/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2006

 * 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.

 *

 */

#ifndef LEMON_LP_BASE_H

#define LEMON_LP_BASE_H

#include<vector>

#include<map>

#include<limits>

#include<cmath>

#include<lemon/bits/utility.h>

#include<lemon/error.h>

#include<lemon/bits/invalid.h>

///\file

///\brief The interface of the LP solver interface.

///\ingroup gen_opt_group

namespace lemon {

  ///Internal data structure to convert floating id's to fix one's

  ///\todo This might be implemented to be also usable in other places.

  class _FixId 

  {

  protected:

    int _first_index;

    int first_free;

  public:

    std::vector<int> index;

    std::vector<int> cross;

    _FixId() : _first_index(-1), first_free(-1) {};

    ///Convert a floating id to a fix one

    ///\param n is a floating id

    ///\return the corresponding fix id

    int fixId(int n) const {return cross[n];}

    ///Convert a fix id to a floating one

    ///\param n is a fix id

    ///\return the corresponding floating id

    int floatingId(int n) const { return index[n];}

    ///Add a new floating id.

    ///\param n is a floating id

    ///\return the fix id of the new value

    ///\todo Multiple additions should also be handled.

    int insert(int n)

    {

      if(cross.empty()) _first_index=n;

      if(n>=int(cross.size())) {

	cross.resize(n+1);

	if(first_free==-1) {

	  cross[n]=index.size();

	  index.push_back(n);

	}

	else {

	  cross[n]=first_free;

	  int next=index[first_free];

	  index[first_free]=n;

	  first_free=next;

	}

	return cross[n];

      }

      else {

	///\todo Create an own exception type.

	throw LogicError(); //floatingId-s must form a continuous range;

      }

    }

    ///Remove a fix id.

    ///\param n is a fix id

    ///

    void erase(int n) 

    {

      int fl=index[n];

      index[n]=first_free;

      first_free=n;

      for(int i=fl+1;i<int(cross.size());++i) {

	cross[i-1]=cross[i];

	index[cross[i]]--;

      }

      cross.pop_back();

    }

    ///An upper bound on the largest fix id.

    ///\todo Do we need this?

    ///

    std::size_t maxFixId() { return cross.size()-1; }

    ///Returns the first (smallest) inserted index

    ///Returns the first (smallest) inserted index

    ///or -1 if no index has been inserted before.

    int firstIndex() {return _first_index;}

  };

  ///Common base class for LP solvers

  ///\todo Much more docs

  ///\ingroup gen_opt_group

  class LpSolverBase {

  protected:

    _FixId rows;

    _FixId cols;

  public:

    ///Possible outcomes of an LP solving procedure

    enum SolveExitStatus {

      ///This means that the problem has been successfully solved: either

      ///an optimal solution has been found or infeasibility/unboundedness

      ///has been proved.

      SOLVED = 0,

      ///Any other case (including the case when some user specified

      ///limit has been exceeded)

      UNSOLVED = 1

    };

      ///\e

    enum SolutionStatus {

      ///Feasible solution hasn't been found (but may exist).

      ///\todo NOTFOUND might be a better name.

      ///

      UNDEFINED = 0,

      ///The problem has no feasible solution

      INFEASIBLE = 1,

      ///Feasible solution found

      FEASIBLE = 2,

      ///Optimal solution exists and found

      OPTIMAL = 3,

      ///The cost function is unbounded

      ///\todo Give a feasible solution and an infinite ray (and the

      ///corresponding bases)

      INFINITE = 4

    };

    ///\e The type of the investigated LP problem

    enum ProblemTypes {

      ///Primal-dual feasible

      PRIMAL_DUAL_FEASIBLE = 0,

      ///Primal feasible dual infeasible

      PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,

      ///Primal infeasible dual feasible

      PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,

      ///Primal-dual infeasible

      PRIMAL_DUAL_INFEASIBLE = 3,

      ///Could not determine so far

      UNKNOWN = 4

    };

    ///The floating point type used by the solver

    typedef double Value;

    ///The infinity constant

    static const Value INF;

    ///The not a number constant

    static const Value NaN;

    static inline bool isNaN(const Value& v) { return v!=v; }

    friend class Col;

    friend class ColIt;

    friend class Row;

    ///Refer to a column of the LP.

