Let G be a graph with V vertices and E edges
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Let G be a graph with V vertices and E edges

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Let G be a graph with V vertices and E edges. One can implement Kruskal's Algorithm to run in O(E log V) time, and Prim's Algorithm to run in O(E + V log V) time.

If G is a dense graph with an extremely large number of vertices, determine which algorithm would output the minimum-weight spanning tree more quickly. Clearly justify your answer.

Hint
ComputerPrim's algorithm: It is also called as Jarník's algorithm. It is a greedy algorithm which finds a minimum spanning tree for the weighted undirected graph. It also means it finds the subset of the edges which forms the tree that includes every vertex, where the total weight of all the edges in the tree is minimized....
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