// -*- 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 <graph_wrapper.h>

#include <lemon/preflow.h>

#include <augmenting_flow.h>

//#include <preflow_res.h>

#include <lp_solver_wrapper.h>

// Use a DIMACS max flow file as stdin.

// max_flow_demo < dimacs_max_flow_file

using namespace lemon;

namespace lemon {

  template<typename Edge, typename EdgeIndexMap> 

  class PrimalMap {

  protected:

    LPSolverWrapper* lp;

    EdgeIndexMap* edge_index_map;

  public:

    PrimalMap(LPSolverWrapper& _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]);

    }

  };

  // excess: rho-delta

  template <typename Graph, typename Num,

	    typename Excess=typename Graph::template NodeMap<Num>, 

	    typename LCapMap=typename Graph::template EdgeMap<Num>,

	    typename CapMap=typename Graph::template EdgeMap<Num>,

            typename FlowMap=typename Graph::template EdgeMap<Num>,

	    typename CostMap=typename Graph::template EdgeMap<Num> >

  class MinCostGenFlow {

  protected:

    const Graph& g;

    const Excess& excess;

    const LCapMap& lcapacity;

    const CapMap& capacity;

    FlowMap& flow;

    const CostMap& cost;

  public:

    MinCostGenFlow(const Graph& _g, const Excess& _excess, 

		   const LCapMap& _lcapacity, const CapMap& _capacity, 

		   FlowMap& _flow, 

		   const CostMap& _cost) :

      g(_g), excess(_excess), lcapacity(_lcapacity),

      capacity(_capacity), flow(_flow), cost(_cost) { }

    void run() {

      LPSolverWrapper lp;

      lp.setMinimize();

      typedef LPSolverWrapper::ColIt ColIt;

      typedef LPSolverWrapper::RowIt RowIt;

      typedef typename Graph::template EdgeMap<ColIt> EdgeIndexMap;

      EdgeIndexMap edge_index_map(g);

      PrimalMap<typename Graph::Edge, EdgeIndexMap> lp_flow(lp, edge_index_map);

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

	ColIt col_it=lp.addCol();

	edge_index_map.set(e, col_it);

	if (lcapacity[e]==capacity[e])

	  lp.setColBounds(col_it, LPX_FX, lcapacity[e], capacity[e]);

	else 

	  lp.setColBounds(col_it, LPX_DB, lcapacity[e], capacity[e]);

	lp.setObjCoef(col_it, cost[e]);

      }

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

	typename Graph::template EdgeMap<Num> coeffs(g, 0);

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

	coeffs.set(e, coeffs[e]+1);

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

	coeffs.set(e, coeffs[e]-1);

	RowIt row_it=lp.addRow();

	typename std::vector< std::pair<ColIt, double> > row;

	//std::cout << "node:" <<g.id(n)<<std::endl;

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

	  if (coeffs[e]!=0) {

	    //std::cout << " edge:" <<g.id(e)<<" "<<coeffs[e];

	    row.push_back(std::make_pair(edge_index_map[e], coeffs[e]));

	  }

	}

	//std::cout << std::endl;

	lp.setRowCoeffs(row_it, row.begin(), row.end());

	lp.setRowBounds(row_it, LPX_FX, 0.0, 0.0);

      }

      lp.solveSimplex();

      //std::cout << lp.colNum() << std::endl;

      //std::cout << lp.rowNum() << std::endl;

      //std::cout << "flow value: "<< lp.getObjVal() << std::endl;

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

      flow.set(e, lp_flow[e]);

    }

  };

}

int main(int, char **) {

  typedef ListGraph MutableGraph;

  typedef SmartGraph Graph;

  typedef Graph::Node Node;

  typedef Graph::Edge Edge;

  typedef Graph::EdgeIt EdgeIt;

  Graph g;

  Node s, t;

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

  //readDimacsMaxFlow(std::cin, g, s, t, cap);

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

  Timer ts;

  Graph::EdgeMap<int> flow(g); //0 flow

  Preflow<Graph, int, Graph::EdgeMap<int>, Graph::EdgeMap<int> > 

    max_flow_test(g, s, t, cap, flow);

  AugmentingFlow<Graph, int, Graph::EdgeMap<int>, Graph::EdgeMap<int> > 

    augmenting_flow_test(g, s, t, cap, flow);

  Graph::NodeMap<bool> cut(g);

  {

    std::cout << "preflow ..." << std::endl;

    ts.reset();

    max_flow_test.run();

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

    std::cout << "flow value: "<< max_flow_test.flowValue() << std::endl;

    max_flow_test.minCut(cut);

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

      if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

	std::cout << "Slackness does not hold!" << std::endl;

      if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

	std::cout << "Slackness does not hold!" << std::endl;

    }

  }

//   {

//     std::cout << "preflow ..." << std::endl;

