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2. Shortest Distances and Shortest Paths. a. Answer the following questions (by placing a mark in the appropriate column) regarding Dijkstra's algorithm DijkstraShortestPaths (G,v). Statement True/ False? True False Dijkstra's algorithm computes shortest paths from v to all nodes Dijkstra's algorithm computes shortest distances from v to all nodes The sequence of nodes visited by the algorithm defines a shortest path Nodes enter the cloud in the order of increasing shortest distance from v All the nodes inside the cloud have a shorter shortest distance from v than all the nodes outside the cloud (in priority queue Q). No shortest path from v to a node in the cloud goes through a node outside the cloud. If we are interested in the shortest distance from v to some node X, we may stop the iteration as soon as X enters the cloud. Even if we are interested in the shortest distance from v to some node X, we must execute Dijsktra's algorithm until all nodes are in the cloud. b. Consider two nodes X and Y of a graph on which you have executed Dijkstra's algorithm, let D(X) and D(Y) be their shortest distance from v and let d(X,Y) be the length of arc(X,Y). How do you interpret each of the following three cases: i. D(Y)=D(X)+d(X,Y). ii. D(Y)D(X)+d(X,Y). c. Why do we talk about the shortest distance from v to a node X and a shortest path from v to X ? d. Explain how you find a shortest path from v to some node X