Let G = (V, E) be a weighted, directed graph with positive integer weights and marimum weight W. (a) Modify Dijkstra's algorithm to compute the shortest paths from a given source vertex s in 4 O(W|V|+|E) time. (b) Give an O(E| lg W) time algorithm for the problem by improving your algorithm of part (a).

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Q: algorithm

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A: So algorithms are given below for both

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A:

Q: shortest path

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A: Answer: I have given answered in the handwritten format

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A: Hi.. check below for the algorithm on given scenario.

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A: To solve in G(VE) time using Bellman Ford.

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A: The correct solution for the above mentioned question is given in the next steps for your reference

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A: The answer is given below.