Introduction to Algorithms
September 20, 2004
Massachusetts Institute of Technology
6.046J/18.410J
Professors Piotr Indyk and Charles E. Leiserson
Handout 8
Problem Set 2
Reading:
Chapters 59, excluding 5.4 and 8.4
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 writeup
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, 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. Full credit will be given only to correct algorithms
which are
which are described clearly
. Convoluted and obtuse descriptions will receive low marks.
Exercise 21.
Do Exercise 5.24 on page 98 in CLRS.
Exercise 22.
Do Exercise 8.23 on page 170 in CLRS.
Problem 21.
Randomized Evaluation of Polynomials
In this problem, we consider testing the equivalence of two polynomials in a finite field.
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 Fall '04
 PiotrIndykandCharlesE.Leiserson
 Algorithms, Prime number, Gladiator, Polly

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