/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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;

}