[2 pts] Figure 1 shows a search tree with 21 nodes. Please uses BFS, and DFS algorithms showing in Figures 2, 3, and 4 to report the order of the nodes being visited, and the Fringe structure of each method (report fringe structure of each step as show in the table below) [1 pt]. Please compare the fringe structure and explain the memory consumption of each method, with respect to branching factor (b) and the search depth (d) [1 pt].

Fringe	Node visited	Fringe Size	Search depth

1 procedure DFS-iterative(G,v): 2 let S be a stack 3 S.push(v) 4 while S is not empty V : S.pop() if v is not labeled as discovered: label v as discovered for all edges from v to w in G.adjacentEdges(v) do S.push(w) Figure 2 Depth First Search DFS (Method 1) s stack s.push(initial node) add initial node to visited while s is not empty: Figure 1 Set all nodes to not visited" q new Queue(); q.enqueue (initial node); wile q empty do V s.peek() if for all E(v,u) there is one unvisited u: x q.dequeue(); mark u as visited if ( x has not been visited) s.push(u) visited[x] true; // Visit node x else for every edge (x, y) /* we are using all edges) if (y has not been visited) .pop q.enqueue(y) // Use the edge (x,y)!!! Figure 3 Depth First Search (Method 2) Figure 2: Breath First Search (BFS)