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Chris Pollett >Old Classes
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CS255 Spring 2006Practice Midterm 1The practice exam will appear one week before the exam.To study for the midterm I would suggest you: (1) Know how to do (by heart) all the practice problems. (2) Go over your notes at least three times. Second and third time try to see how much you can remember from the first time. (3) Go over the homework problems. (4) Try to create your own problems similar to the ones I have given and solve them. (5) Skim the relevant sections from the book. (6) If you want to study in groups, at this point you are ready to quiz each other. The practice midterm is below. Here are some facts about the actual midterm: (a) The midterm will be in class Feb 20. (b) It is closed book, closed notes. Nothing will be permitted on your desk except your pen (pencil) and test. (c) You should bring photo ID. (d) There will be more than one version of the test. Each version will be of comparable difficulty. (e) If your cell-phone or beeper goes off you will be excused from the test at that point and graded on what you have done till your excusal. (f) One problem (less typos) on the actual test will be from the practice test. [Practice Midterm1 Student Solutions-PDF] 1. Explain the reasoning behind the worst case analysis of the hiring problem. 2. What is a distribution? What is a random variable? Explain how an indicator random variable allows one to convert from a question about distributions to one about expectations. 3. Suppose we choose n numbers using Random(1,n2). Bound the likelihood that two of them will be the same. Do the same for Random(1, n4). 4. Estimate using indicator random variables how many people need to be in the same room for 3 people to share the same birthday. 5. Suppose one has 10 servers being used to handle transactions. When a request for a transaction comes in a server is assigned at random to handle the request. What is the expected number of transaction requests until every server has been requested at least once? 6. Prove or disprove: There is a way to add a comparator to a sorting network so that it is no longer a sorting network. 7. Draw the diagram for Bitonic-Sorter[16]. 8. Prove the zero-one principle for merging networks. 9. Briefly describe how the network Sorter[n] from class is defined. 10. How many bitonic sequence of length n are there over 0-1? |