/* -*- 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_UTILS_H

 #define LEMON_LP_UTILS_H

 #include <lemon/lp_base.h>

 #include <lemon/lemon_reader.h>

 #include <lemon/lemon_writer.h>

 #include <map>

 #include <set>

 namespace lemon {

   /// \ingroup lp_utils

   ///

   /// \brief The map for the result of the lp variables.

   ///

   /// The map for the result of the lp variables.

   class LpResultMap {

   public:

     typedef LpSolverBase::Col Key;

     typedef LpSolverBase::Value Value;

     /// \brief Constructor

     ///

     /// Constructor

     LpResultMap(const LpSolverBase& _lp) : lp(_lp) {}

     LpSolverBase::Value operator[](const LpSolverBase::Col col) const {

       return lp.primal(col);

     }

   private:

     const LpSolverBase& lp;

   };

   /// \ingroup lp_utils

   ///

   /// \brief Returns an \ref LpResultMap class

   ///

   /// This function just returns an \ref LpResultMap class.

   /// \relates LpResultMap

   LpResultMap lpResultMap(const LpSolverBase& lp) {

     return LpResultMap(lp);

   }

   /// \ingroup lp_utils

   ///

   /// \brief The map for the name of the lp variables.

   ///

   /// The map for the name of the lp variables.

   class LpColNameMap {

   public:

     typedef LpSolverBase::Col Key;

     typedef std::string Value;

     /// \brief Constructor

     ///

     /// Constructor

     LpColNameMap(const LpSolverBase& _lp) : lp(_lp) {}

     std::string operator[](const LpSolverBase::Col col) const {

       return lp.colName(col);

     }

   private:

     const LpSolverBase& lp;

   };

   /// \ingroup lp_utils

   ///

   /// \brief Writeable map for the name of the lp variables.

   ///

   /// Writeable map for the name of the lp variables.

   class LpColNameWriteMap {

   public:

     typedef LpSolverBase::Col Key;

     typedef std::string Value;

     /// \brief Constructor

     ///

     /// Constructor

     LpColNameWriteMap(LpSolverBase& _lp) : lp(_lp) {}

     std::string operator[](const LpSolverBase::Col col) const {

       return lp.colName(col);

     }

     void set(const LpSolverBase::Col col, const std::string& name) {

       lp.colName(col, name);

     }

   private:

     LpSolverBase& lp;

   };

   /// \ingroup lp_utils

   ///

   /// \brief Returns an \ref LpColNameMap class

   ///

   /// This function just returns an \ref LpColNameMap class.

   /// \relates LpColNameMap

   LpColNameMap lpColNameMap(const LpSolverBase& lp) {

     return LpColNameMap(lp);

   }

   LpColNameWriteMap lpColNameMap(LpSolverBase& lp) {

     return LpColNameWriteMap(lp);

   }

   /// \ingroup lp_utils

   ///

   /// \brief Lp variable item reader for Lemon IO

   ///

   /// This class is an Lp variable item reader for Lemon IO. It makes

   /// possible to store lp variables in lemon file. The usage of this

   /// class is very simple:

   ///

   ///\code

   /// Graph graph;

   /// Lp lp;

   /// Graph::EdgeMap<Lp::Col> var(graph); 

   ///

   /// GraphReader<Graph> reader(cin, graph);

   /// reader.readEdgeMap("lpvar", var, LpColReader(lp));

   /// reader.run();

   ///\endcode

   ///

   /// If there is already a variable with the same name in the lp then

   /// it will be used for the return value. If there is no such variable

   /// then it will be constructed. The file could contain \c '-' as value

   /// which means that no lp variable associated to the current item and

   /// in this case INVALID will be returned.

   class LpColReader {

   public:

     /// \brief The value type of reader.

     ///

     /// The value type of reader.

     typedef LpSolverBase::Col Value;

     /// \brief Constructor for the reader.

     ///

     /// Constructor for the reader.

     LpColReader(LpSolverBase& _lp) : lp(_lp) {}

     /// \brief Reads an lp variable from the given stream.

