Boyer-Moore string searching is a good example of a simple but non-obvious "idea" (search backwards; it's much faster).
http://www.cs.utexas.edu/users/moore/best-ideas/string-searc...
http://www.cs.utexas.edu/users/moore/best-ideas/string-searc...
The details of Boyer-Moore seem obvious to me, in that you bump into them in trying to get it working, even if you don't foresee them. They are like workshop improvements. Did you manage to implement a version of it, as a kid? Or is this another instance of showing that actually doing it is what counts?
An idea itself is of little value. If it were, the really hard stuff, like math itself, would be patentable.
Binary search, among the very basic algorithms, is toward the other extreme. An incorrect version of the algorithm was published something like 20 years before a bug-free version was published.