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				/* -- mode: C++; indent-tabs-mode: nil; --
				*
				* This file is a part of LEMON, a generic C++ optimization library.
				*
				* Copyright (C) 2003-2013
				* 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<iostream>
				#include<vector>
				#include<map>
				#include<limits>
				#include<lemon/math.h>

				#include<lemon/error.h>
				#include<lemon/assert.h>

				#include<lemon/core.h>
				#include<lemon/bits/solver_bits.h>

				///\file
				///\brief The interface of the LP solver interface.
				///\ingroup lp_group
				namespace lemon {

				///Common base class for LP and MIP solvers

				///Usually this class is not used directly, please use one of the concrete
				///implementations of the solver interface.
				///\ingroup lp_group
				class LpBase {

				protected:

				_solver_bits::VarIndex rows;
				_solver_bits::VarIndex cols;

				public:

				///Possible outcomes of an LP solving procedure
				enum SolveExitStatus {
				/// = 0. It means that the problem has been successfully solved: either
				///an optimal solution has been found or infeasibility/unboundedness
				///has been proved.
				SOLVED = 0,
				/// = 1. Any other case (including the case when some user specified
				///limit has been exceeded).
				UNSOLVED = 1
				};

				///Direction of the optimization
				enum Sense {
				/// Minimization
				MIN,
				/// Maximization
				MAX
				};

				///Enum for \c messageLevel() parameter
				enum MessageLevel {
				/// No output (default value).
				MESSAGE_NOTHING,
				/// Error messages only.
				MESSAGE_ERROR,
				/// Warnings.
				MESSAGE_WARNING,
				/// Normal output.
				MESSAGE_NORMAL,
				/// Verbose output.
				MESSAGE_VERBOSE
				};


				///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;

				friend class Col;
				friend class ColIt;
				friend class Row;
				friend class RowIt;

				///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.
				///
				///\note This class is similar to other Item types in LEMON, like
				///Node and Arc types in digraph.
				class Col {
				friend class LpBase;
				protected:
				int _id;
				explicit Col(int id) : _id(id) {}
				public:
				typedef Value ExprValue;
				typedef True LpCol;
				/// Default constructor

				/// \warning The default constructor sets the Col to an
				/// undefined value.
				Col() {}
				/// Invalid constructor \& conversion.

				/// This constructor initializes the Col to be invalid.
				/// \sa Invalid for more details.
				Col(const Invalid&) : _id(-1) {}
				/// Equality operator

				/// Two \ref Col "Col"s are equal if and only if they point to
				/// the same LP column or both are invalid.
				bool operator==(Col c) const {return _id == c._id;}
				/// Inequality operator

				/// \sa operator==(Col c)
				///
				bool operator!=(Col c) const {return _id != c._id;}
				/// Artificial ordering operator.

				/// To allow the use of this object in std::map or similar
				/// associative container we require this.
				///
				/// \note This operator only have to define some strict ordering of
				/// the items; this order has nothing to do with the iteration
				/// ordering of the items.
				bool operator<(Col c) const {return _id < c._id;}
				};

				///Iterator for iterate over the columns of an LP problem

				/// Its usage is quite simple, for example, you can count the number
				/// of columns in an LP \c lp:
				///\code
				/// int count=0;
				/// for (LpBase::ColIt c(lp); c!=INVALID; ++c) ++count;
				///\endcode
				class ColIt : public Col {
				const LpBase *_solver;
				public:
				/// Default constructor

				/// \warning The default constructor sets the iterator
				/// to an undefined value.
				ColIt() {}
				/// Sets the iterator to the first Col

				/// Sets the iterator to the first Col.
				///
				ColIt(const LpBase &solver) : _solver(&solver)
				{
				_solver->cols.firstItem(_id);
				}
				/// Invalid constructor \& conversion

				/// Initialize the iterator to be invalid.
				/// \sa Invalid for more details.
				ColIt(const Invalid&) : Col(INVALID) {}
				/// Next column

				/// Assign the iterator to the next column.
				///
				ColIt &operator++()
				{
				_solver->cols.nextItem(_id);
				return *this;
				}
				};

				/// \brief Returns the ID of the column.
				static int id(const Col& col) { return col._id; }
				/// \brief Returns the column with the given ID.
				///
				/// \pre The argument should be a valid column ID in the LP problem.
				static Col colFromId(int id) { 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.
				///
				///\note This class is similar to other Item types in LEMON, like
				///Node and Arc types in digraph.
				class Row {
				friend class LpBase;
				protected:
				int _id;
				explicit Row(int id) : _id(id) {}
				public:
				typedef Value ExprValue;
				typedef True LpRow;
				/// Default constructor

				/// \warning The default constructor sets the Row to an
				/// undefined value.
				Row() {}
				/// Invalid constructor \& conversion.

				/// This constructor initializes the Row to be invalid.
				/// \sa Invalid for more details.
				Row(const Invalid&) : _id(-1) {}
				/// Equality operator

				/// Two \ref Row "Row"s are equal if and only if they point to
				/// the same LP row or both are invalid.
				bool operator==(Row r) const {return _id == r._id;}
				/// Inequality operator

				/// \sa operator==(Row r)
				///
				bool operator!=(Row r) const {return _id != r._id;}
				/// Artificial ordering operator.

				/// To allow the use of this object in std::map or similar
				/// associative container we require this.
				///
				/// \note This operator only have to define some strict ordering of
				/// the items; this order has nothing to do with the iteration
				/// ordering of the items.
				bool operator<(Row r) const {return _id < r._id;}
				};

				///Iterator for iterate over the rows of an LP problem

				/// Its usage is quite simple, for example, you can count the number
				/// of rows in an LP \c lp:
				///\code
				/// int count=0;
				/// for (LpBase::RowIt c(lp); c!=INVALID; ++c) ++count;
				///\endcode
				class RowIt : public Row {
				const LpBase *_solver;
				public:
				/// Default constructor

				/// \warning The default constructor sets the iterator
				/// to an undefined value.
				RowIt() {}
				/// Sets the iterator to the first Row

				/// Sets the iterator to the first Row.
				///
				RowIt(const LpBase &solver) : _solver(&solver)
				{
				_solver->rows.firstItem(_id);
				}
				/// Invalid constructor \& conversion

				/// Initialize the iterator to be invalid.
				/// \sa Invalid for more details.
				RowIt(const Invalid&) : Row(INVALID) {}
				/// Next row

