Let G be a directed, weighted graph, where each edge weight is a positive integer. Let s and t be particular vertices in the graph. Suppose we attempt to update Dijkstra$$s algorithm, so that it finds the path of maximum total weight path from vertex s to t$.$

Show how to update the pseudo$-$code of Dijkstra$$s algorithm so that it uses a max priority queue. Ensure that you update all parts of the pseudo$-$code so that the algorithm is greedily selecting maximum routes.

Does this updated version correctly find the maximum path from s to t on any graph G$?$ Justify your answer by either explaining why or providing an example where it fails.