算法日记贝尔曼-福德算法

Posted 2020-09-28 子木子木

 

 

如上图使用Dijkstra算法将无法获取到最短路径

1.A->C->D   5

2.A->B...没有

最近路径为5.但是实际上B->C的路径为-2. A->B->C->D的最短开销为3

Dijkstra算法无法判断含负权边的图的最短路。如果遇到负权，在没有负权回路存在时（负权回路的含义是，回路的权值和为负。）即便有负权的边，也可以采用贝尔曼-福德算法算法正确求出最短路径。

 

算法实现

 1 def bellman_ford( graph, source ):  
 2       
 3     distance = {}  
 4     parent = {}  
 5       
 6     for node in graph:  
 7         distance[node] = float( \'Inf\' )  
 8         parent[node] = None  
 9     distance[source] = 0  
10   
11     for i in range( len( graph ) - 1 ):  
12         for from_node in graph:  
13             for to_node in graph[from_node]:  
14                 if distance[to_node] > graph[from_node][to_node] + distance[from_node]:  
15                     distance[to_node] = graph[from_node][to_node] + distance[from_node]  
16                     parent[to_node] = from_node  
17   
18     for from_node in graph:  
19         for to_node in graph[from_node]:  
20             if distance[to_node] > distance[from_node] + graph[from_node][to_node]:  
21                 return None, None  
22   
23     return distance, parent  
24   
25 def test():  
26     graph = {  
27         \'a\': {\'b\': -1, \'c\':  4},  
28         \'b\': {\'c\':  3, \'d\':  2, \'e\':  2},  
29         \'c\': {},  
30         \'d\': {\'b\':  1, \'c\':  5},  
31         \'e\': {\'d\': -3}  
32     }  
33     distance, parent = bellman_ford( graph, \'a\' )  
34     print distance  
35     print parent  
36   
37 if __name__ == \'__main__\':  
38     test()