# 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 original 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))