// -*- c++ -*-

#include <iostream>

#include <fstream>

#include <lemon/smart_graph.h>

#include <lemon/list_graph.h>

#include <lemon/dimacs.h>

#include <lemon/time_measure.h>

#include <lp_solver_base.h>

using std::cout;

using std::endl;

using namespace lemon;

template<typename Edge, typename EdgeIndexMap> 

class PrimalMap {

protected:

  LPGLPK* lp;

  EdgeIndexMap* edge_index_map;

public:

  PrimalMap(LPGLPK& _lp, EdgeIndexMap& _edge_index_map) : 

    lp(&_lp), edge_index_map(&_edge_index_map) { }

  double operator[](Edge e) const { 

    return lp->getPrimal((*edge_index_map)[e]);

  }

};

// Use a DIMACS max flow file as stdin.

// max_flow_expresion < dimacs_max_flow_file

int main(int, char **) {

  typedef ListGraph Graph;

  typedef Graph::Node Node;

  typedef Graph::Edge Edge;

  typedef Graph::EdgeIt EdgeIt;

  Graph g;

  Node s, t;

  Graph::EdgeMap<int> cap(g);

  readDimacs(std::cin, g, cap, s, t);

  Timer ts;

  typedef LPGLPK LPSolver;

  LPSolver lp;

  lp.setMaximize();

  typedef LPSolver::ColIt ColIt;

  typedef LPSolver::RowIt RowIt;

  typedef Graph::EdgeMap<ColIt> EdgeIndexMap;

  EdgeIndexMap edge_index_map(g);

  PrimalMap<Edge, EdgeIndexMap> flow(lp, edge_index_map);

  // nonnegativity of flow and capacity function

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

    ColIt col_it=lp.addCol();

    edge_index_map.set(e, col_it);

    // interesting property in GLPK:

    // if you change the order of the following two lines, the 

    // two runs of GLPK are extremely different

      lp.setColLowerBound(col_it, 0);

      lp.setColUpperBound(col_it, cap[e]);

  }

  for (Graph::NodeIt n(g); n!=INVALID; ++n) {

    LPSolver::Expression expr;

    for (Graph::OutEdgeIt e(g, n); e!=INVALID; ++e)

      expr+=edge_index_map[e];

    for (Graph::InEdgeIt e(g, n); e!=INVALID; ++e)

      expr-=edge_index_map[e];

    // cost function

    if (n==s) {

      lp.setObjCoeffs(expr);      

    }

    // flow conservation constraints

    if ((n!=s) && (n!=t)) {

      RowIt row_it=lp.addRow();

      lp.setRowCoeffs(row_it, expr);

      lp.setRowLowerBound(row_it, 0.0);

      lp.setRowUpperBound(row_it, 0.0);

    }

  }

  lp.solveSimplex();

  cout << "elapsed time: " << ts << endl;

}