Lines 1 through 5 set up the initial conditions on the matrix s, and line 8 corresponds
to the recurrence that allows us to fill in later table entries based on
earlier ones. Most of the dynamic programming algorithms we will develop
in the context of DNA sequence comparison will look just like MANHATTAN TOURIST
with only minor changes. We will generally just arrive at a
recurrence like line 8 and call it an algorithm, with the understanding that
the actual implementation will be similar to MANHATTAN TOURIST.