Question

Assume an algorithm that takes log2 n microseconds to solve a problem. Find the largest input size n such that the algorithm solves the problem in time in 24 days

Answer 1

Since the given algorithm is based on time in microseconds, let us convert 24 days into microseconds:

Days into microseconds ---> multiply the time value by 8.64e+10

24 days = 24 × 8.64e+10 = 2.074e+12 microseconds

log₂(n) = 2.074e+12 microseconds

To remove log₂ from left side, take 2^(x) on right hand side of equation.

n = 2^{2.074e+12}

n = 2^(2000000000000) is the largest input size.