Design an algorithm, which runs in time O(|V| + |E|), that takes as input an undirected graph G = (V, E) in adjacency list format and an edge e € E, and determines whether G has a cycle containing e....

Extracted text: Design an algorithm, which runs in time O(|V| + |E|), that takes as input an undirected graph G = (V, E) in adjacency list format and an edge e € E, and determines whether G has a cycle containing e. Argue your algorithm's correctness and time complexity.