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Unformatted text preview: Introduction to Algorithms April 25April 29, 2005 Massachusetts Institute of Technology 6.046J/18.410J Professors Charles E. Leiserson and Ronald L. Rivest Quiz 2 Practice Quiz 2 This takehome quiz contains 5 problems worth 25 points each, for a total of 125 points. Each problem should be answered on a separate sheet (or sheets) of 3hole punched paper. Mark the top of each problem with your name, 6.046J/18.410J, the problem number, your recitation time, and your TA. Your exam is due between 9:00 and 11:00 A . M . on Friday, April 29, 2005 . Late exams will not be accepted unless you obtain a Dean’s Excuse or make prior arrangements with your recitation instructor. You must hand in your own exam in person. The quiz should take you about 10 hours to do, but you have four days in which to do it. Plan your time wisely. Do not overwork, and get enough sleep. Ample partial credit will be given for good solutions, especially if they are well written. Of course, the better your asymptotic bounds, the higher your score. Bonus points will be given for exceptionally efficient or elegant solutions. Writeups: Each problem should be answered on a separate sheet (or sheets, stapled separately for each problem) of 3hole punched paper. Mark the top of each problem with your name, 6.046J/18.410J, the problem number, your recitation time, and your TA. Your solution to a prob lem should start with a topic paragraph that provides an executive summary of your solution. This executive summary should describe the problem you are solving, the techniques you use to solve it, any important assumptions you make, and the running time your algorithm achieves. Write up your solutions cleanly and concisely to maximize the chance that we understand them. Be explicit about running time and algorithms. For example, don’t just say you sort n numbers, state that you are using heapsort, which sorts the n numbers in O ( n lg n ) time in the worst case. When describing an algorithm, give an English description of the main idea of the algorithm. Use pseudocode only if necessary to clarify your solution. Give examples, and draw figures. Provide succinct and convincing arguments for the correctness of your solutions. Do not regurgitate material presented in class. Cite algorithms and theorems from CLRS, lecture, and recitation to simplify your solutions. Part of the goal of this exam is to test engineering common sense. If you find that a question is unclear or ambiguous, make reasonable assumptions in order to solve the problem, and state clearly in your writeup what assumptions you have made. Be careful what you assume, however, because you will receive little credit if you make a strong assumption that renders a problem trivial....
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 Spring '11
 Prof.CharlesLeiserson
 Graph Theory, Data Structures

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