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ps4 - Introduction to Algorithms Massachusetts Institute of...

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Introduction to Algorithms October 9, 2002 Massachusetts Institute of Technology 6.046J/18.410J Professors Erik Demaine and Shafi Goldwasser Handout 16 Problem Set 4 This problem set is due in lecture on Monday, October 21. Reading: Chapter 12; 18.1-18.2, Chapter 13 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 by 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. Each problem should be done on a separate sheet (or sheets) of three-hole punched paper. 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 your essay should provide the following: 1. A description of the algorithm in English and, if helpful, pseudocode. 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. Graders will be instructed to take off points for convo- luted and obtuse descriptions. Exercise 4-1. Do exercise 12.4-3 on page 268 of CLRS. Exercise 4-2. Do exercise 12.1-2 on page 256 of CLRS. Exercise 4-3. Do exercise 12.2-7 on page 260 of CLRS. Exercise 4-4. Do exercise 12.3-5 on page 264 of CLRS. Exercise 4-5. Do exercise 18.2-6 on page 449 of CLRS. Exercise 4-6. Do exercise 13.1-5 on page 277 of CLRS. Exercise 4-7. Do exercise 13.2-2 on page 278 of CLRS.
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2 Handout 16: Problem Set 4 Problem 4-1. Given two strings and , where each and is in some ordered set of characters, we say that string is lexically less than string if either: 1. there exists an integer , , such that
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