Please answer the following question in general algorithm ONLY, DO NOT answer it in ONE specific programming language. Thank you! A vertex is "disconnected" if it does not lie on any cycle. Given an undirected graph G, give an efficient algorithm to count the number of "disconnected" vertices in G. Prove that your algorithm is correct. Analyze the running time of your algorithm. What I've done so far: I get that I'm supposed to use a depth first searching tree, so I devised an algorithm to do just that, DFS(v) | mark v | v.pre = clock++ | for each edge vw | | if w is unmarked | | v = parent(w) | | DFS(w) | v.post = clock++ I just dont know how to find the "disconnected" vertices. My thought process is that I can perhaps find all the vertices in a cycle, and take them out of the total number of vertices to find the number of disconnected vertices. If this thought process is correct, could you help me by showing me how to make such an algorithm? Possible method to find cycles could be to see if there are loops where a chile vertex is an ancestor to it's parent vertex, but I'm not sure how to create a method for that either.
Please answer the following question in general
A vertex is "disconnected" if it does not lie on any cycle. Given an undirected graph G, give an efficient algorithm to count the number of "disconnected" vertices in G. Prove that your algorithm is correct. Analyze the running time of your algorithm.
What I've done so far:
I get that I'm supposed to use a depth first searching tree, so I devised an algorithm to do just that,
DFS(v)
| mark v
| v.pre = clock++
| for each edge vw
| | if w is unmarked
| | v = parent(w)
| | DFS(w)
| v.post = clock++
I just dont know how to find the "disconnected" vertices. My thought process is that I can perhaps find all the vertices in a cycle, and take them out of the total number of vertices to find the number of disconnected vertices. If this thought process is correct, could you help me by showing me how to make such an algorithm?
Possible method to find cycles could be to see if there are loops where a chile vertex is an ancestor to it's parent vertex, but I'm not sure how to create a method for that either.
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