【算法日记】路径算法

此算法适合带有负边权的和无负边权的有向图。算法会计算出所有可能的路径和每个路径的长度

 1 ways={
 2         "A":{
 3             "B":5,
 4             "C":2
 5         },
 6         "B":{
 7             "C":4
 8         },
 9         "C":{
10             "D":5,
11         },
12         "D":None
13     }
14
15 def findWay(ways,start,end):
16
17     wayList={}
18
19     def search(string):
20         node=string[-1]
21         if ways[node]:
22             nodeList=ways[node].keys()
23             for item in nodeList:
24                 if item==end:
25                     wayList[string+item]=getValue(string+item)
26                 else:
27                     newPath=string+item
28                     search(newPath)
29
30     def getValue(string):
31         l=len(string)
32         v=0
33         for i in range(l-1):
34             key1=string[i]
35             key2=string[i+1]
36             v+=int(ways[key1][key2])
37         return v
38
39     for key in ways[start]:
40         new=start+key
41         search(new)
42     print wayList
43
44 findWay(ways,"A","D")

输出：

负边权图：

 1 ways={
 2         "A":{
 3             "B":5,
 4             "C":2
 5         },
 6         "B":{
 7             "C":-4
 8         },
 9         "C":{
10             "D":5,
11         },
12         "D":None
13     }
14
15 def findWay(ways,start,end):
16
17     wayList={}
18
19     def search(string):
20         node=string[-1]
21         if ways[node]:
22             nodeList=ways[node].keys()
23             for item in nodeList:
24                 if item==end:
25                     wayList[string+item]=getValue(string+item)
26                 else:
27                     newPath=string+item
28                     search(newPath)
29
30     def getValue(string):
31         l=len(string)
32         v=0
33         for i in range(l-1):
34             key1=string[i]
35             key2=string[i+1]
36             v+=int(ways[key1][key2])
37         return v
38
39     for key in ways[start]:
40         new=start+key
41         search(new)
42     print wayList
43
44 findWay(ways,"A","D")

输出：