|
| 1 | +classEdge(object): |
| 2 | +def__init__(self,u,v,w): |
| 3 | +self.source=u |
| 4 | +self.sink=v |
| 5 | +self.capacity=w |
| 6 | + |
| 7 | +def__repr__(self): |
| 8 | +return"%s->%s:%s"% (self.source,self.sink,self.capacity) |
| 9 | + |
| 10 | + |
| 11 | +classFlowNetwork(object): |
| 12 | +def__init__(self): |
| 13 | +self.adj= {} |
| 14 | +self.flow= {} |
| 15 | + |
| 16 | +defadd_vertex(self,vertex): |
| 17 | +self.adj[vertex]= [] |
| 18 | + |
| 19 | +defget_edges(self,v): |
| 20 | +returnself.adj[v] |
| 21 | + |
| 22 | +defadd_edge(self,u,v,w=0): |
| 23 | +ifu==v: |
| 24 | +raiseValueError("u == v") |
| 25 | +edge=Edge(u,v,w) |
| 26 | +redge=Edge(v,u,0) |
| 27 | +edge.redge=redge |
| 28 | +redge.redge=edge |
| 29 | +self.adj[u].append(edge) |
| 30 | +self.adj[v].append(redge) |
| 31 | +self.flow[edge]=0 |
| 32 | +self.flow[redge]=0 |
| 33 | + |
| 34 | +deffind_path(self,source,sink,path): |
| 35 | +ifsource==sink: |
| 36 | +returnpath |
| 37 | +foredgeinself.get_edges(source): |
| 38 | +residual=edge.capacity-self.flow[edge] |
| 39 | +ifresidual>0andedgenotinpath: |
| 40 | +result=self.find_path(edge.sink,sink,path+ [edge]) |
| 41 | +ifresultisnotNone: |
| 42 | +returnresult |
| 43 | + |
| 44 | +defmax_flow(self,source,sink): |
| 45 | +path=self.find_path(source,sink, []) |
| 46 | +whilepathisnotNone: |
| 47 | +residuals= [edge.capacity-self.flow[edge]foredgeinpath] |
| 48 | +flow=min(residuals) |
| 49 | +foredgeinpath: |
| 50 | +self.flow[edge]+=flow |
| 51 | +self.flow[edge.redge]-=flow |
| 52 | +path=self.find_path(source,sink, []) |
| 53 | +returnsum(self.flow[edge]foredgeinself.get_edges(source)) |
| 54 | + |
| 55 | + |
| 56 | +defmain(): |
| 57 | +g=FlowNetwork() |
| 58 | + [g.add_vertex(v)forvin"sopqrt"] |
| 59 | + |
| 60 | +g.add_edge('s','o',3) |
| 61 | +g.add_edge('s','p',3) |
| 62 | +g.add_edge('o','p',2) |
| 63 | +g.add_edge('o','q',3) |
| 64 | +g.add_edge('p','r',2) |
| 65 | +g.add_edge('r','t',3) |
| 66 | +g.add_edge('q','r',4) |
| 67 | +g.add_edge('q','t',2) |
| 68 | + |
| 69 | +print(g.max_flow('s','t')) |
| 70 | + |
| 71 | +if__name__=='__main__': |
| 72 | +main() |