    ///This type is used to refer to a column of the LP.

    ///

    ///Its value remains valid and correct even after the addition or erase of

    ///other columns.

    ///

    ///\todo Document what can one do with a Col (INVALID, comparing,

    ///it is similar to Node/Edge)

    class Col {

    protected:

      int id;

      friend class LpSolverBase;

      friend class MipSolverBase;

    public:

      typedef Value ExprValue;

      typedef True LpSolverCol;

      Col() {}

      Col(const Invalid&) : id(-1) {}

      bool operator< (Col c) const  {return id< c.id;}

      bool operator> (Col c) const  {return id> c.id;}

      bool operator==(Col c) const  {return id==c.id;}

      bool operator!=(Col c) const  {return id!=c.id;}

    };

    class ColIt : public Col {

      LpSolverBase *_lp;

    public:

      ColIt() {}

      ColIt(LpSolverBase &lp) : _lp(&lp)

      {

	id = _lp->cols.cross.empty()?-1:

	  _lp->cols.fixId(_lp->cols.firstIndex());

      }

      ColIt(const Invalid&) : Col(INVALID) {}

      ColIt &operator++() 

      {

	int fid = _lp->cols.floatingId(id)+1;

	id = unsigned(fid)<_lp->cols.cross.size() ? _lp->cols.fixId(fid) : -1;

	return *this;

      }

    };

    static int id(const Col& col) { return col.id; }

    ///Refer to a row of the LP.

    ///This type is used to refer to a row of the LP.

    ///

    ///Its value remains valid and correct even after the addition or erase of

    ///other rows.

    ///

    ///\todo Document what can one do with a Row (INVALID, comparing,

    ///it is similar to Node/Edge)

    class Row {

    protected:

      int id;

      friend class LpSolverBase;

    public:

      typedef Value ExprValue;

      typedef True LpSolverRow;

      Row() {}

      Row(const Invalid&) : id(-1) {}

      bool operator< (Row c) const  {return id< c.id;}

      bool operator> (Row c) const  {return id> c.id;}

      bool operator==(Row c) const  {return id==c.id;}

      bool operator!=(Row c) const  {return id!=c.id;} 

    };

    static int id(const Row& row) { return row.id; }

  protected:

    int _lpId(const Col& col) const {

      return cols.floatingId(id(col));

    }

    int _lpId(const Row& row) const {

      return rows.floatingId(id(row));

    }

  public:

    ///Linear expression of variables and a constant component

    ///This data structure strores a linear expression of the variables

    ///(\ref Col "Col"s) and also has a constant component.

    ///

    ///There are several ways to access and modify the contents of this

    ///container.

    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle

    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can

    ///read and modify the coefficients like

    ///these.

    ///\code

    ///e[v]=5;

    ///e[v]+=12;

    ///e.erase(v);

    ///\endcode

    ///or you can also iterate through its elements.

    ///\code

    ///double s=0;

    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)

    ///  s+=i->second;

    ///\endcode

    ///(This code computes the sum of all coefficients).

    ///- Numbers (<tt>double</tt>'s)

    ///and variables (\ref Col "Col"s) directly convert to an

    ///\ref Expr and the usual linear operations are defined, so  

    ///\code

    ///v+w

    ///2*v-3.12*(v-w/2)+2

    ///v*2.1+(3*v+(v*12+w+6)*3)/2

    ///\endcode

    ///are valid \ref Expr "Expr"essions.

    ///The usual assignment operations are also defined.

    ///\code

    ///e=v+w;

    ///e+=2*v-3.12*(v-w/2)+2;

    ///e*=3.4;

    ///e/=5;

    ///\endcode

    ///- The constant member can be set and read by \ref constComp()

    ///\code

    ///e.constComp()=12;

    ///double c=e.constComp();

    ///\endcode

    ///

    ///\note \ref clear() not only sets all coefficients to 0 but also

    ///clears the constant components.

