2018-03-08 20:52:16 +00:00
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# Ford-Fulkerson Algorithm for Maximum Flow Problem
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"""
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Description:
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(1) Start with initial flow as 0;
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(2) Choose augmenting path from source to sink and add path to flow;
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"""
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def BFS(graph, s, t, parent):
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# Return True if there is node that has not iterated.
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visited = [False]*len(graph)
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queue=[]
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queue.append(s)
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visited[s] = True
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while queue:
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u = queue.pop(0)
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for ind in range(len(graph[u])):
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if visited[ind] == False and graph[u][ind] > 0:
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queue.append(ind)
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visited[ind] = True
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parent[ind] = u
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return True if visited[t] else False
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2018-03-08 20:53:10 +00:00
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2018-03-08 20:52:16 +00:00
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def FordFulkerson(graph, source, sink):
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# This array is filled by BFS and to store path
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parent = [-1]*(len(graph))
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max_flow = 0
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while BFS(graph, source, sink, parent) :
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path_flow = float("Inf")
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s = sink
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while(s != source):
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# Find the minimum value in select path
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path_flow = min (path_flow, graph[parent[s]][s])
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s = parent[s]
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max_flow += path_flow
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v = sink
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while(v != source):
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u = parent[v]
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graph[u][v] -= path_flow
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graph[v][u] += path_flow
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v = parent[v]
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return max_flow
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graph = [[0, 16, 13, 0, 0, 0],
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[0, 0, 10 ,12, 0, 0],
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[0, 4, 0, 0, 14, 0],
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[0, 0, 9, 0, 0, 20],
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[0, 0, 0, 7, 0, 4],
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[0, 0, 0, 0, 0, 0]]
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source, sink = 0, 5
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print(FordFulkerson(graph, source, sink))
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