A reservoir computing system with a memristor reservoir is simulated. The efficiency of the memristor reservoir system is compared with the classical ESN (echo state network) and DeepESN in solving the classification problem. The classification accuracy of a system consisting of only a few dozen memristors can exceed the classification accuracy of ESN and DeepESN with thousands of nodes. As experimental data show, networks with random polarity of voltages on memristors are usually better than networks with uniform polarity of voltages due to their ability to generate richer nonlinear dynamics. In general, for the same number of memristors, a smaller number of network nodes improves the nonlinear mapping ability of the system by enhancing the interaction between memristors. The optimal number of network nodes should correspond to the number of memristors and should be determined experimentally.