What is Asymptotic Notation?
If you are here for the first time and looking to start from scratch. Here's the order I have learned about Algorithms.
To properly learn something you have to start from the beginning. In this series of articles, We(yes me too) will learn about algorithms step by step. There are many books, tutorials, and blogs available on Algorithms, and it is often confusing to choose anyone from this large pool of resources. I was also confused but now I have decided that I will provide a summary of all the resources available and people don't have to look in different websites for every different topic.
We will be continuing our study on algorithms and discussing the analysis of algorithms.
Who is this article for?
This article, and the possible series I'll create from it, is meant for those who want to learn algorithms in an efficient way step by step and from a single resource or looking to revise concepts before a coding interview.
Goals
The goal of this article is to focus on understanding the need for analysis of algorithms and move toward the other topics as mentioned here.
So, let's begin 🚀
Analysis of Algorithms
We discussed in last article that there can be many ways to solve a given problem but to decide which one is efficient, we use different types of analysis methods.
Types of Analysis
To analyze a given algorithm, we need to find how much time the algorithm takes for different inputs.
We represent the algorithm with multiple expressions:
 Case 1: Algorithm takes less time > bestcase
 Case 2: Algorithm takes more time > worstcase
There are three types of analysis:
 Worst Case: Slowest time to complete for a given input > Upper Bound
 Best Case: Fastest time to complete for a given input > Lower Bound
 Average Case: Prediction about the running time of the algorithm by taking the average of total running time with the number of trials> Average Time
Now, we can form a mathematical relation between these three types.
Lower Bound <= Average Time <= Upper Bound
Asymptotic Notation
After having relation between worst, average, best cases, we are ready to dive into different types of asymptotic notations, before that, we need to know about terms running time and rate of growth.

Running Time
 The time an algorithm takes on a computer to run and that depends on the speed of the computer, the programming language, and the compiler that translates the program from the programming language into code that runs directly on the computer, among other factors.

Rate of growth
 The rate at which running time increases as a function of input.
Some Commonly used growth rates in increasing order:
 1 Constant
 logn Logarithmic
 n Linear
 nlogn Linear Logarithmic
 n^2 Quadratic
 n^3 Cubic
 2^n Exponential
Let's understand by taking an algorithm, running on input size n
with function 10n^2 + 100n + 100
. Here 10n^2
is larger than other terms, we can say that the running time of this algorithm grows as n^2
and removing the 10
will also not make much difference.
Moving forward, we can imply that we need to simplify the function to keep the most important part and dropping less significant terms and the constant coefficients which we call asymptotic notation.
There are three types of asymptotic notation:
 BigO Notation > Upper Bounding Function
 OmegaΩ Notation > Lower Bounding Function
 ThetaΘ Notation > Order Function
We have reached at the end of this article, in the next article, we will be discussing BigO notation.
Here are the next articles on Algorithms.
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