quiz2_2009

quiz2_2009 - 6.034 Quiz 2 Name EMail Circle your TA and...

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6.034 Quiz 2 October 21, 2009 Name EMail
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Problem 1:Games (50 points) For your reference in working this problem, pseudo code for the standard version of minimax with alpha beta is given on the tear off sheet at the end. Part A: Working with a maximally pruned tree (25 points) For the following min-max tree, cross out those leaf nodes for which alpha-beta search would not do static evaluations in the best case possible (minimum number of static evaluations, maximum pruning of nodes to be statically evaluated). AX MIN MAX MIN
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Part A2 What is the final value returned by the alpha beta search in the best case possible for the given tree? Express your answer as the simplest function of the static values of the leaf nodes (e.g. take n to be the static value at the leaf node labeled n). Your function may contain operations such as max and min . Part A3 What constraints ensure best case possible (minimum static evaluation) for the given tree? State your constraints as inequalities on the static values of the leaf nodes. Part A4 Suppose your static evaluation function, S ( node), is modified as follows: S'( node) = 42 x S ( node) + 1000. (If S(node) = 1, S'(node) = 1042) Would your answer for Part A1 be the same for all possible S(node) values? Suppose your function were S'( node) = - 42 x S ( node) + 1000. Would your answer for Part A1 be the same for all possible S(node) values? Yes No No 3
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Explain your reasoning in less than 4 meaningful sentences or give a short proof. Part B1: Digging Progressively Deeper (10 points) You decide to put your 6.034 knowledge to good use by entering an adversarial programming contest. In this contest, one player (your opponent) is tasked with optimizing the running time of alpha beta search with progressive deepening . Your goal, as her adversary, is to slow down her algorithm. Remembering a key insight from 6.034: node order affects the amount of alpha-beta
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quiz2_2009 - 6.034 Quiz 2 Name EMail Circle your TA and...

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