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# ps7 - Introduction to Algorithms Massachusetts Institute of...

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Introduction to Algorithms November 6, 2006 Massachusetts Institute of Technology 6.046J/18.410J Professors Erik Demaine and Madhu Sudan Problem Set 7 Problem Set 7 This problem set is due in lecture on Monday, November 13, 2006. The homework lab for this problem set will be held 2–4 P . M . on Sunday, November 12, 2006, in room 32-124. Reading: Chapter 15, 16.1–16.3, 22.1, and 23. Problem 7-1 is mandatory. Failure to turn in a solution will result in a serious and negative impact on your term grade! Both exercises and problems should be solved, but only the problems should be turned in. Exercises are intended to help you master the course material. Even though you should not turn in the exercise solutions, you are responsible for material covered in the exercises. Mark the top of each sheet with your name, the course number, the problem number, your recitation section, the date and the names of any students with whom you collaborated. You will often be called upon to “give an algorithm” to solve a certain problem. Your write-up should take the form of a short essay. A topic paragraph should summarize the problem you are solving and what your results are. The body of the essay should provide the following: 1. A description of the algorithm in English and, if helpful, pseudo-code. 2. At least one worked example or diagram to show more precisely how your algorithm works. 3. A proof (or indication) of the correctness of the algorithm. 4. An analysis of the running time of the algorithm. Remember, your goal is to communicate. Full credit will be given only to correct solutions which are described clearly . Convoluted and obtuse descriptions will receive low marks. Exercise 7-1. Do Exercise 15.4-5 on page 356 of CLRS. Exercise 7-2. Do Exercise 16.1-3 on page 379 of CLRS. Exercise 7-3. Do Exercise 22.1-5 on page 530 of CLRS. Exercise 7-4. Do Exercise 23.1-5 on page 566 of CLRS. Exercise 7-5. Do Exercise 23.2-4 on page 574 of CLRS. Exercise 7-6. Do Exercise 23.2-5 on page 574 of CLRS.

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2 Problem Set 7 Problem 7-1. Typesetting In this problem you will write a program (real code that runs!) to solve the following typesetting scenario. Because of the trouble you may encounter while programming, we advise you to START THIS PROBLEM AS SOON AS POSSIBLE.
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