Question

Which of the following growth rates are tractable?

A. O(2^n)
B. O(n logn)
C. O(n^n)
D. O(n!)
E. O(n^10)
F. O(n^3)
G. O(n^2 logn)

Answer 1

Tractable growth rates from the given options are B. O(n logn), E. O(n^10), F. O(n^3), and G. O(n^2 logn) since they are polynomial or quasi-polynomial, unlike the exponential or super-exponential rates A. O(2^n), C. O(n^n), and D. O(n!), which are intractable.

Step-by-step explanation:

The tractability of various growth rates, specifically in terms of computational complexity. In the context of algorithm analysis, growth rates are used to describe how the completion time of an algorithm increases with the size of the input (commonly denoted as 'n'). A growth rate is considered tractable if an algorithm with that rate of complexity can be solved in a reasonable amount of time as the input size grows.

B. O(n logn), E. O(n^10), F. O(n^3), and G. O(n^2 logn) are all polynomial or quasi-polynomial and, therefore, are generally considered tractable, especially for smaller inputs. On the other hand, A. O(2^n), C. O(n^n), and D. O(n!) are exponential or super-exponential and are typically considered intractable due to their very rapid growth rates which lead to impractical computation times for even moderate-sized inputs.