【演算法日記】貝爾曼-福德演算法

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如使用Dijkstra演算法將無法擷取到最短路徑

1.A->C->D   5

2.A->B...沒有

最近路徑為5.但是實際上B->C的路徑為-2. A->B->C->D的最短開銷為3

Dijkstra演算法無法判斷含負權邊的圖的最短路。如果遇到負權，在沒有負權迴路存在時（負權迴路的含義是，迴路的權值和為負。）即便有負權的邊，也可以採用貝爾曼-福德演算法演算法正確求出最短路徑。

 

演算法實現

 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()  

 

【演算法日記】貝爾曼-福德演算法