Algoritmo de ordenação C ++ não vê meu operador “<” sobrecarregado para o tipo definido pelo usuário.

Ok, então eu tenho 1 tipo definido pelo usuário chamadofraction e representa e fração ordinária com um numerador e denominador. Aqui está o código:

class Fraction
{
private:
  int numerator;
  int denominator;

public:
  Fraction(int numer,int denom)
    :numerator(numer),denominator(denom){}

  int get_denom(){return denominator;}
  int get_numer(){return numerator;}
};

Como você vê, ele é implementado em um arquivo de cabeçalho.

Então, o que eu quero fazer com isso é classificar um vetor de frações usando o algoritmo de classificação. Aqui está o código do operador "<" sobrecarregado (note: Ele é colocado no mesmo arquivo que a classe Fraction, mas fora da classe):

bool operator<(Fraction& first,Fraction& second)
{
  if(first.get_denom() == second.get_denom())
  {
    return first.get_numer()<second.get_numer()?true:false;
  }
  int first_num=first.get_denom();
  int second_num=second.get_denom();
  int lcm=(first_num*second_num)/gcd(first_num,second_num);
  int first_new_numerator=(lcm/first_num)*first.get_numer();
  int second_new_numerator=(lcm/second_num)*second.get_numer();

  return first_new_numerator<second_new_numerator?true:false;
}

O que faz é verificar se os denominadores são iguais, se eles são, então, ele testa os valores dos numeradores. Se eles não são iguais, equaliza-os usando o mínimo múltiplo comum e o mdc.

O problema real começa quando eu quero usar o algoritmo de ordenação no principal (erro de tempo de compilação). Aqui está o código principal:

Fraction parse_fraction(string& input)
{

  stringstream fraction_string(input);
  int numer;
  fraction_string>>numer;
  char seperator;
  fraction_string>>seperator;
  int denom;
  fraction_string>>denom;

  return Fraction(numer,denom);
}


int main()
{
  vector<Fraction> fractions;
  string input;
  while(cin>>input)
  {
    if(input=="|") break;
    fractions.push_back(parse_fraction(input));
  }

  sort(fractions.begin(),fractions.end);

  for(int i=0;i<fractions.size();i++)
  {
    cout<<fractions[i];
  }

  return 0;
}

Os erros que recebo são (Nota: eu sobrecarreguei o operador "<<" para frações, mas não quero fazer confusão aqui):

/usr/include/c++/4.6/bits/stl_algo.h||In function ‘_RandomAccessIterator std::__unguarded_partition(_RandomAccessIterator, _RandomAccessIterator, const _Tp&) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<Fraction*, std::vector<Fraction> >, _Tp = Fraction]’:|

/usr/include/c++/4.6/bits/stl_algo.h:2253|70|instantiated from ‘_RandomAccessIterator std::__unguarded_partition_pivot(_RandomAccessIterator, _RandomAccessIterator) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<Fraction*, std::vector<Fraction> >]’|

/usr/include/c++/4.6/bits/stl_algo.h:2284|54|instantiated from ‘void std::__introsort_loop(_RandomAccessIterator, _RandomAccessIterator, _Size) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<Fraction*, std::vector<Fraction> >, _Size = long int]’|

/usr/include/c++/4.6/bits/stl_algo.h:5330|4|instantiated from ‘void std::sort(_RAIter, _RAIter) [with _RAIter = __gnu_cxx::__normal_iterator<Fraction*, std::vector<Fraction> >]’|

/home/vanio/Desktop/workspace/C++/Ordner/main.cpp:35|43|instantiated from here|

/usr/include/c++/4.6/bits/stl_algo.h|2212|error: no match for ‘operator<’ in ‘__first.__gnu_cxx::__normal_iterator<_Iterator, _Container>::operator* [with _Iterator = Fraction*, _Container = std::vector<Fraction>, __gnu_cxx::__normal_iterator<_Iterator, _Container>::reference = Fraction&]() < __pivot’|

