Final answer:
The student's question cannot be fully answered without additional context. Generally, dynamic programming involves solving subproblems iteratively and storing results to optimize overall runtime, often yielding polynomial time complexity. More specifics on the function would be necessary to provide an accurate algorithm.
Step-by-step explanation:
The student is asking for a dynamic programming algorithm to compute a function, presumably related to a problem described in a previous question. The algorithm needs to be iterative and in the specific form of COUNTSPLITDP(S[1, . . . , n]), although the explicit function or problem is not provided. Without the context of the specific function or computation task, the detailed algorithm cannot be written. However, we can discuss the general approach to writing a dynamic programming algorithm of this form and the typical runtime associated with these types of algorithms.
Dynamic programming algorithms typically store the results of subproblems in a table to avoid redundant calculations. The COUNTSPLITDP function would iteratively fill in this table, usually starting from the base case and building up to the solution for the overall problem. The runtime of such an algorithm generally depends on the number of subproblems and the time required to solve each one, often resulting in a polynomial time complexity, such as O(n^2) or O(n^3), depending on the specific problem details.
To ensure accuracy and relevance, more information about the specific function or problem is necessary to write the algorithm and define its runtime. Dynamic programming is a powerful technique, particularly for optimization problems and combinatorial problems where the direct approach might be infeasible due to exponential time complexity.