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Brian Williams

# Brian Williams - 16.410-13 Principles of Automated...

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16.410-13: Principles of Automated Reasoning and Decision Making Midterm Solutions October 31 st , 2005 Name 16.410-13 Staff E-mail Note: Budget your time wisely. Some parts of this quiz could take you much longer than others. Move on if you are stuck and return to the problem later. Problem Number Max Score Grader Problem 1 40 Problem 2 40 Problem 3 40 Total 120

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Problem 1 Search (40 points) Part 1.A Uninformed Search (15 points) Consider the problem of navigating a mouse through a pentagonal-star shaped maze, shown below. The mouse is located at node S and the cheese is located at node G. S I H G F E D C B A Part 1.A.1 Mouse Strategy for Maze Search (7 points) The poor mouse unfortunately has a bad memory and cannot remember where he has been to already. From any one node, he can look in all directions and see the adjacent nodes . As any intelligent mouse, he orders them alphabetically . After looking around, he always takes the path to the neighboring node that appears earliest in the alphabet (e.g., from node S, he would go to A instead of B). Since there are no dead ends, he never backtracks. List the first five steps of the path taken by the mouse. At each step list the node the mouse is at and the adjacent nodes seen. Step At Node Sees Nodes Does the mouse get to the cheese using this strategy? Why or why not? 1
What search method or methods is the mouse’s search strategy most similar to? Part 1.A.2 Breadth-first Maze Search (8 points) S I H G F E D C B A Using a different approach, the mouse decides to leave a little excrement at each node he goes to, so that he can keep track of where he has gone. He now decides to use these marks to implement a breadth first approach, when going through the maze. Model his behavior using breadth-first search , with a visited list and a queue . Keep track of the visited list and elements taken off and put on the queue at each step (it is not necessary to rewrite the whole queue at each step unless you find it helpful). Stop when a path to G is found . Step Dequeued Enqueued Visited List 2

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Part 1.B Informed Search (25 points) The mouse finds and eats the cheese at G. Now we consider a new piece of cheese at node J, as shown below. Note that J is closer to B and C than it is to E and F. The mouse becomes smarter and uses his sense of smell to guide him. He uses the fact that the cheese smells stronger when he is physically closer to it, to estimate his straight-line distance to the goal. He tries out three search methods: greedy, uniform cost, and A*.
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