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This problem is from the archived puzzle from ITA Software, Since the puzzle is retired I guess it is ok to discuss.
How long a chain of overlapping movie titles, like “Live and Let Die Another Day of the Dead Poet’s Society”, can you find?
I would like to know what is the best approach/algorithm to solve such puzzle.
This is a graph problem.
First you build a graph, where each vertex represents a movie. There is an edge (a,b) if the movie a end in the same word as the one with which the movie b starts.
Now you want to find the longest path in the graph. This is NP-complete problem, so it doesn’t have polynomial solution. (wikipedia)