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-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...