     ///

     /// Reads an lp variable string from the given stream.

     void read(std::istream& is, LpSolverBase::Col& col) const {

       char x;

       is >> std::ws;

       if (!is.get(x))

         throw DataFormatError("Wrong Lp Column format!");

       if (varFirstChar(x)) {

         std::string var;

         var += x;

         while (is.get(x) && varChar(x)) {

           var += x;

         }

         if (!is) {

           is.clear();

         } else {

           is.putback(x);

         }

         col = lp.colByName(var);

         if (col == INVALID) {

           col = lp.addCol();

           lp.colName(col, var);

         }

       } else if (x == '-') {

         col = INVALID;

         is >> std::ws;

       } else {

         std::cerr << x << std::endl;

         throw DataFormatError("Wrong Lp Column format");

       }

     }

   private:

     static bool varFirstChar(char c) {

       return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z');

     }

     static bool varChar(char c) {

       return (c >= '0' && c <= '9') || 

         (c >= 'a' && c <= 'z') || 

         (c >= 'A' && c <= 'Z') ||

         c == '[' || c == ']';

     }

     LpSolverBase& lp;

   };

   /// \ingroup lp_utils

   ///

   /// \brief Lp variable item writer for Lemon IO

   ///

   /// This class is an Lp variable item writer for Lemon IO. It makes

   /// possible to store lp variables in lemon file. The usage of this

   /// class is very simple:

   ///

   ///\code

   /// Graph graph;

   /// Lp lp;

   /// Graph::EdgeMap<Lp::Col> var(graph); 

   ///

   /// GraphWriter<Graph> writer(cin, graph);

   /// writer.writeEdgeMap("lpvar", var, LpColWriter(lp));

   /// writer.run();

   ///\endcode

   ///

   /// If there is no name associated to the current item then the name

   /// will automatically constructed. If the value is INVALID then it

   /// will write an \c '-' value to the file.

   class LpColWriter {

   public:

     /// \brief The value type of writer.

     ///

     /// The value type of writer.

     typedef LpSolverBase::Col Value;

     /// \brief Constructor for the writer.

     ///

     /// Constructor for the writer.

     LpColWriter(const LpSolverBase& _lp) : lp(_lp), num(0) {}

     /// \brief Writes an lp variable to the given stream.

     ///

     /// Writes an lp variable to the given stream.

     void write(std::ostream& os, const LpSolverBase::Col& col) const {

       if (col != INVALID) {

         std::string name = lp.colName(col);

         if (name.empty()) {

           std::ostringstream ls;

           ls << "x" << num;

           ++num;

           while (lp.colByName(ls.str()) != INVALID) {

             ls.str(std::string());

             ls << "x" << num;

             ++num;

           }

           const_cast<LpSolverBase&>(lp).colName(col, ls.str());

           os << ls.str();

         } else {

           os << name;

         }

       } else {

         os << "-";

       }

     }

   private:

     const LpSolverBase& lp;

     mutable int num;

   };

   /// \ingroup lp_utils

   ///

   /// \brief Lp section reader for lemon IO

   ///

   /// This section reader provides an easy way to read an Lp problem

   /// from a file. The lemon lp section format contains three parts.

   ///

   ///\code

   /// @lp

   /// constraints

   ///   7 == x1 - 1 * x2

   ///   2 * x1 + x3 / 2 <= 7

   ///   x2 + -3 * x3 >= 8

   ///   3 <= x2 - 2 * x1 <= 8

   /// bounds

   ///   x1 >= 3

   ///   2 <= x2 <= 5

   ///   0 <= x3 <= 8

   /// objective

   ///   min x1 + 2 * x2 - x3

   ///\endcode

   ///

   /// The first part gives the constraints to the lp. The constraints

   /// could be equality, lower bound, upper bound or range for an

   /// expression or equality, less or more for two expressions.

   ///

   /// The second part gives the bounds for the variables. The bounds

   /// could be the same as for the single expression so equality,

   /// lower bound, upper bound or range.

   ///

   /// The third part is the objective function, it should start with

   /// \c min or \c max and then a valid linear expression.

   ///

   /// The reader constructs automatically the variable for a name if

   /// there is not already a variable with the same name.

