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Unformatted text preview: Introduction to Algorithms December 14, 2009 Massachusetts Institute of Technology 6.006 Fall 2009 Professors Srini Devadas and Constantinos (Costis) Daskalakis Final Exam Final Exam 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 150 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 booklet contains 13 pages, including this one. Two extra sheets of scratch paper are attached. Please detach them before turning in your quiz at the end of the exam period. 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. 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. Good luck! Problem Parts Points Grade Grader Problem Parts Points Grade Grader 1 10 30 5 1 20 2 1 10 6 1 15 3 1 10 7 1 20 4 1 20 8 3 25 Total 150 Name: 6.006 Final Exam Name 2 Problem 1. True or False [30 points] (10 parts) For each of the following questions, circle either True, False or Unknown. 1.After hashing n keys into a hash table of size m that uses chaining to handle collisions, we hash two new keys k 1 and k 2 . Under the simple uniform hashing assumption, the probability that k 1 and k 2 are hashed into the same table location is exactly 1 /m with no dependence on the number of keys n . Answer = True False 2.Under the uniform hashing assumption, if we use a hash table of size m with open addressing to hash 3 keys, the probability that the third inserted key needs exactly three probes before being inserted into the table is exactly 2 m ( m- 1) . Answer = True False 3.We use a hash table of size m with open addressing to hash n items. Under the uniform hashing assumption, the expected cost to insert another element into the table is at most 1 + , where = n/m is the average load....
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- Fall '08