What is the exact difference between prim's minimum spanning tree algorithm and dijkstra's single source shortest path algorithm?

Question

I mean if we run prim's algorithm on a weighted directed graph, will it give the same shortest path? And vice-versa?

Also if we run dijkstra's algorithm on a graph with negative weight cycle reachable from source, what will happen?

What if we run kruskal's MST algorithm on a graph with negative weights and negative weight cycles?

Thanks in advance.

Comments

1.from prims algo. - we will get MST

from dijsktra algo - we will get shortest path from source(i.e single source) to destination.

2. if we run dijsktra on graph with negative weight edges then dijsktra algo is going to compute the shortest path but it may or may not be correct .since it is not a sin to run dijsktra algo with graph having negative weight edges .And becoz of this demerit of dijsktra algo. we switch to bellman ford algo.

since practically it is not possible to have negative wieght edges (for ex -travelling salesman problem ) therefore dijskta algo is more practically used as compared to bellman ford algo.

3. kruskal algo is also an algo so u can run it with graph containing negative weight edges and negative weight cycles since the output will be an tree(without cycles) not an graph.

Answer 1

1.from prims algo. - we will get MST

from dijsktra algo - we will get shortest path from source(i.e single source) to destination.

2. if we run dijsktra on graph with negative weight edges then dijsktra algo is going to compute the shortest path but it may or may not be correct .since it is not a sin to run dijsktra algo with graph having negative weight edges .And becoz of this demerit of dijsktra algo. we switch to bellman ford algo.

since practically it is not possible to have negative wieght edges (for ex -travelling salesman problem ) therefore dijskta algo is more practically used as compared to bellman ford algo.

3. kruskal algo is also an algo so u can run it with graph containing negative weight edges and negative weight cycles since the output will be an tree(without cycles) not an graph.

Answer 2

Please refer to this.I hope your doubt will get clear:http://cs.stackexchange.com/questions/18797/minimum-spanning-tree-vs-shortest-path