ZOJ Problem Set - 1953
The company "21st Century Fruits" has specialized in creating new sorts of fruits by transferring genes from one fruit into the genome of another one. Most times this method doesn't work, but sometimes, in very rare cases, a new fruit emerges that tastes like a mixture between both of them.
A big topic of discussion inside the company is "How should the new creations
be called?" A mixture between an apple and a pear could be called an apple-pear,
of course, but this doesn't sound very interesting. The boss finally decides
to use the shortest string that contains both names of the original fruits as
sub-strings as the new name. For instance, "applear" contains "apple"
and "pear" (APPLEar and apPlEAR), and there is no shorter string that
has the same property.
Your job is to write a program that computes such a shortest name for a combination of two given fruits. Your algorithm should be efficient, otherwise it is unlikely that it will execute in the alloted time for long fruit names.
Source: University of Ulm Local Contest 1999