//     FOR_EACH_LOC(Graph::EdgeIt, e, g) flow.set(e, 0);

//     ts.reset();

//     max_flow_test.preflow(Preflow<Graph, int, Graph::EdgeMap<int>, Graph::EdgeMap<int> >::GEN_FLOW);

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

//     std::cout << "flow value: "<< max_flow_test.flowValue() << std::endl;

//     FOR_EACH_LOC(Graph::EdgeIt, e, g) {

//       if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

// 	std::cout << "Slackness does not hold!" << std::endl;

//       if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

// 	std::cout << "Slackness does not hold!" << std::endl;

//     }

//   }

//   {

//     std::cout << "wrapped preflow ..." << std::endl;

//     FOR_EACH_LOC(Graph::EdgeIt, e, g) flow.set(e, 0);

//     ts.reset();

//     pre_flow_res.run();

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

//     std::cout << "flow value: "<< pre_flow_test.flowValue() << std::endl;

//   }

  {

    std::cout << "physical blocking flow augmentation ..." << std::endl;

    for (EdgeIt e(g); e!=INVALID; ++e) flow.set(e, 0);

    ts.reset();

    int i=0;

    while (augmenting_flow_test.augmentOnBlockingFlow<MutableGraph>()) { ++i; }

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

    std::cout << "number of augmentation phases: " << i << std::endl; 

    std::cout << "flow value: "<< augmenting_flow_test.flowValue() << std::endl;

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

      if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

	std::cout << "Slackness does not hold!" << std::endl;

      if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

	std::cout << "Slackness does not hold!" << std::endl;

    }

  }

//   {

//     std::cout << "faster physical blocking flow augmentation ..." << std::endl;

//     FOR_EACH_LOC(Graph::EdgeIt, e, g) flow.set(e, 0);

//     ts.reset();

//     int i=0;

//     while (max_flow_test.augmentOnBlockingFlow1<MutableGraph>()) { ++i; }

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

//     std::cout << "number of augmentation phases: " << i << std::endl; 

//     std::cout << "flow value: "<< max_flow_test.flowValue() << std::endl;

//   }

  {

    std::cout << "on-the-fly blocking flow augmentation ..." << std::endl;

    for (EdgeIt e(g); e!=INVALID; ++e) flow.set(e, 0);

    ts.reset();

    int i=0;

    while (augmenting_flow_test.augmentOnBlockingFlow2()) { ++i; }

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

    std::cout << "number of augmentation phases: " << i << std::endl; 

    std::cout << "flow value: "<< augmenting_flow_test.flowValue() << std::endl;

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

      if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

	std::cout << "Slackness does not hold!" << std::endl;

      if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

	std::cout << "Slackness does not hold!" << std::endl;

    }

  }

//   {

//     std::cout << "on-the-fly shortest path augmentation ..." << std::endl;

//     FOR_EACH_LOC(Graph::EdgeIt, e, g) flow.set(e, 0);

//     ts.reset();

//     int i=0;

//     while (augmenting_flow_test.augmentOnShortestPath()) { ++i; }

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

//     std::cout << "number of augmentation phases: " << i << std::endl; 

//     std::cout << "flow value: "<< augmenting_flow_test.flowValue() << std::endl;

//     FOR_EACH_LOC(Graph::EdgeIt, e, g) {

//       if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

// 	std::cout << "Slackness does not hold!" << std::endl;

//       if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

// 	std::cout << "Slackness does not hold!" << std::endl;

//     }

//   }

//   {

//     std::cout << "on-the-fly shortest path augmentation ..." << std::endl;

//     FOR_EACH_LOC(Graph::EdgeIt, e, g) flow.set(e, 0);

//     ts.reset();

//     int i=0;

//     while (augmenting_flow_test.augmentOnShortestPath2()) { ++i; }

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

//     std::cout << "number of augmentation phases: " << i << std::endl; 

//     std::cout << "flow value: "<< augmenting_flow_test.flowValue() << std::endl;

//     FOR_EACH_LOC(Graph::EdgeIt, e, g) {

//       if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

// 	std::cout << "Slackness does not hold!" << std::endl;

//       if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

// 	std::cout << "Slackness does not hold!" << std::endl;

//     }

//   }

  ts.reset();

  Edge e=g.addEdge(t, s);

  Graph::EdgeMap<int> cost(g, 0);

  cost.set(e, -1);

  cap.set(e, 10000);

  typedef ConstMap<Node, int> Excess;

  Excess excess(0);

  typedef ConstMap<Edge, int> LCap;

  LCap lcap(0);

  MinCostGenFlow<Graph, int, Excess, LCap> 

    min_cost(g, excess, lcap, cap, flow, cost); 

  min_cost.run();

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

  std::cout << "flow value: "<< flow[e] << std::endl;

}