We propose an active tomography technique for inferring directed acyclic graph (DAG) logical topologies where intermediate nodes need to perform network coding. Unlike traditional traceroute-based techniques, our technique requires only unidirectional communication on each link, and does not require the nodes to reveal their unique identities. Also, unlike other recent techniques, our technique requires a single probing experiment with only one probe packet flowing on each link and the deterministic outcome always gives the exact logical topology. As a preparation, we first present two network coding based topology inference schemes for tree topologies which are also of independent interest.