# Day 27: Big 'O' Notation

Before diving into the other common time complexities, I'm so happy I made my first contribution to open-source!

![](https://cdn.hashnode.com/res/hashnode/image/upload/v1697026917083/27ca69a8-49a6-4127-a655-4c16de78eebf.png align="center")

I decided to take part in this year's Hacktoberfest and frankly, I was a bit nervous in the beginning. I won't say my first code was life-changing but it has given me the courage to tackle some more difficult problems before the end of the challenge.

Now over to **Big O Notation**

Today I'd like to discuss **Quadratic "O on n squared"** and **Logarithmic "O of log n".**

**Quadratic Time Complexity**

This time complexity is when the runtime scales quadratically with the input. As the input size increases, the runtime of the algorithm also increases in a quadratic fashion. So if the input size is 10, the runtime is 100 steps. If the input size is 100, the runtime is 10,000 steps. Some examples of this include:

* **Nested Loops -** when nested loops both iterate over the same array or input
    
* **Bubble Sort**
    
* **Insertion Sort**
    
* **Brute Force Algorithms**
    

**Logarithmic Time Complexity**

This time complexity is when the runtime grows logarithmically with the input size. As the input size increases, the runtime of the algorithm increases, but at a much slower rate compared to linear or quadratic time complexities. Some examples include:

* **Binary Search**
    
* **Binary Tree Operations**
    
* **Heap Operations**
    
* **Graph Algorithms**
    

I haven't gotten this far in my course to talk in-depth about these different problems. Once I across these I will be sure recap on how these different complexities are used within these DSA problems.