Given a connected, non-negatively weighted, and undirected graph G, a spanning tree of G is defined as the tree that connects any pair of nodes in G. The minimum spanning tree (MST) is defined as the spanning tree that has the minimum total weight (the sum of the weights of all edges contained in the tree). One proposes the following recursive algorithm to solve the problem:(给定一个连通的、非负加权的无向图 G，G 的生成树被定义为连接 G 中任意一对节点的树。最小生成树 (MST) 被定义为具有最小值的生成树 总权重（树中包含的所有边的权重之和）。 有人提出以下递归算法来解决这个问题)
MST_rec(G=(V,E,W))
if(|V|≤1) return 0
arbitrarily partition G into two subgraphs G_1 and G_2
e=(u,v)← the minimum weighted edge where u∈G_1 and v∈G_2
return MST_rec(G_1=(V_1,E_1,W_1))+ MST_rec(G_1=(V_2,E_2,W_2))+w_e
Determine whether the algorithm is correct. If yes, find the time complexity of the algorithm; If not, discuss the issue(s) of the algorithm. (判断算法是否正确。 如果是，求算法的时间复杂度； 如果不是，请讨论算法的问题)