Added Bellman Ford Algorithm

Author: robinsingh-ai

Algorithms/Dynamic Programmming/Bellman_Ford_Algorithm.py

@@ -0,0 +1,69 @@
+"""
+Author : Robin Singh
+Implementation of Bellman Ford Algorithm(Dynamic Programming)
+Bellman Ford algorithm helps us find the shortest path from a vertex to all other vertices of a weighted graph.
+It is similar to Dijkstra's algorithm but it can work with graphs in which edges can have negative weights.
+
+Time Complexity : Best Case = O(E)
+                  Worst Case = Average Case  = O(VE)
+
+"""
+
+
+def bellman_ford_SSS(graph,src):
+    dist = dict()
+    prev = dict()
+    for node in graph:
+        dist[node] =float('Inf')
+        prev[node] = None
+    dist[src] = 0
+
+    for _ in range(len(graph)-1):
+        for node in graph:
+            for neighbour in graph[node]:
+                if dist[neighbour]  > dist[node]+graph[node][neighbour]:
+                    dist[neighbour] = dist[node]+graph[node][neighbour]
+                    prev[neighbour] = node
+
+    for node in graph:
+        for neighbour in graph[node]:
+            assert dist[neighbour] <= dist[node]+graph[node][neighbour],"Error,Graph Has Negative Weight Cycle"
+
+
+    return dist,prev
+
+if __name__ == '__main__':
+    #Case 1
+    graph = {
+        'a':{'b':6,'c':4,'d':5},
+        'b':{'e':-1},
+        'c':{'e':3,'b':-2},
+        'd':{'c':-2,'f':-1},
+        'e':{'f':3},
+        'f':{}
+    }
+
+    distance,prev = bellman_ford_SSS(graph,'a')
+    print("Distances From point A")
+    print(distance)
+
+    print("Predecssor Vertices")
+    print(prev)
+
+
+    #graph with Negative Weight Cycle
+    #Case 2
+    graph = {
+        'a':{'b':4,'c':5},
+        'b':{'d':7},
+        'c':{'b':7},
+        'd':{'c':-15}#change value from -15 to -14 to make graph Postive Weight Cycle
+    }
+    distance,prev = bellman_ford_SSS(graph, 'a')
+    print("")
+    print("Distances From point A")
+    print(distance)
+
+    print("Predecssor Vertices")
+    print(prev)
+