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# Minimum cut on Ford_Fulkerson algorithm.

test_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],

]

def BFS(graph, s, t, parent):

# Return True if there is node that has not iterated.

visited = [False] * len(graph)

queue = [s]

visited[s] = True

while queue:

u = queue.pop(0)

for ind in range(len(graph[u])):

if visited[ind] == False and graph[u][ind] > 0:

queue.append(ind)

visited[ind] = True

parent[ind] = u

return True if visited[t] else False

def mincut(graph, source, sink):

"""This array is filled by BFS and to store path

>>> mincut(test_graph, source=0, sink=5)

[(1, 3), (4, 3), (4, 5)]

"""

parent = [-1] * (len(graph))

max_flow = 0

res = []

temp = [i[:] for i in graph] # Record orignial cut, copy.

while BFS(graph, source, sink, parent):

path_flow = float("Inf")

s = sink

while s != source:

# Find the minimum value in select path

path_flow = min(path_flow, graph[parent[s]][s])

s = parent[s]

max_flow += path_flow

v = sink

while v != source:

u = parent[v]

graph[u][v] -= path_flow

graph[v][u] += path_flow

v = parent[v]

for i in range(len(graph)):

for j in range(len(graph[0])):

if graph[i][j] == 0 and temp[i][j] > 0:

res.append((i, j))

return res

if __name__ == "__main__":

print(mincut(test_graph, source=0, sink=5))

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