Time complexity of nested for-loop

Question

I need to calculate the time complexity of the following code:

for (i = 1; i <= n; i++)
{
  for(j = 1; j <= i; j++)
  {
   // Some code
  }
}
         


        

Answer 1

A quick way to explain this is to visualize it.

if both i and j are from 0 to N, it's easy to see O(N^2)

O O O O O O O O
O O O O O O O O
O O O O O O O O
O O O O O O O O
O O O O O O O O
O O O O O O O O
O O O O O O O O
O O O O O O O O

in this case, it's:

O
O O
O O O
O O O O
O O O O O
O O O O O O
O O O O O O O
O O O O O O O O

This comes out to be 1/2 of N^2, which is still O(N^2)