Consider the following weighted directed graph,

$(10$ pts$)$ Run Dijkstra's Algorithm starting on vertex B$,$ and provide the single$-$source shortest path distances from B to all other vertices in the graph. State the order in which vertices were visited.

$(10$ pts$)$ Technically speaking, the definition of the single source shortest path problem doesn't require that a given edge is only traversed one time by the shortest path between two vertices. However, all of our algorithms assume that this is the case. Prove that, on a graph with non$-$negative edge weights, the shortest path between any two vertices will never include the same edge more than once.