Welcome! In my previous post, I wrote about the use of different notations for Asymptotic (Algorithmic) Analysis. Today, let’s discuss how the analysis is done.

## Why is it called Asymptotic Analysis?

In every case, for a given function, f(n), we define a function g(n) which approximates f(n) at higher values of n. Thus, g(n) is a curve, approximating f(n) at higher values of n. Such a curve is called an Asymptotic Curve. For this reason, the Algorithm Analysis is called Asymptotic Analysis.

## Rates of Growth

The Rate at which the running time increases as a function of input is called rate of growth. In case of a total time of execution

`C`

, since the smaller elements and constants are insignificant for large values of n, the actual rate of grown is considered to be _{0}n^{2} + C_{1} + (C_{2} + C_{3})n`n`

.^{2}

This, rate of growth: `O(n`

^{2})

Here is a chart with commonly used Rates of Growth: