The tricky thing with dynamic programming is realizing that it fits—you have to understand how the problem you're solving decomposes into overlapping subproblems that are worth caching. Once you know what the subproblems are, implementing the algorithm is mostly a matter of getting some fiddly indexing logic right.

Take string edit distance for example: the key to the dynamic programming problem is seeing how the exponential blow up of possibilities actually has a rich overlapping structure that you can cache in a table. If you didn't know string edit distance was amenable to dynamic programming, you might not realize it at all even if you are constantly thinking about caching results. Once you see the structure, the algorithm becomes relatively straightforward.