Exercise 6.23. Let G=(V,A) be a directed acyclic graph and let sV. a. Show that if we add a constant to the length of all outgoing arcs of s, the shortest paths from s to all other vertices remain the same. b. What is the relationship between the shortest path distances of the modified problem and the shortest path distances of the original problem? c. Show that Dijkstra's algorithm runs correctly if there are arcs with negative length in the graph, provided they are all outgoing arcs from s