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final-f2007 - 6.006 Fall 2007 Final Examination...

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Introduction to Algorithms December 19, 2007 Massachusetts Institute of Technology 6.006 Fall 2007 Professors Ron Rivest and Srini Devadas Final Examination Final Examination Do not open this exam booklet until you are directed to do so. Read all the instructions on this page. When the exam begins, write your name on every page of this exam booklet. This exam contains 7 sections with multiple parts. You have 180 minutes to earn 160 points. This exam booklet contains 16 pages, including this one. Two extra sheets of scratch paper are attached. Please detach them before turning in your exam at the end of the examination. This exam is closed book. You may use two 8 1 2 00 × 11 00 crib sheets. No calculators or programmable devices are permitted. Write your solutions in the space provided. If you need more space, write on the back of the sheet containing the problem. Do not put part of the answer to one problem on the back of the sheet for another problem, since the pages may be separated for grading. Do not waste time and paper rederiving facts that we have studied. It is sufficient to cite known results. Do not spend too much time on any one problem. Read them all through first, and attack them in the order that allows you to make the most progress. Show your work, as partial credit will be given. You will be graded not only on the correct- ness of your answer, but also on the clarity with which you express it. Be neat. There are True/False questions scattered throughout the exam. As usual, you must justify those answers to receive full credit. Good luck! Topic Problem Parts Points Grade Grader Python & Asymptotics 1 5 25 Hashing 2 5 25 Dynamic Programming 3 2 20 Sorting 4 3 15 Search 5 2 10 Shortest Paths 6 4 40 Numerics 7 4 25 Total 27 160 Name:
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6.006 Final Examination Name 2 Problem 1. Python and Asymptotics [25 points] (5 parts) (a) [5 points]
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