Introduction to Algorithms
October 21, 2002
Massachusetts Institute of Technology
6.046J/18.410J
Professors Erik Demaine and Shafi Goldwasser
Handout 17
Problem Set 5
This problem set is due
in lecture
on
Wednesday, October 30.
Reading:
Chapter 14;
33.133.2
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 section, the date, and the names of any students with whom you collaborated.
Each problem should be done on a separate sheet (or sheets) of threehole 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 51.
Do Exercise 14.15 on page 307 of CLRS.
Exercise 52.
Do Exercise 14.22 on page 310 of CLRS.
Exercise 53.
Do Exercise 14.35 on page 317 of CLRS.
Exercise 54.
Do Exercise 33.14 on page 939 of CLRS.
Exercise 55.
Do Exercise 33.26 on page 947 of CLRS.
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Handout17:ProblemSet5
Problem 51.
We have seen in class how S
EARCH
and I
NSERT
can be performed on a randomized
skip list in
time, with high probability (where
is the total number of elements in the
structure). However, this assumes that the structure is used as a “black box”: the actual layout of
the structure is opaque to its user, and the operations performed are independent of the random
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 Fall '01
 CharlesE.Leiserson
 Algorithms, Skip list, longest uninterrupted chain

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