Introduction to Algorithms
November 6, 2006
Massachusetts Institute of Technology
6.046J/18.410J
Professors Erik Demaine and Madhu Sudan
Problem Set 7
Problem Set 7
This problem set is due in lecture on
Monday, November 13, 2006.
The homework
lab for this problem set will be held 2–4
P
.
M
. on Sunday, November 12, 2006, in room
32124.
Reading:
Chapter 15, 16.1–16.3, 22.1, and 23.
Problem 71 is mandatory. Failure to turn in a solution will result in a serious and negative
impact on your term grade!
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 71.
Do Exercise 15.45 on page 356 of CLRS.
Exercise 72.
Do Exercise 16.13 on page 379 of CLRS.
Exercise 73.
Do Exercise 22.15 on page 530 of CLRS.
Exercise 74.
Do Exercise 23.15 on page 566 of CLRS.
Exercise 75.
Do Exercise 23.24 on page 574 of CLRS.
Exercise 76.
Do Exercise 23.25 on page 574 of CLRS.
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Problem Set 7
Problem 71.
Typesetting
In this problem you will write a program (real code that runs!) to solve the following typesetting
scenario.
Because of the trouble you may encounter while programming, we advise you to
START THIS PROBLEM AS SOON AS POSSIBLE.
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 Fall '08
 ErikDemaine
 Algorithms, Space, Spacetime, CLRS

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