How can I create my own comparator for a map?

typedef map<string, string> myMap;

When inserting a new pair to myMap, it will use the key string to compare by its own string comparator. Is it possible to override that comparator? For example, I'd like to compare the key string by its length, not by the alphabet. Or is there any other way to sort the 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.

Since C++11, you can also use a lambda expression instead of defining a comparator struct:

auto comp = [](const string& a, const string& b) { return a.length() < b.length(); };
map<string, string, decltype(comp)> my_map(comp);

my_map["1"]      = "a";
my_map["three"]  = "b";
my_map["two"]    = "c";
my_map["fouuur"] = "d";

for(auto const &kv : my_map)
    cout << kv.first << endl;

Output:

> 1
> two
> three
> fouuur

I'd like to repeat the final note of Georg's answer: When comparing by length you can only have one string of each length in the map as a key.

Code on Ideone

Yes, the 3rd template parameter on map specifies the comparator, which is a binary predicate. Example:

struct ByLength : public std::binary_function<string, string, bool>
{
	bool operator()(const string& lhs, const string& rhs) const
	{
		return lhs.length() < rhs.length();
	}
};

int main()
{
	typedef map<string, string, ByLength> lenmap;
	lenmap mymap;

	mymap["one"] = "one";
	mymap["a"] = "a";
	mymap["fewbahr"] = "foobar";

	for( lenmap::const_iterator it = mymap.begin(), end = mymap.end(); it != end; ++it )
		cout << it->first << "\n";
}

Specify the type of the pointer to your comparison function as the 3rd type into the map, and provide the function pointer to the map constructor:
map<keyType, valueType, typeOfPointerToFunction> mapName(pointerToComparisonFunction);

Take a look at the example below for providing a comparison function to a map, with vector iterator as key and int as value.

#include "headers.h"

bool int_vector_iter_comp(const vector<int>::iterator iter1, const vector<int>::iterator iter2) {
    return *iter1 < *iter2;
}

int main() {
    // Without providing custom comparison function
    map<vector<int>::iterator, int> default_comparison;

    // Providing custom comparison function
    // Basic version
    map<vector<int>::iterator, int,
        bool (*)(const vector<int>::iterator iter1, const vector<int>::iterator iter2)>
        basic(int_vector_iter_comp);

    // use decltype
    map<vector<int>::iterator, int, decltype(int_vector_iter_comp)*> with_decltype(&int_vector_iter_comp);

    // Use type alias or using
    typedef bool my_predicate(const vector<int>::iterator iter1, const vector<int>::iterator iter2);
    map<vector<int>::iterator, int, my_predicate*> with_typedef(&int_vector_iter_comp);

    using my_predicate_pointer_type = bool (*)(const vector<int>::iterator iter1, const vector<int>::iterator iter2);
    map<vector<int>::iterator, int, my_predicate_pointer_type> with_using(&int_vector_iter_comp);


    // Testing 
    vector<int> v = {1, 2, 3};

    default_comparison.insert(pair<vector<int>::iterator, int>({v.end(), 0}));
    default_comparison.insert(pair<vector<int>::iterator, int>({v.begin(), 0}));
    default_comparison.insert(pair<vector<int>::iterator, int>({v.begin(), 1}));
    default_comparison.insert(pair<vector<int>::iterator, int>({v.begin() + 1, 1}));

    cout << "size: " << default_comparison.size() << endl;
    for (auto& p : default_comparison) {
        cout << *(p.first) << ": " << p.second << endl;
    }

    basic.insert(pair<vector<int>::iterator, int>({v.end(), 0}));
    basic.insert(pair<vector<int>::iterator, int>({v.begin(), 0}));
    basic.insert(pair<vector<int>::iterator, int>({v.begin(), 1}));
    basic.insert(pair<vector<int>::iterator, int>({v.begin() + 1, 1}));

    cout << "size: " << basic.size() << endl;
    for (auto& p : basic) {
        cout << *(p.first) << ": " << p.second << endl;
    }

    with_decltype.insert(pair<vector<int>::iterator, int>({v.end(), 0}));
    with_decltype.insert(pair<vector<int>::iterator, int>({v.begin(), 0}));
    with_decltype.insert(pair<vector<int>::iterator, int>({v.begin(), 1}));
    with_decltype.insert(pair<vector<int>::iterator, int>({v.begin() + 1, 1}));

    cout << "size: " << with_decltype.size() << endl;
    for (auto& p : with_decltype) {
        cout << *(p.first) << ": " << p.second << endl;
    }

    with_typedef.insert(pair<vector<int>::iterator, int>({v.end(), 0}));
    with_typedef.insert(pair<vector<int>::iterator, int>({v.begin(), 0}));
    with_typedef.insert(pair<vector<int>::iterator, int>({v.begin(), 1}));
    with_typedef.insert(pair<vector<int>::iterator, int>({v.begin() + 1, 1}));

    cout << "size: " << with_typedef.size() << endl;
    for (auto& p : with_typedef) {
        cout << *(p.first) << ": " << p.second << endl;
    }
}