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+20 votes

What is the time complexity of Bellman-Ford single-source shortest path algorithm on a complete graph of n vertices?

  1. $\theta(n^2)$     
  2. $\theta(n^2\log n)$     
  3. $\theta(n^3)$     
  4. $\theta(n^3\log n)$
asked in Algorithms by Veteran (399k points)
edited by | 3.4k views

3 Answers

+39 votes
Best answer
Time complexity of Bellman-Ford algorithm is $\Theta(|V||E|)$ where $|V|$ is number of vertices and $|E|$ is number of edges. If the graph is complete, the value of $|E|$ becomes $\Theta\left(|V|^2\right)$. So overall time complexity becomes $\Theta\left(|V|^3\right)$. And given here is $n$ vertices. So, the answer ends up to be $\Theta\left(n^3\right)$.

Correct Answer: $C$
answered by Boss (19.9k points)
edited by
Absolutely correct !

And if it for finding All pairs shortest path for every vertex, then it will be

(n*e)*n = $n^{4}$
+13 votes

as we know time complexity of bellman-ford is O(En) where E is no of edges and n is no of vertices

and in complete graph no of edges is E=n(n-1)/2  where n is no of vertices

here E=O(n2

so time complexity of bellman-ford algorithm on complete graph with n vertices is O(n3)

so ans is C.)

answered by Active (2.4k points)
0 votes

option c is correct.

answered by Boss (33.6k points)

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