c++ - Error using std::set to implement a sparse 3D grid

I'm trying to implement a sparse 3D grid with std::set container, but I can't understand the error returned from the compiler, this is the minimal example I'm trying to run:

#include 

#include 
#include 
#include 

#include 

using namespace std;

class Cell {
public:

    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    Cell(const Eigen::Vector3i idx=Eigen::Vector3i::Zero()):_idx(idx) {
        _center = Eigen::Vector3f::Zero();
        _parent = 0;
        _distance = std::numeric_limits::max();
    }

    inline bool operator < (const Cell& c){
        for (int i=0; i<3; i++){
            if (_idx[i]
                return true;
            if (_idx[i]>c._idx[i])
                return false;
        }
        return false;
    }

    inline bool operator == (const Cell& c) { return c._idx == _idx;}

private:

    Eigen::Vector3i _idx;
    Eigen::Vector3f _center;
    vector _points;
    Cell* _parent;
    size_t _closest_point;
    float _distance;
    int _tag;
};



int main(int argc, char* argv[]) {

    set grid;

    float max = 1, min = -1;
    int dim = 5;
    float delta = (max-min)/(dim-1);

    for(int k = 0; k < dim; k++)
        for(int j = 0; j < dim; j++)

            for(int i = 0; i < dim; i++)
                grid.insert(Cell(Eigen::Vector3i(i,j,k)));

    return 0;
}

and this is the compiler error:

In file included from /usr/include/c++/4.8/string:48:0,
from /usr/include/c++/4.8/bits/locale_classes.h:40,
from /usr/include/c++/4.8/bits/ios_base.h:41,
from /usr/include/c++/4.8/ios:42,
from /usr/include/c++/4.8/ostream:38,
from /usr/include/c++/4.8/iostream:39,
from /home/dede/build/sparse_grid/main.cpp:1: /usr/include/c++/4.8/bits/stl_function.h: In instantiation of 'bool
std::less<_Tp>::operator()(const _Tp&, const _Tp&) const [with _Tp =
Cell]': /usr/include/c++/4.8/bits/stl_tree.h:1324:11: required from
'std::pair

std::_Rb_tree<_Key, _Val, _KeyOfValue, _Compare,
_Alloc>::_M_get_insert_unique_pos(const key_type&) [with _Key = Cell; _Val = Cell; _KeyOfValue = std::_Identity; _Compare = std::less; _Alloc = std::allocator; std::_Rb_tree<_Key,
_Val, _KeyOfValue, _Compare, _Alloc>::key_type = Cell]' /usr/include/c++/4.8/bits/stl_tree.h:1377:47: required from
'std::pair, bool> std::_Rb_tree<_Key,
_Val, _KeyOfValue, _Compare, _Alloc>::_M_insert_unique(_Arg&&) [with _Arg = Cell; _Key = Cell; _Val = Cell; _KeyOfValue = std::_Identity; _Compare = std::less; _Alloc =
std::allocator]' /usr/include/c++/4.8/bits/stl_set.h:472:40:
required from 'std::pair, _Compare, typename
_Alloc::rebind<_Key>::other>::const_iterator, bool> std::set<_Key, _Compare, _Alloc>::insert(std::set<_Key, _Compare, _Alloc>::value_type&&) [with _Key = Cell; _Compare = std::less; _Alloc = std::allocator; typename std::_Rb_tree<_Key, _Key, std::_Identity<_Key>, _Compare, typename
_Alloc::rebind<_Key>::other>::const_iterator = std::_Rb_tree_const_iterator; std::set<_Key, _Compare,
_Alloc>::value_type = Cell]' /home/dede/build/sparse_grid/main.cpp:53:57: required from here
/usr/include/c++/4.8/bits/stl_function.h:235:20: error: passing 'const

Cell' as 'this' argument of 'bool Cell::operator<(const Cell&)'
discards qualifiers [-fpermissive]
{ return __x < __y; }
^ make[2]: * [CMakeFiles/sparse_grid.dir/main.cpp.o] Error 1 make[1]: *
[CMakeFiles/sparse_grid.dir/all] Error 2 make: *** [all] Error 2

I would really appreciate if someone could tell me what I'm doing wrong.

Thanks,

Federico

Answer

You should declare your boolean operator functions as const members:

inline bool operator < (const Cell& c) const {
                                    // ^^^^^
    for (int i=0; i<3; i++){
        if (_idx[i]            return true;
        if (_idx[i]>c._idx[i])

            return false;
    }
    return false;
}

inline bool operator == (const Cell& c) const { return c._idx == _idx;}
                                     // ^^^^^

Otherwise these cannot be used with rvalue objects of Cell.