boost::multi_index_container, operations on std::s

I've created a boost::multi_index_container (containerSet) over a container class and indexed the containerSet by std::string and std::set<int>. Is it possible to get the container, which store a specific int inside their set? Furthermore is it possible to get all container, which store at least one value between int1 and int2 within their set?

#include <boost/multi_index_container.hpp>
#include <boost/multi_index/member.hpp>
#include <boost/multi_index/ordered_index.hpp>
#include <boost/multi_index/hashed_index.hpp>
#include <boost/format.hpp>
#include <boost/lambda/core.hpp>
#include <iostream>

using boost::multi_index_container;
using namespace boost::multi_index;

class Container {
public:
    std::set<int> set;
    std::string name;

    Container(std::string name, std::set<int> set);
    ~Container();

    friend std::ostream& operator<<(std::ostream& os,const Container& c) {
        os << c.name << ", [ ";
        for (int i : c.set) {
            os << i << "  ";
        }
        os << "]";
        return os;
    }
};

Container::Container(std::string name = "noName", std::set<int> set = {}) : name{name} ,set{set} {}
Container::~Container() {}

struct setTag{};
struct nameTag{};

typedef multi_index_container<Container, indexed_by<
        ordered_unique<tag<nameTag>, BOOST_MULTI_INDEX_MEMBER(Comp, std::string, name)>,
        ordered_unique<tag<setTag>, BOOST_MULTI_INDEX_MEMBER(Comp, std::set<int>, set)>
>> ContainerSet;

//don't see how I could get the compare structs to work, because
//a) can't fullfill the strict weak odering requirements and
//b) because of the setTag ordering, not all set's get called
struct compSetRange {
        bool operator()(int x,const std::set<int> &c) const {}
        bool operator()(const std::set<int> &c, int x) const {}
};
struct compSetFind {
    bool operator()(int x,const std::set<int> &c) const {}
    bool operator()(const std::set<int> &c, int x) const {}
};

int main() {
    Container c1{"c1", {5, 6, 7, 18, 61, 77}};
    Container c2{"c2", {2, 4, 5, 21, 36, 88, 99}};
    Container c3{"c3", {2, 3, 9, 10, 65, 75, 91}};
    ContainerSet cs;
    cs.insert(c1);
    cs.insert(c2);
    cs.insert(c3);

    std::cout << "print by name (ordered)" << std::endl;
    for (auto e : cs.get<nameTag>()) {
        std::cout << e << std::endl;
    }
    std::cout << std::endl;

    std::cout << "print by set (ordered)" << std::endl;
    for (auto e : cs.get<setTag>()) {
        std::cout << e << std::endl;
    }
    std::cout << std::endl;

    typedef ContainerSet::index<setTag>::type compBySetIndex;
    //find(std::set) works but isn't useful in my case
    compBySetIndex::iterator it1 = cs.get<setTag>().find(std::set<int>{2, 4, 5, 21, 36, 88, 99});
   //TODO: find all comps with int 5 -> c1 and c2
//  compBySetIndex::iterator it1 = cs.get<setTag>().find(200, compSetFind());
    if (it1 !=cs.get<setTag>().end()) {
        std::cout << *it1 << std::endl;
    }

    //TODO: find all container with values between 70 and 80 -> c1 and c3
//  compBySetIndex::iterator it1_low = cs.get<setTag>().lower_bound(70, compSetRange());
//  compBySetIndex::iterator it1_upp = cs.get<setTag>().upper_bound(80, compSetRange());

    //.range() also not applicable

    return 0;
}

With the sets:
c3 = {2, 3, 9, 10, 65, 75, 91}
c2 = {2, 4, 5, 21, 36, 88, 99}
c1 = {5, 6, 7, 18, 61, 77}
I want to be able to call ...find(5); and get at least c2, maybe even c1 on the next invocation. This might be doable with the right Compare function, but I can't think of a way to make the operator() functions compatible.
Furthermore after ...lower_bounds(70) and ...upper_bounds(80) I should get c3 and c1. Because of the ordering of the std::set's, this requirement seems unachievable with boost.

Am I missing something? Thanks in advance!

I know I could do a linear search over all containers and their sets to achieve my goal, but that would negate the performance advantage of the multi_index_container. If boost is the wrong tool for this job I will have to resort to an individual class containerSet.