   ///

   /// The basic way to read an LP problem is made by the next code:

   ///\code

   /// Lp lp;

   ///

   /// LemonReader reader(filename_or_istream);

   /// LpReader lpreader(reader, lp);

   /// 

   /// reader.run();

   ///\endcode

   ///

   /// Of course instead of \c LemonReader you can give a \c

   /// GraphReader to the LpReader constructor. Also useful that you

   /// can mix lp problems and graphs in the same file.

   class LpReader : public LemonReader::SectionReader {

     typedef LemonReader::SectionReader Parent;

   public:

     /// \brief Constructor.

     ///

     /// Constructor for LpReader. It creates the LpReader and attachs

     /// it into the given LemonReader. The lp reader will add

     /// variables, constraints and objective function to the

     /// given lp solver.

     LpReader(LemonReader& _reader, LpSolverBase& _lp, 

              const std::string& _name = std::string())

       : Parent(_reader), lp(_lp), name(_name) {} 

     /// \brief Destructor.

     ///

     /// Destructor for LpReader.

     virtual ~LpReader() {}

   private:

     LpReader(const LpReader&);

     void operator=(const LpReader&);

   protected:

     /// \brief Gives back true when the SectionReader can process 

     /// the section with the given header line.

     ///

     /// It gives back true when the header line starts with \c \@lp,

     /// and the header line's name and the nodeset's name are the same.

     virtual bool header(const std::string& line) {

       std::istringstream ls(line);

       std::string command;

       std::string id;

       ls >> command >> id;

       return command == "@lp" && name == id;

     }

   private:

     enum Part {

       CONSTRAINTS, BOUNDS, OBJECTIVE

     };

     enum Relation {

       LE, EQ, GE

     };

     std::istream& readConstraint(std::istream& is) {

       LpSolverBase::Constr c;

       char x;

       LpSolverBase::Expr e1, e2;

       Relation op1;

       is >> std::ws;

       readExpression(is, e1);

       is >> std::ws;

       readRelation(is, op1);

       is >> std::ws;

       readExpression(is, e2);

       is >> std::ws;

       if (!is.get(x)) {

         if (op1 == LE) {

           if (e1.size() == 0) {

             c = e2 >= e1;

           } else {

             c = e1 <= e2;

           }

           c = e1 <= e2;

         } else if (op1 == GE) {

           if (e1.size() == 0) {

             c = e2 <= e1;

           } else {

             c = e1 >= e2;

           }

         } else {

           if (e1.size() == 0) {

             c = e2 == e1;

           } else {

             c = e1 == e2;

           }

         }

       } else {

         is.putback(x);

         LpSolverBase::Expr e3;

         Relation op2;

         readRelation(is, op2);

         is >> std::ws;

         readExpression(is, e3);

         if (!e1.empty() || !e3.empty()) {

           throw DataFormatError("Wrong range format");

         }

         if (op2 != op1 || op1 == EQ) {

           throw DataFormatError("Wrong range format");

         }

         if (op1 == LE) {

           c = e1.constComp() <= e2 <= e3.constComp();

         } else {

           c = e1.constComp() >= e2 >= e3.constComp();

         }

         is >> std::ws;

         if (is.get(x)) {

           throw DataFormatError("Wrong variable bounds format");

         }

       }

       lp.addRow(c);

       return is;

     }

     std::istream& readObjective(std::istream& is) {

       is >> std::ws;

       std::string sense;

       is >> sense;

       if (sense != "min" && sense != "max") {

         throw DataFormatError("Wrong objective function format");

       }

       LpSolverBase::Expr expr;

       is >> std::ws;

       readExpression(is, expr);

       lp.obj(expr);

       if (sense == "min") {

         lp.min();

       } else {

         lp.max();

       }

       return is;

     }

     std::istream& readBounds(std::istream& is) {

       LpSolverBase::Col c;

       char x;

       is >> std::ws;

       if (!is.get(x)) {

         throw DataFormatError("Wrong variable bounds format");

       }

       if (varFirstChar(x)) {

         is.putback(x);

         readCol(is, c);

         is >> std::ws;

         Relation op1;

         readRelation(is, op1);

         double v;

         readNum(is, v);

         if (op1 == EQ) {

           lp.colLowerBound(c, v);

           lp.colUpperBound(c, v);

         } else if (op1 == LE) {

           lp.colUpperBound(c, v);

         } else {

           lp.colLowerBound(c, v);

         }

         is >> std::ws;

         if (is.get(x)) {

           throw DataFormatError("Wrong variable bounds format");

