mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
1f8a21d727
* Tighten up psf/black and flake8
* Fix some tests
* Fix some E741
* Fix some E741
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
67 lines
1.6 KiB
Python
67 lines
1.6 KiB
Python
# 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] is 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))
|