Chapter 9.6, Problem 9.14CP

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.

 It is enough to show that $100n^3+50n^2+75$$\le K(20n^3)$ for some constant K. So that it means $100n^3+50n^2+75$ is in $O(20n^3)$ for all $n\ge 1$.

Proof:

 Observe that for all  $n\ge 1$

  $\begin{array}{l}100n^3+50n^2+75=20n^3\\ \frac{100n^3+50n^2+75}{}\end{array}$