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ford_fulkerson.py
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97 lines (69 loc) · 3 KB
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# Python program for implementation of Ford Fulkerson algorithm
from collections import defaultdict
#This class represents a directed graph using adjacency matrix representation
class Graph:
def __init__(self,graph):
self.graph = graph # residual graph
self. 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))