    ///

    ///\sa Constr

    ///

    class Expr : public std::map<Col,Value>

    {

    public:

      typedef LpSolverBase::Col Key; 

      typedef LpSolverBase::Value Value;

    protected:

      typedef std::map<Col,Value> Base;

      Value const_comp;

  public:

      typedef True IsLinExpression;

      ///\e

      Expr() : Base(), const_comp(0) { }

      ///\e

      Expr(const Key &v) : const_comp(0) {

	Base::insert(std::make_pair(v, 1));

      }

      ///\e

      Expr(const Value &v) : const_comp(v) {}

      ///\e

      void set(const Key &v,const Value &c) {

	Base::insert(std::make_pair(v, c));

      }

      ///\e

      Value &constComp() { return const_comp; }

      ///\e

      const Value &constComp() const { return const_comp; }

      ///Removes the components with zero coefficient.

      void simplify() {

	for (Base::iterator i=Base::begin(); i!=Base::end();) {

	  Base::iterator j=i;

	  ++j;

	  if ((*i).second==0) Base::erase(i);

	  i=j;

	}

      }

      void simplify() const {

        const_cast<Expr*>(this)->simplify();

      }

      ///Removes the coefficients closer to zero than \c tolerance.

      void simplify(double &tolerance) {

	for (Base::iterator i=Base::begin(); i!=Base::end();) {

	  Base::iterator j=i;

	  ++j;

	  if (std::fabs((*i).second)<tolerance) Base::erase(i);

	  i=j;

	}

      }

      ///Sets all coefficients and the constant component to 0.

      void clear() {

	Base::clear();

	const_comp=0;

      }

      ///\e

      Expr &operator+=(const Expr &e) {

	for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)

	  (*this)[j->first]+=j->second;

	const_comp+=e.const_comp;

	return *this;

      }

      ///\e

      Expr &operator-=(const Expr &e) {

	for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)

	  (*this)[j->first]-=j->second;

	const_comp-=e.const_comp;

	return *this;

      }

      ///\e

      Expr &operator*=(const Value &c) {

	for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)

	  j->second*=c;

	const_comp*=c;

	return *this;

      }

      ///\e

      Expr &operator/=(const Value &c) {

	for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)

	  j->second/=c;

	const_comp/=c;

	return *this;

      }

    };

    ///Linear constraint

    ///This data stucture represents a linear constraint in the LP.

    ///Basically it is a linear expression with a lower or an upper bound

    ///(or both). These parts of the constraint can be obtained by the member

    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),

    ///respectively.

    ///There are two ways to construct a constraint.

    ///- You can set the linear expression and the bounds directly

    ///  by the functions above.

    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>

    ///  are defined between expressions, or even between constraints whenever

    ///  it makes sense. Therefore if \c e and \c f are linear expressions and

    ///  \c s and \c t are numbers, then the followings are valid expressions

    ///  and thus they can be used directly e.g. in \ref addRow() whenever

    ///  it makes sense.

    ///\code

    ///  e<=s

    ///  e<=f

    ///  e==f

    ///  s<=e<=t

    ///  e>=t

    ///\endcode

    ///\warning The validity of a constraint is checked only at run time, so

    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a

    ///\ref LogicError exception.

    class Constr

    {

    public:

      typedef LpSolverBase::Expr Expr;

      typedef Expr::Key Key;

      typedef Expr::Value Value;

    protected:

      Expr _expr;

      Value _lb,_ub;

    public:

      ///\e

      Constr() : _expr(), _lb(NaN), _ub(NaN) {}

      ///\e

      Constr(Value lb,const Expr &e,Value ub) :

	_expr(e), _lb(lb), _ub(ub) {}

      ///\e

      Constr(const Expr &e,Value ub) : 

	_expr(e), _lb(NaN), _ub(ub) {}

      ///\e

      Constr(Value lb,const Expr &e) :

	_expr(e), _lb(lb), _ub(NaN) {}

      ///\e

      Constr(const Expr &e) : 

	_expr(e), _lb(NaN), _ub(NaN) {}

      ///\e

      void clear() 

      {

	_expr.clear();

	_lb=_ub=NaN;

      }

      ///Reference to the linear expression 

      Expr &expr() { return _expr; }

      ///Cont reference to the linear expression 

      const Expr &expr() const { return _expr; }

      ///Reference to the lower bound.

