Purpose: Demonstrate the ability to use and implement graph traversal algorithms Question 1 (30 POINTS): Given a graph G and the Breadth First Search (BFS) and Depth First Search (DFS) traversal algorithms as follows BFS(G, ) 1 for each vertex u e G.V-s u.color WHITE 11 , ? = NIL 5 s.color=GRAY 7 S.NIL 9 ENQUEUE (Q. 12 for each v e G.Adiu] 11 ) 10 while Q? 12 13 13 if v.color. WHITE v.color = GRAY 15 16 17 18 ENQUEUE Q.v u,color BLACK DFS-VISIT (G, u) DFS(G) 1 for each vertex u e G.V time = time+ 1 2 u.d time 11 . color WHITE 3 u.color GRAY 4 for each v E G.Adj[u] 4 time- 5 for each vertex u E G.V if v.colorWHITE if u. color WHITE DFS-VISIT (G, u) DFS-VISIT (G, v 8 u.color=BLACK time-time1 10 u.f-time 1.A.) (10 POINTS) Assume that node 1 wants to reach node 6 in graph G by using the Breadth First Search (BFS) traversal algorithm. What is the largest number of nodes (starting from node 1 ending at node 6) need to be visited via this traversal? Run the BFS traversal algorithm to show your step by step work. You need to show your work to get credit for this question. 1.B.) (10 POINTS) Assume that node 1 wants to reach node 6 in graph G by using the Depth First Search (DFS) traversal algorithm. What is the largest number of nodes (starting from node 1 ending at node 6) need to be visited via this traversal? Run the DFS traversal algorithm to show your step by step work. You need to show your work to get credit for this question. 1.?.) (10 POINTS) Compare the results you have obtained in IA and IB. which traversal requires visiting more steps? Why? Please explain