Algorithms  CSE 202
Mathematical Preliminaries and Introductory Problems
Writing Style: We suggest the following steps in writing up your solutions, when they are applicable. For a detailed
writing style guidelines, please consult http://cseweb.ucsd.edu/˜ paturi/cse202/guide.html.
1. Understand the problem. Take a small concrete example and work it out manually to get a clear idea about the
problem. Do not hesitate to contact us if you do not understand what you are supposed to do.
2. Be prepared to reformulate the problem.
3. Give an informal description (at most 10 lines of english text) of your solution. The informal description should
highlight the
key ideas
of your solution. Your solution may just be graded by the quality of this informal
description.
4. Write up your design; Use the pseudo programming languge from the book to write your algorithms. Write your
algorithms modularly. Provide sufﬁcient detail as warranted by the problem.
5. Analyze the time complexity.
6. Argue that your algorithm is correct.
7. Think about the structural properties that led to an efﬁcient algorithm and articulate them.
Problem 1: Function order
Rank the following functions by descending order of growth; that is, ﬁnd an enumeration
f
1
, f
2
, . . .
of the functions
so that
f
1
= Ω(
f
2
)
, f
2
= Ω(
f
3
)
,
···
. Also partition your list into equivalence classes such that
f
and
g
are in the same
class if and only if
f
= Θ(
g
)
.
(
√
2)
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 Spring '06
 Hu
 Algorithms, Big O notation, Analysis of algorithms, LG, Recurrence relation

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