Problems using a map with a bitset as a key

Question

I am trying to create a map in C++ with bitset as a key. However the compiler generates the following error messages

In file included from /usr/include/c++/4.6/string:50:0,
                 from /usr/include/c++/4.6/bits/locale_classes.h:42,
                 from /usr/include/c++/4.6/bits/ios_base.h:43,
                 from /usr/include/c++/4.6/ios:43,
                 from /usr/include/c++/4.6/ostream:40,
                 from /usr/include/c++/4.6/iostream:40,
                 from test2.cpp:1:
/usr/include/c++/4.6/bits/stl_function.h: In member function ‘bool std::less<_Tp>::operator()(const _Tp&, const _Tp&) const [with _Tp = std::bitset<8u>]’:
/usr/include/c++/4.6/bits/stl_map.h:452:2:   instantiated from ‘std::map<_Key, _Tp, _Compare, _Alloc>::mapped_type& std::map<_Key, _Tp, _Compare, _Alloc>::operator[](const key_type&) [with _Key = std::bitset<8u>, _Tp = int, _Compare = std::less<std::bitset<8u> >, _Alloc = std::allocator<std::pair<const std::bitset<8u>, int> >, std::map<_Key, _Tp, _Compare, _Alloc>::mapped_type = int, std::map<_Key, _Tp, _Compare, _Alloc>::key_type = std::bitset<8u>]’
test2.cpp:22:30:   instantiated from here
/usr/include/c++/4.6/bits/stl_function.h:236:22: error: no match for ‘operator<’ in ‘__x < __y’
/usr/include/c++/4.6/bits/stl_function.h:236:22: note: candidates are:
/usr/include/c++/4.6/bits/stl_pair.h:207:5: 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:291:5: 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:341:5: 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:2510:5: 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:2522:5: 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:2534:5: 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_tree.h:856:5: note: template<class _Key, class _Val, class _KeyOfValue, class _Compare, class _Alloc> bool std::operator<(const std::_Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>&, const std::_Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>&)
/usr/include/c++/4.6/bits/stl_set.h:713:5: note: template<class _Key, class _Compare, class _Alloc> bool std::operator<(const std::set<_Key, _Compare, _Alloc>&, const std::set<_Key, _Compare, _Alloc>&)
/usr/include/c++/4.6/bits/stl_multiset.h:696:5: note: template<class _Key, class _Compare, class _Alloc> bool std::operator<(const std::multiset<_Key, _Compare, _Alloc>&, const std::multiset<_Key, _Compare, _Alloc>&)
/usr/include/c++/4.6/bits/stl_map.h:894:5: note: template<class _Key, class _Tp, class _Compare, class _Alloc> bool std::operator<(const std::map<_Key, _Tp, _Compare, _Alloc>&, const std::map<_Key, _Tp, _Compare, _Alloc>&)
/usr/include/c++/4.6/bits/stl_multimap.h:812:5: note: template<class _Key, class _Tp, class _Compare, class _Alloc> bool std::operator<(const std::multimap<_Key, _Tp, _Compare, _Alloc>&, const std::multimap<_Key, _Tp, _Compare, _Alloc>&)

The progam code is given below I am trying to use bitset as a key to a map in C++. However, everytime I run the code below I run into errros.

#include <iostream>
#include <algorithm>
#include <string>
#include <bitset>
#include <set>
#include <utility>

using namespace std;

int main(int argc, char *argv[])
{
    bitset<8> test;
    test = 9;
    cout<<"Set to 9"<<endl;
    map <bitset<8> , int> mymap;
    pair <biset<8> , int> p;
    p.first = test;
    p.second = 9;
    string teststring;
    teststring = test.to_string<char,char_traits<char>,allocator<char> >();
    cout<<teststring<<temymap[test]<<endl;
    return 0;
}

Answer 1

This will allow map<bitset<N>,int> stuff directly:

namespace std{
    template<size_t N>
    struct less<bitset<N> > : binary_function <bitset<N>,bitset<N>,bool>{
        bool operator()(const bitset<N> &L, const bitset<N> &R) const{
            for(unsigned int i=0;i<L.size();i++)
                if(L.test(i)){
                    if(!R.test(i))return false;
                }else{
                    if(R.test(i))return true;
            }
            return false; //same
        }
    };
}

Answer 2

You can define your comparison function. If you assume your bitset models an unsigned integral value then the following function will order the bitsets in increasing order (and works for any N).

template <size_t N>
class LessThan { 
public:
   bool operator() (const std::bitset<N> &lhs, const std::bitset<N> &rhs) const 
   { 
      size_t i = N;
      while ( i > 0 ) {
         if ( lhs[i-1] == rhs[i-1] ) {
            i--;
         } else if ( lhs[i-1] < rhs[i-1] ) {
            return true;
         } else {
            return false;
         }
      }
      return false;
   } 
}; 

If you run the following snippet:

  const size_t mysz = 10;
  std::map< std::bitset<mysz>, size_t, Less<mysz> > mymap;
  for ( size_t i = 0; i < 10; i++ ) {
     mymap.insert( std::make_pair(std::bitset<mysz>(i),i) );
  }

You will have this map:

mymap[0]    is the pair ((0,0,0,0,0,0,0,0,0,0), 0)  
mymap[1]    is the pair ((1,0,0,0,0,0,0,0,0,0), 1)  
mymap[2]    is the pair ((0,1,0,0,0,0,0,0,0,0), 2)  
mymap[3]    is the pair ((1,1,0,0,0,0,0,0,0,0), 3)  
mymap[4]    is the pair ((0,0,1,0,0,0,0,0,0,0), 4)  
mymap[5]    is the pair ((1,0,1,0,0,0,0,0,0,0), 5)  
mymap[6]    is the pair ((0,1,1,0,0,0,0,0,0,0), 6)  
mymap[7]    is the pair ((1,1,1,0,0,0,0,0,0,0), 7)  
mymap[8]    is the pair ((0,0,0,1,0,0,0,0,0,0), 8)  
mymap[9]    is the pair ((1,0,0,1,0,0,0,0,0,0), 9)

Answer 3

An alternative solution would be to simply use an unordered_map, if this still meets your requirements.

This could be std::unordered_map<bitset<N>, T> or boost::unordered_map<bitset<N>, T>, depending on C++ version or performance considerations.

This avoids the need for comparison and may prove faster, depending on requirements.

Answer 4

Just use your own comparator class:

struct Comparer {
    bool operator() (const bitset<8> &b1, const bitset<8> &b2) const {
        return b1.to_ulong() < b2.to_ulong();
    }
};
/* ... */
map <bitset<8> , int, Comparer> mymap;

Note that you can extend this solution to support arbitrary length bitsets, as long as they are small enough to be converted to an unsigned long:

template<size_t sz> struct bitset_comparer {
    bool operator() (const bitset<sz> &b1, const bitset<sz> &b2) const {
        return b1.to_ulong() < b2.to_ulong();
    }
};
map <bitset<8> , int, bitset_comparer<8> > mymap;
map <bitset<16> , int, bitset_comparer<16> > mymap16;