/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2008

  * 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_BEZIER_H

 #define LEMON_BEZIER_H

 ///\ingroup misc

 ///\file

 ///\brief A simple class implementing polynomials.

 ///

 ///\author Alpar Juttner

 #include<vector>

 namespace lemon {

   /// \addtogroup misc

   /// @{

   ///Simple polinomial class

   ///This class implements a polynomial where the coefficients are of

   ///type \c T.

   ///

   ///The coefficients are stored in an std::vector.

   template<class T>

   class Polynomial

   {

     std::vector<T> _coeff;

   public:

     ///Construct a polynomial of degree \c d.

     explicit Polynomial(int d=0) : _coeff(d+1) {}

     ///\e

     template<class U> Polynomial(const U &u) : _coeff(1,u) {}

     ///\e

     template<class U> Polynomial(const Polynomial<U> &u) : _coeff(u.deg()+1)

     {

       for(int i=0;i<int(_coeff.size());i++) _coeff[i]=u[i];

     }

     ///Query the degree of the polynomial.

     ///Query the degree of the polynomial.

     ///\warning This number differs from real degree of the polinomial if

     ///the coefficient of highest degree is 0.

     int deg() const { return _coeff.size()-1; }

     ///Set the degree of the polynomial.

     ///Set the degree of the polynomial. In fact it resizes the

     ///coefficient vector.

     void deg(int d) { _coeff.resize(d+1);}

     ///Returns (as a reference) the coefficient of degree \c d.

     typename std::vector<T>::reference operator[](int d) { return _coeff[d]; }

     ///Returns (as a const reference) the coefficient of degree \c d.

     typename std::vector<T>::const_reference

     operator[](int d) const {return _coeff[d];}

     ///Substitute the value u into the polinomial.

     ///Substitute the value u into the polinomial.

     ///The calculation will be done using type \c R.

     ///The following examples shows the usage of the template parameter \c R.

     ///\code

     ///  Polynomial<dim2::Point<double> > line(1);

     ///  line[0]=dim2::Point<double>(12,25);

     ///  line[1]=dim2::Point<double>(2,7);

     ///  ...

     ///  dim2::Point<double> d = line.subst<dim2::Point<double> >(23.2);

     ///\endcode

     ///

     ///\code

     ///  Polynomial<double> p;

     ///  Polynomial<double> q;

     ///  ...

     ///  Polynomial<double> s = p.subst<Polynomial<double> >(q);

     ///\endcode

     template<class R,class U>

     R subst(const U &u) const

     {

       typename std::vector<T>::const_reverse_iterator i=_coeff.rbegin();

       R v=*i;

       for(++i;i!=_coeff.rend();++i) v=v*u+*i;

       return v;

     }

     ///Substitute the value u into the polinomial.

     ///Substitute the value u into the polinomial.

     ///The calculation will be done using type \c T

     ///(i.e. using the type of the coefficients.)

     template<class U>

     T operator()(const U &u) const 

     {

       return subst<T>(u);

     }

     ///Derivate the polynomial (in place)

     Polynomial &derivateMyself()

     {

       for(int i=1;i<int(_coeff.size());i++) _coeff[i-1]=i*_coeff[i];

       _coeff.pop_back();

       return *this;

     }

     ///Return the derivate of the polynomial

     Polynomial derivate() const

     {

       Polynomial tmp(deg()-1);

       for(int i=1;i<int(_coeff.size());i++) tmp[i-1]=i*_coeff[i];

       return tmp;

     }

     ///Integrate the polynomial (in place)

     Polynomial &integrateMyself()

     {

       _coeff.push_back(T());

       for(int i=_coeff.size()-1;i>0;i--) _coeff[i]=_coeff[i-1]/i;

       _coeff[0]=0;

       return *this;

     }

     ///Return the integrate of the polynomial

     Polynomial integrate() const

     {

       Polynomial tmp(deg()+1);

       tmp[0]=0;

       for(int i=0;i<int(_coeff.size());i++) tmp[i+1]=_coeff[i]/(i+1);

       return tmp;

     }

     ///\e

     template<class U>

     Polynomial &operator+=(const Polynomial<U> &p)

     {

       if(p.deg()>deg()) _coeff.resize(p.deg()+1);

       for(int i=0;i<=int(std::min(deg(),p.deg()));i++)