				/// Assign the iterator to the next row.
				///
				RowIt &operator++()
				{
				_solver->rows.nextItem(_id);
				return *this;
				}
				};

				/// \brief Returns the ID of the row.
				static int id(const Row& row) { return row._id; }
				/// \brief Returns the row with the given ID.
				///
				/// \pre The argument should be a valid row ID in the LP problem.
				static Row rowFromId(int id) { return Row(id); }

				public:

				///Linear expression of variables and a constant component

				///This data structure stores 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.
				///\code
				///e[v]=5;
				///e[v]+=12;
				///e.erase(v);
				///\endcode
				///or you can also iterate through its elements.
				///\code
				///double s=0;
				///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
				/// s+=i primal(i);
				///\endcode
				///(This code computes the primal value of the expression).
				///- 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
				///2v-3.12(v-w/2)+2
				///v2.1+(3v+(v12+w+6)3)/2
				///\endcode
				///are valid expressions.
				///The usual assignment operations are also defined.
				///\code
				///e=v+w;
				///e+=2v-3.12(v-w/2)+2;
				///e*=3.4;
				///e/=5;
				///\endcode
				///- The constant member can be set and read by dereference
				/// operator (unary *)
				///
				///\code
				///*e=12;
				///double c=*e;
				///\endcode
				///
				///\sa Constr
				class Expr {
				friend class LpBase;
				public:
				/// The key type of the expression
				typedef LpBase::Col Key;
				/// The value type of the expression
				typedef LpBase::Value Value;

				protected:
				Value const_comp;
				std::map<int, Value> comps;

				public:
				typedef True SolverExpr;
				/// Default constructor

				/// Construct an empty expression, the coefficients and
				/// the constant component are initialized to zero.
				Expr() : const_comp(0) {}
				/// Construct an expression from a column

				/// Construct an expression, which has a term with \c c variable
				/// and 1.0 coefficient.
				Expr(const Col &c) : const_comp(0) {
				typedef std::map<int, Value>::value_type pair_type;
				comps.insert(pair_type(id(c), 1));
				}
				/// Construct an expression from a constant

				/// Construct an expression, which's constant component is \c v.
				///
				Expr(const Value &v) : const_comp(v) {}
				/// Returns the coefficient of the column
				Value operator[](const Col& c) const {
				std::map<int, Value>::const_iterator it=comps.find(id(c));
				if (it != comps.end()) {
				return it->second;
				} else {
				return 0;
				}
				}
				/// Returns the coefficient of the column
				Value& operator[](const Col& c) {
				return comps[id(c)];
				}
				/// Sets the coefficient of the column
				void set(const Col &c, const Value &v) {
				if (v != 0.0) {
				typedef std::map<int, Value>::value_type pair_type;
				comps.insert(pair_type(id(c), v));
				} else {
				comps.erase(id(c));
				}
				}
				/// Returns the constant component of the expression
				Value& operator*() { return const_comp; }
				/// Returns the constant component of the expression
				const Value& operator*() const { return const_comp; }
				/// \brief Removes the coefficients which's absolute value does
				/// not exceed \c epsilon. It also sets to zero the constant
				/// component, if it does not exceed epsilon in absolute value.
				void simplify(Value epsilon = 0.0) {
				std::map<int, Value>::iterator it=comps.begin();
				while (it != comps.end()) {
				std::map<int, Value>::iterator jt=it;
				++jt;
				if (std::fabs((*it).second) <= epsilon) comps.erase(it);
				it=jt;
				}
				if (std::fabs(const_comp) <= epsilon) const_comp = 0;
				}

				void simplify(Value epsilon = 0.0) const {
				const_cast<Expr*>(this)->simplify(epsilon);
				}

				///Sets all coefficients and the constant component to 0.
				void clear() {
				comps.clear();
				const_comp=0;
				}

				///Compound assignment
				Expr &operator+=(const Expr &e) {
				for (std::map<int, Value>::const_iterator it=e.comps.begin();
				it!=e.comps.end(); ++it)
				comps[it->first]+=it->second;
				const_comp+=e.const_comp;
				return *this;
				}
				///Compound assignment
				Expr &operator-=(const Expr &e) {
				for (std::map<int, Value>::const_iterator it=e.comps.begin();
				it!=e.comps.end(); ++it)
				comps[it->first]-=it->second;
				const_comp-=e.const_comp;
				return *this;
				}
				///Multiply with a constant
				Expr &operator*=(const Value &v) {
				for (std::map<int, Value>::iterator it=comps.begin();
				it!=comps.end(); ++it)
				it->second*=v;
				const_comp*=v;
				return *this;
				}
				///Division with a constant
				Expr &operator/=(const Value &c) {
				for (std::map<int, Value>::iterator it=comps.begin();
				it!=comps.end(); ++it)
				it->second/=c;
				const_comp/=c;
				return *this;
				}

				///Iterator over the expression

				///The iterator iterates over the terms of the expression.
				///
				///\code
				///double s=0;
				///for(LpBase::Expr::CoeffIt i(e);i!=INVALID;++i)
				/// s+= i primal(i);
				///\endcode
				class CoeffIt {
				private:

				std::map<int, Value>::iterator _it, _end;

				public:

				/// Sets the iterator to the first term

				/// Sets the iterator to the first term of the expression.
				///
				CoeffIt(Expr& e)
				: _it(e.comps.begin()), _end(e.comps.end()){}

				/// Convert the iterator to the column of the term
				operator Col() const {
				return colFromId(_it->first);
				}

				/// Returns the coefficient of the term
				Value& operator*() { return _it->second; }

				/// Returns the coefficient of the term
				const Value& operator*() const { return _it->second; }
				/// Next term

				/// Assign the iterator to the next term.
				///
				CoeffIt& operator++() { ++_it; return *this; }

				/// Equality operator
				bool operator==(Invalid) const { return _it == _end; }
				/// Inequality operator
				bool operator!=(Invalid) const { return _it != _end; }
				};

				/// Const iterator over the expression

				///The iterator iterates over the terms of the expression.
				///
				///\code
				///double s=0;
				///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
				/// s+=i primal(i);
				///\endcode
				class ConstCoeffIt {
				private:

				std::map<int, Value>::const_iterator _it, _end;

				public:

				/// Sets the iterator to the first term

				/// Sets the iterator to the first term of the expression.
				///
				ConstCoeffIt(const Expr& e)
				: _it(e.comps.begin()), _end(e.comps.end()){}