      ///\return

      ///- \ref INF "INF": the constraint is lower unbounded.

      ///- \ref NaN "NaN": lower bound has not been set.

      ///- finite number: the lower bound

      Value &lowerBound() { return _lb; }

      ///The const version of \ref lowerBound()

      const Value &lowerBound() const { return _lb; }

      ///Reference to the upper bound.

      ///\return

      ///- \ref INF "INF": the constraint is upper unbounded.

      ///- \ref NaN "NaN": upper bound has not been set.

      ///- finite number: the upper bound

      Value &upperBound() { return _ub; }

      ///The const version of \ref upperBound()

      const Value &upperBound() const { return _ub; }

      ///Is the constraint lower bounded?

      bool lowerBounded() const { 

	using namespace std;

	return finite(_lb);

      }

      ///Is the constraint upper bounded?

      bool upperBounded() const {

	using namespace std;

	return finite(_ub);

      }

    };

    ///Linear expression of rows

    ///This data structure represents a column of the matrix,

    ///thas is it strores a linear expression of the dual variables

    ///(\ref Row "Row"s).

    ///

    ///There are several ways to access and modify the contents of this

    ///container.

    ///- Its it fully compatible with \c std::map<Row,double>, so for expamle

    ///if \c e is an DualExpr and \c v

    ///and \c w are of type \ref Row, then you can

    ///read and modify the coefficients like

    ///these.

    ///\code

    ///e[v]=5;

    ///e[v]+=12;

    ///e.erase(v);

    ///\endcode

    ///or you can also iterate through its elements.

    ///\code

    ///double s=0;

    ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i)

    ///  s+=i->second;

    ///\endcode

    ///(This code computes the sum of all coefficients).

    ///- Numbers (<tt>double</tt>'s)

    ///and variables (\ref Row "Row"s) directly convert to an

    ///\ref DualExpr and the usual linear operations are defined, so

    ///\code

    ///v+w

    ///2*v-3.12*(v-w/2)

    ///v*2.1+(3*v+(v*12+w)*3)/2

    ///\endcode

    ///are valid \ref DualExpr "DualExpr"essions.

    ///The usual assignment operations are also defined.

    ///\code

    ///e=v+w;

    ///e+=2*v-3.12*(v-w/2);

    ///e*=3.4;

    ///e/=5;

    ///\endcode

    ///

    ///\sa Expr

    ///

    class DualExpr : public std::map<Row,Value>

    {

    public:

      typedef LpSolverBase::Row Key; 

      typedef LpSolverBase::Value Value;

    protected:

      typedef std::map<Row,Value> Base;

    public:

      typedef True IsLinExpression;

      ///\e

      DualExpr() : Base() { }

      ///\e

      DualExpr(const Key &v) {

	Base::insert(std::make_pair(v, 1));

      }

      ///\e

      void set(const Key &v,const Value &c) {

	Base::insert(std::make_pair(v, c));

      }

      ///Removes the components with zero coefficient.

      void simplify() {

	for (Base::iterator i=Base::begin(); i!=Base::end();) {

	  Base::iterator j=i;

	  ++j;

	  if ((*i).second==0) Base::erase(i);

	  i=j;

	}

      }

      void simplify() const {

        const_cast<DualExpr*>(this)->simplify();

      }

      ///Removes the coefficients closer to zero than \c tolerance.

      void simplify(double &tolerance) {

	for (Base::iterator i=Base::begin(); i!=Base::end();) {

	  Base::iterator j=i;

	  ++j;

	  if (std::fabs((*i).second)<tolerance) Base::erase(i);

	  i=j;

	}

      }

      ///Sets all coefficients to 0.

      void clear() {

	Base::clear();

