A greedy algorithm for the minimum spanning tree problem is to start with any vertex and then repeatedly add the edge with the smallest weight that does not create a cycle. Which of the following is NOT true about this algorithm?OptionsIt always produces a minimum spanning tree.It may not produce the minimum spanning tree if the graph contains cycles.It may not produce the minimum spanning tree if the graph contains negative weights.It is always efficient.
Question
A greedy algorithm for the minimum spanning tree problem is to start with any vertex and then repeatedly add the edge with the smallest weight that does not create a cycle. Which of the following is NOT true about this algorithm?OptionsIt always produces a minimum spanning tree.It may not produce the minimum spanning tree if the graph contains cycles.It may not produce the minimum spanning tree if the graph contains negative weights.It is always efficient.
Solution
The statement that is NOT true about this algorithm is: "It may not produce the minimum spanning tree if the graph contains cycles."
This is incorrect because the presence of cycles in the graph does not affect the ability of a greedy algorithm to find a minimum spanning tree. The key characteristic of a greedy algorithm for this problem is that it avoids creating a cycle when adding a new edge, not that it cannot handle graphs that contain cycles.
The other statements are true. The algorithm always produces a minimum spanning tree, it may struggle
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