2. Informed Search ( 20 points) a. Evaluation function (5 points) Recall that an admissible heuristic function always makes a conservative estimate to the goal. With S as initial state and G1,G2, and G3 as final states in the figure above, does the heuristic function h in the graph above satisfy the condition of an admissible heuristic? Explain why or why not? (2 points) If your answer is NO, what is the minimum modification needed to make h admissible? [Type "No modification needed if your answer is YES"] (3 points) b. Greedy Best First Search (5 points) After making the modification, with S as the initial State and G1, G2, and G3 as the Goal States, find the order of node expansion using greedy best first search. Assume successor/children priority order: Left to Right while adding nodes to the fringe, e.g., successors of CF,C. Show the steps in detail. Solve the problem for both cases: keeping track vs. not keeping track of visited nodes. c. Uniform Cost Search (5 points) Repeat the same with A search. Solve the problem for both cases: keeping track of visited nodes vs. not keeping track of visited nodes. d. A* Search (5 points) Repeat the same with A search. Solve the problem for both cases: keeping track of visited nodes vs. not keeping track of visited nodes