GATE | GATE MOCK 2017 | Question 24

If Kruskal’s algorithm is used for finding a minimum spanning tree of a weighted graph G with n vertices and m edges and edge weights are already given in a sorted list, then, What will be the time complexity to compute the minimum cost spanning tree given that union and find operations take amortized O(1) ?
(A) O(m logn)
(B) O(n)

(C) O(m)
(D) O(n logm)

Answer: (C)

O(m) as you are already given edge weights in sorted order. You just have to pick the edges in the increasing order and add it to the current spanning set if its addition does not result in a cycle else throw it away.

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