On-chip communication appears to have an extremely significant role in taking advantage of the inherent parallelization offered by the MPSoCs. If interconnection networks are to be used efficiently in such platforms, designing high-performance routing algorithms is inevitable. In this paper, a deadlock-free and highly adaptive multicast/unicast routing method is presented based on the Hamiltonian routing model. This method strives for a high degree of adaptiveness by finding the maximum number of minimal paths between each pair of source and destination. Experimental results demonstrate that the proposed method significantly outperforms the other adaptive and non-adaptive algorithms in terms of latency and power consumption. This efficiency is achieved by alleviating the number of hotspots through a better traffic distribution all over the network.