Introduction to Algorithms
September 27, 2006
Massachusetts Institute of Technology
6.046J/18.410J
Professors Erik Demaine and Madhu Sudan
Problem Set 3
Problem Set 3
This problem set is due in recitation on
Friday, October 6, 2006
The homework lab
will be held 7–9
P
.
M
. on Wednesday, October 4, 2006, in room 32124.
Reading:
Chapter 9, Sections 11.1–11.3 and Section 11.5
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 solutions
which are described clearly
. Convoluted and obtuse descriptions will receive low marks.
Exercise 31.
Do Exercise 9.38 on page 193 of CLRS.
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 Fall '08
 ErikDemaine
 Algorithms, Analysis of algorithms, hash function, Bloom filter, Cryptographic hash function, Universal hashing

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