Added Bellman Ford Algorithm in Graph

Graph/BellmanFordShortestPath.py

@@ -0,0 +1,51 @@
+"""
+    BellFord is one of the SSSP(Single Source Shortest Path) Algorithms.
+    Its complexity is much worse than Dijkstra Algorithm - O(VE).
+    It is useful in those cases where edge weights are negative.
+    It is also useful to find negative cycles.
+"""
+
+from collections import defaultdict as dd
+from sys import maxsize
+
+
+class Graph:
+    def __init__(self, vertices):
+        self.adjmat = dd(dict)
+        self.vertices = vertices
+        self.ordering = [0 for i in range(self.vertices)]
+        self.vis = [False for i in range(self.vertices)]
+        for i in range(vertices):
+            self.adjmat[i] = dd(int)
+
+    def insert(self, u, v, w=1):
+        self.adjmat[u][v] = w
+
+    def bellman_ford(self, source):
+        dist = [maxsize for i in range(self.vertices)]
+        dist[source] = 0
+        for _ in range(self.vertices - 1):
+            for i in self.adjmat.keys():
+                for j in self.adjmat[i].keys():
+                    dist[j] = min(dist[j], dist[i] + self.adjmat[i][j])
+        # Checking for the negative cycles
+        for _ in range(self.vertices - 1):
+            for i in self.adjmat.keys():
+                for j in self.adjmat[i].keys():
+                    # If a better answer exists for a node than it is in negative cycle
+                    # or is being affected by some negative cycle.
+                    if dist[j] > dist[i] + self.adjmat[i][j]:
+                        dist[j] = -maxsize
+        return dist
+
+
+G = Graph(6)
+G.insert(0, 1, 3)
+G.insert(0, 5, 5)
+G.insert(1, 5, -9)
+G.insert(1, 3, 6)
+G.insert(5, 3, -8)
+G.insert(3, 2, 5)
+G.insert(3, 4, 7)
+G.insert(2, 4, 4)
+print(G.bellman_ford(0))