// -*- 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;
}