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Unformatted text preview: Introduction to Algorithms May 19, 2010 Massachusetts Institute of Technology 6.006 Spring 2010 Professors Piotr Indyk and David Karger Final Examination Final Examination Do not open this quiz booklet until directed to do so. Read all the instructions on this page. When the quiz begins, write your name on every page of this quiz booklet. You have 180 minutes to earn 180 points. 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. This quiz is closed book. You may use three 8 1 2 00 11 00 or A4 crib sheets (both sides). No calculators or programmable devices are permitted. No cell phones or other communications 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. 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. When writing an algorithm, a clear description in English will suffice. Pseudo-code is not required. When asked for an algorithm, your algorithm should have the time complexity specified in the problem with a correct analysis. If you cannot find such an algorithm, you will generally receive partial credit for a slower algorithm if you analyze your algorithm correctly . Show your work, as partial credit will be given. You will be graded not only on the correctness of your answer, but also on the clarity with which you express it. Be neat. Good luck! Problem Parts Points Grade Grader 1 7 21 2 9 54 3 3 15 4 3 20 5 4 25 6 4 25 7 3 20 Total 180 Name: Friday Recitation: Zuzana 10 AM Debmalya 11 AM Ning 12 PM Matthew 1 PM Alina 2 PM Alex 3 PM 6.006 Final Examination Name 2 Problem 1. True or False [21 points] (7 parts) For each of the following questions, circle either T (True) or F (False). There is no penalty for incorrect answers. You are not required to give any justification for your answer. (a) T F [3 points] Every vertex reachable from a vertex v in an undirected graph G is either a descendant or an ancestor of v in any DFS tree of G . (b) T F [3 points] In the DAG representation of a dynamic program, an edge between two sub-problems indicates that they are identical. (c) T F [3 points] Assuming simple uniform hashing, the collision probability of a new key being inserted in a hash table using open addressing is at least as much as in a hash table using chaining. (Assume that both hash tables are of the same size and contain the same set of keys.) (d) T F [3 points] If problem A is polynomial-time reducible to problem B and A is in P , then B is in P as well....
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