$(30$ points$)$ assume that the graph is represented using adjacency lists, and all adjacency lists are sorted, i$.$e$.,$ the vertices in the adjacent list are always in ascending order by vertex IDs. Also assume some stable sorting algorithm is applied to sort the edges by weight. Name edges with their starting and ending vertices, for example, the edge from vertex $v_1$ to vertex $v_2$ is named $(v_1,v_2)$ and has cost $1.$

Run Kruskal's algorithm on this graph, showing the action of Kruskal's algorithm, i$.$e$.,$ either accept or reject an edge into MST$.$

$\backslash$table$[[$Order$,$Edge,Weight,Action$],[1,(v_1,v_2),,],[2,,,],[3,,,]]$

$\backslash$table$[[4,,,],[5,,,],[6,,,],[7,,,],[8,,,],[9,,,],[10,,,]]$

Select $v$ s to start and run Prim's algorithm without using heap on this graph. Fill the provided table using the edges with weights in the order selected by Prim's algorithm.

$\backslash$table$[[$Order$,$Edge,$],[1,,],[2,,],[3,,],[4,,],[5,,],[6,,],[7,,],[8,,],[9,,],[10,,]]$

What is the cost $($weight$)$ of the minimum spanning tree?