added bellman ford algorithm

Algorithms_and_Data_Structures/bellman_ford/Bellman_ford.py

@@ -0,0 +1,56 @@
+def BellmanFord(src, V, graph):
+    '''
+    this algorithm works exactly like dijkistra algorthm except it 
+    can detect negative edge cycle in the graph
+
+    this algo is little slower than dijkistra algortihm 
+    '''
+    #src is source vertex   V is no of vertex  graph is graph in the form of a list of list
+    dist = [float("Inf")]*V
+    dist[src] = 0
+
+    for _ in range(V-1):
+        for u,v,w in graph:
+            if dist[u] != float("Inf") and dist[u] + w < dist[v]:
+                dist[v] = dist[u] + w
+
+
+    for u,v,w in graph:
+        if dist[u] != float("Inf") and dist[u] + w < dist[v]:
+            return -1
+
+    return dist
+
+def printArr(dist):
+    V = len(dist)
+    print("vertex distance from source")
+    for i in range(V):
+        print(f"{i}\t\t{dist[i]}")
+
+#example usage of bellman ford algorithm
+def main():
+    v = 5
+    graph = []              
+    graph.append([0,1,-1])  #[u=initial vertex, final vertex, w = weight of edge btw them]
+    graph.append([0,2,4])
+    graph.append([1,2,3])
+    graph.append([1,3,2])
+    graph.append([1,4,2])
+    graph.append([3,2,5])
+    graph.append([3,1,1])
+    graph.append([4,3,-3])
+
+    dist = BellmanFord(0,v,graph)
+    printArr(dist)                  
+
+if __name__ == "__main__":
+    main()
+
+'''output
+vertex distance from source
+0               0 
+1               -1
+2               2 
+3               -2
+4               1
+'''