A Pedagogical Note on the Design of Dynamic Programming Algorithms

Dynamic programming is extensively used to formulate and solve a wide range of optimization problems, especially those involving sequential decisions. When designing dynamic programming algorithms, either a backward or forward approach can be employed. Previous studies have not explicitly addressed the choices between the two approaches that may lead to different time complexities. This note highlights this question by examining four distinct optimization problems, demonstrating how adopting different design approaches impacts the efficiency and complexity of the developed algorithms. Comparative analysis of the examples suggests the option of selecting an effective strategy for developing efficient dynamic programming algorithms.