Intended Solution

First, one can observe that if a connected component of the graph
contains an edge labeled~$0$ or~$2$ the guarding of the component is
already decided.  In fact, if one knows one vertex in a component this
information propagates throughout the component.  If a component
contains an edge labeled~$0$ or~$2$ we propagate and either say TODO
if conflicts occur and otherwise we count the number of guards needed.

If the component contains only edges labeled~$1$.  Any valid solution
is a $2$-coloring of the graph.  If no such coloring exists we say
TODO and otherwise we position lounges at the color of minimum size.