				/// Convert the iterator to the column of the term
				operator Col() const {
				return colFromId(_it->first);
				}

				/// Returns the coefficient of the term
				const Value& operator*() const { return _it->second; }

				/// Next term

				/// Assign the iterator to the next term.
				///
				ConstCoeffIt& operator++() { ++_it; return *this; }

				/// Equality operator
				bool operator==(Invalid) const { return _it == _end; }
				/// Inequality operator
				bool operator!=(Invalid) const { return _it != _end; }
				};

				};

				///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 fail an assertion.
				class Constr
				{
				public:
				typedef LpBase::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) {}
				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 {
				return _lb != -INF && !isNaN(_lb);
				}
				///Is the constraint upper bounded?
				bool upperBounded() const {
				return _ub != INF && !isNaN(_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.
				///\code
				///e[v]=5;
				///e[v]+=12;
				///e.erase(v);
				///\endcode
				///or you can also iterate through its elements.
				///\code
				///double s=0;
				///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
				/// s+=*i;
				///\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
				///2v-3.12(v-w/2)
				///v2.1+(3v+(v12+w)3)/2
				///\endcode
				///are valid \ref DualExpr dual expressions.
				///The usual assignment operations are also defined.
				///\code
				///e=v+w;
				///e+=2v-3.12(v-w/2);
				///e*=3.4;
				///e/=5;
				///\endcode
				///
				///\sa Expr
				class DualExpr {
				friend class LpBase;
				public:
				/// The key type of the expression
				typedef LpBase::Row Key;
				/// The value type of the expression
				typedef LpBase::Value Value;

				protected:
				std::map<int, Value> comps;

				public:
				typedef True SolverExpr;
				/// Default constructor

				/// Construct an empty expression, the coefficients are
				/// initialized to zero.
				DualExpr() {}
				/// Construct an expression from a row

				/// Construct an expression, which has a term with \c r dual
				/// variable and 1.0 coefficient.
				DualExpr(const Row &r) {
				typedef std::map<int, Value>::value_type pair_type;
				comps.insert(pair_type(id(r), 1));
				}
				/// Returns the coefficient of the row
				Value operator[](const Row& r) const {
				std::map<int, Value>::const_iterator it = comps.find(id(r));
				if (it != comps.end()) {
				return it->second;
				} else {
				return 0;
				}
				}
				/// Returns the coefficient of the row
				Value& operator[](const Row& r) {
				return comps[id(r)];
				}
				/// Sets the coefficient of the row
				void set(const Row &r, const Value &v) {
				if (v != 0.0) {
				typedef std::map<int, Value>::value_type pair_type;
				comps.insert(pair_type(id(r), v));
				} else {
				comps.erase(id(r));
				}
				}
				/// \brief Removes the coefficients which's absolute value does
				/// not exceed \c epsilon.
				void simplify(Value epsilon = 0.0) {
				std::map<int, Value>::iterator it=comps.begin();
				while (it != comps.end()) {
				std::map<int, Value>::iterator jt=it;
				++jt;
				if (std::fabs((*it).second) <= epsilon) comps.erase(it);
				it=jt;
				}
				}

				void simplify(Value epsilon = 0.0) const {
				const_cast<DualExpr*>(this)->simplify(epsilon);
				}

				///Sets all coefficients to 0.
				void clear() {
				comps.clear();
				}
				///Compound assignment
				DualExpr &operator+=(const DualExpr &e) {
				for (std::map<int, Value>::const_iterator it=e.comps.begin();
				it!=e.comps.end(); ++it)
				comps[it->first]+=it->second;
				return *this;
				}
				///Compound assignment
				DualExpr &operator-=(const DualExpr &e) {
				for (std::map<int, Value>::const_iterator it=e.comps.begin();
				it!=e.comps.end(); ++it)
				comps[it->first]-=it->second;
				return *this;
				}
				///Multiply with a constant
				DualExpr &operator*=(const Value &v) {
				for (std::map<int, Value>::iterator it=comps.begin();
				it!=comps.end(); ++it)
				it->second*=v;
				return *this;
				}
				///Division with a constant
				DualExpr &operator/=(const Value &v) {
				for (std::map<int, Value>::iterator it=comps.begin();
				it!=comps.end(); ++it)
				it->second/=v;
				return *this;
				}

				///Iterator over the expression

				///The iterator iterates over the terms of the expression.
				///
				///\code
				///double s=0;
				///for(LpBase::DualExpr::CoeffIt i(e);i!=INVALID;++i)
				/// s+= i dual(i);
				///\endcode
				class CoeffIt {
				private:

				std::map<int, Value>::iterator _it, _end;

				public:

				/// Sets the iterator to the first term

				/// Sets the iterator to the first term of the expression.
				///
				CoeffIt(DualExpr& e)
				: _it(e.comps.begin()), _end(e.comps.end()){}

				/// Convert the iterator to the row of the term
				operator Row() const {
				return rowFromId(_it->first);
				}

				/// Returns the coefficient of the term
				Value& operator*() { return _it->second; }

				/// Returns the coefficient of the term
				const Value& operator*() const { return _it->second; }

				/// Next term

				/// Assign the iterator to the next term.
				///
				CoeffIt& operator++() { ++_it; return *this; }

				/// Equality operator
				bool operator==(Invalid) const { return _it == _end; }
				/// Inequality operator
				bool operator!=(Invalid) const { return _it != _end; }
				};

				///Iterator over the expression

				///The iterator iterates over the terms of the expression.
				///
				///\code
				///double s=0;
				///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
				/// s+= i dual(i);
				///\endcode
				class ConstCoeffIt {
				private:

				std::map<int, Value>::const_iterator _it, _end;

				public:

				/// Sets the iterator to the first term

				/// Sets the iterator to the first term of the expression.
				///
				ConstCoeffIt(const DualExpr& e)
				: _it(e.comps.begin()), _end(e.comps.end()){}

				/// Convert the iterator to the row of the term
				operator Row() const {
				return rowFromId(_it->first);
				}

				/// Returns the coefficient of the term
				const Value& operator*() const { return _it->second; }

				/// Next term

				/// Assign the iterator to the next term.
				///
				ConstCoeffIt& operator++() { ++_it; return *this; }

				/// Equality operator
				bool operator==(Invalid) const { return _it == _end; }
				/// Inequality operator
				bool operator!=(Invalid) const { return _it != _end; }
				};
				};


				protected:

				class InsertIterator {
				private:

				std::map<int, Value>& _host;
				const _solver_bits::VarIndex& _index;

				public:

				typedef std::output_iterator_tag iterator_category;
				typedef void difference_type;
				typedef void value_type;
				typedef void reference;
				typedef void pointer;

