Suppose we start Prim's algorithm from $\backslash ($ S $\backslash )$ on this graph. Write down the state of the Priority Queue being used as the after S is visited, after B is visited, and after the algorithm is completed. Each value in the priority queue should be an integer. Resolve ties by alphabetical order of the vertices. For example: if $\backslash ($ A $\backslash )$ and $\backslash ($ C $\backslash )$ have the same priority, then you should first pop $\backslash ($ A $\backslash )$ since it comes alphabetically first.

Initialize the priority of each vertex as which we'll use to represent $\backslash (\backslash$infty $\backslash ).$ So$,$ before the first iteration, the values of the are:

fringe $=\backslash \{$S:$0,$ A:inf, B:inf, C:inf, D:inf, E:inf, F:inf, G:inf, H:inf, I:inf$\backslash \}$

Order your fringe by priority values. You should use the same alphabetical tie$-$breaking scheme when choosing the order of the Make sure you include the $\backslash \{$ and $\backslash \}$ in your answer. If the fringe is empty, put $\backslash (\backslash \}\backslash )$ Q$3\mathrm{.}2$ down

$0\mathrm{.}6$ Points

Give the state of the priority queue after B is visited

fringe: