hi guys; I just would like to verify about something and hope I get an illustration about;

In programming there's what's called dynamic programming which is depended on recursion like what's in math .. what's confusing me is whenever we are trying to solve sub-problem of the problem itself we solve it as the same the problem itself .. here's an example of what I mean:

lets assume I have a problem which is finding the maximum profit of a "set" (doesn't matter what's a set) so if I want to solve it in dynamic programming we are solving it recursively; what's confusing me why at the sub-problem we are finding also "the maximum profit of a "set" " why maximum over the sub-problem? the maximum has been demanded over the problem itself .. but why we

need to assume that at the sub-problem we want also to find the maximum?! I know it's given to find the maximum at the problem .. but not at sub-problem!! ........... any explanation please?! thanks.

In seeking the maximum of the entire problem, wouldn't you want the candidate results from each subproblem to present the maximum in each of their respective domains? Frankly, if you are searching for a maximum with only a single thread (search path), you will need a very specific world where that will work (maximum gradient and well-behaved, for example). If you truly wish to search the universe, you may need to resort to genetic algorithms. Some will lead down interesting paths. Some will not. That's why it defines children and murders. Good luck.

Note: When you say things like "doesn't matter what a set is," you are saying magic. If you are asking the question you should be open to LEARNING what matters, rather than attempting to dictate what is important. Perhaps you will learn that you really don't understand the problem as well as you thought. Keep a more open mind.