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67 lines
1.6 KiB
Python
67 lines
1.6 KiB
Python
# Minimum cut on Ford_Fulkerson algorithm.
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test_graph = [
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[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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]
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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 = [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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def mincut(graph, source, sink):
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"""This array is filled by BFS and to store path
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>>> mincut(test_graph, source=0, sink=5)
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[(1, 3), (4, 3), (4, 5)]
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"""
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parent = [-1] * (len(graph))
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max_flow = 0
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res = []
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temp = [i[:] for i in graph] # Record original cut, copy.
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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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for i in range(len(graph)):
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for j in range(len(graph[0])):
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if graph[i][j] == 0 and temp[i][j] > 0:
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res.append((i, j))
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return res
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if __name__ == "__main__":
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print(mincut(test_graph, source=0, sink=5))
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