Difference between time complexity O(ab) and O(N^2)

January 27, 2023

I assume that this code ideally representation of O(n^2) complexity. The reason is for function in another for function

for (int i = 0; i < array. length; i++) 
    for (int j = 0; j < array.length; j++) 
             System.out.println(array[i] + "," + arrayfj]);

Also, I read that code below is represent O(ab) time complexity. But why is that way? I don’t undersant, because if (arrayA[i] < arrayS[j]) , this is constant and we can ignore that.

for (int i = 0; i < arrayA.length; i++) 
   for (int j = 0; j < arrayB.length; j++) 
       if (arrayA[i] < arrayS[j]) 
           System.out.println(arrayA[i] + + arrayBfj]);

This also mentioned as O(ab), although for (int k = 0; k < 160800; k++) is also as constant

for (int i = 0j i < arrayA.length; i++)
       for (int j = 0; j < arrayB.length; j++)
          for (int k = 0; k < 160800; k++) 
             System.out.println(arrayA[i] + "," + arrayB[j]);

Different sites write different information about it.

>Solution :

If the first case, each array is the same length (n), and n*n prints are done.

In the second, the sizes of the arrays are a & b, and a*b ifs are done, and (potentially) that many prints are done (maybe everything in A is less than everything in B).

In the thirs, the sizes of the arrays are a & b, and (a*b)*160800 prints are done, but the constant can be ignored.