Let \(G = (V, E)\) be a weighted undirected graph and let \(T\) be a Minimum…

GATE · 2020 · CS · Computer Science & IT

Let G=(V,E)G = (V, E) be a weighted undirected graph and let TT  be a Minimum Spanning Tree (MSTMST) of GG maintained using adjacency lists. Suppose a new weighed edge (u,v)∈V×V(u, v) ∈ V×V is added to GG. The worst case time complexity of determining if TT is still an MSTMST of the resultant graph is

  1. A.

    Θ(∣E∣+∣V∣)\Theta (\mid E \mid + \mid V \mid) \\

  2. B.

    Θ(∣E∣∣V∣)\Theta (\mid E \mid \mid V \mid) \\

  3. C.

    Θ(E∣log⁡∣V∣)\Theta(E \mid \log \mid V \mid) \\

  4. D.

    Θ(∣V∣)\Theta( \mid V \mid)

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