Exercise $10\mathrm{.}1($minimum spanning tree algorithms, $3+3$ marks$)$

Consider the following weighted graph:

$($a$)$ Simulate Kruskal's algorithm on the graph. For each iteration of the while loop, specify the following:

the considered edge

whether the edge is included or discarded

the connected components of the union$-$find structure $($you may omit trivial connected components that contain only one element$).$

Additionally, draw the resulting minimum spanning tree.

$($b$)$ Simulate the lazy variant of Prim's algorithm on the graph, using node $0$ as initial tree. For each iteration of the while loop, specify the edge that is considered and whether it is included or discarded. Additionally, draw the resulting minimum spanning tree.