4、Prim演算法

輸入：無向圖（頂點序列，邊序列）

功能要求：輸出最小生成樹的各組成邊及最小生成樹的權值

原始碼：

 1 import numpy as np
 2 
 3 
 4 class MinTree(object):
 5     def create_graph(self, graph, vertex: int, data: [], weight: []):
 6         for i in range(vertex):
 7             graph.data[i] = data[i]
 8             for j in range(vertex):
 
 9                 graph.weight[i][j] = weight[i][j]
10 
11     def show_graph(self, graph):
12         for link in graph.weight:
13             print(link)
14 
15     def prim_algorithm(self, graph, v: int):
16         total = 0
17         visited = [0] * graph.vertex
18         visited[v] = 1
19         h1 = -1
20
 
         h2 = -1
21         min_weight = 10000
22         for k in range(1, graph.vertex):
23             for i in range(graph.vertex):
24                 for j in range(graph.vertex):
25                     if visited[i] == 1 and visited[j] == 0 and graph.weight[i][j] < min_weight:
26                         min_weight = graph.weight[i][j]
 
27                         h1 = i
28                         h2 = j
29             print('邊 %s -> %s 權值： %d ' % (graph.data[h1], graph.data[h2], min_weight))
30             total += min_weight
31             visited[h2] = 1
32             min_weight = 10000
33         print('最小生成樹的權值： ', total)
34 
35 
36 class MGraph(object):
37     def __init__(self, vertex):
38         self.vertex = vertex
39         self.data = vertex * [0]
40         self.weight = [[0 for row in range(vertex)] for col in range(vertex)]
41 
42 
43 if __name__ == '__main__':
44     """
45     vertex_data = ['A', 'B', 'C', 'D', 'E', 'F', 'G']
46     weights = [[10000, 5, 7, 10000, 10000, 10000, 2],
47                [5, 10000, 10000, 9, 10000, 10000, 3],
48                [7, 10000, 10000, 10000, 8, 10000, 10000],
49                [10000, 9, 10000, 10000, 10000, 4, 10000],
50                [10000, 10000, 8, 10000, 10000, 5, 4],
51                [10000, 10000, 10000, 4, 5, 10000, 6],
52                [2, 3, 10000, 10000, 4, 6, 10000]]
53     """
54 
55     vertex_str = input("請輸入頂點序列（以空格分隔）：")
56     vertex_list = vertex_str.split(" ")
57     vertex_data = [char for char in vertex_list]
58     weight_str = input("請輸入邊序列（以空格分隔）：")
59     weight_list = weight_str.split(" ")
60     weight_list = list(map(int, weight_list))
61     weight_list = np.array(weight_list)
62     weights = weight_list.reshape(len(vertex_data), len(vertex_data))
63     g = MGraph(len(vertex_data))
64     tree = MinTree()
65     tree.create_graph(g, len(vertex_data), vertex_data, weights)
66     tree.show_graph(g)
67     tree.prim_algorithm(g, 0)