In our definition, BFS is a graph search algorithm that begins from a node (a "root" node) and explores all the neighboring nodes. Then for each of those nearest nodes, it explores their unexplored neighbor nodes, and so on, until all the nodes within the graph are explored. DFS is a graph search algorithm that starts from a node (a "root" node) and explores as far as possible along each branch before backtracking (going back to a node that has been explored before). For an undirected and connected graph, such a process could produce a Depth-First Search Tree, in which the starting node serves as the root of the tree. Whenever a new unvisited node is explored for the first time during the DFS search process, it is attached to the DFS tree as a child to the node from which it is being reached. Please note that our BFS and DFS algorithms are defined in a traditional way. The algorithms shown in the textbook try to find a goal node. In our algorithms, we are trying to explore all the nodes within the graph Please use the Figure 1 and answer the questions. The figure shows an undirected graph and all the edges have equal costs (e.g, the lengths of all edges are equal). For simplicity, when we have a number of alternate nodes to explore, we will select them in alphabetical order. The problems can be easily solved by hand. Assume node a is the starting point (the "root" node) from which the search starts. Figure 1 1) Apply the BFS algorithm and show the output (list all the nodes by the order they are being explored) [15 points] 2) Apply the DFS algorithm and show the output (list all the nodes by the order they are being explored) [15 points] 3) Show the output from the previous question in the form of a DFS tree. Edges in a DFS tree are a subset of the original edge set from which a node is visited for the first time during the DFS searching process. [10 points]