1. Show that if a network contains a negative cycle, the generic all-pairs label-correcting algorithm will never terminate.
2. Suppose that the Floyd-Warshall algorithm terminates after detecting the presence of a negative cycle. At this time, how would you detect a negative cycle using the predecessor indices?
3. In an all-pairs shortest path problem, suppose that several shortest paths connect node i and nodej. If we use the Floyd-Warshall algorithm to solve this problem, which path will the algorithm choose? Will this path be the one with the least number of arcs?