for(int i=0; i<n; i++) {
blah;
} <== this has a complexity of O(n)
however if you know n to be 3 before hand won't the complexity become O(1), I mean i could just write out the instructions 3 times.
blah;
blah;
blah;
whereas if you don't know how big n is before you run the program then it's not possible to write down the instructions in the latter way.
Please clarify my misconception if I have it.
First of all the complexity of the first cycle is O(n * <complexity of blah>). Second this is assuming n is an input parameter to your algorithm. If n is a constant known beforehand than your estimation of O(<complexity of blah>) is correct.
Time complexity of algorithms is only meaningful with regard to input size (n in your first example). If an algorithm receives no input such as blah; blah; blah;, then obviously its run time is going to be constant and independent of input size.
An algorithm has time complexity O(1), or O(n), or whatever, in the context of a sequence of inputs of increasing length. So to say something about the complexity, the algorithm must be able to accept arbitrarily long inputs. If you require that inputs are only of length 3, then it isn't meaningful to talk about the complexity of the algorithm.
