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max-flows.py
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72 lines (59 loc) · 1.96 KB
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class Edge(object):
def __init__(self, u, v, w):
self.source = u
self.sink = v
self.capacity = w
def __repr__(self):
return "%s->%s:%s" % (self.source, self.sink, self.capacity)
class FlowNetwork(object):
def __init__(self):
self.adj = {}
self.flow = {}
def add_vertex(self, vertex):
self.adj[vertex] = []
def get_edges(self, v):
return self.adj[v]
def add_edge(self, u, v, w=0):
if u == v:
raise ValueError("u == v")
edge = Edge(u, v, w)
redge = Edge(v, u, 0)
edge.redge = redge
redge.redge = edge
self.adj[u].append(edge)
self.adj[v].append(redge)
self.flow[edge] = 0
self.flow[redge] = 0
def find_path(self, source, sink, path):
if source == sink:
return path
for edge in self.get_edges(source):
residual = edge.capacity - self.flow[edge]
if residual > 0 and edge not in path:
result = self.find_path(edge.sink, sink, path + [edge])
if result is not None:
return result
def max_flow(self, source, sink):
path = self.find_path(source, sink, [])
while path is not None:
residuals = [edge.capacity - self.flow[edge] for edge in path]
flow = min(residuals)
for edge in path:
self.flow[edge] += flow
self.flow[edge.redge] -= flow
path = self.find_path(source, sink, [])
return sum(self.flow[edge] for edge in self.get_edges(source))
def main():
g = FlowNetwork()
[g.add_vertex(v) for v in "sopqrt"]
g.add_edge('s', 'o', 3)
g.add_edge('s', 'p', 3)
g.add_edge('o', 'p', 2)
g.add_edge('o', 'q', 3)
g.add_edge('p', 'r', 2)
g.add_edge('r', 't', 3)
g.add_edge('q', 'r', 4)
g.add_edge('q', 't', 2)
print(g.max_flow('s', 't'))
if __name__ == '__main__':
main()