Assume a connected graph and use the breadth-first search algorithm as the base of the algorithm. 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. Consider the following three points as given 1. Any edge of the graph G that is not included in the BFS tree T causes a cycle if added to T 2. BFS on a graph represented using an adjacency list takes O (m + n) 3. There is a linear-time algorithm for finding a lowest common ancestor (LCA) in a tree assume one is given. Give your answers according to the following specification: a) Outline the key idea of your algorithm design. b) Write your algorithm in pseudocode that is precise enough to be executable. c) Explain how you can implement the algorithm to run in time O(m + n). You should justify the running time complexity of each step in your algorithm.