What is the time complexity of Prim's algorithm?
Prim's algorithm has a time complexity of O(E log V) when using a priority queue implemented with a binary heap, where E is the number of edges and V is the number of vertices.
Can you explain why it has that complexity?
Sure! The complexity arises from the need to repeatedly extract the minimum edge from the priority queue, which takes O(log V) time, and this operation is performed for each of the E edges.
Are there any variations of Prim's algorithm?
Yes, there are variations like the Fibonacci heap implementation, which can reduce the time complexity to O(E + V log V).
How does Prim's algorithm compare to Kruskal's algorithm?
Prim's algorithm is more efficient for dense graphs, while Kruskal's algorithm is better for sparse graphs. Their complexities also differ based on the data structures used.
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