up09-5 (unreachable)

#include <iostream>
#include <string>
#include <map>
#include <set>
#include <vector>
#include <cctype>

std::multimap<char, std::string> clear_unreachable(const std::multimap<char, std::string> &grammar)
{
    std::multimap<char, std::string> cleared;

    std::set<char> reachable;
    reachable.insert('S');
    size_t old_size = 0;

    while (old_size != reachable.size()) {
        old_size = reachable.size();

        for (auto i = reachable.begin(); i != reachable.end(); ++i) {
            auto tmp_range = grammar.equal_range(*i);
            for (auto j = tmp_range.first; j != tmp_range.second; ++j) {
                for (auto &c:j->second) {
                    if (isupper(c)) {
                        reachable.insert(c);
                    }
                }
            }
        }
    }
    for (auto &c:grammar) {
        if (reachable.find(c.first) != reachable.end()) {
            cleared.insert(c);
        }
    }
    return cleared;
}

int main()
{
    std::multimap<char, std::string> grammar;
    char left;
    std::string right;
    while (std::cin >> left >> right) {
        grammar.insert({left, right});
    }

    auto tmp = clear_unreachable(grammar);
    for (auto &c:tmp) {
        std::cout << c.first << " " << c.second << std::endl;
    }
}