athos@1560: /* -*- C++ -*-
athos@1560:  *
alpar@1956:  * This file is a part of LEMON, a generic C++ optimization library
alpar@1956:  *
alpar@2553:  * Copyright (C) 2003-2008
alpar@1956:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
athos@1560:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
athos@1560:  *
athos@1560:  * Permission to use, modify and distribute this software is granted
athos@1560:  * provided that this copyright notice appears in all copies. For
athos@1560:  * precise terms see the accompanying LICENSE file.
athos@1560:  *
athos@1560:  * This software is provided "AS IS" with no warranty of any kind,
athos@1560:  * express or implied, and with no claim as to its suitability for any
athos@1560:  * purpose.
athos@1560:  *
athos@1560:  */
athos@1560: 
athos@1560: ///\ingroup demos
athos@1560: ///\file
athos@1560: ///\brief Max flow problem solved with an LP solver (demo).
athos@1560: ///
athos@1583: /// This demo program shows how to solve a maximum (or maximal) flow
athos@1583: /// problem using the LEMON LP solver interface. We would like to lay
athos@1583: /// the emphasis on the simplicity of the way one can formulate LP
athos@1583: /// constraints that arise in graph theory in our library LEMON .
alpar@1641: ///
alpar@1641: /// \include lp_maxflow_demo.cc
athos@1560: 
alpar@1361: #include<lemon/graph_reader.h>
alpar@1361: #include<lemon/list_graph.h>
alpar@1610: #include <lemon/lp.h>
alpar@1361: 
athos@1560: #include <fstream>
athos@1560: #include <iostream>
athos@1560: 
alpar@1381: 
alpar@1381: 
alpar@1361: using namespace lemon;
alpar@1361: 
alpar@1361: template<class G,class C>
alpar@1361: double maxFlow(const G &g,const C &cap,typename G::Node s,typename G::Node t)
alpar@1361: {
alpar@1610:   Lp lp;
alpar@1361:   
alpar@1361:   typedef G Graph;
alpar@1361:   typedef typename G::Node Node;
alpar@1361:   typedef typename G::NodeIt NodeIt;
alpar@1361:   typedef typename G::Edge Edge;
alpar@1361:   typedef typename G::EdgeIt EdgeIt;
alpar@1361:   typedef typename G::OutEdgeIt OutEdgeIt;
alpar@1361:   typedef typename G::InEdgeIt InEdgeIt;
alpar@1361:   
athos@1518:   //Define a map on the edges for the variables of the LP problem
alpar@1610:   typename G::template EdgeMap<Lp::Col> x(g);
alpar@1361:   lp.addColSet(x);
alpar@1361:   
athos@1518:   //Nonnegativity and capacity constraints
alpar@1361:   for(EdgeIt e(g);e!=INVALID;++e) {
alpar@1361:     lp.colUpperBound(x[e],cap[e]);
alpar@1361:     lp.colLowerBound(x[e],0);
alpar@1361:   }
alpar@1361: 
athos@1518: 
athos@1518:   //Flow conservation constraints for the nodes (except for 's' and 't')
alpar@1361:   for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {
alpar@1610:     Lp::Expr ex;
alpar@1361:     for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];
alpar@1361:     for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
alpar@1361:     lp.addRow(ex==0);
alpar@1361:   }
athos@1518:   
athos@1518:   //Objective function: the flow value entering 't'
alpar@1610:   Lp::Expr obj;
alpar@1571:   for(InEdgeIt  e(g,t);e!=INVALID;++e) obj+=x[e];
alpar@1571:   for(OutEdgeIt e(g,t);e!=INVALID;++e) obj-=x[e];
deba@2369:   lp.obj(obj);
alpar@1571: 
athos@1518: 
athos@1518:   //Maximization
alpar@1361:   lp.max();
alpar@1361: 
alpar@1610: #if DEFAULT_LP==GLPK
alpar@1361:   lp.presolver(true);
alpar@1361:   lp.messageLevel(3);
alpar@1381: #endif
alpar@1361: 
athos@1577:   std::cout<<"Solver used: "<<default_solver_name<<std::endl;
athos@1577: 
athos@1518:   //Solve with the underlying solver
alpar@1361:   lp.solve();
alpar@1361: 
alpar@1361:   return lp.primalValue();
alpar@1361: }
alpar@1361: 
athos@1560: int main(int argc, char *argv[]) 
alpar@1361: {
athos@1560:   if(argc<2)
athos@1560:   {
athos@1577:       std::cerr << "  USAGE: lp_maxflow_demo input_file.lgf" << std::endl;
alpar@1561:       std::cerr << "  The file 'input_file.lgf' has to contain a max "
alpar@1561: 		<< "flow instance in\n"
alpar@1561: 		<< "  LEMON format (e.g. sample.lgf is such a file)."
alpar@1561: 		<< std::endl;
athos@1560:       return 0;
athos@1560:   }
athos@1560: 
athos@1560: 
athos@1560:   //input stream to read the graph from
athos@1560:   std::ifstream is(argv[1]);
athos@1560: 
athos@1560: 
alpar@1361:   ListGraph g;
alpar@1361:   ListGraph::Node s;
alpar@1361:   ListGraph::Node t;
alpar@1361:   
alpar@1361:   ListGraph::EdgeMap<double> cap(g);
alpar@1361:   
athos@1560:   GraphReader<ListGraph> reader(is,g);
deba@1394:   reader.readNode("source",s).readNode("target",t)
deba@1394:     .readEdgeMap("capacity",cap).run();
alpar@1361:   
alpar@1361:   std::cout << "Max flow value = " << maxFlow(g,cap,s,t) << std::endl;
alpar@1361: 
alpar@1361: }