/* -*- C++ -*-
 * src/lemon/lin_expr.h - Part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Combinatorial Optimization Research Group, 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_LIN_EXPR_H
#define LEMON_LIN_EXPR_H

#include<vector>
#include<map>
#include<lemon/utility.h>
///\file
///\brief Classes to handle linear expressions
namespace lemon {
  
  /// Class to handle sparse linear expressions
  template <class _V>
  class SparseLinExpr : public std::map<_V, typename _V::ExprValue>
  {
  public:
    typedef _V Var; 
    typedef typename _V::ExprValue Coeff;
    
  protected:
    typedef typename std::map<_V, typename _V::ExprValue> Base;

    Coeff const_comp;
  public:
    typedef True IsLinExpression;
    ///\e
    SparseLinExpr() : Base(), const_comp(0) { }
    ///\e
    SparseLinExpr(const Var &v) : const_comp(0) {
      Base::insert(std::make_pair(v, 1));
    }
    ///\e
    SparseLinExpr(const Coeff &v) : const_comp(v) {}
    
    ///\e
    void set(const Var &v,const Coeff &c) {
      return Base::insert(std::make_pair(v, c));
    }
//     Coeff &operator[](const Var &v) { return data[v]; }
//     const Coeff &operator[](const Var &v) const { return data[v]; }

    ///\e
    Coeff &constComp() { return const_comp; }
    ///\e
    const Coeff &constComp() const { return const_comp; }

    ///Removes the components with zero coefficient.
    void simplify() {
      for (typename Base::iterator i=Base::begin(); i!=Base::end();) {
	typename Base::iterator j=i;
	++j;
	if ((*i).second==0) Base::erase(i);
	j=i;
      }
    }
   
    ///\e
    SparseLinExpr &operator+=(const SparseLinExpr &e) {
      for (typename Base::const_iterator j=e.begin(); j!=e.end(); ++j)
	(*this)[j->first]+=j->second;
      ///\todo it might be speeded up using "hints"
      const_comp+=e.const_comp;
      return *this;
    }
    ///\e
    SparseLinExpr &operator-=(const SparseLinExpr &e) {
      for (typename Base::const_iterator j=e.begin(); j!=e.end(); ++j)
	(*this)[j->first]-=j->second;
      const_comp-=e.const_comp;
      return *this;
    }
    ///\e
    SparseLinExpr &operator*=(const Coeff &c) {
      for (typename Base::iterator j=Base::begin(); j!=Base::end(); ++j)
	j->second*=c;
      const_comp*=c;
      return *this;
    }
    ///\e
    SparseLinExpr &operator/=(const Coeff &c) {
      for (typename Base::iterator j=Base::begin(); j!=Base::end(); ++j)
	j->second/=c;
      const_comp/=c;
      return *this;
    }
    
  };

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator+(const SparseLinExpr<V> &a,
				const SparseLinExpr<V> &b) {
    SparseLinExpr<V> tmp(a);
    tmp+=b; ///\todo Don't STL have some special 'merge' algorithm?
    return tmp;
  }
  
  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator-(const SparseLinExpr<V> &a,
				const SparseLinExpr<V> &b) {
    SparseLinExpr<V> tmp(a);
    tmp-=b; ///\todo Don't STL have some special 'merge' algorithm?
    return tmp;
  }
  
  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator*(const typename V::ExprValue &c,
			       const SparseLinExpr<V> &e) {
    SparseLinExpr<V> tmp(e);
    tmp*=c;
    return tmp;
  }
  
  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator*(const SparseLinExpr<V> &e,
			       const typename V::ExprValue &c) {
    SparseLinExpr<V> tmp(e);
    tmp*=c;
    return tmp;
  }
  
  
  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator/(const SparseLinExpr<V> &e,
			       const typename V::ExprValue &c) {
    SparseLinExpr<V> tmp(e);
    tmp/=c;
    return tmp;
  }
  