				InsertIterator(std::map<int, Value>& host,
				const _solver_bits::VarIndex& index)
				: _host(host), _index(index) {}

				InsertIterator& operator=(const std::pair<int, Value>& value) {
				typedef std::map<int, Value>::value_type pair_type;
				_host.insert(pair_type(_index[value.first], value.second));
				return *this;
				}

				InsertIterator& operator() { return this; }
				InsertIterator& operator++() { return *this; }
				InsertIterator operator++(int) { return *this; }

				};

				class ExprIterator {
				private:
				std::map<int, Value>::const_iterator _host_it;
				const _solver_bits::VarIndex& _index;
				public:

				typedef std::bidirectional_iterator_tag iterator_category;
				typedef std::ptrdiff_t 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;
				};

				ExprIterator(const std::map<int, Value>::const_iterator& host_it,
				const _solver_bits::VarIndex& index)
				: _host_it(host_it), _index(index) {}

				reference operator*() {
				return std::make_pair(_index(_host_it->first), _host_it->second);
				}

				pointer operator->() {
				return pointer(operator*());
				}

				ExprIterator& operator++() { ++_host_it; return *this; }
				ExprIterator operator++(int) {
				ExprIterator tmp(*this); ++_host_it; return tmp;
				}

				ExprIterator& operator--() { --_host_it; return *this; }
				ExprIterator operator--(int) {
				ExprIterator tmp(*this); --_host_it; return tmp;
				}

				bool operator==(const ExprIterator& it) const {
				return _host_it == it._host_it;
				}

				bool operator!=(const ExprIterator& it) const {
				return _host_it != it._host_it;
				}

				};

				protected:

				//Abstract virtual functions

				virtual int _addColId(int col) { return cols.addIndex(col); }
				virtual int _addRowId(int row) { return rows.addIndex(row); }

				virtual void _eraseColId(int col) { cols.eraseIndex(col); }
				virtual void _eraseRowId(int row) { rows.eraseIndex(row); }

				virtual int _addCol() = 0;
				virtual int _addRow() = 0;

				virtual int _addRow(Value l, ExprIterator b, ExprIterator e, Value u) {
				int row = _addRow();
				_setRowCoeffs(row, b, e);
				_setRowLowerBound(row, l);
				_setRowUpperBound(row, u);
				return row;
				}

				virtual void _eraseCol(int col) = 0;
				virtual void _eraseRow(int row) = 0;

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

				virtual void _getRowName(int row, std::string& name) const = 0;
				virtual void _setRowName(int row, const std::string& name) = 0;
				virtual int _rowByName(const std::string& name) const = 0;

				virtual void _setRowCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
				virtual void _getRowCoeffs(int i, InsertIterator b) const = 0;

				virtual void _setColCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
				virtual void _getColCoeffs(int i, InsertIterator b) const = 0;

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

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

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

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

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

				virtual void _setObjCoeffs(ExprIterator b, ExprIterator e) = 0;
				virtual void _getObjCoeffs(InsertIterator b) const = 0;

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

				virtual void _setSense(Sense) = 0;
				virtual Sense _getSense() const = 0;

				virtual void _clear() = 0;

				virtual const char* _solverName() const = 0;

				virtual void _messageLevel(MessageLevel level) = 0;

				//Own protected stuff

				//Constant component of the objective function
				Value obj_const_comp;

				LpBase() : rows(), cols(), obj_const_comp(0) {}

				public:

				///Unsupported file format exception
				class UnsupportedFormatError : public Exception
				{
				std::string _format;
				mutable std::string _what;
				public:
				explicit UnsupportedFormatError(std::string format) throw()
				: _format(format) { }
				virtual ~UnsupportedFormatError() throw() {}
				virtual const char* what() const throw() {
				try {
				_what.clear();
				std::ostringstream oss;
				oss << "lemon::UnsupportedFormatError: " << _format;
				_what = oss.str();
				}
				catch (...) {}
				if (!_what.empty()) return _what.c_str();
				else return "lemon::UnsupportedFormatError";
				}
				};

				protected:
				virtual void _write(std::string, std::string format) const
				{
				throw UnsupportedFormatError(format);
				}

				public:

				/// Virtual destructor
				virtual ~LpBase() {}

				///Gives back the name of the solver.
				const char* solverName() const {return _solverName();}

				///\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 = _addColId(_addCol()); return c;}

				///\brief Adds several new columns (i.e 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<LpBase::Col>
				///std::list<LpBase::Col>
				///\endcode
				///- a standard STL compatible iterable container with
				///\ref Col as its \c mapped_type like
				///\code
				///std::map<AnyType,LpBase::Col>
				///\endcode
				///- an iterable lemon \ref concepts::WriteMap "write map" like
				///\code
				///ListGraph::NodeMap<LpBase::Col>
				///ListGraph::ArcMap<LpBase::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::LpCol,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::LpCol,
				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::LpCol,
				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(cols(id(c)), ExprIterator(e.comps.begin(), rows),
				ExprIterator(e.comps.end(), rows));
				}

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

				///\param c is the column to get
				///\return the dual expression associated to the column
				DualExpr col(Col c) const {
				DualExpr e;
				_getColCoeffs(cols(id(c)), InsertIterator(e.comps, rows));
				return e;
				}

				///Add a new column to the LP

				///\param e is a dual linear expression (see \ref DualExpr)
				///\param o is the corresponding component of the objective
				///function. It is 0 by default.
				///\return The created column.
				Col addCol(const DualExpr &e, Value o = 0) {
				Col c=addCol();
				col(c,e);
				objCoeff(c,o);
				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 = _addRowId(_addRow()); return r;}

				///\brief Add several new rows (i.e 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<LpBase::Row>
				///std::list<LpBase::Row>
				///\endcode
				///- a standard STL compatible iterable container with
				///\ref Row as its \c mapped_type like
				///\code
				///std::map<AnyType,LpBase::Row>
				///\endcode
				///- an iterable lemon \ref concepts::WriteMap "write map" like
				///\code
				///ListGraph::NodeMap<LpBase::Row>
				///ListGraph::ArcMap<LpBase::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::LpRow,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::LpRow, 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::LpRow, 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)
				void row(Row r, Value l, const Expr &e, Value u) {
				e.simplify();
				_setRowCoeffs(rows(id(r)), ExprIterator(e.comps.begin(), cols),
				ExprIterator(e.comps.end(), cols));
				_setRowLowerBound(rows(id(r)),l - *e);
				_setRowUpperBound(rows(id(r)),u - *e);
				}

