Say I have return A[n-1] + Sum(A, n - 2). I counted the following primitive operations:

return A[n-2] + Sum(A, n - 2)
   1    2 3   4  5  6   7

I know accessing a certain index in A counts as 1 primitive operation, but I am not sure about A in the function call. Did I count the right number of operations?

  • $\begingroup$ Depends on your machine model and cost function. There is no single correct answer. (What does Sum do?) That said, passing a pointer to a method is arguably not even an operation. $\endgroup$
    – Raphael
    Sep 21, 2016 at 21:39

1 Answer 1


As pointed out by Raphael, it depends on the machine model. Under the assumptions of the RAM model of computation ...

  1. Simple operations (+, -, call, return, etc.) take one time step.
  2. Loops and subroutines are not simple operations: they may involve many of them.
  3. Memory accesses (e.g., indexing into an array) take one time step.

... you counted correctly operations [1-4] and 7. As for operation 5, it depends: the subroutine call does count as one single-step operation (according to assumption 1), but the subroutine itself doesn't: it is a composite operation (according to assumption 2). Finally, I would not consider passing A as a parameter to be an operation: A affects running time when it is accessed within the Sum subroutine, not in the subroutine call.


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