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Prims Algorithm Total Running time!

"Thus, the total time for Prim's algorithm is O(V lg V + E lg V) = O(E lg V), which is asymptotically the same as for our implementation of Kruskal's algorithm."

From http://serverbob.3x.ro/IA/DDU0137.html

But why is O(V lg V + E lg V) = O(E lg V) ??

Is it because E is at least V-1 ?

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Guestt Avatar asked Jun 14 '11 22:06

Guestt


2 Answers

Because in the normal case we assume that E is larger than V. So by ignoring the lower order terms we got E lg V

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Abdul Samad Avatar answered Sep 28 '22 03:09

Abdul Samad


Specifically, E can be a maximum of V^2 in a directed graph. If we assume E = v^2 (to account for worst case), E swallows V.

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user1114 Avatar answered Sep 28 '22 03:09

user1114