Big-O complexity of nested for loops?

Definitely O(n squared) of course. Summary explanation for both cases: 1 + 2 + ... + n is n(n+1)/2 that is (n squared plus n) / 2 (and in big-O we drop the second, lesser part, so we're left with n squared / 2 which is of course O(n squared) ).

Definitely O(n squared), of course. Summary explanation for both cases: 1 + 2 + ... + n is n(n+1)/2, that is, (n squared plus n) / 2 (and in big-O we drop the second, lesser part, so we're left with n squared / 2 which is of course O(n squared)).

You are correct, those nested loops are still O(n^2). The actual number of operations is something close to (n^2)/2, which, after discarding the constant 1/2 factor, is O(n^2).

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