fa10-midterm-solutions - CS 188 Introduction to Fall 2010...

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Unformatted text preview: CS 188 Introduction to Fall 2010 Artificial Intelligence Midterm Exam INSTRUCTIONS You have 3 hours. The exam is closed book, closed notes except a one-page crib sheet. Please use non-programmable calculators only. Mark your answers ON THE EXAM ITSELF. If you are not sure of your answer you may wish to provide a brief explanation. All short answer sections can be successfully answered in a few sentences at most. Last Name First Name SID Login GSI Section Time Name of the person to your left Name of the person to your right All the work on this exam is my own. (please sign) For staff use only Q. 1 Q. 2 Q. 3 Q. 4 Q. 5 Total /19 /12 /17 /20 /22 /90 2 THIS PAGE INTENTIONALLY LEFT BLANK NAME: 3 1. (19 points) Search: X-PacMen We will discuss three variants of Pacman in which the goal is always to eat every pellet and there are no ghosts. However, in each question, Pacman has a different superpower. When not otherwise specified, the cost of every action is 1. Notation: Let N and M be the width and height of a board, let F the initial number of food pellets in a start state, and let f be the number of uneaten food pellets remaining in a given state. Quicksilver Pacman: parts (a), (b), and (c) Pacman can run very fast in any direction, and he must pick up all the pellets he encounters along the way. Hes so fast that he can move any number of squares in a single move. He cannot run through walls, he can only run in one of the four directions, and he cannot turn while running. For example, this is a valid move: But this is not: For this problem, we use the following state-space: State: n Pacmans location: ( x,y ), where x [1 ,...,N ] ,y [1 ,...,M ] Flags indicating which dots remain: { f i } , where f i { true,false } , i [1 ,...,F ] (a) (2 pt) Circle the tightest upper bound on the size of this state space: N M , F M N , 2 F N M , 2 N M , 2 F N M (b) (2 pt) Circle the tightest upper bound on the branching factor of this state space (the number of successor states of a single state): 4, F , N + M , N M , F ( M + N ), F N M , 2 F ( M + N ) (c) (3 pt) For each of the following heuristics, indicate (yes/no) whether or not it is admissible. Heuristic Admissible? f (the number of food pellets remaining) No min food (manhattanDistance( pacman,food )) No (smallest Manhattan dist. from Pacman to a remaining food) f/ max( M,N ) Yes f/ ( M + N ) Yes 4 Multiple (Pac)man: parts (d) and (e) Instead of moving, this Pacman will instead make a duplicate of itself in a free (non-wall and non-Pacman) cell that is adjacent to any current Pacman duplicate. Duplicates cannot move, and cannot be deleted; only new duplicates can be made. Only one single duplicate can be created at each turn....
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This note was uploaded on 08/26/2011 for the course CS 188 taught by Professor Staff during the Spring '08 term at University of California, Berkeley.

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fa10-midterm-solutions - CS 188 Introduction to Fall 2010...

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