$4$ Let $G=(V,E)$ be an oriented graph with a nonnegative edge weight function $w$:$E|N.$ The

length of a path is defined as the sum of the edge weights of the path. Your task is to design an

algorithm that finds a shortest path from a given staring vertex $sinV$ to all other graph vertices.

If more that one shortest path exists between $s$ and a vertex $x,$ then the algorithm should return a

shortest path with the minimum number of edges.

$($a$.)$ Adapt the algorithm of Dijkstra to your problem. Make sure to provide a complete descriptions

of the procedures INITIALIZE, RELAX, and Di$.$JKSTRA.

$($b$.)$ Analyze the running time of your algorithm.

$($c$.)$ Justify the correctness of your algorithm.

$5$ Find an oriented graph with $($some$)$ negative edge weights for which the output of the algorithm of

Dijkstra is incorrect.

Why the algorithm of Dijkstra is not extendable to the case of negative edge weights?