Python/networking_flow/ford_fulkerson.py

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# Ford-Fulkerson Algorithm for Maximum Flow Problem
"""
Description:
(1) Start with initial flow as 0;
(2) Choose augmenting path from source to sink and add path to flow;
"""
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def BFS(graph, s, t, parent):
# Return True if there is node that has not iterated.
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visited = [False] * len(graph)
queue = []
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queue.append(s)
visited[s] = True
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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
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def FordFulkerson(graph, source, sink):
# This array is filled by BFS and to store path
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parent = [-1] * (len(graph))
max_flow = 0
while BFS(graph, source, sink, parent):
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path_flow = float("Inf")
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]
graph[u][v] -= path_flow
graph[v][u] += path_flow
v = parent[v]
return max_flow
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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],
]
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source, sink = 0, 5
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print(FordFulkerson(graph, source, sink))