[ 2 pts]. Figure 2 shows a state graph with five states. Assume that " a " is the initial state, and "G" is the goal state. a. Use Breath First Search (BFS) to build a search tree to carry out search from the initial state to the goal state (Show complete search tree). [1 pt] i. Mark order of the search node (on the BFS tree) being visited from initiate state to find the goal state (break tie in favor of node with a lower alphabetic order, e.g., "b" has a higher priority than " c "). ii. Is the solution optimal? Why or why not? iii. Explain why avoiding revised state is important in creating BFS search tree. b. Use Depth First Search (BFS) to build a search tree to carry out search from the initial state to the goal state (Show complete search tree). [1 pt] i. Mark order of the search node (on the BFS tree) being visited from initiate state to find the goal state (break tie in favor of node with a lower alphabetic order, e.g., "b" has a higher priority than " c "). ii. Is the solution optimal? Why or why not? iii. Explain why avoiding revised state is important in creating DFS search tree