         }

       } else {

         is.putback(x);

         double v;

         readNum(is, v);

         is >> std::ws;

         Relation op1;

         readRelation(is, op1);

         is >> std::ws;

         readCol(is, c);

         is >> std::ws;

         if (is.get(x)) {

           is.putback(x);

           is >> std::ws;

           Relation op2;

           readRelation(is, op2);

           double w;

           is >> std::ws;

           readNum(is, w);

           if (op2 != op1 || op1 == EQ) {

             throw DataFormatError("Wrong range format");

           }

           if (op1 == LE) {

             lp.colLowerBound(c, v);

             lp.colUpperBound(c, w);

           } else {

             lp.colLowerBound(c, w);

             lp.colUpperBound(c, v);

           }

           is >> std::ws;

           if (is.get(x)) {

             throw DataFormatError("Wrong variable bounds format");

           }

         } else {

           if (op1 == EQ) {

             lp.colLowerBound(c, v);

             lp.colUpperBound(c, v);

           } else if (op1 == LE) {

             lp.colLowerBound(c, v);

           } else {

             lp.colUpperBound(c, v);

           }

         }

       }

       return is;

     }

     std::istream& readExpression(std::istream& is, LpSolverBase::Expr& e) {

       LpSolverBase::Col c;

       double d;

       char x;

       readElement(is, c, d);

       if (c != INVALID) {

         e += d * c;

       } else {

         e += d;

       }

       is >> std::ws;

       while (is.get(x) && (x == '+' || x == '-')) {

         is >> std::ws;

         readElement(is, c, d);

         if (c != INVALID) {

           e += (x == '+' ? d : -d) * c;

         } else {

           e += (x == '+' ? d : -d);

         }

         is >> std::ws;

       }

       if (!is) {

         is.clear();

       } else {

         is.putback(x);

       }

       return is;

     }

     std::istream& readElement(std::istream& is, 

                               LpSolverBase::Col& c, double& d) { 

       d = 1.0;

       c = INVALID;

       char x, y;

       if (!is.get(x)) throw DataFormatError("Cannot find lp element");

       if (x == '+' || x == '-') {

         is >> std::ws;

         d *= x == '-' ? -1 : 1;

         while (is.get(x) && (x == '+' || x == '-')) {

           d *= x == '-' ? -1 : 1;

           is >> std::ws;

         }

         if (!is) throw DataFormatError("Cannot find lp element");

       }

       if (numFirstChar(x)) {

         is.putback(x);

         double e;

         readNum(is, e);

         d *= e;

       } else if (varFirstChar(x)) {

         is.putback(x);

         LpSolverBase::Col f;

         readCol(is, f);

         c = f;

       } else {

         throw DataFormatError("Invalid expression format");          

       }

       is >> std::ws;

       while (is.get(y) && (y == '*' || y == '/')) {

         is >> std::ws;

         if (!is.get(x)) throw DataFormatError("Cannot find lp element");

         if (x == '+' || x == '-') {

           is >> std::ws;

           d *= x == '-' ? -1 : 1;

           while (is.get(x) && (x == '+' || x == '-')) {

             d *= x == '-' ? -1 : 1;

             is >> std::ws;

           }

           if (!is) throw DataFormatError("Cannot find lp element");

         }

         if (numFirstChar(x)) {

           is.putback(x);

           double e;

           readNum(is, e);

           if (y == '*') {

             d *= e;

           } else {

             d /= e;

           }

         } else if (varFirstChar(x)) {

           is.putback(x);

           LpSolverBase::Col f;

           readCol(is, f);

           if (y == '*') {

             if (c == INVALID) {

               c = f;

             } else {

               throw DataFormatError("Quadratic element in expression");

             }

           } else {

             throw DataFormatError("Division by variable");

           }

         } else {

           throw DataFormatError("Invalid expression format");          

         }

         is >> std::ws;

       }

       if (!is) {

         is.clear();

       } else {

         is.putback(y);

       }

       return is;

     }

     std::istream& readCol(std::istream& is, LpSolverBase::Col& c) {

       char x;

       std::string var;

       while (is.get(x) && varChar(x)) {

         var += x;

       }

       if (!is) {

         is.clear();

       } else {

         is.putback(x);

