You may have heard about  time complexity in computer science or you may heard some keywords about time complexity like "Big O notation". Time complexity and Big O notation are different things but are related to each other. This subject is critical in software development and i will explain why below.

We all remember the moment we wrote a simple algorithm using our favorite programming language that prints something  lighting fast on the screen and our first thought was "woah computers are so fast, it's magic!" Well computers are definitely fast but not magic.  
**A false assumption we quickly made is that computers are really fast and are going to execute any of our algorithms in no time**

**So my computer is not magic ?**  
The simple answer to this is "NO" 

Computers execute tasks like humans do but in different enviroment. For example a daily human task is to find your clothes  want to wear inside a pile of clothes. To do that we are going to check every single cloth if it is the one that we want to wear. So if we are searching in a pile of 10 clothes we need to do 10 checks or less to find our clothes. Well thats not a problem but what happens if the pile consists of 100 clothes ? Well that's about 100 or less checks so it's going to be time consuming. A computer is going to perform the same number of checks like a human would do but the data in a computer is stored in binary format so performing the checks will be faster than humans. The more number of checks that a computer has to perform the more time will take of our algorithm to finish.

**So an algorithm execution time from start to finish depends on the number of steps it has to perform. In computer science these steps are described as input.**

We learned that an algorithm execution time from start to finish can be slow depending on the number of data that will be proccessed(input). Your algorithm must be as fast as possible especially in enterprise software engineering and this is where time complexity is important.

### Time complexity and Big O notation explanation
Time complexity describes the amount of time it takes to run an algorithm.
Time complexity is generally expressed as a function of the size of the input.
Time complexity is commonly expressed using Big O notation
Big O notation is a relative representation of the complexity of an algorithm.
Big O Notation is a way to indicate complexities(Time and Space Complexity)
Big O Notation – O(n)  is being used for the worst case. It gives us an asymptotic upper bound for the growth rate of the runtime of an algorithm.

### Varieties of Big O Notation fast to slow
**O(1) - Constant time complexity - no loops**
Constant runtime, regardless of the size of the input, the algorithm will have the same runtime.

**O(log n) - Logarithmic time complexity**
Time goes up linearly, while the n goes up exponentially. So if it takes 1 second to compute 10 elements, it will take 2 seconds to compute 100 elements and so on. It is O(log n) when we use divide and conquer algorithms e.g binary search.

**O(n) Linear**
Describes an algorithm whose performance will grow linearly and in direct proportion to the size of the input data set.
for loops, while loops through n items.

**O(n log(n))** 
O(log n) - Logarithmic time complexity performance will grow linearly and in direct proportion to the size of the input data set.
 

**O(n^2) Quadratic** 
Every element in a collection needs to be compared to every other element. Two nested loops.

**O(2^n) Exponential**
O(2^n) denotes an algorithm whose growth doubles with each addition to the input data set
ex recursion

**O(n!)**
 Factorial we are adding a loop for every element
 Any algorithm that calculates all permutation of a given array 

What is time complexity and why it's important in software development.

Konstandinos Karagiorgos

Editing "Time complexity" post