/* -*- 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>

 namespace lemon {

   class LpReader : public LemonReader::SectionReader {

     typedef LemonReader::SectionReader Parent;

   public:

     /// \brief Constructor.

     ///

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

     /// 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 NodeSetReader.

     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 SubSection {

       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.setObj(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);

           }

           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);

       }

       ColMap::const_iterator it = cols.find(var);

       if (cols.find(var) != cols.end()) {

         c = it->second;

       } else {

         c = lp.addCol();

         cols.insert(std::make_pair(var, c));

         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;

       SubSection sub = CONSTRAINTS;

       while (getline(is, line)) {

         std::istringstream ls(line);

         std::string type;

         ls >> type;

         if (type == "constraints") {

           sub = CONSTRAINTS;

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

           sub = BOUNDS;

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

           sub = OBJECTIVE;

         } else {

           ls.str(line);

           switch (sub) {

           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:

     typedef std::map<std::string, LpSolverBase::Col> ColMap;

     LpSolverBase& lp;

     std::string name;

     ColMap cols;

   };

   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. The lp writer will add

     /// variables, constraints and objective function to the

     /// given lp solver.

     LpWriter(LemonWriter& _writer, LpSolverBase& _lp, 

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

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

     /// \brief Destructor.

     ///

     /// Destructor for NodeSetWriter.

     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 = 1;

       std::map<std::string, LpSolverBase::Col> inverse;

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

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

         if (!name.empty() && inverse.find(name) == inverse.end()) {

           cols.insert(std::make_pair(it, name));

           inverse.insert(std::make_pair(name, it));

         } else {

           std::ostringstream ls;

           ls << "var" << num;

           ++num;

           cols.insert(std::make_pair(it, ls.str()));

           inverse.insert(std::make_pair(ls.str(), it));

         }

       }

     }

     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 << cols[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 << cols[it] << " ";

           if (upper != LpSolverBase::INF) {

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

           }

         } else {

           os << cols[it] << " == " << upper << " ";

         }

         os << std::endl;

       }

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

       os << "   ";

       if (lp.is_min()) {

         os << "min ";

       } else {

         os << "max ";

       }

       writeExpression(os, lp.obj());

       os << std::endl;

     }

   private:

     typedef std::map<LpSolverBase::Col, std::string> ColMap;

     LpSolverBase& lp;

     std::string name;

     ColMap cols;

   };

 }

 #endif