1. In Dijkstras algorithm, when we add a node to , let be a node not in . Is it possible that the new shortest special path from the source to should pass first by and then by some other node of ?

2. Show by giving an explicit example that if the edge lengths can be negative, then Dijkstras algorithm does not always work correctly. Is it still sensible to talk about shortest paths if negative distances are allowed?

3. picture below

1. Show how Dijkstra's algorithm works on the following graphs (both for finding the shortest paths and their length): 8 7 2 3 4 9 2 4 1 11 9 14 5 7 6 8 10 8 7 6 1 2