Understanding how biological systems solve problems could aid the design of novel computational methods. Information processing in unicellular eukaryotes is of particular interest, as these organisms have survived for more than a billion years using a simple system. The large amoeboid plasmodium of Physarum is able to solve a maze and to connect multiple food locations via a smart network. This study examined how Physarum amoebae compute these solutions. The mechanism involves the adaptation of the tubular body, which appears to be similar to a network, based on cell dynamics. Our model describes how the network of tubes expands and contracts depending on the flux of protoplasmic streaming, and reproduces experimental observations of the behavior of the organism. The proposed algorithm based on Physarum is simple and powerful.