				///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);
				}


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

				///\param r is the row to get
				///\return the expression associated to the row
				Expr row(Row r) const {
				Expr e;
				_getRowCoeffs(rows(id(r)), InsertIterator(e.comps, cols));
				return e;
				}

				///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.
				Row addRow(Value l,const Expr &e, Value u) {
				Row r;
				e.simplify();
				r._id = _addRowId(_addRow(l - *e, ExprIterator(e.comps.begin(), cols),
				ExprIterator(e.comps.end(), cols), u - *e));
				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;
				c.expr().simplify();
				r._id = _addRowId(_addRow(c.lowerBounded()?c.lowerBound()-*c.expr():-INF,
				ExprIterator(c.expr().comps.begin(), cols),
				ExprIterator(c.expr().comps.end(), cols),
				c.upperBounded()?c.upperBound()-*c.expr():INF));
				return r;
				}
				///Erase a column (i.e a variable) from the LP

				///\param c is the column to be deleted
				void erase(Col c) {
				_eraseCol(cols(id(c)));
				_eraseColId(cols(id(c)));
				}
				///Erase a row (i.e a constraint) from the LP

				///\param r is the row to be deleted
				void erase(Row r) {
				_eraseRow(rows(id(r)));
				_eraseRowId(rows(id(r)));
				}

				/// Get the name of a column

				///\param c is the coresponding column
				///\return The name of the colunm
				std::string colName(Col c) const {
				std::string name;
				_getColName(cols(id(c)), name);
				return name;
				}

				/// Set the name of a column

				///\param c is the coresponding column
				///\param name The name to be given
				void colName(Col c, const std::string& name) {
				_setColName(cols(id(c)), name);
				}

				/// Get the column by its name

				///\param name The name of the column
				///\return the proper column or \c INVALID
				Col colByName(const std::string& name) const {
				int k = _colByName(name);
				return k != -1 ? Col(cols[k]) : Col(INVALID);
				}

				/// Get the name of a row

				///\param r is the coresponding row
				///\return The name of the row
				std::string rowName(Row r) const {
				std::string name;
				_getRowName(rows(id(r)), name);
				return name;
				}

				/// Set the name of a row

				///\param r is the coresponding row
				///\param name The name to be given
				void rowName(Row r, const std::string& name) {
				_setRowName(rows(id(r)), name);
				}

				/// Get the row by its name

				///\param name The name of the row
				///\return the proper row or \c INVALID
				Row rowByName(const std::string& name) const {
				int k = _rowByName(name);
				return k != -1 ? Row(rows[k]) : Row(INVALID);
				}

				/// Set an element of the coefficient matrix of the LP

				///\param r is the row of the element to be modified
				///\param c is the column of the element to be modified
				///\param val is the new value of the coefficient
				void coeff(Row r, Col c, Value val) {
				_setCoeff(rows(id(r)),cols(id(c)), val);
				}

				/// Get an element of the coefficient matrix of the LP

				///\param r is the row of the element
				///\param c is the column of the element
				///\return the corresponding coefficient
				Value coeff(Row r, Col c) const {
				return _getCoeff(rows(id(r)),cols(id(c)));
				}

				/// Set the lower bound of a column (i.e a variable)

				/// The lower bound of a variable (column) has to be given by an
				/// extended number of type Value, i.e. a finite number of type
				/// Value or -\ref INF.
				void colLowerBound(Col c, Value value) {
				_setColLowerBound(cols(id(c)),value);
				}

				/// Get the lower bound of a column (i.e a variable)

				/// This function returns the lower bound for column (variable) \c c
				/// (this might be -\ref INF as well).
				///\return The lower bound for column \c c
				Value colLowerBound(Col c) const {
				return _getColLowerBound(cols(id(c)));
				}

				///\brief Set the lower bound of several columns
				///(i.e variables) at once
				///
				///This magic function takes a container as its argument
				///and applies the function on all of its elements.
				///The lower bound of a variable (column) has to be given by an
				///extended number of type Value, i.e. a finite number of type
				///Value or -\ref INF.
				#ifdef DOXYGEN
				template<class T>
				void colLowerBound(T &t, Value value) { return 0;}
				#else
				template<class T>
				typename enable_if<typename T::value_type::LpCol,void>::type
				colLowerBound(T &t, Value value,dummy<0> = 0) {
				for(typename T::iterator i=t.begin();i!=t.end();++i) {
				colLowerBound(*i, value);
				}
				}
				template<class T>
				typename enable_if<typename T::value_type::second_type::LpCol,
				void>::type
				colLowerBound(T &t, Value value,dummy<1> = 1) {
				for(typename T::iterator i=t.begin();i!=t.end();++i) {
				colLowerBound(i->second, value);
				}
				}
				template<class T>
				typename enable_if<typename T::MapIt::Value::LpCol,
				void>::type
				colLowerBound(T &t, Value value,dummy<2> = 2) {
				for(typename T::MapIt i(t); i!=INVALID; ++i){
				colLowerBound(*i, value);
				}
				}
				#endif

				/// Set the upper bound of a column (i.e a variable)

				/// The upper bound of a variable (column) has to be given by an
				/// extended number of type Value, i.e. a finite number of type
				/// Value or \ref INF.
				void colUpperBound(Col c, Value value) {
				_setColUpperBound(cols(id(c)),value);
				};

				/// Get the upper bound of a column (i.e a variable)

				/// This function returns the upper bound for column (variable) \c c
				/// (this might be \ref INF as well).
				/// \return The upper bound for column \c c
				Value colUpperBound(Col c) const {
				return _getColUpperBound(cols(id(c)));
				}