      }

      ///\e

      DualExpr &operator+=(const DualExpr &e) {

	for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)

	  (*this)[j->first]+=j->second;

	return *this;

      }

      ///\e

      DualExpr &operator-=(const DualExpr &e) {

	for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)

	  (*this)[j->first]-=j->second;

	return *this;

      }

      ///\e

      DualExpr &operator*=(const Value &c) {

	for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)

	  j->second*=c;

	return *this;

      }

      ///\e

      DualExpr &operator/=(const Value &c) {

	for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)

	  j->second/=c;

	return *this;

      }

    };

  private:

    template <typename _Base>

    class MappedIterator {

    public:

      typedef _Base Base;

      typedef typename Base::iterator_category iterator_category;

      typedef typename Base::difference_type difference_type;

      typedef const std::pair<int, Value> value_type;

      typedef value_type reference;

      class pointer {

      public:

        pointer(value_type& _value) : value(_value) {}

        value_type* operator->() { return &value; }

      private:

        value_type value;

      };

      MappedIterator(const Base& _base, const LpSolverBase& _lp) 

        : base(_base), lp(_lp) {}

      reference operator*() {

        return std::make_pair(lp._lpId(base->first), base->second);

      }

      pointer operator->() {

        return pointer(operator*());

      }

      MappedIterator& operator++() {

        ++base;

        return *this;

      }

      MappedIterator& operator++(int) {

        MappedIterator tmp(*this);

        ++base;

        return tmp;

      }

      bool operator==(const MappedIterator& it) const {

        return base == it.base;

      }

      bool operator!=(const MappedIterator& it) const {

        return base != it.base;

      }

    private:

      Base base;

      const LpSolverBase& lp;

    };

  protected:

    /// STL compatible iterator for lp col

    typedef MappedIterator<Expr::const_iterator> LpRowIterator;

    /// STL compatible iterator for lp row

    typedef MappedIterator<DualExpr::const_iterator> LpColIterator;

    //Abstract virtual functions

    virtual LpSolverBase &_newLp() = 0;

    virtual LpSolverBase &_copyLp(){

      ///\todo This should be implemented here, too, when we have

      ///problem retrieving routines. It can be overriden.

      //Starting:

      LpSolverBase & newlp(_newLp());

      return newlp;

      //return *(LpSolverBase*)0;

    };

    virtual int _addCol() = 0;

    virtual int _addRow() = 0; 

    virtual void _eraseCol(int col) = 0;

    virtual void _eraseRow(int row) = 0;

    virtual void _getColName(int col, std::string & name) = 0;

    virtual void _setColName(int col, const std::string & name) = 0;

    virtual void _setRowCoeffs(int i, LpRowIterator b, LpRowIterator e) = 0;

    virtual void _setColCoeffs(int i, LpColIterator b, LpColIterator e) = 0;

    virtual void _setCoeff(int row, int col, Value value) = 0;

    virtual Value _getCoeff(int row, int col) = 0;

    virtual void _setColLowerBound(int i, Value value) = 0;

    virtual void _setColUpperBound(int i, Value value) = 0;

//     virtual void _setRowLowerBound(int i, Value value) = 0;

//     virtual void _setRowUpperBound(int i, Value value) = 0;

    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;

    virtual void _setObjCoeff(int i, Value obj_coef) = 0;

    virtual Value _getObjCoeff(int i) = 0;

    virtual void _clearObj()=0;

    virtual SolveExitStatus _solve() = 0;

    virtual Value _getPrimal(int i) = 0;

    virtual Value _getDual(int i) = 0;

    virtual Value _getPrimalValue() = 0;

    virtual bool _isBasicCol(int i) = 0;

    virtual SolutionStatus _getPrimalStatus() = 0;

    virtual SolutionStatus _getDualStatus() = 0;

    ///\todo This could be implemented here, too, using _getPrimalStatus() and

    ///_getDualStatus()

    virtual ProblemTypes _getProblemType() = 0;

    virtual void _setMax() = 0;

    virtual void _setMin() = 0;

    virtual bool _isMax() = 0;

