Problem $2.$ MSTs

In Lecture $21,$ we saw two different greedy algorithms for building MST $-$ "growing a cloud" $($Prim$\text{'}$s algorithm$),$ and "combining clusters" $($Kruskal$\text{'}$s algorithm$).$ Consider the following graph G$,$ for which we want to build an MST$.$

a$)$ Show the order in which Prim's algorithm will add edges to the MST$,$ starting at node A$.$ For each edge $($u$,$v$)$ added, show the value for v in the priority queue at the time it was added. What is the total weight of the MST$?$

b$)$ Repeat $($a$)$ but starting at node H$.$ Hint: the total weight of the MST should be the same.

c$)$ Show the order in which Krusgal's algorithm will add edges to the MST$.$ Any time you skip an edge $($i$.$e$.$ it is the next smallest, but not added$),$ note this and explain why.