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Unformatted text preview: CS221 Midterm Solutions 1 CS 221, Fall 2009 Practice Midterm Solutions Question Points 1 Short Answers /18 2 Motion Planning /12 3 Search Space Formulation /14 4 A* /12 5 Supervised Learning /20 6 Markov Decision Processes /16 7 Computer Vision /8 Total /100 Name of Student: Exam policy: This exam is openbook and opennotes. Any printed material that you brought with you is allowed. However, the use of mobile devices is not permitted. This includes laptops, cellular phones and pagers. Time: 3 hours. The Stanford University Honor Code: I attest that I have not given or received aid in this examination, and that I have done my share and taken an active part in seeing to it that others as well as myself uphold the spirit and letter of the Honor Code. Signed: CS221 Midterm Solutions 2 1. Short answers [18 points] The following questions require a true/false accompanied by one sentence of explanation, or a very short answer (also accompanied by a brief explanation). To discourage random guessing, one point will be deducted for a wrong answer on multiple choice (such as yes/no or true/false) questions! Also, no credit will be given for answers without a correct explanation. (a) [3 points] In class, we noted that gridbased discretization for motion planning works well in 24 dimensional problems, and studied probabilistic roadmaps for higher di mensions. However, since we live in a 3dimensional world, most real motion planning problems in robotics can be solved in a reasonable about of time using gridbased dis cretization. [True/False] Answer: False . A motion planning problem can be highdimensional even if the workspace is 3D. For example, a robot arm with n joints could lead to an ndimensional planning problem. (b) [3 points] Suppose h is an admissible heuristic for a search problem, such that h ′ = 2 h is not admissible. Then A* search with the heuristic function h ′ will never expand more nodes than A* search with the heuristic function h . [True/False] Answer: False . Suppose h = h ∗ with the following state space: A→ B→ Goal1 (costs 1 and 3), A→ C 1→ C 2→ Goal2 (cost 5 for first step, and cost 0.1 for next two steps). A* with heuristic h = h ∗ will only expand A , B and Goal1. But A* with heuristic 2 h will expand nodes A , C 1 , C 2 and Goal2. (c) [3 points] Suppose we are interested in finding all solutions to a constraint satisfac tion problem. Say, for an 8queens problem, instead of asking for any one solution (i.e., any one arrangement in which the 8 queens lie on different rows, columns and diagonals), we want all possible solutions (i.e., all such arrangements). Which of the following techniques would still be useful for constructing efficient algo rithms for finding all solutions?...
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This note was uploaded on 12/15/2009 for the course CS 221 taught by Professor Koller,ng during the Fall '09 term at Stanford.
 Fall '09
 KOLLER,NG

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