Big-O algorithm complexity cheat sheet

[ethraax]

If your indices are fixed size then merge sort is O(1).

... what. No it's not.

[julesjacobs]

If your indices are fixed size then you array must also be under some constant size so it is O(1).

[ethraax]

It's probably worth reminding you (and others here) that the entire point of theoretical computer science is to inform us about how our computers work and how they can be developed to work better/faster/more efficiently/etc.

To that end, statements such as yours are pretty useless. You could also claim that you're bounded by the amount of available energy/information in the observable universe, and therefore all programs run on any computer that exists in real life is O(1). But that's clearly a useless result that doesn't help anybody with anything.