Typically, one doesn't know that a problem is in a specific implementation domain (b-trees) unless one knows that domain. For example, I have M time slots and

Typically, one doesn't know that a problem is in a specific implementation domain (b-trees) unless one knows that domain. For example, I have M time slots and N people that need to be scheduled. Each of the N people has a time schedule for the M slots (either free or busy). If a person doesn't know about bipartite graph matching (or even graphs at all), then they're less likely to come up with a polynomial-runtime solution. Now, if a person knows about bipartite matching, they might as well learn the algorithms (max flow, etc) to solve it (even for fun, at least I know I would).