Big O Notation
Published: 2023-02-11 04:04:54

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As a software engineer, you likely have encountered the term Big O Notation, but do you really understand what it means? 

## What is Big O Notation
Big O Notation is a mathematical notation used to describe the performance or complexity of an algorithm. It is used to express the upper bound on the growth rate of the running time of an algorithm as the size of the input data grows. In other words, it provides us with a way to quantify how well an algorithm scales with increasing data size.

To put it simply, Big O Notation gives us a way to compare the efficiency of algorithms and determine which is the most efficient for a particular problem. This is important because choosing the right algorithm can have a big impact on the performance of your program, especially for large data sets.

The speed and memory usage of an algorithm isn't fixed. It might change depending on the input. So How do we express the performance of an algorithm? Would we say that if the size of the input is small, the algorithm runs in less than 30 milliseconds, however, if the size of the input is large, the algorithm would run in 100 million seconds? This wouldn't really make sense. it's meaningless. 

Big O Notation is used to describe the time complexity and the space complexity of an algorithm. 

Complexity Analysis: is the process of measuring or determining how efficient an algorithm is. Complexity analysis involves finding the time complexity and space complexity of an algorithm. 

Time complexity: is a measure of how fast an algorithm runs. it's expressed using Big O notation.

Space complexity: is a measure of how much additional/extra memory of an algorithm takes up. It's expressed using Big O notation. 


## Common Big O Notations 
There are several common Big O Notations, including:

- O(1), also known as constant time, means that the running time of an algorithm remains constant regardless of the size of the input data.


![O(1)](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/n7s5x2xaasmuqo67j1ec.png)

- O(log n), also known as logarithmic time, means that the running time grows logarithmically with the size of the input data.

![O(log n)](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/x7odsmvv0k6ugiyedgs0.png)

- O(n), also known as linear time, means that the running time grows linearly with the size of the input data.

![O(n)](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/81eikhljk9czz4go8qti.png)

- O(n log n), means that the running time grows as the product of the size of the input data and the logarithm of the size of the input data.

![O(n log n)](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/oamk7881ni1rs8nlmmd3.jpeg)

- O(n^2), also known as quadratic time, means that the running time grows as the square of the size of the input data.

![n^2](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/f0x2akok5h9hu56dpylo.png)

When designing an algorithm, the goal is to choose the one with the lowest possible time complexity. For example, consider two algorithms A and B. Algorithm A has a time complexity of O(n), while algorithm B has a time complexity of O(n^2). This means that as the size of the input data grows, the running time of algorithm A grows linearly, while the running time of algorithm B grows as the square of the size of the input data. In this scenario, algorithm A is considered more efficient than algorithm B for large data sets.

## Conclusion
In conclusion, Big O Notation is a valuable tool for software engineers as it provides a way to quantify the performance of algorithms and make informed decisions about which algorithm to use for a particular problem. By understanding the basics of Big O Notation, you can design efficient algorithms that scale well with increasing data size.

Thank you! 
[Jonny](linkedin.com/in/jonnytilahun)