Problem 2 [20 points]. Consider the graphs on the right, which we denote as a cycle and an in finite diamond strip (IDS). The cycle has n nodes V1, , vn-to that are consecutively ordered, i.e., vi has vi-i bors, with vi-1 before vi+1 mod n. node in the IDS, assume that in its adjacency list, the neighbors on the left appear before the neighbors on the right. Now consider running BFS and DFS tree and graph searches on these two graphs. For the cycle graph, suppose the start node is x1 ui and the goal node is zG = zk, 1 S k <.>