his problem concerns distance between vertices in an unweighted graph. I an unwe
ID: 3728827 • Letter: H
Question
his problem concerns distance between vertices in an unweighted graph. I an unweighted graph, the length of a path is the number of edges in that path, and the distance from one vertex v1 to an shortest from traversal. Either breadth-first or depth-first search can be used, although one might be more efficient than the other for a given problem. For each of the following problems, write an algorithm, using clear pseudocode, that solves the problem. The algorithm in each case can be a variation of basic depth-first or breadth-first search. Explain in words how your algorithm works, and say what you can about its run-time efficiency other vertex v2 is the length of the vi to v2. The following problems can be solved using graph a) Given a starting vertex, x, print out every vertex whose distance from is less than or equal to 5. b) Given a starting vertex r, find a vertex y which can be reached from x, and whose distance from x is as large as possible.Explanation / Answer
Solution:
a)
In this case, we will be starting from vertex x and mark it as visited then we will start visiting its adjacent vertices and also maintaining the count for every vertex in the graph, so when a vertex is visited from mark it as visited and set the count of that vertex to count of the previous vertex + 1, and print that particular vertex if the count value of that vertex is <= 5.
b)
The algorithm is given below:
Algorithm:
The above algorithm will take O(V+E) time to execute, and it will return the farthest vertex from the given vertex v.
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