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The traveling salesperson problem is a harder problem than Dijkstra's single-source shortest path problem. In other words, the typical Greedy algorithm approach does not work for this problem. It is even harder than the all-points shortest path algorithm implemented with Floyd's algorithm. Give an example of a graph that shows that the path that would be chosen by relying on shortest-path information by choosing the closest vertex each time isn't sufficient to find the shortest circuit. What makes this problem harder? Why are the straight forward approaches to this problem exponential?

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