Dynamic programming (DP) is a fundamental and powerful algorithmic paradigm taught in most undergraduate (and many graduate) algorithms classes. DP problems are challenging for many computer science students because they require identifying unique problem structures and a refined understanding of recursion — another difficult topic in computer science. In this paper, we present dpvis, a Python library that assists students in understanding DP via a frame-by-frame animation of dynamic programs. dpvis can easily generate animations of dynamic programs with as little as two lines of modifications compared to a standard Python implementation. For each frame of the animation, dpvis highlights the cells that have been read from and written to during an iteration. Moreover, dpvis allows users to test their understanding of an algorithm by prompting them with questions about the next operation performed by the algorithm.

We deployed dpvis as a learning tool in an undergraduate algorithms class, and report on the results of a survey. The survey results suggest that dpvis is especially helpful for visualizing the recursive structure of DP. While some students struggled with the installation of the tool (which has been simplified since the reported deployment), essentially all other students found the tool to be useful for understanding dynamic programs.