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Unformatted text preview: Introduction to Algorithm s Day 23 Massachusetts Institute of Technology 6.046J/18.410J Singapore-MIT Alliance SMA5503 Professors Erik Demaine, Lee Wee Sun, and Charles E. Leiserson Handout 23 Problem Set 7 MIT students: This problem set is due in lecture on Day 26 . Reading: Chapters 17 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 instructor and time, the date, and the names of any students with whom you collaborated. MIT students: 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 7-1. Do exercise 17.1-1 on page 409 of CLRS. Exercise 7-2. Do exercise 17.3-4 on page 416 of CLRS. 2 Handout 23: Problem Set 7 Exercise 7-3. Do exercise 17.3-7 on page 416 of CLRS. Exercise 7-4. Do exercise 17.4-1 on page 424 of CLRS. Problem 7-1. Reducing the space in the van Emde Boas structure In this problem, we will use hashing to modify the van Emde Boas data structure presented in lecture in order to reduce its space usage....
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- Fall '04