a$)(15$p$)$ Apply Prim's algorithm to your graph using the vertex $\text{'}$ A $\text{'}$ as the source vertex. For the answer, just draw the MST tree that you obtain after the algorithm terminates $($to get full credit, you should reflect the final keys of the vertices to the graph$).$

b$)(15$p$)$ Apply Dijkstra's algorithm to your graph using the vertex $\text{'}\backslash ($ A $\backslash )\text{'}$ as the source vertex. For the answer, just draw the shortest path tree that you obtain after the algorithm terminates $($to get full credit, you should reflect the final keys of the vertices to the graph$).$