   Chapter 11.5, Problem 2ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Suppose an algorithm requires c ⌊ log 2 n ⌋ operations when performed with an input of size n (where c is a constant).a. By what factor will the number of operations increase when the input size is increased from m to m 2 (where m is a positive integer power of 2)?b. By what factor will the number of operations increase when the input size is increased from m to m 10 (where m is a positive integer power of 2)?c. When n increases from 128 ( = 2 7 ) to 268 , 435 , 456 ( = 2 28 ) , by what factor is c ⌊ log 2 n ⌋ increased?

To determine

(a)

By what factor will the number of operations increasewhen the input size is increased from m to m2 (where mis a positive integer power of 2)?

Explanation

Given information:

Suppose an algorithm requires clog2n operations when performed with an input of size n (where c is a constant).

Calculation:

When the input of the algorithm is n, then the algorithm requires clog2n operations

Number of operations at input n = clog2n

Where c is a constant

mis a positive integer power of 2, thus there exists a positive integer k such that

m=2k

When the input is m=2k, then the algorithm requires clog2m operations.

Number of operations at input m=2k

=clog2m

=clog22k

=ck

=ck

To determine

(b)

By what factor will the number of operations increasewhen the input size is increased from m to m10 (where mis a positive integer power of 2)?

To determine

(c)

When n increases from 128(=27) to 268,435,456 (= 228), by what factor is clog2n increased?

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