/* -*- C++ -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2003-2006
 * 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.setObj(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;

}