				///\brief Set the upper bound of several columns
				///(i.e variables) at once
				///
				///This magic function takes a container as its argument
				///and applies the function on all of its elements.
				///The upper bound of a variable (column) has to be given by an
				///extended number of type Value, i.e. a finite number of type
				///Value or \ref INF.
				#ifdef DOXYGEN
				template<class T>
				void colUpperBound(T &t, Value value) { return 0;}
				#else
				template<class T1>
				typename enable_if<typename T1::value_type::LpCol,void>::type
				colUpperBound(T1 &t, Value value,dummy<0> = 0) {
				for(typename T1::iterator i=t.begin();i!=t.end();++i) {
				colUpperBound(*i, value);
				}
				}
				template<class T1>
				typename enable_if<typename T1::value_type::second_type::LpCol,
				void>::type
				colUpperBound(T1 &t, Value value,dummy<1> = 1) {
				for(typename T1::iterator i=t.begin();i!=t.end();++i) {
				colUpperBound(i->second, value);
				}
				}
				template<class T1>
				typename enable_if<typename T1::MapIt::Value::LpCol,
				void>::type
				colUpperBound(T1 &t, Value value,dummy<2> = 2) {
				for(typename T1::MapIt i(t); i!=INVALID; ++i){
				colUpperBound(*i, value);
				}
				}
				#endif

				/// Set the lower and the upper bounds of a column (i.e a variable)

				/// The lower and the upper bounds of
				/// a variable (column) have to be given by an
				/// extended number of type Value, i.e. a finite number of type
				/// Value, -\ref INF or \ref INF.
				void colBounds(Col c, Value lower, Value upper) {
				_setColLowerBound(cols(id(c)),lower);
				_setColUpperBound(cols(id(c)),upper);
				}

				///\brief Set the lower and the upper bound of several columns
				///(i.e variables) at once
				///
				///This magic function takes a container as its argument
				///and applies the function on all of its elements.
				/// The lower and the upper bounds of
				/// a variable (column) have to be given by an
				/// extended number of type Value, i.e. a finite number of type
				/// Value, -\ref INF or \ref INF.
				#ifdef DOXYGEN
				template<class T>
				void colBounds(T &t, Value lower, Value upper) { return 0;}
				#else
				template<class T2>
				typename enable_if<typename T2::value_type::LpCol,void>::type
				colBounds(T2 &t, Value lower, Value upper,dummy<0> = 0) {
				for(typename T2::iterator i=t.begin();i!=t.end();++i) {
				colBounds(*i, lower, upper);
				}
				}
				template<class T2>
				typename enable_if<typename T2::value_type::second_type::LpCol, void>::type
				colBounds(T2 &t, Value lower, Value upper,dummy<1> = 1) {
				for(typename T2::iterator i=t.begin();i!=t.end();++i) {
				colBounds(i->second, lower, upper);
				}
				}
				template<class T2>
				typename enable_if<typename T2::MapIt::Value::LpCol, void>::type
				colBounds(T2 &t, Value lower, Value upper,dummy<2> = 2) {
				for(typename T2::MapIt i(t); i!=INVALID; ++i){
				colBounds(*i, lower, upper);
				}
				}
				#endif

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

				/// The lower bound of a constraint (row) has to be given by an
				/// extended number of type Value, i.e. a finite number of type
				/// Value or -\ref INF.
				void rowLowerBound(Row r, Value value) {
				_setRowLowerBound(rows(id(r)),value);
				}

				/// Get the lower bound of a row (i.e a constraint)

				/// This function returns the lower bound for row (constraint) \c c
				/// (this might be -\ref INF as well).
				///\return The lower bound for row \c r
				Value rowLowerBound(Row r) const {
				return _getRowLowerBound(rows(id(r)));
				}

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

				/// The upper bound of a constraint (row) has to be given by an
				/// extended number of type Value, i.e. a finite number of type
				/// Value or -\ref INF.
				void rowUpperBound(Row r, Value value) {
				_setRowUpperBound(rows(id(r)),value);
				}

				/// Get the upper bound of a row (i.e a constraint)

				/// This function returns the upper bound for row (constraint) \c c
				/// (this might be -\ref INF as well).
				///\return The upper bound for row \c r
				Value rowUpperBound(Row r) const {
				return _getRowUpperBound(rows(id(r)));
				}

				///Set an element of the objective function
				void objCoeff(Col c, Value v) {_setObjCoeff(cols(id(c)),v); };

				///Get an element of the objective function
				Value objCoeff(Col c) const { return _getObjCoeff(cols(id(c))); };

				///Set the objective function

				///\param e is a linear expression of type \ref Expr.
				///
				void obj(const Expr& e) {
				_setObjCoeffs(ExprIterator(e.comps.begin(), cols),
				ExprIterator(e.comps.end(), cols));
				obj_const_comp = *e;
				}

				///Get the objective function

				///\return the objective function as a linear expression of type
				///Expr.
				Expr obj() const {
				Expr e;
				_getObjCoeffs(InsertIterator(e.comps, cols));
				*e = obj_const_comp;
				return e;
				}


				///Set the direction of optimization
				void sense(Sense sense) { _setSense(sense); }

				///Query the direction of the optimization
				Sense sense() const {return _getSense(); }

				///Set the sense to maximization
				void max() { _setSense(MAX); }

				///Set the sense to maximization
				void min() { _setSense(MIN); }

				///Clear the problem
				void clear() { _clear(); rows.clear(); cols.clear(); }

				/// Set the message level of the solver
				void messageLevel(MessageLevel level) { _messageLevel(level); }

				/// Write the problem to a file in the given format

				/// This function writes the problem to a file in the given format.
				/// Different solver backends may support different formats.
				/// Trying to write in an unsupported format will trigger
				/// \ref UnsupportedFormatError. For the supported formats,
				/// visit the documentation of the base class of the related backends
				/// (\ref CplexBase, \ref GlpkBase etc.)
				/// \param file The file path
				/// \param format The output file format.
				void write(std::string file, std::string format = "MPS") const
				{
				_write(file.c_str(),format.c_str());
				}

				///@}

				};

				/// Addition

				///\relates LpBase::Expr
				///
				inline LpBase::Expr operator+(const LpBase::Expr &a, const LpBase::Expr &b) {
				LpBase::Expr tmp(a);
				tmp+=b;
				return tmp;
				}
				///Substraction

				///\relates LpBase::Expr
				///
				inline LpBase::Expr operator-(const LpBase::Expr &a, const LpBase::Expr &b) {
				LpBase::Expr tmp(a);
				tmp-=b;
				return tmp;
				}
				///Multiply with constant

				///\relates LpBase::Expr
				///
				inline LpBase::Expr operator*(const LpBase::Expr &a, const LpBase::Value &b) {
				LpBase::Expr tmp(a);
				tmp*=b;
				return tmp;
				}

