Unformatted text preview: Comprehensive Examination Algorithms, Spring 2004 Instruction: Solve any three of the following four problems. Each problem is worth ten points. Before giving more detailed descriptions of algorithms, briefly describe the main ideas and techniques, in 13 sentences. Complete pseudocode is not required, as long as you clearly state what your algorithm is doing. You may use without proof any wellknown algorithms. Give a proof for all your answers; for algorithms, this should include a convincing argument of correctness as well as a time ananysis. The time complexity of your algorithms will influence your score. For instance, you might get only 6 or 7 points for an O ( n 2 ) algorithm if there is an O ( n log n ) algorithm. The relative weight of efficiency versus correctness is given after the specific problems. 1. Let T ( n ) denote the number of different ways to tile a 2 × n rectangle with n 2 × 1 domino....
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 Fall '08
 jin
 Algorithms, Big O notation, Computational complexity theory, minimum number

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