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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 open-book and open-notes. 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 grid-based discretization for motion planning works well in 2-4 dimensional problems, and studied probabilistic roadmaps for higher di- mensions. However, since we live in a 3-dimensional world, most real motion planning problems in robotics can be solved in a reasonable about of time using grid-based dis- cretization. [True/False] Answer: False . A motion planning problem can be high-dimensional even if the workspace is 3-D. For example, a robot arm with n joints could lead to an n-dimensional 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 8-queens 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