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Exercise 3: Counting Shortest Paths (25 Points) Assume an undirected, weighted, connected directed graph with positive edge weights. Given two nodes s and t in the graph, the problem is to count the number of different shortest paths between s and t. Give an efficient algorithm for the problem, argue its correctness, and analyze its run time. (Hint: Modify Dijsktra's algorithm to identify only those edges that belong to a shortest path between s and t. Then, a DP algorithm will be used to count the number of shortest paths between s and t. As usual, you should specify subproblems and recursive formulas for the DP algorithm.)

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