/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2007

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 ///\ingroup demos

 ///\file

 ///\brief Max flow problem solved with an LP solver (demo).

 ///

 /// This demo program shows how to solve a maximum (or maximal) flow

 /// problem using the LEMON LP solver interface. We would like to lay

 /// the emphasis on the simplicity of the way one can formulate LP

 /// constraints that arise in graph theory in our library LEMON .

 ///

 /// \include lp_maxflow_demo.cc

 #include<lemon/graph_reader.h>

 #include<lemon/list_graph.h>

 #include <lemon/lp.h>

 #include <fstream>

 #include <iostream>

 using namespace lemon;

 template<class G,class C>

 double maxFlow(const G &g,const C &cap,typename G::Node s,typename G::Node t)

 {

   Lp lp;

   typedef G Graph;

   typedef typename G::Node Node;

   typedef typename G::NodeIt NodeIt;

   typedef typename G::Edge Edge;

   typedef typename G::EdgeIt EdgeIt;

   typedef typename G::OutEdgeIt OutEdgeIt;

   typedef typename G::InEdgeIt InEdgeIt;

   //Define a map on the edges for the variables of the LP problem

   typename G::template EdgeMap<Lp::Col> x(g);

   lp.addColSet(x);

   //Nonnegativity and capacity constraints

   for(EdgeIt e(g);e!=INVALID;++e) {

     lp.colUpperBound(x[e],cap[e]);

     lp.colLowerBound(x[e],0);

   }

   //Flow conservation constraints for the nodes (except for 's' and 't')

   for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {

     Lp::Expr ex;

     for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];

     for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];

     lp.addRow(ex==0);

   }

   //Objective function: the flow value entering 't'

   Lp::Expr obj;

   for(InEdgeIt  e(g,t);e!=INVALID;++e) obj+=x[e];

   for(OutEdgeIt e(g,t);e!=INVALID;++e) obj-=x[e];

   lp.obj(obj);

   //Maximization

   lp.max();

 #if DEFAULT_LP==GLPK

   lp.presolver(true);

   lp.messageLevel(3);

 #endif

   std::cout<<"Solver used: "<<default_solver_name<<std::endl;

   //Solve with the underlying solver

   lp.solve();

   return lp.primalValue();

 }

 int main(int argc, char *argv[]) 

 {

   if(argc<2)

   {

       std::cerr << "  USAGE: lp_maxflow_demo input_file.lgf" << std::endl;

       std::cerr << "  The file 'input_file.lgf' has to contain a max "

 		<< "flow instance in\n"

 		<< "  LEMON format (e.g. sample.lgf is such a file)."

 		<< std::endl;

       return 0;

   }

   //input stream to read the graph from

   std::ifstream is(argv[1]);

   ListGraph g;

   ListGraph::Node s;

   ListGraph::Node t;

   ListGraph::EdgeMap<double> cap(g);

   GraphReader<ListGraph> reader(is,g);

   reader.readNode("source",s).readNode("target",t)

     .readEdgeMap("capacity",cap).run();

   std::cout << "Max flow value = " << maxFlow(g,cap,s,t) << std::endl;

 }