# source:lemon-0.x/demo/lp_maxflow_demo.cc@2133:b82e4d2b14ac

Last change on this file since 2133:b82e4d2b14ac was 1956:a055123339d5, checked in by Alpar Juttner, 14 years ago

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
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.
12 *
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
15 * purpose.
16 *
17 */
18
19///\ingroup demos
20///\file
21///\brief Max flow problem solved with an LP solver (demo).
22///
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 .
27///
28/// \include lp_maxflow_demo.cc
29
31#include<lemon/list_graph.h>
32#include <lemon/lp.h>
33
34#include <fstream>
35#include <iostream>
36
37
38
39using namespace lemon;
40
41template<class G,class C>
42double maxFlow(const G &g,const C &cap,typename G::Node s,typename G::Node t)
43{
44  Lp lp;
45
46  typedef G Graph;
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;
53
54  //Define a map on the edges for the variables of the LP problem
55  typename G::template EdgeMap<Lp::Col> x(g);
57
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);
62  }
63
64
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) {
67    Lp::Expr ex;
68    for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];
69    for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
71  }
72
73  //Objective function: the flow value entering 't'
74  Lp::Expr obj;
75  for(InEdgeIt  e(g,t);e!=INVALID;++e) obj+=x[e];
76  for(OutEdgeIt e(g,t);e!=INVALID;++e) obj-=x[e];
77  lp.setObj(obj);
78
79
80  //Maximization
81  lp.max();
82
83#if DEFAULT_LP==GLPK
84  lp.presolver(true);
85  lp.messageLevel(3);
86#endif
87
88  std::cout<<"Solver used: "<<default_solver_name<<std::endl;
89
90  //Solve with the underlying solver
91  lp.solve();
92
93  return lp.primalValue();
94}
95
96int main(int argc, char *argv[])
97{
98  if(argc<2)
99  {
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)."
104                << std::endl;
105      return 0;
106  }
107
108
109  //input stream to read the graph from
110  std::ifstream is(argv[1]);
111
112
113  ListGraph g;
114  ListGraph::Node s;
115  ListGraph::Node t;
116
117  ListGraph::EdgeMap<double> cap(g);
118
122
123  std::cout << "Max flow value = " << maxFlow(g,cap,s,t) << std::endl;
124
125}
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