       }

       c = lp.colByName(var);

       if (c == INVALID) {

         c = lp.addCol();

         lp.colName(c, var);

       }

       return is;

     }

     std::istream& readNum(std::istream& is, double& d) {

       is >> d;

       if (!is) throw DataFormatError("Wrong number format");

       return is;

     }

     std::istream& readRelation(std::istream& is, Relation& op) {

       char x, y;

       if (!is.get(x) || !(x == '<' || x == '=' || x == '>')) {

         throw DataFormatError("Wrong relation operator");

       }

       if (!is.get(y) || y != '=') {

         throw DataFormatError("Wrong relation operator");

       }

       switch (x) {

       case '<': op = LE; 

         break;

       case '=': op = EQ; 

         break;

       case '>': op = GE; 

         break;

       }

       return is;

     }

     static bool relationFirstChar(char c) {

       return c == '<' || c == '=' || c == '>';

     }

     static bool varFirstChar(char c) {

       return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z');

     }

     static bool numFirstChar(char c) {

       return (c >= '0' && c <= '9') || c == '.';

     }

     static bool varChar(char c) {

       return (c >= '0' && c <= '9') || 

         (c >= 'a' && c <= 'z') || 

         (c >= 'A' && c <= 'Z') ||

         c == '[' || c == ']';

     }

   protected:

     /// \brief Reader function of the section.

     ///

     /// It reads the content of the section.

     virtual void read(std::istream& is) {

       std::string line;

       Part part = CONSTRAINTS;

       while (getline(is, line)) {

         std::istringstream ls(line);

         std::string type;

         ls >> type;

         if (type == "constraints") {

           part = CONSTRAINTS;

           ls >> std::ws;

           char x;

           if (ls.get(x))

             throw DataFormatError("Wrong Lp format");

         } else if (type == "bounds") {

           part = BOUNDS;

           ls >> std::ws;

           char x;

           if (ls.get(x))

             throw DataFormatError("Wrong Lp format");

         } else if (type == "objective") {

           part = OBJECTIVE;

           ls >> std::ws;

           char x;

           if (ls.get(x))

             throw DataFormatError("Wrong Lp format");

         } else {

           ls.str(line);

           switch (part) {

           case CONSTRAINTS:

             readConstraint(ls);

             break;

           case BOUNDS:

             readBounds(ls);

             break;

           case OBJECTIVE:

             readObjective(ls);

             break;

           }

         }

       }

     }

     virtual void missing() {

       ErrorMessage msg;

       msg << "Lp section not found in file: @lp " << name;

       throw IoParameterError(msg.message());

     }

   private:

     LpSolverBase& lp;

     std::string name;

   };

   /// \ingroup lp_utils

   ///

   /// \brief Lp section writer for lemon IO

   ///

   /// This section reader provides an easy way to write an Lp problem

   /// to a file. The lemon lp section format contains three parts.

   ///

   ///\code

   /// @lp

   /// constraints

   ///   7 == x1 - 1 * x2

   ///   2 * x1 + x3 / 2 <= 7

   ///   x2 + -3 * x3 >= 8

   ///   3 <= x2 - 2 * x1 <= 8

   /// bounds

   ///   x1 >= 3

   ///   2 <= x2 <= 5

   ///   0 <= x3 <= 8

   /// objective

   ///   min x1 + 2 * x2 - x3

   ///\endcode

   ///

   /// The first part gives the constraints to the lp. The constraints

   /// could be equality, lower bound, upper bound or range for an

   /// expression or equality, less or more for two expressions.

   ///

   /// The second part gives the bounds for the variables. The bounds

   /// could be the same as for the single expression so equality,

   /// lower bound, upper bound or range.

   ///

   /// The third part is the objective function, it should start with

   /// \c min or \c max and then a valid linear expression.

   ///

   /// If an LP variable does not have name in the writer, then it will

   /// automatically created in the writer. This make a slight change

   /// in the \c const variable.

   ///

   /// The basic way to write an LP problem is made by the next code:

   ///\code

   /// Lp lp;

   ///

   /// LemonWriter writer(filename_or_ostream);

   /// LpWriter lpwriter(writer, lp);

   /// 

   /// writer.run();

   ///\endcode

   ///

   /// Of course instead of \c LemonWriter you can give a \c

   /// GraphWriter to the LpWriter constructor. Also useful that you

   /// can mix lp problems and graphs in the same file.

   class LpWriter : public LemonWriter::SectionWriter {

     typedef LemonWriter::SectionWriter Parent;

   public:

     /// \brief Constructor.