Andrew diagnosed the issue quite accutely.

To help you along, let me advertise a widely under-used library in Boost: Boost Interval Container.

I hope this demo can shed some light on how useful Boost ICL can be.

Live On Coliru

#include <boost/icl/separate_interval_set.hpp>
#include <boost/icl/interval_map.hpp>

#include <boost/multi_index_container.hpp>
#include <boost/multi_index/ordered_index.hpp>
#include <boost/multi_index/member.hpp>

#include <iostream>
#include <numeric>
#include <vector>

using Set = std::set<int>;

struct io_wrap { Set const& ref; };
static std::ostream& operator<<(std::ostream& os,const io_wrap& s) { os << "[ "; for (auto i : s.ref) os << i << " "; return os << ']'; }

namespace icl = boost::icl;
namespace bmi = boost::multi_index;

struct Record {
    std::string name;
    Set set;

    Record(std::string name = "noName", Set set = {}) : name{name}, set{set} {}

    friend std::ostream& operator<<(std::ostream& os,const Record& c) { return os << c.name << ", " << io_wrap{c.set}; }
};

using Map      = icl::interval_map<int, std::set<Record const*> >;
using Interval = Map::interval_type;
using Table    = bmi::multi_index_container<
         std::reference_wrapper<Record>,
         bmi::indexed_by<
             bmi::ordered_unique<
                bmi::tag<struct byName>,
                bmi::member<Record, std::string, &Record::name>
             >
         >
     >;

auto interval_set(Set const& is) { return std::accumulate(is.begin(), is.end(), icl::interval_set<int> { } ); }
auto envelope(Record const& r)   { return hull(interval_set(r.set)); }

void insert(Map& into, Set const& is, std::set<Record const*> const& rs = {}) {
    for (auto i : interval_set(is))
        into += Map::value_type { i, rs };
}

int main() {

    ////////////////////////////////
    // Prepare data
    std::vector<Record> backing_storage {
        {"c3", {2, 3, 9, 10, 65, 75, 91}},
        {"c1", {5, 6, 7, 18, 61, 77}},
        {"c2", {2, 4, 5, 21, 36, 88, 99}},
        // outliers
        {"c4", {0}},
        {"c5", {200}},
    };

    Table const byname(backing_storage.begin(), backing_storage.end());
    Map cs;
    for (auto& r : backing_storage) 
        insert(cs, r.set, { &r });

    ////////////////////////////////
    // Usage demos
    std::cout << "print by name (ordered)\n";
    for (auto const& e : byname) { std::cout << " - " << e << " - envelope: " << envelope(e) << "\n"; }
    std::cout << "\n";

    auto perform_match = [&cs](auto key) {
        Map::codomain_type matches;
        Map::codomain_combine combine;

        for (auto p : cs & key)
            combine(matches, p.second);

        std::cout << "matching " << key << ":\n";
        for (auto const* r : matches)
            std::cout << " - " << *r << "\n";
        std::cout << "\n";
    };

    for (auto key : { Set{2}, {99}, {2,99}, {2,99,5} }) {
        perform_match(interval_set(key));
    }

    perform_match(Interval::right_open(70, 81));
}

Prints:

print by name (ordered)
 - c1, [ 5 6 7 18 61 77 ] - envelope: [5,77]
 - c2, [ 2 4 5 21 36 88 99 ] - envelope: [2,99]
 - c3, [ 2 3 9 10 65 75 91 ] - envelope: [2,91]
 - c4, [ 0 ] - envelope: [0,0]
 - c5, [ 200 ] - envelope: [200,200]

matching {[2,2]}:
 - c3, [ 2 3 9 10 65 75 91 ]
 - c2, [ 2 4 5 21 36 88 99 ]

matching {[99,99]}:
 - c2, [ 2 4 5 21 36 88 99 ]

matching {[2,2][99,99]}:
 - c3, [ 2 3 9 10 65 75 91 ]
 - c2, [ 2 4 5 21 36 88 99 ]

matching {[2,2][5,5][99,99]}:
 - c3, [ 2 3 9 10 65 75 91 ]
 - c1, [ 5 6 7 18 61 77 ]
 - c2, [ 2 4 5 21 36 88 99 ]

matching [70,81):
 - c3, [ 2 3 9 10 65 75 91 ]
 - c1, [ 5 6 7 18 61 77 ]