05-midterm_solutions - CS570 Midterm Exam April 23, 2009...

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Unformatted text preview: CS570 Midterm Exam April 23, 2009 Name: Question Your Points Points 1 17 2 14 3 6 4 6 5 4 6 15 7 8 8 15 Total 85 1 1 True/False (17 points) For each of the following statements, answer True or False. Also, add a short explanation of your answer. An answer without any explanation will get zero points. A. (3 points) Best-first search is a greedier algorithm than A* search. Thus, it may find sub-optimal solutions, but by expanding nodes closer to the goal sooner, it is guaranteed to find a goal sooner (after an equal or fewer number of node expansions) than A*. [True / False] Answer: False. A* with a good heuristic can be extremely fast. For instance, with h(n) = h*(n), A* goes straight to the goal via the optimal path. In contrast, best-first search may spend a lot of time on paths that turn out to be dead-ends. B. (3 points) Let h 1 and h 2 be two admissible heuristic functions. Then, max ( h 1 , . 5 * h 2 ) is also admissible. [True / False] Answer: True (assuming h 1 and h 2 are non-negative. h 1 ≤ h * , and . 5 * h 2 ≤ h 2 ≤ h * , hence in any case max ( h 1 , . 5 * h 2 ) ≤ h * , and it is admissible. Note that if we allow h 2 to be negative, the answer would be false. I gave full credit if you answered True without an explicit assumption statement, but there needs to be a reasonable explanation of your answer (like all other True/False questions on this exam). C. Suppose you have a CSP problem, and you run arc consistency starting from the initial state (before any variables are assigned). After apply- ing arc consistency, all variables have one or more possible value, and there is a variable V i whose domain D i has exactly one possible value remaining ( | D i | = 1). (a) (2 points) There must be at least one solution to this CSP problem. [True / False] Answer: False. Arc consistency does not remove all impossible assignments, so we do not know if the remaining possible value corresponds to a solution or not. (b) (2 points) Any solution to this CSP problem must have the vari- able V i instantiated to the value in D i . [True / False] 2 Answer: True. Since arc consistency only eliminates impossible assignments, we know that any solution must use the remaining assignments. D. The standard alpha-beta pruning performs a depth-first exploration (to a specified depth) of the game tree. (a) (2 points) Alpha-beta pruning can be generalized to do a breadth- first exploration of the game tree and still get the optimal answer. [True / False] Answer: False. The alpha-beta pruning algorithm is an optimiza- tion on min-max. Min-max inherently needs to look at the game- tree nodes below the current node in order to assign a value to that node. (b) (2 points) Alpha-beta pruning can be generalized to do an iterative- deepening exploration of the game tree and still get the optimal answer. [True / False] Yes. Iterative-deepening involves repeated death-first searches to increasing depths. This can be done trivially with min-max and alpha-beta pruning as well, even though ID does waste some work.alpha-beta pruning as well, even though ID does waste some work....
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05-midterm_solutions - CS570 Midterm Exam April 23, 2009...

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