6.2

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edges = [  
    ("Pe", "T", 13),  
    ("Pe", "N", 68),  
    ("Pe", "M", 78),  
    ("Pe", "L", 51),  
    ("Pe", "Pa", 51),  
    ("T", "N", 68),  
    ("T", "M", 70),  
    ("T", "L", 60),  
    ("T", "Pa", 61),  
    ("N", "M", 21),  
    ("N", "L", 35),  
    ("N", "Pa",36),  
    ("M", "L", 56),  
    ("M", "Pa", 57),  
    ("L", "Pa", 21),  
]
class UnionFind:  
    def __init__(self, n):  
        self.parent = list(range(n))  
        self.rank = [0] * n  
  
    def find(self, u):  
        if self.parent[u] != u:  
            self.parent[u] = self.find(self.parent[u])  
        return self.parent[u]  
  
    def union(self, u, v):  
        root_u = self.find(u)  
        root_v = self.find(v)  
        if root_u != root_v:  
            if self.rank[root_u] > self.rank[root_v]:  
                self.parent[root_v] = root_u  
            elif self.rank[root_u] < self.rank[root_v]:  
                self.parent[root_u] = root_v  
            else:  
                self.parent[root_v] = root_u  
                self.rank[root_u] += 1  
  
def kruskal(edges):  
    edges.sort(key=lambda edge: edge[2]) 
    uf = UnionFind(len(set(city for edge in edges for city in edge[:2])))  
    mst = []  
      
    for u, v, weight in edges:  
        if uf.find(u) != uf.find(v):  
            uf.union(u, v)  
            mst.append((u, v, weight))  
      
    return mst  

city_map = {  
    "Pe": 0, "T": 1, "N": 2, "M": 3, "L": 4, "Pa": 5  
}  

edges_with_indices = [(city_map[u], city_map[v], weight) for u, v, weight in edges]  

mst_edges = [(list(city_map.keys())[u], list(city_map.keys())[v], weight) for u, v, weight in kruskal(edges_with_indices)]  
  
print("最小生成树的边:")  
for u, v, weight in mst_edges:  
    print(f"{u} - {v}: {weight}")

print("学号：3004")