# GATE | GATE-CS-2016 (Set 2) | Question 51

In an adjacency list representation of an undirected simple graph G = (V, E), each edge (u, v) has two adjacency list entries: [v] in the adjacency list of u, and [u] in the adjacency list of v. These are called twins of each other. A twin pointer is a pointer from an adjacency list entry to its twin. If |E| = m and |V | = n, and the memory size is not a constraint, what is the time complexity of the most efficient algorithm to set the twin pointer in each entry in each adjacency list?
(A) Θ(n2)
(B) Θ(m+n)
(C) Θ(m2)
(D) Θ(n4)

Explanation: First you need to find twins of each node. You can do this using level order traversal (i.e., BFS) once. Time complexity of BFS is Θ(m +n).
And you have to use linked list for representation which is extra space (but memory size is not a constraint here).
Final, time complexity is Θ(m + n) to set twin pointer.

Option (B) is correct.

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