Question

for i <--- 1 step i <--- 2* i while i< n do 
  for j <--- 1 step j <---2* j while j<n do 
    if j = 2*i 
      for k = 0 step k <--- k+ 1 while k < n do 
        .... CONSTANT NUMBER OF ELEMENTARY OPERATIONS 
      end for 
    else 
      for k<--- 1 step k<-- 3*k while k<n do 
        ...CONSTANT NUBER OF ELEMENTARY OPERATIONS 
      end for 
    end if 
  end for 
end for

What is the running time for the following code fragment as a function of n?

The ‘exact answer’ refers to the equation relating to the code BEFORE you determine the asymptotic running time.

Answer 1

It sounds as homework, however, making a few considerations, the asymptotic complexity of that pseudo code should be O(n*log(n)).

You cannot estimate exactly the running time since it highly depends on your system.