I have been learning graph algorithms, and the concept of dynamic programming is quite succinct. However, I read that Bellman Ford is a form of dynamic programming. I am not sure why since given so many unnecessary re-computations, it is not exactly efficient in the likes of other dynamic programming that computes the sub-problems bottom up to the final problem. For example, FloyWarshall has a well defined sub structure of considering all other vertices up to k.
But for Bellman Ford, the implementation is not really relying on any computed sub problems, it is just a brute force algorithm that correctly returns the shortest path but it is not correctly computing the sub-problems in some correct order needed by a dynamic programming algorithm?