Solution Format for Dynamic Programming

In general, we expect a dynamic programming solution to consist of 3 parts. First, it must clearly identify what the subproblems are, and include a short justification that the problems exhibit the optimal substructure property, if this is not obvious. Second, the recurrence relation between subproblems must be stated, including the base cases. For the recurrence relation to be valid, there must be no cyclic dependencies, and if it is not obvious (and we are using an iterative solution), the topological ordering must be stated. Finally, there must be a runtime analysis. These three steps hold necessary whether we are using a recursive (top-down) strategy or an iterative (bottom-up) strategy.