ps4 - Introduction to Algorithms Massachusetts Institute of...

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Introduction to Algorithms October 17, 2005 Massachusetts Institute of Technology 6.046J/18.410J Professors Erik D. Demaine and Charles E. Leiserson Handout 15 Problem Set 4 MIT students: This problem set is due in lecture on Monday, October 24, 2005. The homework lab for this problem set will be held 2–4 P . M . on Sunday, October 23, 2005 . Reading: Chapters 12–13, 18 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. Please staple and turn in your solutions on 3-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 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 4-1. Do Exercise 12.1-5 on page 256 of CLRS. Exercise 4-2. Do Exercise 12.2-4 on page 260 of CLRS. Exercise 4-3. Do Exercise 12.4-3 on page 268 of CLRS. Exercise 4-4. Do Exercise 13.1-6 on page 277 of CLRS. Exercise 4-5. Do Exercise 13.3-1 on page 287 of CLRS. Exercise 4-6. Do Exercise 18.2-6 on page 449 of CLRS.
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2 Handout 15: Problem Set 4 Problem 4-1. Treaps If we insert a set of n items into a binary search tree using T REE -I NSERT , the resulting tree may be horribly unbalanced. As we saw in class, however, we expect randomly built binary search trees
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ps4 - Introduction to Algorithms Massachusetts Institute of...

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