comp-al-sp04 - Comprehensive Examination Algorithms Spring...

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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 1-3 sentences. Complete pseudocode is not required, as long as you clearly state what your algorithm is doing. You may use without proof any well-known 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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