Can the edges of a graph be assigned directions such that all nodes in a given subset have in- or outdegree 0, and every other node indegree > 0? In a directed graph, the indegree of a node is the number of incoming edges and
the outdegree is the number of outgoing edges. Show that the following problem
is NP-complete. Given an undirected graph G and a designated subset C of G’s
nodes, is it possible to convert G to a directed graph by assigning directions to each
of its edges so that every node in C has indegree 0 or outdegree 0, and every other
node in G has indegree at least 1?

I need an idea how to prove it
take $C=\emptyset$ then you want to direct the graph so all node have in degree at least 1($DA1$) and now think about directed Hamiltonian cycle($DHC$) how you can reduce $DHC$ to $DA1$ !