Include functional because of std::less.
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2007
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
21 ///\brief Max flow problem solved with an LP solver (demo).
23 /// This demo program shows how to solve a maximum (or maximal) flow
24 /// problem using the LEMON LP solver interface. We would like to lay
25 /// the emphasis on the simplicity of the way one can formulate LP
26 /// constraints that arise in graph theory in our library LEMON .
28 /// \include lp_maxflow_demo.cc
30 #include<lemon/graph_reader.h>
31 #include<lemon/list_graph.h>
39 using namespace lemon;
41 template<class G,class C>
42 double maxFlow(const G &g,const C &cap,typename G::Node s,typename G::Node t)
47 typedef typename G::Node Node;
48 typedef typename G::NodeIt NodeIt;
49 typedef typename G::Edge Edge;
50 typedef typename G::EdgeIt EdgeIt;
51 typedef typename G::OutEdgeIt OutEdgeIt;
52 typedef typename G::InEdgeIt InEdgeIt;
54 //Define a map on the edges for the variables of the LP problem
55 typename G::template EdgeMap<Lp::Col> x(g);
58 //Nonnegativity and capacity constraints
59 for(EdgeIt e(g);e!=INVALID;++e) {
60 lp.colUpperBound(x[e],cap[e]);
61 lp.colLowerBound(x[e],0);
65 //Flow conservation constraints for the nodes (except for 's' and 't')
66 for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {
68 for(InEdgeIt e(g,n);e!=INVALID;++e) ex+=x[e];
69 for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
73 //Objective function: the flow value entering 't'
75 for(InEdgeIt e(g,t);e!=INVALID;++e) obj+=x[e];
76 for(OutEdgeIt e(g,t);e!=INVALID;++e) obj-=x[e];
88 std::cout<<"Solver used: "<<default_solver_name<<std::endl;
90 //Solve with the underlying solver
93 return lp.primalValue();
96 int main(int argc, char *argv[])
100 std::cerr << " USAGE: lp_maxflow_demo input_file.lgf" << std::endl;
101 std::cerr << " The file 'input_file.lgf' has to contain a max "
102 << "flow instance in\n"
103 << " LEMON format (e.g. sample.lgf is such a file)."
109 //input stream to read the graph from
110 std::ifstream is(argv[1]);
117 ListGraph::EdgeMap<double> cap(g);
119 GraphReader<ListGraph> reader(is,g);
120 reader.readNode("source",s).readNode("target",t)
121 .readEdgeMap("capacity",cap).run();
123 std::cout << "Max flow value = " << maxFlow(g,cap,s,t) << std::endl;