 	_coeff[i]+=p[i];

       return *this;

     }

     ///\e

     template<class U>

     Polynomial &operator-=(const Polynomial<U> &p)

     {

       if(p.deg()>deg()) _coeff.resize(p.deg()+1);

       for(int i=0;i<=std::min(deg(),p.deg());i++) _coeff[i]-=p[i];

       return *this;

     }

     ///\e

     template<class U>

     Polynomial &operator+=(const U &u)

     {

       _coeff[0]+=u;

       return *this;

     }

     ///\e

     template<class U>

     Polynomial &operator-=(const U &u)

     {

       _coeff[0]+=u;

       return *this;

     }

     ///\e

     template<class U>

     Polynomial &operator*=(const U &u)

     {

       for(typename std::vector<T>::iterator i=_coeff.begin();i!=_coeff.end();++i)

 	*i*=u;

       return *this;

     }

     ///\e

     template<class U>

     Polynomial &operator/=(const U &u)

     {

       for(typename std::vector<T>::iterator i=_coeff.begin();i!=_coeff.end();++i)

 	*i/=u;

       return *this;

     }

   };

   ///Equality comparison

   ///\relates Polynomial

   ///\warning Two polynomials are defined to be unequal if their degrees differ,

   ///even if the non-zero coefficients are the same.

   template<class U,class V>

   bool operator==(const Polynomial<U> &u,const Polynomial<V> &v)

   {

     if(u.deg()!=v.deg()) return false;

     for(int i=0;i<=u.deg();i++) if(u[i]!=v[i]) return false;

     return true;

   }

   ///Non-equality comparison

   ///\relates Polynomial

   ///\warning Two polynomials are defined to be unequal if their degrees differ,

   ///even if the non-zero coefficients are the same.

   template<class U,class V>

   bool operator!=(const Polynomial<U> &u,const Polynomial<V> &v)

   {

     return !(u==v);

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U,class V>

   Polynomial<U> operator+(const Polynomial<U> &u,const Polynomial<V> &v)

   {

     Polynomial<U> tmp=u;

     tmp+=v;

     return tmp;

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U,class V>

   Polynomial<U> operator-(const Polynomial<U> &u,const Polynomial<V> &v)

   {

     Polynomial<U> tmp=u;

     tmp-=v;

     return tmp;

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U,class V>

   Polynomial<U> operator*(const Polynomial<U> &u,const Polynomial<V> &v)

   {

     Polynomial<U> tmp(u.deg()+v.deg());

     for(int i=0;i<=v.deg();i++)

       for(int j=0;j<=u.deg();j++)

 	tmp[i+j]+=v[i]*u[j];

     return tmp;

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U,class V>

   Polynomial<U> operator+(const Polynomial<U> &u,const V &v)

   {

     Polynomial<U> tmp=u;

     tmp+=v;

     return tmp;

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U,class V>

   Polynomial<U> operator+(const V &v,const Polynomial<U> &u)

   {

     Polynomial<U> tmp=u;

     tmp+=v;

     return tmp;

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U,class V>

   Polynomial<U> operator-(const Polynomial<U> &u,const V &v)

   {

     Polynomial<U> tmp=u;

     tmp-=v;

     return tmp;

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U>

   Polynomial<U> operator-(const Polynomial<U> &u)

   {

     Polynomial<U> tmp(u.deg());

     for(int i=0;i<=u.deg();i++) tmp[i]=-u[i];

     return tmp;

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U,class V>

   Polynomial<U> operator-(const V &v,const Polynomial<U> &u)

   {

     Polynomial<U> tmp=-u;

     tmp+=v;

     return tmp;

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U,class V>

   Polynomial<U> operator*(const Polynomial<U> &u,const V &v)

   {

     Polynomial<U> tmp=u;

     tmp*=v;

     return tmp;

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U,class V>

   Polynomial<U> operator*(const V &v,const Polynomial<U> &u)

   {

     Polynomial<U> tmp=u;

     tmp*=v;

     return tmp;

   }

   ///\e

   ///\relates Polynomial

   ///

   template<class U,class V>

   Polynomial<U> operator/(const Polynomial<U> &u,const V &v)

   {

     Polynomial<U> tmp=u;

     tmp/=v;

     return tmp;

   }

   /// @}

 } //END OF NAMESPACE LEMON

 #endif // LEMON_POLYNOMIAL_H