    //Own protected stuff

    //Constant component of the objective function

    Value obj_const_comp;

  public:

    ///\e

    LpSolverBase() : obj_const_comp(0) {}

    ///\e

    virtual ~LpSolverBase() {}

    ///Creates a new LP problem

    LpSolverBase &newLp() {return _newLp();}

    ///Makes a copy of the LP problem

    LpSolverBase &copyLp() {return _copyLp();}

    ///\name Build up and modify the LP

    ///@{

    ///Add a new empty column (i.e a new variable) to the LP

    Col addCol() { Col c; c.id=cols.insert(_addCol()); return c;}

    ///\brief Adds several new columns

    ///(i.e a variables) at once

    ///

    ///This magic function takes a container as its argument

    ///and fills its elements

    ///with new columns (i.e. variables)

    ///\param t can be

    ///- a standard STL compatible iterable container with

    ///\ref Col as its \c values_type

    ///like

    ///\code

    ///std::vector<LpSolverBase::Col>

    ///std::list<LpSolverBase::Col>

    ///\endcode

    ///- a standard STL compatible iterable container with

    ///\ref Col as its \c mapped_type

    ///like

    ///\code

    ///std::map<AnyType,LpSolverBase::Col>

    ///\endcode

    ///- an iterable lemon \ref concepts::WriteMap "write map" like 

    ///\code

    ///ListGraph::NodeMap<LpSolverBase::Col>

    ///ListGraph::EdgeMap<LpSolverBase::Col>

    ///\endcode

    ///\return The number of the created column.

#ifdef DOXYGEN

    template<class T>

    int addColSet(T &t) { return 0;} 

#else

    template<class T>

    typename enable_if<typename T::value_type::LpSolverCol,int>::type

    addColSet(T &t,dummy<0> = 0) {

      int s=0;

      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}

      return s;

    }

    template<class T>

    typename enable_if<typename T::value_type::second_type::LpSolverCol,

		       int>::type

    addColSet(T &t,dummy<1> = 1) { 

      int s=0;

      for(typename T::iterator i=t.begin();i!=t.end();++i) {

	i->second=addCol();

	s++;

      }

      return s;

    }

    template<class T>

    typename enable_if<typename T::MapIt::Value::LpSolverCol,

		       int>::type

    addColSet(T &t,dummy<2> = 2) { 

      int s=0;

      for(typename T::MapIt i(t); i!=INVALID; ++i)

	{

	  i.set(addCol());

	  s++;

	}

      return s;

    }

#endif

    ///Set a column (i.e a dual constraint) of the LP

    ///\param c is the column to be modified

    ///\param e is a dual linear expression (see \ref DualExpr)

    ///a better one.

    void col(Col c,const DualExpr &e) {

      e.simplify();

      _setColCoeffs(_lpId(c), LpColIterator(e.begin(), *this), 

                    LpColIterator(e.end(), *this));

    }

    ///Add a new column to the LP

    ///\param e is a dual linear expression (see \ref DualExpr)

    ///\param obj is the corresponding component of the objective

    ///function. It is 0 by default.

    ///\return The created column.

    Col addCol(const DualExpr &e, Value obj=0) {

      Col c=addCol();

      col(c,e);

      objCoeff(c,obj);

      return c;

    }

    ///Add a new empty row (i.e a new constraint) to the LP

    ///This function adds a new empty row (i.e a new constraint) to the LP.

    ///\return The created row

    Row addRow() { Row r; r.id=rows.insert(_addRow()); return r;}

    ///\brief Add several new rows

    ///(i.e a constraints) at once

    ///

    ///This magic function takes a container as its argument

    ///and fills its elements

    ///with new row (i.e. variables)

    ///\param t can be

    ///- a standard STL compatible iterable container with

    ///\ref Row as its \c values_type

    ///like

    ///\code

    ///std::vector<LpSolverBase::Row>

    ///std::list<LpSolverBase::Row>

    ///\endcode

    ///- a standard STL compatible iterable container with

    ///\ref Row as its \c mapped_type

    ///like

    ///\code

    ///std::map<AnyType,LpSolverBase::Row>

    ///\endcode

    ///- an iterable lemon \ref concepts::WriteMap "write map" like 

    ///\code

    ///ListGraph::NodeMap<LpSolverBase::Row>

    ///ListGraph::EdgeMap<LpSolverBase::Row>

    ///\endcode

    ///\return The number of rows created.

