Modify dijkstra''s algorithm

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1. Suppose all the edge weights in a graph are integers between 1 and |E|. How fast can Dijkstra's algorithm be implemented?

2. Write a program to solve the single-source shortest-path problem.

3. a. Explain how to modify Dijkstra's algorithm to produce a count of the number of different minimum paths from v to w.

b. Explain how to modify Dijkstra's algorithm so that if there is more than one minimum path from v to w, a path with the fewest number of edges is chosen.

4. Find the maximum ?ow in the network.

5. Suppose that G = (V, E) is a tree, s is the root, and we add a vertex t and edges of in?nite capacity from all leaves in G to t. Give a linear-time algorithm to ?nd a maximum ?ow from s to t.

Reference no: EM13968291

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