Question

Piovide a numerical value. The objective of this exercise is to find the largest input size N that an algorithm A with time complexity finf can handle in one year. We assume that fin) is expressed in milliseconds. If ifin = 5⁰n⁴, then Algorithm A can handle in 10 vears a problem of size n up to Wo assume a year consists of 365 diys. Yoo can round your answer to the closest integer.

Answer 1

The largest input size N that Algorithm A can handle in one year is approximately 46.

Step-by-step explanation:

Algorithm A can handle a problem of size n up to 107 in one year.

To determine the largest input size N that Algorithm A can handle in one year, we need to solve the equation 510N4 = 107. Taking the logarithm of both sides, we get 10N4 = log5(107). Rearranging the equation, we find N = (√[log5(107)])/102.

Using a calculator, we calculate N ≈ 46. As rounding is allowed, the largest input size N that Algorithm A can handle in one year is 46.