Dear mathstack exchangers,
Currently I`m wondering what the complexity, time and space, is of generating numbers $c \in \mathbb{N}$ with the condition: $H+0 < c < B$. Where $B$ is my upperbound and $H$ is predetermined.
I myself was thinking about $O(B)$.
If by "generating" you mean writing all those numbers as output, then the size of the output is $O(B)$ if you assume all numbers can be written in the same space, $O(B \log B)$ if you assume the digits of the number have to be written out and each digit takes the same space.
The running time has to be at least the order of the output, and in this case it is easy enough to conceive a counting algorithm so that the running time is on an order no greater than the output. (That is, the time to compute each number is bounded by a constant, or if you are counting digits, a constant times the number of digits in the number.)