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1. Let G be an undirected graph with n vertices and m edges. Describe an O(n+m)- time algorithm for traversing each edge of G exactly once in each direction.2. Implement an algorithm that returns a...

Our implementation of shortestPathLengths in Code Fragment 14.13 relies on use of “infinity” as a numeric value, to represent the distance bound for vertices that are not (yet) known to be reachable...

A company named RT&T has a network of n switching stations connected by m high-speed communication links. Each customer’s phone is directly connected to one station in his or her area. The...

Consider the following greedy strategy for finding a shortest path from vertex start to vertex goal in a given connected graph.1: Initialize path to start.2: Initialize set visited to {start}.3: If...

Write a method, components(G), for undirected graph G, that returns a dictionary mapping each vertex to an integer that serves as an identifier for its connected component. That is, two vertices...

1. Show that if all the weights in a connected weighted graph G are distinct, then there is exactly one minimum spanning tree for G.2. An old MST method, called Baruvka’s algorithm, works as follows...