Computer Science: An Overview: Global Edition (12th Edition)

Published by Pearson Higher Education
ISBN 10: 1292061162
ISBN 13: 978-1-29206-116-0

Chapter 12 - Theory of Computation - Section 12.5 - Complexity of Problems - Questions & Exercises - Page 565: 2

Answer

No. As a general rule, the algorithm in $\Theta\left(n^{2}\right)$ will outperform the one in $\Theta\left(2^{n}\right)$ , but for small input values an exponential algorithm often outperforms a polynomial algorithm. In fact, it is true that exponential algorithms are sometimes preferred to polynomial ones when the application involves only small inputs.

Work Step by Step

No. As a general rule, the algorithm in $\Theta\left(n^{2}\right)$ will outperform the one in $\Theta\left(2^{n}\right)$ , but for small input values an exponential algorithm often outperforms a polynomial algorithm. In fact, it is true that exponential algorithms are sometimes preferred to polynomial ones when the application involves only small inputs.
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