Computational offloading is an effective method to address the limited battery power of a mobile device, by executing some components of a mobile application in the cloud. In this paper, a novel offloading algorithm called ‘Dynamic Programming with Hamming Distance Termination’ (denoted DPH) is presented. Our algorithm uses randomization and a hamming distance termination criterion to find a nearly optimal offloading solution quickly. The algorithm will offload as many tasks as possible to the cloud when the network transmission bandwidth is high, thereby improving the total execution time of all tasks and minimizing the energy use of the mobile device. The algorithm can find very good solutions with low computational overhead. A novel and innovative approach to fill the dynamic programming table is used to avoid unnecessary computations, resulting in lower computation times compared to other schemes. Furthermore, the algorithm is extensible to handle larger offloading problems without a loss of computational efficiency. Performance evaluation shows that the proposed DPH algorithm can achieve near minimal energy while meeting an application's execution time constraints, and it can find a nearly optimal offloading decision within a few iterations.