NetworkX之Prim算法(实例讲解)

def prim(G, s):
 dist = {} # dist记录到节点的最小距离
 parent = {} # parent记录最小生成树的双亲表
 Q = list(G.nodes()) # Q包含所有未被生成树覆盖的节点
 MAXDIST = 9999.99 # MAXDIST表示正无穷，即两节点不邻接
 # 初始化数据
 # 所有节点的最小距离设为MAXDIST，父节点设为None
 for v in G.nodes():
  dist[v] = MAXDIST
  parent[v] = None
 # 到开始节点s的距离设为0
 dist[s] = 0
 # 不断从Q中取出“最近”的节点加入最小生成树
 # 当Q为空时停止循环，算法结束
 while Q:
  # 取出“最近”的节点u，把u加入最小生成树
  u = Q[0]
  for v in Q:
   if (dist[v] < dist[u]):
    u = v
  Q.remove(u)
  # 更新u的邻接节点的最小距离
  for v in G.adj[u]:
   if (v in Q) and (G[u][v]['weight'] < dist[v]):
    parent[v] = u
    dist[v] = G[u][v]['weight']
 # 算法结束，以双亲表的形式返回最小生成树
 return parent

import matplotlib.pyplot as plt
import networkx as nx
g_data = [(1, 2, 1.3), (1, 3, 2.1), (1, 4, 0.9), (1, 5, 0.7), (1, 6, 1.8), (1, 7, 2.0), (1, 8, 1.8), (2, 3, 0.9), (2, 4, 1.8), (2, 5, 1.2), (2, 6, 2.8), (2, 7, 2.3), (2, 8, 1.1), (3, 4, 2.6), (3, 5, 1.7), (3, 6, 2.5), (3, 7, 1.9), (3, 8, 1.0), (4, 5, 0.7), (4, 6, 1.6), (4, 7, 1.5), (4, 8, 0.9), (5, 6, 0.9), (5, 7, 1.1), (5, 8, 0.8), (6, 7, 0.6), (6, 8, 1.0), (7, 8, 0.5)]
def draw(g):
 pos = nx.spring_layout(g)
 nx.draw(g, pos, \
   arrows=True, \
   with_labels=True, \
   nodelist=g.nodes(), \
   style='dashed', \
   edge_color='b', \
   width=2, \
   node_color='y', \
   alpha=0.5)
 plt.show()
g = nx.Graph()
g.add_weighted_edges_from(g_data)
tree = prim(g, 1)
mtg = nx.Graph()
mtg.add_edges_from(tree.items())
mtg.remove_node(None)
draw(mtg)