Analysis of Algorithms Fall 2005
OnCampus Final Exam
Page 1 of 11
COT 5405
Analysis of Algorithms
Fall 2005
OnCampus Comprehensive Exam
Name: __________________________________________
UFID: ____________  ____________
Email: _________________________________________
Instructions:
1. Write neatly and legibly
2. While grading, not only your final answer but also your approach
to the problem will be evaluated
3. You have to attempt all three problems (15 + 25 + 60 points).
You have choices under the 3
rd
problem.
5. Total time for the exam is 120 minutes
6. You are not allowed to use a calculator for this exam
I have read carefully, and have understood the above
instructions. On my honor, I have neither given nor received
unauthorized aid on this examination.
Signature: _____________________________________
Date:
____(MM)
/
____(DD)
/
___________(YYYY)
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View Full DocumentAnalysis of Algorithms Fall 2005
OnCampus Final Exam
Page 2 of 11
Q1. (3 * 5 = 15 Points) Complete all three parts.
You must write a very brief explanation for your answer for each question (without the justification,
you will get very little credit):
a)
Consider the following problem:
x
1
,
x
2
, …,
x
n
are Boolean variables that take either 0 (False) or 1 (True)value.
You need to find out if there exists a set of assignments of Boolean values to these
n
variables such
that the statement
Φ
(expressed in the following form: consisting of ORed clauses, and each clause
consisting of literals) is evaluated to be true:
= (
x
1
∧
¬
x
2
∧
x
4
)
∨
(
¬
x
n
2
∧
x
5
∧
¬
x
7
)
∨
…. ….
∨
(
¬
x
3
∧
¬
x
n
5
∧
¬
x
n
)
The problem above is (tick all that applies):
±
In P
±
Not in P
±
Not known to be in P
±
In NP
±
In NPHard
±
In NPComplete
±
All of the above
±
None of the above
The catch is that the expression is not in CNF, but in DNF. Therefore it is not an NPcomplete
problem: it’s rather in P (and thus in NP).
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 Fall '08
 UNGOR
 Algorithms, Analysis of algorithms, Computational complexity theory, NPcomplete, Boolean satisfiability problem, NPHard, oncampus final exam

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