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Question 1 (25 points) The following figure shows an example of Monte Carlo Tree Search, where each leaf node is annotated with the utility value. To maximize the utility, here Monte Carlo Tree Search is applied to return a planning path. Suppose that after several steps, the current state of the MCTS search tree is also shown in the following figure, where the numbers within a node represent "estimated value / the number of visits" and those nodes encircled by dashed lines are not expanded yet. - (5 points) Provided that the hyperparameter C=1 in the UCB bound, please show the path selected by MCTS. - (5 points) Please continue the procedures of selection, expansion, roll out, and backpropagation, and visualize the state of the search tree afterwards. (You can change the value of C.) - (10 points) Try more iterations of the four procedures of MCTS, and see if the leaf node with the largest utility (i.e., 9) can be returned. If not, please give your suggestions on how to modify the algorithm for higher efficiency