ps5 - Introduction to Algorithms Massachusetts Institute of...

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Introduction to Algorithms October 21, 2002 Massachusetts Institute of Technology 6.046J/18.410J Professors Erik Demaine and Shafi Goldwasser Handout 17 Problem Set 5 This problem set is due in lecture on Wednesday, October 30. Reading: Chapter 14; 33.1-33.2 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 5-1. Do Exercise 14.1-5 on page 307 of CLRS. Exercise 5-2. Do Exercise 14.2-2 on page 310 of CLRS. Exercise 5-3. Do Exercise 14.3-5 on page 317 of CLRS. Exercise 5-4. Do Exercise 33.1-4 on page 939 of CLRS. Exercise 5-5. Do Exercise 33.2-6 on page 947 of CLRS.
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2 Handout17:ProblemSet5 Problem 5-1. We have seen in class how S EARCH and I NSERT can be performed on a randomized skip list in time, with high probability (where is the total number of elements in the structure). However, this assumes that the structure is used as a “black box”: the actual layout of the structure is opaque to its user, and the operations performed are independent of the random
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ps5 - Introduction to Algorithms Massachusetts Institute of...

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