Runtime analysis with recursion factor

Question

I have this code:

if n is even
{
for i=1....n
   for j=1...i
      print j
return 8*foo(n/2)
}

Asking to calculate the running time $T (n)$. I thought at first that I can write the function like this:

$$T(n)= 8T(n / 2)+n^2$$ But according to the answers of the quiz, they are saying that the function looks like this:

$$T (n)= T(n / 2)+n^2$$ Why we can delete 8? Thank you very much!

Answer 1

You're asked to calculate the running time of the segment, not the value returned. In terms of running time, multiplication by 8 is a single operation, so the running time is (roughly) $T(n)=T(n/2)+n^2$.