Exercise 2: Assume we have the vacuum cleaner world with four rooms shown in Figure 1 which represents the initial configuration. The vacuum agent can choose to move left, move right, move up, move down or suck up the dirt. The agent want to reach the goal configuration shown in the Figure 2. Remark: you must follow the order of the actions Figure 1 Let M be the number of dirty rooms and V is the distance of the vacuum from its current room to its destination room in the goal state. Thus, consider h is an heuristic function defined as following: h = 2M + V Figure 2 Answer the following questions avoiding the repeated states: a) Show how the A* algorithm works to find the goal. b) Is h consistent in this case? Justify your answer? c) Show how the Greedy best-first search works to find the goal. Is it optimal in this case, Justify your