Q$2(20$ Points$)-$ Minimum Spanning Tree Algorithms

You can find an undirected weighted graph below. Answer the following questions:

a$)$ Apply the Prim's algorithm to calculate the minimum spanning tree from the vertex A$.$ Show the steps and all the values as you go through the algorithm. Also mention the distance for each of the paths. You can break the tie breaker of two paths with the same distance using the alphabetical order.

b$)$ Step through Kruskal's algorithm to calculate a minimum spanning tree of the graph. Show the disjoint sets at each iteration along with the edge cost and running cost. If you can select two edges with the same weight, select the edge that would come alphabetically last $($e$.$g$.,$ select $\backslash (\backslash$mathrm$\{$E$\}-\backslash$mathrm$\{$F$\}\backslash )$ before $\backslash (\backslash$mathrm$\{$B$\}-\backslash$mathrm$\{$C$\}\backslash ).$ Also, select $\backslash (\backslash$mathrm$\{$A$\}-\backslash$mathrm$\{$F$\}\backslash )$ before $\backslash (\backslash$mathrm$\{$A$\}-\backslash$mathrm$\{$B$\}\backslash )).$