Maximum number of binary trees that can be formed with three unlabeled nodes ?

Question

Given a string S and set of strings U. Find the length of longest prefix of S that can be formed using strings in U.

For example you have following -

S= “absolute”
U={“abs”,”xyz”,”ol”,”te”}

Answer: 5 i.e "absol"

Now the task is to have the algorithm/program for the above problem, please help me with this?

Answer 1

Is it not the same as
http://tech.queryhome.com/17786/how-many-number-of-binary-tree-possible-for-n-number-of-nodes

i.e. (2*3)!/(3+1)!*3! i.e. 5