Some random stuff.

problem.cc

#include <string>
#include <vector>
#include <algorithm>
#include <iostream>
#include <iterator>
#include <unordered_map>

using namespace std;

namespace {
template <typename IteratorT, typename OutIteratorT> void
enum_patterns(
        IteratorT it,
        IteratorT end,
        OutIteratorT &out,
        const basic_string<typename iterator_traits<IteratorT>::value_type> &pattern)
{
        typedef typename iterator_traits<IteratorT>::value_type char_t;

        if (it == end) {
                *out++ = pattern;
                return;
        }

        if (*it != char_t('?')) {
                enum_patterns(it+1, end, out, pattern + *it);
        } else {
                enum_patterns(it+1, end, out, pattern + char_t('1'));
                enum_patterns(it+1, end, out, pattern + char_t('0'));
        }
}
}

template<typename IteratorT, typename OutIteratorT> void
enum_patterns(IteratorT first, IteratorT end, OutIteratorT out)
{
        typedef basic_string<typename iterator_traits<IteratorT>::value_type> string_type;
        enum_patterns(first, end, out, string_type(""));
}

template<typename Iterator> Iterator
most_frequent(Iterator first, Iterator end)
{
        typedef typename iterator_traits<Iterator>::value_type value_type;
        typedef unordered_map<value_type, size_t> map_type;
        typedef typename map_type::value_type map_value_type;
        map_type freq_table;

        for_each(first, end, [&freq_table] (const value_type &x) { ++freq_table[x]; });
        return find(
                first,
                end,
                max_element(
                        freq_table.begin(),
                        freq_table.end(),
                        [] (const map_value_type &a, const map_value_type &b)
                                { return a.second < b.second; })->first);
}

int
main(void)
{
        vector<string> v;

        char s[] = "1?0?";
        enum_patterns(begin(s), end(s), back_inserter(v));
        copy(begin(v), end(v), ostream_iterator<string>(cout, "\n"));

        string ss("1?0?");
        v.clear();
        enum_patterns(begin(ss), end(ss), back_inserter(v));
        copy(begin(v), end(v), ostream_iterator<string>(cout, "\n"));

        vector<int> v2 = {1,2,3,3,3,4,5,6};
        cout << *most_frequent(begin(v2), end(v2)) << endl;
        return 0;
}