Consider the below initial and goal states (three equally acceptable goals are given) of a planning problem and answer the following questions. In this problem the agent can move any labelled tile on top of other labelled tiles or on top of the empty tile (colored gray). [2+3+3+2 = 10 Marks] Initial State B 80201/09 Goal State - 1 Goal State-2 Goal State - 3 A B D A B D A D (a) Define a best suitable heuristic to design the cost function and justify your choice. (b) Depict the search tree up to exactly two levels (level-2) and find the heuristic values of all the generated nodes. (Given initial state can be assumed to be on level-0.). C) Using the results of sub parts a) & b), apply Greedy Best First Search algorithm. Show the status of OPEN and CLOSE list at each level and find the approximation toward the space complexity of the algorithm. (d) Informed search is preferred than Local search algorithms. Justify this statement with appropriate plagiarism free scenario or numerical example