Help Understanding Big O

Question

I'm asking more about what this means to my code. I understand the concepts mathematically, I just have a hard time wrapping my head around what they mean conceptually. For example, if one were to perform an O(1) operation on a data structure, I understand that the amount of operations it has to perform won't grow because there are more items. And an O(n) operation would mean that you would perform a set of operations on each element. Could somebody fill in the blanks here? Like what exactly would an O(n^2) operation do? -And what the heck does it mean if an operation is O(n log(n))?

Answer 1

So O(n²) would indicate that you are doing a set of operations on a set of operations- this commonly happens when you perform a for loop within a for loop. For example, if you have a 2D array with 5 rows and 5 columns and you use two for loops to scan through them to find a certain element, the number of operations you perform in the worst case is O(n²). n in this case is the length of the rows and columns so 5, and you go through each row 5 times and each column 5 times leading to a total of 25 checks which is n² since 5²=25.