Sightseeing in an Arbitrary Directed Graph
Let’s look at the longest path problem in an arbitrary directed graph before relating it to the problem of finding the longest common subsequence.
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In reality, the streets in Midtown Manhattan don’t form a perfect rectangular grid because Broadway Avenue cuts diagonally across the grid, but the network of streets can still be represented by a directed graph. In fact, the Manhattan Tourist Problem is just a special case of the more general problem of finding the longest path in an arbitrary directed graph, such as the ones in figure below.
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