What are the complexities of Prim's and Kruskal's algorithms?

What are the complexities of Prim's and Kruskal's algorithms?

Prim's algorithm has a time complexity of O(E log V) with a priority queue, while Kruskal's algorithm has a complexity of O(E log E) or O(E log V) depending on the sorting method used.

Can you explain why their complexities differ?

Certainly! Prim's algorithm grows the MST by adding edges from a single vertex, which requires priority queue operations. Kruskal's algorithm, on the other hand, sorts all edges first and then adds them, leading to different complexities.

Which algorithm is more efficient in practice?

It depends on the graph's density. Prim's is often more efficient for dense graphs, while Kruskal's is better for sparse graphs.

Are there any specific use cases for each algorithm?

Yes! Prim's is commonly used in network design, while Kruskal's is often used in clustering and image processing.