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This question deals with minimum spanning trees in connected edge-weighted graphs. Each algorithm below takes as input a connected graph G = (V, E) with
This question deals with minimum spanning trees in connected edge-weighted graphs. Each algorithm below takes as input a connected graph G = (V, E) with weights l: E N, and outputs a subgraph T = (V,F) of G. For each of the following parts 2.1-2.4 state whether or not T is always a minimum spanning tree of G. There is no need to provide proofs or counter examples. procedure maybeMSTI sort the edges e E by their weights l(e) FE for e E E in non-decreasing order if (V, FU{e}) is acyclic then F FU{e} O correct O incorrect procedure maybeMSTii sort the edges e E by their weights lle) FEE for e E in non-increasing order if (V, F {e}) is connected then F F {e} O correct O incorrect procedure maybeMSTii FE for e E E in any order F -FU{e} if T = (V,F) has a cycle then select a cycle C in T select an edge f of maximum weight on C FF {f} O correct O incorrect procedure maybeMSTiv FEE for xy E E in any order FF {xy} if T = (V,F) is disconnected then select components TX and T Y of T with x X and Y EY select an edge f E of minimum weight between X and Y F-FU{f} O correct O incorrect
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