g={'0':{'1':10,'2':float('inf'),'3':float('inf'),'4':19,'5':21},'1':{'0':10,'2':5,'3':6,'4':float('inf'),'5':11},'2':{'0':float('inf'),'1':5,'3':6,'4':float('inf'),'5':float('inf')},'3':{'0':float('inf'),'1':6,'2':6,'4':18,'5':14},'4':{'0':19,'1':float('inf'),'2':float('inf'),'3':18,'5':33},'5':{'0':21,'1':11,'2':float('inf'),'3':14,'4':33}}defprim(g, s):
r ={}
q =[(0,None, s)]#s的前继顶点为空while q:
_, p, u = heappop(q)#pop the smallest edge wightif u in r:continue
r[u]= p#MST性质:最小权w的pu(堆顶的uv)一定在U和V-U构成的所有顶点的最小生成树中。for v, w in g[u].items():#v:vertex,w:arcs边信息的权值
heappush(q,(w, u, v))#堆顶uv是u的所有邻接点v(V-U)中权最小的print(s,"开始的最小生成树", r)#5 开始的最小生成树 {'5': None, '1': '5', '2': '1', '3': '1', '0': '1', '4': '3'} #prim(g, "5")deffind(c, u):if u != c[u]:
c[u]= find(c, c[u])return c[u]defunion(c, r, u, v):
u, v = find(c, u), find(c, v)if r[u]> r[v]:#层高的做根。第一次c[u]=v,c[v]=v
c[v]= u
else:
c[u]= v
if r[u]== r[v]: r[v]+=1#终点升一层, 起点升一层也可以的。defkruskal(g):
e =[(g[u][v], u, v)for u in g for v in g[u]]#权-点-点表
t =list()
c, r ={u: u for u in g},{u:0for u in g}#c是非连通图T=(v,∮)加入各顶点自为连通分量的并查集,r并查集层for _, u, v insorted(e):#根据权值排序if find(c, u)!= find(c, v):#判断连通与否
t.append((u, v))#新连通
union(c, r, u, v)#用并查集连通print(t)#[('1', '2'), ('1', '3'), ('0', '1'), ('1', '5'), ('3', '4')]