#ifdef DOXYGEN

    template<class T>

    int addRowSet(T &t) { return 0;} 

#else

    template<class T>

    typename enable_if<typename T::value_type::LpSolverRow,int>::type

    addRowSet(T &t,dummy<0> = 0) {

      int s=0;

      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}

      return s;

    }

    template<class T>

    typename enable_if<typename T::value_type::second_type::LpSolverRow,

		       int>::type

    addRowSet(T &t,dummy<1> = 1) { 

      int s=0;

      for(typename T::iterator i=t.begin();i!=t.end();++i) {

	i->second=addRow();

	s++;

      }

      return s;

    }

    template<class T>

    typename enable_if<typename T::MapIt::Value::LpSolverRow,

		       int>::type

    addRowSet(T &t,dummy<2> = 2) { 

      int s=0;

      for(typename T::MapIt i(t); i!=INVALID; ++i)

	{

	  i.set(addRow());

	  s++;

	}

      return s;

    }

#endif

    ///Set a row (i.e a constraint) of the LP

    ///\param r is the row to be modified

    ///\param l is lower bound (-\ref INF means no bound)

    ///\param e is a linear expression (see \ref Expr)

    ///\param u is the upper bound (\ref INF means no bound)

    ///\bug This is a temportary function. The interface will change to

    ///a better one.

    ///\todo Option to control whether a constraint with a single variable is

    ///added or not.

    void row(Row r, Value l,const Expr &e, Value u) {

      e.simplify();

      _setRowCoeffs(_lpId(r), LpRowIterator(e.begin(), *this),

                    LpRowIterator(e.end(), *this));

//       _setRowLowerBound(_lpId(r),l-e.constComp());

//       _setRowUpperBound(_lpId(r),u-e.constComp());

       _setRowBounds(_lpId(r),l-e.constComp(),u-e.constComp());

    }

    ///Set a row (i.e a constraint) of the LP

    ///\param r is the row to be modified

    ///\param c is a linear expression (see \ref Constr)

    void row(Row r, const Constr &c) {

      row(r, c.lowerBounded()?c.lowerBound():-INF,

          c.expr(), c.upperBounded()?c.upperBound():INF);

    }

    ///Add a new row (i.e a new constraint) to the LP

    ///\param l is the lower bound (-\ref INF means no bound)

    ///\param e is a linear expression (see \ref Expr)

    ///\param u is the upper bound (\ref INF means no bound)

    ///\return The created row.

    ///\bug This is a temportary function. The interface will change to

    ///a better one.

    Row addRow(Value l,const Expr &e, Value u) {

      Row r=addRow();

      row(r,l,e,u);

      return r;

    }

    ///Add a new row (i.e a new constraint) to the LP

    ///\param c is a linear expression (see \ref Constr)

    ///\return The created row.

    Row addRow(const Constr &c) {

      Row r=addRow();

      row(r,c);

      return r;

    }

    ///Erase a coloumn (i.e a variable) from the LP

    ///\param c is the coloumn to be deleted

    ///\todo Please check this

    void eraseCol(Col c) {

      _eraseCol(_lpId(c));

      cols.erase(c.id);

    }

    ///Erase a  row (i.e a constraint) from the LP

    ///\param r is the row to be deleted

    ///\todo Please check this

    void eraseRow(Row r) {

      _eraseRow(_lpId(r));

      rows.erase(r.id);

    }

    /// Get the name of a column

    ///\param c is the coresponding coloumn 

    ///\return The name of the colunm

    std::string colName(Col c){

      std::string name;

      _getColName(_lpId(c), name);

      return name;

    }

    /// Set the name of a column

    ///\param c is the coresponding coloumn