I recall the first interesting example usage my professor taught of dynamic programming was this example (well, described, not taught). He basically just said

I recall the first interesting example usage my professor taught of dynamic programming was this example (well, described, not taught). He basically just said that all you do is take the L^2 or L^3 sum of extra space and minimize it using a DP. The fact that that yields great-looking text I thought was pretty cool.