/* -*- 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