Electrofacies using well logs play a vital role in reservoir characterization. Often, they are sorted into clusters according to the self-similarity of input logs and do not capture the known underlying physical process. In this paper, we propose an unsupervised clustering algorithm based on the concept of dynamic programming, in which the underlying physical processes and geological constraints, such as the number of clusters, number of transitions between clusters, and minimal size of formation layers, can be directly integrated. We benchmark the proposed algorithm with synthetic data sets and demonstrate its applications to two field examples, where formations are clustered into zones through automated clustering using a consistent resistivity response. The inputs for our examples are porosity, clay volume fraction from elemental analysis, invaded zone resistivity, and invaded zone water saturation from dielectric interpretation or nuclear magnetic resonance logs. The proposed algorithm provides the optimized cluster pattern/electrofacies that satisfies desired constraints and enables the extraction of relevant petrophysical parameters, such as brine resistivity, cementation, and saturation exponents, as well as parameters that relate to the cation exchange capacity (CEC) of the clay for shaly-sand formations. Beyond the immediate examples demonstrated in this paper, we present the proposed algorithm in a generic form such that it can be easily tailored to the task at hand, taking into account any prior knowledge of the physics of the underlying process.