My friend gave me a problem that he says is easy, but I can't figure out a good algorithm to use to do it.You are given an input of 100 random English words.  You have to find the longest string of words where the last letter in one word matches the first letter in the next word.  You can only use each word once.For example, if you were given the words cat, dog, that, the longest string you could make would be cat -> that.  If you were given the words mouse, moose, unicorn, the longest string you could make would just be one word (since none of those words link).  If you were given the words bird, dish, harb, the longest string you could make would be harb -> bird -> dish (or dish -> harb -> bird or bird -> dish -> harb).I came up with the idea of modeling this as a directed cyclic graph.  Each node would just be a word, with vertices going to each word/node that started with the letter this word ended with.+-------+         \ +------+|  cat  |-----------| that |+-------+         / +------+    |                  |   \|/                 |+-------+ /            ||  the  |--------------++-------+ \This problem appears to be a longest path search, which is NP-Hard.  Is there a better way to do it?  Or even some sort of approximation algorithm that could be used?  Or some way to exploit qualities of English to reduce the search space?
longest list of words with matching start and end letters
algorithms