/* -*- 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