Interactive MST

There is a **weighted undirected connected simple graph** $G$ with $N$ vertices, $M$ edges, with binary weights. The $i$-th edge connects $U_i$ and $V_i$, and has a weight of $W_i$. It is guaranteed that $0 \le W_i \le 1$ for all edges. Alice and Bob are playing a game on the graph. Alice knows everything about the graph, but Bob knows only $N$, $M$ and the edges, i.e. he does not know the weigh