If an algorithm with input n can solve a problem in fn milli

If an algorithm with input n can solve a problem in f(n) milliseconds. What is the effect in the time if you try to solve a problem with input 2n? (That is, to express f(2n) by using f(n))

a) f(n)=100n

b) f(n)=n^2

c) f(n)=2n

d) f(n)=log n

Solution

answer:

now the n value is increased by 2and that can be depicted as 2n, finally that raises the computational ratio time as 2 ²ⁿ / 2 ⁿ = 2 ⁿ .

from this we can conclude that, the time is 2 ⁿ time when the i/p is getting doubled in its size.