				///Multiply with constant

				///\relates LpBase::Expr
				///
				inline LpBase::Expr operator*(const LpBase::Value &a, const LpBase::Expr &b) {
				LpBase::Expr tmp(b);
				tmp*=a;
				return tmp;
				}
				///Divide with constant

				///\relates LpBase::Expr
				///
				inline LpBase::Expr operator/(const LpBase::Expr &a, const LpBase::Value &b) {
				LpBase::Expr tmp(a);
				tmp/=b;
				return tmp;
				}

				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator<=(const LpBase::Expr &e,
				const LpBase::Expr &f) {
				return LpBase::Constr(0, f - e, LpBase::NaN);
				}

				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator<=(const LpBase::Value &e,
				const LpBase::Expr &f) {
				return LpBase::Constr(e, f, LpBase::NaN);
				}

				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator<=(const LpBase::Expr &e,
				const LpBase::Value &f) {
				return LpBase::Constr(LpBase::NaN, e, f);
				}

				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator>=(const LpBase::Expr &e,
				const LpBase::Expr &f) {
				return LpBase::Constr(0, e - f, LpBase::NaN);
				}


				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator>=(const LpBase::Value &e,
				const LpBase::Expr &f) {
				return LpBase::Constr(LpBase::NaN, f, e);
				}


				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator>=(const LpBase::Expr &e,
				const LpBase::Value &f) {
				return LpBase::Constr(f, e, LpBase::NaN);
				}

				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator==(const LpBase::Expr &e,
				const LpBase::Value &f) {
				return LpBase::Constr(f, e, f);
				}

				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator==(const LpBase::Expr &e,
				const LpBase::Expr &f) {
				return LpBase::Constr(0, f - e, 0);
				}

				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator<=(const LpBase::Value &n,
				const LpBase::Constr &c) {
				LpBase::Constr tmp(c);
				LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
				tmp.lowerBound()=n;
				return tmp;
				}
				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator<=(const LpBase::Constr &c,
				const LpBase::Value &n)
				{
				LpBase::Constr tmp(c);
				LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
				tmp.upperBound()=n;
				return tmp;
				}

				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator>=(const LpBase::Value &n,
				const LpBase::Constr &c) {
				LpBase::Constr tmp(c);
				LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
				tmp.upperBound()=n;
				return tmp;
				}
				///Create constraint

				///\relates LpBase::Constr
				///
				inline LpBase::Constr operator>=(const LpBase::Constr &c,
				const LpBase::Value &n)
				{
				LpBase::Constr tmp(c);
				LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
				tmp.lowerBound()=n;
				return tmp;
				}

				///Addition

				///\relates LpBase::DualExpr
				///
				inline LpBase::DualExpr operator+(const LpBase::DualExpr &a,
				const LpBase::DualExpr &b) {
				LpBase::DualExpr tmp(a);
				tmp+=b;
				return tmp;
				}
				///Substraction

				///\relates LpBase::DualExpr
				///
				inline LpBase::DualExpr operator-(const LpBase::DualExpr &a,
				const LpBase::DualExpr &b) {
				LpBase::DualExpr tmp(a);
				tmp-=b;
				return tmp;
				}
				///Multiply with constant

				///\relates LpBase::DualExpr
				///
				inline LpBase::DualExpr operator*(const LpBase::DualExpr &a,
				const LpBase::Value &b) {
				LpBase::DualExpr tmp(a);
				tmp*=b;
				return tmp;
				}

				///Multiply with constant

				///\relates LpBase::DualExpr
				///
				inline LpBase::DualExpr operator*(const LpBase::Value &a,
				const LpBase::DualExpr &b) {
				LpBase::DualExpr tmp(b);
				tmp*=a;
				return tmp;
				}
				///Divide with constant

				///\relates LpBase::DualExpr
				///
				inline LpBase::DualExpr operator/(const LpBase::DualExpr &a,
				const LpBase::Value &b) {
				LpBase::DualExpr tmp(a);
				tmp/=b;
				return tmp;
				}

				/// \ingroup lp_group
				///
				/// \brief Common base class for LP solvers
				///
				/// This class is an abstract base class for LP solvers. This class
				/// provides a full interface for set and modify an LP problem,
				/// solve it and retrieve the solution. You can use one of the
				/// descendants as a concrete implementation, or the \c Lp
				/// default LP solver. However, if you would like to handle LP
				/// solvers as reference or pointer in a generic way, you can use
				/// this class directly.
				class LpSolver : virtual public LpBase {
				public:

				/// The problem types for primal and dual problems
				enum ProblemType {
				/// = 0. Feasible solution hasn't been found (but may exist).
				UNDEFINED = 0,
				/// = 1. The problem has no feasible solution.
				INFEASIBLE = 1,
				/// = 2. Feasible solution found.
				FEASIBLE = 2,
				/// = 3. Optimal solution exists and found.
				OPTIMAL = 3,
				/// = 4. The cost function is unbounded.
				UNBOUNDED = 4
				};

				///The basis status of variables
				enum VarStatus {
				/// The variable is in the basis
				BASIC,
				/// The variable is free, but not basic
				FREE,
				/// The variable has active lower bound
				LOWER,
				/// The variable has active upper bound
				UPPER,
				/// The variable is non-basic and fixed
				FIXED
				};

				protected:

				virtual SolveExitStatus _solve() = 0;

				virtual Value _getPrimal(int i) const = 0;
				virtual Value _getDual(int i) const = 0;

				virtual Value _getPrimalRay(int i) const = 0;
				virtual Value _getDualRay(int i) const = 0;

				virtual Value _getPrimalValue() const = 0;

				virtual VarStatus _getColStatus(int i) const = 0;
				virtual VarStatus _getRowStatus(int i) const = 0;

				virtual ProblemType _getPrimalType() const = 0;
				virtual ProblemType _getDualType() const = 0;

				public:

				///Allocate a new LP problem instance
				virtual LpSolver* newSolver() const = 0;
				///Make a copy of the LP problem
				virtual LpSolver* cloneSolver() const = 0;

				///\name Solve the LP

				///@{

				///\e Solve the LP problem at hand
				///
				///\return The result of the optimization procedure. Possible
				///values and their meanings can be found in the documentation of
				///\ref SolveExitStatus.
				SolveExitStatus solve() { return _solve(); }

				///@}

				///\name Obtain the Solution

				///@{

				/// The type of the primal problem
				ProblemType primalType() const {
				return _getPrimalType();
				}

				/// The type of the dual problem
				ProblemType dualType() const {
				return _getDualType();
				}

