## Introduction

From the previous chapter, you should have a basic understanding of dynamic programming, as well as an effective set of strategies for finding a dynamic programming (DP) solution for an unfamiliar problem. In this chapter, we will develop this understanding further by exploring relationships between problems, particularly in terms of how the basic DP logic for one problem can be modified to find the approach to another. We will also discuss the concept of state space reduction, which allows us to exploit certain aspects of a problem to further optimize a working DP solution by decreasing the number of dimensions and/or operations required to find the result. We will conclude this chapter by revisiting the topic of graphs to demonstrate how the DP approach can be applied to the shortest-path problem.