When can an algorithm be said to have $O(1)$ complexity? My doubt is if $n$ is specified to be a large number but constant and we cannot implement it in reality without a loop even then can we call it to have $O(1)$ time complexity? Consider the following examples.
Algorithm to add first 1000 natural numbers (that is I mean to say if n is specified directly). Then can we say this has $O(1)$ time complexity?
Finding the $7$th smallest element in a min heap. This element is present in anywhere in the first 6 levels of the heap (considering root at level 0). So to find the element we need to check $2^7 - 1$ elements. Then can we say this has $O(1)$ time complexity?