Chapter 16.3, Problem 16.12CP

Explanation of Solution

Complexity of an algorithm:

The complexity of an algorithm solves a computations problem by finding the number of basic steps required for an input.

Proof:

Statement:$f(n)\text{is not in}O(g(n))$

Explanation:

Consider the two algorithms “F” and “G” can be compared for solving a problem which can be done by comparing their complexity functions $f(n)$ and $g(n)$. These two complexity functions can be compared against the ratio $\frac{f(n)}{g(n)}$.

The complexity functions can be compared if there exists a positive constant “K” such that,

 $\frac{f(n)}{g(n)}\le K\text{for}\text{all}n\ge 1$

The algorithm “F” is not worse than “K” times “G” for large problems. For this case, it can be given as $f(n)\text{is in }O(g(n))$