To provide simple proof on a disjoint set forest with union by rank but without path compression run in O ( m lg n ) time.

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Chapter 21.4, Problem 4E

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To provide simple proof on a disjoint set forest with union by rank but without path compression run in O(mlgn) time.

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Hey, Kruskal's algorithm can return different spanning trees for the input Graph G.Show that for every minimal spanning tree T of G, there is an execution of the algorithm that gives T as a result. How can i do that? Thank you in advance!

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