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7 Problems Exam - Design and Analysis of Algorithms. | CS 324, Exams of Computer Science

Ball State University (BSU)Computer Science

Material Type: Exam; Class: Design and Analysis of Algorithms.; Subject: COMPUTER SCIENCE; University: Ball State University; Term: Fall 2005;

Typology: Exams

2009/2010

Uploaded on 03/28/2010

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CS 324 Fall 2005 Name:_____________________________
Test 1
Talking to other students and the use of notes, books, or electronic devices are not
allowed and are considered cheating. There is a total of 84 points plus extra credit; but
you cannot get more than 84 points.
1. (12 points) Give a short definition of the following:
a) algorithm
b) Ω
c) asymptotic notation
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pf4
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Download 7 Problems Exam - Design and Analysis of Algorithms. | CS 324 and more Exams Computer Science in PDF only on Docsity!

CS 324 Fall 2005 Name:_____________________________

Test 1

Talking to other students and the use of notes, books, or electronic devices are not allowed and are considered cheating. There is a total of 84 points plus extra credit; but you cannot get more than 84 points.

  1. (12 points) Give a short definition of the following:

a) algorithm

b) Ω

c) asymptotic notation

  1. (12 points) Prove the following statement by mathematical induction.

If a positive integer is dividable by 3, then the sum of its digits is also dividable by 3.

(Example: 18 is dividable by 3 because 18=3·6. The sum of its digits is 1+8=9, which is also dividable by 3.)

  1. (12 points) Arrange all of the following functions in increasing order of their O()-sets, using the symbols ⊂ and =. n log n 5 2 n n log n nc, with c ≥ 0
  2. (12 points) What is Θ( f(n) )? Give a proof.

f(n) = 3 log n + 25 n² - 345 + sin n

  1. (12 points) Algorithm A takes n hours to solve a given problem with n input objects. Algorithm B takes n^3 milliseconds to solve the same problem. What is the smallest value of n for which A is faster than B?