				/// Return the primal value of the column

				/// Return the primal value of the column.
				/// \pre The problem is solved.
				Value primal(Col c) const { return _getPrimal(cols(id(c))); }

				/// Return the primal value of the expression

				/// Return the primal value of the expression, i.e. the dot
				/// product of the primal solution and the expression.
				/// \pre The problem is solved.
				Value primal(const Expr& e) const {
				double res = *e;
				for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
				res += c primal(c);
				}
				return res;
				}
				/// Returns a component of the primal ray

				/// The primal ray is solution of the modified primal problem,
				/// where we change each finite bound to 0, and we looking for a
				/// negative objective value in case of minimization, and positive
				/// objective value for maximization. If there is such solution,
				/// that proofs the unsolvability of the dual problem, and if a
				/// feasible primal solution exists, then the unboundness of
				/// primal problem.
				///
				/// \pre The problem is solved and the dual problem is infeasible.
				/// \note Some solvers does not provide primal ray calculation
				/// functions.
				Value primalRay(Col c) const { return _getPrimalRay(cols(id(c))); }

				/// Return the dual value of the row

				/// Return the dual value of the row.
				/// \pre The problem is solved.
				Value dual(Row r) const { return _getDual(rows(id(r))); }

				/// Return the dual value of the dual expression

				/// Return the dual value of the dual expression, i.e. the dot
				/// product of the dual solution and the dual expression.
				/// \pre The problem is solved.
				Value dual(const DualExpr& e) const {
				double res = 0.0;
				for (DualExpr::ConstCoeffIt r(e); r != INVALID; ++r) {
				res += r dual(r);
				}
				return res;
				}

				/// Returns a component of the dual ray

				/// The dual ray is solution of the modified primal problem, where
				/// we change each finite bound to 0 (i.e. the objective function
				/// coefficients in the primal problem), and we looking for a
				/// ositive objective value. If there is such solution, that
				/// proofs the unsolvability of the primal problem, and if a
				/// feasible dual solution exists, then the unboundness of
				/// dual problem.
				///
				/// \pre The problem is solved and the primal problem is infeasible.
				/// \note Some solvers does not provide dual ray calculation
				/// functions.
				Value dualRay(Row r) const { return _getDualRay(rows(id(r))); }

				/// Return the basis status of the column

				/// \see VarStatus
				VarStatus colStatus(Col c) const { return _getColStatus(cols(id(c))); }

				/// Return the basis status of the row

				/// \see VarStatus
				VarStatus rowStatus(Row r) const { return _getRowStatus(rows(id(r))); }

				///The value of the objective function

				///\return
				///- \ref INF or -\ref INF means either infeasibility or unboundedness
				/// of the primal problem, depending on whether we minimize or maximize.
				///- \ref NaN if no primal solution is found.
				///- The (finite) objective value if an optimal solution is found.
				Value primal() const { return _getPrimalValue()+obj_const_comp;}
				///@}

				protected:

				};


				/// \ingroup lp_group
				///
				/// \brief Common base class for MIP solvers
				///
				/// This class is an abstract base class for MIP solvers. This class
				/// provides a full interface for set and modify an MIP problem,
				/// solve it and retrieve the solution. You can use one of the
				/// descendants as a concrete implementation, or the \c Lp
				/// default MIP solver. However, if you would like to handle MIP
				/// solvers as reference or pointer in a generic way, you can use
				/// this class directly.
				class MipSolver : virtual public LpBase {
				public:

				/// The problem types for MIP problems
				enum ProblemType {
				/// = 0. Feasible solution hasn't been found (but may exist).
				UNDEFINED = 0,
				/// = 1. The problem has no feasible solution.
				INFEASIBLE = 1,
				/// = 2. Feasible solution found.
				FEASIBLE = 2,
				/// = 3. Optimal solution exists and found.
				OPTIMAL = 3,
				/// = 4. The cost function is unbounded.
				///The Mip or at least the relaxed problem is unbounded.
				UNBOUNDED = 4
				};

				///Allocate a new MIP problem instance
				virtual MipSolver* newSolver() const = 0;
				///Make a copy of the MIP problem
				virtual MipSolver* cloneSolver() const = 0;

				///\name Solve the MIP

				///@{

				/// Solve the MIP problem at hand
				///
				///\return The result of the optimization procedure. Possible
				///values and their meanings can be found in the documentation of
				///\ref SolveExitStatus.
				SolveExitStatus solve() { return _solve(); }

				///@}

				///\name Set Column Type
				///@{

				///Possible variable (column) types (e.g. real, integer, binary etc.)
				enum ColTypes {
				/// = 0. Continuous variable (default).
				REAL = 0,
				/// = 1. Integer variable.
				INTEGER = 1
				};

				///Sets the type of the given column to the given type

				///Sets the type of the given column to the given type.
				///
				void colType(Col c, ColTypes col_type) {
				_setColType(cols(id(c)),col_type);
				}

				///Gives back the type of the column.

				///Gives back the type of the column.
				///
				ColTypes colType(Col c) const {
				return _getColType(cols(id(c)));
				}
				///@}

				///\name Obtain the Solution

				///@{

				/// The type of the MIP problem
				ProblemType type() const {
				return _getType();
				}

				/// Return the value of the row in the solution

				/// Return the value of the row in the solution.
				/// \pre The problem is solved.
				Value sol(Col c) const { return _getSol(cols(id(c))); }

				/// Return the value of the expression in the solution

				/// Return the value of the expression in the solution, i.e. the
				/// dot product of the solution and the expression.
				/// \pre The problem is solved.
				Value sol(const Expr& e) const {
				double res = *e;
				for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
				res += c sol(c);
				}
				return res;
				}
				///The value of the objective function

				///\return
				///- \ref INF or -\ref INF means either infeasibility or unboundedness
				/// of the problem, depending on whether we minimize or maximize.
				///- \ref NaN if no primal solution is found.
				///- The (finite) objective value if an optimal solution is found.
				Value solValue() const { return _getSolValue()+obj_const_comp;}
				///@}

				protected:

				virtual SolveExitStatus _solve() = 0;
				virtual ColTypes _getColType(int col) const = 0;
				virtual void _setColType(int col, ColTypes col_type) = 0;
				virtual ProblemType _getType() const = 0;
				virtual Value _getSol(int i) const = 0;
				virtual Value _getSolValue() const = 0;

				};



				} //namespace lemon

				#endif //LEMON_LP_BASE_H