$

Then show how the algorithm you described behaves on the following graph.

$($b$)$ Explain the Union$-$Find data structure and what it is used for in Kruskal's algorithm.

Also, with the aid of diagrams, outline a possible implementation of this data structure

and give an example showing how its two significant operations work. No code

required here.

$(10$ marks$)$

$($c$)$ Using pseudocode or Java, write down the implementation of the class constructor and

the two significant operations of the Union$-$Find data structure described in part $($b$).$

$(6$ marks$)$

$($d$)$ Illustrate in detail how Kruskal's algorithm computes a Minimum Spanning Tree for

the graph below showing the contents of the union$-$find sets and their representation for

the first $4$ iterations of the algorithm's while loop.