How can I create my own comparator for a map?

std::map takes up to four template type arguments, the third one being a comparator. E.g.:

struct cmpByStringLength {
    bool operator()(const std::string& a, const std::string& b) const {
        return a.length() < b.length();
    }
};

// ...
std::map<std::string, std::string, cmpByStringLength> myMap;

Alternatively you could also pass a comparator to maps constructor.

Note however that when comparing by length you can only have one string of each length in the map as a key.