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.
Answers
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.
Answer:
n = 2^ (2000000000000)
Explanation:
From the given data we have,
Time taken for log2 n algorithm to solve problems: microseconds
Largest input size of the algorithm to be identified for: 24 days
Total number of days to be converted into microseconds
For this,
The time value of the algorithm is multiplied to 8.64e + 10
= 24 days = 24 X 8.64 e + 10
= 2.074e+ 12 microseconds
In order to remove logz we can take 2^(x) at the right side of the equation and this would result into:
n = 2^ {2.074e+12)
n = 2^ (2000000000000)