Big O notation, algorithm time complexity and space complexity

The algorithm complexity is expressed by a Big O notation, like these
O(1)
O(log₂n)
O(n)
O(nlog₂n)
O(n²)
O(n³)
...
O(2ⁿ)
...
The time complexity sequence is 
Ο(1)＜Ο(log₂n)＜Ο(n)＜Ο(nlog₂n)＜Ο(n²)＜Ο(n³)＜…＜Ο(2ⁿ)＜Ο(n!)

Basically, it describes the worst iteration times.  For example, the code below

So the time complexity is O(2n² + n + 1)
The big-O expressions do not have constants or low-order terms. This is because, when N gets large enough, constants and low-order terms don't matter.

• Remove constants, which is 1. Now it is O(2n² + n)
• Remove low-order terms, which is n. Now it is O(2n²)
• Remove constant factor of high-order terms, which is 2 here. Then it is O(n²)

The time complexity is O(n²)， because the inner iteration time is n*n.


Here is the article http://blog.csdn.net/zolalad/article/details/11848739

Another article https://rob-bell.net/2009/06/a-beginners-guide-to-big-o-notation/