Big O notation for triangular numbers?

Question

What\'s the correct big O notation for an algorithm that runs in triangular time? Here\'s an example:

func(x):
  for i in 0..x
    for j in 0..i
      do_som         


        

Answer 1

If you think about it mathematically, the area of the triangle you are computing is ((n+1)^2)/2. This is therefore the computational time: O(((n+1)^2)/2)