I was wondering when one should use Prim's algorithm and when Kruskal's to find the minimum spanning tree? They both have easy logics, same worst cases, and only difference is implementation which might involve a bit different data structures. So what is the deciding factor?
10 Answers
Use Prim's algorithm when you have a graph with lots of edges.
For a graph with V vertices E edges, Kruskal's algorithm runs in O(E log V) time and Prim's algorithm can run in O(E + V log V) amortized time, if you use a Fibonacci Heap.
Prim's algorithm is significantly faster in the limit when you've got a really dense graph with many more edges than vertices. Kruskal performs better in typical situations (sparse graphs) because it uses simpler data structures.
I know that you did not ask for this, but if you have more processing units, you should always consider Borůvka's algorithm, because it might be easily parallelized - hence it has a performance advantage over Kruskal and Jarník-Prim algorithm.
Kruskal can have better performance if the edges can be sorted in linear time, or are already sorted.
Prim's better if the number of edges to vertices is high.
Prim's is better for more dense graphs, and in this we also do not have to pay much attention to cycles by adding an edge, as we are primarily dealing with nodes. Prim's is faster than Kruskal's in the case of complex graphs.
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