Added Bellman-Ford Algorithm

Bellman_Ford_Algorithm/Bellman_Ford.py

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+# Bellman Ford Algorithm in Python
+
+
+class Graph:
+
+    def __init__(self, vertices):
+        self.V = vertices   # Total number of vertices in the graph
+        self.graph = []     # Array of edges
+
+    # Add edges
+    def add_edge(self, s, d, w):
+        self.graph.append([s, d, w])
+
+    # Print the solution
+    def print_solution(self, dist):
+        print("Vertex Distance from Source")
+        for i in range(self.V):
+            print("{0}\t\t{1}".format(i, dist[i]))
+
+    def bellman_ford(self, src):
+
+        # Step 1: fill the distance array and predecessor array
+        dist = [float("Inf")] * self.V
+        # Mark the source vertex
+        dist[src] = 0
+
+        # Step 2: relax edges |V| - 1 times
+        for _ in range(self.V - 1):
+            for s, d, w in self.graph:
+                if dist[s] != float("Inf") and dist[s] + w < dist[d]:
+                    dist[d] = dist[s] + w
+
+        # Step 3: detect negative cycle
+        # if value changes then we have a negative cycle in the graph
+        # and we cannot find the shortest distances
+        for s, d, w in self.graph:
+            if dist[s] != float("Inf") and dist[s] + w < dist[d]:
+                print("Graph contains negative weight cycle")
+                return
+
+        # No negative weight cycle found!
+        # Print the distance and predecessor array
+        self.print_solution(dist)
+
+
+g = Graph(5)
+g.add_edge(0, 1, 5)
+g.add_edge(0, 2, 4)
+g.add_edge(1, 3, 3)
+g.add_edge(2, 1, 6)
+g.add_edge(3, 2, 2)
+
+g.bellman_ford(0)

Bellman_Ford_Algorithm/Bellman_Ford_Algorithm.md

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+# BELLMAN FORD ALGORITHM
+
+
+Bellman Ford algorithm helps us find the shortest path from a vertex to all other vertices of a weighted graph.