#include"lp_solver_skeleton.h"
#include"lp_glpk.h"
#include<lemon/list_graph.h>

using namespace lemon;

void lpTest(LpSolverBase & lp)
{
  typedef LpSolverBase LP;

  std::vector<LP::Col> x;
  for(int i=0;i<10;i++) x.push_back(lp.addCol());

  std::vector<LP::Col> y(10);
  lp.addColSet(y);

  std::map<int,LP::Col> z;
  
  z.insert(std::make_pair(12,INVALID));
  z.insert(std::make_pair(2,INVALID));
  z.insert(std::make_pair(7,INVALID));
  z.insert(std::make_pair(5,INVALID));
  
  lp.addColSet(z);


  LP::Expr e,f,g;
  LP::Col p1,p2,p3,p4,p5;
  LP::Constr c;
  
  e[p1]=2;
  e.constComp()=12;
  e[p1]+=2;
  e.constComp()+=12;
  e[p1]-=2;
  e.constComp()-=12;
  
  e=2;
  e=2.2;
  e=p1;
  e=f;

  e+=2;
  e+=2.2;
  e+=p1;
  e+=f;

  e-=2;
  e-=2.2;
  e-=p1;
  e-=f;

  e*=2;
  e*=2.2;
  e/=2;
  e/=2.2;

  e=((p1+p2)+(p1-p2)+(p1+12)+(12+p1)+(p1-12)+(12-p1)+
      (f+12)+(12+f)+(p1+f)+(f+p1)+(f+g)+
      (f-12)+(12-f)+(p1-f)+(f-p1)+(f-g)+
      2.2*f+f*2.2+f/2.2+
      2*f+f*2+f/2+
      2.2*p1+p1*2.2+p1/2.2+
      2*p1+p1*2+p1/2
     );
  

  c = (e  <= f  );
  c = (e  <= 2.2);
  c = (e  <= 2  );
  c = (e  <= p1 );
  c = (2.2<= f  );
  c = (2  <= f  );
  c = (p1 <= f  );
  c = (p1 <= p2 );
  c = (p1 <= 2.2);
  c = (p1 <= 2  );
  c = (2.2<= p2 );
  c = (2  <= p2 );

  c = (e  >= f  );
  c = (e  >= 2.2);
  c = (e  >= 2  );
  c = (e  >= p1 );
  c = (2.2>= f  );
  c = (2  >= f  );
  c = (p1 >= f  );
  c = (p1 >= p2 );
  c = (p1 >= 2.2);
  c = (p1 >= 2  );
  c = (2.2>= p2 );
  c = (2  >= p2 );

  c = (e  == f  );
  c = (e  == 2.2);
  c = (e  == 2  );
  c = (e  == p1 );
  c = (2.2== f  );
  c = (2  == f  );
  c = (p1 == f  );
  //c = (p1 == p2 );
  c = (p1 == 2.2);
  c = (p1 == 2  );
  c = (2.2== p2 );
  c = (2  == p2 );

  c = (2 <= e <= 3);
  c = (2 <= p1<= 3);

  c = (2 >= e >= 3);
  c = (2 >= p1>= 3);

  e[x[3]]=2;
  e[x[3]]=4;
  e[x[3]]=1;
  e.constComp()=12;
  
  lp.addRow(LP::INF,e,23);
  lp.addRow(LP::INF,3.0*(x[1]+x[2]/2)-x[3],23);
  lp.addRow(LP::INF,3.0*(x[1]+x[2]*2-5*x[3]+12-x[4]/3)+2*x[4]-4,23);

  lp.addRow(x[1]+x[3]<=x[5]-3);
  lp.addRow(-7<=x[1]+x[3]-12<=3);
  lp.addRow(x[1]<=x[5]);

}


template<class G,class C>
double maxFlow(const G &g,const C &cap,typename G::Node s,typename G::Node t)
{
  LpGlpk 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;
  
  typename G::template EdgeMap<LpGlpk::Col> x(g);
  lp.addColSet(x);
  
  for(EdgeIt e(g);e!=INVALID;++e) {
    lp.colUpperBound(x[e],cap[e]);
    lp.colLowerBound(x[e],0);
  }

  for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {
    LpGlpk::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);
  }
  {
    LpGlpk::Expr ex;
    for(InEdgeIt  e(g,t);e!=INVALID;++e) ex+=x[e];
    for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];
    lp.setObj(ex);
  }

  lp.solve();

  return 0;
}

int main() 
{
  LpSolverSkeleton lp_skel;
  LpGlpk lp_glpk;

  lpTest(lp_skel);
  lpTest(lp_glpk);

  ListGraph g;
  ListGraph::Node s=g.addNode();
  ListGraph::Node t=g.addNode();

  ListGraph::EdgeMap<double> cap(g);
  
  maxFlow(g,cap,s,t);

}