How to calculate which US counties border the ocean?

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I have a shapefile with boundaries of US counties. I want to figure out one seemingly simple thing - which counties are on the Atlantic ocean? NOAA maintains a list of coastal counties, but this includes counties that are on the "coastal watershed", which is not quite the same thing (I'm basically trying to identify counties with a coastal view). The same problem comes up when I try to use a NOAA GIS file with coastal boundaries.

It seems like the simplest way to do this would be to calculate whether a county has any border that is not shared with another county. Then I could throw out states that don't border the ocean (to eliminate the Great Lakes) and manually eliminate Texas counties that border Mexico. But I can't figure out how to do this calculation. Any other suggestions would also be appreciated.



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