If Kruskal's algorithm was implemented using BFS to check whether adding an edge with create a cycle, what would the overall Big-O run time of the algorithm be?
What is the overall Big O run time of Kruskal’s algorithm if BFS was used to check whether adding an edge creates a cycle?
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It would be
O(V * E + E * log E). Each BFS takesO(V)time because there areV - 1edges in a tree(or less if the tree is not completely build yet) and it is run for each edge(Vis the number of vertices,Eis the number of edges). So it isO(V * E)in total.E * log Eterm comes from sorting the edges.