/usr/include/c++/4.6/bits/stl_algo.h|2212|note: candidates are:|

/usr/include/c++/4.6/bits/stl_pair.h|207|note: template<class _T1, class _T2> bool std::operator<(const std::pair<_T1, _T2>&, const std::pair<_T1, _T2>&)|

/usr/include/c++/4.6/bits/stl_iterator.h|291|note: template<class _Iterator> bool std::operator<(const std::reverse_iterator<_Iterator>&, const std::reverse_iterator<_Iterator>&)|

/usr/include/c++/4.6/bits/stl_iterator.h|341|note: template<class _IteratorL, class _IteratorR> bool std::operator<(const std::reverse_iterator<_IteratorL>&, const std::reverse_iterator<_IteratorR>&)|

/usr/include/c++/4.6/bits/basic_string.h|2510|note: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const std::basic_string<_CharT, _Traits, _Alloc>&, const std::basic_string<_CharT, _Traits, _Alloc>&)|

/usr/include/c++/4.6/bits/basic_string.h|2522|note: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const std::basic_string<_CharT, _Traits, _Alloc>&, const _CharT*)|

/usr/include/c++/4.6/bits/basic_string.h|2534|note: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const _CharT*, const std::basic_string<_CharT, _Traits, _Alloc>&)|

/usr/include/c++/4.6/bits/stl_vector.h|1290|note: template<class _Tp, class _Alloc> bool std::operator<(const std::vector<_Tp, _Alloc>&, const std::vector<_Tp, _Alloc>&)|

/home/vanio/Desktop/workspace/C++/Ordner/Fraction.h|39|note: bool operator<(Fraction&, Fraction&)|

/home/vanio/Desktop/workspace/C++/Ordner/Fraction.h|39|note:   no known conversion for argument 2 from ‘const Fraction’ to ‘Fraction&’|

/usr/include/c++/4.6/bits/stl_algo.h|2215|error: no match for ‘operator<’ in ‘__pivot < __last.__gnu_cxx::__normal_iterator<_Iterator, _Container>::operator* [with _Iterator = Fraction*, _Container = std::vector<Fraction>, __gnu_cxx::__normal_iterator<_Iterator, _Container>::reference = Fraction&]()’|

/usr/include/c++/4.6/bits/stl_algo.h|2215|note: candidates are:|

/usr/include/c++/4.6/bits/stl_pair.h|207|note: template<class _T1, class _T2> bool std::operator<(const std::pair<_T1, _T2>&, const std::pair<_T1, _T2>&)|

/usr/include/c++/4.6/bits/stl_iterator.h|291|note: template<class _Iterator> bool std::operator<(const std::reverse_iterator<_Iterator>&, const std::reverse_iterator<_Iterator>&)|

/usr/include/c++/4.6/bits/stl_iterator.h|341|note: template<class _IteratorL, class _IteratorR> bool std::operator<(const std::reverse_iterator<_IteratorL>&, const std::reverse_iterator<_IteratorR>&)|

/usr/include/c++/4.6/bits/basic_string.h|2510|note: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const std::basic_string<_CharT, _Traits, _Alloc>&, const std::basic_string<_CharT, _Traits, _Alloc>&)|

/usr/include/c++/4.6/bits/basic_string.h|2522|note: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const std::basic_string<_CharT, _Traits, _Alloc>&, const _CharT*)|

/usr/include/c++/4.6/bits/basic_string.h|2534|note: template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const _CharT*, const std::basic_string<_CharT, _Traits, _Alloc>&)|

/usr/include/c++/4.6/bits/stl_vector.h|1290|note: template<class _Tp, class _Alloc> bool std::operator<(const std::vector<_Tp, _Alloc>&, const std::vector<_Tp, _Alloc>&)|

/home/vanio/Desktop/workspace/C++/Ordner/Fraction.h|39|note: bool operator<(Fraction&, Fraction&)|

/home/vanio/Desktop/workspace/C++/Ordner/Fraction.h|39|note:   no known conversion for argument 1 from ‘const Fraction’ to ‘Fraction&’|
||=== Build finished: 22 errors, 0 warnings ===|

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