  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator+(const typename V::ExprValue &c,
			     const SparseLinExpr<V> &e) {
    SparseLinExpr<V> tmp(e);
    tmp.constComp()+=c;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator+(const SparseLinExpr<V> &e,
			     const typename V::ExprValue &c) {
    SparseLinExpr<V> tmp(e);
    tmp.constComp()+=c;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator+(const V &v,const SparseLinExpr<V> &e) {
    SparseLinExpr<V> tmp(e);
    tmp[v]+=1;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator+(const SparseLinExpr<V> &e,const V &v) {
    SparseLinExpr<V> tmp(e);
    tmp[v]+=1;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator-(const typename V::ExprValue &c,
			     const SparseLinExpr<V> &e) {
    SparseLinExpr<V> tmp(e);
    tmp*=-1;
    tmp.constComp()+=c;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator-(const SparseLinExpr<V> &e,
			     const typename V::ExprValue &c) {
    SparseLinExpr<V> tmp(e);
    tmp.constComp()-=c;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator-(const V &v,const SparseLinExpr<V> &e) {
    SparseLinExpr<V> tmp(e);
    tmp*=-1;
    tmp[v]+=1;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator-(const SparseLinExpr<V> &e,const V &v) {
    SparseLinExpr<V> tmp(e);
    tmp[v]-=1;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator+(const V &v,const typename V::ExprValue &c) {
    SparseLinExpr<V> tmp(v);
    tmp.constComp()=c;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator-(const V &v,const typename V::ExprValue &c) {
    SparseLinExpr<V> tmp(v);
    tmp.constComp()=-c;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator+(const typename V::ExprValue &c,const V &v) {
    SparseLinExpr<V> tmp(v);
    tmp.constComp()=c;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator-(const typename V::ExprValue &c,const V &v) {
    SparseLinExpr<V> tmp(c);
    tmp[v]=-1;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator+(const V &v1,const V &v2) {
    SparseLinExpr<V> tmp(v1);
    tmp[v2]+=1;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator*(const V &v,const typename V::ExprValue &c) {
    SparseLinExpr<V> tmp;
    tmp[v]=c;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator*(const typename V::ExprValue &c,const V &v) {
    SparseLinExpr<V> tmp;
    tmp[v]=c;
    return tmp;
  }

  ///\e
  
  ///\relates SparseLinExpr
  ///
  template <class V>
  SparseLinExpr<V> operator/(const V &v,const typename V::ExprValue &c) {
    SparseLinExpr<V> tmp;
    tmp[v]=1/c;
    return tmp;
  }


  //////////////////////////////////////////////////////////////////////
  /// Constraints
  //////////////////////////////////////////////////////////////////////
  
  template <class E>
  class LinConstr
  {
  public:
    typedef E Expr;
    typedef typename E::Var Var;
    typedef typename E::Coeff Coeff;
    
    static const Coeff INF;
    static const Coeff NaN;
//     static const Coeff INF=0;
//     static const Coeff NaN=1;

    Expr expr;
    Coeff lb,ub;
    
    LinConstr() : expr(), lb(NaN), ub(NaN) {}
    LinConstr(Coeff _lb,const Expr &e,Coeff _ub) :
      expr(e), lb(_lb), ub(_ub) {}
    LinConstr(const Expr &e,Coeff _ub) : 
      expr(e), lb(NaN), ub(_ub) {}
    LinConstr(Coeff _lb,const Expr &e) :
      expr(e), lb(_lb), ub(NaN) {}
  };

  template<class E>
  const typename LinConstr<E>::Coeff LinConstr<E>::INF=
    std::numeric_limits<Coeff>::infinity();
  template<class E>
  const typename LinConstr<E>::Coeff LinConstr<E>::NaN=
    std::numeric_limits<Coeff>::quiet_NaN();

  
  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator<=(const E &e,const E &f) 
  {
    return LinConstr<E>(-LinConstr<E>::INF,e-f,0);
  }

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator>=(const E &e,const E &f) 
  {
    return LinConstr<E>(-LinConstr<E>::INF,f-e,0);
  }

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator==(const E &e,const E &f) 
  {
    return LinConstr<E>(0,e-f,0);
  }
  
  //////////////////////////////

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator<=(const E &e,const typename E::Coeff &n) 
  {
    return LinConstr<E>(e,n);
  }

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator>=(const E &e,const typename E::Coeff &n) 
  {
    return LinConstr<E>(n,e);
  }

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator==(const E &e,const typename E::Coeff &n) 
  {
    return LinConstr<E>(n,e,n);
  }

  //////////////////////////////

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator<=(const typename E::Coeff &n,const E &e) 
  {
    return LinConstr<E>(n,e);
  }

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator>=(const typename E::Coeff &n,const E &e) 
  {
    return LinConstr<E>(e,n);
  }

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator==(const typename E::Coeff &n,const E &e) 
  {
    return LinConstr<E>(n,e,n);
  }

  //////////////////////////////

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator<=(const typename E::Coeff &n,const LinConstr<E> &c) 
  {
    LinConstr<E> tmp(c);
    if(tmp.lb!=tmp.NaN) throw LogicError();
    else tmp.lb=n;
    return tmp;
  }

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator>=(const typename E::Coeff &n,const LinConstr<E> &c) 
  {
    LinConstr<E> tmp(c);
    if(tmp.ub!=tmp.NaN) throw LogicError();
    else tmp.ub=n;
    return tmp;
  }

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator<=(const LinConstr<E> &c,const typename E::Coeff &n) 
  {
    LinConstr<E> tmp(c);
    if(tmp.ub!=tmp.NaN) throw LogicError();
    else tmp.ub=n;
    return tmp;
  }

  template<class E>
  typename enable_if<typename E::IsLinExpression, LinConstr<E> >::type
  operator>=(const LinConstr<E> &c,const typename E::Coeff &n) 
  {
    LinConstr<E> tmp(c);
    if(tmp.lb!=tmp.NaN) throw LogicError();
    else tmp.lb=n;
    return tmp;
  }

  

} //namespace lemon

#endif //LEMON_LIN_EXPR_H