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ROW = len(graph) + #self.COL = len(gr[0]) + + + '''Returns true if there is a path from source 's' to sink 't' in + residual graph. Also fills parent[] to store the path ''' + def BFS(self,s, t, parent): + + # Mark all the vertices as not visited + visited =[False]*(self.ROW) + + # Create a queue for BFS + queue=[] + + # Mark the source node as visited and enqueue it + queue.append(s) + visited[s] = True + + # Standard BFS Loop + while queue: + + #Dequeue a vertex from queue and print it + u = queue.pop(0) + + # Get all adjacent vertices of the dequeued vertex u + # If a adjacent has not been visited, then mark it + # visited and enqueue it + for ind, val in enumerate(self.graph[u]): + if visited[ind] == False and val > 0 : + queue.append(ind) + visited[ind] = True + parent[ind] = u + + # If we reached sink in BFS starting from source, then return + # true, else false + return True if visited[t] else False + + + # Returns tne maximum flow from s to t in the given graph + def FordFulkerson(self, source, sink): + + # This array is filled by BFS and to store path + parent = [-1]*(self.ROW) + + max_flow = 0 # There is no flow initially + + # Augment the flow while there is path from source to sink + while self.BFS(source, sink, parent) : + + # Find minimum residual capacity of the edges along the + # path filled by BFS. Or we can say find the maximum flow + # through the path found. + path_flow = float("Inf") + s = sink + while(s != source): + path_flow = min (path_flow, self.graph[parent[s]][s]) + s = parent[s] + + # Add path flow to overall flow + max_flow += path_flow + + # update residual capacities of the edges and reverse edges + # along the path + v = sink + while(v != source): + u = parent[v] + self.graph[u][v] -= path_flow + self.graph[v][u] += path_flow + v = parent[v] + + return max_flow + + +# Create a graph given in the above diagram + +graph = [[0, 16, 13, 0, 0, 0], + [0, 0, 10, 12, 0, 0], + [0, 4, 0, 0, 14, 0], + [0, 0, 9, 0, 0, 20], + [0, 0, 0, 7, 0, 4], + [0, 0, 0, 0, 0, 0]] + +g = Graph(graph) + +source = 0; sink = 5 + +print ("The maximum possible flow is %d " % g.FordFulkerson(source, sink)) + diff --git a/FordFulkerson/ReferenceLinks.txt b/FordFulkerson/ReferenceLinks.txt new file mode 100644 index 0000000..18b1e56 --- /dev/null +++ b/FordFulkerson/ReferenceLinks.txt @@ -0,0 +1,6 @@ +Reference Links + +https://www.geeksforgeeks.org/ford-fulkerson-algorithm-for-maximum-flow-problem/ +https://en.wikipedia.org/wiki/Ford–Fulkerson_algorithm +https://www.youtube.com/watch?v=Iwc3Uj4aaF4 +https://www.tutorialspoint.com/Ford-Fulkerson-Algorithm \ No newline at end of file