     ///

     /// Constructor for LpWriter. It creates the LpWriter and attach

     /// it into the given LemonWriter.

     LpWriter(LemonWriter& _writer, const LpSolverBase& _lp, 

              const std::string& _name = std::string())

       : Parent(_writer), lp(_lp), name(_name) {} 

     /// \brief Destructor.

     ///

     /// Destructor for LpWriter.

     virtual ~LpWriter() {}

   private:

     LpWriter(const LpWriter&);

     void operator=(const LpWriter&);

   protected:

     /// \brief Gives back true when the SectionWriter can process 

     /// the section with the given header line.

     ///

     /// It gives back the header line of the \c \@lp section.

     virtual std::string header() {

       std::ostringstream ls;

       ls << "@lp " << name;

       return ls.str();

     }

   private:

     void createCols() {

       int num = 0;

       for (LpSolverBase::ColIt it(lp); it != INVALID; ++it) {

         std::string name = lp.colName(it);

         if (name.empty()) {

           std::ostringstream ls;

           ls << "x" << num;

           ++num;

           while (lp.colByName(ls.str()) != INVALID) {

             ls.str(std::string());

             ls << "x" << num;

             ++num;

           }

           const_cast<LpSolverBase&>(lp).colName(it, ls.str());

         }

       }

     }

     void writeExpression(std::ostream& os, const LpSolverBase::Expr& e) {

       bool first = true;

       for (LpSolverBase::Expr::const_iterator jt = e.begin(); 

            jt != e.end(); ++jt) {

         if (jt->second < 0.0) {

           os << "- ";

           if (jt->second != -1.0) {

             os << -jt->second << " * ";

           }

         } else if (jt->second > 0.0) {

           if (!first) {

             os << "+ ";

           }

           if (jt->second != 1.0) {

             os << jt->second << " * ";

           }          

         }

         first = false;

         os << lp.colName(jt->first) << " ";

       }

       if (e.constComp() < 0.0) {

         os << "- " << -e.constComp() << " ";

       } else if (e.constComp() > 0.0) {

         if (!first) {

           os << "+ ";

         }

         os << e.constComp() << " ";

       } 

     }

   protected:

     /// \brief Writer function of the section.

     ///

     /// It writes the content of the section.

     virtual void write(std::ostream& os) {

       createCols();

       os << "constraints" << std::endl;

       for (LpSolverBase::RowIt it(lp); it != INVALID; ++it) {

         double lower, upper;

         lp.getRowBounds(it, lower, upper);

         if (lower == -LpSolverBase::INF && upper == LpSolverBase::INF) 

           continue;

         os << "   ";

         if (lower != upper) {

           if (lower != -LpSolverBase::INF) {

             os << lower << " <= ";

           }

           writeExpression(os, lp.row(it));

           if (upper != LpSolverBase::INF) {

             os << "<= " << upper << " ";

           }

         } else {

           writeExpression(os, lp.row(it));

           os << "== " << upper << " ";

         }

         os << std::endl;

       }

       os << "bounds" << std::endl;

       for (LpSolverBase::ColIt it(lp); it != INVALID; ++it) {

         double lower = lp.colLowerBound(it);

         double upper = lp.colUpperBound(it);

         if (lower == -LpSolverBase::INF && upper == LpSolverBase::INF) 

           continue;

         os << "   ";

         if (lower != upper) {

           if (lower != -LpSolverBase::INF) {

             os << lower << " <= ";

           }

           os << lp.colName(it) << " ";

           if (upper != LpSolverBase::INF) {

             os << "<= " << upper << " ";

           }

         } else {

           os << lp.colName(it) << " == " << upper << " ";

         }

         os << std::endl;

       }

       os << "objective" << std::endl;

       os << "   ";

       if (lp.isMin()) {

         os << "min ";

       } else {

         os << "max ";

       }

       writeExpression(os, lp.obj());

       os << std::endl;

     }

   private:

     const LpSolverBase& lp;

     std::string name;

   };

 }

 #endif