
Is this NPcomplete
Hello,
If there is a decision problem, which is NPcomplete,
question: can the problem A be done in k steps?
then, is the following problem also npcomplete
question: can the problem A be done in k+c steps, where c is some fixed constant?
Basically, I would like to know if a problem is NPcomplete, then whether finding a solution which is a constant away from the optimal is also NPcomplete or not?
Thanks

You're asking two different questions there.
The decision problem "can A be done in k steps" doesn't look for an actual solution, and if you knew (k+c) and c, you'd know k, so for a fixed c, yes, it'd still be NP complete.
The question of "find a solution that is within some error of optimal" is not a decision problem, so it can't be NP complete no matter what error you use. Such problems can be in P though as there are numerous algorithms that give such answers to otherwise difficult questions.