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How do you calculate the amount of iterations the following loop will have in terms of n?:

for (i = 1; i < n^3; i += n) {
    }

I've gotten as far as: $$i=(x-1)n+1\ for\ current\ iteration=x$$ $$Total\ iterations=x\ when\ n(x-1)+1\geq n^3>n(x-2)+1$$

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  • $\begingroup$ n^3 is an exclusive or, changing the lowest two bits in n. $\endgroup$
    – gnasher729
    Mar 12 at 16:17
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    $\begingroup$ @gnasher729: not in Matlab, Scilab, R, Basic nor Excel. :) $\endgroup$
    – user16034
    Mar 12 at 16:53
  • $\begingroup$ @gnasher729 Yeah thanks I know. The idea behind the question is the math not whether the code works. I'm just trying to calculate the amount of iterations it would have. $\endgroup$
    – user19843013
    Mar 13 at 11:36

1 Answer 1

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Hint:

$$i=1,1+n,1+2n,1+3n,\cdots1+(n^2-1)n,1+n^2n\cdots$$

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  • $\begingroup$ During final iteration x, i = 1 + (n^2 - 1)n; Total iterations = x when 1 + (n^2 - 1)n = 1 + (x - 1) = n^2; Thank you. I simply couldn't see it. $\endgroup$
    – user19843013
    Mar 13 at 13:19
  • $\begingroup$ @user19843013: your development is approximate, to say the least. $\endgroup$
    – user16034
    Mar 13 at 14:04
  • $\begingroup$ Whatever that means $\endgroup$
    – user19843013
    Mar 14 at 6:48

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