Give an algorithm to detect whether a given undirected graph contains a cycle. If the graph contains a cycle, then your algorithm should output one. (It should not output all cycles in the graph, just one of them.) The running time of your algorithm should be O(m + n) for a graph with n nodes and m edges. Assume a connected graph. Use breadth-first search as the base of the algorithm. Assume the adjacency list representation of a graph. Explain how you can implement the algorithm to run in time O(m + n). The algorithm description may be in pseudocode but should be precise enough to be executable and justify the running time complexity of each step. Consider the following points as given: (i) any edge of the graph G that is not included in the BFS tree T causes a cycle if added to T (ii) BFS on a graph represented using an adjacency list takes O(m + n) (iii) there is a linear-time algorithm for finding a lowest common ancestor (LCA) in a tree assume one is given.