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What is the largest n for which one can solve within a day

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 16E Chapter 3.3

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 16E

What is the largest n for which one can solve within a day using an algorithm that requires f(n) bit operations, where each bit operation is carried out in 10−11 seconds, with these functions f(n)?

a) log n

b) 1000n

c) n2

d) l000n2

e) n3

f) 2n

Step-by-Step Solution:
Step 1 of 3

Step-1:

In this problem we need to find the largest n for which can solve with in one second problem using an algorithm requires f(n) bit operations, where each bit operation is carried out  second with these functions f(n).

We know that , in a day  there are approximately seconds.So , within a day, the total number of operations is equal to , since .

So, the operation bit per second is

Step-2:

a)consider,f(n) = log(n).

Calculate the value of n.

Consider, the base log is 2.

So,.

Therefore,the largest value of .

Step-3: 

b)consider,f(n) = 1000n.

Calculate the value of n.

So,.

,since .

Therefore,the largest value of  .

Step-4:

c)consider,

Calculate the value of n.

Therefore,the largest value of  

Step-5:

d)consider,

Calculate the value of n.

,since .

.

         

         

Therefore,the...

Step 2 of 3

Chapter 3.3, Problem 16E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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What is the largest n for which one can solve within a day

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