Introduction to Algorithms
October 22, 2001
Massachusetts Institute of Technology
6.046J/18.410J
SingaporeMIT Alliance
SMA5503
Professors Erik Demaine, Lee Wee Sun, and Charles E. Leiserson
Handout 21
Problem Set 6
MIT students:
This problem set is due in lecture on
Monday, October 29
.
SMA students:
This problem set is due after the videoconferencing session on
Wednesday, Oc
tober 31
.
Reading:
Chapter 14; Chapter 33 (
§
33.1–33.3)
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 threehole punched
paper.
SMA students:
Each problem should be done on a separate sheet (or sheets) of twohole punched
paper.
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 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 61.
Do exercise 14.15 on page 307 of CLRS.
Exercise 62.
Do exercise 14.22 on page 310 of CLRS.
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Handout 21: Problem Set 6
Exercise 63.
Do exercise 14.31 on page 316 of CLRS.
Exercise 64.
Do exercise 14.35 on page 317 of CLRS.
Exercise 65.
Do exercise 33.14 on page 946 of CLRS.
Exercise 66.
Do exercise 33.21 on page 946 of CLRS.
Problem 61.
Overlapping rectangles
VLSI databases commonly represent an integrated circuit as a collection of rectangles. Assume that
each rectangle is rectilinearly oriented (sides parallel to the
x
 and
y
axis), so that a representation
of a rectangle consists of its minimum and maximum
x
 and
y
coordinates.
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 Spring '01
 CharlesE.Leiserson
 Algorithms, Analysis of algorithms, Rectangle, CLRS, view rectangle, horizontal roads

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