1+ # Bellman Ford Algorithm for Shortest Path
2+ 3+ import sys
4+ 5+ # Function to create Nodes
6+ class Node (object ):
7+ def __init__ (self ,name ):
8+ self .name = name
9+ self .visited = False
10+ self .predecessor = None
11+ self .adjacencyList = []
12+ # Distance from starting vertex/Node
13+ self .minDistance = sys .maxsize
14+ 15+ # Function to create Edges
16+ class Edge (object ):
17+ def __init__ (self , weight , startVertex , targetVertex ):
18+ self .weight = weight
19+ self .startVertex = startVertex
20+ self .targetVertex = targetVertex
21+ 22+ 23+ # Bellman Ford Algorithm
24+ class BellmanFord (object ):
25+ # Initially set the Negative cycle flag to False
26+ HAS_CYCLE = False
27+ 28+ # Calculate the Shortest Path
29+ def calculateShortestPath (self , vertexList , edgeList , startVertex ):
30+ startVertex .minDistance = 0
31+ for i in range (0 ,len (vertexList )- 1 ):
32+ for edge in edgeList :
33+ u = edge .startVertex
34+ v = edge .targetVertex
35+ 36+ newDistance = u .minDistance + edge .weight
37+ if newDistance < v .minDistance :
38+ v .minDistance = newDistance
39+ v .predecessor = u
40+ 41+ for edge in edgeList :
42+ if self .hasCycle (edge ):
43+ print ('Negative cycle detected...' )
44+ BellmanFord .HAS_CYCLE = True
45+ 46+ 47+ # Check if a negative cycle exists or not
48+ def hasCycle (self ,edge ):
49+ if (edge .startVertex .minDistance + edge .weight ) < edge .targetVertex .minDistance :
50+ return True
51+ else :
52+ return False
53+ 54+ 55+ # Traceback and Print the Shortest Path
56+ def getShortestPath (self , targetVertex ):
57+ if not BellmanFord .HAS_CYCLE :
58+ print ('Shortest path exists with value: ' , targetVertex .minDistance )
59+ node = targetVertex
60+ while node is not None :
61+ print ('%s' % node .name )
62+ node = node .predecessor
63+ else :
64+ print ('Negative cycle detected...' )
65+ 66+ 67+ 68+ 69+ # -------------------------- Testing ------------------------------
70+ if __name__ == '__main__' :
71+ # Create Nodes
72+ node1 = Node ('A' )
73+ node2 = Node ('B' )
74+ node3 = Node ('C' )
75+ node4 = Node ('D' )
76+ node5 = Node ('E' )
77+ node6 = Node ('F' )
78+ node7 = Node ('G' )
79+ node8 = Node ('H' )
80+ 81+ # Create Edges
82+ # Edge Weight, Starting Vertex, Ending Vertex
83+ edge1 = Edge (5 ,node1 , node2 )
84+ edge2 = Edge (8 , node1 , node8 )
85+ edge3 = Edge (9 , node1 , node5 )
86+ edge4 = Edge (15 , node2 , node4 )
87+ edge5 = Edge (12 , node2 , node3 )
88+ edge6 = Edge (4 , node2 , node8 )
89+ edge7 = Edge (7 , node8 , node3 )
90+ edge8 = Edge (6 , node8 , node6 )
91+ edge9 = Edge (5 , node5 , node8 )
92+ edge10 = Edge (4 , node5 , node6 )
93+ edge11 = Edge (20 , node5 , node7 )
94+ edge12 = Edge (1 , node6 , node3 )
95+ edge13 = Edge (13 , node6 , node7 )
96+ edge14 = Edge (3 , node3 , node4 )
97+ edge15 = Edge (11 , node3 , node7 )
98+ edge16 = Edge (9 , node4 , node7 )
99+ 100+ # Adjacency List, append edges
101+ node1 .adjacencyList .append (edge1 )
102+ node1 .adjacencyList .append (edge2 )
103+ node1 .adjacencyList .append (edge3 )
104+ node2 .adjacencyList .append (edge4 )
105+ node2 .adjacencyList .append (edge5 )
106+ node2 .adjacencyList .append (edge6 )
107+ node8 .adjacencyList .append (edge7 )
108+ node8 .adjacencyList .append (edge8 )
109+ node5 .adjacencyList .append (edge9 )
110+ node5 .adjacencyList .append (edge10 )
111+ node5 .adjacencyList .append (edge11 )
112+ node6 .adjacencyList .append (edge12 )
113+ node6 .adjacencyList .append (edge13 )
114+ node3 .adjacencyList .append (edge14 )
115+ node3 .adjacencyList .append (edge15 )
116+ node4 .adjacencyList .append (edge16 )
117+ 118+ # Vertex List
119+ vertexList = (node1 , node2 , node3 , node4 , node5 , node6 , node7 , node8 )
120+ edgeList = (edge1 , edge2 , edge3 , edge4 , edge5 , edge6 , edge7 , edge8 , edge9 , edge10 , edge11 , edge12 , edge13 , edge14 , edge15 , edge16 )
121+ 122+ algorithm = BellmanFord ()
123+ # Calculate Shortest Path with start Vertex node1 : "A"
124+ algorithm .calculateShortestPath (vertexList , edgeList , node1 )
125+ # Get the Shortest Path from node1: "A" to node7: "G"
126+ algorithm .getShortestPath (node7 )
127+ # Get the Shortest Path from node1: "A" to node4: "D"
128+ algorithm .getShortestPath (node4 )
129+ 130+ # ----------------------------- EOC -------------------------------
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