How do Prim's and Kruskal's algorithms differ in finding minimum spanning trees?

What are the main differences between Prim's and Kruskal's algorithms?

Prim's algorithm builds the minimum spanning tree (MST) by starting from a single vertex and adding edges, while Kruskal's algorithm sorts all edges and adds them one by one, ensuring no cycles are formed.

Which algorithm is more efficient for dense graphs?

Prim's algorithm is generally more efficient for dense graphs because it can take advantage of the many edges, while Kruskal's algorithm may require more time to sort the edges.

Can you give an example of when to use each algorithm?

Use Prim's algorithm when you have a dense graph and need to find the MST quickly. Use Kruskal's algorithm for sparse graphs or when the edges are already sorted.

Are there any specific data structures that work best with these algorithms?

Yes, Prim's algorithm often uses a priority queue, while Kruskal's algorithm typically uses a disjoint-set data structure to manage the connected components.